Journal of Mechanical Engineering 2012 5

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58 (2012) 5

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Contents

Papers

300

Željko Đurić, Ljubiša Josimović, Živoslav Adamović, Ljiljana Radovanović, Goran Jovanov: An Evaluation of Formed Maintenance Programme Efficacy

309

Mohsen Mahdavi Adeli, Fatemeh Sobhnamayan, Said Farahat, Mahmoud Abolhasan Alavi, Faramarz Sarhaddi: Experimental Performance Evaluation of a Photovoltaic Thermal (PV/T) Air Collector and Its Optimization

319

Jure Jelenc, Jože Jelenc, Damijan Miklavčič, Alenka Maček Lebar: Low-Frequency Sonoporation in vitro: Experimental System Evaluation

Milosav Ognjanović, Snežana Ćirić Kostić: 327 Gear Unit Housing Effect on the Noise Generation Caused by Gear Teeth Impacts

337

Edvin Raubar, Damir Vrančić: Anti-Sway System for Ship-to-Shore Cranes

344

José Henrique de Freitas Gomes, Aluizio Ramos Salgado Júnior, Anderson Paulo de Paiva, João Roberto Ferreira, Sebastião Carlos da Costa, Pedro Paulo Balestrassi: Global Criterion Method Based on Principal Components to the Optimization of Manufacturing Processes with Multiple Responses

353

Livija Cveticanin, Ratko Maretic, Miodrag Zukovic: Dynamics of Polymer Sheets Cutting Mechanism

Journal of Mechanical Engineering - Strojniški vestnik

Andrej Pirc, Mihael Sekavčnik, Mitja Mori: 291 Universal Model of a Biomass Gasifier for Different Syngas Compositions

5 year 2012 volume 58 no.

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis.

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58 (2012) 5

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Strojniški vestnik Journal of Mechanical Engineering

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 58, (2012), number 5 Ljubljana, May 2012 ISSN 0039-2480 Published monthly

Papers Andrej Pirc, Mihael Sekavčnik, Mitja Mori: Universal Model of a Biomass Gasifier for Different Syngas Compositions Željko Đurić, Ljubiša Josimović, Živoslav Adamović, Ljiljana Radovanović, Goran Jovanov: An Evaluation of Formed Maintenance Programme Efficacy Mohsen Mahdavi Adeli, Fatemeh Sobhnamayan, Said Farahat, Mahmoud Abolhasan Alavi, Faramarz Sarhaddi: Experimental Performance Evaluation of a Photovoltaic Thermal (PV/T) Air Collector and Its Optimization Jure Jelenc, Jože Jelenc, Damijan Miklavčič, Alenka Maček Lebar: Low-Frequency Sonoporation in vitro: Experimental System Evaluation Milosav Ognjanović, Snežana Ćirić Kostić: Gear Unit Housing Effect on the Noise Generation Caused

by Gear Teeth Impacts Edvin Raubar, Damir Vrančić: Anti-Sway System for Ship-to-Shore Cranes José Henrique de Freitas Gomes, Aluizio Ramos Salgado Júnior, Anderson Paulo de Paiva, João Roberto Ferreira, Sebastião Carlos da Costa, Pedro Paulo Balestrassi: Global Criterion Method Based on Principal Components to the Optimization of Manufacturing Processes with Multiple Responses Livija Cveticanin, Ratko Maretic, Miodrag Zukovic: Dynamics of Polymer Sheets Cutting Mechanism

291 300 309 319 327 337 344 353

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 291-299 DOI:10.5545/sv-jme.2011.101

Paper received: 2011-03-29, paper accepted: 2012-03-14 © 2012 Journal of Mechanical Engineering. All rights reserved.

Universal Model of a Biomass Gasifier for Different Syngas Compositions

Pirc, A. – Sekavčnik, M. – Mori, M. Andrej Pirc – Mihael Sekavčnik – Mitja Mori University of Ljubljana, Faculty of Mechanical Engineering, Slovenia This paper presents the theoretical and technical characteristics of biomass gasifiers. The modelling of a gasifier requires a linear system of equations that represents the mass and energy balances of the gasifier. Three variations with regard to a different syngas composition or the technology used are discussed. To analyse the energy system in full detail, all the peripheral units had to be modelled: the mill, the drying house, the oxygen production facility and the gas engine. The IPSEpro commercial code was used for gasifier and energy system modelling. A mathematical model of the complex energy system was used for the parametrical analysis of the biomass moisture, the biomass composition, the outlet syngas temperature and the operating regime’s influence on the exergetic system efficiency. The results are shown in appropriate diagrams and are compared to the operating experience.

Keywords: gasifier, syngas composition, biomass, energy system, model

0 INTRODUCTION The widespread use of fossil fuels has led to higher prices of energy and pollution of the environment. It is therefore a good idea to use the primary sources of energy more efficiently and to increase the share of renewable (e.g. hydro, solar, wind), geothermal and sustainable energy sources (e.g. wood). Slovenia is a country where the amount of wood clearing is less than the extent of forest growth [1]. The primary sources of energy should be used mainly for the production of electricity and heat should be extracted from the process if required [2]. Large energy savings can be introduced by utilising the waste heat from this process. The majority of the residual biomass should not be used just for heating, but also to obtain electrical energy or even to produce synthetic fuels such as syngas or biofuel [3] to [5]. These fuels also allow for the use of more effective technologies, such as gas turbines, combined cycles, internal combustion engines or even fuel cell systems. One advantage of an energy system with a biomass gasifier is the possibility of having full compatibility with a decentralised energy network [7] and [8].

Fig. 1 is a schematic representation of the mass flows for a numerical model of a universal gasifier to produce syngas of different chemical compositions.

Fig. 1. Model of a universal gasifier

Syngas contains a mixture of methane, hydrogen and carbon monoxide in different proportions. A gasifier can also operate with different oxidants, like pure oxygen or air. The use of different oxidants leads to different syngas compositions [9] and consequently also impacts on the system’s energy efficiency. This article is focused on the numerical modelling of syngas production using biomass. The following targets were set: • the development of a system of equations based on: • the stoichiometric relations of ga­sifi­cation, • the heat and mass balances of the gasi­fi­cation model, including the sub­mo­dels; • the integration of a developed universal model of a gasifier into a broader energy system model with an internal combustion engine and the simulation of various gasification parameters.

1 THEORETICAL BACKGROUND The production of syngas is determined by the substoichiometric combustion of solid fuel and the thermochemical decomposition of water. A certain portion of burned (fully oxidised) biomass is necessary to obtain sufficient heat to run the endothermic process of gasification. The products of complete combustion [10] contain nitrogen, water, carbon dioxide, ash and an excess amount of oxygen, whereas the products of gasification [11] contain methane, hydrogen, carbon monoxide, carbon dioxide and a small amount of ash and tar; in the present paper, all combustible contents (tar, char etc.) are assumed to be gasified as well.

Gasification operates with four main processes: wood drying, pyrolysis, sub-stoichiometric combustion and water reduction [9].

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, andrej.pirc@savaprojekt.si

291

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 291-299

Firstly, wood biomass enters the drying process, with moisture decrease being important as some organic acids are discharged during the process of drying, which might shorten the lifetime of the gasifier [11].

Pyrolysis is the thermal decomposition of biomass occurring in the absence of oxygen [8]. It is a fundamental chemical reaction, which is the precursor of both the combustion and gasification processes. The products of biomass pyrolysis include biochar, bio-oil and gases, including methane, hydrogen, carbon monoxide and carbon dioxide.

Depending on the thermal environment and the final temperature, pyrolysis will yield mainly biochar at low temperatures, i.e. less than 450 °C, when the heating rate is quite slow, and mainly gases at high temperatures above 800 °C, with rapid heating rates.

At an intermediate temperature and under relatively high heating rates, the main product is bio-oil.

Due to the endothermic process of gasification, a particular volume of pyrolysis products must be burned. The combustion reactions are: C + 1 2 O 2 → CO − 111 MJ kmol ,

CO + 1 2 O 2 → CO 2 − 283 MJ kmol ,

(1)

H 2 + 1 2 O 2 → H 2 O − 242 MJ kmol.

The combustion air consists of oxygen and unreactive nitrogen that causes ballistic heat losses.

During the reduction process, there are three main reactions: the water-gas reaction, the CO-shift reaction and the steam-methane reforming reaction [9]:

C + H 2 O ↔ CO + H 2 + 131 MJ kmol , CO + H 2 O ↔ CO 2 + H 2 − 41 MJ kmol , (2) CH 4 + H 2 O ↔ CO + 3H 2 + 206 MJ kmol.

The Eq. (2) describes reversible reactions.

In general, the thermodynamic equilibrium of the reaction is achieved when the product formation rate is equal to the decomposition rate of the products into reactants [13]. Molar concentrations are described by the temperature-dependent equilibrium constant K: A + B ↔ C + D,

K=

[ product _ C ] ⋅ [ product _ D ] .

[ reactant _ A] ⋅ [ reactant _ B ]

(3)

The total gas yield of biomass gasification is seriously affected by the constraints of many other operating variables [14] and [6]. An increase in the reaction temperature can lead to increases in gas 292

production and decreases in the solid fraction. A better cracking reaction is achieved with a longer residence time of the volatile phase in the reactor. In addition, the decomposition of the tarry components is improved. Physical pretreatment is predominant for the production of the gas. When the particle size of the biomass feed is smaller, the gas yield increases. In contrast, moisture removal results in a slight decrease, while ash removal yields the same result. The heat transfer improvement exerts a positive effect on the decomposition of the tarry components, while the mass transfer improvement favours the char gasification reaction due to the increased contact between the char and steam surfaces. The gas yield is very sensitive to the temperature in the gasification reactor and also appears to be sensitive to the configuration of the reactor.

2 NUMERICAL MODELLING The universal numerical model of the gasifier is represented by a system of linear equations. This numerical model was made to analyze the same system operation, depending on the most influential parameters. A universal numerical model can operate with different types of biofuel, different oxidants and consequently, produces a syngas with different chemical compositions. The transformation of wood to syngas is divided into four connected processes: wood drying, pyrolysis, incomplete combustion and water reduction. The proportion of an individual product is determined by the temperature, the pressure and the time duration of the process according to the Le Chatelier principle [13] and [19]. The oxidant supply is needed for sub-stoichiometric combustion, whereas the steam supply is needed for the whole reduction process. The model of the gasifier is designed to operate in three different modes and produces syngas with different chemical structures [16]: 1. Syngas consisting of carbon monoxide, methane, hydrogen and carbon dioxide.

2. Syngas consisting of hydrogen and carbon dioxide.

3. A third operating mode is to produce a mix of hydrogen and carbon monoxide in a ratio of one to seven. This specific mix can be used for methanol synthesis.

The model of the universal gasifier also makes possible calculations with different oxidants (oxygen or air). The factors associated with the oxidants used are shown in Table 1. These factors represent the basic values for defining the mass and heat flows of the process.

Pirc, A. – Sekavčnik, M. – Mori, M.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 291-299

The water reduction heat flow is determined as follows: Q red = m C ⋅ 1 − w ( C )burn ⋅ Q red ( C ) +

Table 1. Factors for the oxidants used Oxidant a g

Oxygen 1 0

Air 1 / 0.24 0.76

(

The factors for the operating mode show the basic values needed to determine the different operating modes and the chemical structure of the syngas in one common linear system of equations (Table 2).

CO, CH4, H2 0 0 1 0 1

H2 1 1 0 0 0

CO / H2 = 7 1 0.31 1 1 0

These factors are set for different syngas compositions in such a way that the appropriate terms in the Eqs. (6) to (11) are included and weighted.

Pyrolysis starts after wood biomass pre-warming.

Due to their high reactivity, the products of pyrolysis combust first. The quantity of burned methane and hydrogen also depends on the total quantity of oxygen provided by the oxidant (burning air) and the chemical composition of the wood (wood containing oxygen). This has a direct influence on the chemical composition of the syngas and the heat flow needed for water reduction.

The heat flow of the burned pyrolysis products is therefore: Q = m ⋅ w ( H ) ⋅ H (H ) + burn

H2

2 burn

i

The index burn means burned, Hi is the lower heating value and w is the mass fraction for each component.

The required oxidant mass flow equals:

m oks

  M ( O2 ) +  m CH 4 ⋅ w ( CH 4 )burn ⋅ 2 ⋅  M ( CH 4 )     M ( O2 ) M ( O2 )  =  + m H ⋅ + m C ⋅ w ( C )burn ⋅ − ⋅ a . (5)  M ( H2 ) M (C)     −m fuel ⋅ w ( O 2 )     

M is the molecular mass for each component, a is the factor for the oxidant used and the index fuel means biomass fuel.

(

)

)

red

red

where b stands for the factor of the operating mode and the index red means the process of reduction.

The steam mass flow for the water reduction is calculated from the mass balance: M ( H2O ) − m H 2O = m C ⋅ 1 − w ( C )burn ⋅ M (C)

(

)

−m CH 4 ⋅ w ( CH 4 )burn ⋅ 2 ⋅ −m H 2 ⋅

M ( H2O ) M ( H2 )

M ( H2O )

M ( CH 4 )

−

+

(

)

+ m CH 4 ⋅ 1 − w ( CH 4 )burn ⋅

M ( H2O ) M ( CH 4 )

⋅ b + (7)

  M ( CO ) + m CH 4 ⋅   m C ⋅ 1 − w ( C )burn ⋅ M (C)   + ⋅ M ( CO )  ⋅ 1 − w ( CH )  4 burn ⋅   M CH ( ) 4   M ( H2O ) ⋅kred ⋅ .

M ( CO )

(

)

(

(4)

+ m C ⋅ w ( C )burn ⋅ H i ( C ) .

  M ( CO ) +  m C ⋅ 1 − w ( C )burn ⋅  (6) M (C)   − ⋅ M ( CO )   + m ⋅ 1 − w ( CH 4 )burn ⋅  CH 4 M ( CH 4 )   ⋅k ⋅ Q ( CO ) ,

(

2

+ m CH 4 ⋅ w ( CH 4 )burn ⋅ H i ( CH 4 ) +

)

)

+ m CH 4 ⋅ 1 − w ( CH 4 )burn ⋅ Q red ( CH 4 ) ⋅ b −

Table 2. Factors for the operating mode Gas b kred c d e

(

)

The hydrogen mass flow produced by the water reduction is: M ( H2 ) + m H 2 = m C ⋅ 1 − w ( C )burn ⋅ M (C)

(

)

(

)

+ m CH 4 ⋅ 1 − w ( CH 4 )burn ⋅ 3 ⋅

M ( H2 )

M ( CH 4 )

⋅b +

  M ( CO ) +  m C ⋅ 1 − w ( C )burn ⋅  M (C)   (8) + ⋅ M CO ( )  + m  ⋅ 1 − w ( CH 4 )burn ⋅  CH 4 M ( CH 4 )   M ( H2 ) ⋅kred ⋅ .

M ( CO )

(

)

(

Universal Model of a Biomass Gasifier for Different Syngas Compositions

)

293

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 291-299

The carbon monoxide mass flow equals:   M ( CO ) ⋅c +  m C ⋅ 1 − w ( C )burn ⋅  M (C)   m CO =   ⋅ (9) O C M ( )  + m  ⋅ 1 − w ( CH 4 )burn ⋅  CH 4  CH M ( ) 4   ⋅ (1 − kred ) ⋅ d ,

(

)

(

)

where c and d stand for the factors of the operating mode.

The carbon dioxide mass flow is: m CO 2 = m CH 4 ⋅ w ( CH 4 )burn ⋅ + m C ⋅ w ( C )burn ⋅

M ( CO 2 ) M (C)

M ( CO 2 )

M ( CH 4 )

+

+

 M ( CO ) +  m C ⋅ 1 − w ( C )burn ⋅ M (C)  + M ( CO )  + m ⋅ kred ⋅ 1 − w ( CH 4 )burn ⋅  CH 4 M ( CH 4 )  M ( CO 2 ) ⋅ ⋅ b.

M ( CO )

(

  (10)  ⋅   

)

(

)

The final methane mass flow is:

(

)

m CH 4 , fin = m CH 4 ⋅ 1 − w ( CH 4 )burn ⋅ e ,

(11)

where the index fin means final and e is a factor to determine the operating mode.

The nitrogen mass flow is described in the next equation: m N2 = m oks ⋅ g ,

(12)

where the index oks means the oxidant and g is the factor of the used oxidant.

With regard to all the inlet and outlet energy flows [15], the following energy balance can be postulated: m f ⋅ h f + m oks ⋅ h ( p ,T ) + m H 2O ⋅ h ( p ,T ) + +Qburn ⋅ (1 − ηloss ) − Q red − Q warm = m sg ⋅ h ( p ,T ) ,

(13)

where h is the enthalpy. The remaining indices have the following meanings: loss is the process of heat loss, warm is the preheating and sg is the syngas.

3 DESCRIPTION OF THE ENERGY SYSTEM The modelled units of the gasifier were introduced to the internal combustion engine (ICE) combined 294

heat and power plant (CHP) model (Fig. 1). The power plant model was designed with the Simtech software Process Simulation Environment (PSE) [17], whereas particular submodels were made using Model Development Kit (MDK) [18]. Typical units, such as heat exchangers, pumps, compressors, the ICE and the generator, were taken from the program library. The humid wood is modelled as being first ground by a special mill, which is powered by an electric motor, and then dried in a drying house according to [1], see Fig. 4. The dryer is a direct heat exchanger that mixes hot, dry air and humid, ground wood. The hot, dry air is prepared in a heat exchanger downstream from the internal combustion engine, using the heat of the ICE’s exhaust gases. At the end of the process, moist and cooled air leaves the dryer. The dry and ground wood is taken to the gasifier, where the wood is pre-warmed to start pyrolysis. A certain proportion of the pyrolysis products are burned, with the remaining being reacted in a water-shift reduction. The oxidant is supplied for incomplete combustion. If the oxidant used is pure oxygen, the air is separated into nitrogen and oxygen by an air separation unit using the Linde technique [19]. The reduction process needs some steam supply. Both the oxidant and the steam are heated in regenerative heat exchangers [20]. The cooled syngas is combusted in the ICE, which is connected to the generator. The exhaust gases heat the air used for drying the humid wood. The cooling water of the internal combustion engine can be additionally used to prepare hot sanitary water or for other purposes [21].

The net electrical (exergy) efficiency depends on the particular constants of the sub-models and is defined using the following equation: P − Psub , ηnet = G

(14) m w ⋅ hw where the index G means the generator of internal combustion engine, sub means subsidiary and w means wood. The generator’s electrical power (exergy flow) is reduced by the power consumption for the mill, pumps, compressors and air separation unit [2].

The total (energy) efficiency of the CHP power plant is defined as: P − Psub + QCW , ηtotal = G (15)

m w ⋅ hw where the index CW means the engine’s cooling water and w means wood. It is obvious that terms in the numerator (Eq. (15)) represent the different kinds of energy flows. QCW can be used as a useful heating source in different applications and is therefore

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Fig. 2. Power plant scheme with the corresponding sub-models

treated the same as PG regardless of the fact that their quality with respect to exergy content is considerably different.

The simulation shows that the total (energy) efficiency (sometimes called also CHP efficiency) of the system is 88%, which is achieved in the following way: oxygen is the oxidant, wood moisture is 20% and the syngas contains methane, hydrogen, carbon monoxide.

4 RESULTS Following a numerical simulation [17] of the power plant operation, an analysis of the influential factors was made. The factors which have the greatest influence on the net efficiency of the energy system are: type of wood, the wood moisture, the outlet temperature of the syngas and the operating mode.

4.1 Type of Wood This analysis shows how the chemical composition of the wood influences the heating value of the syngas.

The diagram in Fig. 3 presents the results of the model for the following data: • Wood moisture: 30%.

• Oxidant: oxygen.

• Chemical composition of the syngas: methane, hydrogen, carbon monoxide.

• Mass fraction of burned methane: 0.595.

• Parameter: type of wood (amount of hydrogen and carbon).

The chemical composition of the syngas was calculated according to previously adjusted inputs.

Trees absorb carbon dioxide and change it into cellulose, hemicellulose and lignin in the process of photosynthesis. Different trees absorb different amounts of carbon dioxide over their lifetime; this is why different trees have different chemical compositions. Wood is made up primarily of the following compounds [10] and [22]: • Cellulose 40 to 50%.

• Lignin: 16 to 25% in hardwood, 23 to 33% in softwood.

• Hemicellulose: 20 to 30% in hardwood, 15 to 20% in softwood.

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• •

Other compounds (water, resins, etc.) 5 to 30%.

Minerals 0.1 to 3%.

Fig. 4. Correlation between grinding energy, heating value of the wood and wood moisture

Fig. 3. Chemical composition of the syngas

A different chemical composition has an influence on the heating value of the wood and consequently, on the syngas. This result is confirmed by other authors [1], [3] and [12]. The syngas produced from wood with less hydrogen (w = 0.04) has a larger mass fraction of carbon monoxide and a smaller mass fraction of methane. The results for the syngas made from wood with more hydrogen (w = 0.045) are the opposite, as shown in Fig. 3.

4.2 Wood Moisture Wood consists of carbon, hydrogen, oxygen and also some water, which lowers the net efficiency of the whole energy system. The diagrams in Figs. 4 and 5 show the results of calculations for the following data: • Type of wood: hydrogen content (w = 0.045).

• Oxidant: oxygen.

• Chemical composition of the syngas: methane, hydrogen, carbon monoxide.

• Mass fraction of burned methane: 0.595.

• Parameter: wood moisture.

The mass fraction of water in fresh wood can be greater than 50%. Using totally fresh wood would mean using a lot of energy to dry the wood before processing it in a gasifier. It is therefore advisable to allow fresh wood to lie for a certain period of time in an outdoor store [1]. In addition, due to its better reactivity, the wood should be first ground up, which leads to more efficient drying and a more stable and uniform gasification process [1].

296

Fig. 5. Correlation between net efficiency, mass fraction of burned methane and wood moisture

Increasing the wood moisture reduces the net efficiency, a result obtained in the following research [1], [2] and [9]. The specific grinding energy decreases with the increased moisture of the wood [1], whereas the drying energy is significantly greater. The net efficiency of the system also decreased with a wood moisture increase because of the lower heating value of the fresh wood. In the case of wood that contains 50% moisture, all the mass flows into the gasifier are 50% lower with regard to the dry wood mass, which means less energy for oxidant and steam heating, pyrolysis and water reduction. Due to reduced energy consumption, the amount of burned methane is also smaller (Fig. 5).

Pirc, A. – Sekavčnik, M. – Mori, M.

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4.3 Outlet Temperature of the Syngas The diagram in Fig. 6 shows the results of the model for the following data: • Type of wood: hydrogen content (w = 0.045).

• Wood moisture: 30%.

• Chemical composition of the syngas: methane, hydrogen, carbon monoxide.

• Oxidant: oxygen.

• Parameter: mass fraction of burned methane.

• • •

Wood moisture: 30%.

Mass fraction of burned methane: 0.595.

Parameter: oxidant (oxygen, air) and chemical composition of wood.

Fig. 7. Correlation between net efficiency and operating mode

Fig. 6. Correlation between the net efficiency, the outlet temperature of the syngas and the mass fraction of burned methane

Hydrogen and methane are the gaseous products of pyrolysis. In the presence of an oxidant, hydrogen burns immediately. The mass fraction of burned methane depends on the remaining amount of oxidant.

The oxidant mass flow regulates the heat flow needed for endothermic reactions and the outlet temperature of the syngas. The mass fraction of burned methane should not be below 0.595 because a syngas with a low temperature cannot heat the oxidant and steam to process at a sufficient temperature. If the mass fraction of burned methane is larger than required, the temperature of the syngas increases. There is also a smaller amount of methane that can be burned in the internal combustion engine. This leads to a lower net efficiency.

4.4 Operating Mode The chemical composition of the syngas also depends on the quantities of oxidant and steam supplied.

The diagrams show the results of the model for the following data: • Type of wood: hydrogen content (w = 0.045).

Fig. 8. Correlation between the syngas composition and the operating mode, using oxygen as an oxidant

When using oxygen as an oxidant, the system has to have an air separation unit, which separates the air into oxygen and nitrogen. The energy consumption of this unit is 250 kWh per one tonne of oxygen produced [19]. Due to the energy consumption, a lower net efficiency is to be expected when operating with oxygen. But the use of air as an oxidant leads to larger mass flows connected to higher flow resistances, an increased heat flow to heat the oxidant, a larger mass

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fraction of burned methane needed, twice as large an installation with respect to size and material use [9], and finally a smaller total net efficiency [15] and [23], as shown in Fig. 7. The gasifier can produce a hydrogen-rich syngas. Our analysis only covered operating with an internal combustion engine. It would be sensible to convert this hydrogen to electricity in a fuel cell due to its better net efficiency [2].

The type of oxidant has an influence on the different chemical compositions of the syngas, too (Figs. 8 and 9). The values describing the syngas compositions are in the same range as achieved in practice [9], [23].

• •

•

•

The wood moisture has a major influence on the net efficiency.

The highest net efficiency of 36.5% was achieved at 20% wood moisture. When working as combined heat and power production, the CHP efficiency increases up to 88%.

When the syngas consists of methane, hydrogen and carbon monoxide, the highest net efficiency of the system is achieved. Producing syngas for methanol synthesis is interesting due to its use in a mobile technique. The lowest net efficiency of gasification is achieved when producing a hydrogen-rich syngas; this is because of water reduction, which is an endothermic reaction. It is sensible to use a hydrogen-rich syngas in fuel-cell systems.

Using oxygen as an oxidant is efficient in all cases.

6 ACKNOWLEDGEMENT

The part of presented work has been accomplished within the Centre of Excellence for Low-Carbon Technologies (CO NOT), Slovenia.

7 NOMENCLATURE

Fig. 9. Correlation between the syngas composition and the operating mode, using air as an oxidant

5 CONCLUSIONS This paper presents a model of gasification and the most influential parameters. The energy and mass balances, the numerical model of the gasifier and the complete energy system were designed on the basis of a stoichiometric analysis of the gasifier. The numerical modelling and the simulation took place using the IPSEpro code. Based on the numerical model, the following results, which match well with previous research, experiments and practice, were obtained: • The simulation of the operating gasifier shows that the most influential parameters are: • the type of wood, • the amount of wood moisture, • the outlet temperature of the syngas, • the type of oxidant (oxygen or air).

298

h H k K

m M p P Q T w

enthalpy [kJ/kg] heating value [kJ/kg] ratio of reduction [-] temperature-dependent equilibrium constant [-] mass [kg] molecular mass [kg/kmol] pressure [bar] power [W] heat [J] temperature [°K] portion [-]

Chemistry symbols and compounds C carbon CO carbon monoxide carbon dioxide CO2 CH3OH methanol methane CH4 hydrogen H2 water H2O nitrogen N2 oxygen O2 Greek Letters η efficiency

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Subscripts burn burned CHP combined heat and power production cooling water CW f fuel final fin G generator ICE internal combustion engine loss loss net network oxidant oks red reduction sg syngas sub subsidiary total total/complete w wood warm pre-warming 8 REFERENCES [1] Golob, A. (1999). Farmers guide. Agricultural Publishing Slovenj Gradec, Ljubljana. (in Slovenian).

[2] Tuma, M., Sekavčnik, M. (2004). Energy systems.

University of Ljubljana, Faculty for Mechanical Engineering, Ljubljana. (in Slovenian) [3] Klass, D.L. (1998). Biomass for renewable energy, fuels and chemicals. Elsevier, London.

[4] Minteer, S. (2006). Alcoholic fuels. CRC Press, Berkeley, DOI:10.1201/9781420020700.

[5] Deublein, D., Steinhauser, A. (2008). Biogas from waste and renewable resources. Wiley-VCH, Weinheim, DOI:10.1002/9783527621705.

[6] Lotrič, A., Sekavčnik, M., Kunze, C., Spliethoff, H. (2011). Simulation of Water-Gas Shift Membrane Reactor for IGCC Plant with CO2 Capture. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 12, p. 911-926 DOI:10.5545/sv-jme.2011.100.

[7] Kirjavainen, M., Sipila, K., Savola, T., Salomon, M., Alakangas, E. (2004). Small-scale biomass CHP technologies, Situation in Finland, Denmark and Sweden. Opet report 12, Espoo.

[8] Buragohain, B., Mahanta, P., Moholkar, V.S. (2010).

Biomass gasification for decentralized power generation: The Indian perspective. Renewable and Sustainable Energy Reviews, vol. 14, p. 73-92.

[9] Highman, C., Van der Burt, M. (2008). Gasification.

Elsevier Science, Burlington.

[10] Kraut, B. (2003). Kraut's engineering handbook.

Littera picta, Ljubljana. (in Slovenian).

[11] Goswami, D.Y. (1986). Alternative Energy in Agriculture, CRC Press, vol. 2, p. 83-102, from http:// www.nariphaltan.org/gasbook.pdf accessed on 201204-26.

[12] Sangeeta, C., Anil, K. (2007). A review of fixed bed gasification systems for biomass. CIGR E-Journal, vol. 9, no. 5, from: www.cigrjournal.org/index.php/ Ejounral/article/view/960/954, accessed on 2010-0517.

[13] Brenčič, J., Lazarini, F. (1996). General and inorganic chemistry. DZS, Ljubljana. (in Slovenian) [14] Chen, G., Andries, J., Luo, Z., Spliethoff, H.

(2003). Biomass pyrolysis/gasification for gas production: the overall investigation of parametric effects. Energy Conversion and Management, vol. 44,

p. 1875-1884, DOI:10.1016/S0196-8904(02)00188-7.

[15] Tuma, M., Sekavčnik, M. (2004). Energy machinery and equipment. University of Ljubljana, Faculty for Mechanical Engineering, Ljubljana. (in Slovenian) [16] Haryanto, A.D., Fernando, S.O., Pordesimo, L., Adhikari, S. (2009). Upgrading of syngas derived from biomass gasification: A thermodynamic analysis. Biomass and bioenergy, vol. 33, p. 882-889, DOI:10.1016/j.biombioe.2009.01.010 [17] Simtech (2003). IPSEpro Process Simulator – guide book, Graz.

[18] Simtech (2003). IPSEpro Process Simulator – Model Development Kit user guide, Graz.

[19] Atkins, P.W., Frazer, M.J., Clugston, M.J., Jones, R.A.Y. (1997). Chemistry principles and applications.

TZS, Ljubljana. (in Slovenian) [20] Oprešnik, M. (1988). Thermodynamics of mixtures.

University of Ljubljana, Faculty for Mechanical Engineering, Ljubljana. (in Slovenian) [21] Pehnt, M., Cames, M., Fischer, C., Praetorius, B. (2005). Microcogeneration: towards decentralized energy systems. Springer Verlag, Berlin, Heidelberg.

[22] from: http://ezinearticles.com/ChemicalCompositionof-Wood, accessed on 2010-11-05.

[23] Dowaki, K., Mori, S., Fukushima, C., Asai, N. (2005).

A comprehensive economic analysis of biomass gasificatiton systems. Electrical Engineering in Japan, vol. 153, no. 3, p. 52-63, DOI:10.1002/eej.20089.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 300-308 DOI:10.5545/sv-jme.2008.076

Paper received: 2008-07-16, paper accepted: 2012-03-21 © 2012 Journal of Mechanical Engineering. All rights reserved.

An Evaluation of Formed Maintenance Programme Efficacy Željko

Đurić, Ž. – Josimović, L. – Adamović, Ž. – Radovanović, L. – Jovanov, G. – Ljubiša Josimović2 – Živoslav Adamović3 – Ljiljana Radovanović3,* – Goran Jovanov4 1 Bauxite Corporation Milici, Bosnia and Herzegovina 2 Polytechnical School Pozarevac, Serbia 3 University of Novi Sad, Technical Faculty “Mihajlo Pupin” in Zrenjanin, Serbia 4 International University of Brcko, Bosnia and Herzegovina

Đurić1

This paper presents the basic ideas for programming the maintenance of complex technical systems, which is a set of rules for determining the diagnostic mode of the constituent parts of the system in the actual exploitation process and decision making regarding the need for their replacement or on the extent of the necessary maintenance based on the information of the actual technical condition of the system.

Assuming that the condition based maintenance is, in fact, the management system of the technical state of the system in the exploitation process, upon choosing the strategy for the condition based maintenance we have performed an analysis of the applicability of formed variants of the maintenance programme and evaluated their efficiency by comparing them with basic indicators (for corrective and preventive maintenance). We have pointed out the importance of using the described maintenance programme to increase reliability level and decrease the stagnation of technical systems, which results in high efficiency, and thus increases the productivity of companies where the systems have been installed.

Keywords: reliability of technical systems, maintenance programme, technical diagnostics

0 INTRODUCTION The shortcomings in policies and strategies of preventive maintenance within large fields of practice have recently initiated a trend of the maintenance planning on the basis of the established condition of the system within the exploitation process (condition based maintenance) [1].

