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Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

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Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

Sankt Lorenzen 36, 8715, Sankt Lorenzen, Austria

Mechanics, Materials Science & Engineering Journal

March 2017

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Mechanics, Materials Sciences & Engineering Journal, Austria, Sankt Lorenzen, 2017

Mechanics, Materials Science & Engineering Journal (MMSE Journal) is journal that deals in peerreviewed, open access publishing, focusing on wide range of subject areas, including economics, business, social sciences, engineering etc.

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

CONTENT I. Materials Science MMSE Journal Vol. 8 ..................................................................................... 5 Dynamic Mechanical Property of Kaolinite/Styrene-Butadiene Rubber Composites. Yinmin Zhang, Hongli Song, Qinfu Liu, Shilong Zhang, Yude Zhang ................................................ 6 Investigation on Pure and L-lysine Doped (Tri) Glycine Barium Chloride (TGBC) Single Crystal for Nonlinear Optical Applications. S. Chennakrishnan, S.M. Ravikumar, D. Sivavishnu, M. Packiya Raj, S.Varalakshmi ........................................................................................................ 17 Especially the Transformation of Austenite in High-Strength Cast Iron during Processing With Continuous Cooling. R.K. Hasanli, S.N. Namazov ............................................................... 26 Structural and Dielectric Properties of Mg(1-x)CaxTiO3 (x=0.7, 0.8) Ceramic Materials. V. Sharon Samyuktha, T. Subba Rao, R. Padma Suvarna. ................................................................ 32 Passivation of Titanium Oxide in Polyethylene Matrices using Polyelectrolytes as Titanium Dioxide Surface Coating. Javier Vallejo-Montesinos, Julio Cesar López Martínez, Juan Manuel Montejano-Carrizales, Elías Pérez, Javier Balcázar Pérez, A. Almendárez-Camarillo, J.A. GonzalezCalderon ............................................................................................................................................ 38 II. MECHANICAL ENGINEERING & PHYSICS MMSE JOURNAL VOL. 8 .......................................... 51 Numerical and Experimental Study of Energy Absorption in Aluminum Corrugated Core Sandwich Panels by Drop Hammer Test. Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi ........................................................................................................................................... 52 The Variational Principle and the Phonon Boltzmann Equation. Amelia Carolina Sparavigna ............................................................................................................ 61 Multi-Objective Optimization of Kinematic Characteristics of Geneva Mechanism Using High-Tech Optimization Methods. Arash Mohammadzadeh Gonabadi, Mohammad Nouri Damghani .......................................................................................................................................... 71 Formation of Physical and Mechanical Properties of Surface Layer of Machine Parts. V. Zablotskyi, O. Dahnyuk, S. Prystupa, A. Tkachuk ........................................................................ 87 Assessment of the Possibility to Use Hybrid Electromechanical Transmission in Combat Tracked Platforms. Glebov V.V., Klimov V.F., Volosnikov S.A. .................................................... 99 Identities of Vector Algebra as Associative Properties of Multiplicative Compositions of Quaternion Matrices. Victor Kravets, Tamila Kravets, Olexiy Burov ............................................ 106 Efficient Transient Modes of Synchronous Drive for Mining and Smelting Mechanisms. V.А. Borodai, R. О. Borovyk, О.Yu. Nesterova ....................................................................................... 133 Study of Planar Mechanisms Kinetostatics Using the Theory of Complex Numbers with MathCAD PTC. Matsyuk I.N., Shlyakhov E.М., Zyma N.V. ......................................................... 143 VI. ENVIRONMENTAL SAFETY VOL. 8 ............................................................................................ 153 Global Warming Triggered Heavy Rains and its Effect on the Corrosion of Car Bodies in Uyo Metropolis. Aondona Paul Ihom, Patrick Peters Obot, Ini Umoren Udofia ......................... 154 VIII. ECONOMICS & MANAGEMENT VOL.8 ................................................................................... 177 Analysing the Economic and Operational Indicators for Railways: the Case Study of Egyptian Railways. Ahmed Abd Elmoamen Khalil, Karim Mohamed Eldash, Moustafa Adel Ibrahim .................................................................................................................... 178

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I . M a t e r i a l s S c i e n c e M M S E J o u r n a l V o l . 8

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Dynamic Mechanical Property of Kaolinite/Styrene-Butadiene Rubber Composites1 Yinmin Zhang1, Hongli Song2, Qinfu Liu1, a, Shilong Zhang1, Yude Zhang3 1 – School of Geoscience and Surveying Engineering, China University of Mining & Technology, Beijing, 100083 China 2 – School of Geoscience and Engineering, Hebei University of Engineering, Handan, 056000 China 3 – School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China a – pzqm163@163.com DOI 10.2412/mmse.61.54.732 provided by Seo4U.link

Keywords: kaolinite, styrene-butadiene rubber, microstructure, dynamic mechanical properties.

ABSTRACT. The dynamic properties of kaolinite/styrene-butadiene rubber (SBR) composites filled by kaolinite were investigated to evaluate their real-world engineering applications. The results of field emission scanning electron microscopy (SEM), and transmission electron microscopy (TEM) revealed that the rubber chains were confined within the interparticle space of kaolinites, and that the nanoscale kaolinites exhibited a fine and physical dispersion in the SBR matrix. The dynamic properties of kaolinite/SBR composites were investigated by performing dynamic mechanical analysis (DMA) and rubber processing analysis (RPA). Both the decrease in kaolinite particle size and the increase in kaolinite content can greatly improve the storage modulus and reinforcing effect of kaolinite/SBR composites. A small particle size and a low filled content of kaolinite filler is favourable for the dynamic properties of kaolinite/SBR composites for tire products. The filler networking phenomenon attributed to the agglomeration-de-agglomeration of filler particles intensified as the kaolinite particle size was reduced and the kaolinite content was increased, which resulted from the increase in the unit volume fraction of kaolinite in the rubber matrix and the stronger interaction of kaolinite particles in the composite matrix.

Introduction. Layered clay minerals/polymer nanocomposites have received considerable attention from the industry and academic researchers because these materials have exhibited remarkably improved properties, such as improved mechanical properties and thermal ability, enhanced barrier property, and decreased flammability [1-7]. In particular, rubber is an important class of polymer materials because of its outstanding characteristics and special applications [8]. Many researchers have applied different approaches to modify clay minerals, which are then incorporated into rubber matrix by latex blending and simple melt mixing [5, 9]. Such practices have achieved slight improvements in the mechanical, thermal, and barrier properties of clay/rubber composites [6, 8, 10, 11]. The dynamic mechanical property is one of the important physical properties of rubber compounds, particularly for tire applications and for other dynamic rubber products; this property reflects the actual performance of rubber products[12]. Of considerable significance is the dynamic mechanical behavior of rubber materials determined under a wide range of frequencies and temperatures. This behavior can be evaluated by the storage modulus (E/), the loss modulus (E//), and the loss tangent (tanδ) defined by tanδ= E/// E/, where E/ is the storage modulus resulting from the stored elastic energy in the materials and E//is the loss modulus resulting from viscous dissipation [13-15]. Many studies have investigated dynamic mechanical properties of rubber polymer materials based on various modified fillers, including the carbon black, silica, graphite, cellulose, and organoclay [16-18].

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Previous works on the dynamic mechanical properties of clay minerals/rubber polymer nanocomposites have mostly focused on montmorillonite, and only a few studies have explored kaolinite. Kaolinite is the most commonly 1:1 (two-sheet) - type clay mineral with its basic unit consisting of a tetrahedral sheet of SiO2 siloxane units and an octahedral sheet of AlO2 (OH)4 [11, 1921].After modification, kaolinite particles can become evenly dispersed in the rubber matrix and be used as a functional filler for rubber because of its light color, special stratified structure, and availability[10]. The present study is the first to report on the dynamic mechanical properties of kaolinite/styrene-butadiene rubber (SBR) composite as well as the effect of kaolinite particle size and content on the dynamic properties of these composites. The modified kaolinite and kaolinite/SBR composites are characterized by X-ray diffraction pattern (XRD), Fourier transform infrared (FT-IR) spectroscopy, field emission scanning electron microscopy (FE-SEM), and transmission electron microscopy (TEM). Experimental Materials. The rubber matrix is styrene-butadiene rubber (SBR 1500E), which was supplied by 100℃

ShenHua Chemical Company of Nantong Jiangsu, China, and its Mooney viscosity is 47–57 ML1 4 . The kaolinite sample was obtained from SanXing Advance-New Material Company of Zaozhuang Shandong, China; the sample was a type of sedimentary kaolin with disordered structure. The chemical component of this kaolin is 45.74% SiO2, 35.61% Al2O3, 0.88% Fe2O3, 1.23% TiO2, 0.41% Na2O, 0.32% K2O, 0.11% MgO, and 0.12% CaO. Kaolinite samples with different particle sizes were obtained using a disperser and relative material properties are presented in Table 1.The silane coupling agent bis-(γ-triethoxysilyl-propyl)-tetrasulfide (Si69) was supplied by ShuGuang Chemical Group Limited Company of Nanjing Jiangsu, China. Zinc oxide (ZnO), stearic acid, the accelerator N-tert-butylbenzothiazole-2-sulphenamide (NS), and sulfur were obtained commercially. Table 1. Particle sizes characteristic of kaolinite samples. Samples

D10 /μm

D50 /μm

D90 /μm

% ≤1 μm

Kaolinite-1(K1)

1.06

6.49

22.19

9.05 %

Kaolinite-2(K2)

0.89

3.74

17.94

12.20 %

Kaolinite-3(K3)

0.63

1.93

4.98

22.75 %

Kaolinite-4(K4)

0.28

0.53

1.69

79.27 %

Preparation of the modified kaolin The beneficiated kaolinite was dispersed into water at a content of 25%. Then, 0.5% sodium polyacrylate with an average molecular weight of 3000–3500 was added into the mixture as a dispersant. The pH level of the mixture was maintained at 10.0 by using a sodium hydroxide (NaOH) solution. Subsequently, 0.5% modifier was added into the resulting dispersion, and the dispersion was stirred for 1.5 h by using a mechanical mixer at approximately 60 °C. The modified kaolinite powder was obtained by spray drying at 120 °C [8]. Preparation of the kaolinite/rubber nanocomposites The procedure of preparing kaolin/SBR nanocomposites is briefly described as follows[22, 23]: First, raw SBR was plasticized for 3–5 min in an SK-160B open mill at room temperature. The spacing between the two rolls was approximately 0.15 cm, and the roll rate was 6.98 m/min. ZnO, stearic acid, NS, and sulfur was added into the plasticized compound successively. The two roll spacing was MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

adjusted to 0.05 cm and uniform mixing was performed for 15 min. The formulation of the kaolin/SBR nanocomposites (phr) is as follows: SBR, 100.00; zinc oxide, 3.00; stearic acid, 1.00; accelerator NS, 1.00; sulfur, 1.75; kaolinite, variable. The optimal cure time was determined by using a ZWL-III non-rotor vulkameter. The kaolinite/SBR composites specimens were placed in a 150 mm × 150 mm × 2 mm mold and vulcanized in a 400 mm × 400 mm 25TQLB vulcanizing machine at 153 °C and 10.0 MPa until the optimal cure time was obtained. The cured rubbers were rapidly cooled in air. Characterization and Measurement FT-IR spectroscopy was performed by a FT-IR spectrometer (Magna-IR 750 Nicolet) at a resolution of 4 cm-1 in the range of 4000–500 cm-1. The samples were prepared at potassium bromide (KBr) pellets (ca. 2% by mass in KBr). The morphology of the kaolin/SBR nanocomposites was characterized by a scanning electron microscopy (SEM) using a S4800 low–temperature field emission electron microscope manufactured by Rigaku Corporation. The TEM images of the kaolinite/SBR composites were characterized by a JEM-2100 transmission electron microscope (JEOL, Japan) with an acceleration voltage of 200 kV. The samples were prepared by ultramicrotomy of the bulk cured composites to obtain a section of approximately 50 nm thickness. The dynamic-mechanical properties were measured by utilizing a dynamic mechanical analyzer DMA 242C (Netzsch; Germany). The tests were conducted in the temperature range of −70 °C to 90 °C at a heating rate of 3 °C min-1. The rubber specimens were prepared as a cut strip with the size of 10.00 mm×3.95 mm×2.06 mm (length × thickness × width) under tension mode at a constant frequency of 10 Hz and a strain amplitude of 0.25%. The dynamic elastic modulus (E/) and the mechanical loss tangle (tanδ) as a function of temperature were measured. The temperature corresponding to the peak in tanδ versus the temperature plot was taken as the glass-to-rubber transition temperature (Tg). The experiment on strain sweeps were conducted by using a RPA 2000 (ALPHA, America). A slight excess in testing materials was needed to ensure the testing cavity house was full. The tests were performed under pressured conditions to ensure that porosity did not develop in the samples during the tests. The temperature was maintained at 60 °C before the uncured samples were subjected into the cavity house for conducting stain sweep. Subsequently, the temperature was raised to 170 °C to vulcanize the samples for their optimal cure time (t90). After curing, the temperature was cooled down to 60 °C again. Strain sweep was performed from 0.26% –100% and the frequency was kept at 1.0 Hz. Results and Discussion FT-IR analysis of kaolinite and modified kaolinite The FT-IR spectra of the kaolinite and the organic modified kaolinite are presented in Fig. 1. In the spectrum of virgin kaolinite, well-resolved absorbed bands were located at 3695, 3652, and 3620 cm1. The 3695 and 3652 cm-1 bands were attributed to the stretching vibration of the surface hydroxyl groups, whereas the 3620 cm-1 was attributed to the vibration of the inner surface hydroxyl groups[24]. The stretching vibration bands of Si-O are observed at 1101, 1034, and 1009 cm-1. The spectrum showed the bending vibration of -OH at 913 cm-1, and the stretching and bending vibration of Si-O-Al was found at 696 and 538 cm-1 respectively[20, 25, 26]. Four additional bands at 3450, 2920, 1634, and 1457 cm-1 are observed in the spectrum of the organic modified kaolinite. The bands at 3450 and 1634 cm-1 are attributed to the stretching and bending vibration mode of H2O, respectively, whereas the bands at 2920 and 1457 cm-1 are ascribed to the vibration mode of -CH2 derived from the silane coupling agent [27]. The results indicated that the silane coupling agent have interacted with kaolinite and modified the surface property of the kaolinite particles.

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Fig. 1. FT-IR spectra of kaolinite and modified kaolinite. Microstructure of kaolinite/SBR composites The microstructure of a kaolinite/SBR composite is shown in Fig. 2. The layer-like particles of kaolinite exhibited noteworthy characteristics with diameters ranging from 300 nm to 700 nm and thicknesses ranging from 50 nm to 200 nm. The average distances between the layer-like particles ranged from dozens of nanometers to hundreds of nanometers. The TEM images of the kaolinite/SBR composite with kaolinite are shown in Fig. 3. The kaolinite particles were finely dispersed in the SBR matrix. No significant aggregation occurred among the layered-like particles kaolinite. The kaolinite had a thickness of approximately dozens of nanometers and a diameter of 500 nm; the average distances between the layer-like particles ranged from dozens of nanometers to hundreds of nanometers.

Fig. 2. SEM images of kaolinite/SBR composite.

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Fig. 3. TEM images of kaolinite/SBR composite. Dynamic properties of kaolinite/SBR composites To evaluate the effect of kaolinite particle size and content on the dynamic mechanical behaviours of kaolinite/SBR composites, dynamic mechanical analyses were conducted out on cross-linked systems and rubber compounds without crosslinking among the polymer chains. Cross-linked systems were subjected to dynamic mechanical analysis by applying the temperature sweep methodology described in the Experimental section. The influences of kaolinite particle size on the dynamic storage modulus (E/, in the tensile model) and the loss tangent (tan δ) as a function of temperature for kaolinite/SBR nanocomposites are presented in Figs. 4 and 5. The storage modulus represents the elastic component and is an indicator of the capacity of a material to store the input mechanical energy [15]. As shown in Fig. 4, as the temperature increased from −60 °C to 10 °C, the storage modulus for all samples rapidly decreased, eventually reaching a constant value; this behaviour may be attributed to the glass transition phenomenon. In the low-temperature region, the storage modulus of the vulcanizate samples increased as the particle size of kaolinite decreased; this behavior is ascribed to the reinforcement of kaolinite and the stronger interaction between polymer chains and kaolinite particles as the particle size was reduced [28]. Consequently, the restriction on the motion of molecular chains increased. The storage modulus for vulcanizate samples in the given temperature region decreased more rapidly as the kaolinite particle size was reduced, indicating that the low-temperature rigidity of these vulcanizate were susceptible to the increase in temperature.

Fig. 4. The dynamic storage modulus as a function of temperature for kaolinite/SBR nanocomposites filled with different particle sized kaolinite. MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Table 2. tan δ and Tg of SBR/kaolinite composites filled with kaolinite with different size. Samples

K1-SBR

K2-SBR

K3-SBR

K4-SBR

tanδ(0℃)

0.29

0.28

0.26

0.324

tanδ(60℃)

0.098

0.135

0.119

0.125

Tg/℃

-19.8

-20.1

-20.43

-20.34

Fig. 5. The loss tangent as a function of temperature for kaolinite/SBR nanocomposites filled with different particle sized kaolinite. The tanδ as a function of temperature is shown in Fig. 5. Table 2 summarizes the values of different glass transition temperatures and the loss tangent at 0 °C and 60°C. The temperature corresponding to the maximum of tanδ values is generally related to the glass transition temperature (Tg). The tanδ values at 0 °C and 60 °C are generally considered to be correlated with wet traction and rolling resistance, respectively. For vulcanized rubber materials, the higher tanδ values at 0 °C indicate a desirable wet traction property, whereas the lower tanδ values at 60 °C correspond to a lower rolling resistance property. In this study, we use the tanδ values at 0 °C and 60 °C to assess the wet traction and rolling resistance of kaolinite/SBR composites. The tanδ values at Tg for vulcanizate samples decreased as the kaolinite particle size was reduced; this behavior is due to the favorable dispersion of kaolinite particles and the interaction between filler particles and rubber chains in the composite matrix. This finding is in agreement with those obtained by similar studies mentioned above. However, the Tg for all vulcanization samples were found to be about at −20 °C, which presented no obvious change. Overall, the vulcanizate rubber sample filled by the smaller-particle-sized kaolinite presented higher tanδ values at 0 °C and 60 °C, which indicating that smaller-particle-sized kaolinite can improve the wet traction property but is not conducive to the rolling resistance property of rubber materials. The influences of kaolinite content on the dynamic storage modulus and tanδ as a function of MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

temperature for kaolinite/SBR nanocomposites are presented in Figs. 6 and 7. Table 3 summarizes the values of different glass transition temperatures and loss tangents at 0 °C and 60 °C for kaolinite /SBR composites filled by different contents of kaolinite. As shown in Fig. 6, the storage modulus of vulcanizate samples increased as the kaolinite content increased in the low-temperature region; this effect is also attributed to the reinforcement of kaolinite and the stronger restriction on molecular chains motion as a result of the increase in the volume fraction of kaolinite. A more rapid decrease in the storage modulus was observed in the vulcanizate samples with a higher amount of kaolinite at the temperature range of −60 °C to −20 °C. As could be seen in Fig. 7. The tanδ values at Tg for vulcanizate samples decreased as the kaolinite content increased; this effect is attributed to the increase in the unit volume fraction of kaolinite in the composite matrix. Consequently, the hysteresis of the composite is decreased in the low-temperature region. The tanδ values at 0 °C for vulcanizate samples decreased as the kaolinite content increased, thereby showing the low wet traction of the samples with high amounts of kaolinite. However, the tanδ values at 60 °C for vulcanizate samples increased as the kaolinite content increased, demonstrating the higher rolling resistance of samples with high amounts of kaolinite. These results indicate that the increase in kaolinite content can improve the storage modulus and validates the reinforcing effect of kaolin/SBR composites. However, a high kaolinite content is not beneficial for the wet traction and rolling resistance of vulcanizate rubber materials.

Fig. 6. The dynamic storage modulus as a function of temperature for kaolinite/SBR nanocomposites filled with different kaolinite contents. Table 3. tanδ and Tg of SBR/kaolinite composites filled with different contents. Samples

tanδ(0℃)

tanδ(60℃)

Tg/℃

MK-20-SBR

0.332

0.107

-21.20

MK-30-SBR

0.302

0.112

-21.37

MK-40-SBR

0.326

0.119

-19.2

MK-50-SBR

0.324

0.125

-20.43

MK-60-SBR

0.311

0.129

-20.16

MK-70-SBR

0.308

0.131

-20.2

MK-80-SBR

0.307

0.144

-18.9

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Fig. 7. The loss tangent as a function of temperature for kaolinite/SBR nanocomposites filled with different kaolinite contents. Filler network structure of kaolinite/SBR composites The effect of kaolinite particle size and content on the storage modulus (G/, in the shear model) as a function of shear strain for kaolinite/SBR compounds without crosslinking were evaluated. The storage modulus as a function of shear strain for SBR filled by kaolinite with different particle size is presented in Fig. 8. The G/ values of all SBR filled with kaolinite are higher than that of pure SBR over the entire span of shear strain amplitudes, thus verifying that a significant reinforcement has occurred; this finding is in agreement with the above data. All of the composites displayed a reduction of G/ with the shear strain. This effect was more pronounced as the filler particle size decreased; however, this effect can be ignored in pure SBR. The decrease in the storage modulus with the applied shear strain for rubber melts containing reinforcing fillers is a non-linearity behaviour known as the Payne effect [17, 29]. Such an effect is considered an indication of the occurrence of the so-called filler networking phenomenon, which is attributed to an agglomeration-deagglomeration process of the filler particles above the filler percolation threshold[30]. The reduction of kaolinite particle size resulted in the increase in special surface, surface energy, and the unit volume fraction of fillers in the rubber matrix. These changes enhanced the interaction between the filler particles and intensified the agglomeration-deagglomeration process. Thus, a larger Payne effect was observed for the SBR filled with smaller-particle-sized kaolinite. These results show that the agglomerationdeagglomeration process of kaolinite particles would be intensified as the particle size is reduced and indicates that modifications are necessary to improve the dispersion of fillers in the rubber matrix. The storage modulus as a function of shear strain for SBR filled by different contents of kaolinite is presented in Fig. 9. The G/ values of composites increased as the kaolinite content increased over the entire span of shear strain amplitudes; this behaviour is attributed to the stronger restriction of kaolinite particles on molecular chains motion as result of the increase in the unit volume fraction of kaolinite and the interaction between kaolinite particles and rubber chains. The Payne effect of kaolinite/SBR composites exhibited an enhanced tendency as the kaolinite content increased, indicating that the agglomeration-deagglomeration of filler particles intensified because of the relative increase in the unit volume fraction of kaolinite in the composite matrix.

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Fig. 8. The storage modulus (G/) as a function of strain for kaolinite/SBR nanocomposites filled with different particle sized kaolinite.

Fig. 9. The storage modulus (G/) as a function of temperature for kaolinite/SBR nanocomposites filled with different kaolinite contents. Summary. A series of SBR composites filled with modified kaolinite was prepared by melt blending. The influences of kaolinite particle size and content on the dynamic mechanical properties of kaolinite/SBR composites were investigated. The results of SEM and TEM revealed that the rubber chains were confined within the interparticle space of kaolinite, and that micro-scale kaolinite particles exhibited a physical dispersion in the SBR matrix. Both the decrease in kaolinite particle size and the increase in kaolinite content can greatly improve the storage modulus and reinforcing effect of kaolinite/SBR composites. The reduction of kaolinite particle size is beneficial for the wet traction property but undesirable for the rolling resistance property of kaolinite/SBR composites. However, the increase in kaolinite content is unfavourable for both the wet traction and rolling resistance of the vulcanized rubber samples. The results indicate that smaller particle size and low filled content of kaolinite filler is favourable for the dynamic properties of SBR materials for tire products. The filler networking phenomenon ascribed to the agglomeration-deagglomeration of filler particles was intensified as the particle size was reduced and the kaolinite content was increased as a result of the increase in the unit volume fraction of kaolinite in the rubber matrix and the stronger interaction between kaolinite particles in the composite matrix. MMSE Journal. Open Access www.mmse.xyz

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Acknowledgments The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation Project of China (51034006) and the National Natural Science Foundation Project of China (51604158). References [1] G. Choudalakis, A.D. Gotsis, Permeability of polymer/clay nanocomposites: A review, European Polymer Journal, 45 (2009) 967-984 doi 10.1016/j.eurpolymj.2009.01.027 [2] S. Sinha Ray, M. Okamoto, Polymer/layered silicate nanocomposites: a review from preparation to processing, Progress in Polymer Science, 28 (2003) 1539-1641 doi 10.1016/j.progpolymsci.2003.08.002 [3] J.P.G. Villaluenga, M. Khayet, M.A. López-Manchado, J.L. Valentin, B. Seoane, J.I. Mengual, Gas transport properties of polypropylene/clay composite membranes, European Polymer Journal, 43 (2007) 1132-1143 doi 10.1016/j.eurpolymj.2007.01.018 [4] J.W. Gilman, Flammability and thermal stability studies of polymer layered silicate (clay) nanocomposites, Applied Clay Science, 15 (1999) 31-49. [5] Z.F. Wang, B. Wang, N. Qi, H.F. Zhang, L.Q. Zhang, Influence of fillers on free volume and gas barrier properties in styrene-butadiene rubber studied by positrons, Polymer, 46 (2005) 719-724 [6] Y. Zhang, Q. Liu, Q. Zhang, Y. Lu, Gas barrier properties of natural rubber/kaolin composites prepared by melt blending, Applied Clay Science, 50 (2010) 255-259. [7] C. Lu, Y.-W. Mai, Permeability modelling of polymer-layered silicate nanocomposites, Composites Science and Technology, 67 (2007) 2895-2902 doi 10.1016/j.compscitech.2007.05.008 [8] Y. Zhang, Q. Liu, S. Zhang, Y. Zhang, H. Cheng, Gas barrier properties and mechanism of kaolin/styrene–butadiene rubber nanocomposites, Applied Clay Science, 111 (2015) 37-43. [9] A. Zare Shahabadi, A. Shokuhfar, S. Ebrahimi-Nejad, M.T. Arjmand, M, Modeling the stiffness of polymer/layered silicate nanocomposites: More accurate predictions with consideration of exfoliation ratio as a function of filler content, Polymer Testing, 30 (2011) 408-414. [10] Q. Liu, Y. Zhang, H. Xu, Properties of vulcanized rubber nanocomposites filled with nanokaolin and precipitated silica, Applied Clay Science, 42 (2008) 232-237. [11] Y. Zhang, Q. Liu, J. Xiang, R.L. Frost, Thermal stability and decomposition kinetics of styrenebutadiene rubber nanocomposites filled with different particle sized kaolinites, Applied Clay Science, 95 (2014) 159-166. [12] R.L. Fan, Y. Zhang, F. Li, Y. Zhang, K. Sun, Y.Z. Fan, Effect of high-temperature curing on the crosslink structures and dynamic mechanical properties of gum and N330-filled natural rubber vulcanizates, Polymer Testing, 20 (2001) 925-936. [13] C. Kumnuantip, N. Sombatsompop, Dynamic mechanical properties and swelling behaviour of NR/reclaimed rubber blends, Materials Letters, 57 (2003) 3167-3174. [14] X. Liu, Y. Gao, L. Bian, Z. Wang, Influence of ultrafine full-vulcanized styrene-butadiene powdered rubber on dynamic mechanical properties of natural rubber/butadiene rubber and styrenebutadiene rubber/butadiene rubber blends, Polymer Bulletin, 72 (2015) 2001-2017. [15] F.R.S. Benmesli, Dynamic mehcanical and thermal properties of a chemically modified polypropylene/natural rubber thermoplasitic elastomer blend, Polymer Testing, 36 (2014) 54-61. [16] M. Nematollahi, A. Jalali-Arani, K. Golzar, Organoclay maleated natural rubber nanocomposite. Prediction of abrasion and mechanical properties by artificial neural network and adaptive neurofuzzy inference, Applied Clay Science, 97-98 (2014) 187-199. MMSE Journal. Open Access www.mmse.xyz

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[17] M. Galimberti, M. Coombs, V. Cipolletti, A. Spatola, G. Guerra, A. Lostritto, L. Giannini, S. Pandini, T. Riccò, Delaminated and intercalated organically modified montmorillonite in poly(1,4cis-isoprene) matrix. Indications of counterintuitive dynamic-mechanical behavior, Applied Clay Science, 97-98 (2014) 8-16. [18] A. Malas, P. Pal, S. Giri, A. Mandal, C.K. Das, Synthesis and characterizations of modified expanded graphite/emulsion styrene butadiene rubber nanocomposites: Mechanical, dynamic mechanical and morphological properties, Composites: Part B, 58 (2014) 267-274. [19] H. Cheng, R.L. Frost, J. Yang, Q. Liu, J. He, Infrared and infrared emission spectroscopic study of typical Chinese kaolinite and halloysite, Spectrochim Acta A Mol Biomol Spectrosc, 77 (2010) 1014-1020. [20] R.L. Frost, J. Kristof, E. Horvath, J.T. Kloprogge, The Modification of Hydroxyl Surfaces of Formamide-Intercalated Kaolinites Synthesized by Controlled Rate Thermal Analysis, J Colloid Interface Sci, 239 (2001) 126-133. [21] H. Cheng, Z. Zhang, Q. Liu, J. Leung, A new method for determining platy particle aspect ratio: A kaolinite case study, Applied Clay Science, 97-98 (2014) 125-131. [22] Z. Gu, G. Song, W. Liu, P. Li, L. Gao, H. Li, X. Hu, Preparation and properties of styrene butadiene rubber/natural rubber/organo-bentonite nanocomposites prepared from latex dispersions, Applied Clay Science, 46 (2009) 241-244. [23] A. Lagazzo, S. Lenzi, R. Botter, P. Cirillo, F. Demicheli, D.T. Beruto, A rheological method for selecting nano-kaolin powder as filler in SBR rubber, Particuology, 8 (2010) 245-250. [24] Y. Zhang, Q. Liu, Z. Wu, Q. Zheng, H. Cheng, Thermal behavior analysis of kaolinite– dimethylsulfoxide intercalation complex, Journal of Thermal Analysis and Calorimetry, 110 (2011) 1167-1172. [25] H. Cheng, Q. Liu, J. Yang, Q. Zhang, R.L. Frost, Thermal behavior and decomposition of kaolinite–potassium acetate intercalation composite, Thermochimica Acta, 503-504 (2010) 16-20. [26] H. Cheng, S. Zhang, Q. Liu, X. Li, R.L. Frost, The molecular structure of kaolinite–potassium acetate intercalation complexes: A combined experimental and molecular dynamic simulation study, Applied Clay Science, (2015). [27] Y. Zhang, Research on the dynamic heating built-up and barrier properties of rubber/kaolin composites, College of Geoscience and Surveying Enginerring, China University of Mining & Technology-Beijing, 2013, pp. 47-49. [28] S. Prasertsri, N. Rattanasom, Fumed and precipitated silica reinforced natural rubber composites prepared from latex system: Mechanical and dynamic properties, Polymer Testing, 31 (2012) 593605. [29] A.R. Payen, Whittaker, P.E, Low strain dynamic properties of filled rubbers, Rubber Chemistry and Technology, 44 (1971) 440-478. [30] G.A. Bohm, Tomaszewski, W, Cole, W, Hogan, T, Furthering the understanding of the non-linear response of ﬁller reinforced elastomers, Polymer, 51 (2010) 2057-2068. Cite the paper Yinmin Zhang, Hongli Song, Qinfu Liu, Shilong Zhang, Yude Zhang (2017). Dynamic Mechanical Property of Kaolinite/Styrene-Butadiene Rubber Composites. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.61.54.732

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Investigation on Pure and L-lysine Doped (Tri) Glycine Barium Chloride (TGBC) Single Crystal for Nonlinear Optical Applications2 S. Chennakrishnan1, S.M. Ravikumar2, D. Sivavishnu2, M. Packiya Raj3, S.Varalakshmi4 1 – Dept. of physics, Idhaya Arts & science College for women, Tiruvannamalai-606 603, Tamil Nadu, India 2 – Department of physics, Government Arts College, Tiruvannamalai-606 603, Tamil Nadu, India 3 – Department of Physics, S.K.P. Engineering College, Tiruvannamalai 606 611, Tamil Nadu, India 4 – Department of physics, Kamban College of Arts & Science for Women, Tiruvannamalai 606 601. Tamil Nadu, India DOI 10.2412/mmse.05.501.447 provided by Seo4U.link

Keywords: solution growth, X-ray diffraction, nonlinear optical material, thermal study.

ABSTRACT. Single crystals of pure and L-lysine doped (tri) glycine barium chloride (TGBC) were grown by slow solvent evaporation technique with the vision to improve the physicochemical properties of the sample. Single crystal Xray diffraction analysis of both pure and doped samples was carried out and the results are compared. Optical absorption and FTIR spectroscopic studies are performed to identify the UV cut-off wavelength range and the presence of various functional groups in the grown crystals. The thermos-gravimetric (TG) analysis of L-lysine doped TGBC indicates a marginal increase in the thermal stability of the crystals. The SHG efficiency of pure and doped TGBC was discussed.

1. Introduction. A novel nonlinear optical (NLO) crystal is attracting many theoretical and experimental researchers recently because NLO crystals are used in various applications in the areas like high speed information processing, optical communication, optoelectronics and optical data storage [1-3]. Materials with large second order harmonic optical nonlinearities, transparency at required wavelength and stable physicochemical performance are needed to realize the many of these applications. Currently there is a need for materials with large non linearity, which efficiently double the low peak power sources such as diode laser [4]. Among the different varieties of NLO crystals, semi-organic crystals are gaining rapid interest due to their interesting and intriguing properties. Optical non-linearity of inorganic crystals is generally lower than that of optical device demand organic compounds are often formed by weak Vander walls, hydrogen bond and process a high degree of delocalization [5-8]. A major drawback of organic NLO crystals is the difficulty in growing large size good optical quality and high mechanical stability single crystal [9]. In fact, considerable effort has been made on semi-organic crystals due to their having the combined properties of both inorganic and organic crystals also high damage threshold, wide transparency range, high mechanical strength and chemical stability. Hence, the semi-organic crystals are suitable for the device fabrication [1012]. Amino acid based semi-organic compounds have been recently recognized as potential candidates for second harmonic generation (SHG) [13–15]. Amino acids are interesting materials for NLO applications as they contain proton acceptor carboxyl acid (-COOH) group and the proton donor amino (NH2) group. Glycine (NH2-CH2-COOH) is the simplest amino acid. Unlike other amino acids, it has as symmetric carbon atom and is optically inactive. Also, glycine can be readily combined with variety of acids, organic and inorganic components to produce a host of materials with interesting properties [16-17]. Glycine mixed with metal chlorides such as zinc chloride [18], calcium chloride [19], potassium chloride [20], sodium chloride [21] and lithium chloride [22] has been reported in the 22

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recent years. Interest have been centered on semiorganic crystal which have the combined properties of both inorganic and organic crystals like high damage threshold, wide transparency range, less deliquescence, higher mechanical strength and chemical stability which make them suitable for device fabrication [23]. The advantage of semi-organic materials is that they can be grown from aqueous solution and form large three dimensional crystal of excellent physico-chemical properties. Hence, it is necessary to synthesize and grow novel semiorganic crystals. Hence, the interest has been centered on Glycine Barium chloride and suitable dopants. In this present investigation, we report bulk growth of pure and L-lysine doped (tri) glycine barium chloride crystal by solution growth technique. The grown crystals were characterized using single crystal XRD and powder X-ray diffraction, Fourier transform infrared (FT-IR) analysis, UV-vis-NIR spectroscopy and thermosgravimetric analysis (TGA), differential thermal analysis (DTA). 2. Materials and Methods 2.1. Synthesis for pure TGBC The title compound of (tri) glycine barium chloride was synthesized by reacting glycine (Merck, GR grade) and barium chloride (Merck, GR grade) with stoichiometric ratio of 3:1 at room temperature. A necessary quantity of glycine is dissolved in double distilled water at room temperature until it attains saturated condition. After preparing saturated solution of glycine, the proportionate amount of barium chloride was added with glycine solution while continuous stirring for 4 hours to bring a homogenous mixture of solution of (tri)glycine barium chloride. The (tri) glycine barium chloride was synthesized on the following chemical reaction. 3(NH2-CH2-COOH) + BaCl2

Ba (NH2-CH2-COOH)3Cl2

2.2. Synthesis for doped TGBC An appropriate amount of analytical reagent grade of L-lysine were added with saturated mother solution of (tri) glycine barium chloride to form a aqueous solution of L-lysine doped TGBC. The solution was stirred using magnetic stirrer for 6 hours to obtain the homogeneous solution at room temperature. The chemical reaction of synthesized compound was shown below, CH2N (CH2)4CH (NH2) + Ba (NH2-CH2-COOH)3 Cl2

BaCH2N(CH2)4CH(NH2) (NH2-CH2-COOH)3 Cl2)

2.3. Crystal Growth for Pure and Doped TGBC The saturated solution of pure TGBC and L-lysine doped TGBC were filtered using whattman filter paper to remove impurities. The super saturated solution of pure and doped TGBC was tightly covered with polyethylene sheet, to keep out from dust free area and the solution were allowed to evaporate at room temperature. After 15 to 20 days good quality seed crystal of pure TGBC were obtained whereas the L-lysine doped TGBC has taken 10 days later to get the seed crystal . The good quality and defect free seed crystal of pure and doped TGBC was selected for bulk growth. The (tri) glycine barium chloride crystal of average dimension 18×10×5 mm3 has been harvested in the period of 25 to 35 days but L-lysine doped TGBC were grown with dimension 7 x 9 x 2 mm3 in the period of 45 days with different morphology and the grown crystals are highly transparent. As grown crystal of pure TGBC and L-lysine doped TGBC was shown in Figure 1. The optimized growth condition of pure and L-lysine doped (tri) glycine barium chloride is given the table 1.

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Pure TGBC crystal

Doped TGBC Crystal

Fig. 1. As grown crystal of pure and doped TGBC. Table 1. The optimized growth condition of pure and doped TGBC. Pure TGBC

Doped TGBC

Growth method

Slow evaporation

Solvent used

Double distilled water

Molecular formula

Ba(NH2-CH2-COOH)3 Cl2

Ba CH2N(CH2)4CH(NH2) (NH2- CH2 COOH)3 Cl2

Molar ratio

Glycine + Barium chloride

L-lysine +Glycine + Barium chloride

Temperature

Room temperature

Period of growth

25 to 35 days

45 days

Dimension of the crystal

18×10×5 mm3

7x9x2 mm3

3.0 Results and Discussion 3.1. Single crystal X-Ray Diffraction (XRD) Analysis Single Crystal X-ray diffraction analysis of pure and L-lysine doped TGBC was recorded using ENRAF NONIUS CAD-4 automatic X-ray diffractometer. This analysis reveals that the pure and doped TGBC crystallizes in orthorhombic system with space group pbcn. The calculated lattice parameters of the pure TGBC crystal are a=8.281Ǻ, b=9.410 Ǻ, c=14.898 Ǻ, α=β=γ=90º and volume V= 1160.177 Ǻ3, and doped TGBC a=8.471 Ǻ, b=9.524 Ǻ, c=14.312 Ǻ, volume V= 1154.660 Ǻ3. The lattice parameters are well agreed with reported value [24]. Thus, the XRD results confirm that MMSE Journal. Open Access www.mmse.xyz

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there is no change in crystals structure, but there is a small changes in the lattice parameters. The change in the lattice parameter may due to incorporation of L-lysine with TGBC. 3.2. Powder X-Ray Diffraction Analysis Powder XRD diffraction analysis was carried out using BRUCKER, Germany (model D8 Advance) X-ray diffractometer with CuKalpha (wavelength = 1.5405Ă&#x2026;) radiation. The scanning range form 10 to 80o at a scanned rate of 1o per minute to study the crystalinity of the grown crystal. The diffracted peaks are varying for pure and doped a TGBC crystal, which is shown in figure 2. The well-defined sharp peaks signify the good crystalline nature of the pure and doped TGBC crystal.

