Journal of Mechanical Engineering 2012 12

http://www.sv-jme.eu

58 (2012) 12

Since 1955

Contents Papers

Jose Billerman Robles-Ocampo, Juan Carlos Jauregui-Correa, Peter Krajnik,

Perla Yasmin Sevilla-Camacho, Gilberto Herrera-Ruiz: 693 Nonlinear Model for the Instability Detection in Centerless Grinding Process

Youyu Liu, Jiang Han, Lian Xia, Xiaoqing Tian: 701 Hobbing Strategy and Performance Analyses of Linkage Models for

Non-Circular Helical Gears Based on Four-Axis Linkage

Roman Moravčík, Mária Štefániková, Roman Čička, Ľubomír Čaplovič, Karin Kocúrová, Roman Šturm:

709 Phase Transformations in High Alloy Cold Work Tool Steel

Virginija Gylienė, Vytautas Ostaševičius: 716 Modeling and Simulation of a Chip Load Acting on a Single Milling Tool Insert

Nikola Suzić, Branislav Stevanov, Ilija Ćosić, Zoran Anišić, Nemanja Sremčev: 724 Customizing Products through Application of Group Technology:

A Case Study of Furniture Manufacturing

Shpetim Lajqi, Stanislav Pehan: 732 Designs and Optimizations of Active and Semi-Active Non-linear

Suspension Systems for a Terrain Vehicle

Sebhi Amar, Osmani Hocine, Rech Joel: 744 Tribological Behaviour of Coated Carbide Tools during Turning of Steels

with Improved Machinability

Journal of Mechanical Engineering - Strojniški vestnik

12 year 2012 volume 58 no.

Strojniški vestnik Journal of Mechanical Engineering

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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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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58 (2012) 12

Chamber of Commerce and Industry of Slovenia Metal Processing Industry Association

Since 1955

Strojniški vestnik Journal of Mechanical Engineering

n, Lian Xia, Xiaoqing Tian: nd Performance Analyses of Linkage Models for al Gears Based on Four-Axis Linkage omar, Nenad Vulić: ls Selection for Environmentally Friendly stem ária Štefániková, Roman Čička, Ľubomír Čaplovič, man Šturm: ions in High Alloy Cold Work Tool Steel lav Stevanov, Ilija Ćosić, Zoran Anišić, Nemanja Sremčev: cts through Application of Group Technology: niture Manufacturing slav Pehan: zations of Active and Semi-Active Non-linear s for a Terrain Vehicle Hocine, Rech Joel: our of Coated Carbide Tools during Turning of Steels hinability

Journal of Mechanical Engineering - Strojniški vestnik

les-Ocampo, Juan Carlos Jauregui-Correa, Peter Krajnik, a-Camacho, Gilberto Herrera-Ruiz: r the Instability Detection in Centerless Grinding

year

no. 12 2012 58

volume

Cover: Non linear systems show a time dependent frequency response, such as the instabilities found in a grinding process. For these signals, traditional Fourier Transform is unable to analyze the non linear effects, and other techniques are better fitted. In this case, the phenomenon was reproduced with a time-frequency map. The timefrequency maps were obtained by applying the Continuous Wavelet Transform. The Continuous Wavelet Transform converts the displacement function into a two dimensional vector that is a function of time and frequency.

Image Courtesy: Autonumus University of Queretaro, Faculty of Engineering, Mexico

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 58, (2012), number 12 Ljubljana, December 2012 ISSN 0039-2480 Published monthly

Papers Jose Billerman Robles-Ocampo, Juan Carlos Jauregui-Correa, Peter Krajnik, Perla Yasmin SevillaCamacho, Gilberto Herrera-Ruiz: Nonlinear Model for the Instability Detection in Centerless Grinding Process Youyu Liu, Jiang Han, Lian Xia, Xiaoqing Tian: Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage Roman Moravčík, Mária Štefániková, Roman Čička, Ľubomír Čaplovič, Karin Kocúrová, Roman Šturm: Phase Transformations in High Alloy Cold Work Tool Steel Virginija Gylienė, Vytautas Ostaševičius: Modeling and Simulation of a Chip Load Acting on a Single Milling Tool Insert Nikola Suzić, Branislav Stevanov, Ilija Ćosić, Zoran Anišić, Nemanja Sremčev: Customizing Products through Application of Group Technology: A Case Study of Furniture Manufacturing Shpetim Lajqi, Stanislav Pehan: Designs and Optimizations of Active and Semi-Active Non-linear Suspension Systems for a Terrain Vehicle Sebhi Amar, Osmani Hocine, Rech Joel: Tribological Behaviour of Coated Carbide Tools during Turning of Steels with Improved Machinability

693 701 709 716 724 732 744

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700 DOI:10.5545/sv-jme.2012.649

Paper received: 2012-06-13, paper accepted: 2012-10-17 © 2012 Journal of Mechanical Engineering. All rights reserved.

Nonlinear Model for the Instability Detection in Centerless Grinding Process

Robles-Ocampo, J.B. –Jáuregui-Correa, J.C. –Krajnik, P. –Sevilla-Camacho, P.Y. –Herrera-Ruiz, G. Jose Billerman Robles-Ocampo1,2 – Juan Carlos Jauregui-Correa1,* – Peter Krajnik3 – Perla Yasmin Sevilla-Camacho1,2 – Gilberto Herrera-Ruiz1 1 Autonumus

University of Queretaro, Faculty of Engineering, Mexico University of Chiapas, México 3 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 2 Polytechnic

In this work a novel nonlinear model for centerless grinding is presented. The model describes the dynamic behavior of the process. The model considers that the system’s stiffness depends on the existence of lobes in the workpiece surface. Lobes geometry is treated as a polygonal shape and it is demonstrated that the system can be represented as a Duffing’s equation. It is shown that there is a critical lobe number, where the systems present an unstable behavior; the critical lobe number is identified through the geometric stability index. Instabilities in the centerless grinding process are analyzed with two methods: the phase diagram and the continuous wavelet transform. The presented results show that the dynamic behavior of the centerless grinding process can be represented with a cubic stiffness function that is obtained from the analysis of the surface topology.

Keywords: phase diagram, chatter, nonlinear model, centerless grinding, polygonal shape, instability index

0 INTRODUCTION Grinding technology has an important advantage in terms of productivity and precision in comparison with its competitive machining operations.

Innovations in fixed-abrasive tools with enhanced, wear-resistant abrasives and improved bond systems [1] together with higher process capacity [2] have all contributed to this. Centerless grinding process (CGP) is one of the most productive and precise machining operation for manufacturing of rotationallysymmetrical workpieces. The advantage of the CGP is that the workpiece is not clamped, thus enabling high automation and production rates. The disadvantage of having the workpiece not held between centers is that the process is unstable and the workpieces lobed (nonround).

In the centerless grinding gap the workpiece is supported at its surface in three points; the grinding wheel, the regulating wheel and the workrest blade, as shown in Fig 1. The function of each one of them is the following: • The grinding wheel removes material from the workpiece diameter.

• The regulation wheel controls the workpiece velocity (by friction) and the radial infeed (depending on machine configuration).

• The workrest blade supports the workpiece and keeps the set workpiece height.

Next to workpiece out-of-roundness, chatter is the most significant problem related to CGP. Chatter (self excited vibrations) can deteriorate both the workpiece and the grinding wheel surfaces. The most obvious errors on the workpiece surface are chatter

marks (wavy markings on the workpiece surface) that are rooted in: variation in depth of cut caused by CGPinherent workpiece center displacement; the existence of a too-large angle of the workrest blade; flexibility of the grinding wheel; high workpiece speed; vibrations transmitted to the machine or caused by a defective drive; the interference between grinding wheel out-ofbalance and workpiece waviness [3].

The configuration of the CGP is complex and has a high sensitivity to the grinding gap set-up and process parameters [4] to [7]. Moreover, productivity depends on the process stability. The latter is usually secured by reducing the workpiece speed that ultimately leads to low material removal rates. There are different responses of the CGP as a consequence of the instability: The workpiece looses contact with the workrest blade, presents run-out and chatter [8] to [11].

Many researchers have studied the CGP instability. Some of the first investigations were done by Furukawa et al. [12] and [13], who pointed out that the self-excited vibration is geometrically stable but it changes to an unstable condition as a result of the workpiece regeneration, system dynamic characteristics and low dynamic stiffness due to machine-tool design. Very often, the CGP stability has been analyzed through simulation. Simulations consider the use of kinematic, kinetic and geometric conditions, and mechanical properties of the process.

With a simulation it is possible to obtain: Stability maps showing the stable/unstable geometric configurations, the number of lobes that generate unstable conditions, a qualitative determination of the workpiece roundness error, the dynamical displacement, and the predictions

*Corr. Author’s Address: Autonumus University of Queretaro, Faculty of Engineering, Cerro de las Campanas s/n, Ciudad Universitaria, 76010 Querétaro, Qro., México, jc.jauregui@uaq.mx

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700

of coupled chatter and lobes in the process [5], [8], [14] and [15]. Li and Shin [8] presented a dynamic model that simulated plunge centerless grinding and predicted its instability-related characteristics. They assumed that the workpiece has continuous contact with the workrest blade and the regulating wheel, and that the center position is known if the workpiece is round. Other publications deal with measurements of the dynamic parameters such as horizontal and vertical movement of the workpiece center. Some reported measurements employed an inductive transducer [6].

The vertical movement is more significant than the horizontal movement during the CGP. The characteristic equation of the system has been reported in several publications. The characteristic equation gives a good approximation to several grinding processes. The advantage of the characteristic equation is that it can be analyzed with different solution techniques such as: stability maps and wave growth rate, to name a few [9] to [13] and [16] to [18].

Epureanu et al. [19] developed a model of a centerless grinding. The displacement of the workpiece center and the deformation of the grinding machine frame were included into the instability model. They showed that the amplitude of the cylindricity error decreases when the number of lobes increases. Many researchers have considered that the dynamic model is linear [4], [10], [16], [17] and [20].

Chatter results in a defective surface that can be characterized by a certain lobing order (number of waves). The presence of lobes in the workpiece surface regenerates the vertical displacement of the workpiece center and changes the dynamic equations of motion. These changes are directly reflected as a transformation of a linear model to a nonlinear model [21] and [22]. In particular, the lobing instability is associated with the roundness error or waviness of the workpiece [8]. The roundness error has been approximated as a polygonal shape or as a Fourier series [14], [19] and [23]. Another aspect of the dynamic model is the condition on the grinding wheel as shown in [28] The modeling approach presented in this work considers the polygonal shape as an input perturbation force, whereas the stiffness of the system is represented with a cubic function. The aim of this paper is to introduce a novel nonlinear model for the instability prediction in the CGP. Further, the model incorporates the geometric stability index. The instability is analyzed with the continuous wavelet transform (CWT) and the phase diagram. The feed forces, number of lobes in the workpiece surface and 694

the geometry of the grinding gap are considered for the model.

1 KINEMATIC ANALYSIS The CGP shape formation generally produces a nonround (lobed) workpiece that can be geometrically represented by a polynomial. The kinematic analysis is derived from the motion of a polygon. Geometrically a polygon is tangent only to the grinding and regulating wheels, and it loses contact with the workrest blade.

The grinding gap in the initial, stationary condition is represented in Fig. 1, depicting a round workpiece, supported at three points: the workrest blade, the grinding wheel and the regulating wheel.

Since the polygon has only two points of contact, the vertical position has two possible configurations.

In the first configuration the workpiece (Fig. 2a) one vertex of the polygon is in contact with the grinding wheel (point Pb) and a face is tangent to the regulating wheel. As the workpiece rotates, the workpiece center is displaced and the two faces of the polygon are tangent to the regulating and grinding wheels until the following vertex (Pa) comes into contact with the regulating wheel (Fig. 2b). It is important to notice that the time when the two faces are tangent to the wheels is not symmetrical and depends on the relative position of the vertices.

Fig. 1. CGP set up

are:

The kinematic equations for the first configuration S − RR cos θ R + a cos θ a − Rw cos ( ε − ωW t ) − − Rw cos ( ε + ωW t ) − RG cos θG = 0 ,

(1)

RG sin θG + Rw sin ( ε + ωW t ) − Rw sin ( ε − ωW t ) − −a sin θ a − RR sin θ R = 0.

(2)

In the second configuration, the workpiece also has two contact points: Pa and Pb, as shown in Fig. 2b.

Robles-Ocampo, J.B. –Jáuregui-Correa, J.C. –Krajnik, P. –Sevilla-Camacho, P.Y. –Herrera-Ruiz, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700

S − RR cos θ R − Rw cos ( ε − ωW t ) − − Rw cos ( ε + ωW t ) + b cos θb − RG cos θG = 0 , RG sin θG + b sin θb + Rw sin ( ε + ωW t ) − − Rw sin ( ε − ωW t ) − RR sin θ R = 0.

(4)

The angle between the two tangent faces is calculated as:

y 2 (ωW t ) = RG sin θG +

(3)

21   + RW sin  ε + ωW t − ( 2π / N )  , 60  

where:

  N β1   2π β = int  , (5)  + 1   2π   N

b1 is defined in Fig. 1.

  y1(ωW t ) ; if     y 2 (ωW t ) ; if   0; if 

11  2π    30  N  11  2π  22  2π   ≤ ωW t ≤  30  N  30  N 22  2π  ωW t >   30  N  0 ≤ ωW t ≤

 . 

And for the second configuration T2 as: y11(ωW t ) = RR sin θ R + 51   + RW sin  ε − ωW t − ( 2π / N )  , (7) 60  

y 21(ωW t ) = RG sin θG + 51   + RW sin  ε + ωW t − ( 2π / N )  , 60  

where:

Fig. 2. Workpiece surface with lobes: a) changes of longitude and Pb slides on the grinding wheel surface, b) changes of longitude and Pa slides on the regulating wheel

 0;     y11(ωW t ) ;    y 21(ωW t ) ; 

22  2π    30  N  22  2π  26  2π if   ≤ ωW t ≤  30  N  30  N  2π  26  2π  if   ≤ ωW t ≤   30  N   N 

if ωW t <

 . 

If Eqs. (6) and (7) are plotted as a function of the translation angles ωWt, then it is possible to illustrate the normalized workpiece vertical displacement, as shown in Fig. 3. This figure shows the workpiece center behavior as a function of the number of lobes in the surface.

Eqs. (1) and (2), and Eqs. (3) and (4) were solved using the Newton-Raphson method. θG and θR are function of N and ωW. Then, using θG and θR, the relationship between the displacement of the workpiece center y(t) and ωW is obtained, as shown in Fig. 2. It was found that the two kinematic configurations have a similar pattern. Therefore, the vertical displacement can be calculated for the first configuration T1 as: y1(ωW t ) = RR sin θ R +

21   + RW sin  ε − ωW t − ( 2π / N )  , (6) 60  

Fig. 3. Workpiece center vertical behavior

Nonlinear Model for the Instability Detection in Centerless Grinding Process

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700

The vertical displacement can be approximated as a series of the form:

yw ( t ) = C1 + C2ψ + C3ψ 2 + C4ψ 3 , (8) ,

where the coefficients Ci (i = 1, 2, 3, 4) are a function of the number of lobes N and the workpiece radius Rw, and where ψ represents the translation angle.

The vertical displacement function is included into the dynamic equation as part of the stiffness of the system. In this way, the dynamic equation of the CGP is similar to a Duffing’s equation.

GSI = 1 +

sin α cos ( N β G ) sin β G cos ( Nα ) sin ( β G − α )

, (11)

where   h π − γ − arcsin  , 4  RW + RG  (12)     h h π β G = − arcsin   − arcsin  .

2  RW + RG   RR + RW 

α=

2 DYNAMIC MODEL The deflections of the grinding system are approximately proportional to the vertical displacement of the workpiece center. This allows the introduction of the lobing effect by assuming a nonlinear stiffness (Ksys):

K sys = Kyw ( t ) , (9)

where K is the machining stiffness factor. The contact stiffness and wear stiffness of the grinding wheel have not been considered in the development of dynamic model.

The effect of horizontal workpiece displacement is neglected and only the vertical component of the displacement is considered in the dynamic model [14]. At the initial stable condition it is assumed that the round workpiece is in contact at three points, as shown in Fig. 4.

The workpiece dynamics is modeled as: myW ( t ) + ξ sys yW ( t ) + K sys yW ( t ) =

= FnG ( sin θG − µ cos θG ) + FnR sin θ R + (10) + FnB ( cos γ + µ sin γ ) + FT cos θ R + mg ,

where ξsys is the system’s damping coefficient, Ksys is the nonlinear stiffness coefficient, modeled as a cubic polynomial, m is the mass of the workpiece, m represents the friction coefficient and FT is the traction force between the workpiece and the regulating wheel. FnB, FnG and FnR are the normal forces acting between the workpiece and the workrest blade, the grinding wheel and the regulating wheel, respectively (as shown in Fig. 4).

The geometric stability index (GSI) relates the angles between the center of the workpiece and the center line (Fig. 1). It is defined as: 696

Fig. 4. Forces of the dynamic model

If the GSI is positive, the amplitude of the observed lobing order N will decrease and therefore the CGP is geometrically stable. In the case of negative GSI of a certain lobing order N, the amplitude will increase and the CGP will be geometrically unstable [4]. A negative value of GSI is hence a measure of the growth rate for a lobe order. The inclusion of the stability index improves the sensitivity of the stiffness function. In this way, the effects of the set up conditions of the machine are included into the model.

By incorporating the GSI into the dynamic model, the equation of motion becomes: myW ( t ) + ξ sys yW ( t ) + ( GSI ) K sys yW ( t ) =

= FnG ( sin θG µ cos θG ) + FnR sinn θ R +

(13)

+ FnB ( cos γ + µ sin γ ) + FT cos θ R + mg .

It should be pointed out that a geometric instability is a very timid process compared to the aggressiveness of a dynamic chatter.

The dynamic model is non linear and the displacement of the workpiece is found numerically.

In this case, the nonlinear differential equation is integrated using the Runge-Kutta method.

Robles-Ocampo, J.B. –Jáuregui-Correa, J.C. –Krajnik, P. –Sevilla-Camacho, P.Y. –Herrera-Ruiz, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700

3 RESULTS AND DISCUSSIONS

4.1 Continuous Wavelet Transform Analysis

The main results were obtained by imposing an initial distortion in the workpice surface. This distortion was simulated by assuming that the initial cylinder becomes a polygon with a large number of lobes. The instability was determined by reducing the number of lobes until the vertical displacement shows an erratic behavior.

Once the system becomes unstable, the workpiece is supported only by the wheels, and the waves generated on the workpiece surface grow rapidly. The instability of the system was analyzed with the data listed in Table 1.

The following parameters were considered: m = 0.3, ξsys = 0 [13], and K = 8×106 Nm-2. The nonlinear dynamic model (Eq. (13)) is solved using a Runge-Kutta algorithm. The instability condition is found varying the number of lobes, where the stable condition was simulated by inputting a large number of lobes (N > 360) and the unstable condition was determined decreasing the number of lobes until the solution was unstable.

Table 1. Geometric parameters in the CGP Grinding wheel rotational frequency [rpm] Regulating wheel rotational frequency [rpm] Grinding wheel power [kW] Regulation wheel power [kW] Grinding wheel diameter [mm] Regulating wheel diam. [mm] Workrest blade angle [deg.]

Workpiece radius [mm]

1020 25 22 3.7 355.6 609.6 25 50.39

The CWT converts the displacement function into a two dimensional vector that is a function of time and frequency. This vector can be represented as a timefrequency map.

The main advantage of the CWT is its excellent performance with good time resolution at high frequencies and good frequency resolution at low frequencies. It has been reported [24] that the continuous Morlet function is better for extracting nonlinear characteristics of mechanical systems that other mother functions.

The wavelet transform is defined as:

X ( a1 ,b1 ) =

1

  t − b1   x ( t )ϕ*     dt , (14) −∞   a1   

a ∫ 2

∞

where φ* is the conjugate function of the mother wavelet, x is the signal function, a1 is a scale factor and b1 is the time shift factor. In this work, the timefrequency maps were obtained with the Morlet function:  t 2   − ρ 2σ 2    −t 2   2      4  ei ρ t   2σ 2  

ϕ (t ) = e − 2 e σ  e , (15)  2π    where r is the frequency parameter, and s is the decrease parameter.

Fig. 6. CWT time-frequency map with 47 lobes (N=47)

Fig. 5. CWT time-frequency map with 360 lobes (N=360)

Two analyses were conducted; in the first analysis the GSI was neglected and in the second analysis it was included. The stability of the CPG was identified with the continuous wavelet transform and with the phase diagram. These methods are able to identify nonlinear and transient responses in a dynamic system.

The time-frequency maps were obtained by applying the CWT to Eq. 13. Since the map shows the variation of the frequency response as a function of time, it is possible to identify the instabilities of the system. If the system is stable, the frequency response will be almost constant as a function of time.

Otherwise, it is expected to see significant variations on the frequency response. Fig. 5 shows the timefrequency map for N = 360. There is a dominant frequency at 9 Hz with constant variations every

Nonlinear Model for the Instability Detection in Centerless Grinding Process

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0.133 s. The pattern of the map is constant and the time variations oscillate at the same period. When the number of lobes is reduced to 47, the frequency response is incremented to 20.8 Hz and the frequency presents a steady variation with a period of 0.048 s (Fig. 6). In both cases the system is stable. When the number of lobes is reduced to 38, the frequency is incremented to 23.3 Hz, but the frequency variations are no longer constant, as time passes by the bandwidth diminished reaching a minimum values at 0.5 s and then it increases again (Fig. 7).

in the stability-instability detection in the CGP. Furthermore, this technique can be used to solve both linear and nonlinear differential equations [24] and [25].

The stability analysis was carried out to analyze two models of workpiece dynamics; with the GSI and without the GSI. Fig. 8 shows the evolution of the process stability as the number of lobes reduces. For a high number of lobes (N > 100) the shape of the phase diagram is smooth and almost constant, the pattern is the same at any given time interval. As the number of lobes reaches a critical value (for instance N = 46) the shape of the phase diagram is no longer constant, and there is a significant difference between the two solutions: The pattern is similar but the solution with the GSI has minimum variations with respect to time.

Fig. 7. CWT time-frequency map with 38 lobes (N = 38)

4.2 Phase Diagram Analysis The response of a dynamic system can be represented as a time-dependent energy function. This function depends on the displacement (potential energy) and the velocity (kinetic energy) and time. The projection of the energy function on the real and imaginary plane is called the phase diagram. At certain period, the energy function forms a loop; the smoothness of each loop determines the stability of the system. The energy function of a mechanical system is determined using Hamilton’s equation:

H (q, p ) =

p2 + V ( q ) , (16) 2m

where the dyad (q(t), p(t)) represents the phase diagram of a particle. If the phase diagram can be represented as a smooth function then it represents the system’s evolution in time.

Phase diagrams allow a practical visualization of the physical and qualitative system’s behavior.

The results of the displacement y and velocity y are plotted in the phase diagram. The dynamic stability is determined from Liouville’s theorem: the phase space volume occupied by a collection of systems evolving according to Hamilton’s equations of motion will be preserved in time. Hence, this technique is helpful 698

Fig. 8. Stability analysis with and without the GSI

At N = 39 the system is fully unstable. The solution with the GSI increases exponentially as a function of time and it clearly indicates that the system is unstable or even chaotic. The same cannot be observed by only analyzing the dynamic model without the incorporated GSI. The results of both the phase diagram and the CWT are in agreement with the following reported research works [5], [8], [14], [17], [26] and [27], hence validating the developed models. For example, Brecher and Hannig [5] proved that the process

Robles-Ocampo, J.B. –Jáuregui-Correa, J.C. –Krajnik, P. –Sevilla-Camacho, P.Y. –Herrera-Ruiz, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700

has dynamic instabilities when the workpiece has 56 lobes. Krajnik et al. [14] detected the largest amplitude in the N = 45 lobe order. The results were obtained both in simulation and experimental tests.

Similarly, Hashimoto et al. [17] showed that the dynamic stability is considerably improved when the workpiece surface lobing order is beyond N = 60.

4 CONCLUSIONS This work presents the development of a nonlinear model for analysis of a CGP dynamic stability.

The novel aspect in the model development is the incorporation of the GSI. Beforehand the geometric and the dynamic instability in centerless grinding have been investigated separately. The model assumes that the workpiece has a polygonal shape. The unstable condition results from the moving waveform (regenerative effect) and the vertical workpiece displacement caused by a moving polygon between the grinding wheel and the regulating wheel. These phenomena give rise to a self exited vibration (chatter) and it was found that there is a critical number of lobes (N = 39) when the CGP is totally unstable.

It was shown that the dynamic model can be represented as a Duffing’s equation, where the nonlinear stiffness depends on the vertical displacement of the workpiece center. The unstable threshold is clearly determined with the GSI, otherwise the unstable condition falls within a range of lobes.

The instability condition was analyzed with two techniques: (1) the continuous wavelet transform and (2) the phase diagram. The continuous wavelet transform shows the evolution of the dynamic response as a function of time and frequency. The phase diagram shows the instability condition as a function of the Louville theorem. Both techniques showed that the instability condition occurs when the workpiece has an erroneous surface of 40 lobes.

5 NOMENCLATURE a, b variation of length in the contact points, scale factor, a1 time shift factor, b1 Ci coefficients, feed force, Ffeed FnG , FnR , FnB normal forces of grinding wheel,

regulating wheel and workrest blade, H(q, p) Hamilton’s equation, m N

mass of the workpiece, number of lobes,

Pa, Pb location of contact point between workpiece and wheels, Rw, RR, RG radius of workpiece, regulating wheel and

grinding wheel, ωG, ωR, ωW angular speed of grinding wheel, regulating

wheel, and workpiece, translation angle, ψ θG, θR, θW rotation angle of grinding wheel, regulating

wheel and workpiece, μ friction coefficient, β angle between two tangent faces, Ksys, KG, KR, K stiffness coefficients, ξsys, ξG, ξR damping coefficients,

α angle between the center line and vertical position, βG angle between the center lines and the workpiece, p generalized momentum, q(t), p(t) represent the phase diagram, ρ frequency parameter, t time, σ decrease parameter, V(q) potencial energy, feed velocity of regulating wheel, vfeed x signal function, conjugate function of the mother Wavelet, φ* yw(t) vertical displacement of the workpiece center.

6 REFERENCES [1] Webster, J., Tricard, M. (2004). Innovations in abrasive products for precision grinding. Annals of the CIRP, vol. 53, no. 2, p. 597-617, DOI:10.1016/S00078506(07)60031-6.

[2] Krajnik, P., Kopac, J. (2004). A review of highspeed grinding and high-performance abrasive tools.

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[3] Rowe, W.B. (2009). Principles of Modern Grinding Technology. Elsevier Inc., Oxford.

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[6] Subramanya Udupa, N.G., Shunmugam, M. S., Radhakrishnan, V. (1988). Workpiece movement in centerless grinding and its influence on quality of the ground part. Journal of Engineering for Industry, vol.

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[7] Wu, Y., Wang, J., Fan, Y., Kato, M. (2005).

Determination of waviness decrease rate by measuring the frequency characteristics of the grinding force in centerless grinding. Journal of Materials Processing Technology, vol. 170, no. 3, p. 563-569, DOI:10.1016/j. jmatprotec.2004.11.021.

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3, p. 539-550, DOI:10.1115/1.2716729.

[9] Hashimoto, F., Lahoti, G.D. (2004). Optimization of set-up conditions for stability of the centerless grinding process. Annals of the CIRP, vol. 53, no. 1, p. 271-274, DOI:10.1016/S0007-8506(07)60696-9.

[10] Zhou, S.S., Gartner, J.R., Howes, T.D. (1996). On the relationship between setup parameters and lobing behavior in centerless grinding. Annals of the CIRP, vol. 45, no. 1, p. 341-346, DOI:10.1016/S00078506(07)63076-5.

[11] Gallego, I. (2007). Intelligent centerless grinding: Global solution for process instabilities and optimal cycle design. Annals of the CIRP, vol. 56, no. 1, p. 347352, DOI:10.1016/j.cirp.2007.05.080.

[12] Furukawa, Y., Miyashita, M., Shiozaki, S. (1970).

Chatter vibration in centerless grinding (research 1, Work-rounding mechanics under the generation of selfexcited vibration). Bulletin of the JSME, vol. 13, no. 64, p. 1274-1283, DOI:10.1299/jsme1958.13.1274.

[13] Furukawa, Y., Miyashita, M., Shiozaki, S. (1973).

Chatter vibration in centerless grinding (research 2, influence of Growing up mechanism of self-excited chatter vibration upon finishing accuracy). Bulletin of the JSME, vol. 15, no. 82, p. 544-553, DOI:10.1299/ jsme1958.15.544.

[14] Krajnik, P., Drazumeric, R., Meyer, B., Kopac, J., Zeppenfeld, C. (2008). Simulation of workpiece forming and centre displacement in plunge centreless grinding. International Journal of Machine Tools and Manufacture, vol. 48, p. 824-831, DOI:10.1016/j. ijmachtools.2007.12.008.

[15] Lizarralde, R., Barrenetxea, D., Gallego, I., Marquinez, J.I. (2005). Practical Application of new simulation methods for the elimination of geometric instabilities in centerless grinding. Annals of the CIRP, vol. 54, no. 1, p. 273-276, DOI:10.1016/S0007-8506(07)60101-2.