The main advantages of introducing the condition based maintenance lie mainly in the reduction of the maintenance costs (both direct and indirect) as well as in the decrease of the possibility of bringing to a production halt, although other positive effects can be produced, such as the following: • providing the production of required amounts of proper quality goods, • improving the safety of the working staff (operators and maintenance workers), • decrease in dissipating both energy and raw materials necessary for the production and providing the operation of the constituent parts and/or the system within the regime of the highest level of use, • better relationships with buyers of goods because of immediate deliveries as well as of the adequate quality of goods, • greater satisfaction among the staff, particularly within the departments of production and maintenance etc.

The policy of preventive maintenance based on the realisation of planned activities at particular intervals, independently of the technical condition of the constituent parts and/or the system, does not 300

provide sufficient operation and connection between the process of the alteration of the technical condition and the exploitation process [2].

A closer connection between them, by work planning and its periodical performance depending on the technical condition of the constituent parts and/ or the system obtained on the basis of diagnostics, is provided by maintenance strategies according to the condition.

Technical systems provide the possibility of applying a greater number of maintenance strategies according to the condition.

According to the standard EN 13306: 2001 (Maintenance Terminology) condition based maintenance is preventive maintenance based on performance and/or parameter monitoring and the subsequent actions [1].

The research [2] and [3] have contributed to these strategies being divided into two groups: • maintenance according to condition with parameter control, and • maintenance according to condition with reliability level control.

Maintenance according to condition with parameter control includes constant or periodic control and technical parameters measuring all the system’s components and/or the system as a whole.

The maintenance activities are performed when the values of the control parameters reach the usability level, or the pre-critical level.

The condition based maintenance with the control of the reliability level consists of collecting, processing and analysing the data on the reliability

*Corr. Author’s Address: Tehnical Faculty “Mihajlo Pupin”, Djure Djakovic bb, 23000 Zrenjanin, Serbia, ljiljap@tfzr.uns.ac.rs

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The required local optimality rule (flow time and tardiness rule) is proved, in order to minimize the sum or the linear combination of the tasks’ flow time and tardiness costs. This rule has served to design a scheduling algorithm, with O (n3) complexity when it is applied to schedule a set of n tasks on one processor.

To evaluate its performance, the results are compared with a lower bound that is provided in a numerical case study. Using this algorithm in combination with the tasks’ urgency criterion, a real-time algorithm is developed to schedule the tasks on parallel processors.

This latter algorithm is finally applied to schedule and assign preventive maintenance tasks to processors in the case of a distributed system. Its efficiency enables, as shown in the numerical example, the cost of preventive maintenance tasks expressed as the sum of the tasks’ tardiness and flow time to be minimized.

This corresponds to the costs of critical states and of tardiness of preventive maintenance.

In this paper we have made an attempt to point out the influence of formed variants of the maintenance programme on the increase of the reliability level of technical systems.

of the constituent parts and/or the system and of elaborating the decisions on the necessary planning activities of the maintenance concerning replacing or repairing the constituent parts of the system.

In the general analysis of recent documents [1] to [8] preventive maintenance processes, proactive maintenance, maintenance according to the condition, technical diagnostics and total maintenance are reviewed.

The authors specify the significance and the role of the maintenance according to the condition, while in documents [1], [2], [4] to [6], this kind of maintenance is defined as a form of preventive maintenance whose strategy of decision making on maintenance activities is based on periodic and constant technical control of the system in the exploitation process, and according to the results of the diagnostics control the decisions are made on the necessary deadline and the amount of planned maintenance activities.

Maintenance according to the condition is handled with the control of the parameters and the usage of the endoscopic method [7], so it can be concluded that the existing model of maintenance according to the condition reaches the goal of successful implementation of the diagnostic method in which planned maintenance activity duration is determined.

To some extent, the issue of the improvement of technical systems maintenance process arises, based on the implementation of different models of preventive maintenance, on the knowledge of a certain part of the system’s condition, gained from the routine or constant observation [8].

In their paper Barros, et al. [4] present a new methodology for optimizing maintenance and monitoring performance. The performance of the monitoring device is modelled classically by receiver operating characteristic (ROC) curves. From a practical point of view, this approach leads to a very simple optimization scheme in which the optimal monitoring technology or structure can be chosen among a finite set of possible ones, on the basis of their impact on the maintenance performance and their own cost. At the same time, the maintenance parameters are optimally tuned to adapt to the current monitoring quality level.

Adjallah and Adzakpa [5] give important and useful results relating to the minimization of the sum of the flow time and the tardiness of tasks or jobs with unequal release dates (occurrence date), with application to maintenance planning and scheduling.

First, the policy of real-time maintenance is defined for minimizing the cost of tardiness and critical states.

1 FORMING THE MAINTENANCE PROGRAMME The maintenance programme will here refer to the set of accepted methods formed on the basis of documentary materials and the maintenance regime for the constituent parts and/or systems, which provide the given management of the technical condition as well as the reliability within the given condition of the exploitation process.

The maintenance programme of the constituent part and/or the system must be aimed at providing the highest level of efficacy of the constituent part and/or the system with optimal exploitation costs.

Forming the maintenance programme can be based on rational combining the condition based maintenance with traditional preventive maintenance.

Taking into account a great complexity of technical systems in the industry, this paper deals with forming the maintenance programme for the constituent parts of a section (e.g. the convertor section including the equipment), although this can be done for the constituent parts (fits) of the system as well.

The research into forming the maintenance programme for the constituent parts and/or the system should, in principle, contains three stages: • forming the maintenance programme variants at the first level, 

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•

forming the maintenance variants at the second level, • evaluating the efficacy and choice of the maintenance programme variant.

If the failure of the constituent part does not affect the reliability of the system in operation, then, when it comes to an increase of the intensity of the failure, it is the average costs for corrective and preventive replacement that are compared, and if those costs are the same, the constituent part of the system is maintained according to the condition by controlling the reliability level. If those corrective maintenance costs are greater than those of preventive maintenance, then the maintenance with the control of parameters is applied.

If the failure intensity is approximately constant, then the condition based maintenance with the control of the reliability level is applied.

If the failure of the constituent part of the system affects the reliability of the system in operation, it is the condition based maintenance that will be used with the increase of the failure intensity, whereas the condition based maintenance with the control of the reliability level will be applied with the non-increase intensity.

Evaluating the influence of the failure of the constituent part on the reliability of the system in operation is performed by comparing the probability of the occurrence of one of the possible conditions of the system with corresponding allowable values given by the equipment manufacturer, where the methods of mathematical statistics are used and the failure intensity is analysed. In order to form the diagram of the failure intensity it is necessary to process statistical data of the failures of the constituent parts of the system within the process of technical exploitation during a period of time that is no longer than 2 to 3 years. The analysis of constant proper functioning of the constituent parts can be performed according to the well-known order: • forming the diagram of the failure intensity, • according to the character of the alteration of the failure intensity, the assumption about the law on the distribution of the failure occurrence is made, • checking the hypothesis on the law on the failure distribution according to Pearson etc.

According to the results of modelling the following can be determined: • the frequency of entering particular conditions of the exploitation process, • the average amount of the detected failures of the constituent parts and/or the system within particular conditions etc.

302

In this case, some indicators of the maintenance efficacy can also be calculated, such as the following: • the probability of entering particular exploitation conditions, • the efficiency coefficient of the constituent part and/or the system according to the purpose, • specific stops due to maintenance, • average time of the system renewal, • specific maintenance costs of the constituent part and/or the system etc.

The influence of the characteristics of the constituent parts referring to the construction and exploitation on the efficacy of the application of different maintenance strategies and thus on the efficacy of the maintenance programme on the whole, should necessarily be analysed through the alterations of the reliability indicators and maintenance costs.

The annual economic effect of introducing the maintenance programme of the constituent parts and/ or the system can arise from: • the reduction of the maintenance exploitation costs, • the improvement of efficacy of the constituent parts and/or the system, • the decrease of the amount of the spare parts to be replaced etc.

2 SPARE PARTS SAVING BY INTRODUCING THE MAINTENANCE PROGRAMME The research conducted in steel industry shows that the probability of continuous operation of the constituent parts and/or the system, which are susceptible to accidental failures, can be described by the exponential and Weibull’s distribution for the working period when the failure intensity is either constant or on the rise. For failures due to ageing (gradual failures) the probability of continuous operation can be described as normal, log-normal by Erlang’s and Weibull’s distribution during the working period when the failure intensity is on the rise.

On the basis of this research it is possible to make a maintenance programme for a technical system of a particular type or for more systems combined within working requirements, and thereby a plan of necessary spare parts replacements.

The use of the new maintenance programme, differing from the basic maintenance programme assumes a significant application of the maintenance strategies according to the condition, which results in the reduced use of the amount of spare parts.

Đurić, Ž. – Josimović, L. – Adamović, Ž. – Radovanović, L. – Jovanov, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 300-308

For the amount of the “saved” constituent parts of the i-type, which are maintained according to the condition with the control of parameters Eq. (1) [2].

 1 η ∆ni = η ATef  − i t mt ur 2  uri

  . 

them into Eqs. (2) and (3), the total saving of spare parts is achieved by introducing the maintenance programme Eq. (4) [3]:         ηi  k  1  − n C + ∑  i rd i =1  t  t   ur1 ur 2   l  1  ηi  ∑   −  ni Cr d + i =1  tur1 mtur 2           f  1 η i  ni Cr d + −  ∑   i =1  tur1 m ke     λe            ηi   p 1 + − CR = η ATef  ∑  n C  i r d  , (04) 1β t = i 1  1     ur1  1    T 1 +      β η         n  1   ∑  − ηi λi  ni Cr d +  i =1  tur1          e  1 η i  ni Cr d + −  ∑   i =1  tur1 ke     λe            ηi  q  1  ∑ t −  ni Cr d  1β i =1 ur1 1  1    m   T 1 +       η β       

(1)

It is possible to achieve the following economic effect:

rd  1 η C1R = ηiTef ∑  − i mtur 2 i =1  tur1

  ni Cr d , 

(2)

where: ηA is the efficiency coefficient of the constituent part of the system before introducing the maintenance programme (with the basic maintenance programme), ηB is the efficiency coefficient of the constituent part after introducing the maintenance programme, Tef is the annual number of hours (Tef = 8760 h), rd is the amount of the constituent parts of the system which are maintained according to the condition with the control of parameters, tur1 is the average time during the work between two failures for the i-type constituent part [h], m is the coefficient of the decrease of the output of the i-type constituent part of the system when its parameter reaches the wear out limit, tur2 is the average time while working with the condition based maintenance [h], ηi is the ratio of the efficiency coefficients of the constituent part of the system before and after introducing the maintenance programme (ηi = ηB / ηA), ni is the amount of the spare parts of the i-type within one system, Cr/d is the price of one spare part of the i-type.

The annual economic effect Eq. (3) is produced for the constituent parts of the system which are maintained according to the condition with the control of the reliability level:

nP  1 η  − i  ni Cr d , CR2 = η A ∑  t t i =1  ur1 ur 2 

where: k, l is the amount of the spare parts which are maintained according to the condition with the control of the reliability level and control of the parameters and which have the normal and log- normal distribution of the probability of continuous work, n is the amount of the spare parts which are maintained according to the condition with the control of the reliability level and which have the exponential distribution of the continuous work with the parameter λi , e, f is the amount of the spare parts which are maintained according to the condition with the control of the reliability level and the control of parameters, which have Erlang’s distribution of the probability of continuous work with the parameters ke and λe, p, q is the amount of the spare parts which are maintained according to the condition with the

(3)

where: np is the amount of spare parts which are maintained according to the condition with the control of the reliability level.

Expressing the average time during work (tur1) with the parameters of the exponential, normal, lognormal, Erlang’s and Weibull’s laws and classifying 

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control of the reliability level and the control of parameters, which have Weibull’s distribution of the probability of continuous work with the parameters β and η, tur2 is the mathematical expectation of the average time during work for normal and log-normal distribution, r is gamma function.

In mathematical modeling, when preparing a maintenance strategy, equipment utilization rate and the cost of lost production per tim. should be considered.

The utilization rate must be considered when equipment is designed under competitive conditions.

This rate consists of the following factors: the quality of equipment and its operation and the operational (demand) situation. As a utilization criterion we took the utilization function F, which should be optimized over the planned time T to produce N part, Eq. (5):

F=

P −C , T

(5)

where P is the sale price of N parts, and C is the cost of the parts [9].

The paper [10] explains and justifies the necessity and the importance of using the shift level of the utilization of capacity as the stochastic variable in determining the total level of the capacity utilization in the production process by using the method of work sampling. The conclusion is that the shift level of capacity utilization as the stochastic variable in work sampling is the model that solves the problem of determining the total level of capacity utilization in a convenient way with accurate results.

lost production accurately, the frequency and duration of future break-downs should still be estimated before making a cash flow statement. Accordingly, it is important to have good past records if we are to do any better than just guess a value. If breakdowns are purely random occurrences, then past records are not going to be enough to predict precise savings that could be included in a sound financial case. They may give an indication of the likely cost when a breakdown happens [11].

This is a model for calculating the cost of lost production during maintenance actions in Eq. (6):

The cost of lost production is a random set of peaks in the cash flow diagram as shown in Fig. 1. If treated independently, this cost can appear as a minor problem, but if aggregated, the result can be quite startling. Even if it is possible to calculate the cost of 304

(6)

where CLP is the cost of lost production, NWP the number of days without production, and RC the replacement cost.

A model for determining the distribution of the net present value (NPV) characterizing the production systems is developed in the paper [12]. The model has significant advantages compared to models based on the expected value of the losses from failures. The model developed in this study reveals the variation of the NPV due to the variation of the number of critical failures and their times of occurrence during the entire useful life-cycle of the systems.

At the heart of the NPV-model there is a model for tracking the losses from failures Li. These have three major components: • cost of lost production CLP, • cost of intervention CI to initiate repair which also includes the cost of mobilization of resources for repair, and • cost of replaced components and cost of repair CR. As a result, the losses from failures L can be presented as a sum of these three components, Eq. (7).

The losses from failures Li = CLP,i + CI,i + CR,i in the i-th year are a sum of the cost of lost production CLP,i, the cost of intervention CI,i and the cost of repair/ replacement CR,i in the ith year.

Fig. 1. Typical cash flow diagram illustrating the cost of lost production

CLP = NWP × RC,

Li = CLP,i + CI,i + CR,I .

(7)

The cost of lost production CLP is calculated from Eq. (8):

CLP = Ld × Vd × PV ,

(8)

where Ld is the number of lost production unit-days, Vd is the volume of production per day per production unit and PV is the selling price per unit volume production.

Đurić, Ž. – Josimović, L. – Adamović, Ž. – Radovanović, L. – Jovanov, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 300-308

RMK is the reliability of magnetic crane, RN is the reliability of engine room of non-metal additives, RT1 is the reliability of conveyor T1, RT2 is the reliability of conveyor T2, RD1, RD2 are the reliability of engine-rooms of blowers, Ri1, Ri2 are the reliability of water and oxygen armature, RND1, RND2 are the reliability of delivery of non-metal additives, RS1, RS2 are the reliability of scrubber, RV1, RV2 are the reliability of exhaust fan, KSK, KMK, KT are coefficients.

The coefficients KSK, KMK, KT are a measure of aggravation of total productivity on condition that a failure occurs on the branch (i) (if they equal 0, the system does not function on the whole).

The analysis of constant proper functioning of the constituent parts (subsystems) of the engine-room of convertors (systems) can be performed on the basis of the statistical data obtained during the time of exploitation. The aim of processing the statistical data is to adopt a law on work distribution until the failure of all the subsystems. By breaking the above mentioned subsystems into their constituent parts, it is also possible to make a proper functioning analysis of all the constituent parts of the subsystems.

3 FORMING THE MAINTENANCE PROGRAMME FOR THE ENGINE-ROOM OF CONVERTORS The engine-room of convertors (Fig. 2) consists of: a firth crane, a charging crane, a magnetic crane, the preparation of non-metal additives, conveyors T1 and T2, the engine-room of blowers, the installation for water and oxygen, the delivery of non-metal additives, a scrubber, an exhaust fan and a convertor.

The reliability of the engine-room of convertors (Ruk) can be calculated as in Eq. (9) (the signs are from Fig. 2):

((

) ) ((1 − R ) R ) ,

Ruk = R1' 1 − 1 − R3' RK1 

' 4

K2

(9)

R1' = Ruk 1 − (1 − Rsk ) (1 − K SK )  ⋅ ⋅ 1 − (1 − RMK ) (1 − K MK )  ⋅

⋅ 1 − (1 − RN RT 1 RT 2 ) (1 − KT )  , R3' = RD1 Ri1 RND1 RS1 RV 1 ,

R4' = RD 2 Ri 2 RND 2 RS 2 RV 2 ,

where: Ruk is the reliability of firth crane, RK1 is the reliability of convertor 1, RK2 is the reliability of convertor 2, Rsk is the reliability of charging crane,

Table 1. The results of the analysis of constant proper functioning and the proposed variants of the maintenance for the constituent parts of the engine-room of convertors Position of Name of const. part const. part of the engine-room of convertors 1 Firth crane 2

Charging crane

3

Magnetic crane

4 5 6 7 8 9 10

Engine-room of non-metal additives Conveyor, T1 Conveyor, T2 Engine-room of blowers Water&oxygen armature Delivery of non-metal additives Scrubber

11

Exhaust fan

12

Convertor

Law on distribution of continuous work and its parameters exponential λ = 204 ∙ 10-6 Weibull

Character of alteration of failure intensity ≈ const

Proposed application of maintenance strategy CBM-CRL

1.95 − t 6294 ) R=e (

increases

CBM-CP

1.68

≈ const

CBM-CRL; CBM-CP

increases increases increases ≈ const increases increases increases

CBM-CRL PM PM CBM-CRL CBM-CP PM CBM-CRL

1.85

increases

CBM-CP

2.2

increases

CBM-CP

−( t 5893)

Weibull R = e Erlang 2nd progression λ = 2.22 ∙ 10-6 normal m = 9864, δ = 3869 normal m = 8434, δ = 3904 exponential λ = 1.86 ∙ 10-6 Erlang 2nd progression λ = 4.15 ∙ 10-6 normal m = 7647, δ = 4098 normal m = 8868, δ = 3338 Weibull

− t R=e (

4682 )

−( t 4468 )

Weibull R = e PM - preventive maintenance according to “constant durability” CBM-CP – condition based maintenance with the control of parameters CBM-CRL – condition based maintenance with the control of the reliability level 

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Fig. 2. Schema of the engine-room of convertors

The confirmed hypotheses on the congruence of the statistical distributions with the theoretical ones enable determining the distribution parameters of constant proper functioning, primarily drawing conclusions on the character of the alteration of the failure intensity.

When forming the variants of the maintenance programme for the engine-room of convertors, the initial point is that the costs of corrective and preventive maintenance (both direct and indirect) are always greater than those of the preventive maintenance.

The results of the analysis of the constant proper functioning of the constituent parts of the engineroom of convertors, as well as the suggested variant of maintenance are given in Table 1.

It can easily be seen in Table 1 that for 9 out of 12 considered constituent parts of the engine-room of convertors the application of the condition based maintenance is suggested.

306

The performed analysis and the choice of the maintenance strategy for each constituent part separately enable forming the maintenance programme (standard).

The evaluation of the efficacy of the formed programme variants has been made by comparing them with the basic efficacy indicators (for corrective and preventive maintenance), whereby the following results have been obtained: • the operative readiness of the engine-room of convertors has increased by 6.9 to 8.1%, • the reliability of the engine-room of convertors has increased by 4 to 8.5%, • specific maintenance costs (direct and indirect) have decreased by 14 to 21%, • the annual economic effect of the application of the maintenance programme according to the condition is (18 to 22)∙106 €.

Đurić, Ž. – Josimović, L. – Adamović, Ž. – Radovanović, L. – Jovanov, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 300-308

These results also refer to developed maintenance programmes for the constituent parts of some subsystems of the engine-room of convertors.

The influence of the number of the formed variants of the maintenance programme (% of the included constituent parts of the system) on the reliability of the engine-room of convertors is shown in Fig. 3, whereby a field of a relative alteration of the reliability which has been reached at the current level of the chosen maintenance programmes (40% of all the included technical systems within the engine-room of convertors) can be noticed. The alteration of the readiness of the engine-room of convertors in relation to the time at work is shown in Fig. 4.

reliability is a little lower than that of the imported parts.

By introducing the maintenance programme for the engine-room of convertors the specific costs of spare parts and materials have been reduced (Fig. 5).

Some benefits obtained by introducing the maintenance programme are shown in Fig. 6.

Fig. 5. Specific costs of spare parts and materials depending on specific costs of maintaining the engine-room of convertors

4 CONCLUSION Condition monitoring prevents failure modes from occurring by detecting and avoiding failures. Thus, a measured trend of increasing temperature and vibrations in a bearing indicates intensive wear out and incipient failure, which can be prevented by a timely replacement of the worn-out bearing. Condition monitoring of operating components and systems also provides an early problem diagnosis which helps to plan and organise the repair in advance. By reducing the mobilization time and the downtime for repair, condition monitoring reduces the financial losses associated with failure. Controlling all processing parameters in safe ranges is another example of a dual measure reducing both the likelihood of failures and the consequences of failure.

By introducing the maintenance programme it is possible to: improve the efficacy of engine rooms of convertors, reduce the total maintenance costs, improve the organisation of production and maintenance, reduce the consumption of electric power, reduce the number of complaints about products, improve the level of co-operation with partners, improve the level of motivation for work and improve the level of planned activities concerning maintenance etc.

The results obtained upon implementation of the maintenance programme, as well as some other results not presented in this paper, indicate good congruence with the hypothesis of the significance of the above

Fig. 3. The influence % of forming the variants of the maintenance programme on the reliability of the engine-room of convertors

In Fig. 3 RN is System reliability (of engine-room of convertors) after choice of maintenance program, RL Basis reliability (before choice of maintenance program), and Δ RL = RN – RL.

Fig. 4. The alteration of readiness of the engine-room of convertors

The occurrence of the period tk (Fig. 4) can be explained by the following fact: in the past the replacement of spare parts used to be performed without a sufficient use of reserves of usability and the parts were mainly imported. Nowadays, domestic spare parts are used and their basis (projected) 

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described maintenance programme for the increase of the reliability level and its contribution to the reducing the stagnation and high level of utilizing technical systems and company productivity.

5 ACKNOWLEDGMENTS This paper is the result of the research within the project TR 34028, financially supported by the Ministry of Science and Technology of Serbia.

6 REFERENCES

a)

b)

c)

Fig. 6. Benefits obtained by introducing the maintenance programme in the sections of steelworks; a) maintenance work, b) price of damaged constituent parts of the system, c) electric power consumption per day

308

[1] Standard EN 13306, Maintenance terminology (2001).

CEN, European Committee for Standardization, Brussels.

[2] Adamovic, Z., Adamovic, M., (2008). Technical Diagnostics. Technical faculty Mihajlo Pupin Zrenjanin. (in Serbian) [3] Adamovic, Z. (1998). Technology of Maintenance.

University of Novi Sad, Novi Sad. (in Serbian) [4] Barros, A., Grall, A., Berenguer, C. (2007). Joint modelling and optimization of monitoring and maintenance performance for a two-unit parallel system. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol.

221, no. 1, p. 1-11, DOI:10.1243/1748006XJRR31.

[5] Adjallah, K.H., Adzakpa, K.P. (2007). Minimizing maintenance cost involving flow-time and tardiness penalty with unequal release dates. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol. 221, no. 1, p. 57-65, DOI:10.1243/1748006XJRR24.

[6] Puharić, M., Ristić, S., Kutin, M., Adamović, Ž. (2007).

Laser doppler anemometry in hydradynamyc testing.

Journal of Russian Laser Research, vol. 28, no. 6, p.

619-628, DOI:10.1007/s10946-007-0047-y.

[7] Bulatović, M., Šušić, J. (2007). Condition Maintenance - Applying an Endoscopic Method. Strojniški vestnik Journal of Mechanical Engineering, vol. 53, no. 5, p.

329-347.

[8] Semolič, B., Jovanović, P., Kovačev, S., Obradović, V. (2008). Improving Repair Management of Bucket Wheel Excavator SRs1200 by Application of Project Management Concept. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 6, p. 398-412.

[9] Nikiforov, D., Kutukov, A.A. (1994). Method to determine the utilization rate of equipment in the petroleum and chemical industry. Chemical and Petroleum Engineering, vol. 30, no. 3, p. 109-111, DOI:10.1007/BF01147882.

[10] Klarin, M.M., Cvijanovic, J.M., Spasojevic Brkic, V.K. (2000). The shift level of the utilization of capacity as the stochastic variable in work sampling. International Journal of Production Research, vol. 38, no. 12, p.

2643-2651, DOI:10.1080/002075400411402.

[11] Mobley, K.R. (2002). An Introduction to Predictive Maintenance. Plant Engineering, Amsterdam.

[12] Todinov, M.T. (2006) Reliability value analysis of complex production systems based on the losses from failures. International Journal of Quality & Reliability Management, vol. 23, no. 6, p. 696-718, DOI:10.1108/02656710610672498.

Đurić, Ž. – Josimović, L. – Adamović, Ž. – Radovanović, L. – Jovanov, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 309-318 DOI:10.5545/sv-jme.2010.007

Paper received: 2010-01-11, paper accepted: 2011-12-02 © 2012 Journal of Mechanical Engineering. All rights reserved.

Experimental Performance Evaluation of a Photovoltaic Thermal (PV/T) Air Collector and Its Optimization Mahdavi Adeli, M. – Sobhnamayan, F. – Farahat, S. – Alavi, M.A. – Sarhaddi, F. Mohsen Mahdavi Adeli1 – Fatemeh Sobhnamayan2 – Said Farahat3 – Mahmood Abolhasan Alavi2 – Faramarz Sarhaddi*,3 1Department of Mechanical Engineering, Susangerd Branch, Islamic Azad University, Susangerd, Iran 2Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran 3Department of Mechanical Engineering, University of Sistan & Baluchestan, Zahedan, Iran

The aim of the present study is the simultaneous optimization of thermal and electrical efficiencies of a solar photovoltaic thermal (PV/T) air collector. The analytical expressions for thermal parameters and thermal efficiency are derived by developing energy balance equation for each component of PV/T air collector. In order to calculate the electrical parameters and electrical efficiency of PV/T air collector the five–parameter current–voltage (I–V) model and a set of translation equations are used. An experimental setup for a typical PV/T air collector is built to measure its thermal and electrical parameters. The experimental validation of the used thermal and electrical models has been carried out by the measured data. It is observed that there is a good agreement between simulated and experimental results. Finally, the simultaneous optimization of the PV/T air collector has been carried out to maximize thermal and electrical efficiencies, simultaneously. Furthermore, the optimized ranges of inlet air velocity, duct depth and the objective functions in optimal Pareto front have been obtained.

Keywords: solar photovoltaic thermal (PV/T) air collector, simultaneous optimization

0 INTRODUCTION PV systems are one of the main substitutes for fossil fuels since they exhibit many merits such as cleanness, little maintenance and no noise. However, they still present a vast area of competition comparing to conventional energy resources due to their high cost and low efficiency during energy conversion.

The electrical efficiency of a PV system is highly dependent on its surface temperature. If the surface temperature of PV system is reduced its electrical efficiency is increased. In order to increase the electrical efficiency of PV system and reduce its energy payback time (EPBT), it is combined with the solar air/water heater collector. This type of a system is called solar photovoltaic thermal (PV/T) collector.

The PV/T collector produces thermal and electrical energy simultaneously.

A significant amount of theoretical as well as experimental studies on the PV/T systems has been carried out in the last 40 years. Wolf [1] was the first to give the main concept of PV/T collector using water or air as the working fluid. Bhargava et al. [2] have analyzed a hybrid system which is a combination of an air heater and PV system parameters such as channel depth, length of the collector, and air mass flow rate. Hagazy [3] has investigated glazed PV/T air system for a single and double pass air heater for space heating and the drying purposes. Infield et al.

[4] have suggested reducing the temperature of the PV module by flowing air between the PV module

and the double glass wall for space heating. They have developed a steady-state model to evaluate an overall heat loss coefficient and thermal gain factor.

Tiwari et al. [5] have validated the theoretical and experimental results for the PV module integrated with air duct for composite climate of India and concluded that an overall thermal efficiency of PV/T system is significantly increased (18%) due to utilization of thermal energy from PV module. Dubey et al. [6] have derived the expression for temperature dependent electrical efficiency considering glass to glass and glass to tedlar type PV modules. Joshi et al.

[7] have compared thermal performance of a glassto-tedlar PV/T air collector and a glass-to-glass PV/T air collector and concluded that the glass-to-glass PV/T air collector has a better thermal performance than a glass-to-tedlar PV/T air collector. Tiwari and coworkers [8] and [9] have presented a numerical model predicting the performance of PV/T system, and experimentally validated for various configurations.

The exergy analysis and exergetic optimization of PV modules have been carried out by Sarhaddi et al.

[10] and [11]. They have indicated that the exergy efficiency of the PV array may be improved if heat can be removed from the PV array surface. Kim et al. [12] have investigated the effect of ambient temperature on the thermal characteristics of a PV module with and without fins and concluded that the surface temperature of PV module with fins is lesser than the one without fins because heat is emitted at the fins. Agrawal and Tiwari [13] have evaluated the

*Corr. Author’s Address: Department of Mechanical Engineering, University of Sistan & Baluchestan, Zahedan, Iran, fsarhaddi@eng.usb.ac.ir

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energy and exergy performance of a micro-channel photovoltaic thermal (MCPVT) collector under the constant mass flow rate of air. Their numerical computations have shown that the energy and exergy yields of a MCPVT collector are higher than the yields of conventional PV/T air collectors.

The PV/T system produces useful heat and electricity simultaneously and its performance is determined by thermal and electrical efficiencies. An increase in the electrical efficiency of PV/T system causes a decrease in its thermal efficiency and vice versa. In previous studies [1] to [13], the simultaneous optimization of the thermal and electrical efficiencies of PV/T air collector was not carried out. In this paper, a multi-objective optimization is develoved to maximize the thermal efficiency and electrical efficiency of PV/T air collector at the same time.

The simultaneous optimization of PV/T system is parametrically dependent on its thermal and electrical analysis. Hence, in the next sections these analyses will be carried out.

1 THERMAL ANALYSIS The proof of governing equations on the thermal analysis of PV/T air collector is not included to have a brief note. More details of the governing equations derivation is found in [5] to [9].

The analytical expressions for the thermal parameters and thermal efficiency of PV/T air collector can be obtained if the energy balance equation is written for each components of PV/T air collector. Fig. 1 shows the equivalent thermal resistant circuit of a PV/T air collector.

(

Tcell = (ατ )eff G + U t Tamb + U T Tbs

) (U + U

(

Tbs = h p1 (ατ )eff G + U tT Tamb + h f T f

t

) (U

tT

T

) , (1)

)

+ h f , (2)

h p1 h p2 ( ατ )eff G   T f,out =  Tamb +  ⋅ UL   (3)    −WU L L   −WU L L  ⋅ 1 − exp    + T exp  ,  mC  mC   p   f,in  p        p mC

(

)

(

    ⋅ 1 − exp  −WU L L   ,    mC  p    

 p T f,out − T f,in = Qu = mC −U L T f,in − Tamb

)

 h p1 h p2 ( ατ )eff G − UL 

(

(4)

)

 U T −T  p  mC  h p1 h p2 (ατ ) − L f,in amb  ⋅ eff  WLU L  G   (5)   −WU L L   ⋅ 1 − exp   ,  mC  p     where Tcell, Tbs, Tamb, Tf, Tf,in, Tf,out, Qu , G, UL, m , Cp, (ατ)eff, hp1, ,hp2, hf, L, W, and ηth are solar cell temperature, back surface temperature, ambient temperature, average air temperature, inlet air temperature, outlet air temperature, the rate of useful thermal energy, solar radiation intensity, overall heat loss coefficient, the mass flow rate of flowing air, the heat capacity of flowing air, the product of effective absorptivity and transmissivity, the penalty factor due to the presence of solar cell material, glass and EVA, the penalty factor due to the presence of interface between tedlar and working fluid, convective heat transfer coefficient in flow duct, the length of air duct, the width of air duct and PV/T air collector thermal efficiency, respectively.

ηth =

2 ELECTRICAL ANALYSIS

Fig. 1. The equivalent thermal resistant circuit of a PV/T air collector [5] to [9]

310

In order to calculate the electrical parameters and electrical efficiency of PV/T air collector the five– parameter current–voltage (I–V) model (Fig. 2) are used as follows [14].