Fig. 2. Powder XRD pattern of pure and L-lysine doped TGBC crystal. 3.3. Fourier Transform Infrared (FTIR) spectroscopy study The infrared spectral analysis is fruitfully used to understand the chemical bonding and provides information about molecular structure of the synthesized compound. Crushed powder of pure and Llysine doped (tri) glycine barium chloride was pelletized using KBr. The spectrum was recorded using a Thermo Nicolet V-200 FTIR Spectrometer in the range 4000 - 400 cm-1 wavenumber region. The FTIR spectra of powdered TGBC with and without L-lysine are shown in Figure 3. The observed wavenumbers and their corresponding assignments for the title compound were found and listed in the table 2. The peaks around 3432 cm-1 is attributed to NH asymmetric stretching whereas in Llysine doped TGBC crystal this mode was found at 3437 cm-1. The drift in wavenumber of the doped crystal is due to the participation of amino groups in the hydrogen bonding formation. The peaks obtained at 3062, 3059 and 2981 cm-1 for pure and doped crystals, respectively were assigned to CH stretching. The peaks of IR spectrum at 2589, 2590 cm-1 for pure and doped crystal ascribed to NH3+ stretching vibration. The NH3+ deformation of pure and doped TGBC was observed as sharp peak at 1571 cm-1. A very strong peak is observed at 1478 cm-1 may due to vibration of NH2 deformation for pure TGBC whereas this peak is shifted to 1480 cm-1 in L-lysine doped crystal. The COO- symmetric stretching is observed as a sharp peak at 1404 and 1406 cm-1 for pure and doped TGBC respectively . The pure and doped TGBC crystal, the peak at 1330 and 1336 cm-1 are due to C-N-H symmetric bending. The peak around 1116 cm-1 , 896 and 668 cm-1 attributed to CH2 rocking, CCN stretching and C-Cl stretching respectively. A peak at 1031 and 1035 cm-1 for C-C-N-C symmetric stretching for pure and doped TGBC respectively.

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Fig. 3. The FTIR spectrum of pure and doped TGBC. Table 2. Band assignments of FTIR spectrum of doped TGBC. Wavenumber cm-1 Doped TGBC Pure TGBC 3432 3437 3062 3059 2984 2589 2590 1571 1574 1478 1480 1404 1406 1330 1336 1116 1118 1031 1030 896 898 668 669

Assignments NH asymmetric stretching C-H stretching C-H stretching NH3+ stretching NH+3 deformation NH2 deformation COO- symmetric stretching C-N-H symmetric stretching CH2 rocking C-C-N C symmetric stretching CCN stretching C-Cl stretching

3.4. Optical Transmission Study Crystal plates of pure TGBC and doped TGBC with a thickness of 2mm were cut and polished without any coating for optical measurements optical transmission spectra were recorded for the grown crystals in the wavelength region from 200 to 1000 nm using double beam UV visible spectra of pure and doped TGBC crystals is shown in figure 4. From the transmission spectra, it is noticed that pure and L-lysine doped TGBC crystal has high transmittance in the entire visible NIR region of the spectra, and this property enables the materials for the NLO application. A UV cut off wavelength MMSE Journal. Open Access www.mmse.xyz

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for pure TGBC and doped TGBC is observed at 234 nm and 251 nm respectively. This is an augmented characteristic for the fabrication of optoelectronic devices [25].

Fig. 4. Optical transmission of pure and doped TGBC. 3.5 Nonlinear optical study SHG conversion efficiency measurements has been carried out using Kurtz and Perry technique [26]. A Q-switched Nd:YAG laser beam of wavelength 1064 nm with input beam energy of 1.5 mJ/pulse and pulse width 10 ns with a repetition rate of 10 Hz was used. The grown crystals of pure and Llysine doped TGBC crystal was powdered with uniform particle size and tightly packed in a microcapillary of uniform bore and exposed to the laser radiation. The bright green light (ฮป = 532 nm) emission has been observed which indicates that the SHG behaviour of the grown crystals. The relative SHG efficiency of pure TGBC (10.84 mJ) and L-lysine doped TGBC (14.56 mJ) are nearly 1.33 and 1.86 times that of KDP (7.80 mJ) respectively. 3.6 TG - DTA analysis Thermal properties of the material was studied by Thermogravimetric (TGA) and Differential Thermal Analysis (DTA) using STA 409 C instrument between the temperature 50 and 800 ยบC at a heating rate of 20 ยบC per min in the nitrogen atmosphere. Figure 5 and Figure 6 illustrate the TGDTA curve of pure and L-lysine doped TGBC crystals respectively. The absence of water molecule in pure and L-lysine doped TGBC crystal was observed by absence of weight loss at 100 ยบC. DTA curve shows a sharp endothermic peak at 169.3 ยบC for pure and 174.4 ยบC for L-lysine doped TGBC, which corresponds to the melting point of the compound. Hence the thermal stability of pure and doped tri-glycine barium chloride is around 169.3 ยบC and 174.4 ยบC. Due to the addition of L-lysine with TGBC the thermal stability is increased by nearly 5 ยบC. The material decomposes at 321.8 ยบC and 322 ยบC for pure and doped TGBC respectively, which is represented by the sudden loss of mass due to the glycine. From the TG curve, the mass loss is take place after the temperature of 169.3 ยบC. The mass lost from 169 ยบC to 321 ยบC is found to be 43% . Above 321.8 ยบC, the material undergoes irreversible endothermic transition around at 525 ยบC. There is further mass loss of 7% occuring in the temperature limit of 321-525 ยบC which confirms the L-lysine doping into the TGBC crystal. The actual residual amount of mass is 50% which may be considered to be the compound of barium. From the above analysis, the melting point of the pure and doped (tri) glycine barium chloride is 169 ยบC and 174.4 ยบC which is higher than the other semiorganic materials like bisglycine hydrogen chloride (146.8 ยบC), tetra glycine barium chloride (160 ยบC), ฮฑ-glycine sulpho-nitrate (143 ยบC) [16-18].

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954 45.00

5.3%

100.0

40.00 90.0 35.00

43.0%

80.0

30.00 70.0 25.00

50.0

TG %

DTA uV

60.0 20.00

15.00 40.0 10.00 30.0 5.00

169.3Cel 5.36uV

321.8Cel 4.33uV

20.0

0.00 10.0 -5.00 0.0 -10.00 100.0

200.0

300.0

400.0 Temp Cel

500.0

600.0

700.0

800.0

Fig. 5. TG and DTA curve of pure TGBC crystal. 5.1%

0.00

100.0

90.0

-5.00 41.2%

80.0

-15.00

70.0

-20.00

60.0

50.0

-25.00 525.1Cel -29.46uV

40.0

-30.00

-35.00

TG %

DTA uV

-10.00

30.0

174.4Cel -34.88uV

20.0

-40.00

10.0

-45.00

-50.00 100.0

200.0

322.0Cel -49.24uV 300.0 400.0 Temp Cel

0.0 500.0

600.0

700.0

800.0

Fig. 6. TG and DTA curve of L-lysine doped TGBC crystal. Summary. Well-developed good quality transparent crystals of pure and L-lysine doped TGBC was grown successfully by slow evaporation technique. Unit cell parameters and crystal system were determined by single crystal X -ray diffraction technique. Powder XRD shows good crystalline of the grown pure and doped crystal. The various functional groups presence in the grown crystal of pure and doped was identified by FTIR study. The UV cut off wavelength of pure and L-lysine doped TGBC crystal was found to be 234 nm and 251 nm respectively, which reveals grown crystals are potential candidate for NLO applications. The second harmonic generation (SHG) efficiency of pure and L-lysine doped TGBC crystal is about 1.33 and 1.86 times that of KDP respectively and the addition of L-lysine with TGBC the SHG efficiency has increased. Thermal properties of the material was studied by Thermogravimetric (TGA) and Differential Thermal Analysis (DTA), the melting point of the pure and doped tri- glycine barium chloride is 169 ºC and 174.4 ºC. Acknowledgement Acknowledgments The Corresponding author sincerely thankful to UGC for funding minor research project, (MRP06288/15 (SERO/UGC) and also acknowledge Dr. M. Basheer Ahamed, Head, Dept. Of Physics, B. S. Abdur Rahman University, Chennai for carryout the NLO test. References

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[25] V.Venkataramanan, S.Maheswaran, J.N.Sherwood, H.L.Bhat, J.Cryst. Growth 179 (1997) 605610. [26] S.K. Kurtz, T.T. Perry, J.Appl. Phys. 39 (1968) 3798. Cite the paper S. Chennakrishnan, S.M. Ravikumar, D. Sivavishnu, M. Packiya Raj, S.Varalakshmi (2017). Investigation on Pure and L-lysine Doped (Tri) Glycine Barium Chloride (TGBC) Single Crystal for Nonlinear Optical Applications. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.05.501.447

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Especially the Transformation of Austenite in High-Strength Cast Iron during Processing With Continuous Cooling3 R.K. Hasanli 1,a, S.N. Namazov 2,b 1 – Associated professor, Dr., Azerbaijan Technical University, Baku, Azerbaijan 2 – Professor, Dr., Azerbaijan Technical University, Baku, Azerbaijan a – hasanli_dr@mail.ru b – subhan_namazov@daad-alumni.de DOI 10.2412/mmse.11.018.190 provided by Seo4U.link

Keywords: high-strength cast iron, spherical graphite, the transformation of austenite, economical alloying, chill casting, heat treatment, structure, austenite, bainite, properties.

ABSTRACT. The peculiarities of the transformation of austenite in high-strength cast iron with spherical-eminent graphite when machining with continuous cooling. The possibility of obtaining a bainite structure economically-alloyed with nickel and copper, and molded in a metal mold of high strength cast iron with continuous cooling. It is established that in high-strength cast iron processed by bainite, graphite inclusions should have a spherical shape. The amount of vermicular graphite may be in the range of 10-20%.

Introduction.The aim of this work is to study the peculiarities of the transformation of austenite in high-strength nodular cast iron when machining with continuous cooling. According to the literature recommendations, cast iron subjected to heat treatments continuous cooling to ensure it bainite structure should contain additives of Ni, Cu and Mo [1, 2]. The lack of Mo in the composition of the investigated cast irons has demanded carrying out of special research. Analyses of the Especially the Transformation of Austenite in High-Strength Cast Iron during Processing With Continuous Cooling. It is possible to assume, that the continuous air-cooling economically-alloyed cast iron    – transformation occurs at temperatures of 450-3500C (not lower than 3500C). The real strength of cast iron after such treatment may be 800-1100 MPa, which satisfies these requirements. Rightly considered, that the bottleneck for high-strength cast irons are a lack of ductility and toughness. However, it was found that using the chill casting method largely facilitates the solution of this problem [3-12].

Comparison of properties of high-strength cast irons carried out the casting in the mold and sandyargillaceous form an integrated doped Ni - Cu additives or Ni. Heat treatment of castings is carried out in the following mode. Heating was carried out up to temperatures of 870±100C and 900±100C with excerpts 15 and 40 min. The cooling was carried out on the tranquil air and accelerated with a blowing air jet. Quality heat treatment were evaluated by hardness and obtain the structure of the matrix. After air-cooling in the design of all cast irons are observed more or less large areas of ferrite around the graphite inclusions are spherical (Fig. 1). Such areas are enriched in silicon and this is why the process of saturation with carbon is inhibited. It is established that the increase in time of exposure at a temperature of austenitization slightly reduces the size of the ferritic regions. Determined that a small amount of ferrite (2-3%) are located

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Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

on the boundaries of the secondary grains, have no detrimental effect on the tribological properties of chill cast iron [13-15]. Based on the data given in the table for the study was taken on to the next mode of heat treatment with continuous cooling, the dwell time of 30-40 min, cooling, vacation with heating for 3 hours to a temperature of from 200 to 4000C (see table 1).

Fig. 1. Microstructure of non-alloy iron after normalization 9000C, exposure 15 min.: a, b - chill casting; and b - x100; c, d - casting in sand-clay the form of a; b, d - x600. As studies have shown, a vacation at 2000C contributes to the improvement of impact strength of not less than 20% without visible changes in structure. Vacation at 3000C reduces the toughness of all investigated cast irons, while not significantly affecting the wear resistance [6, 7]. Vacation in 4000C promotes the release of fine carbides, also resulting in a significant increase in toughness as Nickel and Nickel - copper cast irons, lower (3-5%) to their durability. The influence of the size of the cross section was investigated on samples with a diameter of 10 and 20 mm. found that in sections of 20 mm or more it is possible to obtain bainite structure by using the analyzed heat treatment in industrial conditions under a powerful fan. In the laboratory banana structure can be reliably obtained in the samples with cross-section not exceeding 10 mm if sufficient quantities of alloying elements (Fig. 2). If the cross section of the part is 20 mm, cast iron acquires the structure of pearlite with different number of top bainite (Fig. 3). MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Table 1. The influence of the mold and heat treatment on the structure of the doped Ni (1.0%) and Cu (0.5%) cast iron. Material and mold Steel 40KH Ductile iron cast in metal mold

Ductile iron, cast in sand form

Heat treatment Hardening Normalization with excerpt 15 min. Normalization with excerpt 40 min. Normalization with excerpt 15 min. Normalization with excerpt 40 min. Normalization with excerpt 15 min. Normalization with excerpt 40 min. Normalization with excerpt 15 min. Normalization with excerpt 40 min.

870 C,

Hardness,, HRC 49 53

M+B B+F(2%)

870 0C,

900 0C,

B+F(5%)

900 0С,

B+F(3%)

870 0С,

B+P(40%)+Ф(15%)

870 0С,

B+F(30%)

900 0С,

B+P+F(20%)

900 0С,

B+F (10%)

Structure

The amount of alloying elements and their composition determine the homogeneity of the structure and structural components formed in the cast iron after to normalize. Nickel - copper cast irons, containing 1.0% of Ni and 0.5% Cu, in laboratory conditions, tended to lower the needle bainite (Fig. 4). On the calm air in these alloys is formed pearlitic-bainitic structure (Fig. 5, b). In cast iron, only Nickel doped (2%) after heat treatment with rapid cooling in the laboratory is produced bainite the top, in the factory, the lower needle bainite. A decrease in doping leads to the fact that in the cast iron with the addition of 1.5% Ni in the laboratory it is practically impossible to fully bainite structure. Typically, a mixture of perlite with a small amount bainite. At low doping (1% Ni) observed the presence of ferrite on the boundaries of the secondary grains. The matrix is mostly pearlite, sometimes with insignificant portions of the upper bainite (Fig. 2, a). The mutual arrangement of the structural components (perlite and bainite) reflects the kinetics of recrystallization alloy. Often bainite is around the perlite at the grain boundaries (Fig. 3, b), or around graphite inclusions radiating rays (Fig. 5, a). Thus, it can be argued that in traditional cast iron silicon largely localized around graphite inclusions (Fig. 6). In pearlitic-bainitic cast iron, formed during the slow cooling, lower bainite is located in characteristic alternating strips. It is important to cast iron, processed by bainite, graphite inclusions were globular form, allowed a small amount of vermicular graphite in the range of 10-20%.

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

а)

c) d) Fig. 2. The microstructure of alloyed 1% Ni +0.5% of Cu metal after normalization a-8700C, casting in sand-clay the form; b-9000C, the same; c-9350C, the same; d-9000C, chill casting. x600. Crosssection 10 mm.

а)

c) Fig. 3. The microstructure of alloyed 1% Ni +0.5% of Cu metal after normalization a - 8700C; b900℃; c-9350C. x600. Section 20 mm.

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Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

Fig. 4. The microstructure of alloyed 1% Ni +0.5% of Cu metal after normalization with the blowing. x600. Cross-section 10 mm.

Đ°)

Fig. 5. Microstructure of alloy cast iron after normalization on the tranquil air: a-1% Ni-0,5% Cu; b-1.5% of Ni+0,5% Cu. x600. Cross-section 10 mm.

Fig. 6. The microstructure of alloyed 1% Ni-0,5% Cu iron after normalization with the blowing. x600. The cross section of 20 mm. Summary. Thus, the peculiarities of the transformation of austenite in high-strength cast iron when machining with continuous cooling. It is revealed that the pearlite-bainite cast iron, formed during the slow cooling, lower bainite is located in a characteristic alternating bands corresponding to the axes of the dendrites. The possibility and efficiency of producing bainite structure in the economically alloyed with Nickel and copper in cast iron, cast in the mold using continuous cooling. Determined that the cast iron processed by bainite, graphite inclusions should have a spherical shape, with perhaps a small amount (between 10-20%) vermicular graphite.

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References [1] R.K. Hasanli. Structure and properties of ductile iron. Baku, Science, 2013, 250 p. [2] A.I. Belyakov and others. Production of castings from high-strength nodular cast iron. M., Mechanical engineering, 2010, p. 712 [3] I.P. Bunin, Y.N. Malinochka, B.P. Taran. Fundamentals of metallography of cast iron. Moscow, Metallurgy, 1998, 413 p. [4] V.A. Ilyinsky, A.A. Zhukov and others. New in the theory of graphitization. The relationship between primary and secondary crystallization graffitists iron-carbon alloys // Metallography and heat treatment of metals, 2001, No.10. P.10-16 [5] High-strength cast iron with spherical graphite. Theory, production technology, properties and applications / ed. by M. V. Voloshchenko. Kiev: Sciences. Dumka, 2004. 203 p. [6] A.I. Belyakov, A.A. Belyakov. A.A. Zhukov Isothermal quenching of cast iron with nodular graphite // Blank production in mechanical engineering. 2008, No. 1, pp. 44-48 [7] V.V. Dubrov and others, The use of high-strength cast iron in valve. In proc. High-strength cast iron with nodular graphite. Kiyev, Naukova Dumka, 1998, pp. 78-81 [8] L.P. Ushakov. Wear-resistant cast iron with spheroidal graphite. M., Mechanical engineering, 2005, 153 p. [9] R. K. Hasanli. High-Strength cast iron with spherical graphite. Baku: Science, 1998, 203 p. [10] E.A. Silva, L.F.V.M. Fernandes, N.A.S. Sampaio, R.B. Ribeiro, J.W.J. Silva, M.S.Pereira (2016), A Comparison between Dual Phase Steel and Interstitial Free Steel Due To the Springback Effect. Mechanics, Materials Science & Engineering Journal Vol.4, Magnolithe GmbH, doi: 10.13140/RG.2.1.3749.7205 [11] L.I. Ă&#x2030;fron, D.A. Litvinenko (1994), Obtaining high-strength weldable steels with bainite structure using thermomechanical treatment, Metal Science and Heat Treatment, Vol. 36, Is. 10, Springer, doi [12] R.K. Hasanli. Investigation of wear resistance of economically alloyed high-strength cast iron with nodular graphite obtained by molding in metal forms // Bulletin of engineering. 2012, number 1. p. 47-49 [13] I.N. Bogachev, R.I. Mints. Cavitation-erosion fracture of cast iron. Sat. Theory and practice of foundry production. Ural Polytechnic Institute, vol. 89, 1999, pp. 71-78 [14] N.W. Ismailov. Features of producing engineering castings, using silica sand and bentonite clay in Azerbaijan // Journal of mechanical engineering 2012, No. 6, pp. 11-14 [15] R.K. Hasanli. Peculiarities of structure and phase composition of heat-treated high-strength cast irons with nodular graphite // Journal of mechanical engineering, 2013, No. 10, pp. 31-33 Cite the paper R.K. Hasanli, S.N. Namazov (2017). Especially the Transformation of Austenite in High-Strength Cast Iron during Processing With Continuous Cooling. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.34.581.343

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Structural and Dielectric Properties of Mg(1-x)CaxTiO3 (x=0.7, 0.8) Ceramic Materials4 V. Sharon Samyuktha 1, T. Subba Rao 2, R. Padma Suvarna1 1 – JNTUA, Anantapuram, Andhra Pradesh, India-515001 2 – Sri Krishna Devaraya University, Andhra Pradesh, India-515003 DOI 10.2412/mmse.30.345.847 provided by Seo4U.link

Keywords: calcium magnesium titanate, solid state reaction method, dielectric response, XRD.

ABSTRACT. Calcium Magnesium titanate ceramic materials with the molar formula Mg(1-x)CaxTiO3 in which the x varies from 0.7 to 0.8 were synthesized by conventional Solid State Reaction method. The XRD pattern revealed that the samples exhibit Orthorhombic structure. The microstructure and surface morphology for the samples was studied by SEM. The elemental composition was studied by EDAX. The dielectric response of both samples was measured by HIOKI 3532-50 LCR HiTESTER in the frequency range of 1KHz-1MHz from room temperature to 350 0C. These samples find applications in capacitors, microwave antennas, stainless steel electrodes and data storage devices.

Introduction. Over more than 200 years, Ceramic materials are known for technical applications. To overcome the limitations of other conventional materials, various special tailored ceramics are developed with novel chemical, electrical, biological and mechanical properties. In the last three decades there has been a phenomenal transformation in microwave communication systems such as mobile telecommunication systems, satellite communication and broadcasting systems, and global positioning systems. The rapid development in microwave communication systems was made possible with the use of dielectric ceramics as enabling materials for resonators, filters and other key components in microwave components. For these applications the ceramic materials are required to have a high relative permittivity (εr), low dielectric loss, and near zero temperature coefficient of resonant frequency (τf). The combination of these requirements greatly restricts the ceramic dielectrics available for applications in microwave systems [1]. Magnesium titanate ceramics play an important role in microwave technologies such as global positioning system operating at microwave frequencies, resonators, filters, antennas for communication system and multilayer capacitors [2-5]. It is a multifaceted material of low dielectric loss with high quality factor (Q above 20000 at 8GHz) and intermediate dielectric constant (εr=17) [6]. Calcium titanate is a popular ceramic material which has a wide range of applications in industry and technology. The Calcium titanate ceramic material has high dielectric constant (εr=170) Qxf value ̴ 3600 at 7GHz and τf value ̴ 800ppm/0C [7] and modest dielectric losses which makes it a suitable candidate for microwave applications. In the present work, the magnesium calcium titanate ceramic materials of different compositions such as Mg(1-x)CaxTiO3 (x=0.7-0.8) were synthesized by conventional Solid State diffusion method and the phase, crystallite size, microstructure and dielectric properties were investigated. Experimental Procedure. MCT CaxMg(1-x)TiO3 (x=0.7&0.8) was synthesized using Solid- state reaction method. High purity materials such as CaO (99.6% purity, Sigma Aldrich), TiO2 (99.4% purity, Sigma Aldrich), and MgO (99.6% purity, Sigma Aldrich) were used as precursor materials. These materials were weighed, taken according to the composition and mixed uniformly. The mixed 4

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

powders were milled for 12h in a Bill Miller (Retsch PM 200). The ground mixtures were dried and placed in alumina crucibles calcined at 1100-11200C for 36h in air in a programmable furnace. Thus obtained calcined powders were again milled for 10h and were pressed into pellets by adding PVA binder and by applying pressure of 8 ton using Hydraulic press. These readily formed pellets were sintered at a temperature of 1200-12500C for 4h in the furnace with a heating rate of 100C/min and then cooled to room temperature. X-Ray diffractometer (Rigaku), using CuK α radiation was used to identify the crystalline phase of the samples. Microstructural analysis of the sintered samples was performed by SEM (Hitachi: S4700) and Energy Dispersive X-Ray Spectroscopy (EDAX) for elemental composition. The dielectric constant and dielectric loss were measured by LCR meter HIOKI 3252-50 in the frequency range 1KHz to 1MHz. The dielectric constant was calculated by [8]:

r 

C *d 0 * A

(1)

where C – is capacitance of the pellet; d – is thickness of the pellet; A – is the area of the cross section of the pellet;

 0 – is the permittivity of free space. Results and Discussion. XRD Analysis: The XRD profiles have shown that the sample sintered at 1150 °C (optimized) has displayed well-defined features is shown in fig. 1. XRD peaks are in good agreement with the (ICDD#22-0153) confirming the Orthorhombic structure. The maximum intensity peak occurs at 330of 2θ for (1 1 2) reflection.

Fig. 1. XRD pattern for Mg(1-x)CaxTiO3 (x=0,0.7 & 0.8) Ceramic Materials. The lattice parameters of the samples CaxMg(1-x)TiO3 (x=0.7&0.8) are tabulated in table 1. The average crystalline size (Dp) is obtained using Scherer formula [9] MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

Dp = đ?&#x2018;&#x2DC;Îť/Î˛CosÎ¸

(3)

where k â&#x20AC;&#x201C; is a constant and is equal to 0.9; Î¸ â&#x20AC;&#x201C; is diffraction angle, Îť=0.154056 nm (CuKÎą) and Î˛ is full width half maxima. Table 1. Lattice parameters of CaxMg(1-x)TiO3 (x=0.7, 0.8) samples. Compound

Crystal System

a(A0)

b(A0)

c(A0)

Vol(A0)3

CaTiO3

Orthorhombic

5.386

5.444

7.660

224.49

Ca0.2Mg0.8TiO3

Orthorhombic

5.381

5.440

7.652

224.08

Ca0.3Mg0.7TiO3

Orthorhombic

5.386

5.444

7.660

224.67

The dislocation density (Ď ) of the samples is calculated by the formula Ď =D-2 (m-2) and avg. Crystalline size are also tabulated in the table 2. Table 2. Average Crystalline size and Dislocation Density. Sample Name

Average Crystalline size(nm)

Dislocation Density (m-2)

Ca0.2Mg0.8TiO3

48.54

4.244x1014

Ca0.3Mg0.7TiO3

53.58

3.483 x1014

Surface Morphology: The surface morphology is studied by Scanning Electron Microscopy (SEM). Fig. 2 shows SEM images of CaxMg(1-x)TiO3 (x=0.7, 0.8) which have been made at two different spots having 5000X and 10,000X magnifications in 10Îźm and 5Îźm range respectively. In the images the grains are almost spherical in shape containing homogeneous distribution containing with distinguished boundaries with less porosity have been observed. The average grain size for the CaxMg(1-x)TiO3 (x=0.7, 0.8) samples was determined to be 5-6Îźm from the equation [10]

Average grain size=

1.5 L MN

where L â&#x20AC;&#x201C; is total test line length; M â&#x20AC;&#x201C; the magnification; N â&#x20AC;&#x201C; the total number of intercepts which the grain boundary makes with the line.

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(4)

Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

Fig. 2. SEM images of a)Mg0.3Ca0.7TiO3 and b)Mg0.2Ca0.8TiO3 ceramic samples.

Fig. 3. EDAX images of a) Mg0.3Ca0.7TiO3 and b)Mg0.2Ca0.8TiO3 ceramic samples. EDAX: EDAX was performed to determine the concentrations of elements such as Mg, Ca, Ti and O present in the ceramic samples. Fig.3 gives the At% and Wt% of various elements. Dielectric Properties. The dielectric properties of the sintered ceramic samples of Magnesium Calcium titanate CaxMg(1-x)TiO3 (x=0.7, 0.8) are studied in the temperature range from room temperature to 3500C of varying frequency of 1KHz to 1MHz are depicted in fig. 4-5. At low frequencies, the increase in dielectric constant with temperature was due to accumulation of charge at the grain boundary and at the interface of the electrode sample and the electrode, which was called Space Charge Polarization [11]. As the frequency increased dielectric constant decreases due to gradual diminishing of the space charge polarization, indicating the ionic contribution. The dielectric constant is almost stable with temperature but at high temperature its value increased.

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Fig. 4. Variation of Dielectric constant with Fig. 5. Variation of Dielectric constant with Temperature at different frequencies for Temperature at different frequencies for Mg0.2Ca0.8TiO3 ceramic sample. Mg0.3Ca0.7TiO3 ceramic sample. The variation of dielectric loss of the sintered samples CaxMg(1-x)TiO3 (x=0.7, 0.8) with temperature at different frequencies were shown in the fig. 5-6. At low frequency there is increase in dielectric loss with temperature nearly at 2000C and then decreases. At higher frequencies the dielectric loss is very low and almost stable. This may be an extrinsic loss dominated by secondary phases, oxygen vacancies, grain sizes and densification.

Fig. 6. Variation of Dielectric Loss with Fig. 7. Variation of Dielectric Loss with Temperature at different frequencies for Temperature at different frequencies for Mg0.3Ca0.7TiO3 ceramic sample. Mg0.2Ca0.8TiO3 ceramic sample. Summary. The XRD confirmed the formation of Calcium Magnesium titanate and is of Orthorhombic structure. The SEM images describe the uniform distribution of grains. EDAX confirms the presence of elements of Mg, Ca, Ti and O. The dielectric constant increases with temperature at low frequencies for both the samples and at high frequencies it value is almost constant with temperature. At 1MHz frequency for both the samples exhibit very low dielectric loss which these suggest that these materials can be used in microwave applications. References [1] Wersing W. Microwave ceramics for resonators and filters, Current Opinion in Solid State & Materials Science, 1996, 1(5); 715-731, http://dx.doi.org/10.1016/S1359-0286(96)80056-8 MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

[2] C.L. Huang, et al., Mater. Res. Bull. 37(2002) 2483-2490. [3] W.W. Cho, K. Kakimoto, H. Ohsato, Mater. Sci. Eng. B 121 (2005) 48. [4] R.Z. Chen, et al., Mater. Sci. Eng. B 99 (2003) 302-305. [5] C.C. Cheng, T.E. Hsieh, I.N. Lin, J. Eur.Ceram. Soc. 23 (2003) 2553-2558. [6] Yuan- Fu Deng, Shi-Di Tang, Liang-Qiang Lao, Shu-Zhang Zhan, Synthesis of magnesium titanate nanocrystallites from a cheap and water-soluble single source precursor, Inorganica Chimica Acta 363 (2010) 827-829, http://dx.doi.org/10.1016/j.ica.2009.11.020 [7] R.C.Kell, A.C. Greenhem, G.C.E. Olds, Low-Loss Temperature-Stable High-Permittivity Microwave Ceramics, J.Am.Ceram.Soc. (1973) 352 [8] V. Sharon Samyuktha, T.Subba Rao, R.Padma Suvarna. Synthesis and Dielectric Properties of MgTiO3 Ceramic Material, International Journal of Engineering Research and Technology, ISSN: 2278-0181, Vol. 5 Issue 05, May-2016, http://dx.doi.org/10.17577/IJERTV5IS050349 [9] K. C. Babu Naidu, T. Sofi Sarmash, M. Maddaiah, et.a l., Journal of Ovonic Research 11(2), 79 (2015) [10] M. Maddaiah, K.Chandra Babu Naidu, D.Jhansi Rani, T. Subbarao, Synthesis and Characterization of CuO-Doped SrTiO3 Ceramics, Journal of Ovonic Research 11(3), (2015) 99–106 [11] Liqiang J, Xiaojun S, Baifu X, Baiqi W, Weimin C, Hongganga F. The preparation and characterization of La doped TiO2 nanoparticles and their photocatalytic activity. J Solid State Chem. 2004;177:3375–82. Cite the paper Sharon Samyuktha, T. Subba Rao, R. Padma Suvarna (2017). Structural and Dielectric Properties of Mg(1x)CaxTiO3 (x=0.7, 0.8) Ceramic Materials. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.30.345.847

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Passivation of Titanium Oxide in Polyethylene Matrices using Polyelectrolytes as Titanium Dioxide Surface Coating5 Javier Vallejo-Montesinos1,a, Julio Cesar López Martínez1, Juan Manuel Montejano-Carrizales2, Elías Pérez2, Javier Balcázar Pérez1, A. Almendárez-Camarillo3 and J.A. Gonzalez-Calderon4,b 1 – División de Ciencias Naturales y Exactas, Universidad de Guanajuato, Campus Guanajuato, Col. Noria Alta s/n, 36050 Guanajuato, Guanajuato, México 2 – Instituto de Física, Universidad Autónoma de San Luis Potosí, Alvaro Obregón #64, 78000, San Luis Potosí, México 3 – Departamento de Ingeniería Química, Instituto Tecnológico de Celaya, Av. Tecnológico y Antonio García Cubas s/n. Celaya, Guanajuato 38010, México 4 – Posgrado en Ciencias en Ingeniería Bioquímica. Instituto Tecnológico de Celaya, Av. Tecnológico y Antonio García Cubas s/n. Celaya, Guanajuato 38010, México a – javas210@ugto.mx b – amir.gonzalez@iqcelaya.itc.mx DOI 10.2412/mmse.96.48.950 provided by Seo4U.link

Keywords: polyelectrolytes, titanium oxide, coating, passivation, polyethylenimine, sodium polystyrene sulfonate, photodegradation.

ABSTRACT. One of the major challenges of the polyolefins nowadays is the ability of those to resist weathering conditions, specially the photodegradation process that suffer any polyolefin. A common way to prevent this, is the use of hindered amine light stabilizers (HALS) are employed. An alternative route to avoid photodegradation is using polyelectrolites as coating of fillers such as metal oxides. Composites of polyethylene were made using titanium dioxide (TiO2) as a filler with polyelectrolytes (polyethylenimine and sodium polystyrene sulfonate) attached to its surface, to passivate its photocatalytic activity. We exposed the samples to ultraviolet-visible (UV-Vis) light to observe the effect of radiation on the degradation of coated samples, compared to those without the polyelectrolyte coating. From the experimental results, we found that polyethylenimine has a similar carbonyl signal area to the sample coated with hindered amine light stabilizers (HALS) while sodium polystyrene sulfonate exhibit more degradation than the HALS coated samples, but it passivates the photocatalytic effect when compared with the non-coated TiO2 samples. Also, using AFM measurements, we confirmed that the chemical nature of polyethylenimine causes the TiO2 avoid the migration to the surface during the extrusion process, inhibiting the photodegradation process and softening the sample. On this basis, we found that polyethylenimine is a good choice for reducing the degradation caused by TiO2 when it is exposed to UV-Vis light.

1. Introduction. Nowadays, titanium oxide (TiO2) is the most studied crystalline system in the area of metallic oxide surfaces, with rutile and anatase being the most important forms. This material is very important in society because of its multiple uses. For example, it is used in heterogeneous catalysis, photocatalysis, solar cells for hydrogen and electric power, for gases sensors, white pigments, corrosion protective coatings, optical coatings, ceramics and electronic devices like varistors. Also, it has an important role in the biocompatibility of osseous implants and it is studied for door insulating in the new generation of Metal Oxide Semiconductor Field Effect Transistor (MOSFET) transistors and spacer materials in magnetic spin valve systems [1]. It also used in the nanostructured form for lithium batteries and electronic devices [1, 2]. The defects of titanium crystals have an important role in many surface phenomena [1]. Water is the most important adsorbent in the TiO2 surface. Many of its applications, for example, almost all of its 5

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photocatalytic processes, are carried out in aqueous environments. Steam from the environment interacts with the TiO2 surfaces and superficial hydroxyls can easily affect adsorption and the reaction processes. For further information, we highly suggest the work of Henderson, in which details regarding water adsorption in the crystalline surfaces of TiO2 are given [3]. Results from different spectroscopic methods have shown that water adsorbs in a dissociative and molecular way [3]. Wang et al. have shown that water dissociation which occurs in free oxygen produces a macroscopic effect in the wet capacity of the water. Generally, the surfaces of TiO2 are oleophilic and hydrophobic, however, when TiO2 is exposed to UV radiation, the contact angle of water drops to zero. By keeping them in darkness, these amphiphilic surfaces restore the hydrophobicity of the original surface. This is because new free surfaces appear which dissociate the water and generate hydrophilic microscopic sites [1, 3]. Recently, TiO2 has found new applications in the area of nanomaterial because of the various techniques used to obtain it, such as the sol-gel method, hydrothermal method, sol method, chemical deposition steam method and direct oxidation. These materials have mainly found usage in photocatalytic applications, photovoltaic and electronic devices [4]. The principal problem of this project deals with the plastic used for agricultural padded, which is used to protect crops and soil from the action of atmospheric agents. For the development of bright white polyethylene films, TiO2 particles can be used, where the crystalline structure consists mainly of rutile, for a pigment with a higher refractive index (2.73), in all white pigments scale. TiO2 particles are not chemically stable, so when they are used in plastic which is exposed to the environment, the TiO2 particles have to be coated with alumina (Al2O3), silica (SiO2), zirconia (ZrO2) or a mix of these materials to prevent photocatalytic activity. This is because, TiO2 behaves like a semiconductor, which with UV radiation (less than 400 nm) means the electrons have the capacity to exceed the band gap of 3 eV, which produces free radicals that cause plastic degradation [1,3]. Due to the previously described behavior, it is necessary to gain insight into the role of the coatings (silica and alumina) in influencing the decreased catalytic activity of TiO2. Also, is very important to know the role that water plays when it is in contact with the plastic film which contains TiO2, as this is an essential part of polymer degradation. The main plastic used in the manufacture of plastics is low density polyethylene (LDPE). The degradation of LDPE is a complicated process. The main degradation mechanisms are known, but in most cases, more than one mechanism is performed simultaneously and interactively during weathering of the film [5-8]. Photodegradation is generally considered to be a result of an oxidative processes, changing the primary structure of a polymer chain scission or crosslinking of a photon of total solar radiation may activate a link or group in a macromolecule. The most harmful part of solar radiation is ultraviolet (UV) radiation (290 to 400 nm), which may be the most important in the degradation of polymers used for outdoor purposes. It is not expected that polyethylene (PE) in the pure form can absorb UV radiation in the wavelength region of 290 to 400 nm. Photooxidation of PE can be induced only for a few impurities, known as chromophores. In this context, chromophore refers to the group primarily responsible for a given absorption band and may be the result of a polymerization process, polymerization catalysts and commercial additives, such as stabilizers, lubricants and plasticizers [5-18]. Photodegradation involves the natural tendency of most polymers to undergo a gradual reaction with atmospheric oxygen in the presence of light. Typically, a photosensitizing agent is employed to accelerate this natural tendency. The mechanism of photodegradation involves the absorption of UV light, which then leads to the generation of free radicals. An auto-oxidation process then occurs, which leads to the eventual disintegration of the plastic [7]. It is believed, that the instability of polyolefins is brought about by the presence of impurities (such as carbonyl and hydroperoxide groups) that form during the fabrication or processing of the polyolefin products. The hydroperoxide group (–CH–OOH) is the primary oxidation product and is both thermally and photolytically unstable. It decomposes to produce two radicals, each of which can MMSE Journal. Open Access www.mmse.xyz

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participate in a chain reaction. The presence of carbonyl groups in a degraded polymer indicates that oxidation has taken place and it also means that the material is vulnerable to further degradation since these groups are photolabile [8]. The ketones that are introduced to the polymer backbone by photooxidation can undergo Norrish I and/or Norrish II degradation [8]. Some of the most dramatic changes that can occur in an irradiated polymer concern their mechanical properties (mechanical degradation). In general, the mechanical properties of polymers depend on their molecular weight, crystallinity and the presence of branching and crosslinking effects [5-6]. The combined effects, or the respective environmental pollution and the use of agrochemicals in the greenhouse, also affect the life of the polymers. In this type of degradation, for example, hydrolysis and oxidation can occur to macromolecules. These processes are strongly dependent on the type of bond and the presence of catalysts and temperature [5-6]. To avoid degradation, some coatings have been used with silica, alumina and hindered amine light stabilizers (HALS). High efficiency HALS (the amine and amino ether derivatives 2,2,6,6-tetramethylpiperidine), as inhibitors of polymer photooxidation, are considered to be determined primarily by a complex set of reactions involving compaction active alkyl and peroxy radicals, formed during oxidation [19]. An alternative approach is to use silica and alumina with a polymer coating. This type of coating has proven effective in preventing the degradation of organic dyes [20]. The use of polymers has even allowed the formation of hybrid with TiO2 particles, which suppress the photocatalytic activity of the latter [20]. This paper is focused on reducing the catalytic properties of TiO2 particles embedded in a polymer matrix. Our approach is based on the adsorption properties of polyelectrolytes, in the transformation of the ionic and covalent link passivation radicals by the cyclic structure of the used polyelectrolytes. Materials and methods Materials Titanium n-butoxide (Aldrich, 99%, Mexico), acetic acid (JT Baker, 99.8%, Mexico), ethanol (Jalmek, 99%, Mexico), sulfuric acid (CTR Scientific, 97.1%, Mexico), polyethylenimine (solution 50% water, Mw 750000 g/mol, Mn 60000 g/mol, Aldrich, Mexico), sodium polystyrene sulfonate (Mw 70000 g/mol, Acros Organics, Mexico), poli[(6-morfolino-s-triazina-2,4-diil)[2,2,6,6-tetrametil-4piperidil)imino]hexametileno[(2,2,6,6-tetrametil-4-piperidil)imino]] (HALS) (Chimasorb 944, Mexico) and LDPE (640I, Dow Chemical Company, Mexico) were used as received. TiO2 particles preparation The synthesis of TiO2 was done according to the literature procedure [21]. With magnetic stirring, 20 ml of acetic acid was added dropwise to a flask containing 10 ml of titanium n-butoxide, Ti(OC4H9n)4 diluted in 30 ml of ethanol, followed by the addition of 1 ml of sulfuric acid. Then, the clear liquid obtained was (sonicated) at 313 K for 1 h and 333 K for 3 h, resulting in the formation of a milk-like sol, which was further transferred to a 100 ml steel autoclave Telflon innerliner and maintained at 393 K for 13 h. The resulting precipitates were separated from the mother liquor by centrifugation, washed thoroughly with deionized water and ethanol several times, and then dried at 373 K in air for 12 h. Finally, the obtained powders were further calcined with a 1073 K background temperature for 2 h. Polyelectrolyte coating preparation The coating of TiO2 colloidal particles was made according to the literature procedure [20]. The TiO2 particles are coated first with the polyelectrolyte polyethylenimine (PEI) and sodium polystyrene sulfonate (PSS) and HALS, by the addition of a known amount of polymer to an aqueous suspension of TiO2 particles. The concentration was 150 mg/1 g of TiO2. The suspension was sonicated and stirred before the removal of water on a rotary evaporator. The polymer powder was first dried and then the TiO2 was coated in an oven overnight at 353 K. Preparation of LDPE/TiO2 composites MMSE Journal. Open Access www.mmse.xyz

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First, 40 g of granules of virgin LDPE with a weight percentage of 0.25% of TiO2 were mixed. Then, the mixture was added to a twin screw co-rotation to form the LDPE/TiO2 composites. UV-Vis exposure of LDPE/TiO2 composites LDPE/TiO2 composites with different coatings (uncoated, PSS, PEI and HALS) were exposed to UV light at a temperature of 311 K with a lamp of 9 W at a wavelength of 365 nm, for a maximum time of 1144 h, the collection of samples occurred at 24, 48, 96, 192, 384 and 768 h, respectively. Morphological characterization by transmission electron microscopy (TEM) The size and morphology of the TiO2 colloidal particles were obtained using a JEOL JEM 1230 TEM operated at 100 KV. Characterization by Raman spectroscopy The anatase form of the TiO2 colloidal particles, the presence of polymers obtained by coating the colloidal particles and irradiated LDPE compounds were characterized using a Raman spectrophotometer, ORIBA IHR320. Characterization by Fourier transform infrared spectroscopy (FTIR) Composites irradiated with samples of coated TiO2 LDPE were characterized by FTIR with a total attenuated reflection detector (ATR-FTIR Perkin Spectrum 100 model). Composite topographic surface characterization Topographic and phase images were obtained by atomic force microscopy (AFM) (dimension edge scanning probe microscope, Bruker) in tapping mode using an antimony (n) doped Si tip (RTESP, Bruker), whose nominal frequency and spring constant ranged between 324 and 377 kHz and 20-80 N/m, respectively. Image analysis was performed using tNanoscope Analysis V1.4 software. Results and discussion Synthesis of TiO2 colloidal particles From the Raman characterization, it was found that TiO2 obtained from the synthesis was anatase TiO2, exhibiting the characteristic Raman Shifts of 145, 396, 515, 636 cm-1. This is in agreement with the literature [22]. The spectrum is shown in Figure 1 and TEM characterization shows that the particle size was 266 Âą 56 nm with a pseudo spherical morphology, as shown in Figure 2.