[16] Garitaonandia, I., Fernandez, M.H., Albizuri, J., Hernández, J.M., Barrenetxea, D. (2010). A new perspective on the stability study of centerless grinding process. International Journal of Machine Tools and Manufacture, vol. 50, no. 2, p. 165-173, DOI:10.1016/j. ijmachtools.2009.10.016.

[17] Hashimoto, F., Zhou, S.S., Lahoti, G.D., Miyashita, M. (2000). Stability diagram for chatter free centerless grinding and its application in machine development.

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[19] Epureanu, B.I., Montoya, F.M., Garcia, C.L. (1999).

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2, p. 157-162, DOI:10.1115/1.2831199.

[20] Zhou, S.S., Gartner, J.R., Howes, T.D. (1997).

Lobing behavior in centerless Grinding–Part 1: Stability estimation. Journal of Dynamics Systems, Measurement and Control, vol. 119, no. 2, p. 153-159, DOI:10.1115/1.2801227.

[21] Dombovari, Z., Barton, D.A.W., Wilson, R.E., Stepan, G. (2011). On the global dynamics of chatter in the orthogonal cutting model. International Journal of Non-Linear Mechanics, vol. 46, no. 1, p. 330-338, DOI:10.1016/j.ijnonlinmec.2010.09.016.

[22] Insperger, T., Barton, D.A.W., Stepan, G. (2008).

Criticality of Hopf bifurcation in state-dependent delay model of turning processes. International Journal of Non-Linear Mechanics, vol. 43, no. 2, p. 140-149, DOI:10.1016/j.ijnonlinmec.2007.11.002.

[23] Zhang, H., Lieh, J., Yen, D., Song, X., Rui, X. (2003). Geometry analysis and simulation in shoe centerless grinding. ASME Journal of Manufacturing Science and Engineering, vol. 125, no. 2, p. 304-309, DOI:10.1115/1.1557299.

[24] Strogatz, S.H. (1994). Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering. Perseus Book, New York.

[25] Jauregui-Correa, J.C., Gonzalez-Brambila, O. (2010).

Mechanical Vibrations of Discontinuous Systems. Nova Science Publishers Inc, New York.

[26] Robles Ocampo, J.B., Jáuregui Correa, J.C., Sevilla Camacho, P.Y., Vela Martínez, L., Herrera Ruíz, G. (2010). Nonlinear characterization of self-excited forces on the centerless grinding process. Mechanical Engineering Technology and Development, Journal of The Mexican Society of Mechanical Engineering, vol.

3, p. 179-185. (in Spanish) [27] Li, H., Shin, Y.C. (2007). A study on chatter of cylindrical plunge grinding with process conditiondependent dynamics. International Journal of Machine Tools and Manufacture, vol. 47, no. 10, p. 1563-1572, DOI:10.1016/j.ijmachtools.2006.11.009.

[28] Rabiey, M., Walter, C., Kuster, F., Stirnimann, J., Pude, F., Wegener, K. (2011). Dressing of Hybrid Bond CBN Wheels Using Short-Pulse Fiber Laser. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 7-8, p. 462-469, DOI:10.5545/sv-jme.2011.166.

Robles-Ocampo, J.B. –Jáuregui-Correa, J.C. –Krajnik, P. –Sevilla-Camacho, P.Y. –Herrera-Ruiz, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 701-708 DOI:10.5545/sv-jme.2012.524

Paper received: 2012-04-15, paper accepted: 2012-10-18 © 2012 Journal of Mechanical Engineering. All rights reserved.

Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage Liu, Y. – Han, J. – Xia, L. – Tian, X. Youyu Liu1,2,* – Jiang Han2 – Lian Xia2 – Xiaoqing Tian2

1 School

of Mechanical and Automotive Engineering, Anhui Polytechnic University, China 2 Institute of CIMS, Hefei University of Technology, China

The application of non-circular helical gears has been largely restricted to their manufacturing techniques. For realization of their hobbing, a kind of hobbing strategy based on a four-axis linkage and some fundamental hobbing models have been built by a generating method of helical tooling rack. This method includes profile-linkage models and extra rotation models. Based on the strategy and the models achieved, eighteen kinds of schemes and functional models have been developed according to the variety of hobbing processes in profile movement, axial movement, and extra rotation, which have an effect on profile precision, axial precision and control performance. The effect is analyzed from the aspects of profile-hobbing performance, axial movement performance and extra rotation performance, by using a 3D machining simulation. Excellent strategy and models have been singled out progressively. Finally, the excellent strategy and model (constant revolving velocity of hob & constant axial speed for workpiece & extra rotation of workpiece) is obtained with the characteristics of high precision, high efficiency and ease of control. The excellent strategy and model have been demonstrated to be valid by hobbing tests. The results between the test for tooth flanks and the computer simulations are in good agreement. This work provides the options of schemes for the manufacture of non-circular helical gears, and will promote its application significantly.

Keywords: non-circular helical gears, four-axis linkage, hobbing, linkage models, machining simulation

0 INTRODUCTION Non-circular gears synthesize the advantages of circular gears and cam mechanisms, and can deliver a combination of high output power and excellent level accuracy with a continuously variable transmission.

Non-circular gears have been applied to construction machineries, machine tools, automotives, aerospaces and other fields [1] to [3]. Most of current research is focused on non-circular spur gears. However, the studies for the design and manufacture of non-circular helical gears are few. For the advantages such as larger contact ratio, less impact and noise, smaller teeth be free of undercut, non-circular gears have a fairly good application prospect.

Recently, remarkable progress of non-circular gears has been made in the research of implementing their function and analyzing their performance [4] and [5]. As for their manufacturing technology, some academics have conducted some research.

Wu et al. [6] have proposed a numerical algorithm of the tooth profile of non-circular gears based on the characteristics of cutter envelope, which can only be used for non-circular spur gears by wire electric discharge machining. In the last few years, new approaches to gear cutting have emerged. For example, José Luís Huertas Talón et al. [7] have offered a method of manufacturing a spur gear in Ti-6Al-4V alloy using a wire electrical discharge machine. In addition, a precision gear was cut on 0.4 mm stainless steel sheets with fiber laser precision processing system in paper [8]. The above-mentioned

methods can also be applied to non-circular spur gears regardless of their shape of pitch curve, but does not apply at all to non-circular helical gears. Moreover, those methods above, being hopelessly inefficient, are suitable only for such gears with special materials or extreme thinness. Hobbing is still our first choice for its high efficiency. Hou and Liu [9] have researched a meshing theory model for the manufacturing of noncircular helical gears by a generating method of helical tooling rack, and analysed the geometric features of the tooth profile, but provided no processing program for them.

In this paper, some available hobbing schemes and functional models have been developed based on the strategy of the four-axis linkage and the fundamental linkage models. Profile precision, axial precision and control performance have been analyzed according to the variety of the hobbing process in profile movement, axial movement, and extra rotation by using 3D machining simulation. Thus, excellent strategy and models have been singled out progressively.

1 HOBBING MODEL FOR NON-CIRCULAR HELICAL GEARS BASED ON A FOUR-AXIS LINKAGE 1.1 Hobbing Strategy Based on a Four-Axis Linkage As shown in Fig. 1, the hob rotation ωb and the workpiece rotation ωc must keep a strict transmission ratio, which generates meshing movement.

Meanwhile, the workpiece must move along the y-axis

*Corr. Author’s Address: School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000, China, Liuyoyu1@163.com.

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(namely vy) to form non-circular gears pitch curve.

Moreover, the hob should move along the z-axis, namely vz, to cut a full-depth tooth. For helical gears, extra rotation is essential, which can be implemented by extra rotation of workpiece, namely Δωc , or that of hob, namely Δωb . All of the above is the basic hobbing strategy based on a four-axis linkage.

axis of which is parallel with that of S (o x y z). At the beginning, the Sb ( ob xb yb zb ) and the S (o x y z) coodinate systems are kept in superposition. Sc ( oc xc yc zc ) is a workpiece coordinate system, it revolves with the workpiece, and the zc-axis of which is coincident with the turning spindle axis of the workpiece. At the beginning, the xc-axis is parallel with the y-axis, and the yc-axis is parallel with the x-axis. Moreover, we build a polar coordinate system that has a pole oc and polar axis xc . The pitch curve equation of the noncircular helical gears is r = r (θ ). The modulus of the polar radius is r; the polar angle is θ ; the polar-angular velocity is ω. The forward direction of the θ, the φc , and the ωc is as shown in Fig. 2.

Fig. 1. Schematic diagram of a four-axis hobbing process

Compared to the four-axis linkage, the workpiece should move along the x-axis (namely vx) based on the five-axes linkage, which would increase the number of linkage axes. In addition, machining accuracy may be decreased due to a clearance while reciprocating movement [10]. Consequently, Four-axis Linkage method is a good hobbing strategy for non-circular helical gears.

1.2 Fundamental Hobbing Models Based on a Four-Axis Linkage According to the meshing theory of hobbing noncircular helical gears by a helical tooling rack [9], the pitch line of the helical tooling rack rolls along the pitch curve of the non-circular helical gears without slip. A revolving hob and an extra rotation (Δωc or Δωb) can realize the functions of the helical tooling rack. The cross-section of workpiece is shown in Fig. 2. The tooling rack is formed by the hob projected to the end-face, the pitch line of which tangents to the point P with the pitch curve of the non-circular helical gears on the end-face. For pure rolling between them, the motion of the workpiece is s, and that of the tooling rack is l.

As shown in Fig. 2, S (o x y z) is a machine coordinate system, the x-axis and z-axis of which are independently parallel to the pitch line of the hob and the turning spindle axis of the workpiece, and the y-axis of which passes through the turning spindle axis of that. Sb ( ob xb yb zb ) is a cutting tool coordinate system, moved with the helical tooling rack, and each 702

Fig. 2. Cross-section of workpiece 1.2.1 Profile-Linkage Models As shown in Fig. 2, the angle between the polar radius and the tangent of the pitch curve of the workpiece is μ. From the theory of calculus [11], we can infer the following.

µ = arctan ( r dr / dθ )

sin µ = r

(0 ≤ µ < π ) ,

r 2 + ( dr / dθ ) , 2

(1)

then, 2 2 d µ d µ dθ ( dr / dθ ) − r ⋅ d r dθ dθ = ⋅ = ⋅ . (2) 2 dt dθ dt dt r 2 + ( dr / dθ ) 2

From Fig. 2,

θ = ϕc − µ + π 2 , (3)

then,

dθ d ϕ c d µ dµ = − = ωc − . (4) dt dt dt dt

The Eq. (2) is substituted in the Eq. (4), then

Liu, Y. – Han, J. – Xia, L. – Tian, X.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 701-708

r 2 + 2 ( dr / dθ ) − r ⋅ d 2 r dθ 2 dθ ⋅ . (5) 2 dt r 2 + ( dr / dθ ) 2

ωc =

For the pitch curve (r = r (θ )) being a kind of non-circular curve, ωc varies nonlinearly with ωb in hobbing. As shown in Fig. 2, there is an equialent helical gear that has center of rotation, oc , and reference radius corresponding to the distance R, which is from oc to the tangent of the pitch curve.

Some parameters such as the helix angle βc , the normal module mn , and the transverse module mt are the same as those of non-circular helical gears. The equivalent teeth number is marked as Zv , then,

ωb Z v 2 R cos β c 2R = = = , ωc K Kmt Kmn

(6)

R = r sin( π − µ ) = r sin µ . (7)

The Eqs. (1), (5) and (7) are substituted in the Eq. (6), then, 2r 2 cos β c ( r 2 + 2 ( dr dθ ) -r d 2 r dθ 2 ) dθ . (8) ⋅ 32 2 dt 2 Km r + dr dθ 2

ωb =

n

(

(

)

)

From Eq. (7), the velocity of the workpiece along the normal direction of the pitch line of the tooling rack can be deduced. vy =

2 2 2  2 dR r dr dθ  r + 2 ( dr dθ ) -r d r dθ  dθ = . (9) ⋅ 32 2 dt dt r 2 + ( dr dθ )

(

∫

t

0

t

r ∆ωc dt = tan β c ∫ vz dt . (11) 0

Differentiating Eq. (11) and simplifying it: ∆ωc = ( vz tan β c ) r . (12)

The resultant angular velocity ωc* is as follows.

ωc* = ωc ± ∆ωc , (13)

where the “+” is adopted while the direction of the helix of the hob is in accordance with that of the gears; otherwise, the “–” is adopted.

1.2.2.2 Extra Rotation of Hob

where the K is the lobes of hob.

rotate a week additionally while moving a screw lead along the axle of that [12].

As shown in Fig. 3, an extra rotation Δωb is added to the hob rotation ωb , marked as “B”. The line t–t is a tangent to the inclined tooth flank in the point of P. The component of the vertical motion vz related to the common normal line n–n is v zn . vΔ represents an extra linear velocity in the point of P due to Δωb , the component of which related to the common normal line is v∆n . = vzn = vz sinβ c ,

v∆ = Kmt ∆ωb 2 = Kmn ∆ωb

( 2sinλb ) , (14)

n ∆

v = v∆ sinλb ,

where the “λb” is the lead ascending angle of the hob.

)

From Eqs. (5), (8) and (9), a fundamental linkage model based on hobbing is elicited as follows.

v y = r ( dr dθ ) ωc

r 2 + ( dr dθ ) , 2

ωc = Kmn r + ( dr dθ ) ωb 2

2

( 2r cosβ ) .

2

(10)

c

1.2.2 Extra Rotation Models As mentioned previously, extra rotation can be implemented by a workpiece or hob.

1.2.2.1 Extra Rotation of Workpiece If an extra rotation Δωc is added to the workpiece rotation ωc , marked as “A”, the workpiece should

Fig. 3. Common tangent plane of hobbing

The normal velocity of the hob in the meshing point should equal to that of the workpiece [10].

vzn = v∆n . (15)

Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage

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From Eqs. (14) and (15),

the resultant angular velocity ωb* is as follows:

v y =  Kmn ( dr dθ ) 2r cos β c  ωb ,

∆ωb = ( 2vz sin β c ) Kmn , (16)

* c

ω =

2 REALIZATION STRATEGY OF THE LINKAGE MODEL There are three kinds of hobbing methods [9], such as constant revolving velocity of hob (marked as “U”), constant revolving velocity of workpiece (marked as “V”) and constant polar-angular velocity of workpiece (marked as “W”), in the cross-section of non-circular gears. The constant revolving velocity of hob implies that the velocity of hob keeps constant, consequently the workpiece rotates at constant arc length at the same time. The constant revolving velocity of workpiece implies that the workpiece rotates with a constant angular velocity. The constant polar-angular velocity of the workpiece implies that the workpiece rotates with constant polar-angular velocity. There are three kinds of movement methods for the axial movement vz , such as being coupled with ωb (marked as “α”), being coupled with ωc (marked as “β”) and constant axial speed (marked as “γ”).

For the variety of hobbing process in profile movement, axial movement, and extra rotation, there are eighteen ( C13 C13 C12 = 18) kinds of schemes and functional models that can be realized. For the constant revolving velocity of hob, some schemes such as “UαA”, “UβA”, “UγA” or “UαB”, “UβB”, “UγB” can be constructed from Eqs. (1) and (2), or Eqs. (1) and (3), and the mathematical model of which is Eqs. (18) or (19). The vz = f (ωb , ωc , k3) in Eqs. (18) and (19) can be determined based on the linkage methods of the axial movement, as Eq. (20). For the constant revolving velocity of workpiece, some schemes such as “VαA”, “VβA”, “VγA” or “VαB”, “VβB”, “VγB” can be constructed from Eqs. (1) and (2), or Eqs. (1) and (3), and the mathematical model of which is Eqs. (21) or (22). For the constant polarangular velocity of the workpiece, some schemes such as “WαA”, “WβA”, “WγA” or “WαB”, “WβB”, “WγB” can be constructed from Eqs. (1) and (2), or Eqs. (1) and (3), and the mathematical model of which is Eqs. (23) or (24).

2

2r 2 cos β c

ωb ±

tan β c vz , (18) r

vz = f (ωb ,ωc , k3 ) ,

ωb* = ωb  ∆ωb , (17)

where the “–” is adopted while the direction of the helix of the hob is in accordance with that of the gears; otherwise, the “+” is adopted.

704

Kmn r 2 + ( dr dθ )

v y =  Kmn ( dr dθ ) 2r cos β c  ωb , 2 ωc =  Kmn r 2 + ( dr dθ ) 2r 2 cos β c  ωb , (19)   * ωb = ωb  [ 2 sin β c Kmn ] vz ,

vz = f (ωb ,ωc , k3 ) , k1ωb  vz = f (ωb ,ωc , k3 ) = k2ωc  k3

v y =  r ( dr dθ ) 

(α ) (β ) (γ )

, (20)

2 r 2 + ( dr dθ )  ωc , 

2 ωb =  2r 2 cos β c Kmn r 2 + ( dr dθ )  ωc , (21)   * ωc = ωc ± vz tan β c r ,

vz = f (ωb ,ωc , k3 ) ,

2 v y =  r ( dr dθ ) r 2 + ( dr dθ )  ωc ,   2r 2 cos β c 2 si n β c ωb = ωc  vz , (22) 2 Kmn Kmn r 2 + ( dr dθ )

vz = f (ωb ,ωc , k3 ) ,

(

)

(

)

r ( dr dθ )  r 2 + 2 ( dr dθ ) -r d 2 r dθ 2  vy = 32  r 2 + ( dr dθ )2    2 2r 2 cos β c  r 2 + 2 ( dr dθ ) -r d 2 r dθ 2  ωb = 32 2 Kmn  r 2 + ( dr dθ )    2

ω =

(

r 2 + 2 ( dr dθ ) -r d 2 r dθ 2 2

* c

Liu, Y. – Han, J. – Xia, L. – Tian, X.

r + ( dr dθ ) 2

2

)ω ± v

vz = f (ωb ,ωc , k3 ) ,

z

ω,

ω , (23)

tan β c , r

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 701-708

(

)

r ( dr dθ )  r 2 + 2 ( dr dθ ) -r d 2 r dθ 2    ω, 32  r 2 + ( dr dθ )2    2 2r 2 cos β c  r 2 + 2 ( dr dθ ) -r d 2 r dθ 2    ω  2 sin β c v , ωb* = z (24) 32 2 Kmn 2   Kmn r + ( dr dθ )   2 2 ωc =  r 2 + 2 ( dr dθ ) -r d 2 r dθ 2  ω  r 2 + ( dr dθ )  ,     vz = f (ωb ,ωc , k3 ) , 2

vy =

(

(

)

)

3 ANALYSIS AND SELECTION OF LINKAGE MODELS BASED ON VIRTUAL MACHINING Including the basic function of hobbing and the linkage strategy properly, an excellent linkage model should have the performance qualities of high precision, high efficiency and ease of control. An

a)

elliptical helical gear will be analyzed as an example in this paper, which has the essential feature of any non-circular helical gears. The conclusions drawn can be expanded to other non-circular helical gears with arbitrary pitch curve. Its principal parameters are as follows: major semi-axis a = 100 mm, eccentricity e = 0.6, K = 1, mn = 5 mm, βc = 14.251°, number of teeth Z = 35, tooth width b = 50 mm. The mathematical models (see Eqs. (18) to (24)) applied to the elliptical helical gear are discussed from three aspects. These are profile precision, axial precision and control performance by virtual machining process using MATLAB [13], to single out the excellent strategy and models progressively. For example, three kinds of models of constant axial speed (γ) & extra rotation of the workpiece (“A”) are simulated and shown in Fig. 4.

b)

c)

Fig. 4. Constant axial speed & extra rotation of workpiece; a) scheme of the “UγA”, b) scheme of the “VγA”, c) scheme of the “WγA”

a)

b)

c) d) Fig. 5. Profile-hobbing performance; a) scheme of the “UγA”, b) scheme of the “VγA”, c) scheme of the “WγA”, d) graph of ωb – θ Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage

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3.1 Analysis of Profile-Hobbing Performance Involute profiles are formed by the meshing movement between ωb and ωc on the end-face, which means that the profile precision is determined only by the methods of the profile hobbing process. That is to say, the profile precision has nothing to do with the methods of axial movement and extra rotation. To compare different profile hobbing process features, 3D machining simulations, taking the same axial movement (γ) and the same extra rotation (“A”) as a case, are conducted and shown in Fig. 4. Their tool paths on the end-face (z = 0) are shown in Fig. 5.

From Figs. 5a and d, we can find that ωb is constant on any polar angle to the scheme of the “UγA”, which makes cutting marks of any tooth uniform, and the precision is basically identical. As illustrated in Figs. 5a and d, ωb of the scheme of the “VγA” fluctuates. All variables in MATLAB can be inquired conveniently [14]. We find that the minimum ωb is 98 rad/s when θ is 0 or π, and its maximum is 191.4 rad/s while θ is 0.3 π or 1.7 π. The maximum is 1.95 times as much as the minimum, which makes the cutting marks of every tooth nonuniform. Thus, the precision is different. As shown in Fig. 5c d, the ωb of the scheme of the “WγA” fluctuates sharply.

The figures show that the maximum ωb is 612.5 rad/s when θ is 0, and its minimum is 38.28 rad/s while θ is π. The maximum is 16 times more than the minimum, which makes the precision of every tooth vary greatly.

The precision of the gear should be measured at its lowest level. Therefore, the constant revolving velocity of hob should be adopted, and can obtain the highest manufacturing precision under a given efficiency. The next ordinal is the constant revolving velocity of the workpiece, the constant pola-angular velocity of the workpiece.

lie in 0.14 π and 1.86 π. Table 1 lists the final axial displacement of hob and its successive clearance in 0, 0.14 π, π, and 1.86 π. The successive clearances of the “UαA” and the “UγA” are constant to any axial displacement and any polar angle. The successive clearances of the “UβA” are constant to any axial displacement and the same polar angle, not to any polar angle. The minimum of that lies in 0.14 π, which means that the cutting marks are the most plentiful, so the precision is the highest. However, the maximum lies in 1.86 π, which means that the cutting marks are the thinnest, so the precision is the lowest. Therefore, the schemes of the “UαA” and the “UγA” can obtain the highest precision under a given efficiency.

a)

3.2 Analysis of Axial Movement Performance The full-depth tooth can be hobbed through the vz movement, and the axial precision is determined only by the methods of axial movement. To compare the features of different axial movement, three kinds of axial movement methods with the same profile hobbing process (“U”) and the same extra rotation (“A”) are analyzed. As shown in Fig. 6a, Sz is an axial displacement of hob at a polar angle, and ΔSz is its successive clearance. The Sz of the schemes of the “UαA”, the “UβA” and the “UγA” are shown in Fig. 6b, which shows that the Sz of the “UαA” and the “UγA” change linearly with θ, but the “UβA” varies nonlinearly. The maximum and the minimum each 706

b)

Fig. 6. Axial movement performance; a) elevation view of tool-path, b) axial displacement Table 1. Axial displacement and successive clearance in specific polar angle θ [rad] Sz [mm] UαA ΔSz [mm] Sz [mm] UβA ΔSz [mm] Sz [mm] UγA ΔSz [mm]

Liu, Y. – Han, J. – Xia, L. – Tian, X.

0 -50.000 -5.000 -50.205 -5.021 -50.000 -5.000

0.14 π -50.336 -5.000 -50.000 -4.966 -50.336 -5.000

π -52.723 -5.000 -52.989 -5.027 -52.723 -5.000

1.86 π -55.169 -5.000 -56.058 -5.089 -55.169 -5.000

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 701-708

The scheme of the “UαA” has the characteristics of constant revolving velocity of hob (“U”) and being coupled with ωb (α). From Eq. (20), it is fined that vz (= k1 ω1) is unchanging, which means that the essence between the “UαA” and the “UγA” is the same, and their axial movement performance is the same. Due to controlling less synchronal axis being relatively simple, the scheme of the “UγA” is suitable to adopt.

drawn. Compared to the results between the computer simulations and the experimental studies, the results have shown that they are in good agreement.

3.3 Analysis of Extra Rotation Performance Through analyzing the hobbing methods under the same profile movement (e.g. “U”) and the same axial movement (e.g. γ), it can be concluded that they have the same precision and efficiency regardless of the extra rotation of the workpiece (“A”) or extra rotation of hob (B). To the scheme “UγB”, Δωb is attached to hob rotation, which causes angular acceleration of the synthesis angular velocity ωb* to be nonzero.

The machine should adopt a servomotor driver, which would restrict its output power. However, Δωb is attached to workpiece rotation in the scheme “UγA”, and there is little difference between the synthesis angular velocity ωc* and ωc , which increases no difficulty in control. In this case, the hob can be driven by an AC motor, and its angle or angular velocity can be measured by a detecting element. The testing signal can be turned into a digital signal, as a fundamental frequency, which can make up a double-fundamentalfrequency control system with another fundamental frequency that controls the vz [15]. Therefore, the scheme “UγA” is the best.

Fig. 7. Machining process and elliptic helical gear

4 HOBBING TESTS AND DETECTION FOR TOOTH FLANKS The excellent scheme of the “UγA” has been brought into operation based on a hobbing platforms with ARM (Advanced RISC Machines) & DSP (Digital Signal Processor) & FPGA (Field Programmable Gata Array) [16]. The actual hobbing process with the elliptical helical gear hobbed is presented in Fig. 7, from which we find that the gear can be hobbed corrected.

The surface roughness of the 1st tooth (θ = 1.3°) and the 17th tooth (θ = 187°) of the elliptical helical gear can be detected by a surface roughness measuring instrument [17]. The point cloud figures of roughness for tooth flanks are shown in Figs. 8a and b, which shows that both of the two are very close, and there is no discernible difference between the two tooth flanks including their profile precision and their axial precision. Therefore, a conclusion that all of the profile precisions of the gear are uniform can be

a)

b) Fig. 8. Point cloud of roughness for tooth flanks, a) θ =187°, b) θ =1.3°

5 CONCLUSIONS (1) The hobbing strategy based on the four-axis linkage has been built by the generating method of helical tooling rack, and some fundamental hobbing models have been deduced, which includes profile-linkage models and extra rotation models. These works make the hobbing of noncircular helical gears possible.

(2) Eighteen kinds of schemes and functional models have been developed based on the fundamental hobbing models built, according to the variety of hobbing processes in profile movement, axial

Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage

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movement, and extra rotation. Profile precision is determined only by methods of profile movement, and its axial precision is determined only by those of axial movement, and control performance is determined only by those of extra rotation. The excellent strategy and model have been selected orderly.

(3) The scheme of the “UγA” is an excellent linkage obtained, the mathematical model of which is the simultaneous Eqs. (18) and (20). Morever, schemes of the “UγB”, the “UαA” and the “UαB” can also realize a hobbing with high precision and high efficiency, while those machine tools have a special requirement, and the control systems can also meet the requirement of dynamic characteristics. Then, those schemes are also available as options.

(4) Through the hobbing tests, it has been concluded that the excellent strategy and the model are correct and feasible. The results between the tests for tooth flanks and the computer simulations are in good agreement.

6 ACKNOWLEDGEMENTS This work was financially supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 51275147).

7 REFERENCES [1] Litvin, F.L., Gonzalez-Perez, I., Fuentes, A. (2008).

Design and investigation of gear drives with noncircular gears applied for speed variation and generation of function. Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 45-48, p. 3783-3802, DOI:10.1016/j.cma.2008.03.001.

[2] Wayne, C. (2008). A new tolerance modeling and analysis methodology through a two-step linearization with applications in automotive body assembly.

Journal of Manufacturing Systems, vol. 27, no. 1, p. 2635, DOI:10.1016/j.jmsy.2008.05.002.

[3] Petre, A., Dragoş, M., Cătălin, A. (2012). A gear with translational wheel for a variable transmission ratio and applications to steering box. Mechanism and Machine Theory, vol. 52, no. 6, p. 267-276, DOI:10.1016/j. mechmachtheory.2012.02.005.

[4] Mundo, D., Gatti, G., Dooner, D.B. (2009).

Optimized five-bar linkages with non-circular gears for exact path generation. Mechanism and Machine Theory, vol. 44, no. 4, p. 751-760, DOI:10.1016/j. mechmachtheory.2008.04.011.

[5] Erika, O., Domenico, M., Guido, A.D., Marco, C. (2008). Numerical and experimental analysis of non-circular gears and cam-follower systems

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as function generators. Mechanism and Machine Theory, vol. 43, no. 8, p. 996-1008, DOI:10.1016/j. mechmachtheory.2007.07.004.

[6] Wu, C.Y., Jin, Y.Z., He, L.Y. (2008). Numerical algorithm of tooth profile of noncircular gear based on the characteristics of cutter envelope. China Mechanical Engineering, vol. 19, no. 15, p. 1796-1799. (in Chinese) [7] Huertas Talón, J.L., Cisneros Ortega, J.C., Cisneros Ortega, L., Ros Sancho, E., Faci Olmos, E. (2010).

Manufacture of a spur tooth gear in Ti–6Al–4V alloy by electrical discharge. Computer-Aided Design, vol.42, no. 3, p. 221-230, DOI:10.1016/j.cad.2009.11.001.

[8] Guan, B.G., Liao, J.H., Meng, H.Y., Liu, S.H., Chang, M. (2005). Study of cutting precision gear wheel with fiber laser. Applied Laser, vol. 25, no. 6, p. 365-368. (in Chinese) [9] Hou, D.H., Liu, Z.M. (2003). Meshing theory analysis model for the manufacturing of helical noncircular gear by the helical tooling rack generating method. Chinese Journal of Mechanical Engineering, vol. 39, no. 8, p.