Mahdavi Adeli, M. – Sobhnamayan, F. – Farahat, S. – Alavi, M.A. – Sarhaddi, F.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 309-318

F4 = Vmp,ref

Fig. 2. Equivalent electrical circuit in the five–parameter photovoltaic model [14]

  (V + IRs )   (V + IRs ) I = I L − I o exp  , (6)  − 1 −  a Rsh    

where, I and V represent current and voltage at load, a, IL, Io, Rs, Rsh are ideality factor, light current, diode reverse saturation current, series resistance and shunt resistance, respectively. In order to calculate five reference parameters (aref, IL,ref, Io,ref, Rs,ref, and Rsh,ref), the five pieces of information are needed at reference conditions. These five pieces of information are defined as follows [14]: • At short circuit current: I = Isc,ref , V = 0.

• At open circuit voltage: I = 0 , V = Voc,ref .

• At the maximum power point: I = Imp,ref , V = Vmp,ref .

• At the maximum power point:  d ( IV )   dI  + I = 0 .   = V  mp  dV  mp  dV At short circuit: [dI / dV]sc = –1 / Rsh,ref.

The subscript ref indicates the value of parameters at the reference conditions. Reference conditions or standard rating conditions (SRC) are defined as follows [14]: • Solar cell temperature at reference conditions is Tcell,ref = 25 °C. • The solar radiation intensity at reference conditions is Gref = 1000 W/m2.

Substituting the mentioned five pieces of information into Eq. (6), the following equations are obtained: F1 = − I sc ,ref + I L ,ref − I sc ,ref Rs ,ref Rsh ,ref −

(7) − I o ,ref exp I sc ,ref Rs ,ref aref − 1 = 0 ,   •

(

)

(

)

F2 = I L ,ref − I o ,ref exp Voc ,ref aref − 1 −   (8) − Voc ,ref Rsh ,ref = 0 ,   Vmp ,ref + I mp ,ref Rs ,ref F3 = − I mp ,ref − I o ,ref exp   aref  

(

+ I L ,ref − Vmp ,ref + I mp ,ref Rs ,ref

)

   − 1 +   (9)  

Rsh ,ref = 0 ,

 Vmp,ref + I mp,ref Rs,ref        aref  − I o,ref e 1  −  aref Rsh,ref   Vmp,ref + I mp,ref Rs,ref        aref   Rs,ref  I o,ref e Rs,ref +  1+ R a sh,ref ref  + I mp,ref = 0,

 I sc ,ref Rs ,ref        aref   − I e 1  o ,ref −  aref Rsh ,ref F5 =   I sc ,ref Rs ,ref        aref   Rs ,ref I e  o ,ref Rs ,ref + 1 +  Rsh ,ref aref  1 + = 0, Rsh ,ref

     + (10)     

    +   (11)   

where Voc, Vmp, Isc and Imp are open-circuit voltage, maximum power point voltage, short-circuit current and maximum power point current, respectively.

Functions F1, F2, F3, F4 and F5 form a set of five nonlinear equations in five unknown variables x1 = aref, x2 = IL,ref, x3 = Io,ref, x4 = Rs,ref and x5 = Rsh,ref.

There is a solution for above set in the Type 94 of TRNSYS [6]. However, in this study the mentioned set is solved by iterative methods. Since the Eqs. (7) to (11) are implicit and nonlinear equations, the NewtonRaphson method is used to solve them [14]. The simultaneous equations set of the Newton Raphson method in matrix form is defined as follows:  ∂F1 ∂F1 ∂F1 ∂F1 ∂F1   ∂x ∂x2 ∂x3 ∂x4 ∂x5   1   ∂F2 ∂F2 ∂F2 ∂F2 ∂F2     x1,t  ∂x1 ∂x2 ∂x3 ∂x4 ∂x5   x  ∂F3 ∂F3 ∂F3 ∂F3 ∂F3   2 ,t   ×  x3,t  ∂x1 ∂x2 ∂x3 ∂x4 ∂x5   x4 ,t  ∂F ∂F4 ∂F4 ∂F4 ∂F F4   4   x5 ,t  ∂x1 ∂x2 ∂x3 ∂x4 ∂x5    ∂F   5 ∂F5 ∂F5 ∂F5 ∂F5   ∂x1 ∂x2 ∂x3 ∂x4 ∂x5 

− x1,c   F1  − x2 ,c   F2  − x3,c  =  F3  ,    − x4 ,c   F4  − x5 ,c   F5 

Jacobian Matrix

where subscripts t and c refer to temporary and correct values of unknown variables. Solving the equations set of the Newton Raphson method gives the value of five parameters (aref, IL,ref, Io,ref, Rs,ref, and Rsh,ref), at the reference conditions (Tcell,ref = 25° C, Gref = 1000

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W/m2). In order to calculate the model parameters at new climatic and operating conditions (Gnew, Tcell,new), a set of translation equations is used such as follows [14]: a aref = Tcell Tcell,ref , (12)

Io

I o,ref

 T =  cell  Tcell,ref 

(

3

εN   exp  c  aref   

)

   , (13) 

 Tcell,ref  1 − Tcell 

(

)

I L = G Gref  I L,ref + α Tcell − Tcell,ref  , (14)  

∆T = Tcell − Tcell,ref , (15)

∆I = α G Gref ∆T + G Gref − 1 I sc,ref , (16)

∆V = β∆T − Rs ∆I , (17)

I sc = I sc,ref + ∆I , (18)

Voc = Voc,ref + ∆V , (19)

Rs

(

)

(

)

Dh =

The electrical efficiency of PV/T air collector is defined as the ratio of actual electrical output power to input the rate of solar energy incident on the PV/T surface as follows: Vmp I mp − Pfan

ηel = . (24) GAPV/T In the previous equations, Dh, APV/T , δ, hf , μ, k, ρ and ηfan are hydraulic diameter of flow duct, PV/T surface area, duct depth, the viscosity, conductivity, density of agent fluid and fan efficiency, respectively.

3 FORMULATION OF OPTIMIZATION PROBLEM The formulation of simultaneous problem is given as follows:

( 2Vmp − Voc ) ln (1 − I mp I sc ) + V − V oc mp I mp ( I sc − I mp ) + ln (1 − I mp I sc ) = , (20)

I mp

Rsh =

I sc Rs

I L − I o exp ( I sc Rs a ) − 1 − I sc

, (21)

where ε, Nc, α and β are semiconductor band gap energy (1.12 eV for silicon solar cell), cells number in series, current temperature coefficient and voltage temperature coefficient, respectively. PV module manufacturers usually give temperature coefficients.

The new value of Vmp and Imp is obtained from the maximum area of rectangle under the I – V characteristic curve, [d(IV) / dV]mp = 0, at new climatic and operating conditions. It is necessary to mention the equation [d(IV) / dV]mp = 0, (Eqs. (6), (20) and (21)) are constituted a set of implicit and nonlinear equations to update the value of Vmp, Imp, Rs and Rsh. This set of equations is solved by the NewtonRaphson method [14].

The consumed electrical power by fans to circulate working fluid in the PV/T air collector is calculated from [15]: 1.2465 × 10 APV / T h3f .5 µ1.83 Dh0.5 k 2.33C1p.17 ρ 2η fan

4 × Cross − sec tional area of duct 4δ W = , (23) 2( δ + W ) Wetted perimeter

optimization

 ηth = Eq. (5)  Maximize :   , ηel = Eq. (24)   subject to  0.01 ≤ δ ≤ 0.2 m,  0.01 ≤ Vin ≤ 12 m/s,  Tcell , T f,out , Tbs , T f , m , C p , I o , I L ,Rs , Rsh , a ,    I sc , Voc , I mp , Vmp , U L , U t , U T , U tT ,h f , Qu ,  D , µ , ρ , k , P , ( ατ ) , h ,h ,etc. ≥ 0 fan eff p1 p 2  h and  other nonlinear constraints [5] to [9]. 

Fig. 3. A sketch of NSGA-II algorithm [16]

4

312

Pfan =

, (22)

The simultaneous optimization problem of the PV/T colletor is a type of constraint multi-objective optimization problems. The objective functions and the constraint equations are nonlinear. Parameters

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δ and Vin are independent variables in optimization problem. In order to solve the optimization problem, NSGA-II agorithm is used. A schematic sketch of NSGA-II algorithm is shown in Fig. 3 [16].

More details of the NSGA-II algorithm and its solution are found in Ref. [16].

4 EXPERIMENTAL SETUP AND EXPERIMENTAL VALIDATION The experimental setup consists of one polycrystalline silicon PV module (45 W) integrated with an air duct.

Two DC fans (12 V) blow air into air duct. Fig. 4 shows the front view of PV/T air collector setup and its components.

plane of the PV module. Fifteen temperature sensors (DS18B20 (×8), DS1620 (×7)) were used to measure temperatures at a different location in the PV module and air duct. Wind speed was measured 30 cm above the PV modules by a Lutron Digital Anemometer (LM-8000). Two Digital Multimeter (Victor) were been used to measure various currents (Isc, Imp) and voltages (Voc, Vmp). Another Lutron Digital Anemometer (LM-8000) was used to measure air flow while entering the air duct.

The design parameters of the PV/T air collector are described in Table 1.

Table 1. The design parameters of the PV/T air collector Parameter PV Module L×W×δ Isc,ref Voc,ref Imp,ref Vmp,ref α β βcell Vin,exp

Fig. 4. Photograph of experimental setup of hybrid PV/T air collector

The experiments have been carried out on the constructed PV/T air collector in the Department of Mechanical Engineering, University of Sistan & Baluchestan, Zahedan (Iran), which is located at 60°:54'E longitude and 29°:32'N latitude. The measurements were recorded on a clear day from 9:00 a.m. to 5:00 p.m. in July 2011 with experimental data being recorded every 30 minutes. The measured data include the solar radiation intensity, ambient temperature, inlet and outlet air temperature, solar cell temperature, inlet air velocity, wind speed, opencircuit voltage, short-circuit current, maximum power point current and maximum power point voltage.

Solar radiation intensity was measured by a Digital Lux-meter (LX-1108) at the same incident

Value Polycrystalline silicon 45 W 0.997 m × 0.462 m × 0.05 m 2.98 A 20.5 V 2.76 A 16.3 V 5.6 mA/°C –0.12 V /°C 0.8 3 m/s

The simulated values of outlet air temperature, solar cell temperature, open-circuit voltage, shortcircuit current, maximum power point voltage and maximum power point current validated by their corresponding experimental values. Furthermore, a comparison between the experimental and simulated values of thermal efficiency and electrical efficiency were carried out.

In order to compare the simulated results with the experimental measurements, a root mean square percentage deviation (RMS) was evaluated by following equation [5] to [9]: RMS = ∑ 100 × (X sim,i − X exp,i ) X exp,i 

2

n , (25)

where n is the number of the experiments carried out.

The inlet air velocity was kept in a constant value during the course of experiments (Vin,exp ≈ 3 m/s). The variations of solar radiation intensity, and wind speed during the test day are shown in Fig. 5.

The experimental and simulated values of various temperatures (solar cell temperature, outlet air temperature, inlet air temperature, ambient temperature) during the test day are shown in Fig. 6. According to this figure, it has been observed that there is a good agreement between the experimental and simulated values of the mentioned temperatures.

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Furthermore, the root mean square percentage deviations of these temperatures are 4.75 and 3.69%, respectively.

The experimental and simulated values of thermal efficiency and electrical efficiency on the test day are shown in Fig. 8.

Fig. 5. The variations of solar radiation intensity and wind speed during the test day

The experimental and simulated values of opencircuit voltage, maximum power point voltage, shortcircuit current and maximum power point current during the test day are shown in Fig. 7. A comparison between the experimental and simulated values of these parameters are carried out in this figure. The root mean square percentage deviations of these parameters are 3.66, 4.24, 7.75, and 7.23%, respectively.

Fig. 7. The experimental and simulated values of various voltage and current during the test day

Fig. 8. The experimental and simulated values of thermal efficiency and electrical efficiency

Fig. 6. The experimental and simulated values of the various temperatures of PV/T air collector during the test day

314

According to this figure, it has been observed that there is a good agreement between the experimental and simulated values of these efficiencies.

Furthermore, the root mean square percentage

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deviations of these efficiencies are 8.89 and 5.94%, respectively.

The simulated parameters errors compared with those obtained by the experimental measurement are explained as follows: • temperature coefficients of current and voltage have been assumed constant. In practical cases, there is slight fluctuation due to the solar radiation intensity and PV module temperature variations; • radiative properties of absorbing surface has been assumed constant while they are changing during the day with the change of solar incidence angle on PV/T collector surface.

5 OPTIMIZATION RESULTS AND PARAMETRIC STUDIES Fig. 9 shows the values of objective functions and decision variables in optimal Pareto front.

Fig. 9. The optimum values of objective functions and decision variables in optimal Pareto front

The numerical range of the points shown in Fig. 9 is given in Table 2. The non-sensitive regions of the thermal efficiency and the electrical efficiency are also indicated in the same figure.

Table 2. The results of simultaneous optimization Optimum range of decision variables 0.109 ≤ δ ≤ 0.148 1.68 ≤ Vin ≤ 7.74 m/s

Optimum range of objective function 46.46 ≤ ηth ≤ 51.61% 5.43 ≤ ηel ≤ 9.26%

Unlike the conventional multi-objective optimization algorithms, the NSAG-II algorithm gives a range for each decision variables. In optimal Pareto front all the points have the same condition.

Each point shown in Fig. 9, introduces a vector of decision variables, X (δ ,Vin ) . In other words, each decision variable can not be selected solely; designer should choose a vector of decision variables. It is clear from Fig. 9 that choosing appropriate values for the decision variables, namely duct depth (δ) and inlet air velocity (Vin), to obtain a better value of one objective would normally cause a worse value of another objective. This subject shows Pareto optimal conditions. A designer can choose the desired vector of decision variables among optimal Pareto solutions according to their considerations such as thermal or electrical point of view, design limitations, economic costs, etc.

According to the results obtained from simultaneous optimization (Fig. 9), the thermal efficiency can be increased from ~46.5 to ~49%, while the electrical efficiency remains constant (~9.3%), approximately. On the other hand, the electrical efficiency can be increased from ~5.5 to ~7.5%, while the thermal efficiency has no sensible variations (~51.5%). This subject is suitable from engineering design perspective as it leads to nonsensitive selection from a thermal or electrical point of view.

In order to plot the following figures some parameters are assumed which are mentioned above each figure. Fig. 10 shows the variations of thermal efficiency and electrical efficiency with respect to inlet air velocity.

The thermal efficiency increases from 0 to ~52% while inlet air velocity is increasing from 0.001 to 12 m/s. On the other hand, the electrical efficiency decreases from ~9 to 0% while inlet air velocity is increasing. The increase of inlet air velocity increases pressure drop in air duct, therefore the consumed power by fans is raised and in consequence, the electrical efficiency decreases.

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solar radiation intensity for given climatic and design parameters (Table 1). On the other hand, thermal efficiency has a slight change (~52%) with respect to solar radiation intensity variations.

Fig. 10. The variations of thermal efficiency and electrical efficiency with respect to inlet air velocity

The variations of thermal efficiency and electrical efficiency with respect to duct depth are shown in Fig. 11.

Fig. 12. The effect of solar radiation intensity on the thermal efficiency and electrical efficiency

Fig. 13 shows the variations of thermal efficiency and electrical efficiency according to the changes of wind speed.

Fig. 11. The variations of thermal efficiency and electrical efficiency with respect to duct depth

According to this figure, the thermal efficiency increases from 0 to ~48% when duct depth increases from 0.001 to 0.2 m. On the other hand, the electrical efficiency has a slight change with respect to duct depth (~8%).

Fig. 12 shows the effect of solar radiation intensity on the thermal efficiency and electrical efficiency.

It has been observed that the electrical efficiency increases from 0 to ~8% initially and then it remains constant after the solar radiation intensity reaches about 200 W/m2. This indicates the optimum value of 316

Fig. 13. The variations of thermal efficiency and electrical efficiency with respect to wind speed

Acoording to Fig. 13, thermal efficiency decreases from ~51 to ~29% while wind speed increases from 0 to 10 m/s. On the other hand, electrical efficiency increases from ~8 to ~9.5% while wind speed is increasing. The increase of wind speed increases overall heat loss coefficient, therefore solar

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cell temperature is decreased and in consequence, the thermal efficiency decreases and the electrical efficiency increases.

6 CONCLUSION On the basis of the present study, the following conclusions have been drawn: • The numerical simulation results are in good agreement with the experimental measurements carried out; • Unlike the conventional optimization methods, the simultaneous optimization by NSAGII algorithm gives a range for each decision variables; • The thermal efficiency can be increased from ~46.5­to ~49%, while electrical efficiency remains constant (~9.3%), approximately. On the other hand, electrical efficiency can be increased from ~5.5­to ~7.5%, while the thermal efficiency has not sensible variations (~51.5%). This subject is desired from a perspective of engineering design as a designer can choose the desired vector of decision variables among optimal Pareto solutions according to their considerations such as thermal or electrical application, design limitations, economic costs, etc.; • Increasing the solar radiation intensity, the electrical efficiency of PV/T air collector increases initially and then it remains constant after attaining solar radiation intensity of about a maximum point.

7 NOMENCLATURE a A Cp G h hp I L m P T U V W

ideality factor [eV] area [m2] specific heat capacity of air [J/(kg·K)] solar radiation intensity [W/m2] heat transfer coefficient [W/(m2·K)] penalty factor current [A] dimensions of PV/T air collector [m] mass flow rate of air [kg/s] power [W] temperature [K] overall heat loss coefficient [W/(m2·K)] circuit voltage [V], wind speed [m/s] width of PV/T air collector [m]

Greek symbols α current temperature coefficient [mA/°C]

β packing factor, voltage temperature coefficient [V/°C] δ duct depth [m] η efficiency [%] ρ density [kg/m3] Subscripts amb ambient bs back surface of tedlar cell cell, module el electrical exp experimental f fluid flow fan fan in inlet L light current mp maximum power point o reverse saturation oc open-circuit out outlet PV/T PV/T ref reference s series sc short-circuit sh shunt sim simulated th thermal u useful w wind 8 REFERENCES [1] Wolf, M. (1976). Performance analysis of combined heating and photovoltaic power systems for residences.

Energy Conversion and Management, vol. 16, p. 79-90, DOI:10.1016/0013-7480(76)90018-8.

[2] Bhargava, A.K., Garg, H.P., Agarwall, R.K. (1991).

Study of a hybrid solar system-solar air heater combined with solar cells. Energy Conversion and Management, vol. 31, no. 5, p. 471-479, DOI:10.1016/01968904(91)90028-H. [3] Hegazy, A.A. (2000). Comparative study of the performances of four photovoltaic/thermal solar air collectors. Energy Conversion and Management, vol.

41, p. 861-881, DOI:10.1016/S0196-8904(99)00136-3.

[4] Infield, D., Mei, L., Eicker, U. (2004). Thermal performance estimation of ventilated PV facades.

Solar Energy, vol. 76, p. 93-98, DOI:10.1016/j. solener.2003.08.010.

[5] Tiwari, A., Sodha, M.S., Chandra, A., Joshi, J.C. (2006). Performance evaluation of photovoltaic thermal solar air collector for composite climate of India. Solar Energy Materials & Solar Cells, vol. 90, no. 2, p. 175-189, DOI:10.1016/j.solmat.2005.03.002.

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[6] Dubey, S., Sandhu, G.S., Tiwari, G.N. (2009).

Analytical expression for electrical efficiency of PV/T hybrid air collector. Applied Energy, vol. 86, no. 5, p.

697-705, DOI:10.1016/j.apenergy.2008.09.003.

[7] Joshi, A.S., Tiwari, A., Tiwari, G.N., Dincer, I. (2009).

Performance evaluation of a hybrid photovoltaic thermal (PV/T) (glass-to-glass) system. International Journal of Thermal Sciences, vol. 48, p. 154-164, DOI:10.1016/j.ijthermalsci.2008.05.001.

[8] Gaur, M.K., Tiwari G.N. (2010). Optimization of number of collectors for integrated PV/T hybrid active solar still. Applied Energy, vol. 87, p. 1763-1772, DOI:10.1016/j.apenergy.2009.10.019.

[9] Agrawal, B., Tiwari, G.N. (2010). Optimizing the energy and exergy of building integrated photovoltaic thermal (BIPVT) systems under cold climatic conditions. Applied Energy, vol. 87, p. 417-426, DOI:10.1016/j.apenergy.2009.06.011.

[10] Sarhaddi, F., Farahat, S., Ajam, H., Behzadmehr, A. (2010). Exergetic performance evaluation of a solar photovoltaic (PV) array. Australian Journal of Basic and Applied Sciences, vol. 4, no. 3, p. 502-519.

[11] Sarhaddi, F., Farahat, S., Ajam, H., Behzadmehr, A. (2010). Exergy efficiency of a solar photovoltaic

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array based on exergy destructions. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 224, no. 6, p. 813-825, DOI:10.1243/09576509JPE890.

[12] Kim, J.P., Lim, H., Song, J.H., Chang, Y.J., Jeon, C.H. (2011). Numerical analysis on the thermal characteristics of photovoltaic module with ambient temperature variation. Solar Energy Materials & Solar Cells, vol. 95, p. 404-407, DOI:10.1016/j. solmat.2010.05.016.

[13] Agrawal, S., Tiwari, G.N. (2011). Energy and exergy analysis of hybrid micro-channel photovoltaic thermal module. Solar Energy, vol. 85, no. 2, p. 356-370, DOI:10.1016/j.solener.2010.11.013.

[14] De Soto, W. (2004). Improvement and validation of a model for photovoltaic array performance. M.Sc thesis, University of Wisconsin-Madison, p. 20-74.

[15] Kakaç, S., Liu, H. (2003). Heat exchangers: selection, rating and thermal design. 2nd ed., CRC Press Florida.

[16] Deb, K. (2001). Multi-objective optimization using evolutionary algorithms, 1st ed., John Wiley & Sons Ltd., Chichester.

Mahdavi Adeli, M. – Sobhnamayan, F. – Farahat, S. – Alavi, M.A. – Sarhaddi, F.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 319-326 DOI:10.5545/sv-jme.2011.172

Paper received: 2011-09-23, paper accepted: 2012-01-27 © 2012 Journal of Mechanical Engineering. All rights reserved.

Low-Frequency Sonoporation in vitro: Experimental System Evaluation

Jelenc, J. – Jelenc, J. – Miklavčič, D. – Maček Lebar, A. Jure Jelenc1 – Jože Jelenc1 – Damijan Miklavčič2 – Alenka Maček Lebar2,* 1 Iskra Medical d.o.o., Slovenia 2 University of Ljubljana, Faculty of Electrical Engineering, Slovenia Sonoporation is a phenomenon where ultrasound increases cell membrane permeability. As the result, molecules that are otherwise deprived of transport mechanisms can be transported across the cell membrane. Several different experimental exposure systems are described in the literature. Low-frequency ultrasound (<500 kHz) exposure systems can be divided into two groups: systems with the transducer directly immersed in the cell suspension and systems with the transducer in a water bath.

We developed an experimental system based on progressive ultrasound wave in a water bath. It consists of a transducer operating at 29.6 kHz submerged in a water bath, and bath walls lined by ultrasound absorbing lining. Using a hydrophone, we evaluated ultrasound reflections inside the bath, both with and without acoustic lining on the bath’s boundaries. We also built a finite element model of the system in order to calculate ultrasound parameters that are inaccessible by conventional hydrophone measurement due to equipment limitations. The experimental system will enable exposure of cells to pre-measured and pre-calculated ultrasound conditions.

Keywords: ultrasound, hydrophone, cavitation, finite element model

0 INTRODUCTION Sonoporation is a phenomenon where ultrasound increases cell membrane permeability. As a result, molecules that are otherwise deprived of transport mechanisms can be transported across the cell membrane. Transport through the membrane becomes possible for molecules with both small and large molecular mass [1] to [3]. If the cell remains capable of repairing the damage to the membrane and re-establishing a normal state, the phenomenon is called reversible sonoporation. If the cell dies as a consequence of ultrasound exposure, sonoporation is irreversible.

The mechanisms of in vitro sonoporation have not yet been fully explored, but are most often associated with cavitation. Cavitation is defined as the creation of new surfaces or expansion/contraction/distortions of pre-existing ones in a liquid [4] and [5], and is strongly depended on gas content of the liquid [6]. Cavitation occurs when a liquid is subjected to rapid changes of pressure; therefore ultrasound could be the reason for its appearance [4], [7] and [8]. Althought cavitation is usually related to gas bubbles in the extracellular fluid [9], recently cell intramembrane cavitation has been proposed [10]. However, to control the effects of sonoporation and connect them with the transient or stable cavitation [4], it is necessary to measure and control spatial and temporal ultrasound pressure.

Sonoporation was demonstrated using ultrasound waves of different frequencies. The most commonly used frequencies are those in therapeutic (1 to 3 MHz) and diagnostic ultrasound transducers (3 to 18 MHz) as well as lithotripsy transducers [11]. Nevertheless,

several experiments have also been conducted with low-frequency ultrasound transducers (below 500 kHz).

Ultrasound frequencies above 1 MHz have been used in a number of studies where fluorescent dyes, genetic material and chemotherapeutic drugs were efficiently delivered into cells [1] and [12] to [15]. Less research has been done on low-frequency sonoporation using frequencies below 500 kHz, which has also been demonstrated with dye delivery [16] to [19], genetic material delivery [11] and [20] and chemotherapeutic drug delivery into cells [21]. Regardless of the ultrasound frequency used in the sonoporation experiments; other ultrasound parameters needed for efficient sonoporation were reported inconsistently. Ultrasound pressure to which the cells are exposed is insufficiently reported; instead authors report on ultrasound intensity, energy or some other derived quantity [22].

Sonoporation studies are usually performed on cells suspended in the growth medium. Different types of experimental systems have been developed for research of low-frequency sonoporation. Depending on the way ultrasound waves are delivered to cells, these systems can be divided into two groups: systems where the ultrasound transducer and cells suspension are in direct contact and systems where dish containing the cell suspension is submerged in a water bath.

Exposure with direct contact between the ultrasound transducer and cell suspension is achieved by directly inserting the ultrasound transducer into the dish with the cell suspension. In addition to custom made ultrasound transducers, transducers for mixing and homogenizing mixtures in laboratory equipment

*Corr. Author’s Address: University of Ljubljana, Faculty of Electrical Engineering, Tržaška 25, 1000 Ljubljana, Slovenia, alenka.maceklebar@fe.uni-lj.si

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have also been used for exposure of cells [23]. In this cylinder or horn-shaped transducer, the piezoelectric ultrasound transducer is located in the upper part. The ultrasound propagates along the cone or cylinder, with the tip of the object inserted into a dish with the cell sample. This method has been frequently used due to its simplicity, but has several disadvantages. The exposure of the cells in suspension to ultrasound is non-homogeneous because the ultrasound transducer is only inserted into part of the cell sample. Moreover, the small sample size does not allow insertion of ultrasound measurement devices into the cell sample.

Furthermore, the sample can heat up quickly.

In the experiments with an ultrasound transducer submerged in water, ultrasound propagates through water to a submerged dish (usually a laboratory centrifuge tube) filled with a cell suspension.

The main drawbacks of this method are possible ultrasound reflections caused by centrifuge tube, which are usually neglected as tubes are made of ultrasound transparent materials [24]. Heating of the cell suspension is minimized due to heat dissipation in water. A hydrophone inserted into the water bath allows ultrasound pressure inside the bath to be measured, and therefore the cells can be exposed to known, previously measured ultrasound pressure.

The most important parameter in sonoporation experimental system is ultrasound pressure, which is usually measured by a hydrophone. The hydrophone responds to acoustic waves generating a voltage proportional to the acoustic pressure [25]. The hydrophone measures the combination of the incident ultrasound pressure and the pressure due to reflections from the bath boundaries. The incident ultrasound can be measured directly either by using measurements of pulsed ultrasound or by avoiding reflections.

Measurements of pulsed ultrasound allow ultrasound pressure to be measured before the reflected waves reach the hydrophone [25]. This approach does not reduce reflected waves, but simply allows us not to measure them. On the other hand, lining the walls of the water bath with an ultrasound absorber reduces the amount of reflected waves; therefore, only progressive ultrasound propagation is obtained. Such exposure conditions have been frequently used in sonoporation experiments [2], [20] and [26], but the amount of wave reflection reduction in sonoporation exposure systems using absorbing lining has not been reported.

The aim of the study was to design a system for observing influence of low frequency ultrasound in sonoporation in vitro, with well defined ultrasound pressure at the position of the cell sample. We constructed and evaluated a water bath experimental 320

system based on progressive wave ultrasound propagation. The evaluation was performed by acoustic pressure measurements and by a finite element numerical model. Good agreement of measured and calculated pressure will allow us to report verified spatial and temporal ultrasound pressure characteristics, and relate them to the effects on the exposed cells.

1 METHODS 1.1 Experimental System A water bath with a length of 68 cm, width of 38 cm and height of 34 cm was filled with distilled water up to a height of 24 cm (Fig. 1). Ultrasound was generated using a prototype center bolt (Langevin type) piezoelectric ultrasound transducer [27] and [28] with an operating frequency of 29.6 kHz (Iskra Medical, Slovenia). The transducer was submerged in a water bath at a depth of 12 cm. Ultrasound pressure was measured with a piezoelectric hydrophone (8103 hydrophone, Brüel & Kjær, Denmark) that was located on the central axis of the ultrasound transducer. Hydrophone positioning system allowed the distance between the hydrophone and transducer to be adjusted. The walls of the bath were made from Plexiglas®. In some experiments the walls of the water bath were lined with the SA-J35 ultrasound absorber (Hangzhou Applied Acoustics Institute, China).

According to the manufacturer this material decreases ultrasound reflection by 20 dB at a frequency of 30 kHz.

Fig. 1. Experimental system consisting of: an ultrasound transducer (1), a hydrophone (2), water bath walls (3), ultrasound absorbing lining (4) and a positioning system (5)

1.2 Measuring Equipment Ultrasound pressure in the water bath was measured using a calibrated 8103 hydrophone (Brüel & Kjær,

Jelenc, J. – Jelenc, J. – Miklavčič, D. – Maček Lebar, A.

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Denmark). The active element of the hydrophone is a piezoelectric transducer. The 8103 hydrophone is designed for measuring pressure changes with frequencies between 0.1 Hz and 180 kHz. The sensitivity of the hydrophone to pressure changes as a function of the wave frequency was supplied by the manufacturer. We used the sensitivity value 0.08764 pC/Pa, acquired at a frequency of 28 kHz. The hydrophone sensitivity changes by less than 0.5% when frequency increases up to 31.4 kHz. The hydrophone signal was amplified with a dedicated “Measuring amplifier 2525” (Brüel & Kjær, Denmark). Real-time signal acquisition was performed by connecting the hydrophone output via the amplifier to a TPS 2024 oscilloscope (Tektronix, USA). Since the low-amplitude hydrophone signal may be distorted due to reflected waves or environmental disturbances, the signal acquisition was triggered by the voltage exciting the ultrasound transducer.

1.3 Measuring the Ultrasound Pressure In order to study ultrasound reflection, we generated 8 periods of an ultrasound wave (29.6 kHz, power set to 50%) and measured the pressure with a hydrophone at a distance of 3.5 cm from the transducer. After measuring the amplitude of incident pressure over the first 0.6 ms, we measured the reflected waves from 0.6 to 10 ms. The measurement procedure was first performed in a bath with no absorbable lining.

Then, the walls were lined with an absorber and the procedure was repeated. In both cases, the maximum amplitude of the signal was estimated. To evaluate the reduction of the reflection by the lining in the system, we evaluated an integral of absolute pressure from 0.6 to 10 ms, which represents the area of the signal.

The reduction is presented as a ratio of the area of the reflections measured with and without the absorbable lining.

The spatial distribution of ultrasound pressure was evaluated by measuring ultrasound at the axial center of transducer while varying the distance between the ultrasound transducer and hydrophone using a manual positioning system. The distance between the ultrasound transducer and hydrophone was varied from 1.5 to 10 cm in steps of 0.5 cm.

The walls of the bath were lined with the absorber. A continuous wave ultrasound (cw) with power setting at 20% was used. The absolute measured value of peak compression was the same as the absolute value of peak rarefaction pressure. Root mean square pressure (RMS) is given as the mean and standard deviation of nine measurements, performed on 3 separate days.

Interday measurements were taken in order to take into account an error resulting from repositioning of the measuring system and changing the concentration of the dissolved gasses in the water. The nonlinear regression model was fitted to the measured data and the coefficient of determination R2, was calculated using SigmaPlot 11 (Systat, USA).