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Fig. 1. Raman spectra of the obtained TiO2 colloidal particles.

Fig. 2. TEM image of the obtained TiO2 colloidal particles. Preparation of coating with polyelectrolytes The presence of polyelectrolytes, capping the colloidal particles, was observed by Raman spectroscopy, as described in the spectra of Figure 3. The typical Raman shifts for PEI of 1090, 1320, 1460 and 1620 cm-1 are observed, the Raman shifts at 1130, 1270 and 1600 cm-1 correspond to PSS, and finally the shifts attributed to the HALS are at 1310 and 1620 cm-1. Please note that the intensity of the Raman peak shift of the coatings is much less intense than those of TiO2, as shown in Figure 3.

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Fig. 3. Raman spectra of different coatings applied to the TiO2 colloidal particles. A) HALS, B) PSS and C) PEI. Atomic force measurements AFM was performed to quantify the roughness of the composite materials and topography using intermittent contact with the surface of the composites. In order to obtain the differences for the studied samples, the behavior of the dissipated across the length of the analyzed field in tapping mode were included in Figure 4 (b, d, f and h), as well as a histogram of the quantified values (Figure 5).

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Fig. 4. AFM pictures of the composites studied (a: TiO2, c: HALS, e: PEI, g: PSS) and energy dissipation of the same samples (b: TiO2, d: HALS, f: PEI, h: PSS).

Fig. 5. Energy dissipated against counts for the several composites made. MMSE Journal. Open Access www.mmse.xyz

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Figure 4 (a, c, e and g) shows the surface of the PE composites that contain neat TiO2 and coatedTiO2 as fillers, which exhibit reliefs in their topography ascribed to the titanium particles that migrate to the surface of the composites samples. Furthermore, an analysis by computer software was used to estimate the roughness values of the samples, which are shown in Table 1. In this table, it can be observed that the PE filled with PEI-TiO2 had the lowest roughness compared with the others composites, which is because PE chains tend to encapsulate the TiO2 particles avoiding its migration to the surface and because of this, they are present mainly in the bulk and is related to the highly elastic behavior obtained in the energy dissipation analysis at this composite surface (Figure 5) [23, 24]. However, for the other composites, the incompatibility of TiO2 particles with the PE matrix becomes evident from the topographical images and energy dissipation analysis in Figure 5 (b, d and h). The protruding reliefs are attributed to particles that migrate to the material surface by exclusion from the PE matrix [23, 24]. In contrast to these observations, the PE/TiO2-PEI sample had a homogeneous surface that indicates favorable dispersion that could prevent cluster formation at the surface level and better integration into the polymer matrix. In this case, the polyethylene-imine molecules act as nuclei to improve the integration of particles inside the polymer matrix. Table 1. Roughness values of the obtained composites. PE/TiO2 PE/ PEI-TiO2 PE/HALS-TiO2 PE/PSS-TiO2 Rq (root mean squared)

4.31

2.08

4.21

5.20

Ra (arithmetic average)

2.80

1.12

2.64

3.08

The lower dissipated energy corresponds to the PE sample with PEI as the coating of TiO2 particles, as is shown in Figure 4. In contrast, the dissipated energy for the other samples is approximately two times higher than the dissipated energy for the PE/TiO2-PEI sample. The absence of highly amounts of PEI-TiO2 particles in the PE surface could directly affect the photodegradation process, since UV aging experiments applied the radiation to the exterior of the composites [23, 24]. 3.4 Photooxidation process The extruded samples were analyzed by FTIR. Analysis of the degraded samples is shown in Figure 6. Carbonyl bond formation as products of photooxidation is clearly shown, as this species is a clear sign of the degradation of polyethylene. These species appear as bands at 1720 cm-1, and in some cases bands up to 1090 cm-1, which are different vibrations of the carbonyl bond observed by FTIR. Also, the presence of associated hydroperoxides and hydroxy groups (3500 cm-1) is noteworthy [9, 12, 16]. We observe how these signals become clearly visible as time goes by achieving a maximum peak and later decaying as the degradation process continues. This could indicate that the chain scission takes place before 700 h and this could be associated with the decay of these signals (Figure 7).

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Fig. 6. FTIR spectra of the samples at different times for the bands of groups A) alkoxycarbonyl and B) hydroperoxide and hydroxy groups.

Fig. 7. Change in the area of the different signals from carbonyl groups, hydroperoxide and hydroxy groups present in the sample according to different times. MMSE Journal. Open Access www.mmse.xyz

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The presence of triple unsaturation caused by photodegradation was observed by Raman spectroscopy, as shown in Figure 8. Please note that this broad band around 2200 cm-1 is very strong for all samples in the first 48 h and then disappeared completely at 1144 h, which means that the unsaturation, even if triple bonds are forming instead of the double bonds that usually appear, is an intermediate step, as suggested in the literature [9, 15]. This intermediate could be due to the TiO2 photocatalytic activity that allows the formation of triple bonds, which act as an intermediate for a higher photodegradation, as we observe how the area of this signal decreases as time passes (Figure 9). We propose a plausible mechanism in order to explain this phenomenon, as depicted in Figure 10. Also, the signal area was measured over time and is plotted in Figure 9.

Fig. 8. Raman spectra of the samples at different times for the alkyne groups present in the samples.

Fig. 9. Change in the area of different signals for alkyne groups present in the sample according to different times. MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Fig. 10. Proposed photodegradation mechanism. Summary. It was observed, that the water present in the sample plays an important role because it is the initiator of the degradation of the material, as the intermolecular water makes contact with TiO2, immediately causes its dissociation, which causes the generation of free radical species that promotes degradation. As observed by Raman spectroscopy, all composites, even varying the polyelectrolyte coating, had triple unsaturation in the early hours, this indicates that this unsaturation goes beyond the double bond, which is commonly accepted in the literature, may be a step in the photooxidation process, since their presence decreases significantly as time increases. We have shown the excellent performance of PEI, comparable to HALS, this may be because the PEI, with an amino group in its structure, could have similar behavior towards free radicals as HALS molecules, and the fact that its chemical affinity with the polymeric matrix does not allow the TiO2 to float to the surface of the composite during the extrusion, avoiding much of the degradation, as we have demonstrated by AFM analysis. As a final conclusion, we found that polyelectrolytes are an alternative choice for passivation TiO2 photocatalytic properties. Acknowledgments The authors would like to thank to the Cuerpo Académico de Materiales Nanoestructurados del Instituto de Física de la Universidad Autónoma de San Luis Potosí and Programa para el Desarrollo Profesional Docente (PRODEP) for their support via a postdoctoral residence PRODEP. We also thank Aurora Robledo Cabrera for her support regarding the Raman characterization. References [1] Diebold, U. (2003). The surface science of titanium dioxide. Surface Science Reports, 48(5), 53– 229. https://doi.org/10.1016/S0167-5729(02)00100-0 [2] Bonhôte, P., Gogniat, E., Grätzel, M., & Ashrit, P. (1999). Novel electrochromic devices based on complementary nanocrystalline TiO2 and WO3 thin films. Thin Solid Films, 350(1), 269–275. https://doi.org/10.1016/S0040-6090(99)00229-1 [3] Henderson, M. A. (2002). The interaction of water with solid surfaces: fundamental aspects revisited. Surface Science Reports, 46(1), 1–308. https://doi.org/10.1016/S0167-5729(01)00020-6 [4] Chen, X., & Mao, S. S. (2007). Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications. Chemical Reviews, 107(7), 2891–2959. https://doi.org/10.1021/cr0500535 [5] Dilara, P. A., & Briassoulis, D. (2000). Degradation and Stabilization of Low-density Polyethylene Films used as Greenhouse Covering Materials. Journal of Agricultural Engineering Research, 76(4), 309–321. https://doi.org/10.1006/jaer.1999.0513 MMSE Journal. Open Access www.mmse.xyz

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[6] Briassoulis, D., Aristopoulou, A., Bonora, M., & Verlodt, I. (2004). Degradation Characterisation of Agricultural Low-density Polyethylene Films. Biosystems Engineering, 88(2), 131–143. https://doi.org/10.1016/j.biosystemseng.2004.02.010 [7] Feldman, D. (2002). Polymer Weathering: Photo-Oxidation. Journal of Polymers and the Environment, 10(4), 163–173. https://doi.org/10.1023/A:1021148205366 [8] Miyazaki, K., & Nakatani, H. (2009). Preparation of degradable polypropylene by an addition of poly (ethylene oxide) microcapsule containing TiO2. Polymer Degradation and Stability, 94(12), 2114–2120. https://doi.org/10.1016/j.polymdegradstab.2009.10.001 [9] Chiellini, E., Corti, A., D’Antone, S., & Baciu, R. (2006). Oxo-biodegradable carbon backbone polymers – Oxidative degradation of polyethylene under accelerated test conditions. Polymer Degradation and Stability, 91(11), 2739–2747. https://doi.org/10.1016/j.polymdegradstab.2006.03.022 [10] Hisyam, A., Yunus, R. M., & Bag, D. H. (2013). Thermo-oxidative Degradation of High Density Polyethylene Containing Manganese Laurate. International Journal of Engineering Research and Applications, 3(2), 1156–1165. [11] Arutchelvi, J., Sudhakar, M., Arkatkar, A., Doble, M., Bhaduri, S., & Uppara, P. V. (2008). Biodegradation of polyethylene and polypropylene. Indian Journal of Biotechnology, 7(1), 9–22. [12] Massey, S., Adnot, A., Rjeb, A., & Roy, D. (2007). Action of water in the degradation of lowdensity polyethylene studied by X-ray photoelectron spectroscopy. Express Polymer Letters, 1(8), 506–511. https://doi.org/10.3144/expresspolymlett.2007.72 [13] Rex, I., Graham, B. A., & Thompson, M. R. (2005). Studying single-pass degradation of a highdensity polyethylene in an injection molding process. Polymer Degradation and Stability, 90(1), 136– 146. https://doi.org/10.1016/j.polymdegradstab.2005.03.002 [14] Pinheiro, L. A., Chinelatto, M. A., & Canevarolo, S. V. (2004). The role of chain scission and chain branching in high density polyethylene during thermo-mechanical degradation. Polymer Degradation and Stability, 86(3), 445–453. https://doi.org/10.1016/j.polymdegradstab.2004.05.016 [15] Singh, B., & Sharma, N. (2008). Mechanistic implications of plastic degradation. Polymer Degradation and Stability, 93(3), 561–584. https://doi.org/10.1016/j.polymdegradstab.2007.11.008 [16] Tidjani, A. (2000). Comparison of formation of oxidation products during photo-oxidation of linear low-density polyethylene under different natural and accelerated weathering conditions. Polymer Degradation and Stability, 68(3), 465–469. https://doi.org/10.1016/S0141-3910(00)000392 [17] Zhao, X., Li, Z., Chen, Y., Shi, L., & Zhu, Y. (2008). Enhancement of photocatalytic degradation of polyethylene plastic with CuPc modified TiO2 photocatalyst under solar light irradiation. Applied Surface Science, 254(6), 1825–1829. https://doi.org/10.1016/j.apsusc.2007.07.154 [18] Corrales, T., Catalina, F., Peinado, C., Allen, N. S., & Fontan, E. (2002). Photooxidative and thermal degradation of polyethylenes: interrelationship by chemiluminescence, thermal gravimetric analysis and FTIR data. Journal of Photochemistry and Photobiology A: Chemistry, 147(3), 213–224. https://doi.org/10.1016/S1010-6030(01)00629-3 [19] Klemchuk, P. P. (1994). Mechanism of Polymer Stabilization by Hindered-Amine Light Stabilizers (HALS ). Model Investigations of the Interaction of Peroxy Radicals with HALS Amines and Amino Ethers. Macromolecules, 27(1), 2529–2539. DOI: 10.1021/ma00087a022 [20] Ziolkowski, L., Vinodgopal, K., & Kamat, P. V. (1997). Photostabilization of Organic Dyes on Poly (styrenesulfonate) - Capped TiO 2 Nanoparticles. Langmuir, 13(9), 3124–3128. DOI: 10.1021/la970075p MMSE Journal. Open Access www.mmse.xyz

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[21] Tong, T., Zhang, J., Tian, B., Chen, F., & He, D. (2008). Preparation and characterization of anatase TiO2 microspheres with porous frameworks via controlled hydrolysis of titanium alkoxide followed by hydrothermal treatment. Materials Letters, 62(17–18), 2970–2972. https://doi.org/10.1016/j.matlet.2008.01.085 [22] Scepanovic, M., Grujic-Brojcin, M., Dohcevic-Mitrovic, Z. D., & Popovic, Z. V. (2009). Characterization of anatase TiO2 nanopowder by variable-temperature Raman spectroscopy. Science of Sintering, 41(1), 67–73. https://doi.org/10.2298/SOS0901067S [23] Huo, H., Jiang, S., An, L., & Feng, J. (2004). Influence of Shear on Crystallization Behavior of the Isotactic Polypropylene with -Nucleating Agent. Macromolecules, 37, 2478–2483. [24] Qin-Bao Lin, He Li, Huai-Ning Z., Quan Z., Da-Hui X., Zhi-Wei W. (2014). Migration of Ti from nano-TiO2-polyethylene composite packaging into food simulants. Food Additives & Contaminants, 31, 1284-1290. http://dx.doi.org/10.1080/19440049.2014.907505 Cite the paper Javier Vallejo-Montesinos, Julio Cesar López Martínez, Juan Manuel Montejano-Carrizales, Elías Pérez, Javier Balcázar Pérez, A. Almendárez-Camarillo, J.A. Gonzalez-Calderon (2017). Passivation of Titanium Oxide in Polyethylene Matrices using Polyelectrolytes as Titanium Dioxide Surface Coating. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.96.48.950

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II. Mechanical Engineering & Physic s M M S E J o u r n a l V o l . 8

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Numerical and Experimental Study of Energy Absorption in Aluminum Corrugated Core Sandwich Panels by Drop Hammer Test6 Mohammad Nouri Damghani 1,a, Arash Mohammadzadeh Gonabadi 1,b 1 – Department of mechanical engineering, Semnan University, Semnan, Iran a – mnoori@semnan.ac.ir b – arash_mg@semnan.ac.ir DOI 10.2412/mmse.85.747.458 provided by Seo4U.link

Keywords: sandwich panel, honeycomb core, impact loading, energy absorption, numerical simulation.

ABSTRACT. This paper is aimed to study the behavior of sandwich panels made of Aluminum face sheet and Aluminum corrugated core under impact loading. Sandwich panels with square and triangular corrugated cores of two different heights are constructed and the effect of corrugated geometry on the level of absorbed energy as well as the panel strength are investigated. Drop Hammer by a cylindrical impactor with the weight of 25 kg is applied for exerting the impact. Acceleration, velocity, and displacement of impactor as well as the absorbed energy are evaluated throughout the test. The damage mechanisms include the buckling of core walls, separation of core from surface sheets, and formation of plastic hinges in the core plate. The results show that panel height and the geometry of its core play an important role in the energy absorbability impact strength, as the panels with more height have higher energy absorbability and panels with square core have higher impact strength than ones with triangular core. At the end, the numerical method confirms the Experimental method.

Introduction. In recent years, sandwich panels have been widely used for constructing bridge decks, temporary landing mats and thermal insulation wall boards due to better performance in comparison to other structural materials in terms of enhanced stability, higher strength to weight ratios, better energy absorbing capacity and ease of manufacture and repair. In sandwich panels, low density material, known as core, is usually adopted in combination with high stiffness face sheets to increase the moment of inertia and to resist high loads. The main functions of core materials are to absorb energy and provide resistance to face sheets to avoid local buckling [1]. The most applicable core materials include Aluminum honeycomb structure and Aluminum/polymeric foams. Foam core materials are applied to improve acoustical, thermal and moisture insulation properties. In addition, polymeric foams have an important role in reducing the panel production costs. Aluminum foam is preferred where the ballistic properties are of important significance. Although foam core sandwich panels have a high strength-to-weight ratio the main drawback of such structures is the low area of common surfaces between foam cells and facesheets. This problem results in low core-to-facesheets adhesion that, besides the production defects and extreme service conditions, will finally cause panel delamination and its rupture. Since honeycomb panels are frequently applied as energy absorbers against impact loads, predicting their dynamic behavior is of important consideration for their optimum utilization. Numerous studies made on the sandwich panels with foam or honeycomb cores under high velocity impact or explosive loading have revealed excellent energy absorption of such structures in comparison with integrated solid structures [1-6]. Zhu et al. assessed the effect of various parameters on the behavior of honeycomb sandwich panels under the air blast loading. Their study signified dependency of deformation and failure mechanism on the facesheets thickness as well as core 6

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characteristics such as pores size and wall thickness. By experimenting on the honeycomb sandwich panels subjected to underwater blast loading, Fan et al. [8] studied the influence of design parameters on the structure stiffness and its failure mechanism. Li et al. [9] investigated failure modes of honeycomb sandwich panels, including core compression, progressive buckling, shear deformation, and fracture. They found that by closing the explosive to the specimen the maximum pressure on the panel facesheet gets increased, while taking away the explosive from the specimen will increase the plastic deformation. Dharmasena et al. [6] showed that honeycomb sandwich panels has less deflection in comparison with solid panels with the same mass. Nurick et al. [10] studied the effect of core height, facesheet thickness and the interaction of panel components on its failure modes. Theobald et al. [11] found that the facesheet thickness has the most impressive factor on the impact loading of sandwich panels. Wadley et al. [12] studied the deformation and fracture in sandwich panels with triangular corrugated core under the impact of accelerated sand grains. Yahaya et al. [13] evaluated the effect of core configuration on the panel deformation behavior under the impact of aluminum projectile with various velocities. Damghani et al. [14,15,16,17] studied the deformation and energy absoring in sandwich panels with corrugated core filled aluminum foam under low velocity impact. In this paper, drop hammer tests are carried out to investigate the effect of core geometry on the mechanical behavior and energy absorption of aluminum corrugated core sandwich panels. 1. Materials and experiments. 1200 aluminum sheets with thickness of 0.3 mm and 0.8 mm were used to make core and facesheets, respectively. Tow triangular configurations and two square configurations were considered as core geometry with 10 cm width and dimensions according to Fig. 1.

(a)

(b)

(c)

(d)

Fig. 1. Core geometries of sandwich panels: (a) sample 1, (b) sample 2, (c) sample 3, (d) sample 4. Spot welding machine was used to attach the panel components together. Figs. 2-5 illustrate the prepared specimens of sandwich panel. Drop hammer apparatus was applied to exert the impact by releasing a cylindrical weight of mass 25 kg from the height of 11 cm [15].

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Fig. 2. Picture of sample 1.

Fig. 3. Picture of sample 2.

Fig. 4. Picture of sample 3.

Fig. 5. Picture of sample 4.

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Fig. 6. Picture of drop hammer apparatus.

Fig. 7. Deformed configuration of sample 1.

Fig. 8. Deformed configuration of sample 2.

Fig. 9. Deformed configuration of sample 3. MMSE Journal. Open Access www.mmse.xyz

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Fig. 10. Deformed configuration of sample 4. 2. Experimental results. Pictures of deformed specimens are shown in Figs. 7-10. Extracted data from the test apparatus are used to obtain time variations of displacement, velocity and acceleration of panel facesheet as well as absorbed energy. Fig. 11 shows the variation of impactor acceleration against its displacement for various core geometries. The variation of impactor velocity in terms of its displacement for different core geometries is shown in Fig. 12. Time variation of impactor displacement for different core geometries is illustrated in Fig. 13. The curves of absorbed energy over time is plotted in Fig. 14. Regarding to Fig. 11 it can be seen that samples with square core possess higher values of average acceleration and thus more impact strength. Also according to Fig. 12 the compression speed of all samples are rather the same except for sample 1. As shown in Fig. 15 the samples 1, 3 absorb less energy in comparison with the others because of their less height.

Fig. 11. Effect of core geometry on the acceleration-displacement curve of sandwich panels.

Fig. 12. Effect of core geometry on the velocity-displacement curve of sandwich panels. MMSE Journal. Open Access www.mmse.xyz

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Fig. 13. Effect of core geometry on the displacement-time curve of sandwich panels.

Fig. 14. Effect of core geometry on the energy-displacement curve of sandwich panels. 3 Numerical Simulation. In this section the drop hammer test is simulated using finite element code ABAQUS. Mesh types used in the finite element model are Quad (4 node quadrilateral element) and Four-node shell element S4R from the ABAQUS/Explicit library. Figs. 15 and 16 show the stress contour in the deformed models with triangular and square cores, respectively [14,16,17]. Figs. 17-20 shows time-variation of impactor displacement, impactor velocity in terms of its displacement, imposed force of impactor in terms of its displacement, and impactor kinetic energy in terms of its displacement for samples No. 1, 2, 3 and 4, respectively.

Fig. 15. Stress contour in deformed Sample 2.

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Fig. 16. Stress contour in deformed Sample 4.

Fig. 17. Time-variation of impactor displacement, impactor velocity in terms of its displacement, imposed force of impactor in terms of its displacement, and impactor kinetic energy in terms of its displacement for Sample 1.

Fig. 18. Time-variation of impactor displacement, impactor velocity in terms of its displacement, imposed force of impactor in terms of its displacement, and impactor kinetic energy in terms of its displacement for Sample 2. MMSE Journal. Open Access www.mmse.xyz

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Fig. 19. Time-variation of impactor displacement, impactor velocity in terms of its displacement, imposed force of impactor in terms of its displacement, and impactor kinetic energy in terms of its displacement for Sample 3.

Fig. 20. Time-variation of impactor displacement, impactor velocity in terms of its displacement, imposed force of impactor in terms of its displacement, and impactor kinetic energy in terms of its displacement for Sample 4. Summary. In this paper, the impact behavior of sandwich panels made of aluminum facesheets and aluminum corrugated core with different geometries is investigated using drop hammer apparatus. It is concluded from the absorbed energy that increasing panel height will cause increasing of absorbed energy and triangular core with the height of 30 mm absorbs the most energy. Deformed configuration of panels implies that initial deformation is due to the core wall buckling. After buckling, the core will undergo the plastic deformation and plastic hinges occur. On the other hand, separation of core from the facesheet signifies the existence of high shear stress between them. Regarding to high value of average acceleration in panels with square core, it is concluded that they possess higher impact strength. Also, comparison of simulation results with experimental ones signifies a good agreement between them. References [1] Guruprasad S., Mukherjee A., 2000. Layered sacrificial claddings under blast loading Part 1analytical studies, Int. Journal of Impact Engineering, 24, 957-973. [2] Guruprasad S., Mukherjee A., 2000. Layered sacrificial claddings under blast loading: Part 2experimental studies. International Journal of Impact Engineering, 24, 975-984. MMSE Journal. Open Access www.mmse.xyz

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[3 Shen] J.W., Lu G.X., Zhao L.M., Qu Z.H., 2011. Response of Curved Sandwich Panels Subjected to Blast Loading. Journal of Performance of Constructed Facilities, 25, 382-393. [4] Rizov V., Shipsha A., Zenkert D., 2011. Indentation study of foam core sandwich 365 composite panels. Composite Structures, 93, 1300-1308. [5] Radford D.D., McShane G.J., Deshpande V.S., Fleck N.A., 2006. The response of clamped 367 sandwich plates with metallic foam cores to simulated blast loading. International Journal of Solids and Structures, 43, 2243-2259. [6] Dharmasena K.P., Wadley H.N.G., Xue Z.Y., Hutchinson J.W., 2008. Mechanical response of 370 metallic honeycomb sandwich panel structures to high-intensity dynamic loading, International Journal of Impact Engineering, 35, 1063-1074. [7] Zhu F., Zhao L.M., Lu G.X., Wang Z.H., 2008. Deformation and failure of blast-loaded 373 metallic sandwich panels—Experimental investigations. International Journal of Impact Engineering, 35, 937-951. [8] Fan Z., Liu Y., Xu P., 2016. The blast resistance of metallic sandwich panels subjected to proximity underwater explosion, International Journal of Impact Engineering, 93, http://dx.doi.org/doi: 10.1016/j.ijimpeng.2016.03.001. [9] Li X., Zhang P., Wang Z., Wu G., Zhao L., 2014. Dynamic behavior of aluminum honeycomb sandwich panels under air blast: Experiment and numerical analysis, Composite Structures, 108, 1001–1008. [10] Nurick G.N., Langdon G.S., Chi Y., Jacob N., 2009. Behaviour of sandwich panels subjected to intense air blast – Part 1: Experiments. Composite Structures, 91, 433-441. [11] Theobald M.D., Langdon G.S., Nurick G.N., Pillay S., Heyns A., Merrett R.P., 2010. Large inelastic response of unbonded metallic foam and honeycomb core sandwich panels to blast loading. Composite Structures, 92, 2465-2475. [12] Wadley H.N.G., Børvik T., Olovsson L., Wetzel J.J., Dharmasena K.P., Hopperstad O.S., Deshpande V.S., Hutchinson J.W., 2013. Deformation and fracture of impulsively loaded sandwich panels. Journal of the Mechanics and Physics of Solids, 61, 674-699. [13] Yahaya M.A., Ruan D., Lu G., Dargusch M.S., 2015. Response of aluminium honeycomb sandwich panels subjected to foam projectile impact - An experimental study, International Journal of Impact Engineering, 75, 100-109. [14] Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi (2016).Analytical and Numerical Study of Foam-Filled Corrugated Core Sandwich Panels under Low Velocity Impact. Mechanics, Materials Science & Engineering, Vol 7. doi: http://seo4u.link/10.2412/mmse.6.55.34 [15] Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi (2016).Investigation of Energy Absorption in Aluminum Foam Sandwich Panels By Drop Hammer Test: Experimental Results. Mechanics, Materials Science & Engineering, Vol 7. doi: http://seo4u.link/10.2412/mmse.6.953.525 [16] M Nouri Damghani, A Mohammadzadeh Gonabadi (2017). Numerical study of energy absorption in aluminum foam sandwich panel structures using drop hammer test. Journal of Sandwich Structures & Materials. First published date: January-11-2017. doi:10.1177/1099636216685315 [17] M.Noori-Damghani, H.Rahmani, Arash Mohammadzadeh, S.Shokri-Pour. 2011. "Comparison of Static and Dynamic Buckling Critical Force in the Homogeneous and Composite Columns (Pillars)." International Review of Mechanical Engineering - (Vol. 5 N. 7) - Papers 5 (7): 1208-1212. Cite the paper Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi (2017). Numerical and Experimental Study of Energy Absorption in Aluminum Corrugated Core Sandwich Panels by Drop Hammer Test. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.85.747.458

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The Variational Principle and the Phonon Boltzmann Equation7 Amelia Carolina Sparavigna1, a 1 – Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy a – amelia.sparavigna@polito.it DOI 10.2412/mmse.11.97.135 provided by Seo4U.link

Keywords: Boltzmann equation, thermal conductivity, variational method, phonons, rare gas solids.

ABSTRACT. The thermal transport in a solid happens when the material is subjected to a thermal gradient. If free electrons are absent, the thermal transport is due to the phonons, the quasiparticles corresponding to the vibrations of the atoms of the crystal. The equation that describes this transport is the phonon Boltzmann equation. Here we show how to solve it by means of the variational principle.

Introduction. As discussed in [1], the equation that is today known as the phonon Boltzmann equation was first derived by Rudolf Peierls in 1929 [2]. Peierls actually studied the zones of the reciprocal lattices before Léon Brillouin, applying his approach to evaluate the thermal transport by phonons. In this manner he introduced, besides the Boltzmann equation for phonons, also the notion of three-phonon Normal and Umklapp processes [3]. According to Peierls [1], the thermal transport   equation can be written as n drift(q, p)  n scatt (q, p)  0 , where n drift is the rate of change of the number of phonons due to the presence of a temperature gradient and n scatt is the rate of change due to the scattering of phonons against other phonons, the boundaries of the sample, and electrons,  impurities, dislocations and other defects present in the material. q, p are indicating the wave-vector and the polarization of the considered phonons. We discussed the solution of the Boltzmann equation in the case of the presence of isotope impurities and electrons in some previous articles [4-8]. In these papers, we approached the solution by means of the relaxation time approximation and by a more specific analysis, containing the true Brillouin zone of the crystal and the three-phonon scattering matrices. In this last case, the solution was achieved through an iterative method [9-10]. From the solution of the Boltzmann equation, we determined the thermal conductivity of the crystals considered in the abovementioned studies. Other methods for determining the lattice thermal conductivity are based on ab-initio and first-principle calculations, and on molecular dynamics simulations [11-23]. Here we will consider another method for solving the phonon Boltzmann equation, based on the variational principle. The exposition of the related theory is aimed to introduce researchers and students of solid-state physics to a different approach to the determination of the thermal transport in crystals. Before discussing the variation method for the Boltzmann equation, let us see the problem in a more general context. Variational method. Actually, the Boltzmann equation is, in its standard form, an integraldifferential equation [24]:

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X (k )   (k )  (k ) P(k , k ) dk 

(1)

In (1), X (k ) is a known function that can be dependent on external fields. The integration is on a vector space, which is here simply represented by the single variable k . Function P(k , k ' ) is positive because it is representing a measure of probability. Moreover, P(k , k ' )  P(k ' , k ) . The problem is to find the function (k ) . Let us define the internal product of two functions  and  in the following manner:

(, )   (k ) (k ) dk

(2)

Let us introduce the scattering operator  , so that: X  

(3)

This operator changes the function  in another function by an integration. Properties of the operator  are the following. It is linear and symmetric. Therefore, for any  and  , we can write:

(, )  (, )

(4)

This property is coming from the abovementioned symmetry of k , k ' , that is, from:

k , k '   k ' , k 

(5)

(, )  0 

(6)

(, )  (, X )

(7)

Moreover,  is positive, so that:

From (3), we deduce the relation:

According to the variational principle, among all the functions satisfying equation (7), the solution of the integral equation is that giving the maximum value of the product (, ) .

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This fact is easy to demonstrate. If  is any solution of (7), but not of (3), we have (using (6) and (4)):

0  (  , (  ))  (, )  (, )  (, )  (, )  (, )  (, )  2 (, X )  (, )  (, )

(8)

Then:

(, )  (, )

(9)

To apply this property to the solution of the Boltzmann equation, we use a trial function, made by known functions, which are containing some parameters the value of which we can change. Then, these parameters are varied until the function (, ) attains its maximum value. Let us stress that, in this manner, we do not find the true solution. However, in the case that we have made a good choice of the trial function, the solution is a good approximation of the true result. Usually, the trial function is of the following type:

(k )   i i (k )

(10)

In (10),  i are the parameters we can change, and i (k ) are the known functions. Then, we can write the elements of the matrix and vector corresponding to operator  and function X , that is ij and

X i according to the set of functions i : ij  (i ,  j )

(11)

X i  ( X , i )

(12)

Therefore, we have: (, )   ( ii ,  j j )   i j (i ,  j )   ij  i  j ij

(, X )   ( ii , X )   i ( X , i )   X i  i i

According to the variational principle, parameters  i must satisfy the equation:

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(13)

(14)

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

X i   ij  j

(15)

Equation (15) can be solved by means of an algebraic or numerical approach. However, let us stress once more that the choice of functions i is quite important, because from it we have a solution which is close to the true solution or not. However, we have also to choose the functions i in order to have the products (11), (12) that can be easily calculated. Therefore, these two constraints have to be matched opportunely. The method outlined here is also known as the Rayleigh–Ritz method, after Walther Ritz and Lord Rayleigh. It is widely used to approximate eigenvalues and eigenvectors.  Phonon Boltzmann equation. Let us express the phonon distribution n(q, p) in term of the deviation function  qp :  n(q, p)  nqp  nqop   qp nqop (1  nqop ) ,

(16)

where nqop is the equilibrium Bose-Einstein distribution. In (16), the phonon distribution in the material is supposed being disturbed by the presence of a thermal gradient. Writing the Boltzmann equation in the form given in the previous section, we have that it is like:

X qp 

pp'  Pqq'  q' p' ,

X qp   v qp

nqop

q' p'

T

 T

(17)

In (17), we have the phonon group velocity v qp and the gradient of the temperature, which is perturbing the equilibrium of phonons. We can deduce the deviation function  qp applying the Rayleigh-Ritz variational procedure to the trial function: (q, p)   arp r (q, p)

(18)

In (18), r  is a set of functions that need to be suitably chosen. According to Srivastava in [25], we can obtain the thermal conductivity  as:



k BT 2  T

 arp X rp , X rp   X qpr (q, p) rp

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(19)

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We have here the volume of the crystal  and the Boltzmann constant k B . The coefficients a rp are obtained by solving the system: pp' pp' pp' X qp   arp' '  rr ' ,  rr'    r (q, p) Pqq '  r ' (q' , p' ) r'

(20)

q q'

As we have discussed in [9] and [10] for instance, the phonons are scattered through three-phonon pp' processes and therefore the matrix elements  rr ' can be written as: 1 q '' p '' pp' p p ' [(q, p)  (q', p' )  (q' ' , p' ' )]2     rr  Q ' ar ar ' 2 qp q' p ' q'' p '' qp,q' p ' rr' pp'

(21)

In (21), we find the intrinsic transition probability rate for the three-phonon scattering processes:

Qqqp'',pq''' p ' 

2 q' ' p' ' | H | qp, q' p' 

2 o o nqp nq' p ' (1  nqo'' p'' )

 (qp  q' p'  q'' p'' )

(22)

We have, in (22), the phonon angular frequency for given wave-vector and polarization.  is the reduced Planck constant or Dirac constant.  represents the function delta of Dirac. In (22) we find also the Hamiltonian H , used to describe the set of interacting phonons. Actually, the explicit form of (17) is:

X qp  







Qqqp'',pq''' p '  qp   q' p '   q' ' p '' 

q' p ' q'' p ''



1   Qqqp' p',q'' p''  qp  q' p'  q'' p'' 2 q' p ' q'' p ''



(23)

Calculating the thermal conductivity. From what we have previously told, it is clear that the evaluation of the thermal transport by means of the variational approach is a non-trivial task. We have solved it in a previous paper [26], where we considered the variational approach to determine the thermal conductivity of the rare gas crystals. To account for the crystal lattice, we used an isotropic model made of successive shells surrounding the atoms of the crystal. The potential describing the interaction among atoms was a Lennard-Jones potential. In the framework of the model, we can calculate the dispersions of the longitudinal and transversal angular frequency of phonons by means of the eigenvalue equation:

 1  cos (q  h)(OhU )   (h) hh ε qp

( h  0)

 Mq2p ε qp

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(24)

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In the equation (24) we find the mass M of each reticular center, h runs over all the neighbors of the central atom considered as origin ( h is the modulus), U is the Lennard-Jones potential,

Oh  h 1 d / dh and  (h)  Oh2U . ε qp are the unit vectors of polarizations. Let us remember that the Lennard-Jones potential is:

 r 12  r  6  U (h)  U o  o    o    h    h 

(25)

In (25), we have two parameters U o , ro , which are specific of the material. The Hamiltonian necessary for giving the intrinsic transition probability (22) is:

H

1 3 1    (h)h  (ξ lh  ξ l )     (h)h  (ξ lh  ξ l ) ξ lh  ξ l 12 l (h0) 4 l (h  0)

(26)

Vector l gives the atomic positions and  (h)  Oh3U . ξ l is the displacement of the atom from its average position given by vector l (the same for l  h ). Let us define the dimensionless quantities y  q / QD , y'  q' / QD , y' '  q' ' / QD , in which QD is the radius of the Debye sphere, and (q, p)  f p ( y) (u q  u) , where u q  q / q and u  T / T . In the framework of the isotropic model, the result does not depend on u [26]. Then, equation (21) becomes:

1 q '' p '' pp' p'    Qqp,q' p '      rr' arp ar ' 6 qp q ' p ' q '' p '' rr ' pp'

(27)

  f p2 ( y )  f p2' ( y ' )  f p2'' ( y ' ' )  2a f p ( y ) f p ' ( y ' )  2b f p ( y ) f p '' ( y ' ' )  2c f p ' ( y ' ) f p '' ( y ' ' ) In (27), a, b and c are the cosines u q  u q' , u q  u q'' and u q'  u q'' , respectively. Functions f p ( y ) are those that we must describe by the trial functions:

f p ( y)  

 p ( y )  1 R p r    ar y  y  y r 0 

(28)

In (28), we have R the maximum value of the exponent involved. We have also the reduced angular frequency:

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 2M  p ( y)  h1   Uo

  

qp

(29)

In it, we find h1 which is the nearest-neighbor distance and U o , the parameter of the Lennard-Jones potential (25). The choice of the trial function of the form given in (28) was made in agreement to the behaviour of the Boltzmann equation in the long wavelength limit. For q  0 , we have that [26]:

 qp  

( v qp  T )

(30)

That is:

f p ( y)  

1  p y y

(31)

According to Srivastava, using (19) we have the thermal conductivity [26]:



U o2 N 16 27  M l12 k BT 2

 brp rp

(32)

In (32), we have N the number of atoms in the crystal and parameter l1  4.37511 for a F.C.C. lattice. We have also used:

a rp   brb ;  

rp

 y 0

 r 1   p

64 2 T NU o  4 9 k B T 2  QD



(33)



 o o   y   p ( y ) n p ( y ) 1  n p ( y ) dy  

In dimensional terms, (32) means:

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(34)

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[ ]   

energy 3  time volume  mass  energy  temperatur e energy 2  time 2 length 3  mass  temperatur e  time

(32)

energy 2 power  length  energy  temperatur e  time length  temperatur e

In [26], we have calculated the matrix elements in (27) and numerically found coefficients brb to use in (32). The result for the thermal conductivity in solid argon is shown in the Figure 1. For solid argon, the parameters of the interatomic potential and the nearest-neighbor distance at 10 K and 80 K, as deduced from [27] are in the following data: U o  0.58356  10 13 erg , ro  3.4447  10 8 cm , h1  3.7559  10 8 cm at 10 K, and h1  3.8571 10 8 cm at 80 K.