49-54, DOI:10.3901/JME.2003.08.049. (in Chinese) [10] Hu, C.B., Ding, H.Y., Yan, K.M., Wu, Z.X. (2005).

Simultaneous-control model for hobbing of noncircular helical gears. Journal of Lanzhou University of Technology, vol. 31, no. 24, p. 43-45. (in Chinese) [11] Meredith, L.G., Radestock, M. (2005). A reflective higher-order calculus. Electronic Notes in Theoretical Computer Science, vol. 141, no. 5, p. 49-67, DOI:10.1016/j.entcs.2005.05.016.

[12] Bouzakis, K.-D., Friderikos, O., Tsiafis, I. (2008).

FEM-supported simulation of chip formation and flow in gear hobbing of spur and helical gears. CIRP Journal of Manufacturing Science and Technology, vol. 1, no.

1, p. 18-26, DOI:10.1016/j.cirpj.2008.06.004.

[13] Fetvaci, C. (2010). Generation simulation of involute spur gears machined by pinion-type shaper cutters.

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[14] Vijay Sekar, K.S., Pradeep Kumar, M. (2012).

Optimising flow stress input for machining simulations using Taguchi methodology. International Journal of Simulation Modelling, vol. 11, no. 1, p. 17-28, DOI:10.2507/IJSIMM11(1)2.195.

[15] Staniek, R. (2011). Shaping of Face Toothing in Flat Spiroid Gears. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 1, p. 47-54, DOI:10.5545/sv-jme.2010.093.

[16] Fei, J.Y., Deng, R., Zhang, Z., Zhou, M. (2011).

Research on Embedded CNC Device Based on ARM and FPGA. Procedia Engineering, vol. 16, no. 11, p.

818-824, DOI:10.1016/j.proeng.2011.08.1160.

[17] Abouelatta, O.B., Mádl, J., Zhou, M. (2001). Surface roughness prediction based on cutting parameters and tool vibrations in turning operations. Journal of Materials Processing Technology, vol. 118, no. 1-3, p.

269-277, DOI:10.1016/S0924-0136(01)00959-1.

Liu, Y. – Han, J. – Xia, L. – Tian, X.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 709-715 DOI:10.5545/sv-jme.2012.531

Paper received: 2012-04-18, paper accepted: 2012-10-05 © 2012 Journal of Mechanical Engineering. All rights reserved.

Phase Transformations in High Alloy Cold Work Tool Steel Moravčík, R. – Štefániková, M. – Čička, R. – Čaplovič, L’. – Kocúrová, K. – Šturm, R. Roman Moravčík1,* – Mária Štefániková1 – Roman Čička1 – Ľubomír Čaplovič1 – Karin Kocúrová1 – Roman Šturm2 1 Slovak

University of Technology, Faculty of Materials Science and Technology, Institute of Materials Science, Slovak Republic 2 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Phase transformations in the alloy tool steels have a crucial effect on the final properties of the steels. High alloy systems have different solidification conditions compared to construction steels. This paper deals with the phase evolution in high alloy tool steel in quasi-equilibrium state.

For analysis various methods such as differential thermal analysis, thermomagnetometry, light microscopy, scanning electron microscopy with energy dispersive analysis, X-ray diffraction analysis and dilatometry, were used. The analysed tool steel solidifies in three steps, and at lower temperatures secondary carbides are formed. Solidification begins at 1340 °C and is finished at 1208 °C. The Curie temperature of this steel is approximately 780 °C. Keywords: high alloy cold work tool steel, differential thermal analysis, scanning electron microscopy, X-ray diffraction analysis, dilatometry

0 INTRODUCTION The development of high alloy tool steel is important due to the requirement for achieving better mechanical and physical properties. High alloy tool steels of ledeburitic type produced by powder metallurgy (PM) contain a high amount of carbon and alloying elements (mainly V, Cr, Mo) that form carbides [1] to [3]. Conventional methods preparation of ledeburitic type tool steels (mould casting and forming) was influenced by the liquation and segregation processes, which lead to anisotropy of microstructure and properties of high alloy tool steels with high carbon content. This fact limits the applications of these steels as performance tools [4] to [8]. To improve the properties of the ledeburitic tool steels, the technology of powder metallurgy can be used [7], [9] and [10].

The main advantages of PM high alloy tool steel are the homogeneous distribution and fine size of carbides and uniform chemical composition in cross section, thereby better properties are achieved [11] and [12]. Due to specific properties cold work tool steels have found a wide spectrum of applications in various industries at blanking, forming, shearing, punching and other applications [13] to [15].

Solidification of ledeburitic steel in quasiequilibrium conditions starts by austenite formation, then the formation of morphologically different MC, M7C3, M6C and M23C6 carbides follows and the solidification is finished by eutectic reactions [16] to [19]. Some aspects of solidification of the high alloyed tool steels are described in [20].

In the case of rapidly solidified powders the solidification usually starts by the formation of solid

solution with the dendritic, equiaxed and mixed types of solidification microstructures. However, due to recalescence effects also some amount of eutectic is usually formed [17] and [21] to [23]. For consolidation of powder the hot isostatic pressing (HIP) is often used. During HIP processing of rapidly solidified powder particles of high alloy tool steel significant changes in their microstructure and properties occur.

The differential thermal analysis technique/ thermomagnetometry is often used to determine the phase transitions including melting and solidification, liquation and formation of eutectics, recrystallization, dissolution and precipitation of new phases, solid-state transformation, and ferromagnetic to paramagnetic transition in a wide range of materials. Thermal analyses together with appropriate thermodynamic calculations can be used for analysis of such different materials as lead-free solders [24] and [25], carbon steels [26] and tool steels [27].

The aim of this work is the investigation of microstructure and phase transformations in selected high alloy cold work tool steel.

1 EXPERIMENTAL PROCEDURE The investigated material was equivalent to high alloy cold work tool steel K390 Microclean. The chemical composition of steel is given in Table 1.

Higher vanadium content ensures good tool wear resistance and high hardness (about 66 HRC) after heat treatment.

Analysed high alloy cold work tool steel has an extremely high wear resistance, outstanding toughness and high compressive strength. [15]

*Corr. Author’s Address: Institute of Materials Science, Faculty of Materials Science and Technology, Slovak University of Technology, Paulínska 16, 917 24 Trnava, Slovak Republic, roman.moravcik@stuba.sk

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Table 1. Chemical composition of the investigated high alloy tool steel [wt. %] C 2.47

Cr 4.15

Mo 3.62

Si 0.41

V 8.94

W 1.13

Co 2.02

The compacts were prepared by HIP processing of the rapidly solidified powders. The parameters of processing were: 1100 °C, 100 MPa, during 90 minutes with protective gas Ar [28]. From compacts the samples for differential thermal analysis/ thermomagnetometry (DTA/TM) and dilatometry were prepared.

For simultaneous DTA and TM experiment the sample with total weight of 105 mg was prepared and Netzsch STA 409 CD apparature with heating up to 1600 °C in Ar protective gas (60 ml/min.) was used. The heating and cooling rates for measurement were 10 K/min, during three measurement runs. The differences in DTA curves in the 2nd run and in 3rd run were negligible. This fact indicates that the sample was in quasi-equilibrium state after the 1st run, so only the 2nd run was further analyzed.

The microstructure of sample obtained from DTA experiment after standard metallographical procedure and chemical etching in 3% Nital was observed using the Neophot 32 light microscope and Jeol JSM-7600F scanning electron microscope (SEM).

The experimental technique of scanning electron microscopy and energy dispersive X-ray spectroscopy (EDS) was used to characterize the composition of the phases in the steel after DTA. X-ray diffraction analysis was carried out by means of Philips PW 1810 X-ray diffractometer with Co anode (λCoKα = 1.72091×10-10 m) and secondary monochromator. The measuring step was 0.02°, for each step the holding time 10 s was used. For X-ray diffraction analysis the sample from DTA experiment was used.

To characterize the phase transformations in solid state the dilatometry analysis of bulk sample prepared from the HIP compact was used. The initial sample length was 9.58 mm. The analysis was performed using Netszch 402 C dilatometer in Ar protective gas with heating rates of 3 K/min, during two measurement runs. Also, in this case only the second run was further analysed.

2 RESULTS 2.1 Microscopy The microstructure of the sample after DTA obtained by light microscopy is shown in Fig. 1. It can be seen 710

that the microstructure is dendritic, however, each dendrite consists from carbide eutectic colonies. At the boundaries of eutectic colonies (Fig. 2) a secondary skeleton eutectic is present.

Fig. 1. Microstructure of the tool steel after DTA

For the more detailed interpretation of the microstructure SEM and EDS mapping techniques were used. On the base of element distribution (Fig. 3) it is shown that eutectic colonies contain the vanadium carbide and ferrite. The white carbides localized at the boundaries between eutectic colonies are on the base of molybdenum carbide. The eutectic colonies are rich in molybdenum and chromium. Cobalt and tungsten are distributed uniformly in all phases in material.

Fig. 2. Detail of the microstructure

2.2 X-ray Diffraction Analysis X-ray diffraction pattern of sample after DTA is shown in Fig. 4. The following phases were observed: ferrite, MC carbide (vanadium type), M2C and M6C carbides (molybdenum types). Due to mixing of different substitutional atoms in carbide lattices the diffraction patterns of carbides are slightly shifted, compared to ICDD database [29] and [30].

Moravčík, R. – Štefániková, M. – Čička, R. – Čaplovič, L’. – Kocúrová, K. – Šturm, R.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 709-715

Mapped image (SEM)

C Kα1,2

V Kα1

Cr Kα1

Fe Kα1

Mo Lα1

Co Kα1

W Lα1

Fig. 3. Element mapping of high alloy tool steel, showing distribution of C, V, Cr, Fe, Mo, Co and W Phase Transformations in High Alloy Cold Work Tool Steel

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5 represents the transformation from ferromagnetic to the paramagnetic state (781 °C). The second endothermic peak (onset 856 °C) can be considered as the transformation of ferrite to austenite. Next peaks characterize the melting of the present phases. The melting begins at 1209 °C, and the end of melting the temperature is about 1389 °C. 2.4 Dilatometry Analysis

Fig. 4. X-ray diffraction pattern

2.3 Differential Thermal Analysis and Thermomagnetometry Figs. 5 and 6 show DTA curves during heating and cooling of sample, respectively. The first peak in Fig.

The dilatometry curve of analysed tool steel is shown in Fig. 7. The onset around temperature 660 °C is possibly caused by dissolving the secondary carbides in matrix. The steep decrease in length corresponding to the transformation of ferrite to austenite is present at about a temperature of 832 °C. DTA curve during cooling (Fig. 6) shows that solidification proceeds in three steps. Solidification probably begins by austenite formation from

Fig. 5. DTA curve of the investigated high alloy tool steel during heating

Fig. 6. DTA curve of the investigated high alloy tool steel during cooling

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Fig. 7. Dilatometry curve of analysed tool steel during heating

Fig. 8. Thermomagnetometry curves

undercooled melt at a temperature of 1340 °C. The solidification continues with two eutectic reactions.

During the first reaction probably eutectic with vanadium carbides is formed (at 1327 °C). During the second reaction the eutectic with molybdenum carbides is formed (at 1214 °C). The solidification is finished at a temperature of 1208 °C. Fig. 8 shows the TM curve during heating and cooling of sample.

About the temperature 780 °C the transformation from paramagnetic to ferromagnetic state is seen.

During heating the curve slowly decreases from 1110 °C, probably due to dissolution of paramagnetic MC carbides. The cooling curve shows that at 486 °C also some secondary carbides form.

3 DISCUSSION During heating of the high alloy cold work tool steel K390 Microclean the first secondary carbides start to dissolve in matrix at 660 °C. The transition from ferromagnetic to paramagnetic state takes place at

781 °C (determined by DTA) or 783 °C (determined by TM). Then, the transformation of ferrite to austenite at a temperature of 856 °C (determined by DTA) occurs.

This temperature is higher than the temperature of ferrite to austenite transition determined by dilatometry (832 °C), probably due to higher heating rate at DTA measurements. Melting process of tool steel begins at temperature 1209 °C and continues in three steps. The first step is probably the melting of molybdenum carbide eutectics at 1209 °C. They are localised on the boundary of eutectic colonies Melting of the material continues by melting of vanadium carbide eutectic colonies. Finally, melting finishes when the last amount of austenite is dissolved in the melt at temperature 1389 °C. Also, solidification of the material proceeded in three steps. In undercooled melt the austenite grains grow at the temperature 1340 °C. Next, solidification continues by the evolution of eutectic colonies based on the vanadium carbide (starts at 1327 °C).

Molybdenum is diffusing to the melt and in the

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last step of solidification the molybdenum carbide eutectics at the boundaries are formed. The cooling in solid state shows only two transitions in TM curve.

The first change is the transition from paramagnetic to ferromagnetic state at 793 °C and the second one is the formation of the secondary carbides in the matrix at 486 °C. The resulting microstructure is mainly dendritic where most dendrites consist from vanadium carbide eutectics. At the boundaries molybdenum carbide eutectics are localised. The small amount of austenite dendrites was also present. This type of microstructure is quite differrent compared to [11], [16] to [18], [22], [23], [27], [28], [31] and [32], where microstructures containing a large amount of austenite dendrites or a large amount of primary carbides in dependence from the chemical composition of the ledeburitic tool steels are present.

4 CONCLUSIONS The aim of the article is to describe the phase transformations in high alloy cold work tool steel K390 Microclean during slow heating and cooling.

These conditions are different compared to those used in production of the alloy steels, but they enable a description of the solidification and phase transitions in quasi-equilibrium conditions.

The microstructure of high alloy cold work tool steel has a dendritic morphology, however, dendrites consists from eutectic colonies based on the vanadium carbides. On the boundaries there are localised molybdenum carbide eutectics. The transformation of austenite to ferrite occurs at about 830 °C. The transition from ferromagnetic to paramagnetic state is about 780 °C. The knowledge about the quasi-equilibrium phase transformations in high alloy cold work tool steel can help to a better understanding of processes occurring in the material during the heat treatment. The obtained results extend the data obtained by others authors related to ledeburitic tool steels [1], [11], [16], [17], [23], [27], [31] and [32]. The results may be useful for the next thermodynamic analysis of phase transitions using the Thermo-Calc and Dictra software.

5 ACKNOWLEDGEMENTS The authors would like to thank to the financial support provided within the Program for Research and Development for the project Centre for Development and Application of Progressive Diagnostic Methods in the Process of Metallic and Non-metallic Material’s Processing, ITMS: 26220120048, co-financed by the 714

European Foundation for Regional Development.

This study was also funded by the Grant Agency of the Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences (VEGA) under the contract No. 1/0339/11.

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Analysis of microstructure and mechanical properties of selected binary and ternary lead-free bulk solders and soldered joints. COST Action MP0602 Advanced Solder Materials for High Temperature Application.

2010 Annual Meeting, International Doctoral Seminar: Proceedings, Trnava, p. 119-125.

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[28] Štefániková, M., Moravčík, R. (2010). Influence of the powder particle size on the microstructure of Cr-Mo-V tool steel compacts produced by hot isostatic pressing.

International Doctoral Seminar: Proceedings, Trnava, p. 502-511.

[29] Sales catalog 2012-2013 (2012). International Centre for Diffraction Data, from http://www.icdd.com/ products/pdf2.htm, accessed on 2012-04-12.

[30] Grazulis, S., Chateigner, D., Downs, R. T., Yokochi, A. T., Quiros, M., Lutterotti, L., Manakova, E., Butkus, J., Moeck, P. & Le Bail, A. (2009). Crystallography Open Database – an open-access collection of crystal structures. Journal of Applied Crystallography, vol. 42, p. 726-729, DOI:10.1107/S0021889809016690.

[31] Behulova, M., Grgac, P., Kabat, E. (1996) In: Duhaj P., Mrafko, P., Svec, P. (eds.). Proceeding of the 9th International Conference on the Rapidly Quenched and Metastable Materials, Bratislava, Elsevier, p. 10.

[32] Grgač, P., Kusý, M., Behúlová, M. (2010).

Microstructures developed during rapid solidification of tool steels of ledeburite type. COMEC, VI. Proceeding of the International Scientific Conference of Mechanical Engineering. Las Villas.

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Paper received: 2011-12-14, paper accepted: 2012-11-09 © 2012 Journal of Mechanical Engineering. All rights reserved.

Modeling and Simulation of a Chip Load Acting on a Single Milling Tool Insert

Gylienė, V. – Ostaševičius, V. Virginija Gylienė1,* – Vytautas Ostaševičius1 1 Kaunas University of Technology, Faculty of Mechanical Engineering and Mechatronics, Department of Engineering Design, Lithuania The paper presents experimental and numerical study of the end-milling process. The aim of this study is to define the force acting on a single cutting tool insert. It was accomplished by transforming cutting force signals from coordinate system of Kistler dynamometer into milling tool coordinate system.

In addition, a finite element model of the milling process was composed by adopting the hypothesis of the cut cross-section. Finally, finite element simulations were performed in order to determine the residual stress distribution across the depth of the machined surface.

Keywords: finite element (FE) modeling, end-milling, cross-cut section

0 INTRODUCTION Metal removal is a key technology in the aerospace and automotive manufacturing sectors, where the demand for high productivity and high accuracy is steadily increasing [1].

A large number of theoretical and experimental studies on surface profile and roughness of machined products have been reported. These studies show that cutting conditions, tool wear, the material properties of tool and workpiece, as well as cutting/process parameters significantly influence the surface finish of machined parts [2]. Geometrical deviations with respect to the nominal surface are associated with the changes in component shape, periodical surface irregularities and structural modifications. Residual stresses are considered as the fifth- and sixth-order deviations and are attributed to the physicochemical factors that influence the structural changes of the surface [2]. However, component processing by cutting induces stress gradients in the structure, which may have either a positive or negative effect on the component [3] and [4]. It is common that the residual stresses accompanied by the fatigue arising due to cyclic loading lead to the unexpected component fracture [4], while compressive stresses generated as a result of cutting operations are usually beneficial [5].

Therefore, it is of particular importance to consider residual stresses in those mechanical components that operate under conditions characterized by fatigue loading, e.g. parts in power stations, structures in aviation, etc. ([3] and [4]).

Evaluation of residual stresses is performed by taking into account the type of tested material, while specific characterization methods are selected based on a particular type of the residual stress ([4] and [6] to [8]). The need for evaluation of residual stresses is 716

associated with extensive application of numerical techniques based on the finite element (FE) method ([7] and [9] to [13]).

The influence of a cutting process on the formation of residual stresses is ambiguous. Increase of the residual stresses is related with the majority of machining parameters including cutting speed, depth of cut and tool edge radius [12]. However, the layer of removed material has the greatest effect on the formation of the residual stresses. Authors [5] defined that the superficial residual stresses at the surface slightly decreased when the rake angle increased from –5 to 5°. This decrease on superficial residual stresses with the rake angle was accomplished with a reduction of the thickness of the tensile layer [5] and [12]. On the other hand, when the uncoated tool was replaced by a coated one, the superficial residual tensile stresses increase by 240 MPa, when the highest cutting speed value was used [12].

Thus, numerical analysis is an attractive alternative for evaluating residual stresses allowing to substitute the application of high-cost experimental methods. On the other hand, some of the computational results do not correlate with the experimental findings [7].

In summary, despite the fact that there exists a large variety of different analytical, numerical and experimental techniques, currently there is no proven analytical model enabling to reliably predict the residual stresses that arise in the course of cutting operations [7].

For ensuring reliability of the developed FE model it must be verified against experimental data which includes magnitudes of the measured cutting force. Cutting force is a parameter which is also evaluated for the structural design of machine tools, selection of optimum cutting parameters, design

*Corr. Author’s Address: Kaunas University of Technology, Kęstučio st. 27, LT-44312 Kaunas, Lithuania, virginija.gyliene@ktu.lt

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of workpiece-holding fixtures, tool stress analysis, spindle bearing design, and the real time monitoring of tool wear and breakage [14].

This study proposes a FE model for a case of the milling process. The milling operation is performed by using end–milling tool – a cutting tool of complex geometry that is used for machining of curvilinear surfaces. Therefore, a FE model was constructed for performing mesoscopic analysis of the milling process in terms of the removed material cut cross-section.

Cutting forces were evaluated during experimental testing, while the effect of the cutting force on a single cutting insert was determined by means of a transformation matrix.

Furthermore, it was confirmed with respect to material deformation that it is necessary to apply several criteria for verification of the FE model [15].

Therefore, numerical analysis was carried out by using dynamic material characteristics taken from the available literature sources [16], meanwhile dynamic material deformation constants were acquired from the performed turning experiments [15].

Force measurements were performed according to cutting depth. In this paper, analysis will be performed only with respect to cutting depth. Scheme of experiments is presented in Fig. 1.

Workpiece was mounted on Kistler dynamometer, longitudinal cutting force was in axis Y, and transversal cutting force was in axis X. Equipment calibration was performed, using tension – compression setup Instron 5569.

Fig. 1. Milling experimental scheme from top

Dynamometer signal curves allowed to characterize a cutting process. It was observed that the influence of the cutting forces onto the cutter tooth is stable.

1 EXPERIMENTAL SETUP FOR END-MILLING End milling (or partial face milling) experiments were performed on a universal milling machine Dufour–164 (3–axis). Force measurement was executed using a 3–component piezoelectric force sensor - Kistler dynamometer 9257A. Workpiece material was steel AISI 1034 (or Afnor standard XC38). Cutter was 25 mm diameter with two uncoated carbide inserts (APKT 16 04 PD ER–43 from Stellram). No cutting fluids were used. Milling experiments were performed with the medium carbon steel. Its chemical composition and mechanical properties are presented in Table 1. Milling conditions are presented in Table 2.

Fig. 2. Milling tool position evaluation according to Kistler dynamometer coordinate system

In order to define the real influence on the cutting tool insert, the transfer of the measured forces from

Table 1. Chemical and mechanical properties of AISI 1034 steel a) Chemical composition of AISI 1034 steel (% weight) C 0.32 to 0.38

Fe 98.73 to 99.18

Mn 0.50 to 0.80

P ≤ 0.04

S ≤ 0.05

Cr ≤ 0.25

b) Mechanical properties of AISI 1034 steel Density [×1000 kg/m3] 7.8

Elastic modulus [GPa] 200

Strength limit [MPa] 698

Failure strain 0.72

Hardness HRC 35

Table 2. Cutting conditions Cutting speed [m/min] (calculated) 118

Spindle speed [rev/min] 1500

Feed [mm/th] 0.1

Feed rate [mm/min] 310

Width of cut [mm] 10

Modeling and Simulation of a Chip Load Acting on a Single Milling Tool Insert

Depth of cut [mm] 0.5; 0.75; 1.0

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dynamometer coordinate system into the tool system was executed.

Cutting force measurements were performed in the coordinate system of the dynamometer RK (0, XK, YK, ZK). Fig. 2 presents the explication scheme of the cutting tool coordinate system according to the Kistler dynamometer coordinate system.

In order to define the measured cutting force by dynamometer, the coordinate system transfer is expressed:

 − cos θ P =  sin θ  0

− sin θ − cos θ 0

0 0  . (1) 1 

The transfer of coordinate system is expressed:

[ X tool ] =  P −1  × [ X K ] . (2)

Finally, the total measured force is expressed in the tool coordinate system: r uuur uur n = − cos θ ⋅ X K + sin θ ⋅ YK r uur uuur

Rtool t = − cos θ ⋅ YK − sin θ ⋅ X K , Z tool = Z K where θ is an edge engagement angle [°].

The total cutting tool force in the horizontal plane was evaluated:

Transformation of the coordinate system enables establishment of the magnitude of a cutting force acting on a single tooth of the mill cutter. Fig. 3 provides measured longitudinal (Y direction) and transverse (X direction) resultant force variations in time according to Eq. (4). Fig. 3 indicates that the duration of cutting pass of a single mill tooth is approximately 0.01 s.

According to Eq. (3), Fig. 4 provides tangential and normal forces acting on the cutter tooth. Forces acting on a single mill tooth, which were measured and subsequently recalculated, are not equal because of possible differences in the mounting of inserts. → → In the case of end milling, forces Ft and Fn are equal to zero from θ = 0 and acquire maximum values 2 × ae  at θ = π − arccos 1 − , where D is the diameter D   of the cutting tool [mm] and ae width of cut. Finally, the forces diminish to zero upon tooth retraction from the material when θ = π.

As mentioned above, the 25 mm diameter tool cuts the width of cut of 10 mm. Therefore, in Fig. 4, it is observed that the cutting insert is not removing the material, while tool rotates 1.7 rad.

It is also observed from Fig. 4 that cutting force Ft when it reaches maximum cross-section of the chip is about 180 N. Normal cutting force Fn is about 145 N (variation between 130 and 160 N). For further FE analysis the average of cutting forces will be taken.

R 2 = FxK2 + FyK2 , (4)

where FxK, FyK are cutting forces measured by Kistler dynamometer in [V] X, Y plane workpiece system.

Only one milling tool insert was performing a cutting action at a time. Therefore, the force load onto a single cutting insert was estimated.

2 NUMERICAL STUDY OF MILLING PROCESS 2.1 Evaluation of Dynamic Behavior Law FE numerical software ANSYS as pre-processor and LS-DYNA as post-processor were used to compose FE geometrical model of the milling process and

Fig. 3. Total force action on a single cutting tool insert (cutting depth = 0.5 mm)

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Fig. 4. Tangential Ft and radial Fn force action onto a two milling inserts, during one milling tool rotation (cutting depth=0.5 mm)

define dynamic behavior of material subjected to cutting.

The classic tension experiments were performed to determine actual material characteristics, which are presented in Table 1. The obtained stress-strain relationship allowed to determine tangential modulus of elasticity; Et = 582.6 MPa. Dynamic effects of strain rates are taken into account by scaling static yield stress with the factor, assumed by Cowper - Symonds relation [16]:

1    ε  P   σ y = 1+   σ + β E p ε effp , (5)  C  y  

(

)

where ε = εij εij is a strain rate, and C, P constants of Cowper – Symonds relation.

The current radius of the yield surface, σy is the sum of the initial yield strength, σ0 plus the growth β E p ε effp , where Ep is the plastic hardening modulus:

Ep =

Et E , (6) E − Et

where Et is tangent modulus.

On the basis of the presented relation in Eq. (5), it is obvious that static and dynamic yield stress ratio depends on deformation speed. Isotropic, kinematic, or a combination of isotropic and kinematic hardening may be obtained by varying a parameter, called β between 0 and 1 [16].

Cowper–Symonds material deformation model is frequently used to perform simulations of dynamic processes by means of FE method.

Although the majority of material constants are determined by using a classical tension test, the largest problem is associated with determination of CowperSymonds constants C, P. The values of constants for the steel are taken as follows: C = 40 s–1, P = 5 [16].

The authors in the report [17] established the values of Cowper-Symonds constants at different deformation rates. Relative error of ca. 20% is obtained between the measured cutting force and its numerical value, which was calculated by applying dynamic constants provided in LS-DYNA library [18]. The cutting force, which was evaluated on the basis of constants obtained in [17] (C = 802 s–1, P = 3.585) and taking into account the average chip crosssection [19], is smaller by 10% [20]. The experiment for the turning process was carried out by machining a workpiece of the same material by applying cutting speed that was comparable in magnitude with that of the milling process ([15] and [20]). Therefore, further numerical analysis was performed by using the following constants: C = 220 s–1, P = 5. The influence of material strengthening coefficients on cutting force fluctuations and residual stresses was determined.

Failure strain was another parameter to define, which initiate the chip separation from workpiece in numerical calculation. Some authors claim that the magnitude of the fracture strain does not affect simulation results [21]. Thus, taking into consideration that in the course of the cutting process the material was subjected both to temperature effect and influences arising from high deformation rate, the actual failure strain value may be 1.16 to 1.75 times larger than its static equivalent [22]. For further FE analysis the value of 1.16 was considered. The friction coefficient was assumed to be 0.5.

2.2 Finite Element Modeling The milling process FE model was composed taking in account the Hulle theory and the following aspects: 1) the tool cuts by single cutting point, which removes the straight cross-section; 2) the direction of cutting force is perpendicular to cutting edge.

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Using ANSYS as pre-processor geometrical FE model was created, assuming rake angle (0°), clearance angle (11°), and edge radius 20 μm. Fig. 5 illustrates the composed FE model. Boundary conditions of the FE model were as follows. The workpiece was constrained in all 6 DOFs. Load of type U = f (t) (displacement according to time) was imposed on the tool with the purpose to simulate cutting motion with respect to cutting velocity.

The dimensions of workpiece were 2×0.2×0.75 mm. FE tool model was constrained using 'Swap' application. Geometric FE model contained 44112 nodes and 38512 elements.

SOLID164 elements were chosen, as they are used in explicit analysis, assuming large deformation speed and nonlinear contact. For composition of the geometric model, workpiece mesh size sensitivity study was performed [18]. The size of FE used to model workpiece was set to 0.02 mm. The size of FE was established after definition by modeling of force stability, as presented in [18]. This FE size influences time step, so mass scaling was adjusted to be –1.6 e–9 in order to reduce CPU time. A Lagrangian explicit analysis was performed. In LS-DYNA contact interaction between two bodies was formulated using “master–slave” methodology and penalty method. For selection and specification dynamic constants by FEM the problem is interaction of deformable body – rigid body. Deformable body is workpiece and defined as “slave” for contact search and chip separation in numerical analysis. A milling tool is a rigid body, assuming tool dynamics and defined as a “master” for contact search in explicit numerical analysis.