1.4 Finite Element Model The acoustic pressure generated in water by a composite Langevin type [27] sandwich transducer was modeled using finite element method (FEM) numerical calculations in Comsol 3.5 (Comsol Group, USA), by coupling structural mechanic, piezoelectric and pressure acoustic equations. The transducer’s geometries (Fig. 2) were measured on a prototype transducer (Iskra Medical, Slovenia) that consists of two Lead Zirconate Titanate (PZT-4) elements sandwiched between the aluminum and the iron part. Three 0.2 mm adhesive layers were modeled between the metals and PZT-4 elements. The system was simplified by omitting the inner bolt and also the mechanical bias generated inside the transducer by the bolt. Material properties of the iron, two piezoelectric layers PZT-4, aluminum, and water were modeled using Comsol 3.5’s material library. Additional three adhesive layers were described using Young's modulus (1010 Pa), Poisson’s ratio (0.38) and density (1700 kg/m3).

The tension inside the structural mechanic model was obtained using alternating current (AC) conditions. On each of the piezoelectric elements voltage electrical boundary condition was applied; amplitude was set on 260 V and frequency on 29.6 kHz. This voltage condition corresponds to the voltage measured on the transducer with power on the voltage generator set to 20%. An electrical ground condition was applied to the other side of each piezoelectric element. The applied voltage induces mechanical stress σ inside the piezoelectric material as described by equations:

σ = cE · ε – eT · E ,

(1)

D = e · ε + ε0εrs · E ,

(2)

where ε is the strain vector, cE is the elastic stiffness matrix of the material under a constant electric field, e is the piezoelectric stress matrix, ε0εrs is electric permittivity matrix under constant strain, E is the electrical field vector and D is the electrical displacement vector [29]. The stress and strain inside

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the transducer are calculated using the principle of virtual work [30]: δW = 0 .

(3)

Movement of the solid domain boundaries was unconstrained, but the displacement of the boundaries was considered small; thus, there was no need to remesh the model during calculation. The acceleration an of the transducer-water boundary in the normal direction na (outward-pointing from the water domain) is a source of pressure changes in water p, and ∇p is pressure gradient: 1 na ⋅ ( ⋅ (∇p )) = an . ρ

(4)

The pressure p in the water generates force Fn on the water/solid boundary to the solid domain in the normal direction ns (outward-pointing from the solid domain): Fn= – ns · p .

(5)

Ultrasound pressure in water was modeled using the homogeneous Helmholtz equation:

1 ∂2 p 1 ⋅ + ∇ ⋅ (− ⋅∇p ) = 0, ρ ρ ⋅ c 2 ∂t 2

(6)

where p is pressure, ρ is the density of water, and c is the speed of sound in water. The equation was solved for a time-harmonic wave with an excitation frequency of 29.6 kHz. With arbitrary coordinate x, the pressure p becomes periodic with an angular frequency ω, and i as imaginary unit: p(x,t) = p(x) · eiωt .

(7)

Therefore, the homogeneous Helmholtz equation simplifies to:

−

ω2 ⋅ p 1 ⋅ +∇ ⋅ (− ⋅∇p ) = 0.

2 ρ ρ ⋅c

(8)

A perfectly matched layer was added on the far boundary of the liquid, which acts as a material where the loss factor increases, therefore damps the wave and does not cause any reflections on the boundary.

Boundaries of the other materials are allowed to move without constraints.

To reduce the computational cost, the 3D model was reduced to a 2D axial symmetry model. The finite element mesh was generated with the maximum element size restricted to at least 1/5 of the maximum wavelength. Due to the low computation cost of axial 322

symmetry, and in order to achieve high precision, we used denser mesh consisting of 2·105 triangular elements.

2 RESULTS 2.1 Measuring the Ultrasound Pressure The measured pulsed signal can be divided into two parts. The first 0.6 milliseconds represent eight pulses of incident ultrasound with maximum pressure amplitude of 135 kPa. Reflections of pulsed ultrasound from boundaries are shown in Fig. 3.

Reflections with no acoustic lining are shown in Fig. 3a, while reflections using the acoustic lining on the boundaries of the water bath are shown in Fig. 3b. In both cases, the measurement of the incident pressure causes measurement saturations. We have therefore omitted the first 0.6 seconds from Fig. 3. Fig. 3 thus only shows reflections. If no absorptive material is used, the maximum value of the reflected wave is 42 kPa or 31% of the incident pressure. The maximum value of reflection pressure using absorber is 7.8 kPa or only 6% of the incident pressure. Use of the absorptive material reduces the area of the reflected wave signal to 7.8% of the area of the signal acquired without the use of the absorber.

The effect of the distance between the ultrasound transducer and hydrophone on the effective value of continuous-wave ultrasound pressure was observed at distances from 1.5 to 10 cm. The largest effective value of ultrasound pressure was measured closest to the transducer at a distance of 1.5 cm: 111±10.6 kPa. Ultrasound pressure decreases exponentially as the distance between the transducer and hydrophone increases (Fig. 4). The standard deviation was considerably smaller within experiment done on the same day (less than 5%), and increased when measurements from multiple days were pooled together (up to 15%).

2.2 Finite Element Model The calculated RMS pressure distribution in liquid induced by the transducer is shown in Fig. 2. In order to compare it to the measured results, we used results from the center of the axial symmetry (Fig. 4).

The maximum RMS pressure value calculated using the FEM model was at the transducer’s boundary and had a value of 127 kPa. Experimental data at this distance was not accessible, due to spatial restrictions of our experimental setup. The first common measurement was therefore done at 1.5 cm from the

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transducer with a measured value of 111±10.6 kPa and calculated value of 91 kPa. Both results showed expected exponentially decaying RMS pressure value on the axial center of the transducer. Using nonlinear regression we fitted experimental results and FEM results onto a three parameters exponential decaying curve: pr (d ) = c1 ⋅ e − c2 ⋅d + c3 ,

(9)

where d is a distance between the transducer and the hydrophone. The regression parameters c1, c2 and c3 and coefficient of determination R2 are shown in Table 1.

Table 1. Nonlinear regression parameters Experiment FEM

c1 [kPa] 143.649 120.387

c2 [1/cm] 0.342 0.338

c3 [kPa] 24.515 17.984

R2 0.938 0.999

Fig. 2. Axial symmetry transducer geometry (1) and axial symmetry root mean square (RMS) pressure filed inside the water domain (2a), with a corresponding RMS pressure scale (2b); transducer geometry is composed of aluminum layer (1a), two piezoelectric layers (1b), iron layer (1c), bolt head made of iron (1d) and three narrow adhesive layers (1e); only one half of symmetry is shown

Fig. 3. Reflection of the eight periods of ultrasound signal from the boundaries; the reflections are shown 0.6 seconds after the signal was generated, so the incident ultrasound has already passed the hydrophone; signal a) without absorptive lining of the water bath walls and b) with the lining Low-Frequency Sonoporation in vitro: Experimental System Evaluation

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3 DISCUSSION Even though a number of investigators have shown that cavitation, as the main mechanism of sonoporation, can more easily be induced by a standing wave than by a progressive wave [26] and [31], a standing wave is difficult to achieve in clinical settings due to variations of geometries inside the human body [31].

To increase the possibility of translation of the future results achieved in our in vitro exposure system to in vivo settings, we thus designed experimental system based on progressive wave ultrasound propagation.

As expected, the results of our study show that in an experimental system with finite dimensions reflected waves are present. Reflected waves are especially strong if no absorbable material is used.

Though reflected waves are weaker than the waves coming directly from the ultrasound transducer, the pressure of the reflected waves in our system represents up to 31% of the pressure of the waves coming directly from the transducer. Reflected ultrasound waves are present in the water bath up to 2 ms after the ultrasound transducer has stopped emitting waves. At this time, ultrasound can travel across the longest dimension of the water bath four times. It is thus very likely that reflections of reflected waves are also present in the water bath. All these reflections are superimposed onto the incident pressure, thus preventing accurate measurements of the incident pressure. If the system is working continuously (cw), stationary waves may also occur and further reduce the accuracy of the incident pressure measurements.

In our system, reflections were successfully reduced by lining the walls of the water bath with a special material that absorbs ultrasound. The area of the reflected wave signal was reduced by a factor of 12, thus rendering the reflected waves barely noticeable (Fig. 3b).

To be able to expose cells to ultrasound in a water bath, we also need to determine spatial distribution of ultrasound waves in the bath. Therefore, we measured ultrasound pressure as a function of distance from the ultrasound transducer during continuous operation, in water bath with walls lined with ultrasound absorber.

Measurements were performed at the transducer’s central axis and showed an exponential decrease in ultrasound pressure as a function of distance. The standard deviation of the measurements was up to 15%. This is a reasonable value considering we are dealing with a continuous (cw) low frequency ultrasound transducer. We have observed that intraday experiments had much smaller standard deviation of only a few percent. Some of the interday 324

uncertainty can be associated to the positioning error of the hydrophone and the transducer and some to the change of water quality due to internalization of gasses from the air. The cavitation phenomenon could also alter ultrasound pressure in the water, but 120 kPa ultrasound pressure is still considered to be a subcavitational level in a carefully processed water [20], and thus does not affect the measurements.

Fig. 4. The root mean square (RMS) value of ultrasound pressure at axial center of the transducer, as a function of distance between the transducer and hydrophone; the data was acquired using hydrophone measurements (diamonds) and calculation of FEM model (triangles); distance on transducer’s central axis was varied from 1.5 to 10 cm in steps of 0.5 cm The results from the FEM model gave a good description of the system’s behavior, although the calculated values were slightly smaller than those obtained experimentally. The FEM model results were affected by the model simplifications; mainly by omitting the inner bolt and the mechanical bias generated by the bolt. These were omitted due to a lack of relevant data needed for implementation into the FEM model. Bolt generated mechanical bias is known to increase ultrasound pressure amplitude [28]. Calculated values that do not incorporate mechanical bias thus must be lower than the measured ones. Also, some minor geometry features and a copper plate that serves as the electrical conductor for the PZT element have been omitted. When these limitations are resolved, the model accuracy could be further improved, especially the response at different frequencies.

By achieving good agreement between the hydrophone measurements and FEM model results we can conduct experiments at known ultrasound pressure anywhere in the experimental bath. In such a

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system, it is possible to expose biological materials to incident ultrasound under known pressure.

4 CONCLUSIONS We have developed a system for low-frequency in vitro sonoporation experiments based on progressive ultrasound wave in water bath. It consists of a transducer submerged in a water bath, and bath walls lined by ultrasound absorbing lining. Using a hydrophone, we evaluated ultrasound reflections inside the bath, both with and without acoustic lining on the bath’s boundaries. By using a specialized acoustic lining and sufficient size of the water bath, we were able to reduce the reflections to a level where measurements of low-frequency (29.6 kHz) continuous wave ultrasound were made possible. In this regime, we evaluated the spatial characteristics of the system and confirmed them with a finite element model. This experimental system will enable exposure of cells to pre-measured and pre-calculated ultrasound conditions.

5 ACKNOWLEDGMENTS Operation is part financed by the European Regional Development Fund (Biomedical Engineering Competence Center, Slovenia), European Social Fund and Slovenian Research Agency (L2-2044).

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[26] Kinoshita, M., Hynynen, K. (2007). Key factors that affect sonoporation efficiency in in vitro settings: the importance of standing wave in sonoporation. Biochemical and Biophysical Research Communications, vol. 359, no. 4, p. 860-865, DOI:10.1016/j.bbrc.2007.05.153.

[27] Radmanovic, M.D., Mancic, D.D. (2004). Design and modeling of the power ultrasonic transducers, University of Niš, Niš.

[28] Moreno, E., Acevedo, P., Fuentes, M., Sotomayor, A., Borroto, L., Villafuerte, M.E., Leija, L. (2005).

Design and construction of a bolt-clamped Langevin transducer. International Conference on Electrical and Electronics Engineering, Proceedings, p. 393-395, DOI:10.1109/ICEEE.2005.1529652.

[29] Abboud, N.N., Wojcik, G.L., Vaughan, D.K., Mould, J., Powell, D.J., Nikodym, L. (1998). Finite element modeling for ultrasonic transducers. Proceedings of the SPIE International Symposium on Medical Imaging, p.

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[30] Szabó, B.A., Babuska, I. (1991). Finite element analysis. John Wiley & Sons, New York.

[31] Barati, A.H., Mokhtari-Dizaji, M., Mozdarani, H., Bathaie, Z., Hassan, Z.M. (2007). Effect of exposure parameters on cavitation induced by low-level dualfrequency ultrasound. Ultrasonics Sonochemistry, vol. 14, no. 6, p. 783-789, DOI:10.1016/j. ultsonch.2006.12.016.

Jelenc, J. – Jelenc, J. – Miklavčič, D. – Maček Lebar, A.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 327-337 DOI:10.5545/sv-jme.2010.232

Paper received: 2010-11-15, paper accepted: 2012-01-27 © 2012 Journal of Mechanical Engineering. All rights reserved.

Gear Unit Housing Effect on the Noise Generation Caused by Gear Teeth Impacts Ognjanović, M. – Ćirić Kostić, S. Milosav Ognjanović1,* – Snežana Ćirić Kostić2 1 University of Belgrade, Faculty of Mechanical Engineering, Serbia 2 University of Kragujevac, Faculty of Mechanical Engineering, Serbia The basic hypothesis of the paper is that machine part surfaces are membranes that divide inner and outer space, receive disturbance power from inner space and emit it to the surroundings. Additionally, machine systems operation causes numerous disturbances such as collisions, sliding, rolling, etc. Gear drives are a very interesting case for analysis of teeth impacts, which cause restorable free vibrations and spreading of disturbance power through elastic structure. The gear unit housing has a dominant role in the transformation of disturbance power and modulation of the sound emitted to the surroundings. This is an important detail for monitoring and diagnostics by emitted noise measurements. By combination of theoretical, numerical and experimental analyses, using a classical gear drive unit (reducer), this article explains the process of spreading disturbance power through the elastic structure, especially the role of the gear unit housing. Its role in the noise frequency spectrum modulation is determined by modal sensitivity to disturbances and noise isolation ability of the housing. The analysis of modal behavior of the housing and its modal shape excitation presents the main content of the paper.

Keywords: gears, noise, vibration, modal analysis

0 INTRODUCTION The process of gear unit noise generation is complex and it is usually studied through investigations of three sub-processes: generation of disturbance power by the action of gear unit components (gears and bearings), spreading of disturbances through the gear unit structure and disturbance power emission through vibrations and noise of the gear unit. Identification of dominant causes of noise at the place where disturbances are generated was extensively studied and considered in numerous papers. Velex and Ajmi [1] introduced their theoretical approach to the modeling of pinion-gear excitation valid for three-dimensional models of single-stage geared transmissions. Tuma [2] studied the problem of the simple gear set transmission error measurement. On the other hand, De la Cruz [3] described a model of impact dynamics of meshing gear teeth-pairs under medium to heavy loads in the presence of backlash. The model incorporates the classical Hertzian impact, governed by instantaneous geometry of the contact and the prevailing kinematics of contiguous surfaces for pairs of helical teeth.

Houser and Harianto [4] considered bearing forces that are the result of mesh forces analyzing the influence of gear meshing impact forces, effective transmission error forces, shuttling forces, friction forces and forces due to the entrapment of air and lubricants. In paper [5], Houser, Harianto and Ueda presented a procedure of selection and optimization of gear profile with respect to noise reduction. Bartod et al. [6] analyzed the phenomenon of rattle noise caused by the fluctuation of the engine torque (acyclic

excitation) which, under special conditions, can cause multiple impacts inside the gearbox. Thodossiades and Rahnejat with collaborators have extensively investigated vibrations at the source of excitation of geared systems. In paper [7], they analyzed nonlinear dynamic response of a gear pair system with periodic stiffness characteristics and backlash. Later, in paper [8], they used theoretical and experimental methods to analyze the impact-induced vibrations in vehicular driveline systems. The results showed high-frequency contributions in driveline vibrational response of certain structural modes of driveshaft pieces, which are induced by remote impact of meshing transmission teeth through backlash. Also, Theodossiades et al. in [9] and [10] introduced their approach for understanding the interactions between the transmission gears during engine idle conditions by taking into account the effect of lubrication. They showed that the lubricant film under these conditions behaves like a nonlinear spring damper, which significantly affects the response of idler gears during the meshing cycle. Kartik and Houser [11] analyzed the effects of shaft dynamics on gear vibration and noise excitations. A method for suppression of gear pair vibration by active shaft control is developed in [12] by Guan et al. The effects of bearing stiffness on critical rotational speeds of gearboxes are analyzed by Rigaud et al. in [13].

Several papers present the possibilities of numerical prediction of sound pressure level. Houser et al. compared numerical predictions for a simple gearbox to experimentally measured data [14].

Inoue [15] proposed an optimum design method,

*Corr. Author’s Address: University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11000 Belgrade, Serbia, mognjanovic@mas.bg.ac.rs

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which minimizes the vibration energy, for a thinplate structure, and applied it to the gearbox housing design for low vibrations and noise. In [16], Abbes et al. developed an FEM based model with the goal to estimate acoustic radiation of a simplified gearbox internally excited by gear mesh stiffness fluctuation.

Tuma in paper [17] reviews the research work on reducing truck gearbox noise considering various relevant factors, from the source of noise to housing design. He concluded that a low noise gearbox requires sufficiently rigid housing, shafts and gears, tooth surface modifications and application of HRC (High Contact Ratio) gears.

The main goal of this paper is to present the investigation of the influence of the gear unit housing on vibrations and acoustic emission of a gear unit.

Disturbances caused by teeth impacts are the strongest during the initial contact of a teeth pair, and they are periodically repeated. That is why these disturbances are selected for the definition of disturbance power and analysis of spreading the disturbance power through the gear unit structure. A casted housing of a general use gearbox is selected as the object of the research, but the obtained results are of a general nature and are applicable to all mechanical systems with a periodic generation of disturbances.

arise. The natural frequency is proportional to the square root of average stiffness of meshed teeth cγ (according to DIN 3990 and ISO 6336) and inversely proportional to the equivalent mass me: Fc = vc c ' me ,

fn =

1 2π

cγ me

,

mt1mt 2 J J me = , mt1 = 21 , mt 2 = 22 . mt1 + mt 2 rb1 rb 2

(1)

1 GEAR DISTURBANCES CAUSED BY TEETH IMPACTS Gear teeth meshing is accompanied by different kinds of gear teeth impacts. In spur gears, teeth impact is the most intense during addendum collision. The impact is dependent on elastic deformations of the gear teeth, but deviations of dimensions and the shape of teeth profiles can intensify the impact force. The teeth deformations are proportional to the teeth load and inversely proportional to teeth stiffness. The spur gear teeth contact begins along the whole width of the gear, having the maximal stiffness c’ at the beginning of the impact. On the other hand, in helical gears, teeth meshing starts with the contact at one end of the teeth and gradually extends along the contact path. Therefore, the initial stiffness c’ and the initial impact force of helical gears are considerably smaller in comparison to spur gears.

The impact deformation of spur gears changes the initial contact point from position A to position A’, which is ahead of point A (Fig. 1). The contact of the teeth pair starts with an intensive addendum impact, with the collision force Fc. The collision speed vc is proportional to the deformation of the teeth, speed of rotation n and gear design parameters. After each collision of teeth, natural vibrations of meshed gears 328

Fig. 1. Restorable gear vibrations caused by successive impacts repetition

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For the purpose of natural frequency calculation, the model of rotating masses is transformed into the model of harmonic oscillator. Moments of inertia of the rotating masses J1 and J2 are transformed to the concentrated masses along the direction of the teeth contact line. The radii of the basic circle of the gear pair are rb1 = (m z1 / 2) cosα and rb2 = (m z2 / 2) cosα, where the profile angle is α = 20°, m represents the gear module, and z1 and z2 are the corresponding gear teeth numbers.

Gear vibrations are non-linear because of the variation of stiffness of teeth in mesh. The variation is related to the profile of the contact position and to the number of teeth in mesh. For the purpose of practical application, the gear calculation is linearized by introducing average stiffness of teeth in mesh cγ, as described in standards DIN 3990 and ISO 6336. As further analysis is directed at the effects of gear housing, the nonlinearity of vibrations has no significant effects on the obtained results.

Teeth collision produces free damped vibrations of gear masses with the natural frequency fn. These free vibrations are very quickly damped (Fig. 1), but the subsequent collisions restore them again.

Teeth collisions repeat with each tooth entering the mesh, i.e. with the disturbance frequency (frequency

of forced vibrations) f = nz / 60 (n is the number of gear revolutions per minute, and z the number of gear teeth). Each subsequent collision restores vibrations, and a specific type of restorable free vibrations arises.

Fig. 1 shows time variation of acceleration of a gear during restorable free vibration in the case of small speed of gear rotation. With the increase of the rotational speed, the frequency of teeth collision f increases and resonance arises when frequency f becomes equal to the natural frequency fn. In the supercritical range, the frequencies of teeth collisions are higher than the natural frequency of the gears, f > fn. Vibrations are rea­lized by their natural frequency, but due to the increased intensity of teeth collisions, the level of free vibrati­ons with the frequency fn is higher [18].

2 TRANSMISSION OF DISTURBANCES THROUGH THE GEAR UNIT STRUCTURE Disturbances (impacts, rolling, sliding, etc.) produce micro elastic deformations which absorb disturbance power inside machine parts. This process presents a special subject for analysis. The absorbed disturbance power is transmitted through the gearbox parts in the form of elastic waves. One part of this power

Fig. 2. General structure of disturbance energy transformation Gear Unit Housing Effect on the Noise GenerationCaused by Gear Teeth Impacts

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is attenuated inside the machine parts, and the remaining power is emitted to the surroundings and transmitted to the other machine parts via contacts in the assembly. Propagation of the waves through the elastic structure of the gear unit (gears, shafts, housing) can excite natural vibrations of the gear unit parts, thus increasing disturbance power transferred to the other parts and emitted to the surroundings.

Fig. 2 shows processes of distribution, spreading and transmission of disturbance energy in the gear transmission unit, while Fig. 3 shows energy flows through the gear unit assembly. The elastic structure of the gear absorbs the disturbance power Wg, generated by teeth impacts, in the form of inner elastic waves. A part of this power is transmitted from the gear to the shaft Wsh via direct contact. The quantity ζT(g – sh) = Wsh / Wg presents the transmission factor of disturbance energy from the gear to the shaft.

In addition, excited natural (modal) vibrations of the housing modulate frequencies of emitted noise.

The third effect of housing is the noise isolation of outer space from the inner noise ∑Win . The noise transmission factor through the housing walls may be defined as ζT(n) = W'on / ∑Win .

The presented analysis makes use of transmission factors to describe a transmission of disturbance power components. The calculation of disturbance power and transmission factors is a complex problem.

It represents a wide area for research and this paper proposes a method for calculation of transmission factors that relies on experimental measurements.

Fig. 4. Stress distribution in the elastic structure after teeth impact

The disturbance energy Wg is absorbed by elastic deformations of machine parts. Fig. 4 represents the distribution of stress within teeth at the moment of collision. The value of wave energy Ew absorbed by elastic deformation may be calculated by integration of the stress σ over the deformed volume V. The wave energy Ew represents the energy of one impact of the teeth. As the teeth collide with the teeth mesh frequency f, the disturbance power absorbed by the gear Wg may be calculated as follows: Fig. 3. Disturbance energy transmission through the elastic structure of the gear unit

The remaining part of disturbance energy W'in is transmitted via other gear surfaces into the inner space of the transmission unit. The disturbance energy transmitted to the shaft Wsh is partially transmitted to the housing Who , while a part of the energy is emitted to the inner space of the gearbox W''in .

The disturbance power transmitted to the housing Who can produce several effects. The first effect is further transmission of disturbance energy to the air outside and inside the gearbox, in the form of outer noise Won and inner noise W'''in . The second effect of the housing is attenuation or intensification of the energy Who due to the excitation of natural vibrations.

330

Wg = Ew f = Ew

zn , E w = σ dV .

60 V

∫

(2)

The respective stress distribution which leads to a calculation of disturbance power may be calculated using FEM or by experimental measurements using the photometric method.

The transmission factors ζT depend on the characteristics of materials, shape and size of the contact surface, surface roughness and other influences, which makes the theoretical calculation of transmission factors a very difficult task. However, experimental measurement of the transmission factors is possible. Fig. 5 presents two examples of experimental setups, which are adapted for the photometric measurements of stress distribution

Ognjanović, M. – Ćirić Kostić, S.

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caused by impact. Transmission through the surface contact between two parts (Fig. 5a) may be characterized by simultaneous photometric measurements of stress distributions in the parts. Input disturbance may be generated by a modal hammer that enables measurement of impact force variation.

Fig. 6. Motion of surface particles and disturbance energy transmission

a) b) Fig. 5. Experimental setups for determination of the transmission factor

By numeric integration of stress distributions according to Eq. (2), the transmission factor may be calculated from experimental data as follows: ζT =

Ew 2 + , Ew1+ = ∫ σ1+ dV , Ew2 + = ∫ σ2 + dV , (3) Ew1+ V V

with indices 1 and 2 referring to the contact parts, and indices + and – referring to the receiving and emitting sides of the parts, respectively.

A measurement of transmission factors through bearings is more intricate, but can be accomplished in a similar manner, and by using the same devices.

A possible experimental setup, in which the bearing is placed between two parts whose stress distributions are measured, is shown in Fig. 5b. The procedure for calculation of transmission factors is the same as in the previous example.

The power of an emitted sound may be determined on the basis of the fact that machine parts, including the gear unit housing, emit sounds by vibration of their surfaces as membranes. The surface motion is the result of elastic wave motion in the elastic structure of the parts. Sound waves in the air are longitudinal waves and only surface displacements along a certain direction contribute to the emitted sound. Fig. 6 presents motions of an elementary part of the surface.

Displacements with the components normal to the surface, and therefore translation in the x direction and rotations around the y and z-axes, contribute to the sound emission. Other motions, translation in the y and z directions, and rotation around the x-axis do not contribute to the sound emission. Using the Helmholtz calculation model and the method of boundary elements, the pressure p of the sound wave emitted by the motion of the elementary part may be calculated.

Sound pressure enables calculation of the intensity of the emitted sound, and the sound power Wn, emitted by the machine may be calculated by integrating the sound intensities emitted by all elementary parts over a surface that envelopes the machine. Due to large differences between densities of the machine parts and the surrounding air, an extremely small part of disturbance energy is transmitted from the machine part to the surroundings.

The sound power Wn of the gear unit is the result of multiple noise components. The first component is the result of forced vibrations of the housing surface due to the conduction of disturbances caused by gear meshing. The second component is the noise produced by natural (modal) vibrations of the housing. The housing sensitivity to modal excitation and the intensity of modal vibrations are parameters influencing the outside noise. The third component of the noise emitted to the surroundings is the noise that comes through the housing walls. Isolation abilities of the housing walls and the level of inside noise define the effect of the third component on the total level of sound power of the gear unit.

The presented analysis underlines important effects of the gear unit housing on the emitted sound power. In addition, the housing modulates sound frequencies with respect to the frequencies of disturbances. For that reason, the modal behavior of the housing has a strong influence on the emitted

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sound. Also, the way (mechanism) of certain modal shape excitation and intensity of respective vibrations provide important information for establishing the model of noise generation in machine systems.

3 THE SOUND MODULATION BY HOUSING MODAL BEHAVIOR According to Fig. 3 and the analysis presented, the sound (noise) emitted by a gear unit is the part of disturbance energy released via the outer surface of the housing. The sound power Won is the result of modal behavior of the housing walls, and the sound power W'in is the result of transmission of the inner noise ∑Win through the housing walls. The relative contributions of Won and W'on depend on housing modal sensitivity and isolation ability. The spectrum of the outer noise is different in comparison to vibration spectra of disturbance sources. In this way, the housing performs modulation of the sound emitted to the surroundings. It is an extremely important detail for diagnostics and similar application of noise emission measurements. With the goal of identifying the modulation process, the modal analysis by FEM, a numerical calculation of frequency responses and modal testing of real gearbox housing were performed. a)

b)

Fig. 7. The selected gearbox housing; a) discretized model, b) modal shape of a vibration mode

332

The research of modal behavior effects was performed on a housing model shown in Fig 7.

It is a casted housing of a two-degree gear drive, reinforced with ribs and rings for increasing stiffness.

The complex shape of the housing is suitable for the investigation of excitation mechanisms of natural vibrations of mechanical structures.

Modal analysis of the given housing was performed by an application of the finite elements method. The linear 3D-brick finite element with 12 degrees of freedom (three translations per each node) was used. The finite elements mesh shown in Fig. 3a contains 6,385 finite elements, 12,950 nodes with 38,850 degrees of freedom. For the frequency range 0-3000 Hz, 88 natural frequencies and modal shapes of vibrations were calculated. Each vibration mode implies the existence of standing waves within separate zones of the considered structure. As an illustration, one of the vibrating modes is presented in Fig. 7b.

3.1 Conditions for Certain Modal Shape Excitations The sound power Won is the result of excited modal shapes of the housing walls. In real conditions, only a small number of vibration modes, out of a large number (theoretically infinite) of possible modes, are active. The main conditions for excitation of a certain modal shape are the following: • The direction of elastic deformations caused by excitation (completely or partly) should coincide with the elastic deformations of a certain modal shape; • The frequency of excitation should be close or equal to the frequency of the modal shape which is excited; • The modal attenuation should be sufficiently small to prevent partial or complete attenuation of the vibration mode.

These conditions were investigated by the numerical integration method and experimental modal testing for various cases of excitation. The main investigated variable was the excitation impact force.

Variations of its direction, place of action and intensity provided a possibility to excite various modal shapes.

The excitation frequency depends on variation of the intensity of excitation force during impacts. In numerical integration, the intensity of impact force was increased linearly from zero to 1000 N and decreased back to zero in 0.02 s. In experimental tests, the excitation was performed by a modal hammer.

In both cases, the excitation had sufficiently wide frequency spectra to excite all the vibration modes

Ognjanović, M. – Ćirić Kostić, S.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 327-337

obtained by FEM analysis. Modal attenuation depends on the material and modal shape. The performed numerical integration considered housings made of steel and cast iron, while experimental tests were carried out on the housing entirely made of cast iron. a)

b)

c)

Fig. 8. The example of using the results of numerical modal excitation by impulse force; a) numerical integration results, b) modal shape displacement in chosen sections (359 Hz), c) exciting force directions

Fig. 8 presents, as an example, one of the results of numerical integration of response of the housing, which was excited in the area of maximal modal displacement of vibration mode with the frequency of 359 Hz. In addition to the corresponding modal shape, modes with similar shapes and frequencies were also excited. By the force in the z direction, in the area of the middle hole, vibration modes with

the natural frequencies 155 and 359 Hz are excited (Fig. 8a), because the force direction is the same as the direction of maximal displacement for these modal shapes (Figs. 8b and c). By action of the force in the x and y directions, the modal shape with 359 Hz is not excited, because these directions do not correspond to the displacements of the vibration mode. The force in the y-direction excites only the modal shape with 155 Hz, because the force direction corresponds to the displacement direction of vibration mode with this frequency. The maximal response is obtained with the excitation force that acts at the place and in the direction of maximal displacement of a vibration mode and has the frequency equal to the natural frequency of the vibration mode.

Measurements and analysis of vibrations and noise were performed by the application of B&K PULSE measurement system [19]. Modal testing of the gear unit housing was carried out by means of impulse excitation – the modal hammer, and measurement of vibrations, which were analyzed by an FFT frequency analyzer in the frequency range 0 to 3000 Hz. Fig. 9a, shows the positions of points of modal hammer action T1 to T11, and of point MT0 where the response was measured. As an example, Fig. 9b shows a comparison of frequency responses obtained by excitation at points T6 (in the middle of the lateral side of the housing) and T7 (at the front vertical wall, right above the point MT0). The results of experimental measurements of modal response are similar to the numerically obtained results.

Differences between the calculated and measured natural frequencies vary between 0.7 and 9%. With the increase of frequency, the difference decreases.

Considering that the research was aimed at studying vibrations caused by gear impacts, further research was focused on the vibrations that are excited by force acting at point T11. The point is located at the contact surface between the housing and the bearing, and the corresponding excitation force has a radial direction, aimed at the y-direction at point T11.

Fig. 10a shows the measured transfer function.

Out of the possible 88 vibration modes numerically calculated by modal analysis, the impulse excitation at point T11 excites 23 modes. Some of excited modal shapes are shown in Fig. 10b.

3.2 Modal Excitation by Teeth Impacts The response obtained with the modal hammer acting on the housing walls can be different in comparison to vibrations of the transmission unit in operating conditions.