Fig. 1. Thermal conductivity of solid argon (in mW/(cm·°C)) as a function of temperature. The result of the variational calculation is given by the line. The experimental points are from [28-33]. In the calculation of the thermal conductivity we applied the variational procedure in the temperature range between 7 K and 80 K. We have not considered the temperature below 7 K in order to avoid the boundary scattering, which is responsible for the peaks at low temperature that we see in the experimental data. Summary. In this paper we have shown how a variational method can be used to solve the phonon Boltzmann equation for the determination of the thermal conductivity of a crystal, such as a crystal of solid argon, where only the phonons are transporting the heat. The exposition of the theory is maintained to an introductory level, aiming to show to researchers and students a different approach to the problem of the thermal transport by phonons, different from those previously exposed in [4] and [5]. The variational method is based on the use of a set of trial functions, that need to be chosen in order to have a solution which is quite close to the true solution. Here we have used, to solve the phonon Boltzmann equation, a set of trial functions which have the same behaviour of the deviation function in the long wavelength limit. The fact that the choice was a good one is also given, a posteriori, by a good agreement with the experimental data. References MMSE Journal. Open Access www.mmse.xyz

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[1] Petterson, S. (1991). Solving the phonon Boltzmann equation with the variational method. Physical Review B, 43(11), 9238-9246. DOI: 10.1103/physrevb.43.9238 [2] Peierls, R. (1929). Zur kinetischen Theorie der Warmeleitung in Kristallen. Ann. Phys. (Leipzig). 395(8), 1055-1101. DOI: 10.1002/andp.19293950803 [3] Peierls, R. (1985). Bird of Passage: Recollections of a Physicist. Princeton University Press. ISBN-10: 0691083908. [4] Sparavigna, A. C. (2016). The Boltzmann equation of phonon thermal transport solved in the relaxation time approximation – I – Theory. Mechanics, Materials Science & Engineering Journal, 2016(3), 34-45. DOI: 10.13140/RG.2.1.1001.1923 [5] Sparavigna, A. C. (2016). The Boltzmann equation of phonon thermal transport solved in the relaxation time approximation – II – Data analysis. Mechanics, Materials Science & Engineering Journal, 2016(3), 57-66. DOI: 10.13140/RG.2.1.2026.4724 [6] Sparavigna, A. C. (2016). On the Boltzmann equation of thermal transport for interacting phonons and electrons. Mechanics, Materials Science & Engineering Journal, 2016(5), 204-216. DOI: 10.13140/RG.2.1.2824.0885 [7] Omini, M., & Sparavigna, A. (1995). An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity. Physica B: Condensed Matter, 212(2), 101-112. DOI: 10.1016/0921-4526(95)00016-3 [8] Omini, M., & Sparavigna, A. (1997). Effect of phonon scattering by isotope impurities on the thermal conductivity of dielectric solids. Physica B: Condensed Matter, 233(2), 230-240. DOI: 10.1016/s0921-4526(97)00296-2 [9] Omini, M., & Sparavigna, A. (1996). Beyond the isotropic-model approximation in the theory of thermal conductivity. Physical Review B, 53(14), 9064-9073. DOI: 10.1103/physrevb.53.9064 [10] Omini, M., & Sparavigna, A. (1997). Heat transport in dielectric solids with diamond structure. Nuovo Cimento, Società Italiana di Fisica, Sezione D, 19, 1537-1564. [11] Broido, D. A., Malorny, M., Birner, G., Mingo, N., & Stewart, D. A. (2007). Intrinsic lattice thermal conductivity of semiconductors from first principles. Applied Physics Letters, 91(23), 231922 (3 pages). DOI: 10.1063/1.2822891 [12] Ward, A., Broido, D. A., Stewart, D. A., & Deinzer, G. (2009). Ab initio theory of the lattice thermal conductivity in diamond. Physical Review B, 80(12), 125203 (8 pages). DOI: 10.1103/physrevb.80.125203 [13] Ward, A., & Broido, D. A. (2010). Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge. Physical Review B, 81(8), 0852051 (5 pages). DOI: 10.1103/physrevb.81.085205 [14] Narasimhan, S., & De Gironcoli, S. (2002). Ab initio calculation of the thermal properties of Cu: Performance of the LDA and GGA. Physical Review B, 65(6), 064302 (7 pages). DOI: 10.1103/physrevb.65.064302 [15] Karch, K., Pavone, P., Windl, W., Strauch, D., & Bechstedt, F. (1995). Ab initio calculation of structural, lattice dynamical, and thermal properties of cubic silicon carbide. International Journal of Quantum Chemistry, 56(6), 801-817. DOI: 10.1002/qua.560560617 [16] Fugallo, G., Lazzeri, M., Paulatto, L., & Mauri, F. (2013). Ab initio variational approach for evaluating lattice thermal conductivity. Physical Review B, 88(4), 045430 (9 pages). DOI: 10.1103/physrevb.88.045430 [17] Ju, Y. S. (2005). Phonon heat transport in silicon nanostructures. Applied Physics Letters, 87(15), 153106 (3 pages). DOI: 10.1063/1.2089178 MMSE Journal. Open Access www.mmse.xyz

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[18] Volz, S. G., & Chen, G. (2000). Molecular-dynamics simulation of thermal conductivity of silicon crystals. Physical Review B, 61(4), 2651-2656. DOI: 10.1103/physrevb.61.2651 [19] Turney, J. E., Landry, E. S., McGaughey, A. J. H., & Amon, C. H. (2009). Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations. Physical Review B, 79(6), 064301 (12 pages). DOI: 10.1103/physrevb.79.064301 [20] Ladd, A. J., Moran, B., & Hoover, W. G. (1986). Lattice thermal conductivity: A comparison of molecular dynamics and anharmonic lattice dynamics. Physical Review B, 34(8), 5058-5064. DOI: 10.1103/physrevb.34.5058 [21] Sellan, D. P. (2012). Predicting phonon transport in semiconductor nanostructures using atomistic calculations and the Boltzmann transport equation (Doctoral dissertation, University of Toronto). Available at https://tspace.library.utoronto.ca/handle/1807/32882 [22] Li, J., Porter, L., & Yip, S. (1998). Atomistic modeling of finite-temperature properties of crystalline Î˛-SiC: II. Thermal conductivity and effects of point defects. Journal of Nuclear Materials, 255(2), 139-152. DOI: 10.1016/s0022-3115(98)00034-8 [23] McGaughey, A. J., & Larkin, J. M. (2014). Predicting phonon properties from equilibrium molecular dynamics simulations. Ann. Rev. Heat Transfer, 17, 49-87. DOI: 10.1615/annualrevheattransfer.2013006915 [24] Ziman, J. M. (1962). Electrons and Phonons, London, Claredon. ISBN-13: 978-019850779, ISBN-10: 0198507798 [25] Srivastava, G. P. (1990). The physics of phonons. Bristol, Adam Hilger. ISBN-13: 9780852741535 [26] Omini, M., & Sparavigna, A. (1993). Thermal conductivity of rare gas crystals: The role of threephonon processes. Philosophical Magazine B, 68(5), 767-785. DOI: 10.1080/13642819308220158 [27] Wallace, D. C. (1972). Thermodynamics of Crystals. New York, Wiley. ISBN-13: 9780471918554 [28] White, G. K., & Woods, S. B. (1958). Thermal conductivity of the solidified inert gases: Argon, neon and krypton. Philosophical Magazine, 3(32), 785-797. DOI: 10.1080/14786435808237015 [29] Berne, A., Boato, G., & De Paz, M. (1966). Experiments on solid argon. Il Nuovo Cimento B (1965-1970), 46(2), 182-209. DOI: 10.1007/bf02711421 [30] Christen, D. K., & Pollack, G. L. (1975). Thermal conductivity of solid argon. Physical Review B, 12(8), 3380-3391. DOI: 10.2172/4234979 [31] Clayton, F., & Batchelder, D. N. (1973). Temperature and volume dependence of the thermal conductivity of solid argon. Journal of Physics C: Solid State Physics, 6(7), 1213-1228. DOI: 10.1088/0022-3719/6/7/012 [32] I.N. Krupskii, V.G. Manzhelii (1969) Multiphonon Interactions and the Thermal Conductivity of Crystalline Argon, Krypton, and Xenon, JETP, 28(6), 1097-1100 (Russian original - ZhETF, 55(6), 2075, June 1969). [33] Daney, D. E. (1971). Thermal conductivity of solid argon, deuterium, and methane from onedimensional freezing rates. Cryogenics, 11(4), 290-297. DOI: 10.1016/0011-2275(71)90185-8 Cite the paper Amelia Carolina Sparavigna (2017). The Variational Principle and the Phonon Boltzmann Equation. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.11.97.135

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Multi-Objective Optimization of Kinematic Characteristics of Geneva Mechanism Using High-Tech Optimization Methods8 Arash Mohammadzadeh Gonabadi 1,a, Mohammad Nouri Damghani 1,b 1 – Department of mechanical engineering, Semnan University, Semnan, Iran a – arash_mg@semnan.ac.ir b – mnoori@semnan.ac.ir DOI 10.2412/mmse.26.65.331 provided by Seo4U.link

Keywords: Geneva wheel mechanism; dynamic modeling; kinematic characteristics; multi-objective optimization; GA; ICA

ABSTRACT. This research is aimed toward using variable input speed for triple-objective optimization of kinematic characteristics of a Geneva wheel mechanism. High-tech optimization methods including genetic algorithm (GA) and imperialist competitive algorithm (ICA) are used in this study. The objective functions in both methods are magnitude of the maximum output angular velocity, magnitude of the maximum output angular acceleration as well as magnitude of the maximum output angular jerk of driven wheel. The motion equations of Geneva mechanism are first extracted with their boundary conditions determined. Then, above objective functions are minimized using the considered algorithms. Utilization of the input velocity may contribute to improve output kinematic characteristics of the mechanism.

Introduction. Developments achieved in the industries and widespread application of mechanisms throughout various industries have motivated researchers to rise their efforts in the course of enhancing mechanisms’ functions as well as performance of automatic machines. Today, correspondingly, many undergoing researches are dedicated to analysis of mechanisms as well as their synthesis. In conventional methods, a constant input speed is assumed for any mechanism; so as an improvement in mechanism performance is impossible in many cases where researchers are forced to design a new mechanism with higher kinematic performance [5]. For instance, the researchers designed a new mechanism to enhance kinematic characteristics of a cam mechanism [10]. The idea to use variable input speed into mechanisms was first implemented in a cam mechanism whose input mechanism was, in fact, the output of a Whitworth quick-return mechanism [13]. These researches utilized variable input speeds to reduce the cam dimensions and consequently, its pressure angle. Other researchers showed, in both experimental and theoretical way, that considering a variable input speed, one can control and improve output characteristics of a mechanism [2, 4, 14]. Optimization of kinematic characteristics of a Geneva mechanism is addressed in this research. Geneva mechanism is one of the most applied and simple mechanisms for generating periodic motions. Such mechanisms are widely used in many devices such as clocks, machine tools, printing and pressing machineries, packaging machineries as well as automotive machines. Although numerous kinds of tools are designed for the sake of periodic motion generation, but Geneva mechanisms are among the first choices for this purpose due to their simplicity, lower price, higher safety factor, long life and also smooth motion curves they produce [1, 7-8]. While simple Geneva mechanisms (with constant input speed) are popular, they suffer from a set of associated deficiencies. In Geneva mechanisms, output plots are not under control by the designer with angular acceleration of driven wheel having non-zero values at the beginning and the end of 8

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contact. This issue causes an angular jerk to be generated at the beginning and the end of contact. Furthermore, the angular jerk has non-zero values along the contact. Such an angular jerk will result in shock, vibration, abrasion and also noise generation which may lead to serious damages to the production line as well as machineries at high speeds. In addition, the maximum angular acceleration over the contact between the pin and the slot is as high as it leads the mechanism to exhibit a poor performance in accurate applications. Many modification techniques are already proposed to adjust a Geneva mechanism including placing two Geneva wheels besides each other [7], a Geneva wheel with curved slots [9], a Geneva wheel with two input cranks [11] and a flywheel with a quad-rod mechanism [16]. Controlling input speed of the mechanism is one of the methods used to control its output characteristics. In recent years, variable input speed is widely used to improve kinematic as well as dynamic characteristics of many popular mechanisms [3, 6]. Although extensive studies have focused on Geneva mechanisms and designing different structures for them, little has been done on optimization of their characteristics via optimization procedures. Heidari et al. used a single-objective optimization via genetic algorithm (with acceleration as the objective function) to improve output characteristics of a Geneva wheel [15]. The researchers implemented a double-objective optimization method, namely NSGA II, as well as MOSO optimization method to improve output characteristics of a Geneva wheel [12] In this research, two triple-objective optimization methods, namely the genetic algorithm and imperialist competitive algorithm, are presented in order to achieve better design points within a fourslot Geneva mechanism. The objective functions included the maximum angular velocity, the maximum angular acceleration as well as the maximum angular. The optimization goal is to find polynomial coefficients of input angular displacement function (as a variable input) and to generate plots of suitable input angular velocities which cause an improvement in kinematic characteristics of the Geneva wheel. Motion Equations for Four-Slot Geneva Mechanism The Geneva mechanism is the one used to transform continuous rotational motion into intermittent rotatory motion. Here a four-slot Geneva wheel is used that is an intermittent gear where the drive wheel has a pin that reaches into a slot of the driven wheel and thereby advances it by one step. The drive wheel also has a raised circular blocking disc that locks the driven wheel in a position between steps (see Figure 1).

Fig. 1. The four-slot Geneva mechanism. MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

According to Figure 1 we have:

r1 sin θ =r2 sin φ

(1)

r1 cos θ +r2 cos φ = R

(2)

and

Combining Eqs. (1) and (2) we will get:

tan φ =

r1 sin θ R r1 cos θ

(3)

Taking derivative of the Eq. (3) one may obtain angular speed and acceleration of the driven wheel as follows:

φ = r1θ

R cos θ r1 R +r12 2 Rr1 cos θ

(4)

and

 = r1θ φ

R cos θ r1 2 R +r12 2 Rr1 cos θ

Rr1θ 2 sin θ

R2 ( R 2 +r12

r12 2 Rr1 cos θ) 2

(5)

In a four-slot Geneva wheel, the wheel makes 90 degrees rotation when a 360-degree revolution of the driving wheel is realized. Furthermore, the same distance is assumed from the contact point of the pin toward center points of the driving and the driven wheel (Geneva wheel) at the starting moment when the pin contacts the slot (the beginning of the contact). The starting moment of motion is considered to be the moment at which pin contacts the slot. Geneva wheel will complete one fourth of its motion by the time τ , when the driving wheel has rotated 90 degrees. Dimensionless motion equations are derived using the following dimensionless parameters:

T

t τ

(6)

Θ=

θ π/2

(7)

and

also

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π π  π  θ(t ) = Θ(T ) , θ (t ) = Θ (T ) , θ(t ) = 2 Θ (T ) 2 2τ 2τ

(8)

Time variable, t , and angular variable, θ , vary in the ranges of [0, τ] and [0, π / 2] , respectively, so that dimensionless parameters of T and Θ vary within the ranges of [0,1] and [ 0.5,0.5] , respectively. Substituting the Eqs. (6), (7) and (8) into the Eqs. (4) and (5), angular velocity, angular acceleration and angular jerk relationships may be rewritten as follows:

 =C Φ

π  cos(π Θ / 2) C Θ 2τ 1 +C 2 2C cos( π Θ / 2)

(9)

and

π  cos(π Θ/2) C Θ 2 2τ 1 +C 2 2C cos(π Θ/2)

 =C Φ C

π  Θ 2τ

π sin Θ 2 [1 +C 2

1 C2 2C cos(π Θ/2)]2

(10)

where,

r1 R

(11)

Based on the above equations, one may suggest that all kinematic characteristics (including output angular velocity, acceleration and jerk) depend on the input angular displacement, while output characteristics can be controlled by manipulating input angular displacement. Angular displacement, angular velocity, angular acceleration, and angular jerk are plotted in Figure 2 for a constant input angular speed of 1 rad/sec and constant coefficient of   1 . As shown on this figure, the angular acceleration along with its derivative has non-zero values at the beginning and the end of the contact, while they exhibit high amplitude fluctuations along the contact. Such fluctuations are not appropriate for the mechanism and may cause damages and shocks to the mechanism as well as production line.

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Angular Velocity

0 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular

a) 20

Angular Acceleration

-10

-20 -0.5

-0.3

-0.1

0.1

0.3

0.5

0.3

0.5

Dimensionless Angular

b) 100

Angular Jerk

-100

-200 -0.5

-0.3

-0.1

0.1

Dimensionless Angular

c) Fig. 2. The plots of angular velocity (a), angular acceleration (b) and angular jerk (c) for the driven wheel (Geneva wheel). MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Optimization Methods This section deals with minimization of the magnitude of the maximum angular velocity, the magnitude of the maximum angular acceleration as well as the magnitude of the angular jerk (as the objective functions) of a Geneva wheel. A polynomial form is considered for the input angular displacement function (as the variable input). This function can be utilized to simply calculate input angular speed values. Input polynomial coefficients are considered as the design variables. In general, polynomial function and its associated boundary conditions are defined as follows: n

Θ(T ) = a0 +∑aiT i

(12)

i =1

Also Θ(0) = 0.5 , Θ(1) =0.5

(13)

From the Eqs. (12) and (13), we have: n

∑a

a0 = 0.5 , a1 =1

(14)

i =2

The value of angular speed of the driving wheel must always be positive; this is considered as a constraint through the problem, so as we have:  >0 ∀T ∈[0,1] Θ

(15)

Here a 7 order polynomial is taken into account as the input function (input angular displacement function) for the mechanism. Considering the boundary conditions of the problem, 6 out of 8 coefficients of this polynomial are unknown which are to be taken as the design variables. Genetic Algorithm This highly powerful algorithm has the capability of solving constrained and unconstrained, linear and nonlinear, single- and multi-variable as well as continuous- and discrete-variables problems [2128]. Optimization parameters depicted in Table 1 are used to solve the optimization problem via GA. Table 1. Parameters of the optimization problem, genetic algorithm (GA). Number of population

Number of generation

Probability of mutation

Probability of crossover

400

0.015

0.7

Imperialist Competitive Algorithm MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

This is an extremely powerful algorithm to find the global optimum point for complex problems [1726]. To solve the problem via this algorithm, we used the optimization parameters shown in Table 2. Table 2. Parameters of the optimization problem, imperialist competitive algorithm (ICA). Initial countries

Early empire

The number of repetitions

0.5

0.02

1900

Results Once optimization was performed (using MATLAB), a set of points are obtained in terms of a convergence plots drawn in Figures 3 and 4. The optimum point obtained in this research is more improved compared to those given in previous researches [21-28].

Fig. 3. Globally optimized points (GA).

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Fig. 4. Globally optimized points (ICA) - (Red: best fitness & Black: mean fitness). According to Figure 3, the optimum point has an angular jerk of 22.0464, an angular acceleration of 7.6855 and an angular velocity of 2.4421 in terms of magnitude. Furthermore, the best chromosome containing all 6 design variables has the following form (a 1 Ă&#x2014; 6 matrix):

[ 2.0617

0.2172

6.1314

9.9460 7.5002

]

2.1461

(16)

The optimum polynomial may be expressed as follows:

Î&#x2DC;(T ) = 0.5 +1.7394T

2.0617T 2

9.9460T 5 +7.5002T 6

0.2172T 3 +6.1314T 4

2.1461T 7

(17)

The curves of angular displacement and angular velocity of the driving wheel are plotted in Figure 5 for the optimum point (obtained via GA). As can be seen, the provided constraint in the Eq. (15) is met while the value of angular velocity of the driving wheel is positive all along the contact.

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Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954 0.5

Angular Displacement

0.3 0.1 -0.1 -0.3 -0.5 0

0.2

0.4

0.6

0.8

Dimensionless Time

a) 1.8

Angular Velocity

1.6

1.4 1.2 1

0.8 0.6 0

0.2

0.4

0.6

Dimensionless Time

b) Fig. 5. Curves of angular displacement (a) and angular velocity (b) of the input disk after optimization, GA method. Figure 6 compares kinematic characteristics of the Geneva mechanism (including angular velocity, angular acceleration and angular jerk of the Geneva wheel) for constant input speed (i.e. before optimization) with those for variable input speed (i.e. after triple-objective optimization by GA).

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Angular Velocity

0 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular Constant Input Speed

Optimization (GA)

a) 15

Angular Acceleration

10 5 0 -5 -10

-15 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular Constant Input Speed

Optimization (GA)

b) 50

Angular Jerk

0 -50 -100 -150 -200 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular Constant Input Speed

Optimization (GA)

c) Fig. 6. Curves of angular velocity (a), angular acceleration (b) and angular jerk (c) of Geneva wheel before and after optimization, GA method.

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Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

According to Figure 4, the optimum point obtained by imperialist competitive algorithm has an angular jerk of 21.5687, an angular acceleration of 7.8631 and an angular velocity of 2.4296 in terms of magnitude. Furthermore, the best chromosome with all 6 design variables has the following form (a 1 Ă&#x2014; 6 matrix):

[

2.1303

0.1001

6.0014

9.7303 7.2063

]

2.0021

(18)

The optimum polynomial may be expressed as follows:

Î&#x2DC;(T ) = 0.5 +1.7543T

2.1303T 2

9.7303T +7.2063T

0.1001T 3 +6.0014T 4

2.0021T

(19)

The curves of angular displacement and angular velocity of the driving wheel are plotted in Figure 7 for the optimum point (obtained via ICA). As can be seen, the provided constraint in the Eq. (15) is met while the value of angular velocity of the driving wheel is positive all along the contact.

0.5

Angular Displacement

0.3 0.1

-0.1 -0.3 -0.5 0

0.2

0.4

0.6

0.8

Dimensionless Time

a) 1.8

Angular Velocity

1.6 1.4 1.2

1 0.8 0.6 0

0.2

0.4

0.6

0.8

Dimensionless Time

b) Fig. 7. Curves of angular displacement (a) and angular velocity (b) of the driving wheel after optimization, ICA method. MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, March 2017 â&#x20AC;&#x201C; ISSN 2412-5954

Figure 8 compares kinematic characteristics of the Geneva mechanism (including angular velocity, angular acceleration and angular jerk) for constant input speed (i.e. before optimization) with those for variable input speed (i.e. after triple-objective optimization by ICA). 4

Angular Velocity

0 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular

Constant Input Speed

a) 15

Angular Acceleration

10 5 0 -5

-10 -15 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular Constant Input Speed

Optimization (ICA)

b) 50

Angular Jerk

0 -50 -100 -150 -200 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular Constant Input Speed

Optimization (ICA)

c) Fig. 8. Curves of angular velocity, angular acceleration and angular jerk of Geneva wheel before and after optimization, ICA method. MMSE Journal. Open Access www.mmse.xyz

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Table 3 presents the results when considering a constant input angular velocity (before optimization) as well as optimized results from [1], [15] and [16] along with those optimized via two methods presented in this research. Table 3. A comparison over the results obtained for constant input speed and those given by different optimization methods. The maximum angular velocity 3.7922 2.5517 2.6134 2.5212

Constant input velocity of 1 rad/s Optimized input via [1] Double-objective optimization (NSGA II), [15] Triple-objective optimization, [16] Triple-objective optimization, present research via GA Triple-objective optimization, present research via ICA

The maximum angular acceleration

The maximum angular jerk

13.3370 6.96 6.8874 6.907

186.199 36.7 34.975 34.2064

2.4421

7.6855

22.0464

2.4296

7.8631

21.5687

Numerical Method Finally, the obtained results were modelled in MSC Visual Nastran Desktop 4D (see Figure. 9). It is one of the powerful dynamic software which can simulate dynamic motion [29-33]. The results had good agreement with each other as is observed on Figure 10.

Fig. 10. Curve of angular velocity of Geneva wheel after optimization, was modelled in MSC. Visual Nastran, ICA method. MMSE Journal. Open Access www.mmse.xyz

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Angular Velocity

0 -0.5

-0.3

-0.1

0.1

0.3

0.5

Dimensionless Angular MSC. Visual Nastran

MATLAB

Fig. 11. A comparison of angular velocity of Geneva wheel after optimization, MATLAB and MSC. Visual Nastran Desktop 4D, ICA method. Summary. According to Figures 6 and 7, the maximum values of angular velocity, angular acceleration and angular jerk were significantly reduced after optimization via either GA or ICA method. The values of magnitudes of the maximum angular velocity, the maximum angular acceleration as well as the maximum angular jerk were decreased by 35.6%, 42.38% and 88.16%, respectively, for GA method, while they are reduced by 35.9%, 41.04% and 88.42%, respectively, for ICA method. It is worth to note that the optimized values of angular velocity and jerk were slightly more satisfying via ICA rather than those obtained by GA. In addition, the results of this study in terms of maximum value of angular velocity as well as the maximum angular jerk are improved with respect to the results of [1], [15] and [16]. Such an improvement reduces the risk of shock and damages to the production line and machinery along the contact. It should be noted that selecting higher number of objective functions will let the designer to achieve superior kinematic characteristics when designing a Geneva mechanism with variable input speed. Therefore, for similar case study with non-linear equations such as Geneva and Four-bar mechanism ICA method is one of the significant methods for dynamic optimization. References [1] Al-Sabeeh, A.K. 1993. Double-crank external Geneva mechanism, Journal of Mechanical Design, 115: 666-670. [2] Bickford, J.H. 1972. Mechanism for intermittent motion, Industrial press INC, New York. [3] Coelo, C.A. 2004. Handling multiple objective with particle swarm Ooptimization, IEEE Tranactions on Evolutionary Computation, 8: 256-279. [4] Fenton, R.G. 1976. Geneva mechanism connected in series, Journal of Manufacturing Science and Engineering, 97: 603-608. [5] Heidari, M. 2010. Production and modification of intermittent rotatory motion using slider, worm gear and cam mechanisms, MSc Thesis, Tehran University, Tehran, Iran. [6] Heidari, M., Zahiri, M. and Zohoor, H. 2008. Optimization of Kinematic Characteristic of Geneva Mechanism by Genetic Algoritm, World Academy of Science: Engineering and Technology, 44: 387395. [7] Hunt, H.K., Fink, N. and Nayar, J. 1960. Proceedings of the Institution of Mechanical Engineers (London), 174: 643-656. MMSE Journal. Open Access www.mmse.xyz

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[8] Lee, H.P. 1998. Design of a geneva mechanism with curved slots using parametric polynomial, Mechanism and Machine Theory, 33: 321-329. [9] Lee, J.J. and Cho, C.C. 2002. Improving kinematic and structural performance of Geneva mechanism using the optimal cotrol method, Proceedings of the Institution of Mechanical Engineers - Part C: Journal of Mechanical Engineering Science, 216: 761-774. [10] Mills, J.K., Notash, L. and Fenton, R.G. 1993. Optimal design and sensitivity analysis of flexible cam mechanisms, Mechanism and Machine Theory, 28: 563-581. [11] Mundo, D. and Yan, H.S. 2007. Kinematic optimization of ball-screw transmisson mechanisms, Mechanism and Machine Theory, 42: 34-47. [12] PurMohammadi, A., Felezi, M.E. and NarimanZadeh, N. 2013. Optimization of kinematic characteristics of Geneva mechanism with constant input speed, 8th students Conference on Mechanical Engineering, Malayer University, Iran. [13] Rothbart, H.A. 1956. Cams: design, dynamics and accuracy, Wiley, New York. [14] Tesar, D. and Matthew, G.K. 1976. The dynamics synthesis, analysis and design of modeled cam systems, Lexington Book, Lexington. [15] Yan, H.S. and Yan, G.J. 2009. Integrated control and mechanism design for the variable inputspeed servo fuor-bar linkage, Mechatronics, 19: 274-285. [16] Benjamin Ivorra, Bijan Mohammadi, Angel Manuel Ramos ,A multi-layer line search method to improve the initialization of optimization algorithms, European Journal of Operational Research, Volume 247, Issue 3, 16 December 2015, Pages 711-720 [17] Weihong Zhang, Hu Liu, Tong Gao, Topology optimization of large-scale structures subjected to stationary random excitation: An efficient optimization procedure integrating pseudo excitation method and mode acceleration method, Computers & Structures, Volume 158, 1 October 2015, Pages 61-70 [18] Julie Coloigner, Laurent Albera, Amar Kachenoura, Fanny Noury, Lotfi Senhadji, Seminonnegative joint diagonalization by congruence and semi-nonnegative ICA, Signal Processing, Volume 105, December 2014, Pages 185-197 [19] Visa Koivunen, Traian Abrudan, Riemannian optimization in complex-valued ICA, Advances in Independent Component Analysis and Learning Machines, 2015, Pages 83-94 [20] Arash Mohammadzadeh, A.Ghoddoosian, M. Noori-Damghani. 2011. “Balancing of the Flexible Rotors with Particle Swarm Optimization Method.” International Review of Mechanical Engineering - (Vol. 5 N. 3) - Papers 5 (3): 490-496. [21] A. Fereidoon, H. Hemmatian, A. Mohammad Zadeh, E. Elahe Asareh, “Optimization of sandwich panels based on yielding and buckling criteria by using imperialist competitive algorithm,” Modares Mech. Eng., vol. 13(4), July 2013, pp. 25-35 [in Persian]. [22] Nader Mohammadi, Arash Mohammadzadeh. 2015. “BALANCING OF THE FLEXIBLE ROTORS WITH ICA METHODS.” International Journal of Research and Reviews in Applied Sciences - (Vol. 23 N. 1) - Papers 23 (1): 54-64. [23] Nader Mohammadi, Arash Mohammadzadeh, ”Optimizing the Collector Performance of a Solar Domestic Hot Water System by the Use of Imperialist Competitive Algorithm with the Help of Exergy Concept,” International Journal of Engineering & Technology Sciences, Volume 3, Pages 6578, 2015 [24] Nader Mohammadi, Farahnaz Fallah Tafti, Ahmad Reza Arshi, Arash Mohammadzadeh, Raghad Mimar, “Extracting the Optimal Vibration Coefficients of Forefoot Offloading Shoes Using

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Genetic Algorithms,” International Journal of Engineering and Technology, Volume 2, Pages 487496, 2014 [25] Amir Mohammadzadeh, Nasrin Mahdipour, Arash Mohammadzadeh, “Forecasting the Cost of Water Using a Neural Network Method in the Municipality of Isfahan,” Journal of Optimization in Industrial Engineering, Volume 5, Pages 73-85, 2012 [26] [Amir Mohammadzadeh, Nasrin Mahdipour, Arash Mohammadzadeh, Mohammad Ghadamyari, “Comparison of forecasting the cost of water using statistical and neural network methods: Case study of Isfahan municipality,” Volume 6, Pages 3001, 2012 [27] Arash Mohammadzadeh, N. Etemadee. 2011. " Optimized Positioning of Structure Supports with PSO for Minimizing the Bending Moment." International Review of Mechanical Engineering (Vol. 5 N. 3) - Papers 5 (3): 422-425. [28] Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi (2016). Analytical and Numerical Study of Foam-Filled Corrugated Core Sandwich Panels under Low Velocity Impact. Mechanics, Materials Science & Engineering, Vol 7. doi:10.2412/mmse.6.55.34 [29] Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi (2016). Investigation of Energy Absorption in Aluminum Foam Sandwich Panels By Drop Hammer Test: Experimental Results. Mechanics, Materials Science & Engineering, Vol 7. doi:10.2412/mmse.6.953.525 [30] M Nouri Damghani, A Mohammadzadeh Gonabadi (2017). Numerical study of energy absorption in aluminum foam sandwich panel structures using drop hammer test. Journal of Sandwich Structures & Materials. First published date: January-11-2017. doi:10.1177/1099636216685315 [31] M.Noori-Damghani, H.Rahmani, Arash Mohammadzadeh, S.Shokri-Pour. 2011. "Comparison of Static and Dynamic Buckling Critical Force in the Homogeneous and Composite Columns (Pillars)." International Review of Mechanical Engineering - (Vol. 5 N. 7) - Papers 5 (7): 1208-1212. [32] Mohammad Nouri Damghani, Arash Mohammadzadeh Gonabadi (2017). Numerical and Experimental Study of Energy Absorption in Aluminum Corrugated Core Sandwich Panels by Drop Hammer Test. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.85.747.458 [33] A. Mohammadzadeh, A.Ghoddoosian. 2010. “Balancing of Flexible Rotors with Optimization Methods.” International Review of Mechanical Engineering - (Vol. 4 N. 7) - Papers 4 (7): 917-923. Cite the paper Arash Mohammadzadeh Gonabadi, Mohammad Nouri Damghani (2017). Multi-Objective Optimization of Kinematic Characteristics of Geneva Mechanism Using High-Tech Optimization Methods. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.26.65.331

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Formation of Physical and Mechanical Properties of Surface Layer of Machine Parts9 V. Zablotskyi1,a, O. Dahnyuk1, S. Prystupa1,b, A. Tkachuk1,c 1 – Lutsk National Technical University, Lutsk, Ukraine a – v.zablotsky@lntu.edu.ua b – s.prystupa@lntu.edu.ua c – a.tkachuk@lntu.edu.ua DOI 10.2412/mmse.99.57.43 provided by Seo4U.link

Keywords: dynamometer, the cut power, detail, machining, lathe, sensitivity, precision, measuring installation, tool holder.

ABSTRACT. The aim of the paper is to solve scientific and practical problem that is to explore the impact of operations of machining surfaces of parts of the "body rotation" type on the formation of the physical and mechanical properties of the surface layer. The method of research and analysis planned is by measuring the cutting force. It is suggested that components of cutting force affect the formation of physical and mechanical properties in varying degrees. For the analysis and separation of components of the cutting force specialized measuring equipment such as multi dynamometer was developed. The complex of theoretical studies, calculations and simulations revealed major sensitive zones of mechanical dynamometer.

Introduction. In connection with the development of technology higher demands on the quality of the surface layers of parts are put forward. In engineering machining operations in general cause major influence on the physical and mechanical, geometric characteristics of the surface layer and on the quality of machined parts in particular. Thus, new demands require the use of modern highprecision equipment and improved methods of treatment. Is not possible to get details accurately regulated in the size and quality of the surface layer without the introduction of new methods of research and machining accuracy process control and improvement of existing ones. Thus, ensuring the quality characteristics of parts using active control at every stage of their production and especially in the treatment of operational control quality parameters of the surface layer is important and urgent scientific and practical issue. One of the important parameters of machining which directly affects the quality of received surface is a cutting force [1]. This option can be divided into three components: – Constant component of cutting force; – The random component of cutting force, resulting from accidental changes of the surface parameters of the workpiece and the dynamic processes while cutting; – Monotonically increasing component due to the wearing out of a cutting tool. Making control of all components of cutting force it is possible to analyze the cutting process parameters in real time and consequently to foresee the further processing of the procedure to make active influence on the input process parameters. To effective cutting forces measuring during cutting lathe it is developed, designed and manufactured 9

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a device that gives accurate results on a wide range of measurements and adequately reflects the dynamics of cutting force components. Another condition for a device of such type is the simplicity of use that does not need complicated and expensive technological re-equipment and the ability to use standard cutting tool. The process of lather turning is a powerful dynamic process with complex relationships and many disturbing factors. It is therefore necessary to monitor its progress with high precision and speed. To measure the components of the cutting forces that arise during the turning processing we have designed and produced a design tool (Fig. 1), which is designed as a set of four elastic elements that allow you to record the deformation resulting from the impact component of treatment in node points of elastic elements. The device is designed as a mechanism that is installed on a seat tool holder of a screw-cutting lathe, a cutter is attached with screws to a boarding hole [2]. A part of the device with a fixed cutter is joined to a massive body with four elastic elements in the form of semirings with facets outside. Tenzogivers are placed on the faces and the inner cylindrical surface of the nodal points of each elastic element.

Fig. 1. Multicomponent dynamometer for measuring cutting forces components: a) dynamometer model; b) installation piece for measuring components of cutting forces. Measurement procedure: when performing machining operations cutting force is perceived through the instrument power link where the registration of the processing components is made (Fig. 2). The radial component of Py cutting force is perceived by elastic elements which are weakened by longitudinal sections in order to improve the sensitivity of the system. Clutching four elastic links it provides tensile deformation to sensors which are placed outside the elastic elements (1у, 2у, 5у, 6у), and provides compression deformation to sensors which are placed inside – (3у, 4у, 7у, 8у). The vertical Pz component creates a bending moment, which results in stretching the top of elastic elements and shrinking the bottom elements. Sensors, which receive Pz power, are pasted on the same sides as the Py power sensors while sensors of the lower zone (2z, 4z, 6z, 8z) get the same sign deformation as the neighboring sensors (2у, 4у, 6у, 8у), while sensors of the upper zone (1z, 3z, 5z, 7z) perceive deformation with the opposite sign. To increase the sensitivity Pz power sensors are placed as far away as possible from the point of application of the measured force. Power sensors, Py on the contrary are placed as close as possible to the vector of the component of this force. Their sensitivity doesn’t dependend on its height location, the ability to influence their index by mixed force components in this case is minimal. MMSE Journal. Open Access www.mmse.xyz

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Fig. 2. Block diagram of the measurement setup. The third component of the Рх in relation to other parts of the dynamometer is a tangential force. For its registration shift in the maximums nodal points diagrams of stresses in the annular elastic element under the action of tangential forces is used. Appropriate sensors are placed on the sloping sides of sensing elements symmetrically to maximum points. The strength of Рх causes tension of sensors (3х, 4х, 5х, 6х) and compression of sensors (1х, 2х, 7х, 8х). Connection of strain gauges in bridge circuits was carried according to two general rules: to try to achieve the greatest sensitivity of the measuring system and to provide automatic compensation of mutual influence of components of cutting forces. To confirm the hypothesis of the location of key areas of placing strain gauge sensors for registering components of Рх, Ру, Рz cutting forces software Autodesk Inventor Pro 2010 was used. The model of the dynamometer taking into account its design features was developed. The dynamometer was made of the material with such characteristics – Steel 45 GOST 1050-88, the mass of 6.04424 kg, volume – 769,967 mm3, the center of gravity of the body is located at the following coordinates: x = 80.496 mm; y = 40 mm; z = 37,3697 mm. The first stage of the simulation was the creation of a solid state computer model taking into account the material and selection of fixing dependencies of the object. In this case, the fixation of the object is provided through a landing slot of the dynamometer (Fig. 3a).

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Fig. 3. Basic verge fixation а) the line to which the component machining forces Pz b) is exerted upon. The second stage is the creation of loads acting on the object in the course of its work, namely a choice of facets of operating forces and determining their specific vectors (Fig. 3b). Since this load cell is designed to measure three components of cutting force, the main objective was to determine the location of nodal points where maximum deformations of each component of forces are observed. A series of studies in which a total cutting force was laid on its components Px, Py, Pz was conducted. The values of the applied load were determined experimentally according to technological modes of the machine and taking into account the material of the workpiece and the tool. So in the first case there was modeled an impact of Рz component resulting from the rotation of the workpiece, according to the calculations it equals to 465 Н (Table. 1). Table 1. Strength and depending reaction time caused by Pz component. Reaction strength Name of the dependence Size

Jet point

Component

Size

(X, Y, Z) 0N

Fixing dependence: 1

465 N

Component (X, Y, Z) 0 N·m

48,2435 N·m

465 N

-48,2435 N·m 0 N·m

As a result of the simulation there was received a calculation of a number of parameters (tab. 2) and the creation of its graphical visualization (Fig. 4).