Fig. 5. FE model of milling process with removable cross-section geometric parameters

a) β = 0.2

3 FE MODELING RESULTS Analysis of isotropic, kinematic or a combination of both hardening models was performed in order to define their influence on residual stress and cutting force (tangential cutting force). This material hardening aspect was performed by defining parameter β (0 for kinematic, 1 for isotropic hardening). Fig. 6 presents calculated chip formation by FE method in time of 0.15 ms (time, when cutting forces are regular).

It is evident that material hardening coefficient does not affect the shape of chip in material removing. In addition to the variation of hardening coefficient in the range of 0.2 to 0.8 increase of cutting force up to 50 N is observed, (Fig. 7). Cutting force, calculated with β = 0.2 is 150 N (16% difference with experimental results). Cutting force, calculated with β = 0.5 is 175 N (3% difference with experimental results). Cutting force, calculated with β = 0.8 is 200 N (11% difference 720

b) β = 0.5

c) β = 0.8 Fig. 6. Chip formation according to material hardening in milling process, after cutting force stabilization

Gylienė, V. – Ostaševičius, V.

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Fig. 7 also presents cutting force fluctuations.

Numerically, these vibrations correspond to element deletion after reaching defined failure strain.

Physically these fluctuations correspond to chip separation from the material. For this reason it was proven to introduce not only cutting force estimation but also chip form [15] in order to validate FE analysis.

Numerical analysis of residual stresses was performed in the same distance (and in the longitudinal direction (X)) from the edge of the workpiece.

This analysis demonstrated that on the surface of machined layer tensile stress varies in the range of 300 MPa according to hardening coefficient. In addition, analysis revealed high compression stresses (close to –800 MPa) with material hardening coefficient β = 0.8. And in all cases of work hardening the maximum of stresses was obtained at depth of 0.04 mm. In all cases the stabilized zone according to longitudinal stresses is at the distance of 0.1 mm.

It should be noted that these surface stresses are evaluated by taking into account contact interaction, friction, material deformation rate as well as material strengthening. However, Cowper-Symonds material deformation model does not account for thermal effects.

Calculated residual stresses without temperature effect should be compared both with experimentally determined residual stresses as well as simulation results that take into consideration thermal effects.

The main application of the developed FE model is in the field of high-speed machining (HSM) processes. During these processes the residual stresses in the workpiece are formed due to tertiary deformation zone (contact interaction, friction are predominant factors). While only 17% of primary heat zone flows into the workpiece [23].

b) β = 0.2

a) β = 0.5

c) β = 0.8 Fig. 7. Calculated cutting force (tangential cutting force)

with experimental results). Elastic-plastic behavior with kinematic and isotropic hardening artificially increases material yield point. On the other hand, when forming a FE model by taking into account material strengthening it is possible to obtain either discontinuous, segmented or continuous chip (under particular deformation rate). It is observed that this significantly influences the variation of the cutting force.

4 CONCLUSIONS This paper reports the results of investigation of cutting forces that act on a single cutting tooth during milling process. Cutting force measurements were performed in the coordinate system of the Kistler dynamometer therefore a transformation matrix was applied in order to determine cutting forces acting on a single insert within the tool coordinate system.

Experimental results indicate that cutting forces are stable during the milling process. However, forces acting on a single mill tooth (which were obtained through the application of the transformation matrix) undergo fluctuations, which may be attributed to the

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different insert mounting conditions. Although the experiment was repeated four times, the expected effect of tool wear-out is discarded here because in this case it is unlikely: tool material used in experiments was a hard-metal [24], while the feedrate was comparatively low (0.1 mm/tooth).

The FE model for the milling process was developed by assuming the hypothesis of the removed cut cross-section. The tool was imposed with rectilinear motion. The presented simulation results are the continuation of earlier research work, which was concerned with the evaluation of the influence of material dynamic constants and fracture deformations on the process of chip formation. Selection of appropriate dynamic constants is a tedious and timeconsuming procedure, which requires specialized experimental investigations. On the other hand, the latter aspect is responsible for the increasingly widespread adoption of the approach based on the application of turning experiments as an attractive alternative for the testing procedures that are used to evaluate dynamic material constants. Numerical results obtained with the developed model, which uses material constants determined from Fig. 7 match experimental findings very well with an error of 3%.

Obtained numerical results correspond well to the measurements.

Numerical analysis enabled prediction of distribution of machining-induced residual stresses across the depth of the workpiece surface: maximal stress values are observed at 0.04 mm and they vanish at a distance of 0.1 mm from the surface.

Future research work will be targeted towards further verification of the developed models by comparing them with the Johson-Cook constitutive model for work material behavior and application of FE modeling in ultrasonically assisted manufacturing process [25] and [26].

5 ACKNOWLEDGEMENTS This research was funded by a grant (No MIP113/2010) from the Research Council of Lithuania.

6 REFERENCES [1] Shi, B., Attia, H. (2010). Current status and future direction in the numerical modeling and simulation of machining processes: A critical literature review.

Machining Science and Technology, vol. 14, no. 2 p.

149-188, DOI:10.1080/10910344.2010.503455.

[2] Chen, L. (2008). Study on prediction of surface quality in machining process. Journal of Materials

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Processing Technology, vol. 205, no. 1-3, p. 439-450, DOI:10.1016/j.jmatprotec.2007.11.270.

[3] Le Calvez, C. (1995). Thermal and Metallurgical Aspects of Carbone Steel Orthogonal Cutting. PhD Thesis. Ensam, Paris. (in French) [4] Withers, P.J., Bhadeshia, H.K.D.H. (2001). Residual stress. Part 1 – Measurement techniques. Materials Science and Technology, vol. 17, no. 4, p. 355-365, DOI:10.1179/026708301101509980.

[5] Outeiro, J.C., Dias, A.M., Jawahir, I.S., (2006). On the effects of residual stresses induced by coated and uncoated cutting tools with finite edge radii in turning operations. CIRP Annals - Manufacturing Technology, vol. 55, no. 1, p. 111-116, DOI:10.1016/S00078506(07)60378-3.

[6] Withers, P.J., Bhadeshia, H.K.D.H. (2001). Residual stress. Part 2 – Nature and origins. Materials Science and Technology, vol. 17, no. 4, p. 366-375, DOI:10.1038/35070640.

[7] Jawahir, I.S., Brinksmeier, E., M’Saoubi, R., Aspinwall, D.K., Outeiro, J.C., Meyer, D., Umbrello, D., Jayal, A.D. (2011). Surface integrity in material removal processes: Recent advances. CIRP Annals Manufacturing Technology, vol. 60, no. 2, p. 603-626, DOI:10.1016/j.cirp.2011.05.002.

[8] Mittal, S., Liu, C.R., (1998). A method of modeling residual stresses in superfinish hard turning. Wear, vol. 218, no. 1, p. 21-33, DOI:10.1016/S00431648(98)00201-4.

[9] Schulze, V., Autenrieth, H., Deuchert M., Weule, H. (2010). Investigation of surface near residual stress states after micro-cutting by finite element simulation.

CIRP Annals - Manufacturing Technology, vol. 59, no.

1, p. 117-120, DOI:10.1016/j.cirp.2010.03.064.

[10] Mohammadpour, M., Razfar, M.R., Jalili Saffar, R. (2010). Numerical investigating the effect of machining parameters on residual stresses in orthogonal cutting.

Simulation Modelling Practice and Theory, vol. 18, no.

3, p. 378-389, DOI:10.1016/j.simpat.2009.12.004.

[11] Dattoma, V., De Giorgi, M., Nobile, R. (2006). On the evolution of welding residual stress after milling and cutting machining. Computers & Structures, vol. 84, no. 29-30, p. 1965-1976, DOI:10.1016/j. compstruc.2006.08.008.

[12] Outeiro, J.C., Umbrello, D. M’Saoubi, R., (2006).

Experimental and numerical modelling of the residual stresses induced in orthogonal cutting of AISI 316L steel. International Journal of Machine Tools and Manufacture, vol. 46, no. 14, p. 1786-1794, DOI:10.1016/j.ijmachtools.2005.11.013.

[13] Rizzuti, S., Umbrello, D., Filice, L., Settineri, L. (2010). Finite element analysis of residual stresses in machining. International Journal of Material Forming, vol. 3, suppl. 1, p. 431-434, DOI:10.1007/s12289-0100799-8.

[14] Bhattacharyya, A. (2008). Predictive Force Modeling of Peripheral Milling. PhD Thesis, University of Florida, Gainesville.

Gylienė, V. – Ostaševičius, V.

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[15] Gylienė, V., Ostaševičius, V. (2010). FE modeling of orthogonal cutting process, assuming chip segmentation frequency. HSM-8 Conference Proceedings, p. 1-6.

[16] Hallquist, J.O. (1998). LS-DYNA Theoretical Manual.

Livermore Software Technology Corporation, Livermore.

[17] Bohdal, Ł., Kukiełka, L. (2006). The effect of selected material parameters on the stress and strain states in the process of cutting a sheet plate with circular cutters.

TASK Quarterly, vol. 10, no. 4, p. 391-400.

[18] Gyliene, V., Ostasevicius, V., Sergent, A. (2011).

Milling process study, assuming estimation of cutting force. Assembly and Manufacturing (ISAM), 2011 IEEE International Symposium. p. 1-7, DOI:10.1109/ ISAM.2011.5942363.

[19] Koenigsberger, F., Sabberwal, A.J.P., (1961). An investigation into the cutting force pulsations during milling operations. International Journal of Machine Tool Design and Research, vol. 1, no. 1-2, p. 15-33, DOI:10.1016/0020-7357(61)90041-5.

[20] Gyliene, V., Ostasevicius, V. (2011). Cowper-Symonds material deformation law application in material cutting process using LS-DYNA FE code: turning and milling.

LS-DYNA® 8th European User’s conference, p. 1-12.

[21] Hamann, J.C., Grolleau, V., Le Maītre, F. (1996).

Machinability improvement of steels at high cutting speeds-study of tool/work material interaction. CIRP

Annals-Manufacturing Technology, vol. 45, no.1, p. 8792, DOI:10.1016/S0007-8506(07)63022-4.

[22] Dey, S., Borvik, T., Hopperstad, O.S., Langseth, M. (2006). On the influence of fracture criterion in projectile impact of steel plates. Computational Materials Science, vol. 38, no. 1, p. 176-191, DOI:10.1016/j.commatsci.2006.02.003.

[23] Abukhshim, N.A., Mativenga, P.T. Sheikh, M.A. (2006). Heat generation and temperature prediction in metal cutting: A review and implications for high speed machining. International Journal of Machine Tools and Manufacture, vol. 46, no. 7-8, p. 782-800, DOI:10.1016/j.ijmachtools.2005.07.024.

[24] Fallbohmer, P., Rodriguez, C.A., Ozel, T., Altan, T. (2000). High-speed machining of cast iron and alloy steels for die and mold manufacturing. Journal Materials Processing Technology, vol. 98, no. 1, p.

104-115, DOI:10.1016/S0924-0136(99)00311-8.

[25] Ostaševičius, O., Gaidys, R., Gylienė, V., Jurėnas, V., Daniulaitis, V., Liepinaitis, A. (2011). Passive optimal tool structures for vibration cutting. Journal of Vibroengineering, vol. 13, no. 4, p. 769-777.

[26] Vijay, S.K.S., Pradeep, K.M. (2012). Optimising flow stress input for machining simulations using Taguchi methodology. International Journal of Simulation Modelling, vol. 111, p. 17-28, DOI:10.2507/ IJSIMM11(1)2.195.

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Paper received: 2012-07-20, paper accepted: 2012-10-05 © 2012 Journal of Mechanical Engineering. All rights reserved.

Customizing Products through Application of Group Technology: A Case Study of Furniture Manufacturing Suzić, N. – Stevanov, B. – Ćosić, I. – Anišić, Z. – Sremčev, N. Nikola Suzić* – Branislav Stevanov – Ilija Ćosić – Zoran Anišić – Nemanja Sremčev University of Novi Sad, Faculty of Technical Sciences, Serbia Satisfying customer needs becomes increasingly complex when a product customization element is included. This paper presents a case of transforming a manufacturing system, as a part of implementing mass customization strategy in the panel furniture manufacturing company.

The need for an effective implementation of customization strategy shows that shop-floor reconfiguration is necessary in order to produce what customer wants at a low cost and on time. One way of achieving this is to implement group technology approach, by creating product and machine groups and simplifying material flows. The aim of the presented study is to show an application of production flow analysis in the process of converting the mass production company to a mass customization system. The paper presents benefits of synergy created by using group technology and production flow analysis in enabling mass customized production.

Keywords: mass customization, group technology, production flow analysis

0 INTRODUCTION With an increased range of products offered on the global market, customers have an opportunity to choose what they want and even creating and designing their own products. Once exclusivity, offered only to buyers of luxury products, product customization today comes to a wider range of customers with an approach known as mass customization. Customer participation in product realization is becoming essential for market success [1]. Dealing with new market trends and an emergence of “markets of one” [2], production companies today must take mass customization into account in order to stay competitive. In order to organize production system to be suitable for the implementation of mass customization strategy, a company should consider issues related to optimizing the way the products are created.

The research conducted in this paper represents an effort towards successful implementation of mass customization strategy into the furniture industry company. The introduction of the mass customization strategy into the production system is based on successfully dealing with technical capabilities of the company on one hand and the needs and wishes of customers on the other. In order to achieve this goal, the application of group technology (GT) and production flow analysis (PFA) has been proposed.

The group technology appliance offers better control of the production process and is applied towards achieving optimal use of capacities and flexibility of the production system [3].

The first part of the paper brings the literature overview of mass customization and production flow analysis approach. The second part of the paper 724

shows the case study of the furniture company and implementation of mass customization in practice.

Conclusions provide advantages of proposed system organization.

1 LITERATURE OVERVIEW 1.1 The Mass Customization Concept Mass customization (MC) is a relatively new paradigm based on the production of customized products with mass production efficiency [2]. Emerged in late 20th century the paradigm is today more relevant than ever.

Companies which embraced this strategy in sales and production added a new value to their business [4].

This has proven as a good strategy for some small and medium enterprises (SME’s) [5] as well as for big multinational companies (Dell, Nike, Adidas, etc.) [6]. Nevertheless, implementation of mass customization strategy still presents a challenge for companies and dealing with the new combination of company resources is seen as crucial by many authors [7]. Although a number of companies proved that implementation of mass customization is possible, there is still a question of combination of factors that lead to the success of one but failure of another on the MC market.

Mass customizers are today able to customize products quickly for individual customers or for niche markets, in some cases responding to customer orders at greater speeds than a mass producer can. Using the same principles, mass customizers can Build-to-Order both customized products and standard products without forecasts, inventory, or purchasing delays.

The critical moments in mass customized production are product variety, product prices and

*Corr. Author’s Address: University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, Novi Sad, Serbia, suzic@uns.ac.rs

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period of the product delivery. These are factors relevant to the solution space mentioned by Piller and Tseng [8], which is to be determined by the production company. The variety of customized production is based on product families, modular or scaled, and product platforms, created either with top-down or bottom-up approach [9].

MC production is supported by configuration tools, either online (external) or offline (internal) [10].

The configuration tools enable the full capacity of mass customization and with usage of a good customer database can lead to enhanced customer loyalty [9].

In the work of Fain et al. [11] the important role of the user in product development is emphasized.

Furthermore, dealing with an optimal number of product variants becomes an important task of design process in production company [12].

The mass customized production is in practice realized with flexible production systems [13] able to deal with a variety of manufactured parts and adjustable assembly operations. In order to embrace mass customization production companies must determine the depth of the customization [14] which is suitable for company’s level of technology. In order to be successful in MC production a company must be successful in designing products, the marketing of products, create a functional configuration process and configuration tool, but first of all it should have a production configured in a way that can support the needs for product variety and individual orders.

1.2 Group Technology Group technology is an approach to production system organization which has existed for many decades.

Group technology first appeared in the book of Mitrofanov [15]. GT is based on the idea of grouping parts by using similarity. The approach results with cellular organization of machines in production systems [16] and [17]. This approach gave many benefits to solving problems like long lead times, large setup times, increased Work-In-Progress inventories, large inventories of finished goods, poor part quality and high unit costs, as shown in Wemmerlöv and Hyer [18] and in Wemmerlöv and Johnson [19].

Grouping of parts can be achieved in several ways, firstly through finding similarities in part geometry by using classification and coding system (C&C), but this method is not always the most suitable. Burbidge [20] indicates several reasons which make the use of classification and coding system unsatisfactory.

Such reasons lie in the facts that C&C system does not group machines, it also tends to group parts made of different materials and size, and is time consuming and complex. Grouping of parts can also be done by using part drawings which is known as the visual inspection method. This method is hardly practical as the part number grows. Another way of part group creation is by finding same processing technology steps that are shared by parts. Parts that have the same technological operations can be grouped together. This method is known as PFA which has been developed

by John. L. Burbidge [21] and [22]. PFA consists of several phases which include an analysis of material flow in the production system, forming part families and machine groups, analysis of material flows within cells and analysis of tools concerning the setup time reduction criteria. Several cases indicate the benefits of implementation of PFA and can be found in Wemmerlöv and Johnson [19] and [23], in Lee et al.

Fig. 1. Shop-floor process layout Customizing Products through Application of Group Technology: A Case Study of Furniture Manufacturing

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[24], in Ribeiro and de Araújo [25] and Hameri [26].

PFA has proven itself as a simple and efficient method to achieve cellular manufacturing organization.

2 CASE STUDY OF FURNITURE MANUFACTURING 2.1 Shop-Floor For the purposes of research a furniture production company was chosen. The chosen company produces panel furniture on mass production scale. Company produces 440 different products, such as wardrobes, beds, kitchen cabinets and all kinds of smaller pieces of furniture for the household. Shop-floor process layout with transport routes is given in Fig. 1.

Production starts with the cutting of basic shapes of wood panels for future product parts. The cutting operation consists of two cutting machines. The next phase of production is edge finishing which contains three distinctive machines for edge finishing. All three machines have different production and technology capabilities. Next, parts go to the drilling operation which contains three machines. Further into the process, two CNC centers are used for complex shapes of parts. The production process is finalized with visual control of parts, final control and packaging.

Special machining is done on some parts where special features, such as mirrors for an example, are assembled on them.

2.2 Market Research In order to determine the percents of customers who want customized products, market research is conducted. The goal of the research was to reveal the potentials of furniture market in the province in Serbia.

For the purposes of the research a questionnaire was composed. Main subjects of the research included: • Location of participants (showing geographical area in percents).

• Profile of participants (by gender, age, place of living and size of settlement).

• Preferences of furniture buyers (whether they plan to buy small or large pieces of panel or stylish furniture, or both kinds equally).

• Experiences with previous purchase of furniture (where do buyers most frequently go to buy the furniture, and how often does it happen that the offer of standard furniture does not match their needs).

• Properties of standard furniture offer that customers marked as inadequate (by color, dimensions, quality and functionality).

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Significance of customization to customers (whether they would like to have the option to customize their furniture during next purchase).

• Readiness of paying more and waiting longer for customized furniture.

• Internet usage and readiness to use the web in order to customize furniture.

The research has shown that: • The given market is oriented on panel furniture (63%).

• Furniture stores are the place where most buyers purchase their furniture (67%). If the buyer would not find what they were looking for they would go to a craftsman (carpenter). Only every tenth buyer goes directly to a carpenter.

• Dimensions (40%) and functional characteristics (48%) of furniture are the main properties with which customers were not satisfied in their past purchases. Mass customization can meet these needs very successfully.

• Majority of buyers (60%) would like to have the opportunity to change properties of furniture, and 33.3% more would like to have that option even if it would not mean a lot to them.

• The population of internet users in the region is satisfying (82%), and furthermore most of them (70.7%) would be ready to customize their furniture over the Internet.

The research has shown that there is a group of potential buyers of customized furniture ready to pay more and wait longer just to get a product that better fits their needs. Research has also shown that customer needs are not always met with standard panel furniture offer.

The need to embrace and implement mass customization has been recognized by company management. The first step in this process was to find a way to organize production system in a way which can support customization.

•

2.3 System Analysis The analysis of the system was done through several steps which consist of analysis of product assortment, machine line-up, material flow, as well as the technological capabilities of the machines.

This company is not a complex system in terms of PFA, so the company flow analysis was not necessary.

The analysis started with factory flow analysis (FFA).

The whole product assortment of 440 products was analyzed part by part. Every product and product part needs to be compared with similar products and parts from the production assortment. Similarities

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can be found in the attributes of material (such as thickness and color for example), the quality of material and compatibility of parts embedded into multiple products.

The product assortment was analyzed manually by using product explosion and parts material flow (production technology specifications). The production program is wide, but is mostly made up of parts that have similar processing. Fig. 2 shows a chosen example of five products from product assortment: the horizontal dresser, the wardrobe, the shelves, the vertical dresser and the computer table.

The whole product assortment is produced on a number of machines shown in Table 1.

which can have different thickness. Decomposing of 440 products led to the creation of 16 distinct part groups shown in Fig. 3, red represents processing done on each part group. The production process of the part groups, according to the routing can be seen in Table 2.

Table 1. The machine list Machine number 1 2 3 4 5 6 7 8 9 10 11* 12* 13* + 14*

Machine name Cutting machine One side edging machine Two side edging machine with gutter making option Two side edging machine Two side edging machine Drilling machine Drilling machine Drilling machine Multi-purpose machining center (drilling, cutting and trimming) Drilling machining center Visual control of parts and manual finishing Final control of products Special machining Packaging

* The numbers 11, 12, 13 and 14 represent the part operations done after the processing. + Special machining is done on some of the product parts (parts with mirrors, printing, etc.).

Fig. 2. The example of the product assortment part analysis

2.4 Creation of Product Part Groups Based on production technology, available machines and analysis of product parts the part groups were created. During the creation of the part groups, several things were taken into account, like the work operations that are needed to be performed on the machines, the efficiency of the machines and the sizes of the parts which are produced. The parts which, at a first glance, have very similar (almost identical) production technology specifications are classified into different groups because of their size (small, medium and big). All the parts are made of plywood,

Fig. 3. Derived part groups

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Table 2. Routing of part groups Part group 1 2 3 4 5 6 7 8 9 10 11 12

Technology sequence* 1 1-3 1-3-6 1-4-6 1-5-6 1-5-7 1-4-6 1-4-10 1-3-9 1-3-6 1-8 1-9

13 14 15 16

1-3-4-6 1-2-4-6 1-2-4-6 1-2-6

*The technology numbers correspond to the previously given machine list in Table 1.

Obtained part groups as well as their routing and available machines in the system led to the creation of material flow diagram for part groups Fig. 4.

Fig. 4. Material flow diagram for part groups

*There are two cutting machines in the production system. In the next matrix they will be presented separately as 1a and 1b cutting machines.

Fig. 5. The starting matrix

Fig. 6. Resulting incidence matrix - Division into machine groups

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2.5 Incidence Matrix (Clustering Analysis) According to PFA methodology, the starting matrix with machines and part groups is given in Fig. 5.

are treated in this way, so there was no need for tool scheduling in the cells.

2.6 Cell Formation In this initial setting part groups are assigned to machines according to routing criteria. However, some machines are capable of processing other part groups, for example all drilling machines are able to process all of the required parts. This means that the rotation of machines is a possible option for cell formation. In Fig. 6 the resulting incidence matrix is given. It shows that two cells can be formed with no exceptions in the cell formation.

In the process of cell formation some machines were replaced by equivalent machines capable of processing the given part groups. The replacement is done in groups 4, 7 and 8 which are moved from machine number 4 to machine number 5. Also, part groups number 4, 5 and 7 are moved from machine number 6 to machine number 7. Replacement from one machine to another was done with the intention of creating unraveled material flows, thus enabling the creation of the separate material flows and manufacturing cells. The replacement was done without a significant impact on machining time and machine efficiency since the characteristics of drilling machines are comparable and plywood parts are done with similar technology. On the other hand, the intention was to create notable savings in lead times with cellular organization. Lead times of parts are not affected with the machine changes since they will not considerably differ. On the other hand, lead times are impacted greatly by a significant decrease of unfinished production and queues brought by new production organization. This way, the forming of two distinct manufacturing cells is enabled (one cell for complex parts and the other one for less complex parts). Cells are created with no additional costs.

Material flow diagram for these two cells is shown in Fig. 7.

The FROM/TO matrices for two cells are shown in Fig. 8. The matrices show that there are no returning flows in the production system organized this way.

Tooling analysis (TA) as the part of PFA was not conducted because of the nature of manufacturing technology. In the panel furniture industry tools have a high level of standardization and unification; for example, drills used for shelf positioning are equal for all the products that company makes. All tool types

Fig. 7. Material flow diagram for cells

a)

b)

Fig. 8. FROM/TO matrices of manufacturing cells; a) for manufacturing cell 1, b) for manufacturing cell 2

3 CONCLUSIONS Mass customization production environment has evolved over the past two decades. It has developed in theory and as an industrial practice. In this paper, the presented research, theoretical as well as

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Fig. 9. Reconfiguration of shop-floor

that conducted in the industry, showed that mass customization is possible to achieve by implementing GT philosophy.

Implementation of GT principles through analysis of the system has led to a new layout presented in Fig. 9. Shop-floor has been divided into three work units: • Manufacturing cell 1 – for production of complex parts.

• Manufacturing cell 2 – for production of simple parts.

• Area for packaging and commissioning of modules.

This lead to increased effects in the sense of: • decreasing the set-up times (a decrease from 3 up to 10 times, depending on the machine), • simplifying the material flows in the system, • simplifying the launch of orders into the system, • shortening the lead times in the system (from 8 up to 12 times depending on the concrete part), • shortening transport ways and with it the transport times in the system (approx. twice), • decreasing the size of unfinished production and queues between the operations significantly.

However, full transformation from mass production to mass customization system cannot only rely on GT and does not end with shop floor transformation. Manufacturing cells are only the first step, and they enable better organization of production system. Having that in mind, in conclusion we propose the development of several systems (mainly software oriented) for mass customization: • web enabled product configuration tool, so that customers can configure its products in the meaning of choosing the material, customizing design and choosing special features, • implementation of ERP and PDM/PLM systems for an easier understanding of customer 730

• • •

•

needs, product and process data management, information sharing and collaboration, analyses and corrective measures [27], the development of software solution for part groups creation and scheduling in a customized production environment, RFID part tagging, so that every part can be tracked throughout its “life” in a shop floor, and in the warehouse, different manufacturing process execution scenarios simulation [29] and [30], for the prediction of possible problems and the evaluation of solutions, integration of previously mentioned tools and systems through heavy use of XML data representation, a similar solution can be found in the work of Šormaz et al. [28].

4 REFERENCES

[1] Rihar, L., Kušar, J., Duhovnik, J., Starbek, M. (2010).

Teamwork as a precondition for simultaneous product realization. Concurrent Engineering: Research and Applications, vol. 18, no. 4, p. 261-273.

[2] Davis, S.M. (1987). Future Perfect, Addison-Wesley Publishing Company, New York.

[3] Morača, S., Hadžistević, M., Drstvenšek, I., Radaković, N. (2010). Application of group technology in complex cluster type organizational systems, Strojniški vestnik Journal of Mechanical Engineering, vol. 56, no. 10, p.

663-675 [4] Gilmore, J.H., Pine, J.B. (1997). The Four Faces: Customization, Harvard Business Review, no. 75, p. 91101 [5] Piller, F. (2004). Mass customization: Reflections on the state of the concept. The International Journal of Flexible Manufacturing Systems, vol. 16, no. 4, p. 313-334, DOI:10.1007/s10696-005-5170-x.

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[6] Salvador, F., De Holan, P.M., Piller, F. (2009).

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Paper received: 2012-06-13, paper accepted: 2012-10-08 © 2012 Journal of Mechanical Engineering. All rights reserved.

Designs and Optimizations of Active and Semi-Active Non-linear Suspension Systems for a Terrain Vehicle Lajqi, Sh. – Pehan, S. Shpetim Lajqi1,* – Stanislav Pehan2

1 University

2 University

of Prishtina, Faculty of Mechanical Engineering, Kosovo of Maribor, Faculty of Mechanical Engineering, Slovenia

This paper introduces a design and optimization procedure for active and semi-active non-linear suspension systems regarding terrain vehicles. The objective of this approach is the ability to quickly analyze vehicles’ suspension performances resulting from passive, active, or semi-active systems. The vehicle is represented by a mathematical model regarding a quarter of it, and equations for motion are derived and solved by using MATLAB/Simulink. In order to verify the reliability of the derived computer program, a comparison is made with one of the comprehensive commercial software packages. The decision parameters of the active damping device are optimized by using the HookeJeeves method, which is based on non-linear programming. The usefulness of the treated active and semi-active systems on a concrete terrain vehicle is presented and compared with the presented passive systems by analyzing the vehicle’s body acceleration, velocity, displacement, and vertical tire force, namely those aspects that directly influence driving comfort and safety.

Keywords: vehicle design, active, semi-active, suspension system

0 INTRODUCTION The key issue for terrain vehicles is to ensure tire contact with the ground’s surface. In regard to specific ground roughness this can be ensured by more or less comprehensive suspension systems. The suspension system physically connects the vehicle’s chassis with its wheels, cushions all the ground loads to the vehicle, thus enabling the vehicle to be driven, braked, and steered in reasonable comfort and safety.