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Fig. 9. Amplitude-frequency diagrams of vibrations obtained by modal testing and numerically (insert A)

Fig. 10. Modal responses of the housing; a) response measured at point MT0 due to excitation at point T1, b) some of excited modal shapes obtained numerically

There arises a question - which natural frequencies and vibration shapes in the housing walls could be excited by excitation that is transmitted through the bearings? The procedure of predicting modal shapes of vibration primarily begins with the selection and consideration of only those shapes of vibrations in which deformations exist in the area of holes intended for placement of bearings. In order to satisfy the first condition for excitation of a modal shape, it is necessary to have the point of action of disturbance in the area where deformations exist in the modal shape. This means that all modal shapes that do not have deformations in the area of holes for placement of bearings should be excluded from further consideration.

Disturbances are transmitted from the teeth mesh through the bearings to the housing in the axial (z) and radial (x – y) directions. The radial direction corresponds to the direction of the gear pair contact 334

line. Dissipation, i.e. attenuation in the contacts of parts (gear-shaft-bearing-housing) cause a weaker response in comparison to the case of direct impact in the housing walls in the area of bearing hole. For the purpose of characterizing transmission factors of disturbances between the shaft and the housing, a set of experiments in the form of modal testing was carried out. Fig. 11a presents the diagram of response of the housing excited by impact inside the bearing hole, in the direction of the gear contact line. This diagram is compared to the diagram presented in Fig. 11b, which shows the response of the housing with mounted bearings, middle shaft and gear. The excitation was carried out by modal hammer acting at a gear tooth. The additional components changed the modal response of the system, especially its intensity.

From the comparison between the responses presented in Fig. 11 the following may be concluded:

Ognjanović, M. – Ćirić Kostić, S.

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•

In the presented frequency spectra, the strongest response corresponds to the high frequency range, 2 to 3 kHz. • When the excitation force acts in the area of the bearings (the area of thick housing walls), the maximum response corresponds to the frequency range 2 to 2.4 kHz (Fig. 11a).

• When the excitation force acts upon the tooth addendum of the middle gear, the maximum response corresponds to the frequency range 2 to 3 kHz, but its intensity is approximately six times lower than in the previous case (Fig. 11b).

• Frequency spectra of the responses are similar in both cases, having the components with the same frequencies.

In the case of excitation of the tooth addendum with a modal hammer, the absorbed disturbance energy is transmitted from the gear body through the shaft and bearings. A large part of that energy is dissipated, causing a very low level of response of the housing. However, the presented analysis shows that the response of the gear unit in operating conditions consists of the same natural vibrations as the response of the housing to excitation by the modal hammer at the place of the bearing.

4 EXPERIMENTAL PROOF OF THE EFFECT OF THE GEAR UNIT HOUSING ON THE EMITTED NOISE In order to prove the main hypothesis that the housing of housing vibrations and noise caused by gear pair rotation with strong teeth impacts were carried out.

With the goal to separate the influences of gear excitation and housing strong teeth collision in the course of slow rotation were excited. Two teeth, symmetrically distributed around the pinion, were intentionally damaged by welding. The damage

caused strong impacts of the gear flanks. During the test, the pinion rotated with 500 rpm and the two damaged teeth caused impacts with the frequency of 16 Hz. By comparing the response diagram of modal testing (Fig. 11) and the frequency spectrum of housing vibration (Fig. 12a), it is possible to notice that there is only one harmonic with the frequency of 16 Hz produced by teeth impacts, and the remaining spectral components are natural vibrations of the gear housing.

Another experiment was designed to confirm the hypothesis that the noise emitted into the surroundings by the gearbox is the consequence of natural vibrations of the housing. For that purpose, the sound pressure of the gearbox was measured at the distance of 0.5 m above the gearbox. The frequency spectrum of noise of the gear unit, for the driving shaft speed of 500 rpm, is presented in Fig. 12b. By comparing these spectra with the spectrum of housing vibrations in Fig. 12a, the following can be concluded: • Natural vibrations of the gear unit housing produced by impacts of damaged teeth (16 Hz, Fig. 12a) have stronger intensity in the range of lower frequencies because the excitation frequency is low.

• The noise spectrum of the gear unit (Fig. 12b) is similar to the spectrum of vibrations of the housing because the noise is mainly produced by natural vibrations of the housing that follow each of teeth impacts. Vibrations of the structure produce sound, but only if certain conditions (Fig. 6) are met: in this case, strong vibrations with the frequencies around 700, 1000 and 2000 Hz produce only a low level of noise.

• Stronger responses in the frequency spectrum of noise (Fig. 12b) correspond to the frequencies of natural vibrations of the housing that are

a) b) Fig. 11. Comparison of the results of modal tests of the housing with the gear system; a) excited by the impact inside the bearing hole in the direction of the gear contact line, b) excited by the impact at the tooth addendum of the middle gear Gear Unit Housing Effect on the Noise GenerationCaused by Gear Teeth Impacts

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a)

b)

Fig. 12. Comparison of vibration acceleration spectrum; a) and noise pressure spectrum, b) of the gear drive unit with strong impact simulation in the gear mesh

more effective in the sound emission. One of the vibrations has the frequency of around 359 Hz, and it was identified by modal analyses of the housing and by modal testing.

• Vibration and noise spectra presented in Fig. 12 prove the hypothesis that the housing modulates noise emitted by the gear unit.

• The effectiveness of noise modulation of the housing is in direct relation with design parameters of the housing. Housings with lower sensitivity to disturbances and higher attenuation will have lower levels of emitted noise.

The disturbance power Wg is in direct relation with the angular speed of the driving shaft and with intensity of teeth collision. The frequency of impacts, related to the speed, is one of the key parameters of disturbance power absorption Eq. (2). Increase of the angular speed results in a significant increase of the excitation frequency, absorption of disturbance power and the level of noise of the corresponding natural frequencies of the housing.

5 CONCLUSION The main hypothesis of the presented investigation has been proved: the gear unit housing has a dominant effect on the level and frequency content of the emitted noise of the gear unit. The conclusion is 336

supported by the following facts and results of the presented research: • The noise emitted by the gear unit is the consequence of disturbing energy absorbed during the operation of machine parts; • The disturbing power absorbed in the elastic structure by addendum teeth impact contributes to restorable free vibrations of the gears.

• The transmission of disturbance power through the gearbox elastic structure is explained and the corresponding transmission factors are introduced.

• The modal behavior of the gear unit housing is investigated and the mechanism of excitation of certain modal shapes of natural vibration are explained.

• The gearbox noise modulation by the gear unit housing is the result of housing modal sensitivity and housing ability isolation of internal noise.

A set of questions for further research is open. The transmission factors of disturbance energy through the elastic structure are defined, but their exact calculation and measurement need further research efforts.

6 ACKNOWLEDGEMENT This paper is a contribution to the project TR 035006 funded by the Ministry of Education and Science of the Republic of Serbia.

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7 REFERENCES [1] Velex, P., Ajmi, M. (2006). On the Modeling of Excitations in Geared Systems by Transmission Errors.

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[2] Tuma, J. (2006). Dynamic Transmission Error Measurements. Engineering Mechanics, vol. 13, no. 2, p. 101-116.

[3] De la Cruz, M., Rahnejat, H. (2008). Impact dynamic behaviour of meshing loaded teeth in transmission drive rattle. Proceedings of the Sixth EUROMECH Nonlinear Dynamics Conference, p. 418-430.

[4] Houser, D.R., Harianto, J. (2008). Microgeometry and bias in helical gear noise excitations. Gear Solutions, feb., p. 21-39.

[5] Houser, D.R., Harianto, J., Ueda, Y. (2004).

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[6] Barthod, M., Hayne, B., Tebec, J.L., Pin, J.C. (2007).

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[7] Theodossiades, S., Natsiavas, S. (2000). Nonlinear dynamics of gear-pair systems with periodic stiffness and backlash. Journal of Sound and Vibration, vol. 229, no. 2, p. 287-310, DOI:10.1006/jsvi.1999.2490.

[8] Gnanakumarr, M., Theodossiades, S., Rahnejat, H., Menday, M. (2005). Impact-induced vibration in vehicular driveline systems: theoretical and experimental investigations. Proceedings of the Institution of Mechanical Engineers, Part K: Multibody Dynamics, vol. 219, K01804.

[9] Theodossiades, S., Tangasawi, O., Rahnejat, H. (2007).

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[10] Tangasawi, O., Theodossiades, S., Rahnejat, H. (2007).

Lightly loaded lubricated impacts: Idle gear rattle.

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[11] Kartik, V., Houser, D.R. (2003). An investigation of shaft dynamic effects on gear vibration and noise excitation. SAE International, p. 1737-1746, DOI:10.4271/2003-01-1491.

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Experimental study on active vibration control of a gearbox system. Journal of Sound and Vibration, vol. 282, no. 3-5, p. 713-733, DOI:10.1016/j. jsv.2004.03.043.

[13] Rigaud, E., Mayeux, F., Driot, N., Perret-Liaudet, J., Mevel, B. (2003). Dispersion of critical rotational speeds of gearboxes: Effect of bearing stiffnesses.

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[14] Houser, D.R., Sorenson, J.D., Harianto, J., Wijaya, H., Satyanarayana, (2002). Comparison of analytical predictions with dynamic noise and vibration measurements for a simple gearbox. Proceedings of International. Conference on gears, vol. 2, VDIBerichte, p. 995-1002.

[15] Inoue, K., Yamanaka, M., Kihara, M. (2002). Optimum stiffener layout for the reduction of vibration and noise of gearbox housing. Journal of Mechanical Design, vol. 124, no. 3, p. 518-523, DOI:10.1115/1.1480817.

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[17] Tuma, J. (2009). Gearbox noise and vibration prediction and control. International Journal of Acoustics and Vibration, vol. 14, no. 2, p. I-II. [18] Ognjanovic, M., Agemi, F. (2010). Gear vibrations in supercritical mesh-frequency range caused by teeth impacts. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 10, p. 653-662.

[19] Ciric-Kostic, S., Ognjanovic, M. (2007). The noise structure of gear transmission units and role of gearbox walls. FME Transactions, vol.35, no. 2, p. 105-112.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 338-344 DOI:10.5545/sv-jme.2010.127

Paper received: 2010-06-08, paper accepted: 2012-03-14 © 2012 Journal of Mechanical Engineering. All rights reserved.

Anti-Sway System for Ship-to-Shore Cranes Raubar, E. – Vrančić, D. Edvin Raubar1* – Damir Vrančić2 1 Luka

2 Jožef

Koper, d.d., Slovenia Stefan Institute, Slovenia

All ship-to-shore cranes hoisting mechanisms are made of a load attached to the trolley by means of a hoisting rope. In the process of loading and unloading the ship, the trolley moves the load along the boom from ship to shore and vice versa. During movement, the hoisting mechanism structure causes swinging of the load around vertical position. Load swing increases the loading/unloading time and increases the probability of collisions with other objects, like a nearby container, an iron construction for disposal of material (e.g. bunker), etc. Swinging of the load cannot be avoided, but can be radically reduced by using appropriate anti-sway systems.

The paper derives a non-linear and linearized dynamic model of the crane load based on parameters of Panamax ship-to-shore crane in the Port of Koper. The responses of three open-loop anti-sway systems are compared together on the aforementioned dynamic model.

Simulation results show that all three systems reduce load swing significantly, but only the systems based on zero-vibration-derivative and zero-vibration-derivative-derivative methods completely satisfy the given requirements.

Keywords: ship-to-shore crane, load oscillation, anti-sway system, open-loop system

0 INTRODUCTION Permanent increase of productivity of ship-to-shore cranes in Port of Koper is very important in order to remain competitive with other North Adriatic Sea ports. Increasing productivity can be achieved by reducing trans-shipment time. One possible way to increase productivity is to use anti-sway systems, which can efficiently reduce load oscillations. A reduction of oscillations increases the speed of transshipment and consecutively the ship-to-shore crane productivity.

The paper derives a dynamic mathematical model of the crane load with accompanying limitations.

The three open loop anti-sway systems are compared together on the aforementioned dynamic model with parameters taken from technical specification of Panamax ship-to-shore crane in Port of Koper.

The cranes do not have anti-sway system integrated, so the operator must wait until the load oscillation is completely cancelled before positioning the load to the desired position on the ship or on the

truck. The maximum acceptable deviation during positioning the load on the trucks with the ship-toshore cranes in the Port of Koper is 0.1 m, which corresponds to angular deviation of 0.01 rad (0.57º).

Generally, anti-sway systems are divided into two main groups: the open-loop and the closed-loop systems (see Figs. 1 and 2). The closed-loop systems are based on feedback information of the current load angular deviation, trolley position and its velocity (which are measured by additional sensors). The open-loop systems operate by applying feed-forward actions. They foresee error and try to eliminate it before it occurs [1].

In this paper, the open-loop systems will be tested on a model of Panamax ship-to-shore crane in Port of Koper.

The paper consists of three sections. In the first section, a non-linear and linearized mathematical model of the ship-to-shore crane load oscillation is derived. In the second section, three anti-sway systems are presented. In the third section the performance and

Fig. 1. Block diagram of open loop (feed-forward) anti-sway system

Fig. 2. Block diagram of closed loop anti-sway system

338

*Corr. Author’s Address: Vojkovo nabrežje 38, 6501 Koper, Slovenia, edvin.raubar@luka-kp.si

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time responses of all three methods are compared and evaluated. Conclusions are given in section four.

1 MODELING The trolley (see Fig. 3) can travel only when an external force is applied through the hoisting rope.

The force accelerates or decelerates the trolley. The friction force between steel wheels and the rail is very small compared to other forces, so it is neglected.

The length of the hoisting rope is time-invariant function, since the operator does not move the trolley and hoist at the same time. The length of the hoisting rope also does not depend upon load mass. The trolley and the load can be considered as point masses, which move in two dimensions only (x-y coordinate plane).

The applied force to the trolley is managed by the operator. By using the joystick, the operator defines the desired trolley velocity. The information about the desired trolley velocity is sent to frequency inverter, which controls the speed of motors. Motors, by means of gears, wind or unwind the rope on the drum and create force on the trolley. This force is positive when the trolley is accelerating and negative when the trolley is decelerating.

The force, which accelerates or decelerates the trolley, is always the same in magnitude, but changes direction, which depends on the desired velocity.

the angular deviation Θ has a negative sign. During trolley deceleration, the load moves anticlockwise. In this case the angular deviation Θ has a positive sign (see Fig. 3).

In the sequel the following variables will be used: x trolley horizontal position [m], trolley velocity [m/s], x load angular deviation [rad], Θ Θ load angular velocity [rad/s], length of the hoisting rope [m], l M mass of the trolley [kg], mass of the payload [kg], m gravitational acceleration [m/s2]. g 1.1 Mathematical Model  According to Fig. 3, the trolley position vector rv and  load position vector rb are defined as:  rb = ( x + l sin Θ , − l cos Θ ) ,

(1)

r b = x + lΘ cos Θ , lΘ sin Θ , (2)  rv = ( x, 0 ) ,

(3)

0) . r v = ( x,

(4) The horizontal position x is limited between –17 and 37 m. Initial or parking position is defined as x = 0 and Θ = 0.   Initial coordinates of vectors rv and rb are:  rb0 = ( 0 , − l ) ,

(5)

(

)

 rv0 = ( 0 , 0 ) .

(6)

The kinetic and potential energy of the load are described by the following expressions [1]:

Wk = Wv + Wb =

(

1 1 Mrv ⋅ rv + mrb ⋅ rb = 2 2

)

1 1 = Mx 2 + m x 2 + l 2Θ 2 + 2lx Θ cos Θ , 2 2 W p = mgym = −mgl cos Θ.

(7)

(8)

By using Lagrangian function [1], the secondorder non-linear model can be derived as follows: Fig. 3. Model of ship-to-shore crane load and trolley

During trolley acceleration the load moves away from the balance position clockwise. In this case

 x=

Fx + mg cos Θ sin Θ + mlΘ 2 sin Θ (M + m − m cos 2 Θ )

,

(9)

− F cos Θ − mlΘ 2 cos Θ sin Θ − Mg sin Θ − mg sin Θ Θ = x . (10) l(M + m sin 2 Θ )

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1.2 Linearized Model Eqs. (9) and (10) describe nonlinear model. The nonlinear model could be linearized by using certain assumptions [1]. The first assumption is that load swing angle is small during trolley movement. Based on that assumption the expansion of sine and cosine functions can be done by using the first term of Taylor series: Θ3 Θ5 Θ7 sin Θ = Θ − + − + ... ≈ Θ, (11)

3!

5!

7! cos Θ = 1 −

Θ2 Θ4 Θ6 + − + ... ≈ 1.

2!

4!

6!

(12)

Taking Eqs. (11) and (12) into Eqs. (9) and (10), we get two differential equations with two variables:  M + m  Fx  Θ = −   gΘ + Ml  , Ml   

m  x= M

Fx   gΘ + M . 

(13) (14)

1.3 Validation of the Linearized Model In order to validate the linearized model, the responses of linearized and non-linear model to the same input signal have been compared by means of simulation.

Input signal is generated by step functions, which represent force on the trolley. Simulation parameters are given in Table 1. They correspond to the actual parameters of Panamax ship-to-shore crane in Port of Koper.

Table 1. Parameters used in simulation Mass of the trolley Mass of the payload Length of the hoisting rope Max trolley velocity Max acceleration of trolley Gravitational acceleration Force on the trolley

M m l vv av g Fx

25 t 30 t 10 m 2 m/s 0.3 m/s2 9.81 m/s2 20 kN

From Fig. 4 it can be seen that the trolley is not travelling uniformly after the force is taken off, since attached load is swinging with its own natural frequency. This causes slight acceleration or deceleration of the trolley (depends on angular deviation Θ). It can be seen that there are very small differences between linearized and nonlinear model.

The assumptions in Eqs. (11) and (12) are therefore, due to small swing angles, correct.

340

Fig. 4. System response to impulse input excitation signal

2 ANTI-SWAY SYSTEM FOR SHIP-TO-SHORE CRANES 2.1 Main Working Principles All the methods, which will be used for the reduction of oscillation, are generating an input signal that cancels its own oscillation. The simplest method is the so-called Zero-Vibration (ZV) Shaper that consists of two impulses. The first impulse, which starts the system oscillating, is located at time zero, and the second impulse is delayed by half period of the oscillation. The oscillation caused by the second impulse is out of phase with the first oscillation, thereby cancelling it (see Fig. 6) [2].

The input signal can be shaped with any number of impulses. However, the amplitudes and time instants should be derived from the system’s natural frequencies, damping ratios and the following set of constraints [2]: • after the last impulse is applied, the oscillations must be cancelled (zero residual vibration constraints), • the sum of amplitudes must be equal to one (unity magnitude summation constraints),

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 338-344

• •

the derivative of the second-order system response on the Nth impulse must be zero (robustness constraints), time instants of impulses must be calculated so as to get minimum system response delay (time optimality constraints).

θ j = ω0 1 − ξ 2 t j ,

(21)

where Aamp is the multi-impulse vibration amplitude of the response and is obtained at the instant of the last impulse, tN. Bj is the coefficient which determines the amplitude of sine function [2].

To obtain zero vibration after the last impulse, the Eq. (17) must be zero. This happens when Eqs. (18) and (19) are independently zero. With this assumption the first two constrained equations are obtained: N

V1 = ∑ A j

ω0

j =1

1− ξ 2

N

ω0

V2 = ∑ A j j =1

1− ξ

e

2

e

(

)

(

)

(

) cos ω 1 − ξ 2 t = 0, (22) j 0

(

) sin ω 1 − ξ 2 t = 0. (23) j 0

−ξω0 t N −t j

−ξω0 t N −t j

An additional assumption is that the summation of impulse amplitudes must be equal to one and the amplitudes should be positive values: Fig. 5. System response with two impulses; first impulse generates oscillations, while the second impulse cancels them out

2.2 Mathematical Formulation of the Constrained Equations The following equation describes the impulse response of the second-order underdamped system [3]:   ω0 −ξω t −t y (t ) =  A e 0 ( 0 )  ⋅ sin ω0 1 − ξ 2 ( t − t0 ) , (15)   1− ξ 2  

(

)

where A is the amplitude of the impulse, t0 is the impulse time, ω0 is underdamped natural frequency and ξ is damping ratio. The second-order system response on N impulses could be written as [4] and [5]:

(

N

(

))

y ( t ) = ∑ B j sin ω0 1 − ξ 2 t − t j ,

(16)

Aamp = V12 + V2 2 ,

(17)

V1 = ∑ B j cos θ j ,

V2 = ∑ B j sin θ j ,

j =1

N

(18)

j =1 N

(19)

j =1

B j = Aj

ω0 1− ξ

2

e

(

−ξω0 t N −t j

) ,

(20)

N

∑ Ai = 1.

(24)

i =1

When the nonlinear system contains higher sinusoidal harmonics (as in our case), it is necessary to use more impulses to efficiently reduce the oscillation, which request more equations to be solved. In this case the robustness constraints are used that increase system accuracy (and thus stability) forcing higher derivatives of functions toward zero [2]: q

d V1 d ω0q

d qV2 d ω0q

q  Aj t j  N = ∑ j =1   ⋅ cos ω0  q  Aj t j  N = ∑ j =1   ⋅ sin ω0 

( )

(

( )

(

ω0

e

(

−ζω0 t N −t j

) ⋅

  = 0, (25)   1− ζ 2 t j  ω0 −ζω ( t −t )  e 0 N j ⋅ 2 1− ξ  = 0. (26)   1− ζ 2 t j  1− ξ

2

)

)

System stability increases by increasing the order (q) of derivatives.

To get minimal system response delay, the first impulse must be applied at time origin:

t1 = 0 .

(27) 2.3 Methods for Shaping Input Signal In this section three methods for shaping input signal are presented. These methods are frequently used in practice [6] to [9]:

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• • •

Zero-Vibration Shaper (ZV) Zero-Vibration-Derivative Shaper (ZVD) Zero-Vibration-Derivative-Derivative Shaper (ZVDD).

The main difference between the methods is the number of impulses applied for shaping input signal.

ZV method is using two, ZVD three and ZVDD four impulses.

The amplitudes and time instants of impulses can be calculated from Eqs. (17) to (27) [2]. The amplitudes and time instants of ZV shaper are the following: 1 A1 = , t1 = 0 ,

(28) 1+ K A2 =

1−ζ

.

A1 = A2 =

A3 =

1 1 + 2K + K 2 1

1 + 2K + K

3K 2 2

1 + 3K + 3K + K

3

K =e

(31)

π ω0 1 − ζ 2

, t3 =

−

, t1 = 0 ,

, t2 =

2

2π

ω0 1 − ζ 2

,

,

(32)

(33)

ζπ 1−ζ 2

.

(34)

The amplitudes and time instants of ZVDD shaper are as follows: A1 =

A2 =

A3 =

A4 =

342

1 1 + 3K + 3K 2 + K 3 3K

1 + 3K + 3K 2 + K 3

3K 2 2

1 + 3K + 3K + K

3

K3 1 + 3K + 3K 2 + K 3

Method ZV

(30)

The amplitudes and time instants of ZVD shaper are, correspondingly, the following:

, t1 = 0 ,

, t2 =

, t3 = , t4 =

π ω0 1 − ζ 2

2π

ω0 1 − ζ 2 3π

ω0 1 − ζ 2

(35) , (36)

, (37) , (38)

.

(39)

Table 2. Amplitudes and time instants of impulses using ZV, ZVD in ZVDD method

ZVDD 2

ζπ 1−ζ 2

Table 2 shows the amplitudes and times of impulses using ZV, ZVD and ZVDD methods based on calculated system natural frequency and damping ratio (see Table 1)

(29)

ζπ

K =e

K =e

ZVD

π K , t2 = , 1+ K ω0 1 − ζ 2 −

−

Amplitude of impulses A1 = 0.5 A2 = 0.5 A1 = 0.25 A2 = 0.5 A3 = 0.25 A1 = 0.125 A2 = 0.375 A3 = 0.375 A4 = 0.125

Time instant of impulses [s] t1 = 0 t2 = 1.78 t1 = 0 t2 = 1.78 t3 = 3.56 t1 = 0 t2 = 1.78 t3 = 3.56 t4 = 5.34

3 SIMULATION OF TROLLEY AND LOAD MOVEMENT USING ANTI-SWAY SYSTEM This section simulates performance of different anti-sway systems during trolley acceleration and deceleration using the non-linear mathematical model presented in Section 1. In the simulation, ZV, ZVD and ZVDD shapers are used.

The input signal in the simulation represents force on trolley. First, the positive impulse is applied which accelerates the trolley for the first 5 seconds (see Fig. 6). In the next 5 seconds the trolley is traveling uniformly without acceleration. Then, the force is applied in the opposite direction causing the trolley to uniformly decelerate until it stops.

The shaped input signals (the actual forces), when applying ZV, ZVD and ZVDD shapers, are shown in Fig. 7. Trolley positions and angles are shown in Fig. 8.

It can be seen that anti-sway systems noticeably reduce load angular deviation and the amplitude of oscillations in the steady-state. On the the other hand, the anti-sway systems slightly increase settling time.

Considering the requirement for maximum load angular deviation given in the Introduction, it can be seen that the ZV shaping method does not satisfy the requirements, since load angular deviation in the steady-state is higher than 0.01 rad.

In comparison to the ZV shaping method, the ZVD shaping method has better performance. The highest load angular deviation in the steady-state

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 338-344

is now 0.0045 rad (0.26 º). Settling time (when the angular deviation becomes lower than 0.01 rad) is achieved at 17.75 or 2.75 s after the input force stops acting to the trolley (Fig. 6).

a)

Fig. 6. Force to the trolley

b) Fig. 8. a) Trolley position and b) load angle with ZV, ZVD and ZVDD Shaper a)

a) b)

c) Fig. 7. Shaped input force signal, a) ZV shaper, b) ZVD shaper, c) ZVDD shaper

b) Fig. 9. System response with ZV, ZVD and ZVDD Shaper on changing the length of the hoisting rope and the mass of the payload by 5%; a) Trolley position and b) load angle with ZV, ZVD and ZVDD Shaper

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The ZVDD shaping method, when compared to the ZV and the ZVD shaping method, gives the best performance, since oscillations in the steady-state are almost fully cancelled (angular deviation is only 0.001rad). The settling time is now 18.5 s. This is 0.75 s higher than when using the ZVD shaping method.

The length of the hoisting rope and the mass of the payload is always known a-priori on ship-toshore cranes, since the length of the hoisting rope is measured by digital encoders, while the mass of the payload is measured by precise weighting cells. The accuracy of the measurements is 5%. Therefore, it is important to evaluate the robustness of anti-sway systems on smaller variations of parameters. The length of the hoisting rope and the payload mass has been increased by 5% while keeping the same parameters for ZV, ZVD and ZVDD shapers.

Trolley positions and angles are shown in Figure 9. The angular deviation, when using ZVD shaping method, does not change, while it slightly increases for ZVDD shaping method to 0.0012 rad (0.068º).

We could see that both methods are robust to small variations of the length of the hoisting rope and payload mass.

The simulation results show that ZV, ZVD and ZVDD shapers are very efficient in reducing oscillations in the system. The operator (on average) stabilises the load within 15 seconds after reaching the final position (separately at ship and at truck location). The ZVD shaping method needs 2.75 s for stabilisation, while ZVDD method requires 3.5 s. Taking into account that productivity of Panamax ship-to-shore cranes in the Port of Koper is about 19 containers per hour per crane, it can be calculated that the productivity could rise by about 2 containers per hour per crane.

4 CONCLUSION Three open-loop anti-sway systems have been introduced. The systems could be used on Panamax ship-to-shore cranes in the Port of Koper to reduce load oscillations during trans-shipment. The efficiency of the systems was tested on linearized dynamic mathematical model with parameters taken from technical specification of Panamax ship-to-shore crane

344

in Port of Koper. The simulation results show that all three methods reduce load oscillations significantly, but only the ZVD and the ZVDD methods completely satisfy the given requirements. The ZVDD method in comparison to the ZVD method reduces oscillations more efficiently, but results in a slightly slower response. Since ZVD realisation is simpler and faster, it is our preference for anti-sway systems on Panamax ship-to-shore cranes in Port of Koper.

The mathematical model used in the simulation was undamped with a fixed length of the hoisting rope. In our future work, the efficiency of all three anti-sway systems will be tested on a mathematical model with changing hoisting rope length and different damping factors.

5 REFERENCES [1] Omar, H.-M. (2003). Control of Gantry and Tower Cranes. Dissertation for the degree of Doctor of Philosophy in Engineering Mechanics, Blacksburg.

[2] Singer, N.-C. (1989). Residual Vibration Reduction in Computer Controlled Machines. Technical Report 1030, MIT Artificial Intelligence Laboratory, Massachusetts.

[3] Bolz, R.-E., Tuve, G.-L. (1973). CRC Handbook of Tables for Applied Engineering Science. CRC Press, Boca Raton.

[4] Gieck, K. (1983). Engineering Formulas. McGrawHill, New York.

[5] Singer, N.-C., Seering, W.-P. (1990). Preshaping Command Inputs to Reduce System Vibration. Journal of Dynamic Systems, Measurement, and Control, vol.

112, p. 76-82, DOI:10.1115/1.2894142.

[6] Singhose, W., Singer, N., Seering, W. (1995).

Comparison of Command Shaping Methods for Reducing Residual Vibration. Proceeding of the 1995 European Control Conference, vol. 2, p. 1126-1131.

[7] Huh, C., Hong, K. (2002) Input shaping control of container crane systems: limiting the transient sway angle. 15th Triennial World Congress, Barcelona.

[8] Dieulot, J. Y., Thimoumi, I., Colas, F., Bearee, R. (2006). Numerical Aspect and Performances of Trajectory Planning Methods of Flexible Axes. Internal Journal of Computers, Communications & Control, vol. 1, no. 4, p. 35-44.

[9] Pao, Y., Singhose, W. (1995). On the Equivalence of Minimum Time Input Shaping with Traditional Time-Optimal Control. Proceedings of the 4th IEEE Conference on Control Applications, p. 1120-1125.

Raubar, E. – Vrančić, D.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 345-353 DOI:10.5545/sv-jme.2011.136

Paper received: 2011-07-12, paper accepted: 2012-02-07 © 2012 Journal of Mechanical Engineering. All rights reserved.

Global Criterion Method Based on Principal Components to the Optimization of Manufacturing Processes with Multiple Responses Gomes, J.H.F. – Salgado Jr., A.R. – Paiva, A.P. – Ferreira, J.R. – Costa, S.C. –Balestrassi, P.P. José Henrique de Freitas Gomes – Aluizio Ramos Salgado Júnior – Anderson Paulo de Paiva – João Roberto Ferreira – Sebastião Carlos da Costa – Pedro Paulo Balestrassi* Federal University at Itajuba, Institute of Production Engineering and Management, Brazil The necessity of efficient and controlled processes has increased the demand by employing optimization methods to the most diverse industrial processes. For these cases, the Global Criterion Method is described in literature as a technique indicated for multi-objective optimizations. However, if the problem presents correlations between the responses, this technique does not consider such information.

In this context, the Principal Component Analysis is a multivariate tool that can be used to represent correlated responses by uncorrelated components. Given that to negligence the correlation structure between the responses increases the likelihood of the optimization method in finding an inappropriate optimum point, the objective of this work is to combine the GCM and PCA in a strategy able to deal with problems having multiple correlated responses. For this reason, such strategy was used to optimize the 12L14 free machining steel turning process, characterized as an important machining operation. The optimized responses included the mean roughness, total roughness, cutting time and material removal rate. As input parameters, the cutting speed, feed rate and depth of cut were considered. Response Surface Methodology was employed to build the objective functions. The GCM based on principal components was successfully applied, presenting better practical results and a more appropriate location of the optimal point in comparison to the conventional GCM. Keywords: multi-objective optimization, global criterion method, principal component analysis, free machining steel turning

0 INTRODUCTION In industrial environments, it is becoming more and more important that items can be produced to satisfy several requirements simultaneously, and many of them are related to its cost, quality and productivity.

Thus, considering that the manufacturing processes must be configured to obtain the best results for a set of characteristics, the interest in employing multiobjective optimization techniques has been increasing [1] and [2].

Among the optimization methods contemplating multiple responses, the desirability function [3], the multivariate integration [4] and the capacity indexes MCpm and MCpk [5] and [6] are listed as examples.

Rao [7] describes the Global Criterion Method (GCM) as an interesting strategy. According to the author, the multiple objectives are optimized at the same time when the individual objective functions are combined in only one function, defined as the global optimization criterion of the process.

However, if the problem presents multiple correlated characteristics, the Global Criterion Method, as well as other conventional techniques, does not consider the correlation structure between the responses. This negligence, according to some researchers, may conduct the results to inadequate optimum points [8] and [9]. Paiva et al. [10] argue that the transfer functions used to represent the process outputs are strongly influenced by significant correlations existing between the responses of interest.

Therefore, considering that the mathematical models

are of great importance to the problem formulation, non-consideration of the correlation structure will affect the optimal point location.