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Table 2. The result of simulation of the Pz force component. Name

Value (min)

Value (max)

Von Mises stress

0,0000365918 MPa

10,433 MPa

1-st main stress

-1,31019 MPa

11,7692 MPa

3-d main stress

-11,8199 MPa

1,35378 MPa

Shift

0 mm

0,00743231 mm

Ultimate factor of safety

15 br

Stress XX

-7,34826 MPa

7,67991 MPa

Stress XY

-4,83475 MPa

4,64143 MPa

Stress XZ

-2,72776 MPa

1,16707 MPa

Stress YY

-6,53714 MPa

6,7057 MPa

Stress YZ

-5,1942 MPa

5,23698 MPa

Stress ZZ

-8,39489 MPa

8,85921 MPa

Offset by X shaft

-0,0017662 mm

0,00181829 mm

Offset by Y shaft

-0,000401373 mm

0,000396639 mm

Offset by Z shaft

-0,00741761 mm

0,0000110142 mm

Modeling and creating graphical visualization occurs by finite element analysis that form the grid. To increase the accuracy its parameters had the following values (Table. 3). Table 3. The main parameters of finite element net. Average element size (fractional value from the diameter model)

0,05

The minimum element size (fractional value from the average size)

0,1

Diversity factor

1,5

The rotation angle (max)

20 degree

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Fig. 4. Equivalent dynamometer deformation because of Pz component influence. Based on the analysis of simulation results and graphical visualization (Fig. 4) the location of nodal points, which accumulate the greatest stress and therefore having equivalent deformation because of component force Pz was defined. In the second case, there was built a model to investigate the impact of Py component, resulting from longitudinal tool input that is equal to 219 N (Table. 4) according to the calculations but its vector is aimed at the side facet (Fig. 5).

Fig. 5. The facet to which machining force Py component is attached. Table 4. Strength and reaction time in dependences induced by component Py Reaction strength Name of the dependence Size

Jet point

Component

Size

(X, Y, Z) 0N

Fixing dependence: 1

219 N

(X, Y, Z) -0,389908 N·m

22,7247 N·m

0N MMSE Journal. Open Access www.mmse.xyz

Component

0 N·m 22,7213 N·m

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Because of the simulation a number of calculation of parameters (tab. 5) was received and the creation of graphical visualization was made (Fig. 4). The third component of the Рх in relation to other parts of the dynamometer is a tangential force. For its registration shift in the maximums nodal points diagrams of stresses in the annular elastic element under the action of tangential forces is used. Appropriate sensors are placed on the sloping sides of sensing elements symmetrically to maximum points. The strength of Рх causes tension of sensors (3х, 4х, 5х, 6х) and compression of sensors (1х, 2х, 7х, 8х). Connection of strain gauges in bridge circuits was carried according to two general rules: to try to achieve the greatest sensitivity of the measuring system and to provide automatic compensation of mutual influence of components of cutting forces. Table 5. Results of simulation of the Py force component. Name

Value (min)

Value (max)

Von Mises stress

0,0000769117 MPa

6,77654 MPa

1-st main stress

-0,697035 MPa

6,8717 MPa

3-rd main stress

-6,97715 MPa

0,771266 MPa

Shift

0 mm

0,00456053 mm

Ultimate factor of safety

15 br

Stress XX

-2,35183 MPa

2,31139 MPa

Stress XY

-2,41393 MPa

1,97715 MPa

Stress XZ

-0,558817 MPa

0,617342 MPa

Stress YY

-6,72168 MPa

6,59781 MPa

Stress YZ

-1,43862 MPa

1,57453 MPa

Stress ZZ

-1,74296 MPa

1,84711 MPa

Offset by X shaft

-0,00207548 mm

0,00206632 mm

Offset by Y shaft

-0,00455284 mm

0,000015807 mm

Offset by Z shaft

-0,000288796 mm

0,000319023 mm

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Fig. 6. The equivalent dynamometer deformation as a result of Py force component. Based on the analysis of simulation results and graphical visualization (Fig. 6) the location of nodal points, which accumulate the greatest stress and therefore have equivalent deformations as a result of Py force component was determined. In the third case a model has been built to investigate the impact of the resulting Px component, which occurs as a resultant of Pz and Py forces. However, in order to properly direct its vector, vector application efforts were used, which according to the calculations equals to 184 Н (Table. 6), its vector is directed to the bottom and side edges of the dynamometer (Fig. 7).

Fig. 7. Facets to which the resultant Px force component is attached to. Table 6. Strength and reaction time in dependences induced by Px component. Reaction strength Name of the dependence

Size

Jet point

Component (X, Y, Z)

Size

184 N Fixing dependence: 1

318,697 N

184 N

2,61602 N·m 29,0246 N·m

184 N MMSE Journal. Open Access www.mmse.xyz

Component (X, Y, Z)

-21,7062 N·m 19,09 N·m

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As a result of the simulation a number of calculation of parameters (tab. 7) was received and the creation of graphical visualization was made (Fig. 8). Table 7. Results of simulation of the of Px force component. Name

Value (min)

Value (max)

Von Mises stress

0,000122972 MPa

11,7738 MPa

1-st main stress

-1,4375 MPa

12,1039 MPa

3-rd main stress

-8,56584 MPa

1,173 MPa

Shift

0 mm

0,00649382 mm

Ultimate factor of safety

15 br

Stress XX

-6,01391 MPa

5,41856 MPa

Stress XY

-3,89862 MPa

3,94826 MPa

Stress XZ

-2,65661 MPa

0,799517 MPa

Stress YY

-7,03252 MPa

11,3099 MPa

Stress YZ

-3,29472 MPa

3,50969 MPa

Stress ZZ

-4,48025 MPa

5,47884 MPa

Offset by X shaft

-0,00335509 mm

0,00242221 mm

Offset by Y shaft

-0,00427818 mm

0,000119131 mm

Offset by Z shaft

-0,00428961 mm

0,00000714775 mm

Fig. 8. The equivalent dynamometer deformation because of Px force component. Based on the analysis of simulation results and graphical visualization (Fig. 6) the location of nodal points, which accumulate the greatest stress and therefore have equivalent deformation due to the action of Px force component was determined. MMSE Journal. Open Access www.mmse.xyz

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To confirm the hypothesis of stresses locations analyzed the diagram of stress of the ring dynamometer part of the designed tool of carrier (Fig. 9). Nodal point of the stress diagram under the influence of axial component will coincide with the midpoints of sensors of unmeasured components. Therefore, one-half of each of them will be stretched and the other part will equally be compressed. As a result, the sensor resistance will change. Sensors of Pz, and Py components on the Px power will not respond no meter what its values is. The impact on performance of main and radial component of Px force sensors are eliminated automatically in a similar way. Under the influence of the force, the ring resiliently deforms and takes the form of an ellipse Fig. 9, and the ring deflection is calculated by the formula [3-4].

D  0,223

P ( D  h) 3 P ( D  h) ,  1,775 2 Ebh Ebh

(1)

where D – is the diameter of the outer ring; E is a modulus of elasticity; b and h – are the width and thickness of the ring. Fig. 9 presents diagrams of the distribution of relative strain caused by P force on the outer and inner surfaces of the ring. The greatest deformation occur in the plane I-I of the force performance and in diametrical section II-II that must be considered when placing sensors. To get the highest sensitivity sensors should be placed symmetrically relatively to section II-II. Since the deformation of outer and inner rings are opposite in sign, the sensors can be placed on both sides.

Fig. 9. Diagrams of dynamometer ring stress. To determine the strain ε-section at II-II the following formulae can be used:



0,362P( D  h)  (1,5D  h) P  . 2 Ebh D 2Ebh

(2)

If we divide equation (2) in equation (1), after transformations and simplifications a simplified approximate formula can be obtained: MMSE Journal. Open Access www.mmse.xyz

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 D



8 8  , D  2h d

(3)

where d – is the inner diameter of the ring. If you use circular elastic elements with sensors with strain the ratio ε / ΔD should be maximized, as it is tantamount to increasing sensitivity without changing the working movement of elastic link. According to equation (3) internal diameter should be made as small as possible. Its minimum value depends on sensor size, which will be glued to the inner surface of the ring. It should also be noted that in-section III-III and IV-IV, inclined to the plane II-II at an angle of about 50 °, there is no deformation. These are diagram nodes. Their placement depends on the direction of the active force. Before measurement each bridge circuit is connected to the amplifier with a differential input and output and built-in voltage source for tenzomosta LP-04. In turn, each amplifier is connected to the ADC / DAC E-154 module. Module E-154 through the input USB 1.1 (2.0) is connected to the computer. Visualization and registration of data was performed with the software – UM ADC1. Example of flow process of measurement of components of the cutting force is presented in Fig. 10.

Fig. 10. Sample variability flow of components of cutting forces. Thus, the obtained profilogram are used to analyze the components of the cutting force to identify the peculiarities of a particular component on forming the surface layer of the parts. References [1] Y. Ermakov Complex methods of effective machining / Y. Ermakov. – M.: Mashynostroenye, 2005. – 272 p. [2] Ukraine Patent 94828, МПК В23Q 17/00 (2014.01). Multicomponent dynamometer for measuring components of cutting force. The applicant and the patentee: S. Prystupa, A. Tkachuk, V. Zablotskyi, T. Terletskyi, O. Dahnyuk, Lutsk; appl. 20/03/2014; publ. 10/12/2014; Newsletter №23. - 4 p. [3] B. Hessen Ring elastic system for dynamometers with wire sensors / B.Hessen – Proceedings of the Moscow Institute of Chemical Engineering vol.11, 1957. – 203 p. [4] A. Tkachuk, V. Zablotskyi, T. Terletskyi, O. Kaidyk, S.A. Moroz. Increased wear resistance of surfaces of rotation bearings methods strengthening-smoothing processing. Mechanics, Materials Science & Engineering Journal. Volume 5, July 2016, Pages 77-85, DOI: 10.13140/RG.2.1.1757.9125 MMSE Journal. Open Access www.mmse.xyz

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[5] Wang Jiabina, Niu Ditao, Song Zhanping, Damage layer thickness and formation mechanism of shotcrete with and without steel fiber under sulfate corrosion of dry–wet cycles by ultrasound plane testing method, Construction and Building Materials, Vol. 123, 1 October 2016, Pages 346–356, http://dx.doi.org/10.1016/j.conbuildmat.2016.06.146 Cite the paper V. Zablotskyi, O. Dahnyuk, S. Prystupa, A. Tkachuk (2017). Formation of Physical and Mechanical Properties of Surface Layer of Machine Parts. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.99.57.43

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Assessment of the Possibility to Use Hybrid Electromechanical Transmission in Combat Tracked Platforms10 Glebov V.V.1, Klimov V.F.1, Volosnikov S.A.1, a 1 – Kharkiv Morozov Machine Building Design Bureau, Kharkiv, Ukraine a – volosnikov@ukr.net DOI 10.2412/mmse.83.5.981 provided by Seo4U.link

Keywords: tracked platforms, electromechanical transmission, electromechanical traction drives, electric machines.

ABSTRACT. The article gives an estimation of possible using the hybrid electromechanical transmission performed as a series circuit in tracked vehicle of 50-tonnes weight category using the series-manufactured components of hybrid electric drive system. As components of electric drive (motor-generators and traction electric motors) it is invited to use AC induction motors with squirrel-cage rotor, that has no moving contacts and can work both in motor and generator modes, and energy storage buffer is made on the basis of consecutively connected Lithium-ion batteries.

Introduction. As smaller and more powerful electric machines, namely motor-generators (MG) and traction electric motors (TEM), appear, as well as relatively small power converters, we can observe the raise of interest towards the use of electromechanical transmission for combat tracked platforms. Electromechanical traction drives are relatively new devices to be used for combat tracked platforms, that is why the basic principles of their design considering the peculiarities of their application are not yet finalized. This would require rethinking of many of the principled approaches. Attempts to switch from finalization of source data to concrete parameters of devices with the purpose to use them for combat tracked platforms are currently based on the experience of design of similar devices for other fields and ranges of application. In case of using sequential system development, the electric power generated by motor-generator is distributed via flexible electric cables and thus: MG, TEM, controllers and power converters can be placed irrespective of each other, without strict kinematic connection, providing the designers of combat tracked platforms with the possibility to create various design layouts. Total electric power in the range of 800-900 kW generated by MG shall be distributed accurately and effectively for quick and precise execution of commands input by driver to control tractive effort as well as power taken off for steering and braking. Also, the concept of hybrid combat tracked platform requires control of power flow distribution to on-board consumers of electric power, such as weapon station, protection, control systems, air conditioning, etc. Problem Definition. There are currently no validated and standard procedures of selection of basic parameters of electromechanical devices (type of electric motor, supply frequency, energy parameters, etc.) to be used on combat tracked platform. Moreover, there are no quality criteria for design of such systems for tracked platforms. These circumstances largely constrain the development of electric machines (MG and TED) and electric drives on their basis for use in future samples of combat tracked platforms. Analysis of recent achievements and publications. Currently, in developed countries experts in the development of military equipment are working on the creation and implementation of 10

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electromechanical transmissions for the tracked platforms. One of the main advantages of electromechanical transmission is the effect of "continuously variable transmission", the absence of the clutch mechanism and gear shifting with continuous flow of power to the tracks, and the TEM power is supplied directly to the final drives of the sprocket wheels. German company Magnet Motor implemented electric transmission for Marder tracked infantry fighting vehicle [1,2]. Electric drive is an AC-DC-AC type system (alternating current – direct current – alternating current) and has six levels of power transmitted through the transmission. The motor-generator is connected with the diesel engine MV-833Еа500 by MTU company with 440 kW capacity. The power of the AC motor-generator was 420kW (at 2250rpm), and the power of two onboard AC traction electric motors was 750kW (at 3500rpm) each, and they were connected to the tracks via final drives. At the same time, electric motors can do the power recuperation from the lagging track to the leading one during the turn, in case the electric motor of the lagging side is switched to generator mode. The source noted that the Marder IFV with electric transmission with the weight of 29.5 t had a maximum speed of 72km/h, which corresponds to the parameters of the serial vehicle, the vehicle is also highly mobile and manoeuvrable. For the development of GCV combat tracked vehicle, BAE Systems used hybrid electric drive using the on-board energy buffer storage [3]. The source noted that indicative weight of GCV tracked platform is within 70 tonnes and capacity of its motor-generator is about 1,100 kW, hybrid systems provide this product more speed, stealth, and fuel efficiency compared with similar vehicles of this weight category, that use mechanical transmission.

Fig. 1. GCV Combat Tracked Vehicle by BAE Systems. The source [4] reports on the development of a prototype of BMP-3 type tracked platform with side electric transmission. 320kW generator is connected directly to the diesel engine, and two BLDC servomotors (320kW each) are connected to the sprocket wheels via final drive. This provides the possibility for the diesel engine to operate in optimal modes for various driving conditions of the tracked platform with the most efficient use of the power plant capacity. Object of the Article. The object of the article is to assess the possibility to use hybrid electromechanical transmission on combat tracked platforms of up to 50 tonnes weight, as well as to select the type of applied electric machines and other components of the electrical drive system. Main Data. In the movement process of a tracked platform when turning with a radius of less free, the leading track being the leading one in relation to the hull, provides its movement and rolling of the lagging track. Therefore, the main part of the power N2 of the leading track is used to overcome external resistance, and a part of it is driven to the lagging track via the platform hull. If the lagging track is not braked, the mobile platform will turn with free turning radius and power N1 of the lagging track (small one) will be spent for the track idling. Brake the lagging track to make a sharp turn with radius less than free. Therefore, power N1 will be partially or completely be spent to overcome brake MMSE Journal. Open Access www.mmse.xyz

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friction. If the brake of the lagging track were installed on the sprocket wheel of the tank, the supplied power would be N1  ηГД ( ηГД multiplier that takes into account power loss at the track bypassing). This is the way the power is distributed at turning when kinematic connection between leading and lagging tracks is broken, for example, when final drives and steering clutches are used. Therefore, the most efficient kinematic patterns are the patterns when the power is transmitted from the lagging track to the leading one, i.e. with the power recuperation. And only part of the power of the lagging track is consumed by spinning friction device. Such steering mechanisms require less energy and evidently have better dynamic performance. Transmission of T-64 family of armoured vehicles is fitted with steering device that keeps the speed of linear movement V0 when turning along the axis of symmetry of the leading track (Fig. 2a).

Fig. 2. Speed distribution for various steering mechanisms. Such steering mechanism requires relatively less power, but when the vehicle enters the turn the speed of its centre of mass is getting reduced, thus creating moment turning the car around its centre of mass. It is obvious that at high movement speed such steering mechanism can cause skidding and spontaneous pivoting when making a turn. Also, there are steering mechanisms for tracked platforms the turning speed of which is Vc.m.=V0, i.e. the point retaining the linear movement speed is in the centre of mass (Fig.2b). Differential design of steering mechanism meets such requirement. Such steering mechanisms are installed on such tanks as M60A1 Abrams, Leopard, etc. Also apply the steering mechanisms for tracked platforms in which the point that retains linear movement speed at turning is behind the leading track, therefore, not only the speed of the lagging track is reduced when turning but also the speed of the leading one, that is V0> V2> V1 (Fig. 2c). In cases when the steering mechanism ensures transfer of all power from the lagging track to the leading one at any turning radius, it can be called a perfect steering mechanism. In any case, there is a complete power recuperation at any turning radius. Such mechanism can be created using electromechanical transmission. In this case, the recuperation power received from the lagging side of the tracked platform varies constantly, and unlike the recuperation power received on similar tracked platforms with mechanical transmission, is independent of the movement speed. Strict requirements for tractive effort of a tracked platform, especially in turning mode with minimal braking of the lagging side involves complication of the design of electric drive system and is crucial for choosing the type of electromechanical transmission used. Currently there are several main trends in the development of electromechanical transmissions for combat tracked platforms. Let us consider some basic variants of electromechanical transmissions that can be used for combat tracked platforms: - mixed-design electromechanical transmission; MMSE Journal. Open Access www.mmse.xyz

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- consecutive-design electromechanical transmission; - consecutive-design hybrid electric drive. Mixed-design (consecutive-parallel) electromechanical transmission combines a kind of medium variant between mechanical and electromechanical transmission and is a central transmission with the second power flow from internal combustion engine (ICE) [5,6]. Such trend stipulates development of parallel power flows on the basis of electric machines transmitting only a part of the ICE power. The major part of the engine power is transmitted via the main mechanical branch of the transmission, at the same time the transmission remains automatic. The main disadvantage is that there remains kinematic connection between the engine and track sprocket-wheels, lack of layout flexibility and raise of certain difficulties when installing additional equipment (MG, TEM, power converter, etc.) in the existing combat tracked platform. Classical approach to using consecutive electromechanical transmission in combat tracked platforms accepts that motor-generator is driven from ICE, and two traction electric motors, placed at the sides, drive sprocket wheels of the left and right side tracks via final drives. The disadvantage of such transmission is the lack of source of additional power ensuring high mobility capability of the combat tracked platform and the use of more powerful MG. Therefore, it is necessary to achieve full correspondence of the power level generated by MG for the needs of TEM of the left and right sides, and at the same time to provide power supply for operation of other power users of the combat tracked platform mains. Currently the hybrid electric drive is regarded as the most promising option to be used on combat tracked platforms [7,8]. As a rule it includes the following elements: ICE (diesel engine), motorgenerator, two traction electric motors on the left and right side, energy storage buffer (ESB), power electronics unit. For the use on a combat tracked platform, the most appropriate variant is hybrid electric drive with consecutively connected elements (no rigid kinematic connection) and ESB on board. The main advantage of ESB is to enable compensation for the difference between mean and maximum power of the electric drive system, is required for movement and acceleration of the combat tracked platform accordingly. Physical requirements for the power of MG, TEM and their cooling system, as well as ESB are mainly connected with the need to provide minimum requirements of operational and physical characteristics of the combat tracked platform, first of all, generation of the tractive effort required for movement, steering and manoeuvring at high speed. Note the main advantages of consecutive hybrid electric drive used on a combat tracked platform: - possibility to rapidly develop high torque on TEM, when acceleration is required, due to simultaneous operation of MG and ESB; - capability to accumulate energy in the storage buffer generated when the tracked platform is braking in order to use it for the further acceleration, turning, hill climbing, high mobility and stealth actions; - 20-30% reduction of actual power of the used power plant (ICE) with equal tractive parameters compared with the similar vehicles with automatic transmission; - 10-15% reduction of fuel consumption during movement; - capability to move a combat tracked platform over short distances in stealth mode with decrease of visibility in infra-red light using the energy of the storage buffer with the main engine shut down; - ensures the possibility to use a combat tracked platform as an independent power source with around 800-900kW capacity; - ensures the possibility to accumulate considerable amount of power for future weapon types; - reduction of maintenance labour and its cost. The main disadvantages are: MMSE Journal. Open Access www.mmse.xyz

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- relatively big size of converters, ESB, that occupy considerable part of the hull volume of the combat tracked platform; - high voltage on-board requires introduction of additional safety measures for the crew, and the vehicle hull has to be air tight; - requires extensive cooling system for electrical power units (MG, TEM, power converter). The electric motors applied for combat tracked platforms have to be capable to work for a long time at rather high torque at low movement speed of the tracked vehicle. Moreover, they have to ensure the movement of the tracked platform at maximum possible speed providing the required tractive effort, and provide additional (reserve) power required for manoeuvres and steering. Characteristics and manoeuvrability of the currently developed types of electric motors differ greatly [9]. Electric motors comprising permanent magnets cannot generate electric power (generator mode) to be transferred to the leading side and to charge ESB at braking, in addition, they are expensive. Currently, the most preferable variant to be used in electric drive system (MG, TEM) of combat tracked platforms is an AC induction motor with squirrel-cage rotor, which has no moving contacts (no brushes and slip rings). A significant advantage of the induction drive compared with the other types of electric drives is that the power limitation is provided by restriction of power supply voltage of the induction motor due to respective weakening of the magnetic field, which requires less actual power of the power converters, and as a result, the whole drive system becomes cheaper. The absence of moving contacts ensures higher reliability and reduces maintenance requirements. Also the induction drive is characterized by the best price - performance ratio. The use of modern power converters, the maximum output frequency of which can be adjusted in the range of up to 500Hz, provides the possibility to reduce the weight of traction electric motors and motor-generators without significant reduction of their efficiency. Let us formulate the basic requirements for the electric drive system for tracked combat platforms weighing up to 50 tonnes: - power plant - diesel engine with estimated capacity of 800-900kW; - consecutive-design hybrid electric drive with no rigid kinematic connection between ICE and sprocket wheels. The torque developed by diesel engine should be comparable with the torque of MG which should be formed on the working area of the diesel engine; - motor-generator is an AC induction motor (motors) with squirrel-cage rotor, which has no moving contacts with total capacity of 800-900kW with liquid cooling system, connected to the output shaft of the power plant; - two traction electric motors are AC induction motors with squirrel-cage rotor, capable to operate in generator mode to provide ESB charging in braking mode of the combat tracked platform with estimated capacity of 400-450kW each, with liquid cooling system, connected to the sprocket wheels via final drive; - energy storage buffer is developed on the basis of consecutively connected Lithium-ion batteries (LiFePO4)with estimated capacity of 120kW at 600V voltage, which makes it possible to drive the combat tracked platform in stealth mode without starting the main engine for 4-5 km; - power converter is executed using IGBT-transistors, that allow to change direction of power transfer - MG control in the engine mode when starting the powerpack as well and control of generator mode of TEM when the tracked platform is braking or turning; - power converter - (600/28)V DC for power supply of low voltage equipment of the vehicular mains; - vehicular steering and control system with display of current parameters of the main elements of electric drive system (rpm, temperature, voltage, current, etc.) on driver's panel.

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Software of modern CPUs (if equipped with corresponding sensors) makes it possible to implement steering algorithms to avoid skidding and track slip when moving in various road conditions in order to improve characteristics of combat tracked platform acceleration, braking and turning.

Fig. 3. Functional diagram of hybrid traction electrical equipment of a tracked platform. Development of hybrid electric drive for 50 tonnes combat tracked platform, probably using the following components that are currently in mass production. 1. A regular diesel engine 6TD-2 with a capacity of 882kW (1200h.p.) can be used as the power plant. 2. Traction motors HDS200 with a capacity of 200kW and HDS300 with a capacity of 230kW by BAE Systems company with water cooling can be used as the motor-generators. AC induction generators are installed coaxially with the output shaft of the power plant and can operate both in generator and motor modes, providing start of the power plant (diesel engine). Total capacity of the motor-generators, excluding the capacity of the regular starter-generator of the power plant is 860kW. 3. As traction motors there can be used two induction traction motors with liquid cooling, with a capacity of 450kW each, connected to the sprocket wheels of the tracks on left and right sides via final drive. 4. Energy storage buffer can be made on the basis of consecutively connected LithiumMMSE Journal. Open Access www.mmse.xyz

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ion (LiFePO4) batteries (3.2V, 200A·h each) with total nominal voltage of 600V and 120kW·h capacity of the storage buffer. The storage buffer can be placed on the right above-track plate instead of a part of the fuel tanks and regular power unit that is not needed when the hybrid drive is applied. 5. Power control of the traction equipment can be placed symmetrically on the above-track plate of the left side. Energy of the storage buffer goes to the DC voltage converter (600/28V) and then it can be transferred for supply of low-voltage equipment of the power users of the combat tracked platform mains. Summary. 1. It is possible to use consecutive-design hybrid electric drive with no rigid kinematic connection between ICE and sprocket wheels and with the energy buffer on-board for the combat tracked platforms with up to 50 tonnes weight without considerable weight increase of the vehicle with respect to the similar vehicles with mechanical transmission. 2. As components of electric drive (MG and TEM) it is invited to use AC induction motor (motors) with squirrel-cage rotor, that has no moving contacts and can work both in motor and generator modes, and ESB is made on the basis of consecutively connected Lithium-ion (LiFePO4) batteries. References [1] R.M. Ogorkevich, Electric transmission progress in Germany // International defense review. – 1992. - No2. - Pp. 153-154. [2] B.N. Gomberg, S.V. Kondakov, L.S. Nosenko and colleagues, Imitating modelling of the movement of a fast-moving tracked vehicle fitted with electrical transmission // Bulletin of South Ural State University. Power Engineering series. – 2012. - Issue 18. - No.37. - Pp. 73-81. [3] Sergyi Way BAE Stakes on Hybrid Electric Drive for Combat Vehicle. [Online]. Available: http://vpk.name/news/79572_bae_delaet_stavku_na_gibridnyii_elektricheskii_privod_dlya_ boevoi _mashinyi.html. [4] Tractor Plants Develop IFV with Electrical Transmission. [Online]. Available: http://warfiles.ru/show-104145-traktornye-zavody-sozdayut-bmp-s-elektrotransmissiey.html. [5] P.P. Isakov, P.N. Ivanchenko, A.D. Yegorov, Electromechanical Transmissions of Tracked Tractors: Theory and Calculations. – L. Mashinostroyenie. 1981. – 302 p. [6] M.L. Miller, Mechanical Assistance for Electric Drives AMRC / Technion – Israel Institute of Technology, Haifa, Israel Advanced Development Corp. Tel Aviv, Israel. [Online]. Available: http://btvt.narod.ru/4/electric_mech_trans.htm. [7] Sergyi Way, Military Application of Hybrid Electric Drives [Online]. Available: http://www.army-guide.com/rus/article/article_435.html. [8] Filip Polak, Jerzy Walentynowics, Simulation of the hybrid propulsion system for the small unmanned vehicle // Journal of KONES Powertrain and Transport. - 2011 - Vol. 18. - No.1. - Pp. 471-478. [9] Zakladnoi A.N., Zakladnoi O.A., Power Efficient Electric Drive with BLDC Motors. Monograph.- Kiev. - Libra Publishers. - 2012. - 190 p. Cite the paper Glebov V.V., Klimov V.F., Volosnikov S.A. (2017). Assessment of the Possibility to Use Hybrid Electromechanical Transmission in Combat Tracked Platforms. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.83.5.981

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Identities of Vector Algebra as Associative Properties of Multiplicative Compositions of Quaternion Matrices11 Victor Kravets1,a, Tamila Kravets1, Olexiy Burov2 1 – National Mining University, Dnipro, Ukraine 2 – Jack Baskin School of Engineering, University of California-Santa Cruz, CA, USA a – prof.w.kravets@gmail.com DOI 10.2412/mmse.47.87.900 provided by Seo4U.link

Keywords: quaternionic matrices, vector matrices, vector algebra identities, complex vector and scalar products, associative property of vector matrices’ products.

ABSTRACT. This paper is dedicated to the further development of matrix calculation in the sphere of quaternionic matrices. Mathematical description of transfer (displacement) and turn (rotation) in space are fundamental for the mechanics of rigid body. The transfer (displacement) in space is described by the vector (hodograph). The turn (rotation) in space is described by quaternion. Calculation quaternionic matrices generalizes vector algebra and is directly adapted for the computing experiment concerning nonlinear dynamics of discrete mechanical systems in spatial motion. It is proposed to examine the turn and transfer of the rigid body in space with four-dimensional orthonormal basis and corresponding matrices equivalent to quaternions or vectors. The identities of vector algebra, including the Lagrange identity, Euler-Lagrange identity, Gram determinant and others, are found systematically. The associative products of conjugate quaternionic matrices are represented by the multiplicative compositions of vector algebra. The complex vector and scalar products are represented by the introduced matrices. With the use of associative property of conjugate quaternionic matrices’ products, the range of vector algebra identical equations is found, including the known ones, which serve, in particular, to justify the fidelity of the offered method. The method is being developed to represent associative products of conjugate and various quaternionic matrices by multiplicative compositions of vector algebra, containing scalar and vector products. The method is offered to represent complex (vector and scalar) vector algebra products as quaternionic matrices. This fundamental results constitute the first part of the study recommended for engineers, high school teachers and students who in their practical activity set and solve the problems of dynamic design of aeronautical engineering, rocket engineering, space engineering, land transport (railway and highway transport), robotics, etc. and exposed data to be able to contribute to the research area, to permit to enhance the intellectual performance, to provide the engineer with simple and efficient mathematical apparatus.

Introduction. In computational experiment for nonlinear dynamics of discrete mechanical systems in spatial motion to the algorithms’ representation, there are special requirements, which can be satisfied by an appropriate choice of variables and new organization of calculation process. The organization of calculation process is defined by the mathematical model of technical specification formed on the ground of traditional mathematical apparatus: vector algebra, quaternion algebra, calculus of tensors, theory of screws, matrix calculus, and, in particular, matrices equivalent to quaternions. Particular quaternionic matrices’ types were examined by R. Bellman [1], A. Maltsev [2], G. Korenev [3], N. Kilchevskiy [4]. Quaternionic matrices found application in exposing the principles of symmetry in physics [5, 6], in numerical calculation for attitude control [7, 8], in relative quaternions calculation [9], in theory of finite rotation [10, 11], in theory of inertial guidance [12, 13], in kinematics and dynamics of solid bodies [14 - 18]. Yet, methodical fundamental research for quaternionic matrices’ calculation elements (properties, operations) and the sphere of their possible 11

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application in vector algebra was not so far carried out. It is known that the vector form of algorithms’ representation for problem solution in analytical dynamics is basic, and computer technologies application implies the introduction of an established reference system and the reduction of algorithms’ vector notation to a coordinate of matrix form. Consequently, this research is motivated and justified, being focused on efficiency improvement of computational experiment in problems related to nonlinear dynamics of solid bodies’ systems. The work objective is to work out the quaternionic matrices’ calculation elements and their application in vector algebra as a tool for designing symbolic models exclusively adapted for modern computer technologies of calculation experiment [19, 20]. According to the conception of symbolic models’ matrix representation in computational experiment the finite set of quartic monomial matrices is established, which is put in correspondence with the four-dimensional orthonormal basis and creates a multiplicative group. Two noncommutative octic subgroups are fixed on set of monomial matrices isomorphous to the group of quaternions [21]. It is demonstrated that the introduced set of four quatric quaternionic matrices is isomorphous to the quaternions algebra and generalizes the vector algebra on the plane and in three-dimensional space. The formulas are found for matrix representation of the set of complex vector and scalar products of vector algebra. The suggested method of matrix representation of complex vector and scalar products permits also to find systematically the vector algebra identities correlated with the known results, including the Lagrange identity, Euler-Lagrange identity, Gram determinant and other formulas. Formulation of the problem Applying mathematical induction, the procedure of vector representation of associative products for various and conjugate quaternionic matrices is established. Expanded symbolic formulas are found, which establish the equivalent correspondences for quaternionic matrices’ associative products and vector algebra multiplicative compositions. Here the problem of the vector representation of quaternionic matrices’ associative products is regarded as an inverse one. Detailed procedures are provided, and the expanded symbolic formulas are established. The formulas reflect the equivalent correspondences of the set of the quaternionic matrices’ associative products to vector algebra multiplicative compositions containing complex vector and scalar products of several vectors. The compositions of vector matrices’ multiplicative sets equivalent to the algebraic sums’ products of conjugate quaternionic matrices are examined. For the examined compositions, vector representations are found, corresponding to associative and multiplicative vector matrices’ combinations. The vector algebra identical equations are set, which are defined by the matrix products’ associative property. Compositions of vector matrices’ multiplicative combinations t

The quaternionic matrices defined by the basis Ei и Ei with a scalar part equal to zero are examined, i.e., equivalent to vector and opposite to vector:

0 a1 A0  a2 a3

a1 0 a3 a2

a2 a3 0 a1

a3 0 a2 a1 , A0t  a1 a2 0 a3

a1 0 a3 a2

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a2 a3 0 a1

a3 a2 . a1 0

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The vector in three-dimensional space is represented as a matrix  4 1 (column vector): 0 a a0  1 . a2 a3

0 a

a1 a2 a3

The established algebraic sums’ products of conjugate vector matrices are set, and the appropriate multiplicative combinations’ compositions are set. For example: – for two vectors:

1. 2.

 A  A b  A  A b 0

t 0

 A0b0  A0t b0 ;

t 0

 A0b0  A0t b0 ;

– for three vectors:

   2.  A  A  B  B  c 3.  A  A  B  B  c 4.  A  A  B  B  c

1. A0  A0t B0  B0t c0  A0  B0  c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0 , 0

t 0

 A0  B0  c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0 ,

t 0

 A0  B0  c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0 ,

t 0

 A0  B0  c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0 .

– for four vectors we obtain respectively:







1. A0  A0t B0  B0t C0  C0t d0  A0 B0C0d0  A0 B0t C0d 0  A0t B0C0d 0  A0t B0t C0d 0   A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 ,



2. A0  A0t



 B





 B0t C0  C0t d0  A0 B0C0d 0  A0 B0t C0d 0  A0t B0C0d 0  A0t B0t C0d 0 





 A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 ,

3. A0  A0t B0  B0t C0  C0t d0  A0 B0C0d0  A0 B0t C0d0  A0t B0C0d 0  A0t B0t C0d 0   A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 ,

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

4. A0  A0t



 B





 B0t C0  C0t d0  A0 B0C0d 0  A0 B0t C0d 0  A0t B0C0d 0  A0t B0t C0d 0 





 A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 ,

5. A0  A0t B0  B0t C0  C0t d0  A0 B0C0d0  A0 B0t C0d0  A0t B0C0d 0  A0t B0t C0d 0   A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d0  A0t B0t C0t d 0 ,







6. A0  A0t B0  B0t C0  C0t d0  A0 B0C0d0  A0 B0t C0d 0  A0t B0C0d 0  A0t B0t C0d 0   A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 ,







7. A0  A0t B0  B0t C0  C0t d0  A0 B0C0d0  A0 B0t C0d0  A0t B0C0d 0  A0t B0t C0d 0   A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 ,







8. A0  A0t B0  B0t C0  C0t d0  A0 B0C0d0  A0 B0t C0d 0  A0t B0C0d 0  A0t B0t C0d 0   A0 B0C0t d0  A0 B0t C0t d0  A0t B0C0t d 0  A0t B0t C0t d 0 and so on for five and more vectors. The compositions of vector matrices’ associative and multiplicative combinations The compositions of vector matrices’ associative and multiplicative combinations are built with regard to the matrix products’ associative property. For two vectors, the vector matrices’ multiplicative combination is the only one:

1.1. 1.2.

A A

  A b

 A0t b0  ( A0b0 )  ( A0t b0 ); t 0

 ( A0b0 )  ( A0t b0 ).

For three vectors, two vector matrices’ multiplicative and associative combinations are possible:

  1.2.  A  A  B 1.3.  A  A  B 1.4.  A  A  B

  B c  B c  B c

     A   B  c   A   B  c   A   B  c   A   B  c ,  A   B  c   A   B  c   A   B  c   A   B  c ,  A   B  c   A   B  c   A   B  c   A   B  c .

1.1. A0  A0t B0  B0t c0  A0   B0  c0   A0  B0t  c0  A0t   B0  c0   A0t  B0t  c0 , 0

t 0

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  2.2.  A  A  B 2.3.  A  A  B 2.4.  A  A  B

  B c  B c  B c

   A  B c  A  B c  A  B c

   A  B c  A  B c  A  B c

   A  B c ,  A  B c ,   A  B c .

2.1. A0  A0t B0  B0t c0   A0  B0   c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0 , 0

t 0

  A0  B0   c0

t 0

  A0  B0   c0

t 0

  A0  B0   c0

t 0

For four vectors, the following five vector matrices’ associative and multiplicative combinations are possible:

A 1.1.

 A0t

A  1.2.

 A0t

A 1.3.

 A0t

 B





 B0t C0  C0t d0  A0  B0  C0 d0   A0  B0t  C0 d 0    A0t  B0 C0 d 0 

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,         0

 B





 B0t C0  C0t d0  A0  B0  C0 d 0   A0  B0t  C0 d 0    A0t  B0 C0 d 0  

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,         0

 B





 B0t C0  C0t d0  A0  B0  C0 d0   A0  B0t  C0 d 0    A0t  B0 C0 d 0  

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,        

A 1.4.

 A0t

A  1.5.

 A0t

A 1.6.

 A0t

A 1.7.

 A0t

A 1.8.

 A0t

 B





 B0t C0  C0t d0  A0  B0  C0 d0   A0  B0t  C0 d 0    A0t  B0 C0 d 0  

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,         0

 B





 B0t C0  C0t d0  A0  B0  C0 d0    A0  B0t  C0 d 0    A0t  B0 C0 d 0   

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,         0

 B





 B0t C0  C0t d0  A0  B0  C0 d 0   A0  B0t  C0 d 0    A0t  B0 C0 d 0  

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,         0

 B





 B0t C0  C0t d0  A0  B0  C0 d0   A0  B0t  C0 d 0    A0t  B0 C0 d 0  

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,         0

 B





 B0t C0  C0t d0  A0  B0  C0 d0   A0  B0t  C0 d 0    A0t  B0 C0 d 0  

















 A0t  B0t  C0 d0    A0  B0 C0t d 0   A0  B0t C0t d 0   A0t  B0 C0t d 0   A0t  B0t C0t d 0  ,        

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A 2.1.

 B  B C  C  d  A  B C  d   A  B C  d   A  B C  d    A  B C  d   A   B C  d   A   B C  d   A   B C  d   A   B C  d  ,            A  A  B  B C  C  d  A  B C  d   A  B C  d   A  B C  d   2.2.  A  B C  d   A   B C  d   A   B C  d   A   B C  d   A   B C  d  ,           A  A  B  B  C  C  d  A  B C  d   A  B C  d   A  B C  d      2.3.  A  B C  d   A   B C  d   A   B C  d   A   B C  d   A   B C  d  ,           0

t 0

 A0t

t 0

A

t 0

  

t 0



t 0



t 0

 

t 0

 

t 0

 A0t B0  B0t C0  C0t d0  A0  B0C0  d0   A0  B0t C0 d0   A0t  B0C0  d0     2.4. A0t  B0t C0 d0   A0  B0C0t d0   A0  B0t C0t d 0   A0t  B0C0t d 0   A0t  B0t C0t d 0  ,           0

A 2.5.













 B  B C  C  d  A  B C  d   A  B C  d   A  B C  d    A  B C  d   A   B C  d   A   B C  d   A   B C  d   A   B C  d  ,           A  A  B  B  C  C  d  A  B C  d   A  B C  d   A  B C  d      2.6.  A  B C  d   A   B C  d   A  B C  d   A   B C  d   A   B C  d  ,           A  A  B  B  C  C  d  A  B C  d   A  B C  d   A  B C  d      2.7.  A  B C  d   A   B C  d   A   B C  d   A   B C  d   A   B C  d  ,            A  A  B  B C  C  d  A  B C  d   A  B C  d   A  B C  d   2.8.  A  B C  d   A   B C  d   A   B C  d   A   B C  d   A   B C  d  ,           A  A  B  B  C  C  d   A B  C  d   A B  C  d   A B  C  d       3.1.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,         A  A  B  B  C  C  d   A B  C  d   A B  C  d   A B  C  d       3.2.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,          A  A  B  B C  C  d   A B  C  d   A B C  d   A B C  d  3.3.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,         0

t 0

 A0t

t 0

t t 0 0

t 0

t t 0 0

t 0

t t 0 0

t 0

0 0

t 0

0 0

t 0

t 0 0

t 0

t 0 0

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t 0

t t 0 0

t 0

t t 0 0

t 0 0

t 0

t 0 0

t 0

t 0 0

t 0

t 0 0

t 0

t 0 0

t 0

t 0 0

0 0

t 0

t 0 0

0 0

t 0

0 0

t 0

0 0

t 0

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

A 3.4.