The suspension system is fixed onto the vehicle’s chassis and consists of the wheels with tires, springs, shock absorbers, and a few rods and linkages, as well as the steering system, Lajqi et al. [1] and Pehan et al. [2]. The driving comfort is directly related to the vehicle’s vertical body acceleration. Driving safety is dependent on the quality of the contact between the tires and the ground surface, and so the wheels should remain in contact with the ground’s surface as firmly as possible, Belingardi and Demic [3]. Designers devote particular attention to suspension systems in order to improve the characteristics of both driving comfort and driving safety.

The vehicle suspension systems are categorized as passive, active, and semi-active systems, Lajqi et al. [4] and Senthil [5], Fig. 1.

The passive suspension system includes, besides the mechanism, at least one of the conventional spring and shock absorber, Fig. 1a. The spring has linear or non-linear characteristics, whilst the shock absorber exhibits a non-linear relationship between force and relative velocity. In general, the hydraulic shock absorbers are used in vehicles. They work on the principle of fluid friction, Eslaminasab [6]. The 732

damping effect in a hydraulic shock absorber is created by fluid-flow through orifices that are small holes in the shock absorber’s piston. The characteristics of the springs and shock-absorber are immutable and cannot be adapted to any momentary operational condition of the vehicle. Thus the vehicle’s performance is very limited and any improvements can only be made by the optimization of springs’ and shock absorbers’ characteristics. Even though these suspension systems do not fulfill all the expectations regarding comfort and safety, they are widely used. In order to better control vehicle performance under various operational conditions, the presented concept has been developed for an active suspension system, Fig. 1b.

This active suspension system, in addition to the already described components, is also comprised of an actuator, sensors, and a control programming unit (CPU). Actually, the shock absorber is replaced by an active force actuator. The operational conditions of the vehicle are continuously controlled by sensors that measure the velocity of the sprung and un-sprung masses and lead it to the CPU that ensures correct impulses for the actuator, which creates the desired active damping forces when required.

The semi-active suspension system is based on passive and active systems. The presented one contains instead a passive shock absorber, and a variable shock absorber as an active damping force that is automatically controlled by an integrated regulator. The damping force is modulated in accordance with the operational conditions, which are continuously controlled by sensors connected to CPU. The correct damping force can be ensured by adjusting the orifice area within the shock absorber,

*Corr. Author’s Address: University of Prishtina, Faculty of Mechanical Engineering, Bregu i Diellit p.n., 10 000 Prishtinë, Kosovo, shpetim.lajqi@uni-pr.edu

StrojniĹĄki vestnik - Journal of Mechanical Engineering 58(2012)12, 732-743

Fig. 1. Quarter vehicle models; a) passive, b) active, and c) semi-active suspension systems

by which the resistance of fluid flow is adapted, Wong [7]. Variable shock absorber or electro-rheological and magneto-rheological are used widely Taskin et al. [8].

Owing to this device the suspension system becomes semi-active and offers great advantages under extreme driving conditions. When compared with the fullyactive system, the semi-active suspension system requires less energy, is cheaper, the simplest in design, and provides other competitive performances when compared to passive systems, Karnopp et al. [9], Pajaziti [10], Lin and Kanellakopoulos [11], Yi and Song [12], Popovic et al. [13], and Turnip et al. [14].

After short descriptions of different suspension systems, the attention of this paper now focuses on the active and semi-active systems. These systems ensure better performances (driving comfort and driving safety) than passive suspension systems.

The key problem regarding the active and semiactive suspension systems is when determining the optimal active damping force. This force depends on the operational conditions that come from the sensors. CPU controls the actuator or variable shock absorber for producing adequate damping force. The actuator or variable shock absorber needs to respond quickly and precisely. The focus of this paper is a mathematical model of the active damping force and its optimization. The optimization process for design parameters is done by non-linear programming using the stochastic parametric optimization method, Pajaziti [10] and Demic et al. [15]. Optimal design parameters are obtained when the objective function reaches minimal values.

The main characteristic of terrain vehicles suspension systems is their very extensive wheel movements that require sufficient space because of collision risk. Design-effective suspension is an iterative process. Firstly, the designer should conduct

quick and simple analyses in order to estimate the basic geometrical characteristics of the key components. Then, they must create a 3D-model of the suspension in order to prevent the possibility of collisions. In the following steps the componentâ&#x20AC;&#x2122;s design is improved and its strength is computed until the results are acceptable. At this point the designer decides which passive, active or semi-active system is the more suitable. To help the designer make the correct decision, it would be useful to have an effective tool for simulating those suspension characteristics that depend on essential suspension parameters. One of the well-established models for understanding and explaining vehicle suspension is the so-called quarter vehicle model (QVM), Yu and Yu [16] and Ram Mohan Rao et al. [17], Fig. 1.

The QVM is comparatively easy to transform into a mathematical model that actually consists of two second-order differential equations that can be solved in analytical or numerical ways.

Due to simplicity (in special cases it is allowed) it is assumed that the spring and tire stiffness coefficients remain at constant values. At this stage a powerful computing program is needed to calculate the suspension behavior and its characteristics. It is supposed that considering only the vertical ground excitation would provide usable results. Any potential longitudinal and lateral excitations that may arise during vehicle movement are neglected.

The results are the diagrams of accelerations, velocities, displacements and forces at different locations that represent the sensitivities of responses depending on the ground excitation and other parameters. These diagrams would help the designer to evaluate the influences of chosen parameters on driving comfort and safety. By considering these,

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consecutive modifications could be made quicker and more reliably.

d  ∂Ek  dt  ∂zs

 ∂Ek δ W = , (1) −  ∂zs δ zs

1 MATHEMATICAL MODELING OF THE VEHICLE SUSPENSION SYSTEM

d  ∂Ek  dt  ∂zu

 ∂Ek δ W = . (2) −  ∂zu δ zu

The quarter-vehicle model consists of two masses, two springs, one or two shock-absorbers and probably an actuator, Fig 1. The lower mass is the un-sprung mass mu, and the upper one is the sprung mass ms. The un-sprung mass represents one wheel assembly mass, whilst the sprung mass represents approximately ¼ of the remaining total vehicle mass. The lower springs and shock absorber are described by the tire stiffness kt or kt1, kt2, kt3, and the tire damping ct. The tire damping is often neglected due to its insignificant influence on the final results, Jazar [18]. The complete suspension system is represented when the spring and the shock absorber are inserted between two masses. The spring stiffness and shock absorber damping coefficients are denoted by ks or ks1, ks2, and csh or csh1, csh2. The lower or un-sprung mass is excited by the ground surface zr through the tires’ contact.

Forces that act within suspension systems can be described by linear or non-linear characteristics, Fig. 2. Due to experiences, the real behavior is described better using the non-linear characteristics. Below, the mathematic models are detailed for passive, active, and semi-active suspension systems.

The kinetic energy Ek is determined by the following expression:

1 1 ⋅ ms ⋅ zs2 + ⋅ mu ⋅ zu2 . (3) 2 2

The derivatives of Lagrange’s equations can be written as follow:

∂E d  ∂Ek  zs , k = 0,   = ms ⋅   ∂zs dt  ∂zs  (4) ∂Ek d  ∂Ek  = 0. zu ,   = mu ⋅  ∂zu dt  ∂zu 

The elementary work δW is given by the following expression:

δ W = − ( Fs + Fsh ) ⋅ δ zs + ( Fs + Fsh − Ft ) ⋅ δ zu . (5)

The elementary work during a virtual displacement of sprung mass δzs, and un-sprung mass δzu, is expressed as:

1.1 Passive Linear and Non-linear Suspension Systems The linear and non-linear models of the passive quarter-vehicle used for simulation of the terrain vehicle’s suspension, is shown in Fig. 2.

Ek =

δW δW = − ( Fs + Fsh ) , = Fs + Fsh − Ft . (6) δ zs δ zu

The linear forces that act in the suspension system, such as; dynamic tire force Ft, spring force Fs, and shock absorber damping force Fsh, are determined by the following expressions:

Ft = kt ⋅ ( zu − zr ) , (7)

Fs = k s ⋅ ( zs − zu ) , (8)

Fsh = csh ⋅ ( zs − zu ) . (9)

With a few mathematical rearrangements Lagrange’s equations for the passive linear suspension system can be written as follows: ms ⋅  zs = −k s ⋅ ( zs − zu ) − csh ⋅ ( zs − zu ) , mu ⋅  zu = k s ⋅ ( zs − zu ) + csh ⋅ ( zs − zu ) − kt ⋅ ( zu − zr ) .

Fig. 2. The passive quarter vehicle model

Eq. (10) can be expressed in matrix form:

For the presented QVM the differential equations of the motion are derived at by applying Lagrange’s equations, Jazar [18]: 734

Lajqi, Sh. – Pehan, S.

(10)

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 732-743

zs   −csh csh   zs   ms 0    =  0 m  ⋅   ⋅ + u   zu    csh −csh   zu  (11) ks  −ks   zs   0  +  ⋅   +   ⋅ zr .  k s −( ks + kt )  zu  kt 

Non-linear behavioral forces that act in suspension are determined by the following expressions, Pajaziti [10] and Demic [19]: Ft = kt1 ⋅ ( zu − zr ) + kt 2 ⋅ ( zu − zr ) − kt 3 ⋅ ( zu − zr ) , (12) 2

3

Fs = k s1 ⋅ ( zs − zu ) + k s 2 ⋅ ( zs − zu ) , (13) 3

Fsh = csh1 ⋅ ( zs − zu ) + csh 2 ⋅ ( zs − zu ) sign ( zs − zu ) . (14) 2

Differential equations of motion for passive nonlinear suspension systems are:

ms ⋅  zs = −k s1 ⋅ ( zs − zu ) − k s 2 ⋅ ( zs − zu ) − 3

−csh1 ⋅ ( zs − zu ) − csh 2 ⋅ ( zs − zu ) sign ( zs − zu ) , 2

mu ⋅  zu = k s1 ⋅ ( zs − zu ) + k s 2 ⋅ ( zs − zu ) + 3

(15)

+csh1 ⋅ ( zs − zu ) + csh 2 ⋅ ( zs − zu ) sign ( zs − zu ) − 2

− k t 1 ⋅ ( zu − z r ) − k t 2 ⋅ ( zu − z r ) + k t 3 ⋅ ( zu − z r ) , 2

The main problem concerning the alreadymentioned systems is to determine an optimal active damping force. In this paper, this is done by adding two apparent passive shock absorbers. The first one is fixed on the sprung mass, whilst the other is fixed on the un-sprung mass. The second fixingpoint of both shock absorbers is fixed in the fictive hook on the sky. The damping force caused by the first apparent shock absorber bs, always acts in the opposite direction to the velocity of the sprung mass, whereas the other damping force produced by the second apparent shock absorber bu, always acts in the same direction as the velocity of the un-sprung mass.

In reality, any addition of the skyhook approach is impossible because hooking the shock absorber onto the sky is also not possible. The real implementation of the skyhook approach is possible by using an active actuator installed between the sprung and un-sprung masses, Fig. 3. In this case the active damping force is described by the expression:

3

zu , zu , zu denote the zs , zs , zs and  where  acceleration, velocity, and displacement of the sprung and un-sprung masses, respectively. Whilst (zs – zu), (zu – zr), and ( zs – zu ), represent suspension travel, tire deflection, and relative velocity of the shock absorber. Eqs. (10), (11) and (15) represent a system of second-order non-homogeneous linear differential equations of the motion for linear and non-linear passive suspension systems, respectively.

Fa = −bs ⋅ zs + bu ⋅ zu , (16)

where bs and bu denote the damping coefficients of the apparent shock absorbers fitted between the sprung or un-sprung masses and the “sky” hook. The damping coefficients bs and bu are determined by an optimization process. The active damping force Fa given by Eq. (16) can be rewritten as follow:

Fa = bu ⋅ ( zu − zs ) − bs (1 − bu / bs ) ⋅ zs , (17)

where the first member, ( zu – zs ) of Eq. (17) relates to the relative velocity of the active actuator, whilst the second member relates to the absolute velocity of the sprung mass.

1.2 Active and Semi-Active Non-linear Suspension Systems Several attempts and studies on the active and semiactive suspension systems have been performed over the past years to improve driving comfort and driving safety. From the literature review it can be concluded that the active and semi-active systems can provide substantial improvement over the passive systems, in general, Karnopp et al. [9], Pajaziti [10], Lin and Kanellakopoulos [11], Yi and Song [12], Popovic et al. [13] and Turnip et al. [14]. Consequently, a CPUcontrolled active system for adjusting damping force has been implemented. Several control strategies have been developed for the semi-active, such as on-off skyhook, on-off ground-hook, continuous skyhook, fuzzy logic control, Abramov et al. [20].

Fig. 3. Skyhook concept for active and semi-active non-linear suspension systems

In order to fulfill requirements dealing with the active system, the priority is given to the hydraulic

Designs and Optimizations of Active and Semi-Active Non-linear Suspension Systems for a Terrain Vehicle

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active actuators. For semi-active suspension system dealing with variable shock absorber, a regulation of the damping characteristic by using servo-valve will be considered.

The dynamic equations of motion for the active non-linear suspension system derived from Fig. 3, and the employed Lagrange’s Eqs. (1) and (2) are rewritten as follows: ms ⋅  zs = − Fs − Fa , (18) mu ⋅  zu = Fs + Fa − Ft .

semi-active non-linear suspension systems. Whereas for other systems the procedure is the same, here only the output results are given, as obtained from simulation. To speed-up the numerical procedures, the differential equations of motion need to be transformed into more suitable formats, Lavrec and Kastrevc [21]. Eq. (10) is transformed into the state variable equations by simplifying the second-order differential equations into first-order differential equations. It is supposed that the state space variables are given by the following expressions: = x1 z= z= z= zu , s , x2 u , x3 s , x4 (20) dx= x= zs , dx= x= zu , dx3 =  zs , dx4 =  zu .

1 3 2 4

The dynamic equations of motion for semi-active, non-linear suspension systems generate the following form: ms ⋅  zs = − Fs − Fa ,   IF ( Fa ⋅ Fsh ) ≤ 0 − ON mu ⋅  zu = Fs + Fa − Ft .  ms ⋅  zs = − Fs − Fsh ,   IF ( Fa ⋅ Fsh ) > 0 − OFF  mu ⋅ zu = Fs + Fsh − Ft .

By substituting Eq. (20) into Eq. (10), the space state equations are written as follows: (19)

The tire force Ft, spring force Fs, and shockabsorber force Fsh, are determined by the non-linear Eqs. (12), (13) and (14).

The ON-OFF skyhook control given in Eq. (19) presents an effective vibration control strategy. The CPU-respond IF (Fa × Fsh ≤ 0) causes shock absorber adjustment in the high-damping state. The CPUrespond IF (Fa × Fsh > 0) causes the shock absorber adjustment in the low-damping state. Adjusting the shock absorber within high or low states depends on the product regarding the relative speed of the shock absorber ( zs – zu ) and the absolute speeds of the sprung and un-sprung masses ( zs and zu ). If this product is zero or negative, the shock absorber is adjusted to a high state, otherwise it is set to a low state.

Eqs. (18) and (19) represent a system of secondorder non-homogeneous non-linear differential equations regarding the motions for non-linear active and semi-active suspension systems, respectively.

2 VEHICLE SUSPENSION SIMULATIONS

BY NUMERICAL METHODS In order to solve the differential equations of motion for the general case of ground excitation, it is more than necessary to have an efficient tool to speed-up the numerical procedures. Numerical simulations have been developed for all the presented suspension systems. A methodology is presented for solving differential equations of motion for passive linear and 736

 0  dx  1  0 dx   k  2 − s  = m s  dx3   dx4   k  s  mu

0 0 ks ms

−

( k s + kt ) mu

1 0 c − sh ms csh mu

0 1 csh ms

    .  csh   − mu  (21)

 0   x1    x   0    ⋅  2  +  0  ⋅ { zr } .  x3   k   x4   t   mu  The state space variables for the semi-active nonlinear suspension system derived from Eq. (19) are expressed as Eq. (22).

Eq. (21) represents the general form of the state space equations of the passive linear suspension system in matrix form, whilst Eq. (22) shows state space equations for a semi-active non-linear suspension system.

The equations of motion are performed within a MATLAB/Simulink environment. The flowchart diagram is presented in Fig. 4. The solving program starts by reading the suspension parameters, ground excitation, the number of input and output variables, initial conditions, and the number of iterations (time).

Then, the program continues to solve differential equations of motion by applying the Runge-Kutta method. The program is stopped when the iterative condition is fulfilled. The results are presented using diagrams. The output results, depending on time, are the accelerations, velocities and displacements of the

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 732-743

sprung mass. The program also computes vertical tire forces, which act between the ground surface and tire.

Osman [23] have used similar functions for ground excitation as described here.

3 THE PROGRAM VERIFICATION

dx1 = x3 = zs , dx2 = x4 = zu ,

If ( Fa ⋅ Fsh ) ≤ 0 − ON

In order to certificate the presented computer program, the results are compared to those done by commercial Working Model Software. Input data are: ms = 295 kg, mu = 39 kg, ks = 55227 N/m, csh = 5230 Ns/m, and kt = 201441 N/m. These characteristics are taken from a real terrain vehicle, which is at the development stage, Lajqi [24]. A graphical model of the vehicle suspension system is made into a Working Model (WM) environment, Fig. 6. The data correspond to the one explained above.

( HIGH STATE )

dx3 =  zs = 3 −k ⋅ ( x − x ) − k s 2 ⋅ ( x1 − x2 ) +  = (1 / ms ) ⋅  s1 1 2 , +bs ⋅ x3 − bu x4  dx4 =  zu =

k s1 ⋅ ( x1 − x2 ) + k s 2 ⋅ ( x1 − x2 )3 −    = (1 / mu ) ⋅ −bs ⋅ x3 + bu ⋅ x4 − kt1 ⋅ ( x2 − zr ) −  .   2 −kt 2 ⋅ ( x2 − zr ) + kt 3 ⋅ ( x2 − zr )  If ( Fa ⋅ Fsh ) > 0 − OFF

( LOW

STATE )

dx3 =  zs =

(22)

−k s1 ⋅ ( x1 − x2 ) − k s 2 ⋅ ( x1 − x2 )3 −    = (1 / ms ) ⋅ −csh1 ⋅ ( x3 − x4 ) − ,   2 −csh 2 ⋅ ( x3 − x4 ) sign ( x3 − x4 )  dx4 =  zu = k s1 ⋅ ( x1 − x2 ) + k s 2 ⋅ ( x1 − x2 )3 +    +csh1 ⋅ ( x3 − x4 ) +    2 = (1 / mu ) ⋅ +csh 2 ⋅ ( x3 − x4 ) sign ( x3 − x4 ) −  .   2 −kt1 ⋅ ( x2 − zr ) − kt 2 ⋅ ( x2 − zr ) +    3 + kt 3 ⋅ ( x2 − zr )  The output results are within the function of ground excitation that represents road profile or the so-called road bumps. In this paper the ground excitation is demonstrated by two repeated smooth obstacles on a flat road, which is approximated by a smooth function, such as the cosine shown in Fig. 5.

Ground excitation zr(t) is written, as follows: 0.5 ⋅ H1 ⋅ 1 − cos ( 8π ⋅ t )  if t1 ≤ t ≤ t2     zr ( t ) = 0.5 ⋅ H 2 ⋅ 1 − cos ( 4π ⋅ t )  if t3 ≤ t ≤ t4 (23)  else , 0 where, H1, H2 are amplitudes of the first and second bumps. A few authors such as Rill [22] and Sam and

Fig. 4. Flowchart diagram for solving the differential equations of the motion

Fig. 5. Ground excitation represented by double cosine road bumps

The WM environment mimics the “Suspension Test Rig”. Because of the WM limitations, the ground excitation is assumed to be pure sine in nature,

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Fig. 6. a)“Suspension Test Rig” and b) simulation of the ground excitation as a function of time, as performed by the Working Model Software

Fig. 7. Simulation of the displacements of the sprung and un-sprung masses, performed by a) WM and b) MATLAB platforms

Fig. 8. Velocities for sprung and un-sprung masses, performed by a) WM and b) MATLAB platforms

and only the passive linear suspension system is considered. The ground excitation is theoretically simulated by the installation of an hydraulic actuator which produces vertical motion corresponding to the pure sine function: zr(t)=0.1× sin(2t).

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The “Suspension Test Rig” and simulation of ground excitation as a function of time within a WM environment are shown in Fig. 6.

Figs. 7 and 8 show the simulation results in the form of displacements and velocities that correspond

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 732-743

to the sprung and un-sprung masses as a function of time. It is obtained by WM and MATLAB platforms, respectively.

Finally, the displacements and velocities of the sprung and un-sprung masses are compared, as obtained by different approaches.

It is concluded that the program done in MATLAB generates as sufficient precise and reliable results as those produced by the comprehensive commercial WM platform. Consequentially, it can be concluded that the developed program is suitable for use in further analysis of the vehicle’s suspension behavior.

4 OPTIMIZATION OF PARAMETERS FOR THE ACTIVE DAMPING FORCE

A block-scheme for the proposed procedure is shown in Fig. 9. The optimization method was programmed in Pascal language.

The objective function that enables minimization of the sprung and un-sprung masses’ vertical accelerations is written as follows: min f ( x ) =  z 2s +α ⋅  z u2 , (24)

where α is the weight coefficient that describes the influence ranking of the corresponding ground excitation (Eq. (23)) on the objective function “f(x)”.

In the presented case α = 5 is used.

The design variables’ limits are:

0 Ns/m ≤ bs ≤ 5000 Ns/m ,

0 Ns/m ≤ bu ≤ 2800 Ns/m .

(25)

The stochastic parametric optimization method is applied to ensure the optimal active damping force. This method is based on non-linear programming, by using Hooke-Jeeves method. The optimization procedures are carried out in this order: • simulation of the differential equations of motion, • definition of the objective function, • definition of the limit values of the design variables, • simulation of the ground excitation.

For simulation of the differential equations of motion given by Eqs. (15), (18) and (19), the used terrain vehicle’s suspension parameters are used, as shown in Table 1, Pajaziti [10] and Lajqi [24].

Table 1. Suspension parameters for simulation Suspension parameters Sprung mass Un-sprung mass Damping coefficient Linear damping coefficient Non-linear square damping coefficient Spring stiffness coefficient Linear spring stiffness coefficient Non-linear square spring stiffness coefficient Tire stiffness coefficient Linear tire stiffness coefficient Non-linear square tire stiffness coefficient Non-linear cube tire stiffness coefficient

Sym. ms mu csh csh1

Unit [kg] [kg] [Nsm-1] [Nsm-1]

Value 295 39 5230 3482

csh2

[Ns2m-2]

580

ks ks1

[Nm-1] [Nm-1]

55227 15302

ks2

[Nm-2]

2728

kt kt1

[Nm-1] [Nm-1]

201441 60063

kt2

[Nm-2]

42509

kt3

[Nm-3]

22875

Fig. 9. Flowchart of the optimization process Table 2. Initial and optimal design variables Characteristics Initial design: bs* [Nsm-1] bu* [Nsm-1] Optimal design: bs [Nsm-1] bu [Nsm-1] Objec. function: f(x) Nr. iteration

1st option

2nd option

3rd option

0.00 0.00

2500 1400

5000 2800

1895 2181 5.16×E-01 232

841 2512 4.57×E-01 221

1198 2607 5.05×E-01 201

The optimization procedure starts with three options of the initial values of the design variables.

The optimal values of the design variables are reached when the difference between two adjacent values of

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Fig. 10. Flowchart diagram for calculations of ground excitation, vehicle body accelerations, velocities, displacements, and vertical tire forces as function of time for active, semi-active, and passive systems

the objective function reaches 10-9. The initial and optimal values of the design variables are given in Table 2. The best results regarding active damping force Fa­ concerning comfort and safety were achieved in 2nd iteration process, where the design variables are bs = 841 Ns/m and bu = 2512 Ns/m.

5 TERRAIN VEHICLE SUSPENSION DESIGN BY USING MATLAB/SIMULINK Before the comprehensive suspension calculations, the conceived design must be carried out.

The flowchart diagram of the calculations done by MATLAB/Simulink is presented in Fig. 10. It explains in detail the accelerations, velocities, displacements, and forces calculation procedures powered by ground excitation, depending on time. The excitation is presented by repeated cosine road bumps.

The driving comfort is determined by the vehicle body’s acceleration (Fig. 12) Mastinu et al. [25] and Popp and Schienhlen [26], where the greater values are undesirable. The driving safety relates to the vertical tire forces acting between the ground surface and the tire (Fig. 15). The tire forces need to be as stable as possible, Belingardi and Demic [3]. If the vertical tire forces oscillate too much, then the contact between the tire and ground surface would be weak. Consequential the vehicle’s maneuverability and steering would be in 740

question. The vertical tire forces are strictly related to the active safety, Mastinu et al. [25].

Table 3. Description data of the road bumps Road data i

xi [m]

Li [m]

1 2 3 4 5

2.78 1.39 3.47 1.39 8.33

2.78 4.17 7.64 9.03 17.36

Double cosine road bumps H1 = 0.05 [m] H2 = 0.1 [m] for 20 [km/h] for 10 [km/h] ti=Li /v1 [s] ti=Li /v2 [s] 0.50 0.75 0.75 2.00 2.50 2.50 4.00 -

In order to describe the vehicle’s behavior as it runs over road bumps, the ground excitation is simulated by Eq. (23). The vehicle pass the first bump at a speed v1 = 20 km/h, and the second bump pass at a lower speed v2 = 10 km/h. In Table 3 the appropriate data is shown for the correct description of the ground excitation (road bumps) shown in Fig. 11.

Fig. 11 shows ground excitation derived from a cosine function with amplitudes H1 = 0.05 m and H2 = 0.1 m for two different vehicle speeds (v1 = 20 km/h and v2 = 10 km/h).

Figs. 12 to 15 show the appearances of the vehicle’s body accelerations, velocities, displacements, and vertical tire forces, depending on

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time, caused from double road bumps for passive, semi-active, and active non-linear suspension systems.

The non-linear vertical tire forces are composed from static and dynamic ones, given by the following expression: Fz ( t ) = Fsta + Ft = g ⋅ ( ms + mu ) +

+ kt1 ⋅  zu ( t ) − zr ( t )  + 2

+ kt 2 ⋅  zu ( t ) − zr ( t )  −

(26)

3

−kt 3 ⋅  zu ( t ) − zr ( t )  , where Fz(t) denotes vertical tire forces, Fsta is static force, and Ft is termed dynamic tire force.

Fig. 14. Vehicle body displacement as functions of time

6 DISCUSSION OF THE RESULTS Estimation of a terrain vehicle’s suspension system was performed by double cosine road bumps simulation. The vehicle passed over the first bump at an amplitude of 0.05 m and at a speed of 20 km/h, and the second bump at an amplitude of 0.1 m at a speed of 10 km/h, Fig. 11.

Fig. 11. Ground excitation as a function of time

Fig. 15. Vertical tire forces as functions of time

Fig. 12. Vehicle body acceleration as functions of time

Fig. 13. Vehicle body velocity as functions of time

This simplified form of the repeated road bumps is used for better understanding of the appearances of the vehicle’s body accelerations, velocities, displacements and vertical tire forces for active, semiactive, and passive systems.

Fig. 12 shows the vehicle’s body accelerations for passive, active, and semi-active non-linear systems.

The reference acceleration is the passive one. When the vehicle was passing over the first bump the active system reduced it by 40, 54 and 81% (depending on the location). The semi-active system reduced it by 31, 46 and 76% (depending on the location). Similar appearances were observed at the second bump, but the speed was lower and the amplitude higher. The same explanation can also be found in Figs. 13 to 15.

Fig. 13 shows the vehicle’s body velocities for passive, active, and semi-active non-linear systems.

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The reference velocity is the passive one. When passing over the first bump, the active system reduced it by 44 and 81%. The semi-active system reduced it by 36 and 71%.

Fig. 14 shows the vehicle’s body displacements for passive, active, and semi-active non-linear systems. The reference displacement is the passive one. When passing over the first bump the active system reduced it by 43%. The semi-active system reduced it by 38%.

Fig. 15 shows the vertical tire forces for passive, active, and semi-active non-linear systems. The reference force is the passive one. When passing over the first bump the active system reduced it by 45 and 54%. The semi-active system reduced it by 22 and 49%.

When the terrain vehicle equipped with active or semi-active systems drove over the road bumps at 10 and 20 km/h, the driving comfort (  zs < 4 m/s2) and the driving safety (Fz < ±1.4 g), according to Kuznestov et al. [27] were acceptable. When the terrain vehicle was equipped with the passive system, the acceleration and dynamic forces exceeded the limit. These excess values cause driving discomfort and have negative influences on safety.

It can be concluded that the active system provides better performance in comparison to the passive system on account of better isolation of the vibration. Due to the damping capability, the semiactive systems were less effective than the active ones, as can be seen from the presented diagrams.

7 CONCLUSIONS Earlier designs of active and semi-active non-linear terrain vehicle suspension systems were firstly explained in the presented paper. A simplified quarter vehicle model was then introduced, together with a suitably-created mathematical model for passive, active, and semi-active suspension systems.