In attempt to offer a more adequate treatment to the optimization problems with multiple correlated responses, the Principal Component Analysis (PCA) has been shown as a good alternative [11] and [12].

The PCA consists in a multivariate statistical tool that concerns in explaining the variance-covariance structure of a data set, using linear combinations of the original variables. Thus, the original correlated responses are represented by new uncorrelated variables, called principal components.

Given that the Global Criterion Method is presented as a technique to multi-objective optimizations but does not take into account the correlation structure between the responses, the objective of this work is to incorporate the PCA in the original formulation for GCM described by Rao [7], and verify how this analysis influences in determining the optimal solution. For this, such techniques were applied on the 12L14 free machining steel turning process, characterized as one important operation in the modern industry.

Nevertheless, the study of manufacturing processes by optimization tools require that the mathematical relationships between the input parameters and the process responses be known.

Therefore, before the optimization itself, such functions were modeled through Response Surface Methodology.

*Corr. Author’s Address: Federal University of Itajuba, Institute of Production Engineering and Management, Av. BPS, 1303, Itajuba, Brazil, pedro@unifei.edu.br

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1 THEORETICAL FRAMEWORK 1.1 Response Surface Methodology (RSM) According to Montgomery [13], RSM is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response.

The second order polynomial developed for a response surface that relates a given response y with k input variables presents the following format described by Eq. (1):

k

k

i =1

i =1

y = β 0 + ∑ βi xi + ∑ βii xi2 + ∑ ∑ βij xi x j , (1) i< j

where y is the response of interest, xi are the input parameters, β0, βi, βii, βij are the coefficients to be estimated, and k is the number of input parameters considered.

To estimate the coefficients stated in Eq. (1), the Ordinary Least Squares is the typically used algorithm. After the model building, the ANOVA statistical procedure is usually employed to check its significance and its adjustment.

1.2 Global Criterion Method (GCM) A multi-objective optimization problem is one that, considering inequality constraints, can be stated as Eq. (2):

Minimize

f1 ( x ) , f 2 ( x ) ,..., f p ( x )

, (2)

Subject to : g j ( x ) ≤ 0 , j = 1, 2 ,..., m

where fi(x) are objective functions, and gj(x) constraints.

However, under various circumstances, the multiple responses considered in a process present conflict of objectives, with individual optimization leading to different solution sets. For this kind of problem, Rao [7] characterizes the Global Criterion Method as a strategy where the optimal solution is found by minimizing a preselected global criterion, F(x), such as the sum of the squares of the relative deviations of the individual objective functions from the feasible ideal solutions. The GCM formulation is given by:

346

1.3 Principal Component Analysis (PCA) Suppose that the objective functions f1(x), f2(x),..., fp(x), presented in Eqs. (2) and (3), are correlated with values written in terms of a random vector YT = [Y1, Y2,..., Yp]. Assuming that Σ is the variancecovariance matrix associated to this vector, then Σ can be factorized in pairs of eigenvalues-eigenvectors (λi, ei),..., ≥ (λp, ep), where λ1 ≥ λ1 ≥ ... ≥ λp ≥ 0, such as the ith uncorrelated linear combination may be stated as PCi = eiT Y = e1iY1 + e2iY2 + ... + e piYp , with i = 1, 2, ..., p. The ith principal component can be obtained as maximization of this linear combination [16]. This statistical technique is called Principal Component Analysis (PCA), one of the most widely applied tools to summarize common patterns of variation among variables retaining meaningful information in the early PCA axes [17] and [18]. The geometric interpretation of these axes is shown in Fig. 1.

Generally, as the parameters ∑ e ρ are unknown, the sample correlation matrix Rij and the sample variance-covariance matrix Sij may be used [16]. If the variables studied are taken in the same system of units or if they are previously standardized, Sij is a more appropriate choice. Otherwise, Rij must be employed in the factorization. The sample variance-covariance matrix can be written as follows:  s11  s Sij =  21

 s  p1

2

 Ti − fi ( x )  Minimize F ( x ) = ∑   Ti i =1   , (3)  Subject to : g j ( x ) ≤ 0, j = 1, 2 ,..., m p

where F(x) is the global criterion, Ti is the target defined for the ith objective, fi (x) are objective functions, gj (x) are constraints, and p is number of objectives.

Thus, with targets defined for each response of interest, the multiple objectives are combined into an only function, which becomes the global optimization function for the process.

To obtain the optimal point from GCM formulation, several optimization algorithms can be applied. In this work, the Genetic Algorithm was used because it is considered an effective algorithm to global optimizations [14] and [15].

sii =

s12 s22

s p2

s1 p   s21  ,   s pp 

(4)

1 n 1 n 2 ∑ ( yi − yi ) , sij = ∑ ( yi − yi ) y j − y j . n j =1 n j =1

Gomes, J.H.F. – Salgado Jr., A.R. – Paiva, A.P. – Ferreira, J.R. – Costa, S.C. –Balestrassi, P.P.

(

)

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 345-353

Then, the elements of sample correlation matrix Rij can be obtained as: r y ,y

(

i

j

)

=

=

(

) = e ij λ i sii Var ( yi ) × Var ( y j ) Cov yi , y j

sij sii × s jj

In practical terms, the principal component (PC) is an uncorrelated linear combination expressed in terms of a score matrix, defined as:

=

(5)

, i , j = 1, 2 ,..., p .

    x11 − x1    s11       x12 − x1  T  PCk = Z E =  s11    

  x − x   1n 1   s11   

 x − x   p1 p        s pp      x −x  x p2 − x p    22 2     s22  s pp      

  x − x  x −x  pn p 2   2n       s s 22  pp    x −x  21 2  s 22 

T

 e11   e21 ×   e1 p

e12 e22

e2 p

e1 p   e2 p  (6) .  … e pp 

Fig. 1. Geometric interpretation of principal components

1.4 Global Criterion Method Based on Principal Components The global criterion F(x), as stated by Eq. (3), is formulated from the objective functions and the targets defined to each response of interest. If the objective functions are unknown, then they can be modeled by RSM from experimental data. However, when the responses are correlated, this strategy does not take into account the correlation structure between them.

On the other hand, it has been seen in previous section that the principal components are characterized as uncorrelated representations of original correlated variables.

Considering that the principal components, through their scores, can also be modeled by RSM as functions of input parameters [10], then the Global Criterion Method based on principal components is written as:

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2

 ζ PCi − PCi ( x )  Minimize FPC ( x ) = ∑  

ζ PCi i =1   , (7)  g j ( x ) ≤ 0 , j = 1, 2 ,..., m Subject to : k

where FPC(x) is the global criterion based on principal components, ζPCi is the target defined for the ith principal component, PCi(x) are quadratic models developed for the principal components, gj(x) are constraints, and k is the number of principal components considered.

The determination of the targets for principal components requires that the targets for original responses are previously defined. The ζPCi is then calculated as a linear combination between the eigenvectors of principal components and the standardized original responses in relation to their targets. This procedure is showed by Eqs. (8) and (9).

(

p

)

ζ PCi = ∑ e ji ⋅ Z y j ζ y j , (8) j =1

where ζPCi is the target defined for the ith principal component, p is the number of objectives, eji are coefficients of the principal components’ eigenvectors, and Z(yj | ζyj) are the standardized original responses in relation to their targets, calculated as: ζ yj − yj Z yj ζ yj = , (9)

σyj

(

)

where ζ y j are targets defined for the original responses, y j are the means of responses, and σ y j are the standard deviations of responses.

Analogously to the Eq. (3), the obtaining of optimal point for the formulation given in Eq. (7) is done by employing optimization algorithms. The Genetic Algorithm was also used in this work for this purpose.

Finally, for the Global Criterion Method based on principal components, it is important to highlight that this strategy combines the main advantages offered by GCM and ACP, since it continues being a technique for multi-objective optimizations, but now considering the correlation structure existing between the responses.

2 OPTIMIZATION OF THE 12L14 FREE MACHINING STEEL TURNING

performance of manufacturing processes, such strategy was applied to the optimization of 12L14 free machining steel turning process.

This is described as a relevant operation within the current industrial context, since the free machining steels are developed to offer good machining conditions and excellent chip formations.

For this process, other mechanical characteristics, as ductility, strength and response to heat treatments are considered as secondary factors. The free machining steels have been employed in production of elements that do not need to present structural responsibility, as appliances and components to pumps, plugs and connections.

Due to the fact that mechanical properties are not the most important requirements for the 12L14 free machining steel turning process, its optimization is mainly concerned with its productivity and surface quality. The surface quality was then optimized through the mean roughness (Ra) and total roughness (Rt). For the productivity, cutting time (Ct) and material removal rate (MRR) were the optimized characteristics. The cutting speed (V), feed rate (f) and depth of cut (d) were considered as input parameters.

Given that the objective functions between the input parameters and responses were initially unknown, such relationships were modeled using RSM. Thus, data were collected from turning experiments performed with work pieces of 12L14 free machining steel (0.09% C; 0.03% Si; 1.24% Mn; 0.046% P; 0.273% S; 0.15% Cr; 0.08% Ni; 0.26% Cu; 0.001% Al; 0.02% Mo; 0.28% Pb; 0.0079% N2), with dimensions of f40×295 mm. The machine tool used was a NARDINI CNC lathe, with 7.5 cv power and maximum rotation of 4,000 rpm. The hard metal inserts (ISO P35 code SNMG 090304 – PM, Sandvik class GC 4035) were coated with three layers (Ti(C.N), Al2O3, TiN) and a tool holder ISO code DSBNL 1616H09 was employed.

A central composite design with three factors at two levels (2k = 23 = 8), six axial points (2k = 6) and three center points was chosen as experimental matrix, which resulted in 17 experiments. The adopted value for axial distance α was 1.682. Table 1 presents the range defined for input parameters. To record the responses, mean roughness and total roughness were measured by a roughmeter. Cutting time and material removal rate were calculated. At the end of experiments, the experimental matrix (Table 2) was built.

With the aim of verifying the functionality of the GCM based on principal components in improving 348

Gomes, J.H.F. – Salgado Jr., A.R. – Paiva, A.P. – Ferreira, J.R. – Costa, S.C. –Balestrassi, P.P.

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Table 1. Parameters and their levels Parameter

Symbol

Unit

V

Feed rate Depth of cut

Cutting speed

Levels

[m/min]

-1.682 180

-1 220

0 280

+1 340

+1.682 380

f

[mm/rev]

0.07

0.08

0.10

0.12

0.13

d

[mm]

0.53

0.70

0.95

1.20

1.37

Table 2. Experimental matrix Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

V [m/min] 220 340 220 340 220 340 220 340 180 380 280 280 280 280 280 280 280

Parameters F [mm/rev] 0.08 0.08 0.12 0.12 0.08 0.08 0.12 0.12 0.10 0.10 0.07 0.13 0.10 0.10 0.10 0.10 0.10

d [mm] 0.70 0.70 0.70 0.70 1.20 1.20 1.20 1.20 0.95 0.95 0.95 0.95 0.53 1.37 0.95 0.95 0.95

3 RESULTS AND DISCUSSION 3.1 Modeling of Objective Functions Writing the response surface function stated in Eq. (1) for three parameters, the following expression is obtained:

y = β 0 + β1V + β 2 f + β3 d + β11V 2 + β 22 f 2 + + β33 d 2 + β12Vf + β13Vd + β 23 fd

.

(10)

To estimate the coefficients defined in Eq. (10), the statistical software Minitab® was employed and, from the experimental data presented in Table 2, the full quadratic models were developed for each response of interest. Then, the significance of models was tested through ANOVA procedure. Table 3 presents the coefficients for full quadratic models and the main results of ANOVA. From Table 3 it can be observed that, considering a significance level of 95%, all models are adequate, since p-values were lower than 0.05. Furthermore,

Ra [mm] 1.36 1.65 1.78 1.84 2.22 2.20 1.82 2.24

Rt [mm] 9.49 10.70 10.08 10.41 14.71 13.47 11.13 13.20

Responses Ct [min] 2.11 1.36 1.40 0.91 2.11 1.36 1.40 0.91 2.06 0.98

MRR [cm3/min] 12.32 19.04 18.48 28.56 21.12 32.64 31.68 48.96 17.10 36.10

1.90

12.51

2.08

12.49

1.85

10.73

1.89

18.62

1.85 1.68 2.30 2.32 2.23 2.26

10.78 8.89 13.37 12.57 12.84 12.92

1.02 1.32 1.32 1.32 1.32 1.32

34.58 14.84 38.36 26.60 26.60 26.60

the adj. R2 values indicate high adjustments for the models, which means these expressions are reliable in representing the responses.

Finally, after non significant coefficients have been removed, the final models, or the objective functions for responses, were obtained. Eqs. (11) to (14) present these expressions.

Ra = 2.272 + 0.077V + 0.018 f + 0.212d − −0.107V 2 − 0.157 f 2 − 0.106d 2 − 0.123 fd , Rt = 12.708 + 0.172V − 0.254 f + 1.418d −0.643 f 2 − 0.511d 2 + 0.302Vf − 0.518 fd , Ct = 1.325 − 0.315V − 0.277 f + 0.070V 2 +0.047 f 2 + 0.062Vf

,

(11)

(12)

(13)

MRR = 26.600 + 5.679V + 5.082 f + 6.997 d + (14) +1.140Vf + 1.500Vd + 1.400 fd .

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Table 3. Estimated coefficients for full quadratic models

Min G = {[1.5 − (2.272 + 0.077V + 0.018 f +

Responses

Coeff.

+0.212d − 0.107V 2 − 0.157 f 2 − 0.1106d 2 −

Ra

Rt

Ct

MRR

β0

2.272

12.757

1.324

26.600

−0.123 fd )] / 1.5}2 + {[9.0 − (12.708 + 0.172V

β1

0.077

0.172

-0.315

5.679

β2

0.018

-0.254

-0.277

5.082

−0.254 f + 1.418d − 0.643 f 2 − 0.511d 2 +

β3

0.212

1.418

0.000

6.997

β11

-0.107

-0.038

0.070

0.000

β22

-0.157

-0.655

0.048

0.000

β33

-0.106

-0.522

0.002

0.000

β12

0.026

0.301

0.062

1.140

β13

0.006

-0.090

0.000

1.500

β23

-0.123

-0.518

0.000

1.400

0.002

0.005

0.000

0.000

subject to:

V, f, d ≥ –1.682 ,

(19)

85.46

80.63

99.68

99.72

V, f, d ≤ 1.682 .

(20)

p-value adj.

R2 [%]

3.2 Optimization by Conventional Global Criterion Method Before applying the GCM based on principal components to the optimization of 12L14 free machining steel turning, this operation was also optimized by conventional GCM, with the aim of comparing both results.

By taking the objective functions developed for the process responses, the GCM formulation can be built. However, for this formulation, it is necessary that the targets of original responses are defined. These specifications were made by experts and took into account that the process application could be satisfied with good levels of surface quality and productivity.

Table 4 show the targets defined for responses and their respective specification limits.

Thus, the optimization problem was built as stated in Eqs. (15) to (17). All characteristics were considered with the same degree of importance.

2

2

 1.5 − Ra   9.0 − Rt  Min G =   +  +  1.5   9.0  2

2

 1.2 − Ct   35 − MRR  +  ,  + 35   1.2  

+0.302Vf − 0.518 fd )] / 9.0}2 + {[1.2 − +0.047 f 2 + 0.062Vf )] / 1.2}2 + {[35 − −(26.600 + 5.679V + 5.082 f + 6.997 d + +1.140Vf + 1.500Vd + 1.400 fd ) / 35]}2 ,

Table 4. Targets and specification limits for responses Response Ra Rt Ct MRR

(16)

V, f, d ≤ 1.682 ,

(17)

where G is the global criterion, Ra, Rt, Ct, MRR are objective functions, and V, f, d are the input parameters.

Finally, replacing Ra, Rt, Ct and MRR in Eq. (15) by their respective objective functions, the final formulation of the problem was obtained given by:

LSL 1.0 8.0 1.0 30

T 1.5 9.0 1.2 35

USL 2.0 10.0 1.4 40

As can be observed, all optimized responses were established within the specification limits and relatively close to their targets, which suggests that it seems a good solution.

Table 5. Parameters used in Genetic Algorithm Parameters Iterations Convergence Population size Mutation rate

Values 1,000 0.0001 150 0.10

Table 6. Optimal results for 12L14 free machining steel turning obtained by conventional GCM

Optimal Target

V, f, d ≥ –1.682 ,

(18)

-(1.325 − 0.315V − 0.277 f + 0.070V 2 +

(15)

subject to:

350

Ra [µm] 1.53 1.50

Responses Rt [µm] Ct [min] 9.72 1.28 9.00 1.20

MRR [cm3/min] 36.4 35.0

The optimal point was found by applying Genetic Algorithm in the previous formulation. Microsoft Excel® was used for the mathematical programming of problem and the Solver Evolutionary supplement was employed. After some runs executed with random initial solutions and GA parameters given in Table 5, it was observed the optimal solution converged to the same point. Therefore, this was characterized as the global optimal point. Table 6 presents these results,

Gomes, J.H.F. – Salgado Jr., A.R. – Paiva, A.P. – Ferreira, J.R. – Costa, S.C. –Balestrassi, P.P.

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obtained with a cutting speed of 218 m/min, feed rate of 0.13 mm/rev and depth of cut of 1.24 mm.

3.3 Optimization by Global Criterion Method Based on Principal Components Table 7 presents the correlation structure for Ra, Rt, Ct and MRR. Since significant correlations were identified (p-value less than 0.05), the application of GCM based on principal components as optimization strategy is justified.

PC 2 = −0.457 + 0.633V + 0.742 f −

Through Eqs. (8) and (9), the PC’s targets were calculated using data in Table 9. It resulted in values of -1.153 for PC1 and 2.077 for PC2.

Table 9. Used data to calculate the targets for principal components Mean Std. dev.

Target Standardization Eigenvectors PC1 PC2

Table 7. Correlation structure of the responses Ra 0.876 Rt 0.000 –0.283 Ct 0.272 0.613 MRR 0.009 Cells: Pearson correlation p-value

Rt

Ct

0.030 0.909 0.506 0.038

–0.701 0.002

Table 8. Principal Component Analysis Eigenvalues Proportion Cumulative Eigenvectors Ra Rt Ct MRR

PC1 2.534 0.634 0.634 PC1 0.570 0.500 -0.347 0.551

PC2 1.215 0.304 0.937 PC2 -0.289 -0.529 -0.732 0.318

PC3 0.205 0.051 0.989 PC3 -0.552 0.143 0.421 0.705

PC4 0.046 0.011 1.000 PC4 0.536 -0.670 0.409 0.312

Performing the Principal Component Analysis for these responses (Table 8), it can be noticed that 93.7% of data are represented by two principal components.

So, these new uncorrelated variables were used to substitute the original correlated responses.

Then, the objective functions for principal components were modeled taking the scores of each component obtained in the PCA. For this, the same procedure described in section 3.1 was employed.

Eqs. (21) and (22) present such functions for PC1 and PC2, which showed adj. R2 values of 94.18 and 92.81%, respectively.

PC1 = 0.991 + 0.808V + 0.491 f + 1.265d −

−0.291V 2 − 0.564 f 2 − 0.379d 2 + +0.156Vf − 0.331 fd ,

(21)

−0.452d + 0.289 f 2 + 0.279d 2 − (22) −0.202Vf + 0.342 fd .

Ra 1.974 0.280 1.5 -1.692 Ra 0.570 -0.289

Rt 11.781 1.622 9.0 -1.715 Rt 0.500 -0.529

Ct 1.419 0.396 1.2 -0.554 Ct -0.347 -0.732

MRR 26.600 9.707 35 0.865 MRR 0.551 0.318

Finally, the formulation for GCM based on principal components was built, showing the following format: Min GPC =  

2

2

−1.153 − PC1   2.077 − PC 2  +  , (23) −1.153   2.077 

subject to:

V, f, d ≥ –1.682 ,

(24)

V, f, d ≤ 1.682 ,

(25)

where GPC is the global criterion based on principal components, PC1 and PC2 are objective functions for the principal components, and V, f, d are the input parameters.

Replacing PC1 and PC2 in Eq. (23) by their objective functions, the final formulation is written as: Min GPC = {[−1.153 − (0.991 + 0.808V + +0.491 f + 1.265d − 0.291V 2 − 0.564 f 2 −

−0.379d 2 + 0.156Vf − 0.331 fd )] / /(−1.153)}2 + {[2.077 − (−0.457 + 0.633V +

(26)

+0.742 f − 0.452d + 0.289 f 2 + 0.279d 2 − −0.202Vf + 0.342 fd )] / 2.077}2 , subject to:

V, f, d ≥ –1.682 ,

(27)

V, f, d ≤ 1.682 .

(28)

The Microsoft Excel® worksheet with Solver Evolutionary supplement and the Genetic Algorithm with parameters of Table 5 were also used to find the new global optimal point. These results are presented

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in Table 10, obtained for a cutting speed of 212 m/ min, feed rate of 0.13 mm/rev and depth of cut of 1.33 mm.

that do not consider this information can conduct the problem to solutions that do not represent the best process condition.

Table 10. Optimal results for 12L14 free machining steel turning obtained by GCM based on principal components

4 CONCLUSIONS

Optimal Target

Ra [µm] 1.40 1.50

Responses Rt [µm] Ct [min] 9.38 1.33 9.00 1.20

MRR [cm3/min] 38.0 35.0

Again, all optimized responses were established within the specification limits and relatively close to their targets. However, the global solution obtained with GCM based on principal components presented better surface finishing (lower roughness) and higher material removal. Although cutting time was higher, this solution was characterized as a more appropriate optimal point in relation to one obtained with the conventional GCM. Furthermore, this new optimal point was calculated taking into account the correlations between the original responses.

Fig. 2. Overlaid contour plot for the optimization of 12L14 free machining steel turning

Fig. 2 compares both optimal solutions with the feasible region for this problem. As easily noticed, the optimal point obtained with the conventional GCM, although seems a good solution, was established out of the feasible region. On the other hand, the solution found by GCM based on principal components, in addition to showing better practical results, was able to locate the optimal point inside the feasible region. The main argument for this fact is because the correlation structure of responses was considered in the second analysis. Thus, when correlations exist and are significant, the use of optimization strategies 352

This work presented the Global Criterion Method based on principal components as an alternative to optimize manufacturing processes with multiple correlated responses. From previous analysis, it was observed that the correlations are important information for this kind of problem and its negligence can direct the optimal point to inappropriate locations.

The GCM based on principal components was successfully applied to the optimization of 12L14 free machining steel turning process. An optimized condition with good surface finishing and good material removal was found for a cutting speed of 212 m/min, feed rate of 0.13 mm/rev and depth of cut of 1.33 mm. All optimized responses were established within the defined specification limits.

In comparison to the optimal point obtained with the conventional technique, the GCM based on principal components showed an optimal solution with better practical results in terms of roughness and material removal, but with a higher cutting time.

In relation to the feasible region of the problem, the GCM based on principal components directed the optimal point to inside this region, while the solution found by conventional GCM stayed out of it. Due to these reasons, the optimal point found with GCM based on principal components was characterized as a more adequate solution.

Although the technique presented in this work has been effective to the optimization of 12L14 free machining steel turning, it needs to be tested in other processes. Therefore, it is suggested for future research works that this strategy is applied and verified in others turning applications and other manufacturing operations, like milling, cutting or welding.

5 ACKNOWLEDGEMENTS The authors acknowledge the Capes, CNPq, FAPEMIG and the Institute of Mechanical Engineering of UNIFEI for supporting this work.

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Global Criterion Method Based on Principal Components to the Optimization of Manufacturing Processes with Multiple Responses

353

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 354-361 DOI:10.5545/sv-jme.2011.112

Paper received: 2011-05-27, paper accepted: 2012-03-27 © 2012 Journal of Mechanical Engineering. All rights reserved.

Dynamics of Polymer Sheets Cutting Mechanism Cveticanin, L. – Maretic, R. – Zukovic, M. Livija Cveticanin* – Ratko Maretic – Miodrag Zukovic Faculty of Technical Sciences, Novi Sad, Serbia

In the paper the dynamics of a cutting mechanism for polymer sheets is analyzed. The mechanism contains two connected slider-crank mechanisms which transform the rotating motion of the leading element into a straightforward motion of the output slider. The mechanism is driven by an electro motor and the slider represents the cutting tool. The cutting force is required to be constant. Using this assumption the kinematic and dynamic properties of the mechanism are determined. In particular, the influence of the cutting force on the input angular velocity of the leading element is analyzed. In addition, the interaction of geometrical and dynamical properties of the mechanism and of the cutting force is investigated. Angular velocity is a function of the cutting force, damping and inertia properties of the system. Variation of the angular velocity of the driving motor are calculated analytically and numerically. Analytically obtained results are in a good agreement with numerical ones.

Keywords: two joined slider-crank mechanism, kinematic and dynamic analysis, cutting force, non-ideal forcing

0 INTRODUCTION A great variety of mechanisms, tools and devices are made for cutting through materials based on specific requirements connected with the properties of the cutting object, its dimensions and form or strength and elasticity, as well as on the characteristics of the cutting tool and the driving motor [1]. Most of these tools are analysed, discussed and shown in textbooks for mechanical engineers and technicians. They all have a simple construction in common. For example, for cutting of the parts of strings, rods or bands, which represent the continual cutting object, the cutting mechanism may be based on the four-bar one (see [2]).

In this paper a mechanism for throughout cutting of the polymer sheet, which represents the discontinual cutting object, is considered. Due to elastic properties of the polymer sheet and its tendency to crumple, and also to sheet dimensions, it was required that cutting be done with a one-direction cutting force. This was possible by a translatory motion of the cutting tool. As the driving was with an electro motor, the mechanism had to transform the rotating motion of the leading element into a translatory motion of the leaded element. The mechanism which transforms the rotation into straight motion is the slider-crank mechanism. This mechanism and its modifications have been widely analyzed and applied to internal combustion engines and other various purposes (see for example [3] to [6]). In this paper, due to its simplicity the slider-crank mechanism is assumed as a basic one for the cutting device. Joining together two slider-crank mechanisms an appropriate device is obtained which also transforms the rotating motion of the leading element into translatory motion of the slider which is connected with a cutting tool. The idea 354

of joining of two slider-crank mechanisms is not a new one. The double-slider crank mechanisms are already used in air compressors [7], two piston pumps [8], in the cutting machine for elliptical cylinder [9], in the two-side piston engine [10], in the haptic devices to generate pulling or pushing motion [11] and [12], in robotics [13] to [16], and also as a continuous casting mold oscillation device [17].

In Section 1 the structural synthesis of the cutting mechanism is considered. The advantages and disadvantages of the cutting mechanism based on the two slider-crank mechanism in comparison to the slider-crank mechanisms (simple and eccentric) are discussed. In Section 2 kinematic properties of the cutting mechanism are analyzed. In Section 3 the mathematical description of the mechanism’s motion is given and in Section 4 a dynamic analysis is done.

The obtained results are discussed in Section 5.

1 STRUCTURAL SYNTHESIS OF THE CUTTING MECHANISM The structure of the cutting mechanism is required to satisfy the following: • the mechanism has to transform the input rotating motion into a translatory one, • the cutting element has to move translatorily, • the cutting process has to be during motion of the cutting element from up to down.

To fulfill these requirements, in this paper a device which contains two slider-crank mechanisms is suggested (see Fig.1). The system is designed to have an eccentric O1AB and a simple O2DE slidercrank mechanism both of which are connected with a rod BC. The leading element of the mechanism is the crankshaft O1A, while the slider is the cutting tool at point E. The suggested mechanism converts the

*Corr. Author’s Address: Faculty of Technical Sciences, Trg D. Obradovica 6, 21000 Novi Sad, Serbia cveticanin@uns.ac.rs

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rotating motion of the crankshaft O1A into a straightline motion of the slider E. The mechanism has the following elements: O1A = a, AB = b, BC = c, O2C = r, O2D = g, DE = h.

Let us make a connection between these two slider-crank mechanisms. Due to the fact that after the connection with the rod BC the two slider-crank mechanism remains an one-degree-of-freedom system (as it was the case for the simple and eccentric slidercrank mechanisms), the relation between the position of the slider E and leading angle φ of the crankshaft O1A needs to be determined.

From Fig. 1 it is evident that the position of the slider E in the coordinate system xO1y is: y = p + yE .

(7)

Moreover, w = c cosχ + r sinγ . (8) yB + c sinχ = p + r cosγ . (9)

Eliminating c in Eqs. (8) and (9) the yB – γ i.e., φ–γ expression is obtained as: Fig. 1. Model of the cutting mechanism

From Fig.1 the position of the slider B of the eccentric slider-crank mechanism O1AB (see Fig. 1) is given with the coordinates:

xB = a cosφ + b cosθ ≡ l , (1)

yB = –a sinφ + b sinθ . (2)

Eliminating θ in Eqs. (1) and (2) the position of the slider B as a function of the leading angle φ is obtained:

2

 l − a cos ϕ  yB = −a sin ϕ + b 1 −   . (3) b  

For the simple slider-crank mechanism O2DE (see Fig. 1) the translatory motion of the slider is described as:

yE = g cosγ + h cosψ , (4) where the relation between the angles γ and ψ is given with the expression:

g sinγ = h sinψ . (.)

Substituting Eq. (5) into Eq. (4) the following is obtained:

 g2  g2 yE = g cos γ + h 1 − 2  + 2 cos 2 γ , (6)  h  h  

which describes the position of the slider E as a function of the leading angle γ of the slider-crank mechanism O2DE.

(c2 – w2 – r2 – (p – yB)2 – 2r (p – yB) cosγ)2 =

= 4w2 r2 (1 – cos2 γ) ,

(10)

i.e.,

(11)

A2 cos2 γ – A1 cos γ + A0 = 0 ,

where A = c2 – w2 – r2 – (p – yB)2 , A0 = A2 – 4 w2 r2 , A = 4 A r (p – y ) , A = 4 r2 ((p – y )2 + w2 ) (12) 1 B 2 B , and p is a constant distance between fixed points O1 and O2 in y direction. Solving the quadratic equation (11) for cosγ and substituting into Eqs. (7) with (6), the y–φ relation follows.

1.1 Comparison of the Simple, Eccentric and Two SliderCrank Mechanisms In Fig. 2 the displacement-angle relations for: a) simple (Eq. (6)), b) eccentric (Eq. (3)) and c) two slider-crank (Eq. (7)) mechanisms are plotted. It is assumed that for the simple and eccentric slidercrank mechanism the length of the leading shaft (0.8 m) and of the connecting rod (0.32 m) are equal for both mechanisms and the eccentricity is 0.20 m. The dimensions of the two joined slider-crank mechanisms in m are: a = 0.8, b = 0.32, c = 0.14, r = 0.20, g = 0.24, h = 0.18, l = 0.20, p = 0.12, w = 0.16 and the cutting depth is δ = 0.12. In our consideration the common assumption used for comparing the three mechanisms is that the cutting depth has to be equal and the cutting angle is calculated from the lowest position of the slider. In Fig. 2 the full line indicates the motion of the slider in the sheet (where the shaded

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area is for cutting) and the dotted line shows the motion of the slider out of the sheet. Comparing the diagrams in Fig. 2, it can be concluded: • Cutting takes longer with the simple and eccentric slider-crank mechanism than with the two joined slider-crank mechanism.

• The interval in which the slider (cutting tool) is above the cutting object is much longer for the two joined slider-crank mechanism than for the simple and eccentric one. During this period the manipulation with the cutting sheet may be completed. This, however, is not the case for the simple and eccentric slider-crank mechanisms.

Namely, the ‘resting’ period for the simple and eccentric slider-crank mechanisms is extremely short and does not give the opportunity to finish the manipulation with the sheet: setting and its removing from the machine.

γ r ( w cos γ − ( p − yB ) sin γ ) =

= ( p − yB + r cos γ ) y B ,

(14)

where according to Eq. (3) y B = −aϕ

yB cos ϕ + l sin ϕ . (15) yB + a sin ϕ

Substituting Eq. (14) with Eq. (15) into Eq. (13) the velocity of the slider as the function of the angular velocity of the leading crankshaft is obtained: vE = aϕ f (ϕ ) ,

f (ϕ ) =

⋅

yE sin γ g ⋅ ⋅ r yE − g cos γ

p − yB + r cos γ y cos ϕ + l sin ϕ . ⋅ B w cos γ − ( p − yB ) sin γ yB + a sin ϕ

(16)

(17)

Function f(φ) is periodical with a period of 2π.

3 MATHEMATICAL MODEL OF THE MECHANISM

Fig. 2. y–φ diagrams for a) simple slider-crank mechanism, b) eccentric slider-crank mechanism, c) two-joined slider-crank mechanism (shaded area-cutting, dotted line-slider in the sheet, full line-slider out of sheet)

It is the reason that the joined two-slider-crank mechanism is introduced and assumed for the cutting process. During one period of motion of the twojoined slider-crank mechanism the manipulation with the polymer sheet and also the cutting proces is possible to be finished.