 B  B C  C  d   A B  C  d   A B C  d   A B C  d    A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,          A  A  B  B C  C  d   A B C  d   A B C  d   A B C  d  3.5.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,         A  A  B  B  C  C  d   A B  C  d   A B  C  d   A B  C  d       3.6.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,         A  A  B  B  C  C  d   A B  C  d   A B  C  d   A B  C  d       3.7.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,          A  A  B  B C  C  d   A B  C  d   A B C  d   A B C  d  3.8.   A B  C  d   A B  C  d   A B  C  d   A B  C  d   A B  C  d ,         0

 A0t

t t 0 0

t 0

t t 0 0

t 0

t t 0 0

t 0



t 0

0 0

 

t 0 0

t 0



t 0

t 0 0

t t 0 0

t 0

t t 0 0

t 0 0

t 0

t t 0 0

t 0 0

t 0

t 0 0

t t 0 0

t 0

t 0 0

t t 0 0

t 0

t 0 0

t 0

0 0

t 0

0 0



t 0

t 0 0

t 0

0 0

t 0 0

t 0

t 0 0

t 0

t 0 0

t 0

0 0

t 0

0 0

t 0

t t 0 0

A

t 0 0

t 0

0 0

t 0

0 0

t 0

0 0

t 0

t t 0 0

t 0



 A0t B0  B0t C0  C0t d0   A0  B0C0  d0   A0 B0t C0  d 0   A0t  B0C0   d 0    4.1.   A0t B0t C0  d0   A0 B0C0t  d0   A0 B0t C0t  d 0   A0t B0C0t  d 0   A0t B0t C0t  d 0 ,           0



A 4.2.















 B  B C  C  d   A  B C  d   A  B C  d   A  B C  d    A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,            A  A  B  B C  C  d   A  B C  d   A  B C  d   A  B C  d  4.3.   A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,           A  A  B  B  C  C  d   A  B C   d   A  B C   d   A  B C  d     4.4.   A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,           A  A  B  B  C  C  d   A  B C   d   A  B C   d   A  B C   d     4.5.   A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,            A  A  B  B C  C  d   A  B C  d   A  B C  d   A  B C  d  4.6.   A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,           0

 A0t t 0

t 0

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A 4.7.

 B  B C  C  d   A  B C  d   A  B C  d   A  B C  d    A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,            A  A  B  B C  C  d   A  B C  d   A  B C  d   A  B C  d  4.8.   A  B C   d   A  B C   d   A  B C  d   A  B C  d   A  B C  d ,           0

 A0t t 0

t 0

A  A  B  B  C  C  d   A B  C d    A B   C d    A B  C d    5.1.   A B   C d    A B   C d    A B  C d    A B C d    A B C d  ,  A  A  B  B C  C  d   A B C d    A B  C d    A B  C d   5.2.   A B   C d    A B   C d    A B  C d    A B  C d    A B C d  ,  A  A  B  B C  C  d   A B C d    A B  C d    A B  C d   5.3.   A B   C d    A B   C d    A B  C d    A B  C d    A B C d  ,  A  A  B  B C  C  d   A B C d    A B  C d    A B  C d   5.4.   A B   C d    A B   C d    A B  C d    A B C d    A B C d  ,  A  A  B  B C  C  d   A B C d    A B  C d    A B  C d   5.5   A B   C d    A B   C d    A B  C d    A B C d    A B C d  , A  A  B  B  C  C  d   A B  C d    A B   C d    A B  C d    5.6.   A B   C d    A B   C d    A B  C d    A B C d    A B C d  ,  A  A  B  B C  C  d   A B C d    A B  C d    A B  C d   5.7.   A B   C d    A B   C d    A B  C d    A B C d    A B C d  ,  A  A  B  B C  C  d   A B C d    A B  C d    A B  C d   5.8   A B   C d    A B   C d    A B  C d    A B C d    A B C d  t 0

t t 0 0

0 0

t 0

t t 0 0

0 0

t t 0 0

t 0

t t 0 0

0 0

t 0

0 0

t 0 0

0 0

t 0

t 0 0

t 0

0 0

t 0

0 0

t 0 0

t 0

0 0

t t 0 0

t 0

0 0

t 0

t 0 0

0 0

t 0

t 0 0

0 0

t 0

t 0 0

0 0

t 0

0 0

t t 0 0

t 0

0 0

t 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

0 0

t 0 0

t t 0 0

t 0 0

and so on for five and more vectors. Vector representation for compositions of vector matrices’ associative and multiplicative combinations

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With the arranged compositions of associative and multiplicative vector matrices’ combinations, the appropriate multiplicative vector algebra compositions containing scalar and vector products are found. For two vectors, we obtain:

1.1.

1.2.

( A0  b0 )  ( A0t  b0 )  2

a b 0

( A0  b0 )  ( A0t  b0 )  2

a b

For three vectors, we obtain respectively:









1.1. A0   B0  c0   A0  B0t  c0  A0t   B0  c0   A0t  B0t  c0  4

0 , a  b  c  a  b  c 

















0 , 0









0 a  b  c 

1.2. A0   B0  c0   A0  B0t  c0  A0t   B0  c0   A0t  B0t  c0  4 1.3. A0   B0  c0   A0  B0t  c0  A0t   B0  c0   A0t  B0t  c0  4 1.4. A0   B0  c0   A0  B0t  c0  A0t   B0  c0   A0t  B0t  c0  4

and





































0 , 0













0 . a  b   c  b a  c 

2.1.  A0  B0   c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0  4 2.2.  A0  B0   c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0  4 2.3.  A0  B0   c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0  4 2.4.  A0  B0   c0  A0  B0t  c0  A0t  B0  c0  A0t  B0t  c0  4

0 , b a  c   c  a  b 

a  b   c 0

It is convenient to systematize as a table the results provided here (Table 1).

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Table 1. Calculation results. №

A0 B0 c0

A0 B0t c0

A0t B0 c0

A0t B0t c0

( A0  A0t )( B0  B0t )c0

( A0  A0t )( B0  B0t )c0

( A0  A0t )( B0  B0t )c0

( A0  A0t )( B0  B0t )c0

№

A0 ( B0 c0 )

A0 ( B0t c0 )

A0t ( B0 c0 )

A0t ( B0t c0 )



1.1.

1.2.

1.4.

( A0 B0 )c0

( A0 B0t )c0

( A0t B0 ) c0

( A0t B0t ) c0

2.2.

a  b   c 0 0 0

2.3.

2.4.

0  b  c  a

0 b a  c   c  a  b 



2.1.

a  b  c 

0 0

1.3.

№

0 a  b  c 

0 a  b   c  b a  c 

For four vectors the results obtained are systematized in form of tables (Table 2 – Table 7). Table 2. Multiplication results. MMSE Journal. Open Access www.mmse.xyz

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№

A0 B0C0 d0

A0 B0t C0 d0

A0t B0C0 d0

A0t B0t C0 d0

A0 B0C0t d0

A0 B0t C0t d0

№

A0t B0C0t d0

A0t B0t C0t d0

2 3

A A A A A A A A

 A0t

t 0

 B  A  B  A  B  A  B  A  B  A  B  A  B  A  B

  B  C  B  C  B  C  B  C  B  C  B  C  B  C

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  C d  C d  C d  C d  C d  C d  C d

 B0t C0  C0t d0 t 0

t 0

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Table 3. Multiplication results.

A0t [ B0 (C0 d0 )]

A0t [ B0t (C0 d0 )]

A0 [ B0 (C0t d0 )]

A0 [ B0t (C0t d0 )]

1.3

1.4

1.5

1.6

1.7

1.8

№

A0 [ B0 (C0 d0 )]

A0 [ B0t (C0 d0 )]

1.1

1.2

№



A0t [ B0 (C0t d0 )] A0t [ B0t (C0t d0 )]

  a  b  c  d 

1.1

1.2

1.3

1.4

1.5

0 0

1.6

0 0

0   a  b  c  d 

0 0 0

a b   c  d  





a  b  c  d  1.7

1.8



0 

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



a  b  c  d 

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Table 4. Multiplication results. №

A0 [( B0C0 )d0 ]

A0 [( B0t C0 )d0 ]

A0t [( B0C0 )d0 ]

A0t [( B0t C0 )d0 ]

A0 [( B0C0t )d0 ]

A0 [( B0t C0t )d0 ]

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

№

A0t [( B0C0t )d0 ]

A0t [( B0t C0t )d0 ]

2.1

2.2

2.3

2.4

 8

a   b  c   d    a  c   b  d  0







a   b  c  d    a  c  b  d  



0 0



a  b  c  d  

2.5

2.6

2.7

2.8



0 0 0 0

 a  c   b  d    b  c  a  d  0 0  a  c   b  d    a  d  b  c 

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

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Table 5. Multiplication results. №

[( A0 B0 )C0 )]d0

[( A0 B0t )C0 ]d0

[( A0t B0 )C0 ]d0

[( A0t B0t )C0 ]d0

[( A0 B0 )C0t ]d0

[( A0 B0t )C0t ]d0

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

№

[( A0t B0 )C0t ]d0

[( A0t B0t )C0t ]d0

3.1

3.2

3.3

3.4

   a  b  c  d 



0 0



8

   























a b   d c   a  c   d  b   a b  c  d 

3.6

3.8

0    



3.5

3.7



 a b c   d   a b d c    

0 0 0 0

 a  b   c   d  8  0

0  a  c   d  b  a  b c  d  

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





Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Table 6. Multiplication results. №

[ A0 ( B0C0 )]d0

[ A0 ( B0t C0 )]d0

[ A0t ( B0C0 )]d0

[ A0t ( B0t C0 )]d0

[ A0 ( B0C0t )]d0

[ A0 ( B0t C0t )]d0

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

№

[ A0t ( B0C0t )]d0

[ A0t ( B0t C0t )]d0

4.1

4.2

4.3

4.4

4.5









a  b  c   d   a  c  b  d  8 



    

   

    

    

   

     











 









a bc  d  a  bc  d  a  b c  d  b  d   a c   

0 0

0 a  b  c   d  8

0 0

4.6

4.7

4.8.

0 0

 a  c   b  d   b  c  a  d  0

0 a  c  b  d  a  d b  c



Table 7. Multiplication results. MMSE Journal. Open Access www.mmse.xyz

120

 

 



Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

№

( A0 B0 )(C0 d0 )

( A0 B0t )(C0 d0 )

( A0t B0 )(C0 d0 )

( A0t B0t )(C0 d0 )

( A0 B0 )(C0t d0 )

( A0 B0t )(C0t d0 )

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

№

( A0t B0 )(C0t d0 )

( A0t B0t )(C0t d0 )



  a  b  c  d 

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

0 0   a  b  c  d  8

 a  b   c  d   a  c  d  b



0 0 0 0

a  b   c  d  0







a  c  d  b  a  b c  d  

And so on for five and more vectors.

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

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The representation of algebraic sums’ products of vector matrices conjugate to vectors’ multiplicative compositions Using the associative property of matrix products’ and putting the obtained results in correspondence, we find the following vector and matrix correspondences for two vectors:





a b





1. A0  A0t b0  2

2. A0  A0t b0  2

a b

For three vectors:







1. A0  A0t B0  B0t c0  4

0 , a  b  c  a  b  c 













0 , 0







0 . a  b  c 

2. A0  A0t B0  B0t c0  4 3. A0  A0t B0  B0t c0  4 4. A0  A0t B0  B0t c0  4

and



















0 , 0







0 . a  b   c  b a  c 

1. A0  A0t B0  B0t c0  4 2. A0  A0t B0  B0t c0  4 3. A0  A0t B0  B0t c0  4 4. A0  A0t B0  B0t c0  4

0 , b a  c   c  a  b 

a  b   c 0

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





0 0 4 , a  b  c  a  b   c  b a  c 

1. A0  A0t B0  B0t c0  4



 B





2. A0  A0t





 B0t c0  4

3. A0  A0t B0  B0t c0  4







4. A0  A0t B0  B0t c0  4

0 0

a  b  c  0

4

a  b  c 

4

a  b   c

b a  c   c a  b 

For four vectors:

  a  b  c  d  1 A0  A0t B0  B0t C0  C0t d 0   8 0







a   b  c   d    a  c   b  d 

1. 



  a  b  c  d  0



a   b  c   d   a  c   b  d    a  b  c  d      ; 0 0







1 0 0 A0  A0t B0  B0t C0  C0t d 0    8   a  b  c  d    a  b  c  d  2. 



0 0    a  b   c   d   a  b   d  c a   b  c   d    a  c   b  d      0

a  b  c   d    a   b  c    d   a   b  c  d   b  d   a  c 

 A  A  B 8

t 0





t t 0  B0 C0  C0 d 0 

0 0



0 0

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

0 0



0 0



0 0

;

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





1 0 0 A0  A0t B0  B0t C0  C0t d 0    8 a b   c  d    a  b  c   d  4. 



 a  b   d  c   a  c   d  b   a  b   c  d       0



0  a  b  c   d 

;

 a  b    c  d   a   c  d  b













1 0 0 0 0 0 A0  A0t B0  B0t C0  C0t d0      ; 8 0 0 0 0 0

1 0 0 0 0 0 A0  A0t B0  B0t C0  C0t d0      ; 8 0 0 0 0 0 a  b   c  d   1 A0  A0t B0  B0t C0  C0t d 0   8 0



7. 









 a  c   b  d    b  c  a  d  0



 a  b   c   d     0 

 a  b   c  d  ; 0



1 0 A0  A0t B0  B0t C0  C0t d0   8 a  b   c  d   8. 



0 0    a  c   b  d    a  d  b  c   a  c   d  b   a  b  c  d  0 0  .   a  c b  d  a  d b  c       a   c  d  b   a  b  c  d 

And so on for five and more vectors. Setting vector algebra identical equations From previously established equalities of vectors’ multiplicative compositions, the following vector algebra equalities for three vectors are set: MMSE Journal. Open Access www.mmse.xyz

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







1. a  b  c  b  a  c   c a  b ;



 



2. a  b  c  a  b  c ; 3.



0  0;

 



4. a b  c  a  b  c  b  a  c  .

Whence it follows:

 a  b   c  b  a  c   a b  c  , or, using a second-order determinant, we obtain formulas in ordered recording:

a  b  c   (a  b )  c 

a b

a c

b c

a c

; .

For four vectors from the first group of equalities we obtain:



 c  d   a  b  c   d    a  c  b  d ;



 c  d   a  b  c   d   a  c  b  d ;





1.1.1.  a  b 1.1.2.  a  b















1.1.3. a   b  c  d    a  c  b  d  a  b  c   d   a  c  b  d ;



i.e.,







1.1.1. a   b  c  d    a  b



 c  d    a  c  b  d 

a   b  c   d  



a  c 

(c  d )

 a  b  b  d 







a c d c

 

1.1.2.  a  b  c   d   a  c  b  d  a  b



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a b ; d b

 c  d  ,

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

Whence it follows:









1.1.3. a   b  c  d    a  b  c   d .





From the second group of equalities we obtain:



2.1.1.  a  b

 c  d   a  b  c   d    a  c  b  d ;

  c  d    a  b   c   d   a  b   d  c ;   a  b  c  d   2.1.3.  a  b  c   d    a   b  c   d   a   b  c  d   b  d   a  c  ; 2.1.2.  a  b







 







2.2.1. a   b  c  d    a  c  b  d   a  b  c   d   a  b  d  c ; 2.2.2.



a   b  c   d    a  c   b  d  

 a  b  c   d    a   b  c   d   a   b  c  d   b  d   a  c 

And        a  b   c   d   a  b   d  c       2.3.1.         a  b  c   d   a   b  c    d  a   b  c   d   b  d            

 a  c .

Whence it follows:









a c d c

a b ; d b

2.1.1. a   b  c  d    a  c  (b  d )  a  b (c  d )



a   b  c   d  





a  c  a  b 

 c  d  b  d  









2.1.2.  a  b  c   d  [ a  b  d ]c  a  b (c  d )



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

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c  a  b   c   d    c d



2.1.3.  a  (b  c )   d  b  d

a b

a  b   d

;

  a  c    a  b  c  d   a  b  c  d  a b  c   d 

a c  a  (b  c )   d  c d

d a a b  ; b  d d  b  c  a  b  c 

and also







 



2.2.1. a  (b  c )  d    a  b  c   d   a  c  b  d   a  b  d   c



a  (b  c )  d    a  b   c   d 

2.2.2.

a c

a  b   d

b d

;

a  (b  c )  d   a   b  c    d 

  a  c   b  d    b  d   a  c   a  b  c   d   a   b  c  d

a  (b  c )  d    a   b  c   d 

2.3.1.

a  b  c 

b  c   d

(a  b )  c   d   a   b  c    d   

  a  b   d  c   b  d   a  c   a  b  c   d    a   b  c  d

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(a  b )  c   d  a  b  c   d 

a c

b d

a  b   d



a  b  c 

b  c   d

The third group of equalities is a trivial one. From the fourth group of equalities we obtain:









4.1.1. a b  c  d   a  b  c  d  ;

















4.1.2. a b  c  d    a  b  d  c   a  c   d  b   a  b  c  d ;      



 

 







4.1.3. a b  c  d   a  b  c  d  a  c  d  b



and also













4.2.1. a  b  c  d    a  b  d  c   a  c   d  b   a  b  c  d ;      







 







4.2.2. a  b  c  d   a  b  c  d  a  c  d  b





And

4.3.1.

 a  b   d  c   a  c   d  b    a  b   c  d       

  a  b    c  d    a   c  d   b .

Whence it follows:













4.1.2.  c  d  b  a   a  c   d  b   a  b  d  c   a  b  c  d  0       Or



c  d   a c  d   b a  b   c a  b   d MMSE Journal. Open Access www.mmse.xyz

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0

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a b c d a b c d1 and also 1 1 1  0. a2 b2 c2 d 2 a3 b3 c3 d3



 











4.1.3. a  b  c  d  a b  c  d   a  c  d  b



a  b   c  d   b 



 

c  d 

 



a  c  d 

;





4.3.1. a  b  c  d   a  b  d  c   a  b  c  d



 a  b   c  d  

a  b   c

a  b   d

The fifth and sixth groups of equalities are trivial. From the seventh group of equalities we obtain:







  





 







 

 a  d ;







 

7.1.1. a  b  c  d    a  c  b  d  b  c



 a  d ;

7.1.2. a  b  c  d    a  b  c   d ;





7.1.3. a  b  c  d   a  b  c  d



and also





7.2.1.  a  b  c   d   a  c  b  d  b  c







7.2.2.  a  b  c   d  a  b  c  d



And

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







 

7.3.1. a  b  c  d   a  c  b  d  b  c

 a  d .

Whence it follows:





7.1.1. a  b  c  d  











7.2.1.  a  b  c   d 





7.3.1. a  b  c  d 

a c

a d

b c

b d

a c

a d

b c

b d

a c

a d

b c

b d

;

From the eighth group of equities we obtain:















 

b  c ;



 c  d ;



 c  d 

8.1.1. a  b  c  d    a  c  b  d  a  d



8.1.2. a  b  c  d    a  c   d  b  a  b  





8.1.3. a  b  c  d    a  c  d  b  a  b



and also 8.2.1.  a  c  b  d  a  d



 

b  c    a  c   d  b   a  b c  d ;



 

b  c   a   c  d  b   a  b c  d ;



 c  d   a   c  d  b   a  b  c  d .

8.2.2.  a  c  b  d  a  d 8.3.1.  a  c   d  b  a  b Whence it follows:

a  b  (c  d )  

a c b с

b a d  a b b d

c d a  c  d 

Summarizing, we point out that some of the provided results correspond to the Lagrange identity:

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a c

 a  b   c  d   b  c particularly, to

a d b d

a  c и b  d , the Euler-Lagrange formula:

 a  b 2  a 2b 2   a  b 2 , The Gramian matrix:

a  b   a  b   

a a

a b

b a

b b

and other known correlations [22]. Construct of the equalities connecting five and more vectors is obvious but is lengthy for representation. Summary. The research objective is to elaborate the elements of calculation of quaternionic matrices and their application to vector algebra. The problems set: to find the equivalent correspondences to associative products of quaternionic matrices and vector algebra multiplicative compositions; to represent complex vector and scalar vector algebra products with quaternionic matrices; to represent complex vector and scalar vector algebra products with identical equations are solved. The offered formulas of complex vector and scalar products’ representation and the corresponding algorithms as quaternionic matrices acquire symmetry, invariant property, compactness and universality, which makes the programming faster, facilitates verification and makes scientific research more convenient, i.e. improves the productivity of intellectual labor. References [1] Bellman, R. Introduction to matrix analysis, Second edition, Book code: CL19, Series: Classics in Applied Mathematics, 1997, 403 p. DOI: http://dx.doi.org/10.1137/1.9781611971170. [2] Mal'tsev, A.I. Osnovy linejnoj algebry [Fundamentals of linear algebra], Moscow, Nauka Publ., 1970, 400 p. (in Russian).  [3] Korenev, G.V. Tenzornoe ischislenie [Tensor calculus], MFTI Publ., 1995, 240 p. (in Russian). [4] Kil'chevskij, N.A. Kurs teoreticheskoj mexaniki [Course of theoretical mechanics], Moscow, Nauka Publ., 1977, Part 1, 480 p., Part 2, 544 p. (in Russian). [5] Elliot, J.P., Dawber, P.G. Symmetry in physics, Vol. 1: Principles and Simple Applications, Oxford University Press, 1985, 302 p., Vol. 2: Further Applications, Oxford University Press, 1985, 298 p. [6] Berezin, A.V., Kurochkin, Yu.A., Tolkachev, E.A. Kvaterniony v relyativistskoj fizike [Quaternions in relativistic physics], Moscow, Editoreal Publ., 2003, 200 p. (in Russian). [7] Branets, V.N., Shmyglevskij, I.P. Primenenie kvaternionov v zadachax orientatsii tverdogo tela [The use of quaternions in problems of solid-state orientation], Moscow, Nauka Publ., 1973, 320 p. (in Russian).

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[8] Raushenbax, B.V., Tokar', E.N. Upravlenie orientatsiej kosmicheskix apparatov [The orientation of the spacecraft management], Moscow, Nauka Publ., 1974, 600 p. (in Russian). [9] Mejo, R.A. Perexodnaya matritsa dlya vychisleniya otnositel'nyx kvaternionov [The transition matrix to calculate the relative quaternion], Raketnaya texnika i kosmonavtika [Rocketry and Astronautics], 17 (3), 1979, p. 184-189. (in Russian). [10] Lur'e, A.I. Analiticheskaya mexanika [Analytical mechanics], Moscow, Fizmatgiz Publ., 1961, 824 p. (in Russian). [11] Plotnikov, P. K., Chelnokov, Yu. N. Primenenie kvaternionnyx matrits v teorii konechnogo povorota tverdogo tela [Application of quaternion matrices in the final turn in solid state theory], Sbornik nauchn.-metod. statej po teoret. mexanike. − Moscow, Vysshaya shkola Publ., Vol. 11, 1981, p. 122 − 128. (in Russian). [12] Ishlinskij, A.Yu. Orientatsiya, giroskopy i inertsial'naya navigatsiya [Orientation, gyroscopes and inertial navigation], Moscow, Nauka Publ., 1976, 672 p. (in Russian). [13] Onischenko, S.M. Primenenie giperkompleksnyx chisel v teorii inertsial'noj navigatsii. Avtonomnye sistemy [The use of hyper complex numbers in the inertial navigation theory. Standalone systems], Kyiv, Naukova dumka Publ., 1983, 208 p. (in Russian). [14] Pars, L.A. A Treatise on analytical dynamics, Ox Bow Pr. Publ., 1981, 641 p. [15] Chelnokov, Yu.N. Kvaternionnye i bikvaternionnye modeli i metody mexaniki tverdogo tela i ix prilozheniya. Geometriya i kinematika dvizheniya [Quaternion and biquaternions models and methods of solid mechanics and their applications. The geometry and kinematics motion], Moscow, Fizmatgiz Publ., 2006, 512 p. (in Russian). [16] Kravets, T.V. Based on Gibbs vector solution of spatial angular stabilization of solid problem, Avtomatika 2001: Sbornik nauchnyx trudov konferentsii [Automation 2001: Proceedings of the Conference], Odessa Publ., 2001, Volume 2, p. 20. [17] Kravets, V.V., Kravets, T.V. On the nonlinear dynamics of elastically interacting asymmetric rigid bodies, Int. Appl. Mech., 2006, 42(1), p. 110- 114. [18] Kravets, V.V., Kravets, T.V., Kharchenko, A.V. Using quaternion matrices to describe the kinematics and nonlinear dynamics of an asymmetric rigid body, Int. Appl. Mech., 2009, 45 (223), DOI: 10.1007/s10778-009-0171-1. [19] Pivnyak, G.G., Kravets, V.V., Bas, K.M., Kravets, T.V., Tokar', L.A. Elements of calculus quaternionic matrices and some applications in vector algebra and kinematics, MMSE Journal, 3, March 2016, p.p. 46-56. ISSN 2412-5954, Open access www.mmse.xyz, DOI 10.13140/RG.2.1.1165.0329. [20] Kravets, V.V., Bass, K.M., Kravets, T.V., Tokar L.A. Dynamic design of ground transport with the help of computational experiment, MMSE Journal, 1, October 2015, p.p. 105 - 111. ISSN 24125954, Open access www.mmse.xyz, DOI 10.13140/RG.2.1.2466.6643. [21] Kravets, V., Kravets, T., Burov, O. Monomial (1, 0, -1)-matrices-(4х4). Part 1. Application to the transfer in space. Lap Lambert Academic Publishing, Omni Scriptum GmbH&Co. KG., 2016, 137 p. ISBN: 978-3-330-01784-9 [22] Korn, G., Korn, T. Spravochnik po matematike dlya nauchnyh rabotnikov i inzhenerov [Mathematical Handbook for Scientists and Engineers], Moscow, Nauka Publ., 1984, 832 p. (in Russian). Cite the paper Victor Kravets, Tamila Kravets, Olexiy Burov (2017). Identities of Vector Algebra as Associative Properties of Multiplicative Compositions of Quaternion Matrices. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.47.87.900

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Efficient Transient Modes of Synchronous Drive for Mining and Smelting Mechanisms12 V.А. Borodai1, a, R. О. Borovyk2, b, О.Yu. Nesterova3, c 1 – Candidate of Sciences (Tech.), State Higher Educational Institution "National Mining University", Dnipro, Ukraine 2 – Engineer, State Higher Educational Institution "National Mining University", Dnipro, Ukraine 3 – PhD, State Higher Educational Institution "National Mining University", Dnipro, Ukraine a – Boroday_va@mail.ru b – borovikra@bigmir.net c – olnesterova1@rambler.ru DOI 10.2412/mmse.71.21.693 provided by Seo4U.link

Keywords: high-capacity mining and smelting mechanisms, impact load, synchronous electric drive, method for impact load compensation, parameters justification and optimization.

ABSTRACT. Development of starting system for synchronous motors of high-power mechanisms in mining and smelting industry, which enables proper starting characteristics and reasonable compensation of impact loads by means of synchronous drive. Mathematical modelling was applied for the determination of parameters of field winding with direct and indirect split and capacitors, as well as for substantiation of function of purpose choice and limiting the factors of influence for solving the problem of determination of field system parameters and springy mechanic components of synchronous drive. As based on the definite motor evidence, it was proved that it is possible to operate synchronous motors with split field winding and capacitors, which enable obtaining proper starting characteristic for the mechanism requirements. The needed installations for starting system and values of spring linkages rigidity for reasonable impact loads damping were also determined. The methods used enable determining parameters of field winding with indirect split and active-reactive resistance, as well as calculating the reasonable level of voltage forcing, time for field voltage reducing and order of elastic clutch rigidity under the conditions of design load increase. The use of new field windings enables start of high-power mechanisms and thus, prevents equipment from unplanned idle operation. It also makes it possible to improve productivity of operating mechanism by means of motor load increase in the stable operating mode, as well as improves drive energy characteristics. The peculiarity of electric circuit design for winding with direct split enables use of traditional technological process of pole coils production and does not require new production equipment. The use of field system with innovative control procedure and elastic clutch with the proper rigidity significantly decreases amortization of field windings and prevents emergency states of synchronous drive caused by dynamic impact overloads.

Introduction. It is obvious that economic performance of any production activity depends on high competitiveness of the output product. Traditionally, the goal is achieved by means of enterprise productivity increase, innovative technology implementation into the output product, involving energy saving and resource saving. Considering the fact that nowadays the price for new production equipment is near 20% of its annual power supply costs, we can state that the energy saving is the priority for industrial sphere. The possible way of problem solving is the use of modern electrical equipment with high performance index. The synchronous electric drive of controlled driving belongs to this type of equipment. If compared to other electric drives, the synchronous one has the following advantages: better power characteristic; high reliability resulting from significant air gap; high rigidity of speed-torque characteristic; low rate of rotation of driving shaft, which allows elimination of intermediate gears; low costs for drive control converters rather than frequency converters for total power motors. But 12

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the drives also have some disadvantages. They are as follows: the problem of secure triggering and decrease of the influence of impact loads in case of their alternate application. That is the reason for the urgency of the development of synchronous drive as based on the reasons mentioned above. It is known that the mining mechanisms of disintegrating cycle have the starting static moment of variable rate from 1,2 to 2,5 of the rating moment. As a rule, in such cases the problem of complicated start is solved either by the application of additional accelerating engine, which operate only during the starting period, or by choosing the motors of 15 â&#x20AC;&#x201C; 50% power reserve. Both methods have significant capital and power disadvantages. So, developers tend to use synchronous motors, as possessing significant advantages, in drives of high-power mining machines of disintegrating cycle. However, the problems of their start have not been solved yet. Direct asynchronous start at a full grid voltage is the simplest and the most widespread method of asynchronous stock engines start. The main peculiarity of the method is that the starting moment is mainly created by damper winding; the resistance rate of the last one is determined by the type of cross-section and resistivity of its rods. Thus, the changes of geometric parameters and rods material enable variation of total resistance of damper winding. The resistance provides the significant starting moment and decreased input torque for increased active resistance, and vice versa, for the opposite circuit settings. The rational circuit design for the requirements of the definite mechanism with high starting and input torque, is also possible. However, the main disadvantage of the method is significant starting current limiting the number of sequential starts and decreasing the reliability of motor windings. As based on the data of the traditional method of synchronous motor start, we can state that the general starting moment is created by rotor windings, where the main part is related to damper winding. In this case, the ratio of moment of field coil work, which is connected in an ordinary way, is not sufficient. Nevertheless, it is also known that it is possible to improve the startability of synchronous drive and redistribute voltage between rotor windings by means of drive circuit. As a result, the proposed methods allow reliability increase of the completely electromechanical system, as well as improvement of starting characteristic. As the methods of starting characteristic improvement for synchronous electric drives with overvoltage decrease, the windings split with concentrated and allocated connection of capacitors are applied [1]. The ways of reactance decrease of rotor windings enable forming of starting mechanic characteristic with respect to requirements of working mechanism, but trouble the traditional technological process of pole coils production under the industrial conditions. The analysis of existing methods has shown that the synchronous electric drives with improved starting characteristic have a range of advantages and disadvantages. The latter method can be pointed out as the most suitable for reconstruction of high power motors with explicit rotor poles. However, the disadvantage of complications of pole coils production for field coils limits their practical application. That is the reason for the need in designing of split windings with capacitors from both theoretical and practical points of view. It is known that the synchronous motors in high power technological facilities may have more than 20 ports. That is why the direct split of each pole coil can be substituted by indirect way of split [2]. The mentioned circuit design describes the drive circuit, which is shown at the Fig. 1. In such a case the motor drive circuit (Fig. 1 a) includes undivided pole coils 2, with series sequence and creation of separate groups of coils, which are closed-in through the every other pole, where RC-circuits are created between adjacent poles consisting of capacitor C and resistor R (Fig. 1, b). The external terminals according to the working principle, new construction [2] 5, 6 connected to the first and the last pole coils, are also connected to discharge variable resistor R 3, which can be switched by the communicator 4, does not differ from the previous one [1]. However, as for this case, the poles assembly and the process of parameters determination for the circuit of rotor windings substitution are simplified. This is explained by the availability of the coil on the pole, which does not differ from the classical one, and the magnetic conditions are equal for both cases. Owing to the fact, the MMSE Journal. Open Access www.mmse.xyz

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parameters of reactance of the definite pole coil can be determined as based on the published data provided by the producer.

X fi 

X ad  X fs 2p

, R fi 

R fs 2p

(1)

where X ad is reactance of armature reaction; X fs is reactance of dispersion of classical field coil; R fs is field active resistance; 2 р is the number of ports.

Lf Rf

RС

Lf Rf

С R

Lf Rf RС

RС

R 5 6

Fig. 1. Field coil of indirect split. The conditions mentioned above do not require the destruction of magnetic couples of pole coils. The influence of magnetic cohesion of damper and inductor windings with each field bobbin is mentioned as EMF component and, thus, is calculated for the first quadripole according to the compensation theorem. So, the analytical drive circuit is in the form of (Fig. 2). The complex impedances in its structure are calculated in the following way: Z fi  X fi  R fi is the impedance of pole coil; Z ci  r

mzf

j

is the impedance of traversal circuit, where r Zб б  Z б  s 2  C is additional active resistance; mzf convergence ratio of field resistance; б ; Z б are basic cyclic frequency and resistance; s; C are slip and capacitance.

Zc Zf

Fig. 2. Analytical circuit for field coil. MMSE Journal. Open Access www.mmse.xyz

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Zf Zc

Zc Zf

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The presence of various reactive resistances in the circuit (Fig. 2) makes it dependent on the rate of slip value. As a result, the current field impedance value for the process of starting can be calculated by means of power balance. The same as for the previous varieties of split winding, the circuit (Fig. 2) can not be analysed directly. To make it possible we used the abovementioned methods of transition from ladder circuits of passive two-ports to the proper long lines and further its substitution by the single line of the same parameters, and length, which is equal to the sum of lengths of its components (Fig. 3).

Zf` Zf`

Zf`

Zf` Zf`

Zf`

Zf` Zf` Zc

Zc Zf`

Zf`

Zf` Zf`

Fig. 3. Transformed circuit of field coil for interim quadripoles folding. In the proposed interim circuit the longitudinal circuit resistances are equal to the half of impedance Z of pole coil, i.e. Z fi `  fi . 2 For the transition from initial quadripoles to the quadripoles of T-type the auxiliary coefficient is Z fi `  0,5 . The direct transformation of initial T-type quadripoles into a long line determined  k  2Z f i ` requires the calculation of A-type coefficients

А1  1 

2Z f i ` Zс

2Z f i `   1 ; С1  ; D1  А1. ; В1  2Z f i ` 2  Zс  Zс 

and the parameters of the proper long line Z л 

(2)

В1 is wave impedance;  1  a cosh( А1 ) is the С1

parameter of a line. In case of reverse transformation the resistances of the adequate quadripole for the circuit of the folded unit are calculated with respect to the coefficients:

А  cosh(( p  1 )  1 ); В  Z л sinh(( p  1 )  1 ); С

sinh(( p  1 )  1 ) ; D  А. Zл

Then the impedances of quadripole are MMSE Journal. Open Access www.mmse.xyz

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(3)

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Z fv `

А 1 А 1 1 (1   k ); Z fn `  k ; Z fk ` . C C C

(4)

The final simplified split circuit with respect to folded units of quadripoles is transformed into the form of Fig. 4. Zfv`

Zf`

Zfv`

Zf`

Zfk`

Zf`

Zfn`

Zf`

R Fig. 4. Simplified circuit for field coil. To calculate it the empirical coefficients are determined in accordance with power balance

1  2

ZZ  ZZ1  ( Z fv ` Z fk ` Z fn `2Z f ` Z c ) ZZ 3  ZZ 2  ( Z fv ` Z fk ` Z fn `2Z f ` Z c )

1  2  1  2  ;

(5)

2  ( Z fn ` Z f ` Z c )  1 ( Z c  Z fk `) Z fv ` Z fk ` Z fn `2Z f ` Z c

,  2  2  2 ,

where ZZ  ( Z fn`  Z f `  Z c )  ( Z c  Z fk`) ; ZZ1  ( Z fn`  Z f `  Z c  R ) ; ZZ 2  Z fv`  Z fk` Z fn` 2Z f `  Z c  R ; ZZ 3  ( Z c  Z fk`)2

(6)

As based on them, the equivalent resistance of field coil is calculated and its parameters in the motor Re( Z fe ) substitution circuit are determined as: R fs  is active component of resistance; s X fs  j(Im( Z fe )  X ad ) is reactive component of resistance.

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Z fе  1 ( Zf `  Z fv`)  1 ( Zf `  R  Z fn`)  2

  ( 1   2 )2  Z fk ` 2 ( Zf `  Z fv`)  2

  2 ( Zf `  Z fn`)  ( 2  1 )2  Z c . 2

(7)

The studies of motor mathematical model have shown its functionality even under the conditions of connection to each port of capacitors of equal capacitance (Fig. 5). Thus, as based on the studies results for SDSZ-20-29-54-80-UHL4 motor with slightly split field coil, it was stated that the starting moment may reach 1,5 of its rated value for 4 μF capacitance value of capacitors and absence of active resistance. In addition to that, its starting current does not exceed the value of current for the motor in traditional connection.