A computer program for solving the differential equations of motion within a MATLAB/Simulink environment was carried out. Road ground excitation was modeled using two repeated cosine bumps and flat lines. Optimal design parameters for active damping force generation were determined by the stochastic parametric optimization method, which is based on non-linear programming.

Suspension performances were optimized by maximizing driving comfort and safety. The results are presented in diagram form. Each one was obtained by solving differential equations of motion for passive, active, and semi-active non-linear systems.

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The optimal damping forces were provided by the so-called active suspension system that displayed even better behavior than the semi-active one. The result from the optimization procedure was an active suspension system with soft characteristics. Small dynamic tire forces enabled good contact with the ground whilst at the same time ensuring better driving comfort. The active suspension system improved the driving characteristic by up to 80% compared to the passive one.

8 ACKNOWLEDGEMENTS The first author is profoundly grateful to the Slovene Human Resources Development and Scholarship Fund, and the University of Maribor for their continuous support. Special thanks are dedicated to the RTC Company, Maribor and to its director Mr. Jože Pšeničnik, where the project Terrain Vehicle was carried-out in practice.

9 REFERENCES [1] Lajqi, Sh., Pehan, S., Lajqi, N., Gjelaj, A., Pšeničnik, J., Sašo, E. (2012). Design of independent suspension mechanism for a terrain vehicle with four wheels drive and four wheels steering. MOTSP Conference Proceedings, p. 230-237.

[2] Pehan, S., Lajqi, Sh., Pšeničnik, J., Flašker, J. (2011).

Modeling and simulation of off road vehicle with four wheel steering. IRMES Conference Proceedings, p. 7783.

[3] Belingardi, G., Demic, M. (2009). A contribution to shock absorber modeling by using “black box” method.

Scientific Bulletin of Faculty of Mechanical and Technology, Automotive Series, vol. 19, no. B, p. 1-15.

[4] Lajqi, Sh., Gugler, J., Lajqi, N., Shala, A., Likaj, R. (2012). Possible experimental method to determine the suspension parameters in a simplified model of passenger car. International Journal of Automotive Technology, vol. 13, no. 4, p. 615-621, DOI:10.1007/ s12239-012-0059-7.

[5] Senthil kumar, M. (2007). Genetic Algorithm-based proportional derivative controller for the development of active suspension system. Information Technology and Control, vol. 36, no. 1, p. 58-67.

[6] Eslaminasab, N. (2008). Development of a Semi-active Intelligent Suspension System for Heavy Vehicles.

Ph.D. Thesis, University of Waterloo, Waterloo.

[7] Wong, J. (2001). Theory of Ground Vehicle. John Wiley & Sons, Inc., New York.

[8] Taskin, Y., Hacioglu, Y., Yagiz, N. (2007). The use of fuzzy-logic control to improve the ride comfort of vehicle. Strojniški vestnik – Journal of Mechanical Engineering, vol. 53, no. 4, p. 233-240.

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[9] Karnopp, D.C., Crosby, M.J., Harwood, R.A. (1974).

Vibration control using semi-active force generators.

ASME Journal of Engineering for Industry, vol. 96, no.

2, p. 619-626, DOI:10.1115/1.3438373.

[10] Pajaziti, A. (1992). Contribution in the Parametric Optimization of the Shock Absorber Characteristic with Regulation in Aspect of the Vibration Impact in the Comfort and Stability to the Passenger Vehicles. Ph.D. Thesis. University of Prishtina, Prishtina.

[11] Lin, J.S., Kanellakopoulos, I. (1997). Nonlinear design of active suspensions. IEEE Control Systems Magazines, vol. 17, no. 3, p. 45-59, DOI:10.1109/37.588129.

[12] Yi, K.S., Song, B.S. (1999). Observer design for semiactive suspension control. Vehicle System Dynamics, vol. 32, p. 129-148, DOI:10.1076/vesd.32.2.129.2093.

[13] Popovic, V., Vasic, B., Petrovic, M., Mitic, S. (2011).

System approach to vehicle suspension system control in CAE environment. Strojniški vestnik – Journal of Mechanical Engineering, vol. 57, no. 2, p. 100-109, DOI:10.5545/sv-jme.2009.018.

[14] Turnip, A., Hong, K.Sh., Park, S. (2008). Control of a semi-active MR-damper suspension system: A new polynomial model. Proceedings, The International Federation of Automatic Control. Seoul, p. 4683-4688.

[15] Demic, M., Diligenski, D., Demic, I., Demic, M. (2006). A method of active suspension design. Forsch Ingenieurwes, vol. 70, p. 145-158, DOI:10.1007/ s10010-006-0025-5.

[16] Yu, H., Yu, N. (2003). Application of Genetic Algorithms to Vehicle Suspension Design. The Pennsylvania State University, University Park, p. 1-9.

[17] Ram Mohan Rao, T., Venkata Rao, G., Sreenivasa Rao, K., Purushottam, A. (2010). Analysis of passive and semi-active controlled suspension systems for ride comfort in an omnibus passing over a speed bump. International Journal of

Research and Reviews in Applied Science, vol. 5, no. 1, p. 7-17.

[18] Jazar, R. (2009). Vehicle Dynamic: Theory and Application, Springer, New York.

[19] Demic, M. (1997). Optimization of the Oscillation Systems in Vehicles. Faculty of Mechanical Engineering, Kragujevac.

[20] Abramov, S., Mannan, S., Durieux, O. (2009).

Semi-active susp. syst. simulation using Simulink.

International Journal of Engineering System Modelling and Simulation, vol. 1, no. 2/3, p. 101-114.

[21] Lovrec, D., Kastrevc, M. (2011). Modelling and simulating a controlled press-brake supply system.

International Journal of Simulation Modelling, vol. 10, no. 3, p. 133-144, DOI:10.2507/IJSIMM10(3)3.184.

[22] Rill, G. (2009). Vehicle Dynamics. University of Applied Science, Regensburg.

[23] Sam, Y.M., Osman, J.H.S. (2000). Active suspension control: Performance comparison using proportional integral sliding mode and linear quadratic regulator methods. IEEE, p. 274-278.

[24] Lajqi, Sh. (2012). Suspension and Steering System Development of Four Wheels Drive and Four Wheels Steered Terrain Vehicle. Ph.D. Thesis, University of Maribor, Maribor (in process).

[25] Mastinu, G., Gobbi, M., Miano, C. (2006). Optimal Design of Complex Mechanical Systems, with Applications to Vehicle Engineering. Springer, Berlin.

[26] Popp, K., Schienhlen W. (2010). Ground Vehicle Dynamics. Springer, Berlin, DOI:10.1007/978-3-54068553-1.

[27] Kuznestov, A., Mammadov, M., Sultan, I., Hajilarov, E. (2011). Optimization of improved suspension system with inerter device of the quarter-car model in vibration analyses. Archive of Applied Mechanics, vol. 81, no.

10, p. 1427-1437, DOI:10.1007/s00419-010-0492-x.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 744-749 DOI:10.5545/sv-jme.2012.561

Paper received: 2012-05-05, paper accepted: 2012-10-17 © 2012 Journal of Mechanical Engineering. All rights reserved.

Tribological Behaviour of Coated Carbide Tools during Turning of Steels with Improved Machinability Sebhi, A. – Osmani,H. – Rech, J. Amar Sebhi1,* – Hocine Osmani1 – Joel Rech2

1 Optics

and Precision Mechanics Institute, University of Ferhat Abbes, Setif, Algeria LTDS National School of Engineering, Saint Etienne, France

2 Laboratory

When competing with the industrial productivity, respecting the general rules of work and ecology of the environment system by avoiding various types of lubricating liquid, solid or any other form of machining, research is directed towards the steels with improved machinability and coating cutting tools.

In order to best understand this, new and modern study parameters related to the cutting phenomenon have to be used, so it will be closer to the tribology of contact tool/chip/workpiece. In this context, the interaction of tribological of pairs of materials with improved machinability steels / coated carbide tools and the relationship between the friction coefficient, cutting speed, tool wear and surface quality will be studied. In this case a tribometer designed to identify the friction coefficient in difficult cutting conditions is used. The following steels (42CrMo4, 27MnCr5), TiN, AlTiN coated carbide tools have been used in the experimental work.

Keywords: tribology, coated tool, wear, roughness, friction coefficient, specific cutting force

1 INTRODUCTION In metal cutting operations, the turning process, which is the object of this study represents 33% of this domain [1]. There is a constant search for new techniques to improve the productivity while preserving the environment from harmful waste. The rational implementation of such techniques passes indeed by a deep knowledge of the cutting process and the control of different parameters.

Lubricants are not desirable as a solution to minimise the heating of the tool / work piece; because of the permanent and progressive conditions of ecologists [2] and [3]; in some way it must be enviromentally adapted.

Looking for a better productivity of metal cutting is therefore a major concern of researchers. Steels with improved machinability; various coatings of cutting tools, machining at high speeds, the study of tribological interface tool-chip-workpiece, constantly improve product quality and productivity. The main purpose is to participate in the development of new ways of machining or new techniques of programming and control to improve productivity. Depending on the machining conditions, the wear process of cutting tools can affect one, two or all active faces of the tool [4] and [5]. This can lead to inaccurate tolerances of the machined parts. The wear of cutting tools can occur through erosion, abrasion, adhesion and diffusion [6] and [7]. Such problems, essentially of tribological, nature vary considerably from one family to another family of steels. Materials characterization is essential in developing new products of steels [8] and [9].

Therefore, it is necessary to develop an accurate 744

cutting simulation to identify optimal conditions in terms of cutting tool materials, tool geometry and coating in order to support the improvement of productivity and machining operations [10] and [11]. When the cutting speeds are higher than 280 m/min and contact pressures in GPa are also higher, this will lead the designers of machine tools to verify their calculations on the basis of important constraints. The system is known as the pin-on-disk system, which is unfortunately not able to simulate the contact conditions in cutting, since the conditions (temperature, pressure) are not real [12] and [13]. The phenomena occurring at the interface of the tool-chip (secondary shear zone) and at the interface of the toolworkpiece may be identified by the new tribometer in order to achieve a precise modeling using finite element methods [9].

In order to characterize some materials developed

by Ascométal within the LTDS, and particularly the friction coefficient between cutting tool and machined metal, the exchange of heat flow, tool wear, quality of machined surface, series of tests on an axial tribometer have been carried out (Fig 1). The tribological phenomena at the interface tool / machined surface / chip are very complex to model and yet they are the key behavior of the tool, including its resistance to wear.

The present work lays out experimental results on the TiN and AlTiN wear behaviour when applying an agressive machining on 42CrMo4 and 27MnCr5 steels. In addition, surface quality degradation, cutting force and heat flow evolution are related to the tool wear.

*Corr. Author’s Address: Optics and Precision Mechanics Institute, University of Ferhat Abbes, Setif 19000, Algeria, sebhiamar@yahoo.fr

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In fact, all the computer codes treat this problem as a constant Coulomb friction, while the occurrance of intense adhesion phenomena as well as chemical reactions and diffusion processes can be noticed [9].

Coated carbide tools have proved their performance in relation to the uncoated tools [14] and [15]. It is of importance to optimize the cutting parameters, such as sliding speed, the feed per revolution and the lifetime of the tool in order to ensure proper control of machining. A new rule concerning the adherence of friction and sliding speed in machining is on prospect [16] to [18].

parameters: feed rate, f, 0.8 mm/rev for cutting and 2 mm/rev for scratching, cut depth, ap of 2 mm and cutting speed Vc between 20 and 180 m/min.

2 EXPERIMENTAL PROCEDURE The tests were performed in the Laboratory of Tribology and System Dynamics (LTDS) Saint Etienne, France, using round bars made of 42CrMo4 and 27MnCr5 steels with 80 mm diameter and 600 mm length with improved machinability. The longitudinal turning and tribological cutting operations (in orthogonal cutting), were performed on conventional lathe (Gazeneuve). The chemical composition of the material to be tested is given in Table 1.

The machine being used is Gazneuve lathe (Figs.

1 and 2), equipped with KISTLER 9257B standard dynamometer with the objective to measure in real time the three force components along x, y, z.

Fig. 2. Measure principles on a tribometer intended to acquire the efforts and the heat flow

Fig. 3. The different colors of pins coated and their diameter F17, 13 and 9 mm

Roughness measurements have been obtained by means of a surftest 301 roughness meter.

Table 1. Chemical composition of the material test in weight %

Fig. 1. Cutting test and machining on an instrumented Gazeneuve lathe installation

An interface for acquisition of heat flow is directly connected to the pin holder whose principle is based on thermistor transducers (Fig. 2).

The tests have been carried out in a dry environment without lubrication. Wear has been investigated taking into consideration the following

Material Fe designation 42CrMo4 96.7 27MnCr5 96.5

C

Si

Mn

Cr

Mo

0.39 0.26

0.28 0.23

0.89 1.2

1.08 1.1

0.27 0.05

P

S

0.01 0.018 0.01 0.03

After each test, the work piece is dismantled in order to explore the striations and different measures, then reassembled the bar for the next test after turning with a carbide tool and then polished with a very fine sandpaper to get a better surface possible for the next test. Machining parameters are given after each result.

Tribological Behaviour of Coated Carbide Tools during Turning of Steels with Improved Machinability

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The carbide coated pins, AlTiN, TiN (Fig. 3), with spherical heads and of different diameter 9, 13 and 17 mm (Fig. 3), used for stripping have a finite surface by polishing them on a machining center using 5 axes with the aim to get a better possible surface quality.

Stock removal tool with a removable patch made of carbide coated surface is used to regenerate the wear.

In order to measure the wear resistance, a device based on the variation of the width and the depth of the scratch (flank wear or crater) is adapted to an optical microscope.

decreases. In fact, and during the contact pin / work piece at a cutting speed of 120 m/min, intense heat is created and increase steadily as the normal stress increases. At 600 N value, the transmitted heat flow to the pin becomes regular and linear.

A rapid growth of the heat flow transmission between 200 and 400 N can be noticed.

3 RESULTS AND DISCUSSION 3.1 Effect of Cutting Speed on the Coefficient of Friction The tribological cutting tests on 42CrMo4 steel with a hardness (HB 290), using TiN and TiAlN pins of diameter 13 obtained by PVD at different speeds, are shown in (Fig. 4). The test bench can generate furrows along the specimen as shown in (Fig. 2).

It has been noticed that the coefficient of friction decreases considerably when increasing the cutting speed. For the TiN pin, the fall is precipitous until a speed of 60 m/min is achieved. The AlTiN pin behaves otherwise by falling steadily until 0.23 to a speed of 180 m/min. Here, the apparent friction coefficient which is calculated through the measure of the effort using the following equation, should be mentioned: μmacr = FT / FN .

(1)

Fig. 5. Effect of the normal force on the heat flow transmitted to the pin

It is noticed that at 400 N, the appearance of the heat flow changes significantly. This can be explained by the effect of heat diffusion across the pin.

3.3 Wear as a Function of Time During longitudinal turning and in order to prepare the next test, it is of importance to measure the wear of TiN coated carbide inserts as shown in Fig. 1 and meanwhile searching the interaction between the two forms of wear (flank VB and crater KT) as function of time of cutting. It can be noticed from Fig. 6 that the curves are continuous.

Fig. 4. Effect of cutting speed on the coefficient of friction

3.2 The Effect of Normal Stress on the Heat Flow Transmitted to the Pin Fig. 5 shows the heat flow evolution transmitted to the pin. Beyond this value, the slope of the flow growth 746

Sebhi, A. – Osmani,H. – Rech, J.

Fig. 6. Evolution of wear VB and KT with time for the cutting speed 150 m/min

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 744-749

After a rapid wear at the beginning of the test, the shape of frontal wear VB becomes almost linear.

Beyond 0.4 mm the crater wear rate (KT) increases quickly. For finish operations (following ISO standard ISO 3685-1977 (F) 0.3 mm wear finish and 0.6 mm for draft), which is the case, the flank wear VB which is more representative it is then taken into account.

Both wear VB and KT combined lead to the collapse of the insert.

adhesion of iron deposits detached from the piece (Fig. 8).

3.4 Evolution of the Roughness as a Function of Wear As can be seen from the three curves in Fig.7 and at different speeds, it can be noticed that the surface finish obtained (work piece) with unworn tools is almost regular (near 0.4 μm). Gradual damage of the surfaces corresponding to the increased wear can also be noticed . In the case where VB = 300 μm is taken as a wear criterion, a significant degradation of the surface which results in an increase in the value of Ra can be noticed In fact, for fixed upper limit of roughness to Ra = 0.6 μm, it has been observed that the lifetime of the plate is significantly reached.

Fig. 7. Roughness Ra as a function of wear VB

3.5 Observation of Worn Pieces Observation of friction pins allows us to reinforce the assumptions made when interpreting friction measurements. It particularly expresses the respective behavior of materials towards adhesion, diffusion or other tribological phenomena of the contact couple materials (workpiece-pin).

At the end of the experimental test, the optical and electronic micrographes of the pin show that the damaged surface is very torn. This is due to severe adhesive wear. This result is confirmed by the

Fig. 8. Observation and analysis of the wear of the pins to after 30 min of different friction types of observation Vc = 80 m/min, f = 2 mm/rev

Three different types of observation have been performed: on a binocular microscope, on a scanning electron microscope (SEM), and finally an EDS (Energy-dispersive X-ray spectroscopy) chemical analysis of elements found on the surface of the pins.

The SEM technique is based on the principle of electron-matter interactions. It is therefore sufficient to scan the electron beam over its entire surface.

Moreover, the SEM used in the laboratory can also analyze the spectrum of X- ray by dispersive energy using a microprobe EDS or EDX (energy dispersive X-ray spectroscopy). The analyses of structure and composition are performed in a single step, which has the advantage of a fast data acquisition. The observation of pins with a binocular microscope gives little information about their wear. It is quite difficult to distinguish between areas where the coating has been damaged and areas that have been coated by the adhesion of 27MnCr5. The SEM observations are made after being cleaned pins with ultrasound and acetone. This partly reduces steel deposits on the surface, allowing greater precision of analysis. The resulting images show the existence of two types of alteration of the coating depending on the type of the material used. The pin being rubbed against 27MnCr5 rods shows an adhesive wear, with a tearing of two plates at the ends of the contact zone. The center of this same zone is protected by adhesive deposits which are shown in black. For the 42CrMo4 material pin, there is a clear presence of two trenches left by

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 744-749

the edges of the grooves. Here one can talk about an abrasive wear, since such marks are parallel to the direction of motion. The existence of these two types of wear which are specific to each material is common in the tribological behavior when a couple of materials is used. The adhesive regime often leads to sudden changes of wear which can be due to simple modifications of friction parameters.

EDS analyses do not provide further information.

Only deposits of the Iron element in the case of 42CrMo4 confirmed by the density of the alloy, the net propensity to adhere more firmly to the friction surface of the pins compared to 27MnCr5 alloy.

1.8 mm) showing a more pronounced wear of the pin associated with the 27MnCr5 alloy (about 1.25 mm).

After each friction testing, the used piece is removed from the lathe to take measurements of scratch widths left by the pin on it.

Measurements are performed in the middle of the specimen (and therefore at the middle of the experiment). These data will enable us to assess the contact local pressure, to express the densities flow, and to evaluate the speed impact on the sliding conditions of the pin.

3.6 Observation of Track Turning

The main conclusions are: 1. It has been noted that the coefficient of friction between TiN and 42CrMo4 alloy is better than that between AlTiN and 42CrMo4 alloy at a speed of 60 m/min.

2. The heat flow transmitted to the TiN pin at high pressure (for an applied force greater than 400 N) is more important for TiN pin than for AlTiN pin.

3. During the tests, it could be noticed that the flank wear VB and crater wear KT become more and more important, especially at high cutting speeds (more than 150 m/min). They often result in the breakdown of the tool nose and then they result in the inaccuracy of the tolerances of the workpiece.

4. The surface quality is better for low rate of wear VB (lower than 200 mm); beyond this value the roughness Ra increases as function of the cutting speed Vc. 5. The system set-up has showed that the apparent friction coefficient decreases considerably by increasing the cutting speed. This model also showed the important effect of temperature on contact pressure.

The most distinguished wear phenomenon in this case is the abrasive wear which appears by the side of grooving tools. Abrasion is caused by hard particles existing in the material being machined. In this case, particular attention should be given to work pieces dimensioning, tolerances, surface quality and machining precision which could be significantly affected. The graphs found in this work can serve as abacus for selecting the optimum cutting speed, the interpolation surface quality product and service life of the tool optimum.

It is well noticed the existence of striations which are parallel to the pin sliding direction, which qualify this kind of wear as soft abrasion wear. This observation seems consistent with the difference between the two materials in contact.

In addition, there is a discharge of matter towards the edges of tracks (groove), a sign of ploughing, due to the steel ductility. The observation of the pin at the end of the test very clearly shows a non-uniform wear of the head of the pin.

Fig. 9. Comparison of scratches obtained after scratching using pins Ø13 mm and diameters Ø17 mm; 42CrMo4 - magnification ×1 - Vc = 80 m/min

The widths of scratches observed on 27MnCr5 bars remain relatively constant (Fig. 9), during testing. Only those left by the pins in the bars of standard material, increase furtively after the first twenty minutes of friction. This seems to confirm the destabilizing of the recorded coefficients of friction.

Therefore, there is a slight difference in behavior on the friction with time between the two alloys. The scratches left in the 27MnCr5 alloy are in fact much larger than those left on of 42CrMo4 alloy (about 748

4 CONCLUSION

5 ACKNOWLEDGMENTS This work was started at the Laboratory of Tribology and System Dynamics (LTDS) Saint Etienne France,

Sebhi, A. – Osmani,H. – Rech, J.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 744-749

and then completed at the Unit Industrial Equipment Maintenance (IEM) Group SONALGAZ Algeria.

The authors express their gratitude to the Ministry of Higher Education of Algeria and all the people who have collaborated directly or indirectly to this work.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12 Author Index

Author Index

Strojniški vestnik - Journal of Mechanical Engineering Ljubljana, ISSN 0039-2480 Legend: Author, volume (year) issue, page

A Abulimiti, Aibaibu, 58(2012)11, 665 Adam, Frank, 58(2012)10, 571 Adamović, Živoslav, 58(2012)5, 300 Aghanajafi, Cyrus, 58(2012)2, 125 Ahmadzadeh, Mohsen, 58(2012)3, 156 Alavi, Mahmoud Abolhasan, 58(2012)5, 309 Amar, Sebhi, 58(2012)12, 744 Amza, Cătălin Gheorghe, 58(2012)9, 509 Amza, Gheorghe, 58(2012)9, 509 Andrić, Milenko, 58(2012)6, 386 Ang, Haisong, 58(2012)1, 46 Anišić, Zoran, 58(2012)12, 724 Arregui, Francisco, 58(2012)4, 225

B Bach, Friedrich-Wilhelm, 58(2012)10, 571 Bahl, Christian Robert Haffenden, 58(2012)1, 3 Bajić, Dražen, 58(2012)11, 673 Balestrassi, Pedro Paulo, 58(2012)5, 344 Barrio, Jorge, 58(2012)7-8, 431 Bayraktar, Meral, 58(2012)9, 545 Beker, Ivan, 58(2012)4, 281 Bergant, Anton, 58(2012)4, 225 Bernetič, Jure, 58(2012)6, 416 Biskup, Christian, 58(2012)10, 571 Bondžulić, Boban, 58(2012)6, 386 Božičković, Ranko, 58(2012)11, 642 Breñosa, Jose, 58(2012)7-8, 431 Brissaud, Daniel, 58(2012)9, 517 Burzic, Zijah, 58(2012)6, 422 Butala, Peter, 58(2012)7-8, 444 Butala, Vincenc, 58(2012)2, 107

750

C Cai, Baoping, 58(2012)11, 665 Celent, Luka, 58(2012)11, 673 Chen, Yangzhi, 58(2012)11, 633 Costa, Sebastião Carlos, 58(2012)5, 344 Cveticanin, Livija, 58(2012)5, 353

Č Čaplovič, Ľubomír, 58(2012)12, 709 Četina, Matjaž, 58(2012)4, 255 Čička, Roman, 58(2012)12, 709

Ć Ćirić Kostić, Snežana, 58(2012)5, 327 Ćosić, Ilija, 58(2012)11, 642, 58(2012)12, 724

Ç Çay, Yusuf, 58(2012)7-8, 492 Çiçek, Adem, 58(2012)3, 165; 58(2012)7-8, 492 Çolak, Oğuz, 58(2012)11, 683

D Daneshmand, Saeed, 58(2012)2, 125 Demirci,Ibrahim H., 58(2012)10, 587 Dikić, Goran, 58(2012)6, 386 Dikmen, Ferhat, 58(2012)9, 545 Dimitrijević, Dejan, 58(2012)1, 56 Ding, Jiang, 58(2012)11, 633 Dolićanin, Ćemal, 58(2012)1, 56 Dolšak, Bojan, 58(2012)4, 271 Dovjak, Mateja, 58(2012)7-8, 453 Du, Sha, 58(2012)1, 46 Dudić, Slobodan, 58(2012)4, 281 Duehring, Steven, 58(2012)2, 102 Duhovnik, Jožef, 58(2012)1, 23, 58(2012)3, 183

Đ Đurić, Željko, 58(2012)5, 300

E Eberlinc, Matjaž, 58(2012)1, 37 Edwards, Nathan, 58(2012)3, 191 Elek, Predrag, 58(2012)6, 403 Engelbrecht, Kurt, 58(2012)1, 3

F Fabijan, Drago, 58(2012)4, 238 Fajdiga, Matija, 58(2012)2, 115 Fang, Ning, 58(2012)3, 191 Farahat, Said, 58(2012)5, 309 Ferre, Manuel, 58(2012)7-8, 431 Ferreira, João Roberto, 58(2012)5, 344 Finkšt, Tomaž, 58(2012)9, 501 Flašker, Jože, 58(2012)10, 563

G Galiana, Ignacio, 58(2012)7-8, 431 Giménez, Antonio, 58(2012)7-8, 431 Glodež, Srečko, 58(2012)10, 563 Gok, Arif, 58(2012)10, 587 Gologlu, Cevdet, 58(2012)10, 587 Gomes, José Henrique de Freitas, 58(2012)5, 344 Gorenc, Stane, 58(2012)9, 534 Gotlih, Karl, 58(2012)10, 563 Gregorc, Boštjan, 58(2012)4, 238 Grum, Janez, 58(2012)10, 614 Guclu, Rahmi, 58(2012)9, 545 Gucma, Lucjan, 58(2012)10, 607 Gucma, Maciej, 58(2012)10, 607 Gylienė, Virginija, 58(2012)12, 749

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 750-752

H Hajdu, Štefan, 58(2012)2, 102 Han, Jiang, 58(2012)12, 701 Hassel, Thomas, 58(2012)10, 571 He, Zhengjia, 58(2012)9, 527 Heber, Thomas, 58(2012)10, 571 Herrera-Ruiz, Gilberto, 58(2012)12, 693 Hočevar, Marko, 58(2012)1, 37 Hocine, Osmani, 58(2012)12, 743 Hoey, Trevor, 58(2012)4, 263 Hoseini, Ahmad, 58(2012)3, 156 Hufenbach,Werner, 58(2012)10, 571

I Iacob, Robert, 58(2012)11, 653 Ilić, Ivana, 58(2012)9, 553 Ilić, Slobodan, 58(2012)6, 411 Iljaž, Jurij, 58(2012)7-8, 482 Ismar, Hajro, 58(2012)6, 422

J Jakšić, Zoran, 58(2012)6, 367 Janković, Radomir, 58(2012)6, 376 Jaramaz, Dragana, 58(2012)6, 403 Jaramaz, Slobodan, 58(2012)6, 403 Jauregui-Correa, Juan Carlos, 58(2012)12, 693 Jelenc, Jože, 58(2012)5, 319 Jelenc, Jure, 58(2012)5, 319 Jen, Tien-Chien, 58(2012)3, 213 Jensen, Jesper Buch, 58(2012)1, 3 Jeremić, Olivera, 58(2012)6, 394 Jerković, Damir, 58(2012)6, 394 Jezdimirović, Mirko, 58(2012)6, 411 Jocanović, Mitar, 58(2012)4, 281 Joel, Rech, 58(2012)12, 744 Jonrinaldi, Jonrinaldi, 58(2012)2, 81 Josimović, Ljubiša, 58(2012)5, 300 Jovanov, Goran, 58(2012)5, 300 Jozić, Sonja, 58(2012)11, 673

K Kaljun, Jasmin, 58(2012)4, 271 Kapor, Nenad J., 58(2012)6, 422 Karanović, Velibor, 58(2012)4, 281 Kari, Aleksandar, 58(2012)6, 386 Kıvak, Turgay, 58(2012)3, 165, 58(2012)7-8, 492 Klasinc, Roman, 58(2012)4, 238, 58(2012)4, 255 Kocúrová, Karin, 58(2012)12, 709 Kokelj, Tugomir, 58(2012)6, 422 Kovač, Mitar, 58(2012)6, 394 Krainer, Aleš, 58(2012)7-8, 453 Krajnik, Peter, 58(2012)12, 693 Krese, Gorazd, 58(2012)2, 107 Kruisbrink, Arno, 58(2012)4, 225 Kryžanowski, Andrej, 58(2012)4, 245 Krzyk, Mario, 58(2012)4, 255 Kunič, Roman, 58(2012)10, 598 Kurt, Mustafa, 58(2012)10, 587 Kušar, Janez, 58(2012)9, 534 Kuster, Friedrich, 58(2012)7-8, 462 Kuzman, Karl, 58(2012)2, 73