2 KINEMATICS OF THE CUTTING MECHANISM Let us determine the velocity vE of the cutting tool as a function of the angular velocity ϕ of the leading crankshaft. Using the relations Eqs. (6) and (7) the velocity of the cutting tool is: gyE sin γ

(13) vE ≡ y = −γ . yE − g cos γ The time derivative of (10) gives γ ( y B ) as:

356

The considered two slider-crank mechanism has one degree of freedom and the generalized coordinate is the angle φ of the leading crank O1A. The Lagrange differential equation of motion of the mechanism for the generalized coordinate φ is in general:

d ∂T ∂T ∂Φ − + = Qϕ , (18) dt ∂ϕ ∂ϕ ∂ϕ

where T is the kinetic energy of the mechanism, F is the dissipative function and Qφ is the generalized force.

It is assumed that the mass of the cutting tool is m and the moment of inertia of the leading element is J. The inertial properties of other elements in mechanism can be omitted in comparison to the previous. Then, the kinetic energy of the mechanism is a sum of the kinetic energy of the cutting tool and of the leading element: 1 1 T = J ϕ 2 + m vE2 , (19)

2 2 where vE is the velocity of cutting tool given with Eq. (16). Substituting Eq. (16) into Eq. (19) we obtain:

T=

1 1 J ϕ 2 + m a 2 f 2 ϕ 2 , (20) 2 2

where the kinetic energy is the function of the angular velocity ϕ .

Cveticanin, L. – Maretic, R. – Zukovic, M.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, 354-361

Since all the mechanism members are rigid, the elastic energy of the system is zero.

The mechanism is driven by an electro motor whose characteristics is that the driving torque M is the function of the velocity ϕ , [18]:  ϕ M = M 0 1 −  ω0

  , (21) 

where M0 = const. and ω0 is the synchrone angular velocity of the motor. Thereby, the driving load is expressed as a function of the angular coordinate describing the crank rotation. Physically this means that the motion of the mechanism has an influence on the motor torque. Such a mechanism is subjected to non-ideal forcing (see [19 to 21]).

The cutting process is required to be managed during the motion of the cutting tool from up to down in the angle interval [φK, φM] where φM corresponds to the lowest position of the cutting tool which satisfies the relation dy(φM) / dφ = 0 and φK is the angle position for which the cutting starts and has to be adopted to the thickness of the sheet δ: y(φK) = y(φM) + δ. In this interval the cutting force is required to be constant and sufficiently strong to provide the cutting without folding of the sheet. Otherwise, the cutting force is assumed to be zero. Mathematically, for φ ∈ [φK, φM] the constant force is F = F0 and for φ ∈ [0, φK) ∪ (φM, 2π] it is F = 0.

1, x ≥ 0 .

UnitStep ( x ) =  0 , x < 0

The force distribution is plotted in Fig. 3 (φK = 2.06379, φM = 2.55591, δ = 0.03).

The driving torque M and the cutting force F give the virtual works for a virtual angle and displacement variations, respectively, i.e., δA = Mδφ + Fδy . (23)

y is:

According to Eq. (16) the variation of the variable δy = afδφ . (24)

Substituting Eq. (24) into Eq. (23) we obtain δA = Qφδφ where the generalized force is: Qφ = M +afF . (25)

During cutting the damping force acts. For energy dissipation during the slider motion through various materials of the polymer sheet, the damping force is assumed to be proportional to the velocity of the cutting tool, i.e.,  

Fw = −q vE . (26)

The corresponding dissipative function is: 1 Φ = q vE2 , 2

(27)

where q is the damping coefficient. According to Eq. (16), the dissipative function Eq. (24) is: 1

(28) Φ = q a 2 f 2 ϕ 2 .

2 Substituting Eqs. (15), (20) and (28) and the corresponding derivatives calculated in Appendix into Eq. (18), the differential equation of motion is obtained: df 2 J + ma 2 f 2 ϕ + ma 2 f ϕ + qa 2 f 2ϕ = (29)

dφ = M (ϕ ) + a f F (ϕ ) ,

(

Fig. 3. y–φ and F – φ diagrams of the cutting tool

As the cutting process is periodical, the cutting force is modeled as a UnitStep function:

(

F ≡ F (ϕ ) = F0 F (ϕ ) =

= F0 UnitStep ( mod (ϕ , 2π ) − ϕ K ) − (22)

)

− UnitStep ( mod (ϕ , 2π ) − ϕ M ) , where the unit step function is defined as:

)

where f and (df/dφ) are φ - periodical functions with period of 2π. (see Eqs. (17) and (A.5)).

According to Eqs. (17) and (A.5), the functions f(φ), df(φ)/dφ and f(φ)(df(φ)/dφ) are plotted in Fig. 4.

Introducing the dimensionless values:

τ = ω0 t , I =

J ω02 J ω02 , I= , M0 M0

q a 2ω0 ma 2ω02 F a λ= 0 , Q= , µ= , M0 M0 M0

Dynamics of Polymer Sheets Cutting Mechanism

(30)

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the differential equation (29) transforms into:

( I + µ f )ϕ " + µ f ddfϕ (ϕ ' )

φ' = dφ / dτ ,

2

2

+ Q f 2ϕ ' =

= (1 − ϕ ' ) + λ fF (ϕ ) ,

(31)

where φ' = dφ / dτ and φ'' = d2φ / dτ2 , μ is dimensionless mass of the cutting tool, I is dimensionless moment of inertia of the leading crank O1A, Q is the dimensionless damping coefficient, λ is dimensionless cutting force and τ is the dimensionless time.

Differential equation (31) is strong nonlinear one and only for some special parameter values the closed form analytical solution is possible to be obtained.

Otherwise, the Eq. (31) is solved numerically using the Runge-Kutta procedure.

From the analysis of the curves in Fig. 5 it can be concluded: • For the case when the cutting force is zero, F (φ) = 0, and the motion of the mechanism is without loading, the angular velocity of the leading crank O1A varies as it is shown in Fig. 5 (curve I). Variation of the angular velocity is periodical.

• If it is assumed that the mechanism is loaded with a force F (φ) = 1 for all positions of the leading crank, the influence of the force on the angular velocity of the motor motion is extremely high (see curve II in Fig. 5).

• For the case when the cutting process is discontinual and the cutting force has the form Eq. (22) there is a jump in the angular velocity curve (see curve III, Fig. 5).

Fig. 6. φ' – τ curves for various values of λ

Fig. 4. f(φ)–φ, (df/dφ)–φ and f(φ)(df(φ)/dφ)–φ curves

4 DYNAMIC ANALYSES Solving Eq. (31) for various values of F (φ) the influence of the cutting force on the angular velocity of the motor is obtained. In Fig. 5 the φ' – τ curves for various values of F (φ) are plotted. (Dimensionless parameters are λ = 0.033, I = 1.4557·10-4, μ = 1.051·10-3, Q = 0.00134 and the initial conditions φ(0) = 0 and φ'(0) = 1).

For this case the influence of the cutting parameter λ on the φ' – τ is evident (see Fig. 6). The higher the cutting force the higher the velocity variation.

4.1 Analytical Let us consider the case when M0 is significantly larger than the parameters I, μ, Q and λ which for the small parameter ε << 1 have the form:

I = εI1 ,

μ = εμ1 ,

Q = εQ1 ,

λ = ελ1 ,

(32)

Substituting Eq. (32) into Eq. (31) we have:

(1 − ϕ ' ) = ε ( I1 + µ1 f 2 (ϕ ) ) ϕ '' + εµ1 f (ϕ ) +ε Q1 f

2

df (ϕ ) dϕ

ϕ'2 +

(33)

(ϕ ) ϕ ' − ε f (ϕ ) λ1F (ϕ ) .

Using the series expansion of the variable φ and its time derivatives up to the first order of the small parameter, we obtain: Fig. 5. φ' – τ curves for various values of F (φ): I: F (φ) = 0, II: F (φ) = 1, III: UnitStep function

358

Cveticanin, L. – Maretic, R. – Zukovic, M.

φ = φ0 + εφ1 + ... , φ' = φ0' + εφ1' + ... ,

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φ'' = φ0'' + εφ1'' + ... ,

•

f (ϕ ) = f ( ϕ0 + εϕ1 ) ≈ f (ϕ0 ) + ε f ' (ϕ0 ) ϕ1 ,

df (ϕ ) / dϕ = df ( ϕ0 + εϕ1 ) / dϕ ≈

(

(34)

 d 2 f (ϕ )   df (ϕ )   , ≈ + εϕ 1  dϕ   dφ 2   ϕ0  ϕ0

•

F ( ϕ ) ≈ F (ϕ 0 ) .

Substituting Eq. (34) into Eq. (33) and separating the terms with the same order of small parameter ε up to the small value of second order, the system of equations follows:

For the mechanism with omitted mass of the leading crank and of the cutting tool, the angular velocity variation is ϕ ' = 1 + λ fF (ϕ ) / 1 + Qf 2 . For higher values of coefficient of damping the angular velocity is smaller. The influence of the cutting force λ on the angular velocity φ' is significant: the higher the cutting force, the larger the angular velocity variation.

If the mass of the cutting tool and the damping coefficient during cutting are omitted, the differential equation depends on the moment of inertia I of the leading crankshaft and on the cutting force λ and is I ϕ " = (1 − ϕ ' ) + λ fF (ϕ ) .

) (

)

ε 0 : 0 = 1 − ϕ0 ', (35)

(

)

ε 1 : ϕ1 ' = f (ϕ0 ) λ1 F (ϕ0 ) − I1 + µ1 f 2 (ϕ0 ) ϕ0 '' −  df  2 2 − µ1 f (ϕ0 )   ϕ0 ' − Q1 f (ϕ0 ) ϕ0 ' . ϕ d  ϕ0

(36)

Solution of Eq. (35) is φ0' = 1 = const. which after integration gives:

φ0 = τ . (37) Substituting Eq. (37) into Eq. (36) we obtain:

Fig. 7. Comparison of the analytical and numerical φ' – τ functions

•

 df  2 ϕ1 ' = − µ1 f (ϕ0 )   − Q1 f (ϕ0 ) + (38)  dφ φ0 + f (ϕ0 ) λ1 F (ϕ0 ) .

According to Eqs. (37), (38) and (34) the first order approximate analytical solution is:    df  2 ϕ ' (τ ) = 1 +  − µ f (τ )   − Qf (τ ) + f (τ ) λ F (τ )  . (39)   dϕ τ  

The influence of mass and damping parameters, and also of the cutting force on the angular velocity of the leading element is obtained. In Fig. 7 the analytical result Eq. (39) is compared with a numerical one which is valid for differential equation (33). The difference between the results is negligible.

5 RESULTS Let us analyze Eq. (33) and the analytically obtained solution (39). It follows:

•

For the case when damping is neglected and the cutting force is zero, for the initial angular velocity φ0' the angular velocity of the leading element varies as φ' = 1 + (φ0' – 1) exp(–τ/I).

For the steady state motion when time τ tends to infinity, the angular velocity of the leading element tends to a constant value: φ' = 1 = const.

If the dimensionless driving torque M0 is significant in comparison to other parameters of the mechanism, the angular velocity in the first approximation is obtained as φ' ≈ 1 + εφ1', where ϕ1 ' = − µ f ( df / dϕ ) − Qf 2 + λ fF . For certain parameter values the analytically obtained result is compared with exact numerical one (see Fig. 7). The difference between the results is negligible.

6 CONCLUSIONS

The following is concluded: • The damping during cutting has a significant influence on the angular velocity of the leading element of the cutting mechanism. If the mass of the leading crank and of the cutting tool is quite small it is obvious that for higher values of the

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• •

damping, the angular velocity of the leading crank is smaller.

The influence of the cutting force on the angular velocity is also significant: the higher the cutting force, the larger is the angular velocity variation.

The angular velocity variation affects the stability of motion and also the quality of the cutting process. Namely, for high values of angular velocity variation of the leading element, the motor can get from the steady state stable motion into an unstable one. In addition, the higher the cutting force, the cutting process is retarded due to the fact that the averaged velocity is smaller.

7 ACKNOWLEDGEMENT

The investigation has been supported by the Ministry of Science of Serbia (Proj. No. ON174028 and No. IT41007) and Province Secretariat for Science and Technological Development, Autonomous Province of Vojvodina (Proj. No 114-451-2094/2011).

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[3] Metallidis, P., Natsiavas, S. (2003). Linear and nonlinear dynamics of reciprocating engines.

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[5] Ha, J.L., Fung, R.F., Chen, K.Y., Hsien, S.C. (2006). Dynamic modeling and identification of a slider-crank mechanism. Journal of Sound and Vibration, vol. 289, p. 1019-1044, DOI:10.1016/j. jsv.2005.03.011.

[6] Erkaya, S., Su, S., Uzmay, I. (2007). Dynamic analysis of a slider-crank mechanism with eccentric connector and planetary gears. Mechanism and Machine Theory, vol. 42, p. 393-408, DOI:10.1016/j.mechmachtheory.2006.04.011.

[7] Ogura, M., Daidoji, S. (1982). Application and practice of the double slider crank mechanism for the air compressor. JSME (Japan Society of Mechanical Engineers) International Journal, Series B: Fluids and Thermal Engineering, vol.

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[8] Wang, M., Song, Q., Zhong, K. (2012). The double role piston pump based on the symmetrical tears and crank-link-slider mechanism driven by servo motor. Applied Mechanics and Materials, vol. 121-126, p. 2308-2312.

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[10] Kazimierski, Z., Wojewoda, J. (2011). Double internal combustion piston engine. Applied Energy, vol. 88, p. 1983-1985, DOI:10.1016/j. apenergy.2010.10.042.

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[19] Nayfeh, A.H., Mook, D.T. (1979). Nonlinear Oscillations. John Wiley & Sons, New York.

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Appendix.

DERIVATIVES OF THE KINETIC ENERGY FUNCTION The derivatives of kinetic energy function Eq. (20) suitable for Lagrange equation (18) are:

∂T df 2 ϕ , = a 2 mf ∂ϕ dϕ

(A.1)

∂T = J ϕ + a 2 f 2ϕ , ∂ϕ

(A.2)

d ∂T = J ϕ + a 2 2 f f ϕ + f 2ϕ , dt ∂ϕ

(

)

df df f = = ϕ . dt dϕ

(A.4)

g s1 s3 s5 . r s2 s4 s6

(A.7)

The corresponding derivatives of Eq. (A.7) according to Eq. (A.5) are

∂f g s1 s5 ∂  s3  =  , ∂ϕ r s2 s6 ∂ϕ  s4 

(A.8)

∂f g s2 sin γ − s1 s3 s5 , = s4 s6 ∂yE r s22

(A.9)

∂f g s3 ∂  s1 s5  =  , ∂γ r s4 ∂γ  s2 s6 

(A.10)

∂f g s1 ∂ = ∂yB r s2 ∂yB

 s3 s5   ,  s4 s6 

(A.11)

∂s3 ∂s6 = − yB sin ϕ + l cos ϕ , = sin ϕ , ∂ϕ ∂yB

.

f (ϕ ) =

(A.3)

where ( ) = d / dt . The time derivative of the function f expressed with Eq. (17) is:

and substituting into Eq. (17), the function f is:

∂s1 ∂s2 = yE cos γ , = g sin γ , ∂γ ∂γ ∂s5 ∂s4 = −r sin γ , = a cos ϕ ∂γ ∂ϕ ∂s6 = −( p − yB )cos γ − w sin γ , ∂γ ∂s ∂s3 ∂s4 = − 5 = 1. = cos ϕ , ∂yB ∂yB ∂yB

(A.12)

As f explicitely and implicitely depends on the angle φ the total derivative of f is:

For Eqs. (3), (6) and (10) the derivatives in angle φ are:

df ∂f ∂f dyB  ∂f dyE ∂f  d γ = + + + . (A.5)  dϕ ∂ϕ ∂yB dϕ  ∂yE d γ ∂γ  dϕ

s ∂yB ∂yB s ∂γ a s3 s5 . (A.13) = −a 5 , = −g 1 , = ∂ϕ ∂γ s6 s2 ∂ϕ r s4 s6

Substituting Eqs. (A.8) to (A.11) and the also Eqs. (3), (6) and (10) into Eq. (A.5) the (df/dφ)relation is calculated.

Introducing the notation: s1 = yE sin γ , s2 = yE − g cos γ ,

s3 = yB cos ϕ + l sin ϕ , s4 = yB + a sin ϕ , s5 = p − yB + r cos γ ,

(A.6)

s6 = w cos γ − ( p − yB ) sin γ ,

Dynamics of Polymer Sheets Cutting Mechanism

361

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 58, (2012), številka 5 Ljubljana, maj 2012 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki člankov Andrej Pirc, Mihael Sekavčnik, Mitja Mori: Univerzalni model lesnega uplinjevalnika za pripravo sinteznega plina z različno kemijsko sestavo Željko Đurić, Ljubiša Josimović, Živoslav Adamović, Ljiljana Radovanović, Goran Jovanov: Vrednotenje učinkovitosti oblikovanega programa vzdrževanja Mohsen Mahdavi Adeli, Fatemeh Sobhnamayan, Said Farahat, Mahmoud Abolhasan Alavi, Faramarz Sarhaddi: Eksperimentalna analiza zmogljivosti in optimizacija toplozračnega kolektorja z vgrajenim fotonapetostnim sistemom (PV/T) Jure Jelenc, Jože Jelenc, Damijan Miklavčič, Alenka Maček Lebar. Nizkofrekvenčna sonoporacija in vitro: evalvacija eksperimentalnega sistema Milosav Ognjanović, Snežana Ćirić Kostić: Vpliv ohišja menjalnika na nastajanje hrupa zaradi udarcev zob Edvin Raubar, Damir Vrančić: Sistem za izničevanje nihanja bremena pri pretovarjanju z obalnimi dvigali José Henrique de Freitas Gomes, Aluizio Ramos Salgado Júnior, Anderson Paulo de Paiva, João Roberto Ferreira, Sebastião Carlos da Costa, Pedro Paulo Balestrassi: Metoda globalnega kriterija na osnovi glavnih komponent za optimizacijo proizvodnih procesov z več odzivi Livija Cveticanin, Ratko Maretic, Miodrag Zukovic: Dinamika mehanizma za rezanje polimernih folij Osebne vesti Diplomske naloge

SI 61 SI 62 SI 63 SI 64 SI 65 SI 66 SI 67 SI 68

SI 69

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 61

Prejeto: 2011-03-29, sprejeto: 2012-03-14 © 2012 Strojniški vestnik. Vse pravice pridržane.

Univerzalni model lesnega uplinjevalnika za pripravo sinteznega plina z različno kemijsko sestavo Pirc, A. – Sekavčnik, M. – Mori, M. Andrej Pirc1,* – Mihael Sekavčnik2 – Mitja Mori2 1Savaprojekt d.d., Krško, Slovenija 2Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

V prispevku je obravnavan univerzalni model uplinjevalnika lesne biomase, s katerim je mogoče primerjati različne režime delovanja ob proizvodnji sinteznega plina z različno kemijsko sestavo. Model pa obenem omogoča tudi analizo vpliva vhodnih parametrov na obratovanje uplinjevalnika in postrojenja, v katerega je le-ta vgrajen.

Raziskava je bila usmerjena na razvoj numeričnega modela uplinjevalnika lesne biomase ob upoštevanju stehiometričnih reakcij celotnega procesa uplinjanja ter masnih in energijskih bilanc. Potek uplinjanja je razdeljen na štiri zaporedne faze: sušenje lesa, piroliza, delna oksidacija in redukcija. Nadalje je bil izdelan model, umeščen v širši model energetskega sistema, ki je vseboval še mlin za lesno biomaso in sušilnico lesa, pripravo oksidanta in pare za potrebe uplinjanja, regenerativne grelnike in plinski motor z generatorjem električne energije. V motorju z generatorjem se kemična notranja energija proizvedenega sinteznega plina pretvori v električno energijo in toploto, ki se koristno uporablja za sušenje lesa in regenerativno gretje vhodnih tokov. Za modeliranje celotnega energetskega sistema je bil uporabljen program IPSEpro.

Glede na režim obratovanja smo opazovali naslednje sestave sinteznega plina: splošni sintezni plin (ogljikov monoksid, metan, vodik in ogljikov dioksid), sintezni plin, obogaten z vodikom, in sintezni plin, katerega sestava je primerna za nadaljnjo sintezo metanola. Z numerično simulacijo obratovanja takšnega postrojenja in opazovanjem eksergijskega izkoristka so bili ugotovljeni naslednji najvplivnejši dejavniki: kemična sestava in vlažnost lesa, temperatura sinteznega plina na izstopu iz uplinjevalnika in režim obratovanja.

1. Večja vsebnost vodika v lesu vpliva na večjo količino metana in manjšo količino ogljikovega dioksida v proizvedenem sinteznem plinu in obratno.

2. Večja kot je vlažnost vhodne surovine, nižji je eksergijski izkoristek opazovanega postrojenja zaradi dodatno porabljene energije za sušenje lesa.

3. Ob večji količini dovedenega oksidanta je večji tudi delež zgorelega metana, proizvedenega s pirolizo. S tem je dosežena višja temperatura sinteznega plina na izstopu iz uplinjevalnika, obenem pa je na razpolago manj metana za zgorevanje v plinskem motorju, kar prispeva k nižjemu izkoristku. Prenizka temperatura v uplinjevalniku pa onemogoča normalen proces uplinjanja.

4. Najvišji eksergijski izkoristek je bil dosežen ob proizvodnji splošnega sinteznega plina, najnižji pa ob proizvodnji sinteznega plina obogatenega z vodikom, in sicer zaradi endotermičnosti redukcijskih reakcij.

Uporaba kisika kot oksidanta se je v vseh primerih izkazala za boljšo od uporabe zraka.

V nadaljevanju je v modelu predvidena dodatna vključitev modelov za popis vpliva reaktorja in kinetike kemijskih reakcij uplinjevalnega procesa.

Ključne besede: uplinjevalnik, sestava sinteznega plina, biomasa, energetski sistem, modeliranje.

*Naslov avtorje za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, andrej.pirc@savaprojekt.si

SI 61

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 62

Prejeto: 2008-07-16, sprejeto: 2012-03-21 © 2012 Strojniški vestnik. Vse pravice pridržane.

Vrednotenje učinkovitosti oblikovanega programa vzdrževanja

Željko

Đurić1

Đurić, Ž. – Josimović, L. – Adamović, Ž. – Radovanović, L. – Jovanov, G. – Ljubiša Josimović2 – Živoslav Adamović3 – Ljiljana Radovanović3,* – Goran Jovanov4 1 BOKSIT a.d. Milići, Bosna in Hercegovina 2 Politehnika v Požarevcu, Srbija 3 Univerza v Novem Sadu, Tehnična fakulteta ''Mihajlo Pupin'', Srbija 4 Mednarodna univerza Brčko, Bosna in Hercegovina

V članku je predstavljen osnovni pristop k programiranju vzdrževanja kompleksnih tehničnih sistemov, ki predstavlja nabor pravil za določanje načina diagnosticiranja sestavnih delov sistema v realnem procesu eksploatacije, kakor tudi odločanje o potrebi po zamenjavi oz. o obsegu potrebnega vzdrževanja na osnovi podatkov o dejanskem tehničnem stanju sistema.

Ob predpostavki, da je vzdrževanje na osnovi stanja pravzaprav sistem upravljanja s tehničnim stanjem sistema v procesu eksploatacije, smo ob izbiri strategije vzdrževanja na osnovi stanja izvedli analizo uporabnosti oblikovanih različic programa vzdrževanja ter ovrednotili njihovo učinkovitost s primerjavo z osnovnimi kazalniki (za kurativno in preventivno vzdrževanje). Izpostavili smo pomen uporabe opisanega programa vzdrževanja za povečanje ravni zanesljivosti in skrajšanje zastojev v delovanju tehničnih sistemov s ciljem doseganja večje učinkovitosti in s tem posledično tudi produktivnosti podjetij, v katerih obratujejo takšni sistemi. Članek ob upoštevanju visoke stopnje zahtevnosti tehničnih sistemov v industriji obravnava oblikovanje programov vzdrževanja komponent sestava (npr. sestava konverterja), pristop pa je mogoče uporabiti tudi za sestavne dele sistemov.

Oblikovanje programa vzdrževanja za sestavne dele in/ali sistem ima tri korake: • oblikovanje različic programa vzdrževanja na prvi ravni, • oblikovanje različic programa vzdrževanja na drugi ravni, • vrednotenje učinkovitosti in izbira različice programa vzdrževanja.

Nadzor stanja preprečuje načine odpovedi tako, da zaznava in preprečuje odpovedi. Izmerjeni trend povečevanja temperature in vibracij ležaja je tako znak za intenzivno obrabo in grozečo odpoved, ki jo je mogoče preprečiti s pravočasno zamenjavo obrabljenega ležaja. Nadzor stanja komponent in sistemov omogoča tudi zgodnjo diagnostiko težav kot pomoč pri vnaprejšnjem načrtovanju in organizaciji popravil. Nadzor stanja s skrajšanjem odzivnega časa in zastojev zaradi popravil zmanjšuje finančne izgube, ki so povezane z odpovedmi.

Vzdrževanje vseh parametrov procesa v varnem območju je naslednji primer dvojnega ukrepa, ki zmanjšuje tako verjetnost odpovedi kot tudi posledice odpovedi. Z uvedbo programa vzdrževanja je mogoče izboljšati učinkovitost pogonov konverterjev, zmanjšati celotne stroške vzdrževanja, izboljšati organizacijo proizvodnje in vzdrževanja, zmanjšati rabo električne energije in število reklamacij izdelkov, izboljšati raven sodelovanja s partnerji, izboljšati motivacijo za delo ter nivo načrtovanih vzdrževalnih aktivnosti itd.

Rezultati uveljavitve programa vzdrževanja ter nekateri drugi rezultati, ki niso opisani v tem članku, nakazujejo dobro skladnost s hipotezo o pomenu zgoraj opisanih programov vzdrževanja za povečanje ravni zanesljivosti ter njihovem prispevku za skrajšanje zastojev in visoko stopnjo izkoristka tehničnih sistemov ter produktivnosti podjetja.

Ključne besede: zanesljivost tehničnih sistemov, program vzdrževanja, tehnična diagnostika

SI 62

*Naslov avtorja za dopisovanje: Tehnična fakulteta Mihajlo Pupin, Djure Djakovic bb, 23000 Zrenjanin, Srbija, ljiljap@tfzr.uns.ac.rs

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 63

Prejeto: 2010-01-11, sprejeto: 2011-12-02 © 2012 Strojniški vestnik. Vse pravice pridržane.

Eksperimentalna analiza zmogljivosti in optimizacija toplozračnega kolektorja z vgrajenim fotonapetostnim sistemom (PV/T)

Mahdavi Adeli, M. – Sobhnamayan, F. – Farahat, S. – Abolhasan Alavi, M.A. – Sarhaddi, F. Mohsen Mahdavi Adeli1 – Fatemeh Sobhnamayan2 – Said Farahat3 – Mahmoud Abolhasan Alavi2 – Faramarz Sarhaddi*,3 1Fakulteta za strojništvo, Islamska univerza Azad, oddelek v Susangerdu, Iran 1Fakulteta za strojništvo, Islamska univerza Azad, oddelek v Mashhadu, Iran 3Oddelek za strojništvo, Univerza v Sistanu in Baluchestanu, Iran Sistem PV/T hkrati proizvaja uporabno toploto in električno energijo, njegova zmogljivost pa je odvisna od toplotnega in električnega izkoristka. Povečanje električnega izkoristka sistema PV/T povzroči zmanjšanje toplotnega izkoristka, in obratno. Za doseganje maksimalne toplotne in električne moči sistema PV/T je zato potrebna sočasna optimizacija toplotnega in električnega izkoristka sistema. Cilj predstavljene študije je sočasna optimizacija toplotnega in električnega izkoristka toplozračnega sončnega kolektorja z vgrajenim fotonapetostnim sistemom (PV/T).

Obravnavan je vzorčni toplozračni kolektor PV/T. Z razvojem enačbe energijske bilance za vsako komponento PV/T so izpeljani analitični izrazi za toplotne parametre in toplotni izkoristek. Za izračun električnih parametrov in električnega izkoristka toplozračnega kolektorja PV/T je uporabljen tokovno-napetostni (I-V) model s petimi parametri in nabor prenosnih enačb. Vodilne enačbe za toplotno in električno zmogljivost sistema PV/T so nelinearne, zato je bil razvit računski program na osnovi Newton-Raphsonove metode.

Predmet raziskave je uporaba sončne energije za proizvodnjo toplote in električne energije v sistemih PV/T. Za merjenje toplotnih in električnih parametrov je bil zgrajen eksperimentalni model tipičnega toplozračnega kolektorja PV/T. Uporabljen je bil tudi pristop sočasne optimizacije za povečanje izkoristka solarnega sistema PV/T. Na osnovi podatkov meritev je bila opravljena eksperimentalna validacija uporabljenih toplotnih in električnih modelov. Ugotovljeno je bilo dobro ujemanje med rezultati simulacij in eksperimentov. Izvedena je bila tudi sočasna optimizacija toplozračnega kolektorja PV/T za doseganje maksimalnega toplotnega in električnega izkoristka. Nadalje so določena optimalna območja hitrosti vstopnega zraka, globine kanala in ciljne funkcije v naboru optimalnih rešitev Pareto.

V literaturi niso objavljene raziskave o sočasni optimizaciji toplotnega in električnega izkoristka sistemov PV/T. V okviru predstavljene raziskave je bila opravljena sočasna optimizacija toplotnega in električnega izkoristka toplozračnega sončnega kolektorja z vgrajenim fotonapetostnim sistemom (PV/T).

Ključne besede: toplozračni kolektor z vgrajenim fotonapetostnim sistemom (PV/T), sočasna optimizacija

*Naslov avtorje za dopisovanje: Oddelek za strojništvo, Univerza v Sistanu in Baluchestanu, Zahedan, Iran, fsarhaddi@eng.usb.ac.ir

SI 63

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 64

Prejeto: 2011-09-23, sprejeto: 2012-01-27 © 2012 Strojniški vestnik. Vse pravice pridržane.

Nizkofrekvenčna sonoporacija in vitro: evalvacija eksperimentalnega sistema

Jelenc, J. – Jelenc, J. – Miklavčič, D. – Maček Lebar, A. Jure Jelenc1 – Jože Jelenc1 – Damijan Miklavčič2 – Alenka Maček Lebar2,* 1 Iskra Medical d.o.o., Slovenija 2 Univerza v Ljubljani, Fakulteta za elektrotehniko, Slovenija Sonoporacija je pojav, pri katerem ultrazvočno valovanje povzroči povečano prepustnost celične membrane za snovi, ki sicer zaradi svojih lastnosti po naravni poti ne morejo prehajati ali slabo prehajajo skozi celično membrano. Mehanizmi sonoporacije še niso povsem znani. Najpogosteje je kot vzrok omenjen pojav kavitacije.

Pri raziskavah sonoporacije so uporabljeni različni načini izpostavitve celic ultrazvočnemu valovanju. Te raziskave praviloma izkazujejo uspešen vnos barvil, zdravilnih učinkovin in genskega materiala v celice, le redko pa podajajo natančen opis fizikalnih pogojev v izvedenih eksperimentih. V prispevku predstavljamo eksperimentalni sistem za sonoporacijo v področju nizkih ultrazvočnih frekvenc, ki omogoča izpostavitev celic v suspenziji znanemu in vnaprej določenemu ultrazvočnemu tlaku.

V eksperimentalnem sistemu so celice v suspenziji izpostavljene potujočemu nizkofrekvenčnemu ultrazvočnemu valovanju. Glavni element sistema je vodna kopel, ki je napolnjena z destilirano vodo. Vanjo sta potopljena nizkofrekvenčni ultrazvočni izvor (29,6 kHz) in posodica s celično suspenzijo. Z obložitvijo sten kopeli s posebnim materialom za absorpcijo nizkofrekvenčnega ultrazvočnega valovanja je raven odbojev valovanja uspešno zmanjšana, kar omogoča meritev ultrazvočnega tlaka tudi v kontinuiranem načinu delovanja ultrazvočnega izvora. Meritve ultrazvočnega tlaka smo izvedli s hidrofonom, ki je bil pritrjen na mestu, namenjenem posodici s celično suspenzijo. S spreminjanjem oddaljenosti hidrofona od ultrazvočnega izvora smo izmerili prostorsko razporeditev ultrazvočnega tlaka. Rezultate meritev smo primerjali z izračunanim ultrazvočnim tlakom, ki smo ga določili z numeričnim modelom eksperimentalnega sistema. Numerični model smo zasnovali z metodo končnih elementov v programskem paketu Comsol Multiphysics 3.5.