M Mн

3.5 3

6.38

5.5

1.5

4.63

3.75 2.88

0.5

s 0

Iн

7.25

2.5

8.13

0.13 0.25 0.38

0.5

0.63 0.75 0.88

2 0

0.13 0.25 0.38

0.5

0.63 0.75 0.88

Fig. 5. Mechanical starting (а) and electromechanical (b) characteristic of SDSZ-20-29-54-80UHL4 motor: 1 is naturally occurring characteristic; 2, 3, 4 are simulated ones for С = 4, 12,7 and 14 μF respectively. The resultant curves show the decrease of starting point for the whole range of slip scale. The fact is reasoned by the influence of the other circuits, the number of which is halved if compared to the previous structure. In addition, every separate circuit has twice-increased inductive reactance, this caused capacitance reduction of pole capacitors. The further increase of capacitance creates the maximum moment of starting characteristic, although it happens in the limited range. The resistances connected to capacitor in series allow control of circuit quality, as well as broadening of its working interval. The developed circuit creates some more maximum for mechanical characteristic under the conditions of further increase of the capacitance of pole capacitors. Their occurrence is reasoned by the mutual influence of adjacent circuits. So, for working machines with the required starting moment of no more than 1,5 of the rated value (e.g. high-powered rattlers) the capacitance of the capacitors should correspond to the level, which provides no or only single maximum increase of moment. One more problem of mining and smelting mechanisms is the influence of occasional impact loads of the mechanisms of coarse grinding and the machinery for metals soft treatment. As a rule, such equipment used DC motors or asynchronous drive with considerable slip and flywheel kinetic energy storage system. Despite the efficient technological work of electric drive systems, their energy characteristics do not meet modern requirements. Synchronous drive may be considered as an alternative for asynchronous drive for impact loads mechanisms. However, the exploitation of synchronous drive as a component of rolling mill of seamless tube has shown the disadvantages of the drive. MMSE Journal. Open Access www.mmse.xyz

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In case of technologically compliant exploitation of synchronous drive of forming rolls, there arise the contingency caused by mechanical wear of end coils in the output point for working wires in magnetic core. The authors of the paper state that [3] the contingency is caused by significant dynamic current rushes of field magnet, which are attended by mechanical clang of end coils. As a rule, the effect of such impact blows is equilibrated by mechanical or electrical means. They are the following: flywheel mechanism, regulation of deflection rate of elastic clutch, and the use of automatic field system with voltage forcing parameter. The high rate of mechanical characteristic rigidity does not allow use of flywheel mechanism load as a damper of intensified application. The practical use of flywheel, as a component of synchronous drive, has shown its inexpediency because of its incapacity to turn into practice the stored energy resulting from motor speed «slump». The second way of impact loads compensation is the introducing of elastic clutches into kinematic diagram. It should be noted that the most difficult case of absolutely rigid constraint use has uncovered the system inoperability as resulted from the significant decrease of its oscillativity [3]. So, the researchers are required to determine the level of spring linkage rigidity, which enables both positive results of damping and the satisfactory operability of a drive. Besides the mechanical approaches to the problem of synchronous drive operation, the use of automatic field system control should be also considered. But it is needed to formulate the control law or determine the fixed parameters of system setup. As it is shown by [3], at the initial point of impact load application the motor operates at attenuated field, which may cause significant slumps of inductive current. The possible way of effect reduction may be in preliminary voltage forcing of the determined value. The analysis of emergencies origin shows that two methods may be used for impact loads compensation. They are the control of resilient members rigidity in the range, which does not cause considerable mechanical oscillation, and preliminary field forcing of the stated level. The solution should be based on the optimization problem formulation, which will enable the system parameters determination under the definite conditions of drive operation. Using mathematical modelling, let us show the fundamental possibility of parameters determination for SDSZ-20-29-54-80-UHL4 drive of rated load surge from idle operation mode. The frame of optimization factors control is experimental data: - order of field forcing is 1…1,75 of the rated one, which is limited by actuator capacity; - the range of order of elastic clutch rigidity is 1…4, which is limited by the maximum of electromechanical system oscillativity; - the possible time of preliminary forcing turn on is 0…3 second before load occurrence; it is determined by five time constants of field coil. As a function of purpose, the minimum mean square deviation from constant of field magnet current in case of rated load surge is considered [4].



 i 0

( I i  I уст )2 n 1

(8)

where I i , I уст are momentary and constant values of current of field magnet, n is discrete step. The task solution is done by means Minimize operator from MathCAD software package, which is used as gradual way for optimizing. The dynamics of synchronous drive start is traditionally estimated with respect to electromagnetic transients. We used the Park-Gorev equation for motor modelling [5]: MMSE Journal. Open Access www.mmse.xyz

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Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954 dψ  dψ q  d U ψ ω r i ; U ψ ω  r i ; d q д a d q d д a q dt  dt  dψ  f U r i ;  dt f f f  dψ dψ  kd kq  r i ;  r i ;  kd kd kq kq dt dt   (   ) д м M  β(ω  ω )  С  dω d д д м о p д  ω ; dθ  1   ,  д  ; д dt д  dt T dt Mд   (   ) д м M  β(ω  ω )  С dω д м о м p  м ;  dt  T Mм   d м ω  м  dt

(9) Momentary values of currents and moment were determined with respect to subtransient parameters of synchronous motor:  xd 

 xkd 

D  xq xkq  xad 2 ; xq  2 xkq x f xkd  xad

;

 xf 

D xd xkd  xad 2

D D D    ; x dkd  ; x fkd 2 2 2 x f xd  xad x f xad  xad xd xad  xad

xfd 

2 xq xkq  xaq D   x  qkq 2 xad xkd xad  xad ;

;

(10)

2 3 ( xd  x f  xkd )  2 xad where D  xd x f xkd  xad .

The solution of the system of differential equations is done with respect to the forms for currents and electromagnetic moment calculations:

id 

 f  d  kd  q  kq  d  f  kd      ; iq  ; if     xd xfd xdkd xf xfd xfkd xq xqkq

ikd 

 kq  q  kd  f    d ikq        xkd xfkd xdkd xkq xqkq ;

;

M д  (  d iq   q id ) ; ic  id2  iq2

where ic is field magnet current, r.u. MMSE Journal. Open Access www.mmse.xyz

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;

(11)

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

The results of modelling process are shown at Fig. 6, where ic, if, ikd are field magnet current, field current, damper winding current, r.u.; Мд, Му are electromagnetic moment and torque applied by spring, r.u.;  is engine speed; r.u. The value of mean square deviation was determined as σ = 0,002707, order of field forcing and rigidity 0,178012 and 1,436994 respectively for the 1,5 second time of preliminary turning on of field voltage. The system oscillativity increased for the synchronization section, but the quality of transients was improved in whole. In case of lower boundary limitation for order of drive by 1, the optimization problem also has a solution. But then the forcing and time of preliminary y turn on increase in comparison to Fig. 6, and transients quality decreases. The criterion of lower boundary of forcing choice, as being more or less than one, should be minimum power in the field magnet winding, which is determined by the area under the curve of field current in the section of load surge. This is peculiar for the case shown at Fig. 6 (b). Comparing the loss power of control for the classic field system (Fig. 6 (a)) and of optimized one (Fig. 6 (b)), we may state that area increase under the curve of current is not sufficient. The fact proves the possibility of maintenance of heat load of electrical machine almost on the level stated by its producer. 6

ду, r.u.

*4

Мд Му

6 Mд , Mу, r.u.

*4

Мд Му

25 t, s

2 t, s

4 0

25 4

15 If, Ikd, Iс,

If, Ikd, Ic, r.u.

r.u.

ikd 5 0

ikd

t, s

25 5

Fig. 6. The example for optimization problem solution: а) stands for the standard parameters; b) stands for optimized parameters. Summary. The researches carried out drove us to the following conclusions:  The use of indirect split of drive circuit enables decrease of power reserve for driving electric motors;  The technological and economic advantages of the project are substantiated by the decrease of idle periods number caused by mechanism dead starts. This is urgent for mechanisms with significant shearing couple or in the need for increase of motor induction torque in the specific slip zone in case of asynchronous start;  Indirect way of field winding split simplifies the magnetic system of rotor, and, thus, simplifies its calculations and cuts production costs;

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 As for synchronous drive with no flywheel, the compensation of impact loads is possible in case of regulation of rigidity of spring linkages and order of field forcing;  The optimization problem can be solved using the gradual method and function of purpose of the minimum mean square deviation of momentary value of field magnet current from its constant value in case of load surge;  The limitations of optimization factors are substantiated by technical feasibility of field magnet, permissible amplitude of system oscillation and the time constant of field coil;  The fundamental evidence of possibility of impact loads compensation by means of synchronous drive. As based on the evidence of SDSZ-20-29-54-80-UHL4 drive, it was determined for the first time that contingency avoidance for such drive types is possible under the conditions of reduced order of field voltage of 0,18, time for field voltage reducing of 1,5 second, and the order of elastic clutch rigidity of 1,44;  The optimization parameters cause the significant decrease of dynamic current surges of drive windings, as well as improvement of transients quality;  The parameters of system installation cause insignificant loss power of control, which maintains heating rate of synchronous motor. Summary. The paper contains the discussion of the issues of starting characteristic improvement and protection from impact loads of synchronous motors in the drives of high-power mining and smelting mechanisms. The problem of complicated start is proposed to be solved as based on the additional starting moment created by field coil with pointed and distributed active-reactive characteristic. It is proposed to minimize the problem of impact loads of the stable mode by means of complex usage of spring linkage and specific settings for the standard field system. References [1] Patent. UA 31044 A, 6 B 02К 19/36 Ukraine. Synchronous Motor. /V.І. Кyrychenko, V.S. Homilko, V.А. Borodai; patentee and Patent Holder NMU; appl. 03.07.1998; publ. 15.12.2000. Bul. №7-II. [2] Patent. UA 102792 C, 2 Н 02К 19/02, 36 Ukraine. Synchronous Motor. //V.І. Кyrychenko, V.А. Borodai; patentee and Patent Holder NMU; appl. 10.07.2012; publ. 25.04.2013. Bul. №8-II. [3] Development of Recommendations for the Exploitation of Synchronous Motor of the Main Drive for Automatic Tube Rolling Mill OOO “INTERPIPE NIKO TUBE”: Research Report (Final.) / State HEI «NMU»; Scientific Research Work on the Contract №1120/030383 from 04.12.2012. – Dnepropetrovsk, 2013. – 34, pict. [4] Borodai V.А. Method and Criterion for Starting Characteristic Optimization of Synchronous Motors of difficult start conditions / Borodai V.А., М.О. Nesterenko – Dnipr-s'k: Mining Electromechanics and Automation, Sci. – Techn. col. – Issue. 85. – 2010 – P. 180 – 183. [5] Pavliuk D.P. Starting and Asynchronous Modes of Synchronous Motors / D.P. Pavliuk, S. Bidnaryk – Moscow: Energia, 1971. – 271 p. [6] M.S. Mahmoud, F.M. AL-Sunni, Control and Optimization of Distributed Generation Systems, Power Systems, Springer International Publishing Switzerland 2015, DOI 10.1007/978-3-319-169101_2 Cite the paper V.А. Borodai, R. О. Borovyk, О.Yu. Nesterova (2017). Efficient Transient Modes of Synchronous Drive for Mining and Smelting Mechanisms. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.71.21.693

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Study of Planar Mechanisms Kinetostatics Using the Theory of Complex Numbers with MathCAD PTC13 Matsyuk I.N. 1,a, Shlyakhov E.М. 1, Zyma N.V.1 1 – State Higher Educational Institution “National Mining University, Dnipro, Ukraine a – shlyahove@nmu.org.ua DOI 10.2412/mmse.40.52.685 provided by Seo4U.link

Keywords: MathCAD, planar mechanism, vector, complex number, second class Assur group, kinetostatic.

ABSTRACT. The paper describes the convenient method to study the kinematics of planar mechanisms. Very convenient to study the kinematics of planar mechanisms with the help of complex numbers. The current article proposed the kinetostatic analysis also be carried out by operating in the field of complex numbers. It is recommended to use the MathCAD PTC, having great potential for operations with complex numbers. The basic idea is presented by the example of the three second class Assur groups found most frequently in modern planar mechanisms.

Introduction. As it is well known, complex numbers are used to solve geometric problems [1] and for research purposes of the motion of planar bodies and mechanisms [2, 3, 4]. Information about complex numbers usage to solve kinetostatics problems of planar mechanisms has been described insufficiently in known literature. In case, when inertia forces of the links are taking into account for kinetostatics analysis of mechanism, to perform kinematic analysis is necessary first of all. This analysis made with representing vectors as complex numbers and has a definite advantage over other methods. In this case, it is logical to provide force analysis using complex numbers too. This is facilitated by the fact, that the popular modern mathematical software (Maple, Wolfram Mathematica, MathCAD) have appropriate calculation algorithm to operate with such numbers. Analysis of the recent research. The research of the force analysis of mechanisms does not represent any difficulties today. Historically, in the beginning it has been solved only using the graphicalanalytical methods [5]. Gradually graphical-analytical methods are substituted by purely analytical methods, that became a prior due to development of computer technology [6 - 9]. Determination of forces in kinematic pairs can be carried out separating the mechanism on the Assur’s groups [10] which are kinetostatically determined [11]. Another approach is to partition mechanism on links, for each of which the equilibrium equation should be written. Solving the obtained system of equations defines all unknown reactions [12]. These reactions may be represented by two components (normal and tangential [11] or horizontal and vertical [12]), i.e. vectors with known directions, but unknown magnitudes. Representation of required reactions as unknown vectors is more compact. In this case, the number of equations is minimal [7]. The research has been provided using MathCAD PTC that is powerful program for operations with complex numbers. All calculations are performed in the international standard system (NIST).

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Starting with the group, which consists of connected rod 4 and slider 5 (Fig. 1). Assume, that link 4 is connected to link 2 by a revolute joint E, and slider 5 is connected with a frame 0 by a prismatic joint. The mass centre s4 is in the middle of the link EF. The position of the slider s5 mass center coincides with point F.

Fig. 1. Second class Assur group (connecting rod – slider): a – group skeleton; b – calculation scheme. The initial data for the calculation are as follows: • geometrical parameters – l4  lEF  0,15 m,   45 ; • links masses – m4  mEF  6 kg; m5  msl  20 kg; • links inertia moments – I s 4  I EF  11,2 103 kgm2; • resistance force – P  500 N. As it is known, from previous kinematical analysis:  connecting rod EF,  vectors

is interpreted by the vector l4  0.109  0.103i ;

of acceleration of links mass centres as 4  59.32  39.14i and as5  52.69  52.69i ;

 connecting rod

angular acceleration –  4  192 s-2.

The acting loads on the links: (hereinafter use approximate value of the gravitational acceleration g  10 m/s2) G4  60i and G5  400i ;

 gravity forces

 resistance  inertial

force – P  353.6  353.6i ;

loads – Fi 4  355.9  234.8i , Fi5  2105  2105i , Mi 4  2.15 .

Note, that the vectors  4 and M i 4 can not be expressed in complex numbers because they are directed perpendicular to the complex plane. Operations with them will be described below. Following a fragment from MathCAD 11, which shows the input of initial data, is provided (fig. 2).

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

 0.109  0.103 i l  l4  0.109  0.103 i 4  4 4 as4  7.84  5.18 i a  6.959  6.959 i as4  7.84  5.18 s5 i as5  6.959  6.959 i 3 m4  6 m5  10 G4  60 i G5  100 i Is4  11.2 10 3 m4  6 m5  10 G4  60 i G5  100 i Is4  11.2 . 10 Fi4  m4 as4 Fi4  47.04  31.08i Fi4  m4 as4 Fi4  47.04  31.08i Fi5  m5 as5 Fi5  69.59  69.59i Fi5  m5 as5 Fi5  69.59  69.59i  4  25.4 Mi4  Is4 4 Mi4  0.284  4  25.4 Mi4  Is4 4 Mi4  0.284 P  565.7  565.7 i P  565.7  565.7 i

 

Fig. 2. Input of initial data. Let’s proceed directly to the forces analysis of group, in which necessary to determine the forces in external kinematic pairs of groups R24 (action, for instance, of link 2 on link 4) and R05 (action of frame 0 on slider 5), and the force R54 in the internal revolute joint (action of slider 5 on connecting rod 4). Generally, a system of four vector equations can be written: two for each of the links in the group. In the first equation the sum of all the forces acting on the link is zero. In the second one, the sum of the moments of these forces around any centre is zero. In our case, the equation of moments will be one - only for the connecting rod [7]. Vector of equilibrium equations of forces acting on the links: link 4 – R24  G4  Fi 4  R54  0

(1)

link 5 –  R54  G5  Fi5  P  R05  0 .

(2)

The equilibrium equation of moments acting on the connection rod 4 around its mass centre: 0.5l4  R24  Mi 4  0.5l4  R05  0 .

(3)

In formulas (1) and (2) two vectors are unknown R24 and R05 . The last vector’s magnitude is unknown. Its direction is known: it is perpendicular to the trajectory of the slider. From the theory of complex numbers known, that the condition of the perpendicular vector R05 to line, which tilted to X axis on angle  will be equal to:

R05  ei   R05  ei , where the top underline denote the conjugate vectors. Condition (4) must be added to equations (1) and (2). MMSE Journal. Open Access www.mmse.xyz

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(4)

Mechanics, Materials Science & Engineering, March 2017 – ISSN 2412-5954

The vector product represented by complex numbers finds in the following way. If to multiply the conjugate to one of the two complex numbers to the second, then the imaginary part of the multiplication considering the sign is the vector product of these vectors. In MathCAD a small subroutine to determine the moment of force can be arranged in case, if a lever arm h and the force F are known:

M (h, F ) : Im(h  F ) .

(5)

The resulting system of equations in MathCAD solved by a block Given-Find. The corresponding fragment is given below (fig. 3).

 

 M ( h  F)  Im hF

R24  100  100 i

R54  100  100 i Given

R24  G4  Fi4  R54

R05  100  100 i

R54  G5  Fi5  P  R05  R05 exp   i R05 exp   i







M 0.5l4  R24  Mi4  M 0.5l4  R54

 R24





R54 R05  Find R24 R54 R05

R24  532  542i

R05  83  83i

 R54  579  513i

Fig. 3. The resulting system of equations.

Next, consider the Assur group consisting of a connecting rod 2 (triangle BCE), and the rocker 3 (Fig. 4). The rocker and frame form revolute joint D and the connecting rod is connected by joints B and E to links 1 and 4. The mass centre of connecting rod is located at the intersection of medians of the triangle BCE. Consider the following initial data: • geometrical parameters – l2  lBC  0,15 m, l21  lBE  0,09 m, lBE  lCE ; • links masses – m2  4 kg; the rocker mass is small and it has not been took into account; • link’s moment of inertia – I s 2  7,5 103 kgm2.

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Fig. 4. Second class Assur group (connecting rod – rocker): a – group skeleton; b – calculation scheme

In addition, we have previously obtained kinematics analysis: sides of triangular connecting rod is interpreted by vectors: l2  0.145  0.037i , l21  0.061  0.067i and link 3 – by vector l3  0.021  0.072i ;

 the

 the acceleration vector of the mass centre for the link 2:  rocker

as 2  7.415  2.871i ;

angular acceleration 2– 2  42.25 s-2.

The loads acting on the links in the group:  gravity forces  a reaction

(hereinafter use approximate value of the gravity constant g  10 m/s2) G2  40i ;

of link 4 on link 1 (considered above) R42  532  542  i , (N);

 inertia loads

– Fi 2  29.66  11.48i , M i 2  0.317 .

Below a MathCAD fragment is given, which shows the initial data input (fig. 5).

l2  0.145  0.037 i

l21  0.061  0.067 i

as2  7.415  2.871 i

m2  4

l3  0.021  0.072 i

G2  40 i

Fi2  m2 as2

Fi2  29.66  11.48i

Mi2  Is2 2

Mi2  0.317

3

Is2  7.5 10

 2  42.25 R42  532  542 i

Fig. 5. Initial data input. In the force analysis necessary to determine the forces in the external joints of group R12 (action of link 1 on link 2) and R03 (action of frame 0 on rocker 3), and the force in the internal joint R32 (action of rocker 3 on connecting rod 2). The link 3 does not affected by the external loads, so a force R32 is equal to a force R03 and both these forces are directed parallel to the longitudinal axis of link 3. MMSE Journal. Open Access www.mmse.xyz

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Therefore, in this case it is enough to write a system of two vector equations (forces and moments) for link 2 and to add a condition of parallelism of vector R32 to vector l3 .

R32  l3  R32  l3 For writing the equilibrium equation of moments of forces for link 2 around a point B, first, we have to find the vector, that expresses a lever arm l BS2 of forces G2 and Fi 2 .

2 l l l BS2   2 21 . 3 2 The respective fragment of MathCAD is given below (fig. 6).

 M M((hhFF))   Im Im hhFF

22 ll22  ll21 21 llBs2   Bs2 33  22

R R12  100 100  100 100ii 12 

R R32  100 100  100 100ii 32 

 

Given Given R  G  F  R R R12 12  G22  Fi2 i2 R42 42  R32 32





llBs2 0.069  0.035i 0.035i Bs2  0.069

    R ll3 R l R32 R 32 32 3 32 l33

 R   M  ll21 M ll22R R32 21  R42 42 32 R  R32 32 

M  G  F   M M MllBs2 i2  Mi2 i2  M  Bs2  G22  Fi2

RR12 12





R  Find R R32 32  Find R12 12

R  501  565i R12 12  501  565i

R  1.57  5.37i R32 32  1.57  5.37i

R03  R32 R03  R32

R03  1.57  5.37i R03  1.57  5.37i

Fig. 6. MathCAD PTC fragment. At last, consider the Assur group consisting of slotted link 3 and slider block 2 (Fig. 7). The slotted link is rotates about fixed point C, and is connected to link 4 by a joint D. The mass centre of slotted link s3 is located at the middle of it. So, take the following initial data: • geometrical parameters – l3  lCD  0,49 m, l31  lCB  0,329 m; • mass of links – m3  18 kg; the slider mass is small and it does not take into account; • link inertia moment – I s3  0,43 kgm2.

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Fig. 7. A second class Assur group ( slotted link-slider block): a – skeleton of group; b – diagram for a forces calculation In addition, we know from previous kinematic analysis: slotted link CD and its part CB were interpreted by vectors: l3  0.17  0.46i и l31  0.114  0.308i ;

 the

 the acceleration vector of the mass centre for the link:  angular

as3  2.25  0.056i ;

acceleration of the slotted link – 3  8.52 s-2;

The loads acting on the links in the group: (hereinafter are using approximate value of the acceleration of free fall g  10 m/s ) G3  180i ;  gravity forces 2

 a reaction  inertial

of link 4 on link 3 (of considered above) R43  1640  2i ,(N);

loads – Fi3  40.47  1,01i , M i3  3.66 .

Following is a document fragment from MathCAD, which shows the input of initial data (fig. 8).

l3  0.17  0.46 i

l31  0.114  0.308 i

as3  2.25  0.056 i m3  18

G3  180 i

Fi3  m3 as3  3  8.52

Is3  0.43

Fi3  40.5  1.01i Mi3  Is3 3

Mi3  3.66

R43  1640  2 i Fig. 8. Input of initial data.

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It is necessary to determine the forces in the external joints B and C R12 (action of link 1 on link 2) and R03 (action of frame 0 on slotted link 3) and the reaction of slider 2 on slotted link 3 – R32 . On the first stage of forces analysis, we do not include friction, so force R23 is equal to the force R12 , and both these forces are directed perpendicular to the longitudinal axis of slotted link 3. Therefore, in this case it is enough to write a system of two vector equilibrium equations (of forces and moments about a point C) for link 3 and add a condition of perpendicularity of the vector R23 to the vector l3 .

R23  l3   R23  l3 The respective fragment of MathCAD is given below (fig. 9).

 

 M ( h  F)  Im hF

R23  100  100 i

R03  100  100 i Given

R23  G3  Fi3  R43  R03







 R03 

  R23 l3 R23 l3





M l3  R43  Mi3  M l31  R23  M 0.5l3  G3  Fi3   

 R23





R03  Find R23

R23  2075  767i

R03  475.2  945.5i

R12  R23

R12  2075  767i

Fig. 9. MathCAD document fragment. In conclusion, consider the equilibrium of input crank AB (fig. 10). The mass center of the crank s1 is located on its axis of rotation.

Fig. 10. The input crank: a – skeleton of group; b – diagram for a forces calculation. MMSE Journal. Open Access www.mmse.xyz

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Take the following initial data: • crank length – l1  0,49 m; • mass of crank – m1  3 kg. Previously we identified:  the

crank AB was interpreted by vectors: l1  0.114  0.038i ;

 angular

acceleration of the crank – 1  0 .

The loads acting on the crank:  gravity forces  a reaction  inertial

G1  30i ;

value which acts from link 2 to the crank 1 – R21  2072  764i ,(N);

loads – Fi1  0 , M i1  0 .

The following is a fragment MathCAD, which shows the input of initial data (fig. 11). l1  0.114  0.038 i m1  3

G1  30 i

R21  2072  764 i

Fig. 11. MathCAD document fragment. From the equilibrium conditions of the crank ( R21  G1  R01  0 ; M1  l1  R21 ) easily find the force R01 and the torque required to drive the input link 1 M1 (fig. 12).

 

 M ( h  F)  Im hF

R01  G1  R21



M1  M l1  R21

R01  2072  734i



M1  165.8

Fig. 12. MathCAD document fragment.

Summary. Thus, kinematics analysis and force analysis of planar linkage can be performed in a field of complex numbers. MathCAD PTC has enough powerful apparatus for work with them. The vector product of vectors in complex form does not lie in the field of complex numbers and can not be expressed by a complex number. It is proposed to find module of vector product using the properties of complex numbers, which allow including in the equilibrium equations of the moments of force to determine unknown reactions in the kinematics pairs. References. [1] Podolskiy M.E. (1954). O primenenii kompleksnyih chisel k izucheniyu ploskogo dvizheniya tverdogo tela, Trudyi Leningradskogo korablestroitelnogo institute, pp. 213-218. [2] Ponarin Ya. P. (2004) Algebra kompleksnyih chisel v geometricheskih zadachah, MTsNMO, 160 p. MMSE Journal. Open Access www.mmse.xyz

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[ 3 ] Kinematics and dynamics of machines by Martin, George Henry (1969), New York, McGraw-Hill. [4] Fundamentals of Kinematics and Dynamics of Machines and Mechanisms (2000). Oleg Vinogradov, CRC Press Edition, 306 p [5] Yudin V.A. Kinetostatika ploskih mehanizmov (1939). Moscow, Izdanie voenno-inzhenernoy akademii RKKA, 205 p. [6] F.Y. Zlatopolskiy, G.B. FIlImonIhIn, V.V. Kovalenko, O.B. Chaykovskiy (2000). Rozrahunok ploskih mehanizmiv z vikoristannyam PEOM. Navchalniy posibnik, Kirovograd, PP «KOD», 124 p. [7] Matsyuk I.N., Shlyahov E.M. (2015). The research of plane link mechanisms of a complicated structure with vector algebra methods. Eastern-European Journal of Enterprise Technologies, 3 (7 (75)), 34–38. doi: 10.15587/1729-4061.2015.44236. [8] Matsyuk I.N., Zyma N.V., Shlyahov E.M (2014). Kinematika ploskih mehanizmov v programme MathCAD s ispolzovaniem teorii kompleksnyih chisel. Sbornik nauchnyih trudov mezhdunarodnoy konferentsii «Sovremennyie innovantsionnyie tehnologii podgotovki inzhenernyih kadrov dlya gornoy promyishlennosti i transporta 2014», NGU, pp. 514-520. [9] Matsyuk I.N., Shlyahov E.M. (2013) Opredelenie kinematicheskih i kinetostaticheskih parametrov ploskih sterzhnevyih mehanizmov slozhnoy strukturyi, Sovremennoe mashinostroenie. Nauka i obrazovanie: Materialyi 3-y Mezhdunar. nauch.-prakt. Konferentsii, Saint Petersburg, pp. 788-796. [10] Kolovsky M.Z., Evgrafov A.N., Semenov Yu.A., Slousch A.V. (2000) Advanced Theory of Mechanisms and Machines, Berlin, New York, London, Paris, Tokyo: Springer, 394 р. [11] Artobolevskiy I.I. (1988) Teoriya mehanizmov i mashin: Ucheb. dlya vtuzov, 640 p. [12] Bertyaev V.D. Teoreticheskaya mehanika na baze MathCAD (2005), Saint Petersburg, BHVPeterburg, 752 p. Cite the paper Matsyuk I.N., Shlyakhov E.М., Zyma N.V. (2017). Study of Planar Mechanisms Kinetostatics Using the Theory of Complex Numbers with MathCAD PTC. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.40.52.685

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VII. Environmental Safety M M S E J o u r n a l V o l . 8

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Global Warming Triggered Heavy Rains and its Effect on the Corrosion of Car Bodies in Uyo Metropolis14 Aondona Paul Ihom1, a, Patrick Peters Obot 2, b, Ini Umoren Udofia,3,c 1 – Department of Mechanical Engineering, University of Uyo, Uyo, PMB 1017 Uyo- Nigeria a – draondonaphilip@gmail.com b – obotuv@yahoo.com c – iniumoren@yahoo.com DOI 10.2412/mmse.01.39.008 provided by Seo4U.link

Keywords: corrosion, cars, heavy rains, global warming, Uyo Metropolis.

ABSTRACT. Global warning has stimulated several weather conditions; in some parts of the world it is excessive drought, while in others it is excessive rains, cold and heat. This study looked at the effect of excessive rain on the corrosion of car bodies in Uyo metropolis; a city that has been witnessing heavy rains each year with floods occurring in some parts of the city. The study monitored corrosion in different types of cars, noting the materials used for the car body, the year of manufacture of the car, the maintenance culture of the user, the number of years it was used in the area understudy and the effect of corrosion on the different parts of the car body. The highlights of the study revealed that the most critically affected parts of the cars considered were the underneath, and hidden areas around overlapping parts of the cars. The top parts of most cars had faded paints which were almost giving way to corrosion. Steel bodies were affected more than aluminum car bodies. The study also noted that the effectiveness of the corrosion resistance performance of the coating work on the steel used at the underneath of the cars varied from one car manufacturer to another. The underneath corrosion varied from low to very high corrosion signs. The study however, did not include cars with wholly polymer composite bodies.

1. Introduction. In the paper presented at National Development Centre “Towards a Longer Lasting Car: The Corrosion Factor” the author [5] clearly outlined the sources of corrosion attack on the car, how to prevent the corrosion attack and the economics of corrosion attack on cars every year in Nigeria. The summary of his work was that to have a longer lasting car, the user must be in the habit of retouching his car, whenever he notices a damage coating or buy a car with plastic body. Frequent washing and waxing of the chrome is normally very helpful, and the use of inhibitors in the car cooling system should be encouraged. Short runs should be avoided. The fuel tank should be kept half full always and all forms of leakages on the car should be stopped immediately, and repairs carried out. The researcher also opined that much has to be done by the car manufacturer by way of materials selection [5]. Corrosion reduces the life span of cars, the effect is normally significant at coastal areas and cities with heavy rains. Corrosion according to [7] is like corruption if left unabated can destroy national economy. There have been times when cars and vehicles awaiting shipment or clearing at seaports were scrapped as a result of corrosion. The cars were attacked by the salt environment of the sea. The underneath of cars and door edges and hidden points, where water accumulates is commonly susceptible to corrosion [4, 3]. The south-south region as a result of global warming trigger rains coupled with environmental pollution from gas flaring has induced corrosion in autos. The level of pollution from this area is normally evident from dirty water with black suspension particles collected from roof tops, and black-spotted roof tops which the governor of the state said has caused most of his people to resort to the use of black roofing sheets to maintain aesthetics [7, 8]. Salted roads in 14

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cold areas of the world have also being another reason for the corrosion of cars. For corrosion to take place, air and moisture must be present. It therefore means that if any of these is excluded there won’t be corrosion [2]. Global warming have stimulated several weather conditions: in some parts of the world, it is excessive drought, while in others it is excessive rains, cold and heat. This is not without effects; excessive rains have varying degrees of effects both on living and non-living things [6, 7]. Muddy roads and acidic rains are encouraging the corrosion of cars, (see Fig. 1) this is because in most cities today the air is polluted particularly in the south-south region of Nigeria where gas flaring is going on in addition to the combustion of fossil fuels in various types of engines and cooking devices. The region as a result of global warming has been experiencing heavy rains for some years now with effects of flooding, muddy roads and dirty rain water [8].

Fig. 1. Underneath Corrosion Effect on a Car in Uyo-Nigeria. According to corrosion exclusively [1] when owing a car in the seventies and eighties particularly if one lived along the south African coast, some years after purchasing the vehicle the body work would start to discolour and eventually rust. This would occur mostly along the edges of the windows, at the bottom of the doors, the sills under the doors and on the bonnet arising from stone dripping while driving. While we guess many complained about it to their car dealers and thought no one was taking any notice, the Japanese and Koreans car manufacturers in the late eighties and nineties who were looking to get a market share, listened and began their introduction to the market by offering 6-year corrosion warranty on their cars. North American-made vehicles were having “real rust problems” that couldn’t be fought merely with heavier, and more expensive paint. By the mid-1980’s, one really had to galvanise the whole car if you wanted to issue warranties. Zinc in one form or another had been used to protect steel used in automobiles since the 1970’s but corrosion resistance was never a feature until the Japanese cars gained entrance to the US market in the early 1980’s. Several generations of galvanised steels have been developed by steelmakers to meet the demand of automakers for a corrosion free car. Today hot dip free zinc and the zinc/ iron alloy galvanneal are the most common found sacrificial coatings in use by the global automotive industry. From the early 1980’s until the mid 1990’s, automotive manufacturers around the world were steadily increasing the amount of coated steels on their vehicles in order to improve corrosion resistance performance. The percentage of coated steel usage was steadily rising and had increased to 80% by the mid 1990’s from a low of approximately 10%, in the early 1980’s in North America. Currently 80-90% of the metal used in cars in North America and Europe is galvanized compared to just 30% in China, a level expected to grow. In North America, Japan, and Korea over half of all galvanized sheet production is MMSE Journal. Open Access www.mmse.xyz

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destined for the automotive market, whereas, in other countries, the construction industry consumes a larger share [1]. Nigeria is inclusive, the construction industry consumes a larger share of galvanized steel. Some galvanized materials now offer corrosion resistance for 40-60 years, and research by some companies continues to find ever-more resistant options to help deal with problems that may be caused by extreme weather events and climate change [1]. Steel maker Voestalpine has developed zinc magnesium hot dip galvanized steel strip and a‚ galvannealed product which has both zinc and a zinc-iron alloy coating. According to the company, the zinc magnesium coating has‚ the highest degree of corrosion resistance and no limitations with respect to processing properties. Especially in the automotive industry zinc magnesium has the potential to become the standard product over the next decade‚ the Austria-based company said in an emailed statement: “A zinc magnesium galvanized product could then be a similar niche product like an electrolytic galvanized product is today” [1]. The above cited reviews clearly outlined the efforts made by steelmakers and auto-manufacturers to check automotive corrosion over the years, while a great deal has been achieved the menace is yet to be completely rooted out particularly with global warming and changing climatic weather conditions. Progress no doubt has been made over the years. Progressive automotive corrosion resistance has been achieved with newer cars having higher corrosion resistance than older cars or cars of older generation. Cars of the 80’s are still in use particularly here in Nigeria. This work covers automobiles of different models and ages. The objective of the research is to uncover the effect of global warming motivated heavy rains on the corrosion of car bodies in Uyo metropolis, south-south Nigeria. Materials and Method Materials and Equipment The materials used for this work were Japanese cars, Korean cars, American cars, and cars manufactured in Europe, specifically France and Germany. The equipment used were cranes for lifting and spanners of various sizes which were used in loosing of bolts and nuts to expose hidden parts of the cars for proper corrosion monitoring and inspection of the parts for corrosion effect. Camera was used to capture the image of inspected portions of the cars. Method The study of the effect of heavy rains on the corrosion of car bodies in Uyo metropolis was carried out by dividing the work into two parts. The first part was to carry out corrosion monitoring on car bodies. Corrosion monitoring and inspection was carried out on the exposed car body and some parts of the car body were dismantled to expose hidden parts for inspection and corrosion monitoring. The information captured were; car type, model, year of manufacture, corroding region, maintenance culture, corroding material and corrosion condition. The cars which were inspected were, American cars, Japanese cars, European cars from France, Germany, and Korean cars from South Korea, all these cars are imported into Nigeria. The second part of the work was corrosion monitoring and inspection of the underneath of cars. The inspection process requires turning the car up so that the underneath can be properly viewed as shown in Fig. 1. The same information was captured as in the first part of the work. Information on the maintenance culture was obtained from the car owners. The corrosion and attached mud condition of the underneath of the car was noted during the corrosion monitoring and inspection. Images of the corrosion effect were captured using a camera. Maintenance garages in Uyo metropolis and individual car owners made their cars available for the study. Results and Discussion The results of the findings of this work are displayed in Tables 1-2 and in Figs. 2-31.

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Table 1. Corrosion monitoring of body of cars in Uyo metropolis in 2015.

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Table 2. Corrosion monitoring of underneath of cars in Uyo metropolis in 2015.

Fig. 2. Corrosion Effect on different parts of a car body (Manufacturer: Mercedes-Benz Model: Flat booth 200 E, Year of Manufacture: 1975). MMSE Journal. Open Access www.mmse.xyz

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Fig. 3. Corrosion Effect on Different Parts of a Car Body (Manufacturer: Peugeot, Model: 504 SR Year of Manufacture: 1985).

Fig. 4 Corrosion Effect on Different Parts of a Car Body (Manufacturer: Volkswagen Model: Passat 402, Year of Manufacture: 1985)

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Fig. 5. Corrosion Effect on Different Parts of a Car Body (Manufacturer: Mercedes-Benz Model: V booth 230 E, Year of Manufacture: 1985).

Fig. 6, Corrosion Effect on Different Parts of a Car Body (Manufacturer: Mercedes-Benz, Model: V booth 300 E, Year of Manufacture: 1985).

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Fig. 7. Corrosion Effect on Different Parts of a Car Body (Manufacturer: BMW Model: E 30, Year of Manufacture: 1987).

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Fig. 8. Corrosion Effect on Different Parts of a Car Body (Manufacturer: VOLVO Model: 240GL, Year of Manufacture: 1987).

Fig. 9. Corrosion Effect on Different Parts of a Car Body (Manufacturer: NISSAN Model: Sunny 1.4L Year of Manufacture: 1991).

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Fig. 10. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: AUDI Model: Avant A6, Year of Manufacture: 1994).

Fig. 11. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Camry 2.2 GL, Year of Manufacture: 1996).

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Fig. 12. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Almera 1.6 SLX, Year of Manufacture: 1997).

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Fig. 13. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Almera 1.6 SLX, Year of Manufacture: 1997).

Fig. 14. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Blue Bird, Year of Manufacture: 1998).

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Fig. 15. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Corolla, Year of Manufacture: 1998).

Fig. 16. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Camry LE, Year of Manufacture: 1999).

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Fig. 17. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Camry LE, Year of Manufacture: 1999).

Fig. 18. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Almera Tino, Year of Manufacture: 2001).

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Fig. 19. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Camry 2.2 XL, Year of Manufacture: 2001).

Fig. 20. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: Volkswagen Model: GOLF 3.0 Wagon, Year of Manufacture: 2001).

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Fig. 21. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: MercedesBenz Model: BENZ 190, Year of Manufacture: 2002).

Fig. 22. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Primera, Year of Manufacture: 2002).

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Fig. 23. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Serena LMT 200, Year of Manufacture: 2002).

Fig. 24. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Sunny 1.6SLX, Year of Manufacture: 2002).

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Fig. 25. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Corolla S Year of Manufacture: 2003).

Fig. 26. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: RAV4 S, Year of Manufacture: 2004).

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Fig. 27. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: NISSAN Model: Pathfinder, S.E 3.5, Year of Manufacture: 2005).

Fig. 28. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: KIA Model: Porter, Year of Manufacture: 2008).

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Fig. 29. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: HONDA Model: ACCORD 2.0 LX, Year of Manufacture: 2008).

Fig. 30. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: HYUNDAI Model: Accent, Year of Manufacture: 2008).