L Lajqi, Shpetim, 58(2012)12, 732 Lăptoiu, Dan, 58(2012)9, 509 Lebar, Andrej, 58(2012)7-8, 444 Li, Bing, 58(2012)9, 527 Li, Jimeng, 58(2012)9, 527 Liu, Yong-Bin, 58(2012)3, 213 Liu, Yonghong, 58(2012)11, 665 Liu, Youyu, 58(2012)12, 701 Livada, Branko, 58(2012)6, 376 López, Javier, 58(2012)7-8, 431 Luo, Yi, 58(2012)10, 578 Lv, Yueling, 58(2012)11, 633 Lvov, Gennady Ivanovich, 58(2012)3, 175

M Maček Lebar, Alenka, 58(2012)5, 319 Macko, Martin, 58(2012)6, 411 Mahdavi Adeli, Mohsen, 58(2012)5, 309 Majić, Frane, 58(2012)7-8, 470 Maksimović, Mirko, 58(2012)9, 553 Marčetič, Matjaž, 58(2012)6, 416 Maretic, Ratko, 58(2012)5, 353 Marjanović, Dorian, 58(2012)3, 203 Marn, Jure, 58(2012)7-8, 482 Medved, Sašo, 58(2012)11, 623 Micković, Dejan, 58(2012)6, 403 Micković, Dušan, 58(2012)6, 403 Miklavčič, Damijan, 58(2012)5, 319 Mikoš, Matjaž, 58(2012)4, 245, 58(2012)4, 263 Milić, Miodrag, 58(2012)1, 29 Milinović, Momčilo, 58(2012)6, 367, 58(2012)6, 394 Mitrouchev, Peter, 58(2012)11, 653 Moravčík, Roman, 58(2012)12, 709 Mori, Mitja, 58(2012)5, 291 Movaghghar, Ali, 58(2012)3, 175 Možina, Janez, 58(2012)1, 23 Muhasilovic, Mezid, 58(2012)3, 183

N Nagode, Marko, 58(2012)2, 115 Nguyen, Dinh Son, 58(2012)9, 517 Nikolić, Nebojša, 58(2012)6, 376 Nikolić, Vera, 58(2012)1, 56

O Ognjanović, Milosav, 58(2012)5, 327 Ostaševičius, Vytautas, 58(2012)12, 716

751

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 750-752

P Pai, P Srinivasa, 58(2012)3, 191 Paiva, Anderson Paulo, 58(2012)5, 344 Pavlovič, Erik, 58(2012)11, 623 Pehan, Stanislav, 58(2012)12, 732 Perkovic, Marko, 58(2012)10, 607 Petek, Aleš, 58(2012)2, 73 Petelin, Stojan, 58(2012)10, 607 Petrovic, Zlatko, 58(2012)9, 553 Pirc, Andrej, 58(2012)5, 291 Planinc, Igor, 58(2012)4, 245 Popescu, Diana, 58(2012)9, 509, 58(2012)11, 653 Poredoš, Alojz, 58(2012)1, 16 Potočar, Erik, 58(2012)1, 37 Predin, Andrej, 58(2012)4, 238 Prek, Matjaž, 58(2012)2, 107 Przywarty, Marcin, 58(2012)10, 607 Pude, Frank, 58(2012)7-8, 462

R Rabiey, Mohammad, 58(2012)7-8, 462 Radošević, Milan, 58(2012)11, 642 Radovanović, Ljiljana, 58(2012)5, 300 Rajh, Matej, 58(2012)10, 563 Ramšak, Matjaž, 58(2012)3, 147 Randjelović, Danijela, 58(2012)6, 367 Raubar, Edvin, 58(2012)5, 337 Rek, Zlatko, 58(2012)2, 134 Ren, Congkun, 58(2012)11, 665 Rihar, Lidija, 58(2012)9, 534 Rikalović, Aleksandar, 58(2012)11, 642 Robles-Ocampo, Jose Billerman, 58(2012)12, 693 Rudolf, Mitja, 58(2012)2, 134

S Salgado Jr., Aluizio Ramos, 58(2012)5, 344 Salimi, Hamidreza, 58(2012)3, 156 Samtaş, Gürcan, 58(2012)3, 165, 58(2012)7-8, 492 Saranjam, Bahador, 58(2012)3, 156 Sarhaddi, Faramarz, 58(2012)5, 309 Scarpa, Federico, 58(2012)1, 9 Sekavčnik, Mihael, 58(2012)5, 291 Selak, Luka, 58(2012)7-8, 444 Sevilla-Camacho, Perla Yasmin, 58(2012)12, 693 Shukuya, Masanori, 58(2012)7-8, 453 Sobhnamayan, Fatemeh, 58(2012)5, 309 Soković, Mirko, 58(2012)11, 642 Sremčev, Nemanja, 58(2012)12, 724 Stamenković, Dragi, 58(2012)9, 553 Stanković, Tino, 58(2012)3, 203 Starbek, Marko, 58(2012)9, 534 Stefanovska, Aneta, 58(2012)4, 263 Stevanov, Branislav, 58(2012)12, 724 Stirnimann, Josef, 58(2012)7-8, 462 Stupar, Slobodan, 58(2012)9, 553 Sušnik, Janez, 58(2012)10, 614 Suzić, Nikola, 58(2012)12, 724

Š Šafarič, Riko, 58(2012)2, 93 Šarlah, Alen, 58(2012)1, 16 Šević, Dragoljub, 58(2012)4, 281 Širok, Branko, 58(2012)1, 37 Šolc, Tomaž, 58(2012)4, 263 Španielka, Ján, 58(2012)2, 102 Štefániková, Mária, 58(2012)12, 709 Štorga, Mario, 58(2012)3, 203 Šturm, Roman, 58(2012)10, 614; 58(2012)12, 709 Šušteršič, Jakob, 58(2012)4, 245

T Tagliafico, Giulio, 58(2012)1, 9 Tagliafico, Luca Antonio, 58(2012)1, 9 Tan, Jiyong, 58(2012)9, 527 Taraba, Bohumil, 58(2012)2, 102 Tasič, Jurij F., 58(2012)9, 501 Terčelj-Zorman, Marjeta, 58(2012)9, 501 Ternik, Primož, 58(2012)7-8, 482 Tian, Xiaojie, 58(2012)11, 665 Tian, Xiaoqing, 58(2012)12, 701 Tušek, Jaka, 58(2012)1, 16

752

U Ukrainczyk, Velimir, 58(2012)4, 245 Uran, Suzana, 58(2012)2, 93

V Venko, Samo, 58(2012)11, 623 Vidmar, Peter, 58(2012)10, 607 Vidrih, Boris, 58(2012)11, 623 Vignat, Frédéric, 58(2012)9, 517 Virag, Zdravko, 58(2012)7-8, 470 Volk, Matej, 58(2012)2, 115 Voss, Ralph, 58(2012)7-8, 470 Vrabič, Rok, 58(2012)7-8, 444 Vrančić, Damir, 58(2012)5, 337 Vuherer, Tomaž, 58(2012)6, 416 Vukašinović, Nikola, 58(2012)1, 23 Vuruna, Mladen, 58(2012)6, 416

W Walter, Christian, 58(2012)7-8, 462 Wang, Jizhe, 58(2012)2, 81 Wang, Junbiao, 58(2012)2, 81 Wang, Xiaodong, 58(2012)10, 578 Weckend, Nico, 58(2012)10, 571 Wegener, Konrad, 58(2012)7-8, 462

X Xia, Lian, 58(2012)12, 701

Y Yen, Yi-Hsin, 58(2012)3, 213

Z Zajc, Matej, 58(2012)9, 501 Zaremba, David, 58(2012)10, 571 Zhang, Xiwen, 58(2012)10, 578 Zhang, Yanzhen, 58(2012)11, 665 Zhao, Fuqing, 58(2012)2, 81 Zhao, Ji-Wen, 58(2012)3, 213 Zhu, Lin, 58(2012)3, 213 Zrnić, Bojan, 58(2012)6, 386 Zukovic, Miodrag, 58(2012)5, 353 Zun, Iztok, 58(2012)2, 134

Ž Živanović, Zlatomir, 58(2012)1, 29 Žunič, Zoran, 58(2012)7-8, 482

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 58, (2012), številka 12 Ljubljana, december 2012 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki člankov Jose Billerman Robles-Ocampo, Juan Carlos Jauregui-Correa, Peter Krajnik, Perla Yasmin SevillaCamacho, Gilberto Herrera-Ruiz: Nelinearni model za zaznavanje nestabilnosti procesa brušenja brez konic Youyu Liu, Jiang Han, Lian Xia, Xiaoqing Tian: Strategija odvalnega rezkanja in analiza zmogljivosti modelov štiriosne obdelave nekrožnih zobnikov s poševnim ozobjem Roman Moravčík, Mária Štefániková, Roman Čička, Ľubomír Čaplovič, Karin Kocúrová, Roman Šturm: Fazne transformacije v visokolegiranem orodnem jeklu za delo v hladnem Virginija Gylienė, Vytautas Ostaševičius: Modeliranje in simulacija delovanja sil odrezkov na posamezne ploščice rezkalnega orodja Nikola Suzić, Branislav Stevanov, Ilija Ćosić, Zoran Anišić, Nemanja Sremčev: Izdelki po meri z uporabo grupne tehnologije: študija primera iz pohištvene industrije Shpetim Lajqi, Stanislav Pehan: Konstruiranje in optimizacija aktivnega in polaktivnega nelinearnega sistema obes terenskega vozila Sebhi Amar, Osmani Hocine, Rech Joel: Tribološke lastnosti prevlečenih trdokovinskih orodij pri struženju jekel z izboljšano obdelovalnostjo Osebne vesti Doktorske disertacije, znanstvena magistrska dela, diplomske naloge

SI 145 SI 146 SI 147 SI 148 SI 149 SI 150 SI 151 SI 152

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 145

Prejeto: 2012-06-13, sprejeto: 2012-10-17 © 2012 Strojniški vestnik. Vse pravice pridržane.

Nelinearni model za zaznavanje nestabilnosti procesa brušenja brez konic Jose Billerman Robles-Ocampo1,2 – Juan Carlos Jauregui-Correa1,* - Peter Krajnik3 – Perla Yasmin Sevilla-Camacho1,2 - Gilberto Herrera-Ruiz1 1 Avtonomna

univerza Queretaro, Fakulteta za strojništvo, Mehika, 2 Politehnična univerza Chiapas, Mehika 3 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Brušenje brez konic predstavlja enega izmed najproduktivnejših ter najnatančnejših obdelovalnih postopkov, ki se uporablja za proizvodnjo rotacijsko simetričnih obdelovancev. Prednost postopka brušenja brez konic je v tem, da med obdelavo obdelovanec ni vpet, kar omogoča visoko stopnjo avtomatizacije in doseganje velike produktivnosti. Pomanjkljivost postopka, pri katerem obdelovanec ni vpet med konici, je v nestabilnosti sistema brušenja, ki se odraža v odstopanju krožnosti obdelovanca (obdelovanec mnogokotne oblike). Drugi največji problem procesa brušenja poleg nekrožnosti obdelovanca je povezan z drdranjem. Najočitnejša napaka na površini obdelovanca so sledi drdranja (valovita površina obdelovanca), ki so posledica spreminjajoče se globine rezanja zaradi premika središča obdelovanca, prevelikega kota podpore obdelovanca, podajnosti brusa, velike hitrosti obdelovanca, vsiljenih vibracij stroja ali okvarjenega vretena, ter interference med nebalansiranim brusom in valovitostjo površine obdelovanca. Produktivnost je med drugim odvisna od stabilnosti procesa. Slednja je običajno zagotovljena z zmanjšanjem hitrosti obdelovanca, kar pa končno pripelje do majhnih stopenj odvzema materiala. Prisotnost mnogoterne oblike obdelovanca ponovno povzroči vertikalne premike središča obdelovanca in s tem dinamiko obdelovanca.

Zlasti geometrijska nestabilnost je povezana z odstopanjem krožnosti obdelovanca ter valovitostjo obdelovanca. Odstopanje krožnosti je bilo aproksimirano z obliko poligona. Postopek v članku predstavljenega modeliranja upošteva poligonalno obliko obdelovanca kot vhodno silo vzbujanja, medtem ko je togost sistema brušenja brez konic predstavljena s funkcijo polinoma tretjega reda. Model vključuje indeks geometrijske stabilnosti. Nestabilnost procesa brušenja brez konic je analizirana s pomočjo faznega diagrama in zvezne valčne transformacije. Pri tem so v modelu upoštevane podajalna sila brušenja, red nekrožnosti (mnogokotnosti) obdelovanca ter geometrija brusnega območja. Modeliranje procesa brušenja brez konic izhaja iz kinematike obdelovanca. Analiza kinematike obdelovanca temelji na gibanju nekrožnega obdelovanca, podprtega na dveh valjih. Ker je obdelovanec podprt samo v dveh točkah, ima vertikalni položaj obdelovanca le dve možni konfiguraciji: (1) eno oglišče poligona je v stiku z brusom, medtem ko je stranica tangentna glede na regulacijski valj, ali (2) dve stranici sta sočasno v stiku z brusom in regulacijskim valjem. Pri tem je pomembno pripomniti, da je trenutek, v katerem sta dve stranici tangentni tako na brus kakor tudi na regulacijski valj, odvisen od relativnega položaja oglišč poligonalne oblike obdelovanca. Funkcija vertikalnega premika obdelovanca je vključena v dinamski enačbi kot del togosti sistema brušenja brez konic. Pri upoštevanju nelinearne narave togosti to omogoča vpeljavo vpliva mnogokotne oblike obdelovanca. S tem je geometrija odstopanja krožnosti obdelovanca opisana z mnogokotnikom, kar lahko izpeljemo v obliki Duffingove enačbe.

Indeks geometrijske stabilnosti je odvisen od geometrije brusnega območja in se nanaša na kote med središčem obdelovanca ter središčno linijo, ki povezuje brus z regulacijskim valjem. Vključitev indeksa stabilnosti izboljša občutljivost funkcije sistemske togosti. S tem so v modelu upoštevani tudi vplivi nastavitve stroja. Glavni rezultati v članku so dobljeni na osnovi simulacije brušenja namensko nekrožnega obdelovanca (zarezana površina obdelovanca). Pri simulaciji je bila uporabljena predpostavka, da dobimo iz začetne geometrije obdelovanca poligon velikega reda nekrožnosti. Nestabilnost je bila določena z zmanjševanjem reda nekrožnosti obdelovanca, dokler vertikalni premiki središča obdelovanca niso izkazali nerednega obnašanja. Novost pri razvoju nelinearnega modela za zaznavanje nestabilnosti procesa je vključitev indeksa geometrijske stabilnosti. Pred tem sta bili geometrijska ter dinamična stabilnost procesa brušenja brez konic obravnavani ločeno. Model predpostavlja poligonalno obliko obdelovanca. Nestabilnost izhaja iz gibanja poligona med brusom in regulacijskim valjem, ki povzroča vertikalni premik središča obdelovanca. Ta pojav povzroča samovzbujene vibracije; ugotovljeno je bilo, da obstaja kritični red nekrožnosti obdelovanca, pri katerem je proces popolnoma nestabilen. Pokazano je, da je dinamski model lahko predstavljen v obliki Duffingove enačbe, v kateri je vrednost nelinearne togosti odvisna od vertikalnega premika središča obdelovanca. Meja nestabilnosti je jasno določena z indeksom geometrijske stabilnosti. Nestabilnost procesa brušenja brez konic je analizirana s pomočjo dveh metod: (1) zvezno valčno transformacijo in (2) faznim diagramom. Zvezna valčna transformacija prikazuje razvoj dinamskega odziva procesa kot funkcijo časa in frekvence. V faznem diagramu je pogoj nestabilnosti prikazan kot funkcija Louvilleovega teorema. Obe metodi sta pokazali, da postane proces nestabilen pri brušenju obdelovancev s karakterističnim 40. redom nekrožnosti.

Ključne besede: brušenje brez konic, nekrožnost, drdranje, nelinearni model, fazni diagram, indeks geometrijske stabilnosti *Naslov avtorja za dopisovanje:: Avtonomna univerza Queretaro, Fakulteta za strojništvo, Cerro de las Campanas s/n, Ciudad Universitaria, 76010 Querétaro, Qro., Mehika, jc.jauregui@uaq.mx

SI 145

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 146

Prejeto: 2012-04-15, sprejeto: 2012-10-18 © 2012 Strojniški vestnik. Vse pravice pridržane.

Strategija odvalnega rezkanja in analiza zmogljivosti modelov štiriosne obdelave nekrožnih zobnikov s poševnim ozobjem Liu, Y. – Han, J. – Xia, L. – Tian, X. Youyu Liu1,2,* – Jiang Han2 – Lian Xia2 – Xiaoqing Tian2

1 Šola

za strojništvo in avtomatizacijo, Politehnika Anhui, Kitajska 2 Institut CIMS, Tehniška univerza Hefei, Kitajska

Uporaba zobnikov s poševnimi zobmi nekrožne oblike je v veliki meri omejena zaradi izdelovalnih postopkov.

Cilj avtorjev je poiskati tehniko odvalnega rezkanja nekrožnih zobnikov s poševnimi zobmi.

Zobniki nekrožne oblike imajo dober potencial zaradi prednosti, kot so večja stopnja prekritja, manj udarcev in hrupa ter manjši, nespodrezani zobje. Danes je večina raziskav osredotočena na nekrožne čelne zobnike, malo pa je študij, ki bi obravnavale zasnovo in izdelavo nekrožnih zobnikov s poševnimi zobmi. Nekrožne čelne zobnike se je na primer ne glede na obliko delilne krivulje dolgo izdelovalo po postopku žične elektroerozijske obdelave, ki pa je izjemno neučinkovit. Žična elektroerozijska obdelava ni uporabna za vse zobnike s poševnimi zobmi nekrožne oblike in odvalno rezkanje je zaradi visoke učinkovitosti še vedno prva izbira. S tem je utemeljen tudi pomen študije, ki je predstavljena v tem članku.

Ustvarjena je bila strategija štiriosnega odvalnega rezkanja z več fundamentalnimi modeli odvalnega rezkanja, pri čemer se ozobje generira z orodjem s poševnimi zobmi. Metoda vključuje modele profilnega podajanja in modele dodatnega vrtenja. Na osnovi strategije in pridobljenih modelov je bilo razvitih 18 shem in funkcijskih modelov za različne procese odvalnega rezkanja s profilnimi premiki, aksialnimi premiki in dodatnim vrtenjem, ki vplivajo na natančnost profila, aksialno natančnost in zmogljivost krmiljenja. S 3D-simulacijo obdelave so bili analizirani rezultati odvalnega rezkanja profila, aksialnih premikov in dodatnega vrtenja. Postopoma so bili pridobljeni odlični modeli in strategija. Članek obravnava uporabo numeričnih tehnik pri obdelavi zobnikov nekrožne oblike.

Rezultati, ugotovitve: (1) Vzpostavljena je bila strategija štiriosnega odvalnega rezkanja in izpeljanih je bilo več fundamentalnih modelov odvalnega rezkanja. Na osnovi tega je omogočeno odvalno rezkanje zobnikov s poševnimi zobmi nekrožne oblike.

(2) Razvitih je bilo 18 shem in funkcijskih modelov na osnovi fundamentalnih modelov odvalnega rezkanja, z ozirom na različne procese profilnega odvalnega rezkanja, procese aksialnega odvalnega rezkanja in dodatno vrtenje. Izbrana sta bila optimalna strategija in model.

(3) S 3D-simulacijo obdelave je bila analizirana zmogljivost profilnega in aksialnega odvalnega rezkanja ter dodatnega vrtenja. Postopoma so bili pridobljeni odlična strategija in modeli. Končno sta bila določena optimalna strategija in model (konstantna vrtilna hitrost odvalnega rezkarja, konstantna aksialna hitrost obdelovanca in dodatno vrtenje obdelovanca) z visoko natančnostjo, visoko učinkovitostjo in enostavnim upravljanjem.

Omejitve raziskave, implikacije: Pri strategiji odvalnega rezkanja in modelu podajanja v članku se odvalni rezkar med obdelavo ne premika po svoji osi, zato točka ubiranja na osi rezkarja ni fiksna. Os odvalnega rezkarja mora biti zato dovolj dolga, obraba zob rezkarja pa ni enakomerna. V prihodnje bomo razvili modele podajanja pri odvalnem rezkanju z zveznim aksialnim gibanjem rezkarja. Osno gibanje rezkarja omogoča fiksiranje točke ubiranja na osi odvalnega rezkarja, s čimer je omogočena izdelava velikih in močno ekscentričnih nekrožnih zobnikov s poševnimi zobmi tudi z orodji, ki imajo krajše osi. Poveča se tudi razpoložljivost zob rezkarja.

Prispevek, novosti, vrednost: Delo podaja sheme za izdelavo zobnikov nekrožne oblike s poševnimi zobmi ter spodbuja njihovo uporabo.

Metode in rezultate iz tega članka je zaradi podobnosti med brušenjem in odvalnim rezkanjem mogoče uporabiti tudi pri strojih za brušenje elementov polžnih gonil. Vsebina članka je uporabna tudi pri drugih postopkih za izdelavo nekrožnih zobnikov.

Ključne besede: zobniki nekrožne oblike s poševnimi zobmi, štiriosno podajanje, odvalno rezkanje, modeli podajanja, simulacija obdelave.

SI 146

*Naslov avtorja za dopisovanje: Šola za strojništvo in avtomatizacijo, Politehnika Anhui, Kitajska, Liuyoyu1@163.com

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 147

Prejeto: 2012-04-18, sprejeto: 2012-10-05 © 2012 Strojniški vestnik. Vse pravice pridržane.

Fazne transformacije v visokolegiranem orodnem jeklu za delo v hladnem Moravčík, R. – Štefániková, M. – Čička, R. – Čaplovič, L’. – Kocúrová, K. – Šturm, R. Roman Moravčík1,* – Mária Štefániková1 – Roman Čička1 – Ľubomír Čaplovič1 – Karin Kocúrová1 – Roman Šturm2

1 Slovaška

tehnična univerza, Fakulteta za materialne znanosti in tehnologijo, Inštitut materialnih znanosti, Slovaška 2 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Razvoj visokolegiranih orodnih jekel je pomemben zaradi doseganja boljših mehanskih in fizikalnih lastnosti materiala. Fazne transformacije imajo odločilen vpliv na končne mehanske lastnosti legiranih orodnih jekel.

Visokolegirana jekla imajo v primerjavi z navadnimi ogljikovimi jekli drugačne pogoje strjevanja. Namen raziskave je bil popisati fazne transformacije v visokolegiranem orodnem jeklu za delo v hladnem, ki se zgodijo med počasnim segrevanjem in ohlajanjem. Taki pogoji so sicer drugačni kot med samo izdelavo orodnih jekel, vendar nam omogočijo popis strjevanja in faznih prehodov v neravnotežnih pogojih.

Visokolegirana orodna jekla ledeburitne vrste, narejena po postopku prašne metalurgije, vsebujejo veliko ogljika in legirnih elementov, predvsem vanadija, kroma in molibdena, ki tvorijo karbide. Glavne prednosti orodnih jekel, narejenih s postopkom prašne metalurgije, so homogena distribucija majhnih karbidov in homogena kemična sestava po prečnem prerezu orodja. Zaradi teh specifičnih lastnosti je orodno jeklo za delo v hladnem našlo širok nabor izdelovalnih aplikacij v različnih industrijah z namenom deformiranja, prebijanja, striženja.

Uporabljeno orodno jeklo za delo v hladnem je bilo izdelano s postopkom prašne metalurgije. Jeklo je imelo izjemno visoko obrabno odpornost, izredno žilavost in visoko tlačno trdnost. Za take izjemne mehanske lastnosti je odgovorna prava kombinacija legirnih elementov v jeklu z ustrezno toplotno obdelavo. Kemična sestava analiziranega jekla je vsebovala 2,47% C, 4,15% Cr, 3,62% Mo, 8,94% V in manjše deleže drugih legirnih elementov. Po fazi izostatskega sintranja je bilo orodno jeklo najprej kaljeno pri temperaturi 1100 °C, potem pa trikrat popuščano pri temperaturi 550 °C. S tako toplotno obdelavo smo dosegli enakomerno trdoto po preseku, in sicer 66 HRC. Visoka vsebnost vanadija pri tem zagotavlja dobro obrabno odpornost orodja.

Za določitev faznih prehodov v jeklu so bile uporabljene različne metode: diferencialna termična analiza (DTA), termo-magnetometrija (TM), optična mikroskopija, rastrska elektronska mikroskopija z analizatorjem razpršene energije (SEM + EDS), difrakcijska analiza z X-žarki, dilatometrija.

S pomočjo krivulje pridobljene z diferencialno termično analizo (hitrost segrevanja/ohlajanja je bila 10 K/min) in termo-magnetometrije smo ugotovili, da se jeklo strjuje v treh stopnjah. Strjevanje se začne z izločanjem avstenita pri 1340 °C. Temu sledita evtektični reakciji z nastajanjem vanadijevih karbidov pri 1327 °C in molibdenovih karbidov pri 1208 °C, s čimer se strjevanje zaključi. Pri temperaturah okrog 830 °C pride do transformacije avstenita v ferit. Curiejeva temperatura magnetne premene tega jekla je pri 780 °C. Pri temperaturah okrog 500 °C nastanejo v trdni matrici sekundarni karbidi.

S pomočjo optične mikroskopije in SEM+EDS je bilo po izvedeni diferencialno-termični analizi ugotovljeno, da je mikrostruktura analiziranega jekla dendritna, pri čemer so dendriti napolnjeni s kolonijami evtektičnih karbidov. Kolonije evtektičnih karbidov so sestavljene iz vanadijevih karbidov in ferita. Na mejah dendritov so prisotne še nečistoče v obliki molibdenovih karbidov ter kompleksnih kromovih, vanadijevih in železovih sulfidov.

Ločeno od tega smo z difrakcijsko analizo X-žarkov v mikrostrukturi potrdili naslednje faze: ferit, MC karbidi (vanadijev tip), M2C in M6C karbidi (molibdenov tip).

Poznavanje faznih transformacij v visokolegiranih orodnih jeklih za delo v hladnem nam pomaga pri boljšem razumevanju procesov, ki se dogajajo v materialu med toplotnimi obdelavami. Rezultati raziskave bodo uporabni v naslednjih termodinamičnih analizah faznih transformacij tega jekla z uporabo programov Thermocalc in Dictra.

Ključne besede: visokolegirano orodno jeklo, delo v hladnem, diferencialna termična analiza, SEM, difrakcijska analiza z X-žarki, dilatometrija

*Naslov avtorja za dopisovanje: Slovaška tehnična univerza, Fakulteta za materialne znanosti in tehnologijo, Inštitut materialnih znanosti, Paulínska 16, 917 24 Trnava, Slovaška, roman.moravcik@stuba.sk

SI 147

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 148

Prejeto: 2011-12-14, sprejeto: 2012-11-09 © 2012 Strojniški vestnik. Vse pravice pridržane.

Modeliranje in simulacija delovanja sil odrezkov na posamezne ploščice rezkalnega orodja Gylienė, V. – Ostaševičius, V. Virginija Gylienė1,* – Vytautas Ostaševičius1 1 Tehniška univerza v Kaunasu, Oddelek za industrijski inženiring, Litva

Namen članka je predstavitev modeliranja procesa rezkanja po metodi končnih elementov (MKE). Gre za kompleksen proces, ki je odvisen od dinamike orodja in obdelovanca ter od zahtevnosti geometrije orodja. Za pripravo modela po MKE so bili opravljeni poskusi rezkanja, rezalne sile pa so bile izmerjene z dinamometrom Kistler. Ti poskusi so omogočili opredelitev rezalnih sil v koordinatnem sistemu dinamometra Kistler. Ocenjeno je bilo delovanje sil odrezkov na posamezne ploščice rezkalnega orodja.

Izmerjene rezalne sile so bile preračunane z uporabo matrike za transformacijo koordinatnega sistema, pri čemer material obdelovanca vsakič odstranjuje samo ena ploščica rezkalnega orodja. Na ta način je bilo mogoče sestaviti poenostavljen model MKE procesa rezkanja.

Ob upoštevanju prečnega prereza je bil pripravljen model MKE za določitev izhodnih parametrov modeliranja po MKE. Geometrijski model MKE procesa rezkanja in dinamično vedenje obdelovanega materiala sta bila opisana s predprocesorjem ANSYS in postprocesorjem LS-DYNA. Dinamični vplivi hitrosti preoblikovanja so upoštevani s skaliranjem statične meje plastičnosti s faktorjem, dobljenim po Cowper-Symondsovi enačbi.

Cowper-Symondsov deformacijski model se pogosto uporablja pri simulacijah dinamičnih procesov po metodi končnih elementov. V LS-DYNA je bila interakcija na stiku med ploščico in obdelovancem opredeljena z metodologijo „master-slave“ in metodo kazni. Konstante dinamike za MKE so bile izbrane za problem interakcije med deformabilnim telesom in togim telesom.