Odboji ultrazvočnega valovanja v vodni kopeli, ki sten nima obloženih z absorberjem ultrazvočnega valovanja, so tako izraziti, da onemogočajo meritve ultrazvočnega tlaka v kontinuiranem načinu. Amplituda tlaka posameznega ultrazvočnega pulza odbitega od stene kopeli dosega 29% amplitude tlaka izvornega ultrazvočnega valovanja. Ob daljših izpostavitvah pa so v kopeli prisotni tudi večkratni odboji ultrazvočnega valovanja, ki dodatno onemogočajo meritev. Z obložitvijo sten z absorpcijskim materialom smo amplitudo tlaka odboja zmanjšali na 6% amplitude tlaka izvornega ultrazvočnega valovanja. Odboji ultrazvočnega valovanja so na ta način zmanjšani na raven, ki omogoča merjenje ultrazvočnega tlaka v kontinuiranem načinu, kar ustreza načinu izpostavitve celične suspenzije.

V kopeli z obloženimi stenami smo izmerili ultrazvočni tlak v kontinuiranem načinu delovanja ultrazvočnega izvora. Meritev smo izvedli na sredinski osi ultrazvočnega izvora, in sicer na razdaljah od 1,5 do 10 cm.

Izmerjene vrednosti eksponentno upadajo z oddaljenostjo od ultrazvočnega izvora. Največjo efektivno vrednost ultrazvočnega tlaka 111±10,6 kPa smo izmerili na razdalji 1,5 cm. Standardna deviacija devetih meritev ultrazvočnega tlaka je bila manjša od ±15%. Ultrazvočni tlak, izračunan z numeričnim modelom po metodi končnih elementov v programskem paketu Comsol Multiphysics, se dobro ujema z izmerjenimi vrednostmi ultrazvočnega tlaka. Izračunan ultrazvočni tlak na razdalji 1,5 cm od ultrazvočnega vira je 91 kPa. Nekoliko nižje vrednosti izračunanega ultrazvočnega tlaka v primerjavi z izmerjenimi vrednostmi so posledica poenostavitev, ki smo jih privzeli v numeričnem modelu.

V izdelanem sistemu za nizkofrekvenčno sonoporacijo smo ovrednotili ultrazvočni tlak z meritvami in rezultati numeričnega modela. Poznavanje ultrazvočnega tlaka na mestu celične suspenzije bo omogočilo sonoporacijo v kontroliranih pogojih.

Ključne besede: ultrazvok, hidrofon, kavitacija, metoda končnih elementov

SI 64

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za elektrotehniko, Tržaška 25, 1000 Ljubljana, Slovenija, alenka.maceklebar@fe.uni-lj.si

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 65

Prejeto: 2010-11-15, sprejeto: 2012-01-27 © 2012 Strojniški vestnik. Vse pravice pridržane.

Vpliv ohišja menjalnika na nastajanje hrupa zaradi udarcev zob Ognjanović, M. – Ćirić Kostić, S. Milosav Ognjanović1,* – Snežana Ćirić Kostić2 1 Univerza v Beogradu, Fakulteta za strojništvo, Srbija 2 Univerza v Kragujevcu, Fakulteta za strojništvo v Kraljevu, Srbija

Namen članka je raziskava vpliva ohišja na hrup, ki ga oddaja prenosnik.

Udarci zob pri ubiranju zobnikov so eden pomembnejših virov motenj v prenosnikih. Do udarcev prihaja ob začetku in ob koncu ubiranja zob, zaradi resonančnih vibracij zobnikov ter med kotaljenjem bokov zaradi mikroodstopanj oblike in površinske hrapavosti bokov. Del energije, ki se ustvarja pri udarcih, vzbuja lastne frekvence komponent prenosnika. Preostala energija udarcev se prek elastične konstrukcije zobnikov, gredi in ležajev prenaša na ohišje prenosnika. Te motnje vzbujajo proste vibracije ohišja in z njegove površine se v okolico oddajajo zvočni valovi. Ohišje ima zato lahko različen vpliv na emisijo hrupa: odvisno od parametrov zasnove lahko valove motenj absorbira ali pa jih ojačuje. Ohišje ima razen tega tudi funkcijo zvočne izolacije za hrup, ki nastaja v notranjosti prenosnika.

Ohišje prenosnika ima glavno vlogo pri pretvorbi energije motenj in modulaciji zvoka, ki se emitira v okolje, zato ima pomembno vlogo kot predmet nadzora in diagnostike emisije hrupa.

V članku je predstavljena kombinacija teoretične, numerične in eksperimentalne analize klasičnega prenosnika (reduktorja), ki razkriva pogoje in vzroke trkov med zobmi ter določa intenzivnost udarcev. Podana je tudi analiza motenj, ki se prenašajo od zobnikov v ubiranju prek gredi in ležajev na ohišje. Te motnje so primerjane z modalno obliko lastnih vibracij ohišja. Modalni odgovor je odvisen od točke in smeri delovanja vzbujalne motnje, frekvence vzbujanj in dušilnih lastnosti materiala ohišja. Glavni prispevek članka je analiza modalnega vedenja ohišja in modalne oblike vzbujanj. Razvita je metodologija za napovedovanje odziva ohišja (frekvenc in intenzivnosti odziva), ki jih povzročajo motnje zaradi trkov zob.

Glavni prispevek članka je v razvoju modela za vzbujanje energije motenj in prenosa te energije prek konstrukcije prenosnika, kakor tudi razlaga mehanizma vzbujanja lastnih vibracij ohišja prenosnika ter emisije hrupa v okolico. Na osnovi predstavljene raziskave so bili določeni kazalniki prenosa energije motenj (prenosljivosti) na stikih komponent prenosnika.

Dokazana je bila glavna hipoteza raziskave: ohišje prenosnika ima dominanten vpliv na raven in frekvenčno sestavo emitiranega zvoka prenosnika. Ta zaključek je podan na podlagi naslednjih dejstev in rezultatov prikazane raziskave: • Hrup, ki ga oddaja prenosnik, je posledica absorbirane energije motenj med delovanjem strojnih delov.

• Energija motenj, ki se absorbira v elastični konstrukciji med ubiranjem zob, prispeva k lastnim vibracijam zobnikov.

• Pojasnjen je prenos energije motenj po elastični konstrukciji in predstavljeni so dejavniki, ki vplivajo na prenos.

• Preučeno je modalno vedenje ohišja prenosnika in pojasnjen je mehanizem vzbujanja nekaterih modalnih oblik lastnih vibracij.

• Ohišje prenosnika modulira zvok glede na modalno občutljivost ohišja in na sposobnost izolacije notranjega grupa.

Odprta ostaja še vrsta vprašanj za nadaljnje raziskave. Dejavniki prenosa energije motenj prek elastične konstrukcije so sicer določeni, vendar bodo za njihov točen izračun in meritev potrebne še dodatne raziskave.

Ključne besede: zobniki, hrup, vibracije, modalna analiza

*Naslov avtorje za dopisovanje: Univerza v Beogradu, Fakulteta za strojništvo, Kraljice Marije 16, 11000 Beograd, Srbija, mognjanovic@mas.bg.ac.rs

SI 65

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 66

Prejeto: 2010-06-08, sprejeto: 2012-03-14 © 2012 Strojniški vestnik. Vse pravice pridržane.

Sistem za izničevanje nihanja bremena pri pretovarjanju z obalnimi dvigali Raubar, E. – Vrančić, D. Edvin Raubar1* – Damir Vrančić2 1 Luka

Koper, d.d., Slovenija; Jožef Stefan, Slovenija

2 Institut

Dvižni mehanizem obalnih dvigal je izveden tako, da je breme z jeklenimi vrvmi vertikalno vpeto na voziček.

Pri procesu natovarjanja oz. raztovarjanja ladje se voziček giblje vzdolž ročice obalnega dvigala. Zaradi strukture dvižnega mehanizma povzroča gibanje vozička nihanje bremena okoli ravnovesne lege. Nihanje bremena poveča čas natovarjanja oz. raztovarjanja ladje in možnost trkov z drugimi objekti, kot so sosednji kontejnerji, železne konstrukcije ladje ali obalnega dvigala itd. Nihanju bremena se ne moremo izogniti, lahko pa ga zmanjšamo z ustreznim sistemom za izničevanje nihanja bremena. Namen tega dela je poiskati ustrezen sistem, ki bo zmanjšal nihanje bremena pri natovarjanju oz. raztovarjanju ladje z obalnimi dvigali v Luki Koper in s tem povečati produktivnost. V članku sta najprej predstavljena nelinearen in lineariziran matematični model nihanja bremena okoli ravnovesne lege pri gibanju vozička vzdolž ročice obalnega dvigala. Modela temeljita na parametrih Panamax obalnih dvigal, ki se uporabljajo v Luki Koper. V nadaljevanju so predstavljeni in simulacijsko preizkušeni trije sistemi za izničevanje nihanja bremena.

Najprej je bilo treba razviti nelinearen in lineariziran matematičen model, na katerem so temeljili vsi nadaljnji izračuni in simulacije. Rezultati simulacije so pokazali, da je razlika med odzivoma nelinearnega in lineariziranega sistema zanemarljiva, zato smo zaradi poenostavitve v vseh nadaljnjih izračunih uporabili le lineariziran model.

Predstavljeni odprtozančni sistemi za izničevanje nihanja bremena temeljijo na tehniki glajenja vhodnega signala.

S to tehniko razstavimo vhodni signal na več stopničastih signalov. Voziček se tako ne giblje več enakomerno pospešeno do želene končne hitrosti, temveč se v enakomernih časovnih intervalih giblje brez pospeška. Če oscilatorni sistem vzbudimo z impulzom, prične le-ta nihati. V primeru, da ob določenem trenutku pošljemo še en impulz ustrezne amplitude, pa se nihanje izniči. Vhodni signal je lahko preoblikovan s poljubnim številom impulzov, najpomembneje pa je ustrezno določiti amplitudo in časovni razmak med njimi. Tako lahko dosežemo sistem brez oscilacij, pri tem pa je potrebno upoštevati naslednje pogoje in omejitve: (i) po zadnjem impulzu mora biti nihanje izničeno (omejitev ničelnega iznihavanja), (ii) vsota amplitud impulzov, s katerimi je glajen vhodni signal, mora biti enaka ena (omejitev enotske vsote amplitud), (iii) časovni odvod odziva sistema mora biti za večjo stabilnost sistema po zadnjem impulzu enak nič (omejitev stabilnosti sistema), (iv) impulzi morajo biti časovno razporejeni tako, da je zakasnitev sistema čim manjša (omejitev optimalne časovne razporeditve). V članku so predstavljeni trije modeli za glajenje vhodnega signala, ki so tudi najpogosteje uporabljeni v praksi. To so: (i) Zero-Vibration Shaper (ZV), (ii) Zero-Vibration-Derivative Shaper (ZVD), (iii) Zero-Vibration-DerivativeDerivative Shaper (ZVDD). Modeli se med seboj razlikujejo po številu impulzov, ki so uporabljeni za glajenje vhodnega signala. Vsak impulz ima natančno določeno amplitudo in časovno zakasnitev. Oba parametra sta odvisna od lastne frekvence nihanja sistema in stopnje dušenja. V primeru Panamax dvigala v Luki Koper je lastna frekvenca nihanja sistema 1,76 rad/s oz. 0,28 Hz, stopnja dušenja pa je enaka 0, kar pomeni, da je sistem nedušen.

Iz rezultatov simulacij je razvidno, da vsi trije sistemi občutno zmanjšajo nihanje bremena, vendar le modela ZVD in ZVDD izpolnjujeta zahteve Luke Koper. Glede na to, da je ZVD model enostavnejši za uporabo in hitreje doseže stabilno končno lego, je tudi najprimernejši kandidat za implementacijo v obstoječa dvigala.

Sistemi za izničevanje nihanja bremena, ki so predstavljeni v članku, temeljijo na konvoluciji vhodnega signala z nizom impulzov. Na ta način se vhodni signal, ki je sestavljen iz enega impulza, razstavi na več stopničastih signalov in se posreduje sistemu za regulacijo hitrosti pogona vozička. Slaba lastnost omenjenih sistemov je ta, da se nekoliko podaljša čas potovanja vozička iz ene v drugo lego.

V simulaciji je uporabljen nedušen model s fiksno dolžino jeklene vrvi. V nadaljnjem delu bo treba preveriti odziv vseh treh sistemov še na matematičnem modelu s spremenljivo dolžino dvižne jeklene vrvi pri različnih faktorjih dušenja.

Trenutna produktivnost posameznega obalnega dvigala Panamax v Luki Koper je 19 kontejnerjev na uro.

Iz rezultatov simulacij sledi, da lahko z uporabo enega od prikazanih sistemov za izničevanje nihanja bremena povečamo produktivnost za 2 kontejnerja na uro, oziroma za približno 10%.

Ključne besede: obalno dvigalo, nihanje bremena, sistem za izničevanje nihanja bremena, odprtozančni sistem SI 66

*Naslov avtorja za dopisovanje: Vojkovo nabrežje 38, 6501 Koper, Slovenija, edvin.raubar@luka-kp.si

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 67

Prejeto: 2011-07-12, sprejeto: 2012-02-07 © 2012 Strojniški vestnik. Vse pravice pridržane.

Metoda globalnega kriterija na osnovi glavnih komponent za optimizacijo proizvodnih procesov z več odzivi

Gomes, J.H.F. – Salgado Jr., A.R. – Paiva, A.P. – Ferreira, J.R. – Costa, S.C. –Balestrassi, P.P. José Henrique de Freitas Gomes – Aluizio Ramos Salgado Júnior – Anderson Paulo de Paiva – João Roberto Ferreira – Sebastião Carlos da Costa – Pedro Paulo Balestrassi* Zvezna univerza v Itajubi, Institut za proizvodni inženiring in management, Brazilija

Cilj tega dela je združitev metode globalnega kriterija (GCM) in analize glavnih komponent (PCA) v multivariatno strategijo, ki omogoča optimizacijo problemov z več koreliranimi odzivi.

Metoda globalnega kriterija, kot je opisana v literaturi, je tehnika večkriterijske optimizacije. Če so odzivi pri konkretnem problemu med seboj v korelaciji, ta tehnika teh informacij ne upošteva, optimalna točka pa lahko pokaže neustrezno rešitev. Analiza glavnih komponent je po drugi strani multivariatno orodje, ki omogoča predstavitev koreliranih odzivov z nekoreliranimi komponentami. Kombinirana uporaba GCM in PCA za vključitev PCA v originalni zapis GCM je lahko dobra alternativa in daje zanimive rezultate.

Po predstavitvi teoretičnih vidikov metodologije odzivne površine (RSM), metode globalnega kriterija in analize glavnih komponent je razvit matematični zapis metode globalnega kriterija na osnovi glavnih komponent.

Ta strategija je bila nato uporabljena za optimizacijo struženja avtomatnega jekla 12L14 ob upoštevanju treh vhodnih parametrov in štirih koreliranih odzivov. Proces struženja avtomatnega jekla je bil izbran kot relevantna operacija v trenutnem industrijskem kontekstu, ker so avtomatna jekla razvita za dobre pogoje obdelave in odlično oblikovanje odrezkov. Vhodni parametri so bili rezalna hitrost, podajanje in globina reza. Med optimiziranimi odzivi so srednja hrapavost, celotna hrapavost, čas odrezavanja in stopnja odvzema materiala. Za modeliranje procesa je bila uporabljena metoda RSM. Uporabljeni sta bili konvencionalna metoda GCM in GCM na osnovi glavnih komponent, temu pa je sledila primerjava rezultatov. V obeh primerih je bil za ugotavljanje optimalne točke na matematičnih zapisih uporabljen genetski algoritem.

GCM na osnovi glavnih komponent daje boljše praktične rezultate v primerjavi s konvencionalno metodo GCM, zlasti pri hrapavosti in stopnji odvzema materiala. Razvita strategija je dala optimalno rešitev znotraj sprejemljivih meja procesa, rešitev, pridobljena s konvencionalno tehniko, pa je zunaj teh meja. Čeprav daje predstavljena strategija zadovoljive rezultate, jo je treba preizkusiti in verificirati še na drugih procesih in operacijah, zato so potrebne dodatne raziskave v tej smeri.

Konvencionalne metode večkriterijske optimizacije, zlasti metoda globalnega kriterija, obravnavajo več odzivov kot neodvisne spremenljivke, v članku pa je predstavljena alternativna strategija za GCM z optimizacijo glavnih komponent, ki upošteva strukturo korelacij med odzivi.

Ključne besede: Večkriterijska optimizacija, metoda globalnega kriterija, analiza glavnih komponent, metodologija odzivne površine, več koreliranih odzivov, struženje avtomatnega jekla, genetski algoritem

*Naslov avtorje za dopisovanje: Zvezna univerza v Itajubi, Institut za proizvodni inženiring in management, Av. BPS, 1303, Itajuba, Brazilija, pedro@unifei.edu.br

SI 67

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 68

Prejeto: 2011-05-27, sprejeto: 201-03-27 © 2012 Strojniški vestnik. Vse pravice pridržane.

Dinamika mehanizma za rezanje polimernih folij

Cveticanin, L. – Maretic, R. – Zukovic, M. Livija Cveticanin* – Ratko Maretic – Miodrag Zukovic Tehniška fakulteta, Novi Sad, Srbija V članku je opisana dinamika mehanizma za rezanje polimernih folij.

Mehanizem je sestavljen iz dveh povezanih ojničnih mehanizmov z drsnikom, ki pretvarjajo vrtilno gibanje vodilnega elementa v premočrtno gibanje izhodnega drsnika. Mehanizem poganja elektromotor, drsnik pa predstavlja rezalno orodje. Rezalna sila mora biti konstantna. Ta predpostavka je bila uporabljena za določitev kinematičnih in dinamičnih značilnosti mehanizma. Posebej je analiziran vpliv rezalne sile na vhodno kotno hitrost vodilnega elementa. Raziskan je bil tudi vpliv geometrijskih in dinamičnih lastnosti mehanizma in rezalne sile. Kotna hitrost je funkcija rezalne sile, dušenja in vztrajnosti sistema. Spremembe kotne hitrosti pogonskega motorja so izračunane analitično in numerično.

Matematični model rezalnega mehanizma je oblikovan z uporabo Lagrangeeve diferencialne enačbe gibanja.

Močno nelinearna diferencialna enačba drugega reda je bila analizirana z uporabo analitičnega aproksimativnega postopka reševanja z razvojem spremenljivke v vrsto. Obravnavan je prvi približek rešitve. Pridobljeni analitični rezultat je bil primerjan z numeričnim rezultatom in ugotovljeno je bilo, da se analitična rešitev dobro ujema z numeričnim rezultatom.

Povzetek analize rezultatov: • Dušenje ima med rezanjem pomemben vpliv na kotno hitrost vodilnega elementa rezalnega mehanizma. Če je masa vodilne ročične gredi in rezalnega orodja majhna, je kotna hitrost vodilne ročične gredi pri visokih vrednostih dušenja očitno manjša.

• Pomemben je tudi vpliv rezalne sile na kotno hitrost: večja kot je rezalna sila, večje so spremembe kotne hitrosti.

• Variabilnost kotne hitrosti vpliva na stabilnost gibanja in tudi na kakovost rezalnega procesa. Pri visoki variabilnosti kotne hitrosti vodilnega elementa se lahko stabilno stacionarno delovanje motorja spremeni v nestabilno delovanje. Večja kot je rezalna sila, počasnejši je rezalni proces zaradi nižje povprečne hitrosti.

Pridobljeni rezultati so uporabni v tovarnah in v proizvodnih obratih, kjer so mehanizmi za rezanje polimernih folij eden od pomembnejših delov proizvodne linije.

Ključne besede: dva povezana ojnična mehanizma z drsnikom, kinematična in dinamična analiza, rezalna sila, neidealen pogon.

SI 68

*Naslov avtorje za dopisovanje: Tehniška fakulteta, 21000 Novi Sad, Trg D. Obradovića 6, Srbija, cveticanin@uns.ac.rs

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 69-70 Osebne objave

Diplomske naloge

DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 25. aprila 2012: Jurij KERN z naslovom: »Diagnosticiranje ničtega stanja rotacijskega stroja« (mentor: prof. dr.

Jožef Vižintin); Simon KRIŽMAN z naslovom: »Stroškovno vrednotenje montaže« (mentor: prof. dr. Marko Starbek, somentor: izr. prof. dr. Janez Kušar); Jani MERKUN z naslovom: »Numerično modeliranje delovanja električnega generatorja, gnanega s Stirlingovim motorjem« (mentor: izr. prof. dr. Tomaž Katrašnik, somentor: doc. dr. Jernej Klemenc); dne 26. aprila 2012: Benjamin BIZJAN z naslovom: »Model enokolesne centrifuge« (mentor: prof. dr. Branko Širok, somentor: izr. prof. dr. Marko Hočevar); Miha JENSTERLE z naslovom: »Vrednotenje vodikovih tehnologij v naprednem energetskem sistemu z metodo analize življenskih ciklov« (mentor: izr. prof. dr. Mihael Sekavčnik); Tit Črtomir KANDUČ z naslovom: »Vpliv zunanjega zvočnega polja na varjenje po postopku tig« (mentor: prof. dr. Mirko Čudina, somentorja: doc. dr. Jurij Prezelj, izr. prof. dr. Ivan Polajnar); Robert Jože POVŠIČ z naslovom: »Adaptivno krmiljenje parametrov okolja v zgradbah« (mentor: izr. prof. dr. Peter Butala, somentor: prof. dr. Vincenc Butala); Blaž SLATINŠEK z naslovom: »Razvoj zaznavala za mobilno pulzno oksimetrijo v zunanji ušesni votlini« (mentor: prof. dr. Janez Diaci). * Na Fakulteti za strojništvo Univerze v Mariboru sta pridobila naziv univerzitetni diplomirani inženir strojništva: dne 26. aprila 2012: Boštjan ZUPANIČ z naslovom: »Pregled in uporaba postopkov optimiranja obstojnosti pri struženju« (mentor: prof. dr. Franci Čuš, somentor: doc. dr. Uroš Župerl); Macerl MATJAŽ z naslovom: »Možnosti povečanja trajnosti udarnih plošč rotorja v mlinih

za mletje premoga z navarjanjem« (mentor: prof. dr.

Franc Zupanič, somentor: izr. prof. dr. Ivo Pahole). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva (UN): dne 26. aprila 2012: Goran LEDINEK z naslovom: »Udejanjanje uporabe rezalnega orodja Kieninger za obdelavo materiala 1.2379« (mentor: prof. dr. Franci Čuš, somentor: Igor Breznikar). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 12. aprila 2012: Miha ARH z naslovom: »Obračalna miza za jeklene plošče večjih izmer« (mentor: doc. dr. Boris Jerman); Matej ČIBEJ z naslovom: »Brušenje planetnih gredi« (mentor: doc. dr. Peter Krajnik, somentor: prof. dr. Janez Kopač); Vito GALIČIČ z naslovom: »Pravna ureditev zračnega prostora« (mentor: viš. pred. mag.

Aleksander Čičerov, somentor: izr. prof. dr. Tadej Kosel). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 24. aprila 2012: Mario KNEŽEVIČ z naslovom: »Izbor turbinskega agregata HE Markovci« (mentor: prof. dr.

Brane Širok, somentor: doc. dr. Ignacijo Biluš); dne 26. aprila 2012: Boštjan BREČKO z naslovom: »Razvoj robotske mize za varjenje okvirja vgradnega sanitarnega elementa« (mentorica: viš. pred. dr. Marina Novak, somentor: izr. prof. dr. Bojan Dolšak); Branko GRAH z naslovom: »Vpliv goriv na karakteristike sodobnega dizelskega motorja« (mentorica: prof. dr. Breda Kegl, somentor: asist. Blaž Vajda); Boštjan HORJAK z naslovom: »Trdnostna konstrola in izdelava vpenjalne priprave za vpenjanje pločevine« (mentor: prof. dr. Srečko Glodež); SI 69

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)5, SI 69-70

Amadej KVAS z naslovom: »Konstruiranje naprave za navijanje cevi« (mentor: doc. dr. Janez Kramberger); Boris MLADENOVIČ z naslovom: »Izračun toplotne obremenitve hiše po SIST EN in URSA« (mentor: doc. dr. Matjaž Ramšak, somentor: izr. prof. dr. Jure Marn); Uroš OŠLOVNIK z naslovom: »Razvoj novega tehnološkega postopka izdelave velikih preciznih kotalnih ležajev« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Marjan Leber); Tomaž PLANKELJ z naslovom: »Snovanje ohišja stružnice iz debelostenske pločevine« (mentorica: viš. pred. dr. Marina Novak, somentor: izr. prof. dr. Bojan Dolšak); Simon TOMINŠEK z naslovom: »Posodobitev hidravličnega sistema vertikalnih cepilnikov drv« (mentor: doc. dr. Darko Lovrec, somentor: asist. Vito Tič);

SI 70

Uroš VUDLER z naslovom: »Dimenzioniranje aluminijaste hale« (mentor: doc. dr. Kramberger Janez). * Na Fakulteti za strojništvo Univerze v Mariboru sta pridobila naziv diplomirani gospodarski inženir: dne 16. aprila 2012: Lev MIJOČ z naslovom: »Mala vetrna elektrarna z inovativnim generatorjem: Strategija razvoja in trženje« (mentor: prof. dr. Andrej Predin, somentorja: doc. dr. Ignacijo Biluš, prof. dr. Anton Hauc); dne 26. aprila 2012: Primož KEKEC z naslovom: »Simulacija procesa in gospodarnosti izločanja ogljikovega dioksida iz dimnih plinov termoelektrarn« (mentor: prof. dr. Niko Samec, somentor: prof. dr. Duško Uršič).

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis.

The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.

The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

Editor in Chief Vincenc Butala University of Ljubljana Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana (UL) Faculty of Mechanical Engineering SV-JME Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386-(0)1-4771 137 Fax: 386-(0)1-2518 567 E-mail: info@sv-jme.eu http://www.sv-jme.eu Print Tiskarna Knjigoveznica Radovljica, printed in 480 copies Founders and Publishers University of Ljubljana (UL) Faculty of Mechanical Engineering, Slovenia University of Maribor (UM) Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia

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Cover: Development of a test stand and testing software for experimental research of a hydrodinamic torque converter performance and numerical analysis of flow conditions in converters with existing and modified geometry that provided improved performance and increased efficiency.

Image courtesy: Laboratory for heat and power LTE, Faculty of Mechanical Engineering, University of Ljubljana.

International Editorial Board Koshi Adachi, Graduate School of Engineering,Tohoku University, Japan Bikramjit Basu, Indian Institute of Technology, Kanpur, India Anton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, Slovenia Narendra B. Dahotre, University of Tennessee, Knoxville, USA Matija Fajdiga, UL, Faculty of Mech. Engineering, Slovenia Imre Felde, Bay Zoltan Inst. for Mater. Sci. and Techn., Hungary Jože Flašker, UM, Faculty of Mech. Engineering, Slovenia Bernard Franković, Faculty of Engineering Rijeka, Croatia Janez Grum, UL, Faculty of Mech. Engineering, Slovenia Imre Horvath, Delft University of Technology, Netherlands Julius Kaplunov, Brunel University, West London, UK Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Janez Kopač, UL, Faculty of Mech. Engineering, Slovenia Franc Kosel, UL, Faculty of Mech. Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mech. Engineering, Slovenia Miroslav Plančak, University of Novi Sad, Serbia Brian Prasad, California Institute of Technology, Pasadena, USA Bernd Sauer, University of Kaiserlautern, Germany Brane Širok, UL, Faculty of Mech. Engineering, Slovenia Leopold Škerget, UM, Faculty of Mech. Engineering, Slovenia George E. Totten, Portland State University, USA Nikos C. Tsourveloudis, Technical University of Crete, Greece Toma Udiljak, University of Zagreb, Croatia Arkady Voloshin, Lehigh University, Bethlehem, USA President of Publishing Council Jože Duhovnik UL, Faculty of Mechanical Engineering, Slovenia General information Strojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).

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ISSN 0039-2480 © 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

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Announcement: The authors are kindly invited to submitt the paper through our web site: http://ojs.sv-jme.eu. The Author is also able to accompany the paper with Supplementary Files in the form of Cover Letter, data sets, research instruments, source texts, etc. The Author is able to track the submission through the editorial process - as well as participate in the copyediting and proofreading of submissions accepted for publication - by logging in, and using the username and password provided.

Please provide a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and affiliations.

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THE FORMAT OF THE MANUSCRIPT The manuscript should be written in the following format: - A Title, which adequately describes the content of the manuscript.

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- 6 significant key words should follow the abstract to aid indexing.

- An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated.

- A Theory or experimental methods used.

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- References, which must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript.

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Abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG).

Meaning of symbols and units belonging to symbols should be explained in each case or quoted in a special table at the end of the manuscript before References.

Figures must be cited in a consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats.

Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF or JPG. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. When labeling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimize the need to label the axes in two languages.

Multi-curve graphs should have individual curves marked with a symbol. The meaning of the symbol should be explained in the figure caption.

Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. In addition to the physical quantity, e.g. t (in italics), units

(normal text), should be added in square brackets. The tables should each have a heading. Tables should not duplicate data found elsewhere in the manuscript.

Acknowledgement of collaboration or preparation assistance may be included before References. Please note the source of funding for the research.

REFERENCES A reference list must be included using the following information as a guide. Only cited text references are included. Each reference is referred to in the text by a number enclosed in a square bracket (i.e., [3] or [2] to [6] for more references). No reference to the author is necessary.

References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. All non-English or. non-German titles must be translated into English with the added note (in language) at the end of reference. Examples follow.

Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code.

[1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent crosslinked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013.

Journal titles should not be abbreviated. Note that journal title is set in italics.

Please add DOI code when available and link it to the web site.

Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication.

[2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken.

Note that the title of the book is italicized.

Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages.

[3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553-576.

Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages.

[4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied Lean System in Process Industry. MOTSP 2009 Conference Proceedings, p.

422-427.

Standards: Standard-Code (year). Title. Organisation. Place.

[5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva. www pages: Surname, Initials or Company name. Title, from http://address, date of access.

[6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 2009-09-07.

EXTENDED ABSTRACT By the time the paper is accepted for publishing, the authors are requested to send the extended abstract (approx. one A4 page or 3.500 to 4.000 characters). The instructions for writing the extended abstract are published on the web page http://www.sv-jme.eu/ information-for-authors/.

COPYRIGHT Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME and when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original by the authors and not be published elsewhere in any language without the written consent of the publisher.

The proof will be sent to the author showing the final layout of the article. Proof correction must be minimal and fast. Thus it is essential that manuscripts are accurate when submitted.

Authors can track the status of their accepted articles on http://en.svjme.eu/.

PUBLICATION FEE For all articles authors will be asked to pay a publication fee prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 220.00 EUR (for articles with maximum of 10 pages), 20.00 EUR for each addition page.

Additional costs for a color page is 90.00 EUR.

http://www.sv-jme.eu

58 (2012) 5

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Contents

Papers

300

Željko Đurić, Ljubiša Josimović, Živoslav Adamović, Ljiljana Radovanović, Goran Jovanov: An Evaluation of Formed Maintenance Programme Efficacy

309

Mohsen Mahdavi Adeli, Fatemeh Sobhnamayan, Said Farahat, Mahmoud Abolhasan Alavi, Faramarz Sarhaddi: Experimental Performance Evaluation of a Photovoltaic Thermal (PV/T) Air Collector and Its Optimization

319

Jure Jelenc, Jože Jelenc, Damijan Miklavčič, Alenka Maček Lebar: Low-Frequency Sonoporation in vitro: Experimental System Evaluation

Milosav Ognjanović, Snežana Ćirić Kostić: 327 Gear Unit Housing Effect on the Noise Generation Caused by Gear Teeth Impacts

337

Edvin Raubar, Damir Vrančić: Anti-Sway System for Ship-to-Shore Cranes

344

José Henrique de Freitas Gomes, Aluizio Ramos Salgado Júnior, Anderson Paulo de Paiva, João Roberto Ferreira, Sebastião Carlos da Costa, Pedro Paulo Balestrassi: Global Criterion Method Based on Principal Components to the Optimization of Manufacturing Processes with Multiple Responses

353

Livija Cveticanin, Ratko Maretic, Miodrag Zukovic: Dynamics of Polymer Sheets Cutting Mechanism

Journal of Mechanical Engineering - Strojniški vestnik

Andrej Pirc, Mihael Sekavčnik, Mitja Mori: 291 Universal Model of a Biomass Gasifier for Different Syngas Compositions

5 year 2012 volume 58 no.