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Fig. 31. Corrosion Effect on Different Parts of the Underneath of a Car (Manufacturer: TOYOTA Model: Haice bus, Year of Manufacture: 2009). Discussion Global warming activated heavy rains and its effect on the corrosion of car bodies in Uyo metropolis is a study that has been carryout as reflected in Tables 1-2 and Fig. 2-31. It is interesting to note that Fig. 2-9 shows the images of corrosion on the car bodies that were investigated during the study as shown the result of Table 1. Fig. 10-31 are the images of corrosion of the underneath of cars investigated; the images support the result of the corrosion monitoring and inspection as shown in Table 2. Global warming has activated or triggered heavy rains especially in coastal areas; hardly a day passes without rain falling in Uyo this situation has created muddy situation on the untarred roads in the city, trapped muds can be sighted on the underneath of some of the images shown in Fig. 10-31. Polluted air with gas flaring activities, emissions from gen-sets and autos have equally increased the aggressiveness of rain water, the effect on car bodies can be sighted in Fig. 2-9. Hidden areas where moisture is trapped by the cars are badly corroded as in Fig. 2, 5, and 7. Fig. 10- 31 which are images of the underneath of the various cars investigated clearly shows that the underneath of the cars is badly affected. Critical areas include the exhaust system and areas where muds are trapped. Obviously most car manufacturers still need to work on their exhaust system material to make it more corrosion resistant. The problem of most exhaust system is not just wet corrosion but oxidation as a result of the high temperature of the exhaust gases. The effect of the heavy rains on car bodies as can be seen in the study has to do with fading paints. Table 1 which is the result of the effect of heavy rains on car bodies in Uyo metropolis, considers various types of cars, materials used for the car body, their models, year of manufacture, maintenance culture, and the status of corrosion on the car body. The parameters considered normally contribute to the corrosion status of a car, it was however, not possible for the research to know the type of coating provided by the steel makers on the steel sheet used for the body of the cars. Looking at the year of manufacture of some of the cars it may be difficult to provide a true assessment of corrosion MMSE Journal. Open Access www.mmse.xyz

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effect as a result of heavy rains and changing climatic conditions, particularly cars manufactured, in the 70’s, 80’s, and 90’s since they have already lived a good part of their specified lifespans to be considered in a study that is conducted in 2015. The cars that should be of real concern here are cars manufactured from 2000-2015. The result in Table 1 show that for this group of cars the only effect noticed was faded body paint. No doubt this category of cars have benefited from the great improvement of coating work that have occurred over the years (Corrosion, 2015). Today hot dip free zinc and the zinc/ iron alloy galvanneal are the most common found sacrificial coatings in use by the global automotive industry. From the early 1980’s until the mid-1990’s, automotive manufacturers around the world were steadily increasing the amount of coated steels on their vehicles in order to improve corrosion resistance performance. The percentage of coated steel usage was steadily rising and had increased to 80% by the mid 1990’s from a low of approximately 10%, in the early 1980’s in North America. Currently 80-90% of the metal used in cars in North America and Europe is galvanized compared to just 30% in China, a level expected to grow. Some galvanized materials now offer corrosion resistance for 40-60 years, and research by some companies continues to find evermore resistant options to help deal with problems that may be caused by extreme weather events and climate change. Table 2 show the result of corrosion monitoring of underneath of cars in Uyo metropolis the same parameters as in Table 1 were consider during the monitoring; that being the case we maintain that for a fair assessment of the effect of heavy rains on the underneath of the investigated cars, only cars manufactured from 2000-2015 be considered. The result showed that some of the underneath of the cars show low corrosion, some medium, high, and very high; according to the scale of rating for the assessment. This may have to do with the type of coating provided by the steelmakers and the car manufacturers, not ruling out maintenance culture which has to do with frequent washing. This argument is predicated on the fact that some of the cars in Table 2 manufactured in 2001 showed low corrosion sign. The result has shown that the early signs of corrosion are a clear evidence of aggressive environment triggered by heavy and polluted rains. Acidic rains and muddy soils are normally very corrosive to the underneath of cars. As stated above some galvanized materials now offer corrosion resistance for 40-60 years, and research by some companies continues to find evermore resistant options to help deal with problems that may be caused by extreme weather events and climate change, therefore for cars manufactured from 2000 to 2015 to develop serious corrosion problem should elicit curiosity [1, 6-7]. Summary. The study “global warming activated or triggered heavy rains and its effect on the corrosion of car bodies in Uyo metropolis, has been carried out the study extensively investigated the effect of heavy rains on car bodies and the underneath of cars. Different types of cars manufactured by different companies with different years of manufacture were considered in the study, however for the assessment of the effect of heavy rains on the cars only cars manufactured from 2000-2015 were considered for the drawing of conclusions, and the following conclusions were drawn from the study: 1. The effect of heavy rains on car bodies was mainly in terms of faded paint, no corrosion was sighted on car bodies for the period considered (2000-2015) 2. The effect of heavy rains on the underneath of the cars was significant, the corrosion rating was from low to very high. 3. The study noticed that some cars which were manufactured as far back as 2001 had low corrosion sign, this the study concluded that maintenance culture of washing, and the coating used on the underneath of the car must have provided the corrosion resistance against the aggressive muds and dirty water splashing the underneath. 4. The study also concluded that given the advanced coating formulation used by car manufacturers in recent times the corrosion of the underneath of the cars investigated is as a result of global warming triggered heavy rains in Uyo metropolis. MMSE Journal. Open Access www.mmse.xyz

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Acknowledgements The authors of these work are sincerely indebted to all who made their cars available for the study and also provided very useful information to the researchers regarding their cars. In the same vein we wish to sincerely thank the owners of several garages and workshops visited during the course of this research work. Time will fail us to appreciate you by your names individually, however bear with us and accept our heartfelt thanks. References [1] Corrosion, E (2015) Why motor car bodies no longer rust, Corrosion Exclusive, volume 1 issue 1, pp24-28. [2] Cottrell, A. (1980) An Introduction to Metallurgy, 2nd Edition, Arnold publishers, 45p. [3] Evans, U.R. (1976) The Corrosion and oxidation of metals, 2nd supplementary volume, Edwards Arnold. [4] Fontana, M.G. (1987) Corrosion Engineering, 3rd Edition, McGraw-Hill Book Company, pp1-4 [5] Aondona Paul Ihom, Ogbonnaya Ekwe Agwu & John Akpan John (2016). The Impact of Vehicular Emissions on Air Quality in Uyo, Nigeria. Mechanics, Materials Science & Engineering Vol.6, doi: 10.13140/RG.2.1.1813.7845. [6] Ihom, A.P. and Offiong, A. (2014). Zinc-Plated Roofing Sheets and the Effect of Atmospheric Pollution on the Durability of the Sheets, Journal of Multidisciplinary Engineering Science and Technology (JMEST), Germany, ISSN: 31 59-0040, 1(4). [7] Ihom, A.P. (2014) Environmental Pollution Prevention and Control: The Current Perspective (A Review), Journal of Multidisciplinary Engineering Science and Technology (JMEST), Germany, ISSN: 3159-0040, 1 (5). [8] Ogbodo, J.N., Ihom, A.P., Moses, S.A. and Denis, U.J. (2015) Corrosion Resistance Characterisation of 90Al-10Cu-4SiC Metal-Matrix Particulate Composite (MMPC) in Some Selected Media, JMEST Vol2 issue8, 2040-2045. [9] Ryemshak, S.A. and Ihom, A.P. (2015) The Adverse Effects of Flue-Gas Emission and Carbonsoot from combustion of Fossil Fuel Leading to the Phase-out Campaign of Coal-A Review, International Journal of Modern Trends in Engineering and Research,ISSN(Online): 2349-9745, 149161. Cite the paper Aondona Paul Ihom, Patrick Peters Obot, Ini Umoren Udofia (2016). Global Warming Triggered Heavy Rains and its Effect on the Corrosion of Car Bodies in Uyo Metropolis. Mechanics, Materials Science & Engineering Vol.8, doi: 10.2412/mmse.01.39.008

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IX. Economics & Management M M S E J o u r n a l V o l . 8

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Analysing the Economic and Operational Indicators for Railways: the Case Study of Egyptian Railways15 Ahmed Abd Elmoamen Khalil1, a, Karim Mohamed Eldash2, b, Moustafa Adel Ibrahim3, c 1 – Dr. of Railway, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt 2 – Prof. Dr. of Management, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt 3 – Demonstrator of Railway, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt a – ahmed.khalil@feng.bu.edu.eg b – karim.aldosh@feng.bu.edu.eg c – Moustafa.ibrahim245@gmail.com DOI 10.2412/mmse.84.14.772 provided by Seo4U.link

Keywords: railway performance indicators, operating performance, financial performance, railway productivity, freight transportation, passenger transportation, pricing.

ABSTRACT. The aim of this study is analyzing the economic indicators affecting the operation for ENR. ENR has decreased in transport of passengers and goods due to failure in management, limited resources and decrease of fleet. The weight of freight transport decreased from 12.2 million ton at 2004 to 3 million ton at 2013. Also, number of passengers decreased from 450 million passenger at 2002 to 2007 million passenger at 2013.Thus, the authors studied the economic indicators affecting the Operation for Egyptian National Railways and the tools used to analyze it. These analyses included operating performance and financial performance in terms of, passenger traffic, freight volume, overcrowding rate, No. of accidents, existing fleet, time delaying, revenues, costs and deficits. The authors also evaluated these performance indicators in terms of, Labor productivity, pound productivity and trip productivity. Finally, the authors studied the mathematical equation, which used in ENR for calculation of ticket price.

Introduction. Most railways became under state control (1960-1980 period) due to the deficits which began appear which lead to most governments nationalize their railways. Most railways created more flexibility in the organization of their service, reduce costs, adapt with new technologies. Profillidis [1] studied policies and legislations for some countries. Some countries have already privatized their railways operator such as (Japan, Sweden, etc.) for competitive with other transport modes. Other countries tended to liberalization of railways activities and separation of infrastructure from operation such as in Europe. The World Bank [2] analysed some performance indicators for Egyptian national railways which included ENR productivity and technical efficiency, financial operations, passenger and freight traffic, staff productivity and age distribution for (freight wagons, passenger wagons and locomotive). V Graham [3] studied performance indicators and comparative these indicators between different countries. Performance indicators divided to operating indicators and financial indicators. Operating performance indicators included traffic density, labour productivity, freight wagon productivity, passenger coach productivity and locomotive productivity. Financial performance indicators included the cost recovery ratio defined as the degree of coverage of total operating costs with total revenue, including state support and the viability ratio defined as the ratio of commercial revenue divided by 15

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total operating costs. Stenstrom [4] studied performance indicators for railway infrastructure, with primary focus on the railway track, have been mapped and compared with indicators of European Standards. Performance indicators of railway infrastructure categorized into two groups; managerial and condition monitoring indicators. Infrastructure managers use performance measurement to study whether results are in line with set objectives, for predicting maintenance and reinvestments, decision support and benchmarking and business safety. Galar [5] studied it is not possible to measure everything with only quantitative or qualitative methods. Rather a combination of both methods must be used to create a measurement system that is as complete as possible. Qualitative measurement methods are good for measuring soft values, like employee satisfaction, and for checking conformity with quantitative indicators. Mads Veiseth [7] studied the measurement system should be extended to include measurement of effects of punctuality and regularity and of management processes that increases the focus on punctuality and regularity. Railway companies should try to link measurement of rail reliability with other performance measures in the companies. With these suggested extensions, the measurement system will become more balanced and complete. Railways are characterized with high capital cost, low relative return and long period required for recovering it, As a result, private sector is usually reserved about participation. There some problems, which face development of ENR. None measuring the economic and operating indicators that expressing the actual performance in ENR. The available data of operation and finance of ENR have not been analyzed or evaluated in a correct manner. The impact of the Egyptian revolution in 2011 on the productivity and performance of ENR has not been evaluated. So, this paper focuses on the following item: 1. Assessing the economic indicators that affecting the operation of railways and determining the parameters that affecting these indicators. 2.

Analysing and evaluating the operation and financial performance indicators.

3. Analysing the strategy and methodology for calculation of ticket price in ENR, as a local operator of railway in Egypt. 4. Studying the negative effects of Egyptian revolution 2011 on the operating and financial performance of ENR, as it had a major effect on the productivity of the railways. Data Collection The analysis that has been carried out in this research is built on different data collected from Egyptian National Railways and the Central Agency for Public Mobilization and Statistics. This data is collected from different sector such as (Goods sector ,Operational sector, financial sector, long and short-distance sector). Collected data for analysing the operating and financial indicators. Analysing this data will be carried out by using Excel and SPSS program. The collected data is classified into data for indicators such as revenues, costs, No.of passenger, transported tonnage, average travel distance, No.of labors and volume of the fleet as shown in below tables. After that, data for ticket pricing. Other revenues are indicated to the state support and advertisement, while other costs are indicated to maintenance costs, the common service sector and costs of management.

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Table 1. ENR revenues and costs (2008-2015) Years

Passenger Freight revenue revenue LE million LE million

Other revenues

Passenger Freight Costs Costs LE million LE million

Other Costs

2007/2008

1116

149

200.2

772.6

135.2

1023.9

2008/2009

1432

201.5

411.9

1128

180.4

947.8

2009/2010

831.9

245.5

1387.6

1318

237.3

1082.3

2010/2011

1560.8

229.7

1227.2

1861

321

1027.1

2011/2012

1499.5

175.9

715

1642.6

307

1892.4

2012/2013

867

156.9

1082.2

1944

430.3

1901.4

2013/2014

467.3

178.9

1148.8

2650

460.5

2040.8

2014/2015

912.6

163.6

1179.8

3069.8

448.8

2971.1

Table 2. Passenger traffic (2002-2013) No.of Passenger

PassengerKilometers

Average travel

No.of Working Train

Millions

Distance KM

Train

2001/2002

450.0

39083

86.9

416821.0

2002/2003

367.0

46185.0

125.8

426245.0

2003/2004

418.0

52682.0

126.0

413173.0

2004/2005

438.0

55187.0

126.0

412448.0

2005/2006

435.0

54884.0

126.2

416820.0

2006/2007

418.0

52624.0

125.9

385514.0

2007/2008

374.0

50181.0

134.2

365362.0

2008/2009

291.0

27899.0

95.9

370507.0

2009/2010

293.0

28097.0

95.9

382950.0

2010/2011

225.0

27252.0

121.1

401500.0

2011/2012

311.0

13550.0

43.6

389130.0

2012/2013

207

13704.0

66.2

400105

YEARS

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Table 3. Freight traffic (2002-2013) Total transported

TonnageKilometers

Average travel

No.of Running Train

Cargoes(Millions)

Millions

Distance KM

Train

2001/2002

11.9

4188

351.9

18750.0

2002/2003

11.2

4104.0

366.4

17648.0

2003/2004

12.2

4663.0

382.2

17645.0

2004/2005

10.9

4064.0

372.8

16136.0

2005/2006

10.4

3833.0

368.6

15157.0

2006/2007

7.8

2696.0

345.6

11093.0

2007/2008

6.0

2021.0

336.8

9213.0

2008/2009

5.0

1592.0

318.4

7208.0

2009/2010

5.7

1889.0

331.4

7962.0

2010/2011

6.6

1965.0

297.7

7962.0

2011/2012

4.0

1398.0

349.5

6700.0

2012/2013

1166.0

388.7

6000

YEARS

Table 4. ENR fleet for (Freight wagons, Passenger wagons and locomotors) The existing fleet of ENR(2015) Type

Total fleet

Lifespan

Exceed Lifespan

Locomotive

808

283

525

Air wagons

795

765

Long distance wagons

1039

393

646

Short distance wagons

1395

1285

Goods wagons

10718

5444

5274

Table 5. ENR staffing (2010-2015) Years

2010/2009

2011/2010

2012/2011

2013/2012

2014/2013

2015/2014

Staff costs(LE)

1,099,809,779

1,484,662,654

2,031,767,841

2,427,706,157

2,623,340,000

2,694,854,266

No.of labors

63500

60490

60239

63267

60777

57077

The pricing principle in ENR is the "Full cost pricing principle" According to this principle; the tariff level is set so that total revenues from passengers and freight will recover total costs. The costs of MMSE Journal. Open Access www.mmse.xyz

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ENR are divided into direct costs and indirect costs. Where, direct costs are include long distance cost, short distance cost and Freight cost. While, indirect costs are include common services, technical support and Managing authority. The formula, which used by ENR for calculations is illustrated as follows: 1. Passenger ticket pricing Ticket cost = Seat price/km + Locomotive % + Air condition % đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x2DC;đ?&#x2018;&#x2019;đ?&#x2018;Ą đ?&#x2018;?đ?&#x2018;&#x153;đ?&#x2018; đ?&#x2018;Ą = â&#x2C6;&#x2018;

Long distance costs Âˇ Assets ratio % NÂˇ360Âˇ8ÂˇvÂˇNo.of Seats

(1)

2- Freight ticket pricing Ton.km cost = Ton price/km + Locomotive % đ?&#x2018;&#x2021;đ?&#x2018;&#x153;đ?&#x2018;&#x203A;. đ?&#x2018;&#x2DC;đ?&#x2018;&#x161; đ?&#x2018;?đ?&#x2018;&#x153;đ?&#x2018; đ?&#x2018;Ą = â&#x2C6;&#x2018;

Freight costs Âˇ Assets ratio % NÂˇ360Âˇ8Âˇv

(2)

where Assets Ratio% = Assets of (vehicle or locomotive) / Total Assets (Total assets include Track, Signals, Vehicles, stations and locomotives) 360 â&#x20AC;&#x201C; Convert from year to day 8 â&#x20AC;&#x201C; Work hours for labors V â&#x20AC;&#x201C; Speed of Train N â&#x20AC;&#x201C; No. of operated cars or locomotives Analysis and Evaluation This section will illustrate the Economic Indicators affecting the operation for Egyptian National Railways. The researcher will study the strategy of pricing used in ENR, which affecting operating and financial performance for ENR. Then illustrate the negative effect of Egyptian revolution on productivity. Therefore, the researcher will suggest different methodology for tariff pricing to development operating and financial performance of railways. Tariff Structure for Passenger and Freights Tariff structure for passenger and freights is usually effect the operation indicator. The pricing principle in ENR is the "Full cost pricing principle" According to this principle. The tariff level is set so that total revenues from passengers and freight will recover total costs of passengers and freights. Tariff Structure for Passengers According to data from financial department of ENR for year 2014/2015. The research will take case study for Spanish train first class between Cairo and Alexandria to calculate ticket cost for passenger by using the above formula. Revenues of this Spanish train is estimated as 83,160 LE per day based on (6 train / day â&#x20AC;˘ 44 seat â&#x20AC;˘ 9 cars â&#x20AC;˘ 35 LE). Costs is estimated 64,152 LE based on (6 train / day â&#x20AC;˘ 44 seat Special wagon 9 cars â&#x20AC;˘ 27 LE). The cost recovery ratio is calculated at 1.3, showing high profitability also ENR has been suffering from deficits. But this tell us that tariff / cost for of this train is relatively high compared with other trains, i.e. normal and express trains for 2nd and 3rd class. It appear that Spanish trains are cross subsidizing other trains. There are many lines on which tariff seems to be lower than cost. For example, there are many low-income passenger on suburban and branch lines. Their tariff level is kept low in spite costs, which exceed the tariff. The deficits caused

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by suburban lines seems to be cross subsidized by profitable lines in 1st class and 2nd class. This practice is not appropriate for competitive transport market. Tariff Structure for Freights The tariff is evaluated according to the value (market price) of a commodity. According to this principle, tariffs are set by the value of goods owned by the consignor. High value goods require higher tariffs. This principle is reasonable only when cost is less than tariff. Nevertheless, on some ENR lines, tariffs seem to be lower than costs. The same problems in passenger transport occur in freight transport. According to data from financial department of ENR for year 2014/2015. The researcher will take case study for (a special type of wagons) between Cairo and Alexandria to calculate ton.km cost for freights by using the above formula. Steps to calculate ticket price for Spanish train first class between Cairo and Alexandria

Cost of

Ticket cost = 0.09+0.03+0.01 = 0.13 LE / seat.Km

Calculate ticket cost (Cairo-Alex) = Ticket cost· Travel distance = 0.13·208= 27 LE/seat. Actual ticket price = 35 LE/seat.

Steps to calculate transport cost (Ton.Km) for special wagon between Cairo and Alexandria Special wagon

(Ton.km) cost = 0.007+ 0.001= 0.008 LE/ton.km = 0.008 L.E/ton.km Calculate Ton.km cost (Cairo-Alex) = Ticket cost• Travel distance = 0.008•208= 1.7 LE/ton.km. Analysis and Evaluation of performance indicators The pricing methodology in ENR is the full cost pricing principle. This principle leaded to deterioration in performance and productivity indicators of ENR. As shown in below sections MMSE Journal. Open Access www.mmse.xyz

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Development of Rail passenger traffic The total number of passenger.km has oscillation during the study period. The annual average value is (38444) million passengers.Km. It is noted in (2008-2009) a marked deterioration in (passengers.Km), due to the effect of the financial crisis and then returned to a marked deficiency in (2012) because of Egyptian revolution. As illustrated in figure 1. If the railway operation continues with the same situation, it will cause a drop in the passenger.km and decreasing in revenues with continues deficits in the finances of the railway.

PASSENGER-Km (Millions)

60000 50000

52682

52624

46185

40000 30000

55187 54884

50181

39083 27899 28097 27252

20000 10000

13550 13704

Fig. 1. Passenger Traffic. Development of Rail freight traffic The total number of tonnage has oscillation during the study period. The annual average value is (2798) million tonnage. Km. It is noted in (2007-2008) a marked deterioration in (tonnage per Km), due to restructuring of the railway and then returned to a marked deficiency in (2012), because of Egyptian revolution. As illustrated in figure 2.

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TONNAGE-Km (Millions) Tonnage-Kilometers

5000 4000 3000

4188

4663 4104

4064

3833 2696

2000

2021

1000

1592

1889

1965 1398

1166

Fig. 2 .Freight Traffic. Egypt railways Accidents The total number of accidents has oscillation during the study period. The annual average value is (998.5) accident. As illustrated in Figure 3. If the railway safety continues with the same negative situation, it will cause increasing in the total number of accidents and decreasing number of passenger.

No.of Train Accidents 1800 1600 1400 1200 1000 800 600 400 200 0

No.of Accident

1577 975

978

975

1043

1118

1231

1293 1075 781 489

447

Fig. 3. Railway accidents (unit). Overcrowding rate Overcrowding rate means the average number of passengers who are competing for one vacuum. The rate of overcrowding has oscillation during the study period. It is noted in (2011-2012) a marked high growth in overcrowding rate, because of stopping of more lines. In the last 3 years the rate of overcrowding near equal 1 or more, which means no available space. As illustrated in Figure 4.

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Overcrowding rate 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00

overcrowding rate

Fig. 4 .Overcrowding rate in ENR (passenger/available space/trip). ENR Passenger Fleet The coaches availability has oscillation during the study period. As shown in Figure 5. It is noted that No. of coaches in January 2012 equal 1476 and it became 1417 in December 2014 by lack of 4%, in the last 3 years a percentage of coaches availability not exceed about 70% of total fleet, due to lack of continuous maintenance and most of coaches exceeded the life span. Coaches availability in some monthâ&#x20AC;&#x2122;s reached to 50% of total fleet this reflect the increasing which occurred in rate of overcrowding.

Fig. 5. Coaches availability % for passenger short distance, (2012, 2013 and 2014). MMSE Journal. Open Access www.mmse.xyz

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ENR Freight Fleet The coaches availability has oscillation during the study period ranging. As shown in Figure 6. It is noted that No. of coaches in January 2012 equal 10368 and it became 10167 in December 2014 by lack of 2%. In the last year a percentage of coaches availability not exceed about 65% total fleet , due to lack of continuous maintenance and most of coaches exceeded the life span. Coaches availability in some monthâ&#x20AC;&#x2122;s reached to 33.9% total fleet this refer to dropped which occurred in the volume of freights.

Fig. 6. Coaches availability % for freight, (2012, 2013 and 2014). Times delaying As shown in Figure 7. The trains which depart on time has the average value (83.8%), it is noted that delaying percentage of departure time is (14.2%) This large percentage reflect increasing in rate of overcrowding and decreasing in revenues. The average value of arrival time is (38.4%) with delaying percentage (61.6%). This large percentage reflects decreasing number of passenger, decreasing in revenues, increasing deficits

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Punctuality for departure and arrival time ALL TRAINS PUNCTUALITY (DEPARTURE ON TIME) ALL TRAINS PUNCTUALITY (ARRIVAL ON TIME) ALL TRAINS PUNCTUALLY (ARRIVAL WITHIN 15 Min)

100.00% 80.00% 60.00% 40.00% 20.00% 0.00%

JAN

FAB

MAR APRIL MAY JUNE JULY

AUG

SEP

OCT

NOV

DEC

Fig. 7. Punctuality for departure and arrival time, (2012-2013). Passenger revenues The passengers revenue have oscillation during the study period. The average revenue for passengers during the same period is (1085.9) LE Million. It is noted in (2011and 2012), a marked growth in revenues comparing to 2010 in spite of constant passenger.km, due to increasing in tariff and then returned to a marked deficiency in (2013). This is because decreasing in passenger.km. As illustrated in Figure 8.

1800 1560.8

1600

1432

1499.5

1400 1200 1000

1116

912.6

867

831.9

800 600

467.3

400 200 0

Fig. 8. Passengers revenues, (2008-2015). Freight revenues The freights revenue have oscillation during the study period. The average revenue for freights during the same period is (187.6) LE Million. It is noted in (2010 and 2011) a marked growth in revenues comparing to 2008, hence a decreasing in tonnage.km occurred, due to increasing tonnage price and then returned to a marked deficiency in (2012), as a result of decreasing in tonnage.km, as illustrated MMSE Journal. Open Access www.mmse.xyz

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in Figure 9. Freight revenue took a trend variable, thus it cannot predict with freights revenue in the future.

300 245.5

250

229.7

201.5 200

175.9 149

178.9 156.9

163.6

150 100

50 0

Fig. 9. Freight revenues, (2008-2015). Operation and Maintenance costs for passenger traffic The passengers cost have increased during the study period. The average cost for passengers during the same period is (1798.3) L.E million. It is noted in 2015 a marked growth in costs comparing to other years, as a result of increasing in fuel price and increasing in labor wages. As illustrated in Figure 10.

3500 3000

301.79X+440.2 = y 0.9 = Â˛R

3069.8 2650

2500 1642.6

1500 1000

1944

1861

2000 1128

1318

772.6

500 0

Fig. 10. Passenger costs, (2008-2015). Operation and Maintenance costs for freight traffic The freights cost have increased during the study period. The average cost for freight is (315) L.E Million. It is noted on 2014 a marked growth in costs comparing to other years, due to increasing in fuel price and increasing in labor wages. As illustrated in Figure 11.

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49.5X+92.17 = y 0.9 = Â˛R 500

430.3

400

321

300 200

460.5

448.8

307

237.3 180.4 135.2

100 0

Fig. 11. Freight costs, (2008-2015). Comparison between total revenues and total costs The study period has continuous decreasing in revenues. It is noted that passenger revenues are more than freight revenues. This is due to decreasing in tonnage.km and non-concerning for freight operation. As shown in Figure 12. In the last years decreasing in revenues due to decreasing passenger.km and tonnage.km, while increasing costs due to increasing staff salary, increasing fuel price. As illustrated in figure 13.

7000 6000 5000 4000 3000 2000 1000

TOTAL REVENUES

TOTAL COSTS

Fig. 13. Comparison between total revenues and costs, (2008-2015).

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2009/2010

2010/2011

2011/2012

Raw materials and spare parts

Total Wages

Depreciation

The burdens and losses

2012/2013

2013/2014

Administrative expenses

Fig. 14. Components of costs, (2010-2014). Evaluation of performance indicators Labor productivity Productivity of labors for passenger.km has an oscillation during the study period with an annual average 221.2 (passenger.km per labor). The decreasing ratio between passenger.km to labors is a negative indicator for labor productivity. As shown in Figure 15. The productivity of labors wages for total revenues has an oscillation during the study period with an annual average 1.6 (LE), where increasing in this ratio is a positive indicator due to increasing revenues to wages. The bad year is 2013, due to increasing in labor wages comparing to total revenues. As shown in Figure 16.

PASSENGER-KM(thousand) /NO.OF LABORS 900

852.9

808.1

800 700 600 444.3

500

450.5

442.5

400 300

224.9

216.6

2011/2012

2012/2013

200

100 0 2006/2007

2007/2008

2008/2009

2009/2010

2010/2011

Fig. 15. Labour productivity for passenger.km, (2007-2013).

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TOTAL REVENUES/TOTAL WAGES 2.5

2.09

2 1.5

2.24

2.03

1.68 1.32

1.18 0.87

0.5 0 2006/2007

2007/2008

2008/2009

2009/2010

2010/2011

2011/2012

2012/2013

Fig. 16. Labor productivity for total revenues, (2007-2013). Fuel productivity Productivity of fuel for operating revenues has an oscillation during the study period with an annual average 9.9 (LE). The increasing in this ratio is a positive indicator, due to increasing revenues to fuel costs. As shown in Figure 17.

TOTAL REVENUES/FUELCONSUMED 16

14.6

14 12

9.7

10 8

10.3

8.7

7.6

4 2 0 2006/2007

2007/2008

2008/2009

2009/2010

2010/2011

2011/2012

2012/2013

Fig. 17. Fuel productivity for total revenues, (2007-2013). Pound productivity Productivity of revenues to costs has decreased during the study period with an annual average 0.7 (LE). If this ratio is less than 1.0 It is a negative indicator, where reflect inability of revenues to cover costs. The study periods are a bad years, due to increasing financial deficit. As shown in Figure 18.

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REVENUES/COSTS 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0.9

0.8 0.6 0.5

0.5

2006/2007 2007/2008 2008/2009 2009/2010 2010/2011 2011/2012 2012/2013

Fig. 18. Pound productivity for total revenues, (2007-2013). Effects of Egyptian Revolution in 2011 It was found that the Egyptian revolution had affected both of passenger and of freights, so the researchers studied the negative effect of Egyptian revolution on transportation indicators and revenues. The researchers observed that number of (passenger.km) / year reduced from 27252 million in 2011 to 13550 million in 2012. Although, increasing the number of passenger from 225 million to 311 million at the same year. But, the increasing rate of passenger number wasnâ&#x20AC;&#x2122;t suitable for the reduction in travel distance, where travel distance was decreased from 121 (km/passenger) to 43 (km/passenger). The reduction in (passenger.km) was occurred, as a result of stopping operation of more lines. Thus, an increase-overcrowding rate from .94% to 1.34 %. The percentage of accidents was high, although passenger-kilometer was reduced, as illustrated in table 6. Table 6. Passenger Transportation Indicators, (2011-2013). Passenger Transportation Indicators 2010/2011

2011/2012

2012/2013

225

311

207

Passenger-Kilometers (Millions/year)

27252

13550

13704

Average Travel Distance (Km/passenger)

121.1

43.6

66.2

401500

389130

400105

No. Of Accidents

489

447

781

Percentage of Accidents to Passenger-Km

1.8

3.3

5.7

No. Of Passenger (Millions/year)

No. Of Trips

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5.7

27252 25000

20000

3.3

15000

13704 13550

10000

1.8

5000

0 2010-2011

2011-2012

Passenger-Kilometers (Millions/year)

2012-2013

Percentage of Accidents to Passenger-Km

Fig. 19 .Passenger.km & Percentage of accidents, (2011-2013) For freight transportation, it was noticed that tonnage.km decreased from 1965 million in 2011 to 1398 million in 2012, also tonnage transported decreased from 6.6 million to 4 million at the same year as shown in table 7. The reduction in (tonnage.km) was occurred, as a result of stopping operation of more lines and non-concerning of ENR with freight transportation. Table 7. Freight Transportation Indicators, (2011-2013) Freight Transportation Indicators 2010/2011

2011/2012

2012/2013

Tonnage Transported (Millions/year)

6.6

Tonnage-Kilometers (Millions/year)

1965

1398

1166

Average Travel Distance (Km/passenger)

297.7

349.5

388.7

No. Of Trips

7962

6700

6000

2500 2000 1965

1389

1500 1166

1000 500 0

2010-2011

2011-2012 Tonnage-Kilometers (Millions/year)

Fig. 20. Tonnage.km, (2011-2013).

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The operating revenues for passenger and freights decreased from 1560.8 million LE in 2011 to 867 million LE| in 2013 and 229.7 million LE to 156.9 million LE at the same year as respectively. The total revenues decreased from 3017.7 million LE in 2011 to 2106.1 million LE in 2013. The reduction was occurred, lead to increase the deficit from 191 million LE in 2011 to 2169 million LE in 2013. The increasing in total wages were the main reason for increasing the deficit as illustrated in table 8. Although decreasing labor productivity. Table 8. Freight and Passenger Revenues, (2011-2013). Freight and Passenger Revenues 2010/2011

2011/2012

2012/2013

Operating Revenues (Millions LE) for passenger

1560.8

1499.5

867

Operating Revenues (Millions LE) for freight

229.7

175.9

156.9

Total wages

1484.7

2031.8

2427.7

Total Revenues (Millions LE)

3017.7

2390.4

2106.1

Total Cost (Millions LE)

3209.1

3842

4275.7

Total Net (Millions LE)

191.4

1451.6

2169.6 2500

2169.6 2000 1451.6

1500 1000 500

191.4 0 2010-2011

2011-2012

2012-2013

Total Net (Millions. LE)

Fig. 21. Total deficit, (2011-2013). 1- The proposed pricing strategy The principle of individual cost pricing based on costs and revenues of each line. This principle to improve the economic indicator for ENR. Individual costing system by line is used to know the financial status of each line. Individual revenue calculation system by line is used to know contribution of each line to the financial improvement and also, for estimating profitability by line. Tariff per Km must reduce as travel distance lengthens. Where, tariff for long distance is cheaper per Km than short distance travel. The strategy of ticket pricing cost depend on separation infrastructure from operation, where total cost donâ&#x20AC;&#x2122;t include infrastructure cost. Passenger ticket pricing: MMSE Journal. Open Access www.mmse.xyz

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Ticket cost = Seat price.km + Locomotive cost + Air condition cost Total cost of line

đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x2DC;đ?&#x2018;&#x2019;đ?&#x2018;Ą đ?&#x2018;?đ?&#x2018;&#x153;đ?&#x2018; đ?&#x2018;Ą (X) = â&#x2C6;&#x2018; Nâ&#x2C6;&#x2014;360â&#x2C6;&#x2014;Tâ&#x2C6;&#x2014;vâ&#x2C6;&#x2014;No.of Seats

(3)

where 360 â&#x20AC;&#x201C; Convert from year to day; T â&#x20AC;&#x201C; work hours for operation; V â&#x20AC;&#x201C; speed of train; N â&#x20AC;&#x201C; No. of operated cars or locomotives. Total cost of line include (operating and maintenance cost of Line) Cost of vehicles

Seat price. km = NÂˇ360ÂˇTÂˇvÂˇNo.of Seats

(4)

Cost of locomotives

Locomotive cost = NÂˇ360ÂˇTÂˇvÂˇNo.of SeatsÂˇNo.of hauled vehicles Cost of Air condition

Air condition cost = NÂˇ360ÂˇTÂˇvÂˇNo.of SeatsÂˇNo.of hauled vehicles đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x2DC;đ?&#x2018;&#x2019;đ?&#x2018;Ą đ?&#x2018;&#x192;đ?&#x2018;&#x;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x2019; (Y) = X Âˇ L + đ?&#x2018;&#x17E; +

Profit Margin

(5)

(6)

(7)

where X â&#x20AC;&#x201C; ticket cost; L â&#x20AC;&#x201C; Travel Distance; q â&#x20AC;&#x201C; Quality of service. Freight ticket pricing Ton.km cost (X) = Ton price.km + Locomotive cost đ?&#x2018;&#x2021;đ?&#x2018;&#x153;đ?&#x2018;&#x203A;. đ?&#x2018;&#x2DC;đ?&#x2018;&#x161; đ?&#x2018;?đ?&#x2018;&#x153;đ?&#x2018; đ?&#x2018;Ą(X) = â&#x2C6;&#x2018;

Freight costs of commodity

(8)

NÂˇ360ÂˇTÂˇv

Cost of vehicles

Ton price. km = NÂˇ360ÂˇTÂˇvÂˇweight of load car (7) Cost of locomotives

Locomotive cost = NÂˇ360ÂˇTÂˇvÂˇweight of load carÂˇNo.of hauled vehicles (8) đ?&#x2018;&#x2021;đ?&#x2018;&#x153;đ?&#x2018;&#x203A; đ?&#x2018;&#x192;đ?&#x2018;&#x;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x2019; (Y) = X Âˇ L + đ??´ +

Profit Margin L

(9)

where L â&#x20AC;&#x201C; travel distance; A â&#x20AC;&#x201C; additional charges such as (Cost of treatment at station, cost for processing loading and unloading, fee for contract document, costs for insurance of cargoes for damages and loss).

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Summary. The authors used the collection data for analyzing the operating and financial indicators. And then conclusion the reasons deterioration of the railway, which summarized in the following point: 1. ENR has decreased curve in all the performance indicators both of passenger and freights, because of the following points: a) Increasing Overcrowding rate in recent years, as a result of exceeding the most of the existing fleet the lifespan. b) Increasing delay time in recent years, such that it reached to 62% from time of total trips, due to poor operation management and lack of maintenance. c) Decreasing total passenger.km due to increasing number of accidents and negligence in trainâ&#x20AC;&#x2122;s maintenance. d) Decreasing revenues due to decreasing passenger.km and state support for some ministers with no refund. e) In recent years, it is noted that total cost is more than total revenues, thus it leads to increasing deficits. f) Decreasing in total tonnage.km with increasing costs comparing to revenues, which has become a burden on the railway. g) Low productivity for staffing due to decreasing passenger.km, tonnage.km and labor wages become larger than total revenues. h) Reduction in Rolling Stock, where existing fleet is 50% of the required fleet, both of (Locomotives, passenger wagons and freight wagons). i) Passenger revenue is more than freight revenues due to Lack of attention to the volume of freights. 2. The formula, which used by ENR for calculations Tariff for passengers and freights are not accurate formulae. It is a roughly method due to missing some factors such as: a) Tariffs should base on individual cost principle. b) Tariffs should base on cost and revenues of each lines. c) The average tariffs per ton-km should include the following additional charges. d) Cost of treatment at station. e) Fee for contract document. f) Costs for insurance of cargoes for damages and loss. g) Cost of round trips must include empty wagons for return trip. h) Profit margin and Risk costs The average tariffs per ton-km must include added charges (Cost of treatment at station, additional charges for every commodity, cost for processing loading and unloading for every 10 kg, fee for contract document, costs for insurance of cargoes for damages and loss). The deficits caused by suburban lines seems to be cross subsidize by profitable lines with passenger in 1-st class and 2-nd class. The same problems in passenger transport occur in freight transport. Recommendations The researcher studied the causes of decline in the performance of the railway, so it will submit the necessary recommendations to develop the performance of the railway, which summarized in the following point:

1. In order to raise the operational efficiency of passenger and freights. Creating a new freight corridor to solve different speeds between freight and passenger trains, possibility of railways to achieve doorMMSE Journal. Open Access www.mmse.xyz

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to-door leads to increasing tonnage.km. Passenger transportation must construct a new line for speed trains to reduce travel time and increasing traffic, using a new technology to make it more comfortable and safe, reducing delays to reduce the rate of overcrowding, cutting poor lines which don’t have high traffic and increasing running fleet. 2. Legalizing a new technology to reduce costs of rail service. 3. Renewal, maintenance of rolling stock and infrastructure should be provided to meet the client requirements. 4. Clear definition of public service obligations in the passenger sector. Any ministry wants to reduce tariff, it should have refund lost income to the railway operator. 5. Creating relations between rail operators and clients such as (special advantages and free tickets for clients who are frequent users of rail service, cards offering unlimited for users of rail services reduction in tariffs for the elders more than 60 or 65 years old, travel of groups). 6. Reducing of poor lines or unprofitable service. ENR should focus on profit activities. 7. ENR must cut in number of labors and develop clear policy with time frame for achieving average staff productivity levels. This policy needs to base on a traffic volume. 8. ENR must combine between two scenarios; first scenario is Separation infrastructure from operation and passenger from freights. Second scenario is Modernization of infrastructure with important investment. These parts can be covered by (private sector). This will aim at focus on parts of railway activities, reducing the effect of government in the fields and reducing public subsidies. 9. Governmental transport policy should place a railway and road on an equal footing in terms of financial contribution of infrastructure and not control in the transportation tariffs. This will generate enough sources to cover the requirements of infrastructure operation and this will allow users to make socially ideal choice between the models. 10. Governmental transport policy should prevent heavy vehicle from using roads and converted it to railway to reduce roads maintenance, number of accidents, increase tonnage.km and the exploitation of the large fleet located in ENR. 11. ENR must care and develop freight sector and provide facilities to increase freight volume. Using advanced technology to increase the speed of loading and unloading. 12. ENR must use this basic of strategy in pricing :a) Establishment of individual costing system by line to know the financial status of each line and to be used for rational tariff decision. Costing by line is very important for estimating profitability by line. b) Establishment of individual revenue calculation system by line to know contribution of each line to the financial improvement of ENR. Calculation of revenue by line is especially important for estimating profitability by line. c) Tariff per Km must reduce as travel distance lengthens. Where, tariff for long distance is cheaper per Km than short distance travel. References [1] V.A. Profillidis, Railway Management and Engineering, Democritus Thrace University, Ashgate Publishing, Ltd. 2014 [2] World Bank working paper “Egyptian Railways—Diagnosis of Present Situation and Restructuring Strategy, 2005. [3] V Graham, A comparative assessment of operating and financial performance, 2011.

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[4] C. Stenström, A. Parida, D. Galar, Performance Indicators of Railway Infrastructure, nternational Journal of Railway Technology, Volume 1, Issue 3, Pages 1-18, 2012. doi:10.4203/ijrt.1.3.1 [5] D. Galar, Berges-Muro L. et.al. The Issue of Performance Measurement in the Maintenance Function, DYNA ingenieria e Industria, 85 (5), 429-438, 2010. [6] D. Galar, Christer Stenström, Parida Aditya et al. Human Factor in Maintenance Performance Measurement, Industrial Engineering and Engineering Management (IEEM), 2011 IEEE International Conference on, Doi 10.1109/IEEM.2011.6118181 [7] Mads Veiseth, Umit Bititci, Performance measurement in railway operations – improvement of punctuality and reliability, 2011. [8] INNOTRACK, “Rail Inspection Technologies,” D4.4.1, University of Birmingham, Project #TIPS-CT-2006-031415, (2008) [9] Ferrovie Dellostato Italiano, web http://www.fsitaliane.it

Cite the paper Ahmed Abd Elmoamen Khalil, Karim Mohamed Eldash, Moustafa Adel Ibrahim (2017). Analysing the Economic and Operational Indicators for Railways: the Case Study of Egyptian Railways. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.84.14.772

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