Med raziskovalnim delom so bili ovrednoteni vsi numerični parametri, izbrani glede na vedenje materiala pri visokohitrostnih deformacijah. Delo je pokazalo, da so opredeljeni parametri vedenja materiala (natančneje Cowper-Symondsove konstante vedenja materiala) za en proces odrezavanja uporabni tudi za druge procese odrezavanja pri isti rezalni hitrosti.

Najprej je bila opravljena analiza izotropnih, kinematičnih in kombiniranih modelov utrjevanja z namenom ugotavljanja njihovega vpliva na preostale napetosti in rezalno silo (tangencialno rezalno silo). Ugotovljeno je bilo, da elastoplastično vedenje materiala s kinematičnim in izotropnim utrjevanjem pomembno vpliva na spremembe rezalne sile. Preostale napetosti so bile ovrednotene ob upoštevanju interakcij na stiku, trenja, hitrosti preoblikovanja materiala in utrjevanja materiala.

Numerični rezultati razvitega modela se zelo dobro ujemajo z rezultati poskusov, napaka pa znaša 3 %.

Uporaba modela po MKE ima določene omejitve. Razviti model MKE ne more upoštevati toplotnih procesov, zato je uporaben le na področju visokohitrostne obdelave, kjer v obdelovanec prehaja samo 17 % toplote iz primarne cone. Prihodnje raziskovalno delo bo zato usmerjeno v dodatno potrjevanje razvitih modelov s primerjavo z Johson-Cookovim konstitutivnim modelom vedenja materiala obdelovanca, ter v uporabo modeliranja po MKE pri ultrazvočnih obdelovalnih procesih.

Novosti: Malo je res zanimivih študij modeliranja procesov rezkanja in ustvarjanja zanesljivih modelov po MKE. Večina študij MKE obravnava ortogonalne procese struženja. Predstavljena raziskava pojasnjuje interpretacijo rezultatov meritev rezalnih sil po korakih, ter povezuje rezultate s prečnim prerezom med procesom obdelave, ko se prečni prerez odrezka spreminja zaradi gibanja orodja.

Ključne besede: modeliranje po MKE, steblasto rezkanje, prečni prerez, Cowper-Symonds, Ls-Dyna

SI 148

*Naslov avtorja za dopisovanje: Tehniška univerza v Kaunasu, Oddelek za industrijski inženiring, Kęstučio st. 27, LT-44312 Kaunas, Litva, virginija.gyliene@ktu.lt

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 149

Prejeto: 2012-07-20, sprejeto: 2012-10-05 © 2012 Strojniški vestnik. Vse pravice pridržane.

Izdelki po meri z uporabo grupne tehnologije: študija primera iz pohištvene industrije

Suzić, N. – Stevanov, B. – Ćosić, I. – Anišić, Z. – Sremčev, N. Nikola Suzić1,* – Branislav Stevanov1 – Ilija Ćosić1 – Zoran Anišić1 – Nemanja Sremčev1 1 Univerza

v Novem Sadu, Tehniška fakulteta, Srbija

Namen študije je prikazati uporabo analize toka proizvodnje (PFA) v procesu pretvorbe podjetja za masovno proizvodnjo v sistem za masovno prilagajanje. Članek predstavlja prednosti sinergije uporabe grupne tehnologije (GT) in analize toka proizvodnje pri uveljavljanju masovnega prilagajanja (MC).

V članku so predstavljene dejavnosti za uspešno uveljavljanje strategije masovnega prilagajanja v podjetju iz pohištvene industrije. Podlaga za uvajanje strategije masovnega prilagajanja v proizvodni sistem je uspešno obvladovanje tehničnih zmožnosti podjetja na eni strani ter želj in potreb strank na drugi. Za doseganje tega cilja je predlagana uporaba grupne tehnologije in analize toka proizvodnje. Grupna tehnologija omogoča boljši nadzor nad proizvodnim procesom ter je namenjena doseganju optimalne uporabe zmogljivosti in fleksibilnosti proizvodnega sistema.

V prvem delu članka je podan pregled literature ter trenutnega stanja razvoja koncepta masovnega prilagajanja in pristopa grupne tehnologije. Glavni del članka je empirična študija podjetja iz pohištvene industrije. Empirična študija je sestavljena iz več korakov: analize proizvodnje, tržnih raziskav in sistemske analize. Končni rezultat so skupine delov izdelkov, analiza gruč in oblikovanje celic.

Rezultati in izsledki raziskave kažejo, da je pristop učinkovit pri skrajševanju časa priprave (od 3- do 10krat, odvisno od stroja). Poenostavlja tok materiala v sistemu, poenostavlja lansiranje nalogov v sistemu, skrajšuje čas izvedbe (od 8- do 12-kratno skrajšanje, odvisno od konkretnega izdelka), skrajšuje transportne poti in s tem transportni čas v sistemu (približno za dvakrat), ter zmanjšuje količino nedokončane proizvodnje in čakalne vrste med operacijami.

Proizvodne celice so le prvi korak in omogočajo boljšo organizacijo proizvodnega sistema. Popolna transformacija iz sistema masovne proizvodnje v sistem masovnega prilagajanja se ne more zanašati samo na grupno tehnologijo in je ni mogoče omejiti samo na transformacijo delavnice. Avtorji zato predlagajo razvoj več sistemov (pretežno softverskih) za masovno prilagajanje, npr.: spletno orodje za konfiguracijo izdelkov, s katerim lahko stranke konfigurirajo izdelke po meri z izbiro materiala, prilagoditvijo dizajna in izbiro posebnih možnosti; implementacija sistemov ERP in PDM/PLM za boljše razumevanje potreb strank, upravljanje s podatki o izdelkih in procesih, skupno rabo informacij in sodelovanje, analize in korektivne ukrepe; razvoj programske rešitve za ustvarjanje skupin delov in terminiranje v prilagojenem proizvodnem okolju; RFID označevanje za sledenje delom v delavnici in v skladišču, različne simulacije izvajanja proizvodnih procesov za napovedovanje možnih težav in vrednotenje rešitev; integracija prej omenjenih orodij in rešitev z intenzivno predstavitvijo podatkov v formatu XML. Vrednost članka je v uporabi pristopa grupne tehnologije za doseganje masovnega prilagajanja v realnem okolju pohištvene industrije. Članek prispeva k praktični uveljavitvi masovnega prilagajanja v pohištveni industriji. Članek daje vpogled v posebne značilnosti proizvodnje pohištva ter v možnosti izboljšanja proizvodnje prilagojenih izdelkov s teoretičnim in praktičnim znanjem na področju grupne tehnologije.

Ključne besede: masovno prilagajanje, grupna tehnologija, analiza toka proizvodnje, tok materiala, proizvodnja po meri, proizvodnja pohištva

*Naslov avtorja za dopisovanje: Univerza v Novem Sadu, Tehniška fakulteta, Trg Dositeja Obradovića 6, Novi Sad, Srbija, suzic@uns.ac.rs

SI 149

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 150

Prejeto: 2012-09-02, sprejeto: 2012-10-08 © 2012 Strojniški vestnik. Vse pravice pridržane.

Konstruiranje in optimizacija aktivnega in polaktivnega nelinearnega sistema obes terenskega vozila Lajqi, Sh. – Pehan, S. Shpetim Lajqi1,* – Stanislav Pehan2

1 Univerza

2 Univerza

v Prištini, Fakulteta za strojništvo, Kosovo

v Mariboru, Fakulteta za strojništvo, Slovenija

Za terenska vozila je značilno zelo veliko premikanje koles v vertikalni smeri, saj se s tem prepreči nevarnost prevračanja, ko vozilo potuje po neravnem terenu. Zaradi te značilnosti morajo imeti terenska vozila učinkovit sistem obes, saj morajo potnikom pri vožnji zagotavljati tudi ustrezno udobje in varnost. Konstruktorji vozil posvečajo veliko pozornost tako oblikovanju obes kakor tudi njihovi optimizaciji, vse z namenom, da bi izboljšali vozne lastnosti. Osnovni namen sistema obes je zagotoviti dober kontakt koles z neravno podlago, kar je možno izvesti samo z bolj ali manj kompliciranim sistemom obes. Članek prikazuje proces konstruiranja ter postopek optimizacije aktivnega in polaktivnega nelinearnega sistema obes, ki so namenjene za terensko vozilo. Našteta sistema se odlikujeta predvsem po tem, da zagotavljata boljše udobje in varnost kakor pasivni sistem obes.

Za pojasnjevanje in razlaganje delovanja aktivnega in polaktivnega sistema obes se uporablja dobro uveljavljen model četrtine vozila. Model četrtine vozila je mogoče na dokaj enostaven način prevesti v ustrezen matematični model, ki je sestavljen iz dveh diferencialnih enačb drugega reda, rešljivih po numerični poti. Za hitrejši potek numeričnega postopka se diferencialni enačbi prevedeta v primernejšo obliko, na primer v enačbe stanja, pri čemer se diferencialne enačbe drugega reda transformira v diferencialne enačbe prvega reda. Za ta postopek je treba uporabiti zmogljiv računalniški program, ki omogoča končni izračun vedenja obes z vsemi značilnostmi. Numerična simulacija je izpeljana v okolju MATLAB/Simulink. Preverjanje zanesljivosti uporabljenega računalniškega programa je opravljeno s primerjanjem rezultatov, ki so dobljeni z zmogljivim komercialnim paketom.

Ključni problem, ki ga je treba rešiti v zvezi z aktivnim ali polaktivnim sistemom obes, je določitev optimalne aktivne sile dušenja. To silo je teoretično mogoče ustvariti z dodatnima navideznima pasivnima amortizerjema. Prvi je na eni strani pritrjen na vzmeteno maso, drugi pa na nevzmeteno maso. Druga pritrdilna točka obeh navideznih pasivnih amortizerjev je pritrjena na navidezno oporo, ki je v zraku. V resnici takšnih navideznih amortizerjev seveda ni mogoče namestiti, saj pritrdilna točka v zraku ni mogoča. Resnična aplikacija navidezne opore v zraku je mogoča le z namestitvijo aktivnega dajalnika sile, ki bi bil nameščen med vzmeteno in nevzmeteno maso.

Predstavljeni fizikalni model z dodanimi navideznimi pasivnimi amortizerji je opisan z matematičnim modelom, nato pa je opravljena optimizacija njegovih bistvenih parametrov. Optimizacija parametrov, ki najbolj opredeljujejo aktivno silo dušenja, je opravljena z uporabo Hook-Jeevesove metode, ki temelji na nelinearnem programiranju po metodi stohastične parametrične optimizacije. Optimalni konstrukcijski parametri so bili doseženi takrat, ko je bila namenska funkcija minimalna.

Narejena in opisana je praktična aplikacija aktivnega in polaktivnega sistema obes na konkretnem terenskem vozilu. Opisana je primerjava z obnašanjem vozila, ki ima pasiven sistem obes. Za primerjavo se opazujejo pospeški šasije vozila, njeni pomiki in vertikalna sila na kolesu, kar so pravzaprav lastnosti, ki imajo neposreden vpliv na udobnost in varnost vožnje.

Sistem obes je optimiziran tako, da je zagotovljeno največje udobje potnikov in hkrati varna vožnja. V prispevku je pokazano, da je optimalne sile dušenja možno doseči le z aktivnim sistemom obes, ki daje boljše rezultate kot polaktivni sistem obes. Rezultat postopka optimizacije je aktivni sistem obes s sorazmerno mehko karakteristiko. Majhne dinamične obremenitve v sistemu zagotavljajo dober stik koles s podlago, hkrati pa je zagotovljeno tudi največje možno udobje potnikov. Aktivni sistem obes v primerjavi s pasivnim izboljša nekatere vozne karakteristike tudi do 80 %.

Ključne besede: terenska vozila, optimizacija obes, aktivne obese, polaktivne obese, pasivne obese

SI 150

*Naslov avtorja za dopisovanje: Univerza v Prištini, Fakulteta za strojništvo, Bregu i Diellit p.n., 10 000 Priština, Kosovo, shpetim.lajqi@uni-pr.edu

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 151

Prejeto: 2012-05-05, sprejeto: 2012-10-17 © 2012 Strojniški vestnik. Vse pravice pridržane.

Tribološke lastnosti prevlečenih trdokovinskih orodij pri struženju jekel z izboljšano obdelovalnostjo Sebhi, A. – Osmani,H. – Rech, J. Sebhi Amar1,* – Osmani Hocine1 – Rech Joel2

1 Univerza

Ferhat Abbes, Institut za optiko in finomehaniko, Alžirija šola za strojništvo, LTDS laboratorij, Francija

2 Narodna

Izboljševanje produktivnosti v industrijskem okolju kot konkurenčne prednosti, ob upoštevanju splošnih načel dela, ekologije in opustitvi uporabe določenih vrst hladilne tekočine zaradi okoljskih razlogov, zahteva raziskave jekel z izboljšano obdelovalnostjo in prevlečenih rezalnih orodij.

Za boljše razumevanje so potrebna nove in sodobne raziskave procesov odrezavanja, osredotočene na tribologijo stika med orodjem in odrezkom/obdelovancem. V tem kontekstu je preučena interakcija triboloških parov jekel z izboljšano obdelovalnostjo in prevlečenih karbidnih orodij, kakor tudi razmerje med koeficientom trenja, rezalno hitrostjo, obrabo orodja in kakovostjo površine. Uporabljen je bil tribometer, zasnovan za merjenje koeficienta trenja v težavnih pogojih obdelave z odrezavanjem. Pri eksperimentalnem delu sta bili uporabljeni jekli 42CrMo4 in 27MnCr5 ter trdokovinska orodja s prevleko TiN in AlTiN. Cilj tega dela je opredelitev značilnosti nekaterih materialov, ki se pogosto uporabljajo v industriji, ter iskanje optimalnih parametrov odrezavanja za zmanjšanje proizvodnih stroškov.

Glavna metoda, uporabljena v tem delu, je bilo preizkušanje trenja med različnimi rezalnimi orodji in materiali, ki se uporabljajo pri proizvodnji gredi, osi in delov vzmetenja. V prihodnje bodo potrebne dodatne raziskave za izpopolnitev prevlečenih trdokovinskih rezalnih orodij ter izboljšanje selektivnega prenosa plasti (STL) za nižje cene izdelave. Povečanje produktivnosti zahteva delo v raziskovalnih laboratorijih in opremljenost z napravami za vrednotenje lastnosti, kot so tribometri.

V članku je podana ocena koeficienta plastičnega trenja glede na koeficient adhezivnega trenja. Optimalna rezalna hitrost za obdelavo jekel 42CrMo4 in 27MnCr5 je v splošnem primeru pri uporabi trdokovinskih orodij s prevleko TiN 180 m/min, pri prevlekah AlTiN pa 65 m/min. Najdaljša življenjska doba rezalnega orodja je bila dosežena pri hitrosti približno 150 m/min in znaša približno 20 minut v okoljsko primernih pogojih suhe obdelave.

Ključne besede: tribologija, prevlečeno orodje, obraba, hrapavost, koeficient trenja, specifična rezalna sila, rezalna hitrost, doba uporabnosti orodja

*Naslov avtorja za dopisovanje: Univerza Ferhat Abbes, Institut za optiko in finomehaniko, Setif 19000, Alžirija, sebhiamar@yahoo.fr

SI 151

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 152-154 Osebne objave

Doktorske disertacije, znanstvena magistrska dela, diplomske naloge

DOKTORSKE DISERTACIJE Na Fakulteti za strojništvo Univerze v Mariboru sta z uspehom obranila svojo doktorsko disertacijo: dne 5. novembra 2012 Heike Marlene Anne EHMANN z naslovom: »Structuring of Sol-Gel Functionalized Cellulose Hybrid Materials and their Characterization« (Strukturiranje sol-gel funkcionaliziranih celuloznih hibridnih materialov in njihova karakterizacija) (mentor: prof. dr. Karin Stana Kleinschek); Namen doktorske naloge je strukturiranje celuloznih nano-kristalov z uporabo različnih organsko-funkcionalnih silanov in različnih kationskih sredstev za pripravo funkcionalnih materialov s kontroliranimi lastnostmi.Disertacija je razdeljena v štiri dele.

V prvem delu smo se osredotočili predvsem na pripravo in karakterizacijo celuloznih nano-kristalov (CNC), ki smo jih sintetizirali pri različnih hidroliznih pogojih. Kot vir celuloze je bila uporabljena mikrokristalina celuloza (MCC), pridobljena iz bombaža, za hidrolizo pa smo uporabili žveplovo in klorovo kislino, ter mešanico obeh. Glavni namen tega dela raziskave je stabilizacija celuloznih nanokristalov v različnih topilih, kar smo dosegli z uvedbo sulfatnih estrov na površino delcev, ki zagotavljajo elektrostatični odboj. Te skupine izkazujejo negativni naboj v celotnem pH območju in tako učinkovito stabilizirajo CNC delce. Celuloznim nano-kristalom smo določili ζ-potencial v odvisnosti od pH vrednosti disperzije ter koncentracije delcev, z dinamičnim sipanjem svetlobe (DLS) pa smo določili njihov raztros velikosti. Eden najpomembnejših dosežkov predstavljene raziskave je analiza koncentriranih vodnih disperzij celuloznih nano-kristalov z ozkokotnim rentgenskim sipanjem (SAXS).Uporaba posplošene indirektne Fourierjeve transformacije (generalized indirect Fourier transformation; GIFT) omogoča določitev strukturnih lastnosti CNC delcev, kot so oblika, velikost ter površinski naboj. Celulozne nano-kristale smo nanesli na različne substrate (silicijeve ploščice, objektna stekla, polistirenske ploščice) z različnimi načini nanašanja. Morfologijo nastalih filmov smo analizirali z uporabo mikroskopije na atomsko silo (AFM), Sarfus tehniko ter vrstično elektronsko mikroskopijo. Za karakterizacijo površin smo prav tako uporabili sofisticirano sipalno metodo, kar predstavlja drugi pomemben dosežek predstavljenega doktorskega dela.Z določanjem SI 152

proste površinske energije smo raziskali hidrofilno – hidrofoben značaj pripravljenih plasti ter njihovo interakcijsko sposobnost z različnimi tekočinami.

Filme, ki smo jih formirali v vodi in etanolu smo analizirali z ozkokotnim in širokokotnim rentgenskim sipanjem, ter tako določili nanometrske lastnosti CNC delcev.Zelo nabiti CNC delci, pripravljeni s hidrolizo z žveplovo kislino, so se izkazali za najprimernejše za nadaljnjo funkcionalizacijo z različnimi organskofunkcionalnimi silani ter za plastenje z različnimi kationskimi sredstvi.

Drugi del disertacije se osredotoča na karakterizacijo različnih organsko-funkcionalnih silanov. Uporabljene silane lahko razdelimo v tri skupine; prvo skupino predstavljajo silani, ki ne hidrolizirajo in se uporabljajo kot polnilci. V drugi skupini se nahajajo silani za funkcionalizacijo površin; ti imajo tri organske skupine vezane na silicijev atom in le eno skupino, ki hidrolizira. Tretjo skupino pa predstavljajo zamreževalni silani z le eno organsko skupino in tremi skupinami, ki hidrolizirajo in omogočajo zamreženje.Vse alkoksisilane smo hidrolizirali v kislem etanolu ter raziskali njihovo uporabnost. Z merjenjem površinske napetosti smo ugotavljali tendenco akumuliranja silanov na tekočeplinski fazni meji. Predhodno hidrolizirane raztopine silanov smo nanesli na različne substrate ( silicijeve ploščice, objektna stekla, polistirenske ploščice).

Makroskopsko morfologijo teh plasti smo raziskali z optično mikroskopijo in Sarfus tehniko, z določanjem stičnih kotov pa smo okarakterizirali površinsko energijo nastalih filmov.

V tretjem delu disertacije je opisana priprava in karakterizacija hibridnih materialov. Četrti del disertacije se nanaša na aplikacije strukturiranih CNC delcev, ki smo jih pripravili s hidrolizo v žveplovi kislini. Raziskali smo antimikrobno aktivnost teh delcev in izvedli preliminarne raziskave njihove antitrombogene aktivnosti; dne 5. novembra 2012 Tamilselvan MOHAN z naslovom: »Nanometric Cellulosic Layers for Specific Adsorption of Polysaccharides and Immobilization of Bioactive Molecules« (Nanometrske celulozne plasti za specifično adsorpcijo polisaharidov in imobilizacijo bioaktivnih molekul) (mentor: prof. dr. Karin Stana Kleinschek); Namen predstavljenega doktorskega dela je razvoj nanometrskih amorfnih celuloznih modelnih filmov za imobilizacijo funkcionalnih DNA molekul

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 152-154

in uporaba pridobljenega znanja za pripravo DNA mikromrež. Doktorska disertacija je razdeljena v tri dele in sicer; priprava in karakterizacija delno in popolnoma regeneriranih celuloznih filmov; priprava funkcionalnih polisaharidnih konjugatov in priprava DNA mikromrež s polisaharidnimi funkcionalnimi konjugati.

Prvi del se nanasa predvsem na in-situ in exsitu regeneracijo celuloznih filmov in njihovo karakterizacijo. Z uporabo kremenove mikrotehtnice (QCM-D metoda) smo podrobno spremljali hidrolizo in konverzijo trimetilsililne celuloze (TMSC) v celulozo v hlapih klorovodikove kisline. Plinasta HCl v neprekinjenem dotoku reagira s plastjo TMSC in na taksen nacin tvori plast celuloze. Raziskali smo kinetiko procesa regeneracije in dolocili reakcijo prvega reda. Poleg tega smo raziskali tudi vpliv koncentracije kisline na kinetiko reakcije ter na maso in debelino formiranega sloja celuloze.

Za potrebe študija ex-situ regeneracije smo prav tako pripravili TMSC filme s tehniko ‘’spin coat’’. V nasprotju z in-situ metodo regeneracije smo v tem primeru položili substrate s TMSC filmi v zaprto posodo, kjer so bili izpostavljeni hlapom klorovodikove kisline. Postopek regeneracije je potekal pri različnih časih izpostavitve kislinskim hlapom ter volumnih kisline. Spremembe v strukturi, debelini filmov, površinski elementni sestavi ter površinski prosti energiji regeneriranih celuloznih filmov (pri različnih časih regeneracije) smo raziskali z uporabo, ATR-IR, Sarfus, XPS tehnik ter z merjenjem stičnih kotov.

Z interakcijo med delno ter popolnoma regeneriranimi celuloznimi filmi in encimom celulazo (Trichoderma viride) smo dodatno raziskali stopnjo hidrolize TMSC filmov in posledično stopnjo njihove regeneracije. Spremembe v masi filma in disipaciji energije, kot posledice delovanja celulaze, smo korelirali s sposobnostjo omakanja filmov in njihovo elementno sestavo. Stopnja encimske razgradnje regeneriranih celuloznih filmov je v dobri korelaciji s stopnjo regeneracije. V kombinaciji s kvarčno mikrotehtnico smo uporabili tudi kapilarno consko elektroforezo, s katero smo določili razgradne produkte encimske hidrolize celuloznih filmov.

Kombinacija QCM-D tehnike in postopek encimske razgradnje celuloznih filmov se je izkazala koz zanesljiva metoda spremljanja regeneracije TMSC filmov v odvisnosti od časa.

Vpliv toplotne obdelave na tako pripravljene filme smo dolocili z naknadno izpostavitvijo celuloznih filmov povišani temperaturi za daljši čas (6 ur). Segrevanje povzroci preureditev filmov, ki se ne ponašajo s posebnimi strukturnimi artefakti, v fibrilarno strukturo, kar je razvidno iz AFM

posnetkov. Uporabili smo različne analitske metode, s katerimi smo raziskali spremembe v strukturi, elementni sestavi, debelini, sposobnosti omakanja ter prosti površinski energiji regeneriranih celuloznih filmov pred in po toplotni obdelavi; GIXRD, ATRIR, Sarfus tehnika, XPS in goniometrija. Z izvedbo postopka izmenjave topila (D2O/H2O) smo dokazali, da se vsebnost vode in sposobnost navzemanja vode toplotno obdelanih regeneriranih celuloznih filmov občutno zmanjša v primerjavi z neobdelanimi filmi.

ZNANSTVENA MAGISTRSKA DELA Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjala svoje magistrsko delo: dne 11. novembra 2012 Nina MIHOVEC z naslovom: »Koncepiranje oblike lahkih okrovov iz polimerov« (mentor: prof. dr. Jožef Duhovnik).

DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 29. novembra 2012: Matjaž ČERNIVC z naslovom: »Izdelava okvirja očal iz kompozitnih materialov« (mentor: doc. dr.

Joško Valentinčič, somentor: doc. dr. Viktor Šajn); Miha KRESAL z naslovom: »Semantično podprto poizvedovanje po proizvodnih podatkih« (mentor: izr. prof. dr. Peter Butala); Kristjan VUJKOVIĆ z naslovom: »Vpliv temperature na geometrijsko natančnost obdelovalnega stroja« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Franci Pušavec); dne 30. novembra 2012: Miha KAVČIČ z naslovom: »Naprednejša metoda izračuna hladilnih obremenitev stavb« (mentor: prof. dr. Vincenc Butala, somentor: doc. dr. Matjaž Prek); Luka OMEJC z naslovom: »Integracija vakuumskega izolacijskega panela v pokrov toplotne podpostaje« (mentor: prof. dr. Iztok Golobič); Simon POGORELC z naslovom: »Zasnova in analiza delovanja centralno nadzornega sistema v zdravstvenem domu« (mentor: prof. dr. Vincenc Butala). * Na Fakulteti za strojništvo Univerze v Mariboru sta pridobila naziv univerzitetni diplomirani gospodarski inženir: dne 29. novembra 2012: Marko MAVRIČ z naslovom: »Vrednostna analiza kot integralni del razvoja držala za Smart SI 153

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, SI 152-154

telefone na kolesih« (mentor: doc. dr. Marjan Leber, somentorica: prof. dr. Majda Bastič); Žiga VOH z naslovom: »Sodoben pristop obvladovanja stroškov in vodenja projektov po principu kritične verige« (mentor: doc. dr. Marjan Leber, somentorica: prof. dr. Majda Bastič). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir mehatronike (UN): dne 29. novembra 2012: Andrej NOVAK z naslovom: »Senzorski sistemi robota za reševanje« (mentor: izr. prof. dr. Karl Gotlih, somentorica: doc. dr. Suzana Uran). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 8. novembra 2012: Marko FILIPČIČ z naslovom: »Konstruiranje in izdelava orodja za rezanje izolirne plošče« (mentor: doc. dr. Joško Valentinčič, somentor: doc. dr. Tomaž Pepelnjak); Blaž KAMBIČ z naslovom: »Hranilniki toplote v ogrevalnih sistemih« (mentor: prof. dr. Alojz Poredoš);

SI 154

Domen PINTAR z naslovom: »Optimirane tehnologije izdelave izvrtin« (mentor: prof. dr. Janez Kopač); Uroš SOVDAT z naslovom: »Vpliv čistosti površine drsnega obroča iz bakra na lastnosti spoja izdelanega z ultrazvokom« (mentor: prof. dr. Janez Tušek). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 30. novembra 2012: Tomaž BIZJAK z naslovom: »Vpliv biogoriv na karakteristike curka goriva« (mentorica: prof. dr.

Breda Kegl, somentor: Blaž Vajda); * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva (VS): dne 30. novembra 2012: Janez PLAVČAK z naslovom: »Vpliv reducirnih ventilov za vodo na rezultat meritve pretoka vodomera« (mentor: prof. dr. Brane Širok, somentor: doc. dr. Ignacijo Biluš).

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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58 (2012) 12

Chamber of Commerce and Industry of Slovenia Metal Processing Industry Association

Since 1955

Strojniški vestnik Journal of Mechanical Engineering

n, Lian Xia, Xiaoqing Tian: nd Performance Analyses of Linkage Models for al Gears Based on Four-Axis Linkage omar, Nenad Vulić: ls Selection for Environmentally Friendly stem ária Štefániková, Roman Čička, Ľubomír Čaplovič, man Šturm: ions in High Alloy Cold Work Tool Steel lav Stevanov, Ilija Ćosić, Zoran Anišić, Nemanja Sremčev: cts through Application of Group Technology: niture Manufacturing slav Pehan: zations of Active and Semi-Active Non-linear s for a Terrain Vehicle Hocine, Rech Joel: our of Coated Carbide Tools during Turning of Steels hinability

Journal of Mechanical Engineering - Strojniški vestnik

les-Ocampo, Juan Carlos Jauregui-Correa, Peter Krajnik, a-Camacho, Gilberto Herrera-Ruiz: r the Instability Detection in Centerless Grinding

year

no. 12 2012 58

volume

Cover: Non linear systems show a time dependent frequency response, such as the instabilities found in a grinding process. For these signals, traditional Fourier Transform is unable to analyze the non linear effects, and other techniques are better fitted. In this case, the phenomenon was reproduced with a time-frequency map. The timefrequency maps were obtained by applying the Continuous Wavelet Transform. The Continuous Wavelet Transform converts the displacement function into a two dimensional vector that is a function of time and frequency.

Image Courtesy: Autonumus University of Queretaro, Faculty of Engineering, Mexico

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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[6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 2009-09-07.

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58 (2012) 12

Since 1955

Contents Papers

Jose Billerman Robles-Ocampo, Juan Carlos Jauregui-Correa, Peter Krajnik,

Perla Yasmin Sevilla-Camacho, Gilberto Herrera-Ruiz: 693 Nonlinear Model for the Instability Detection in Centerless Grinding Process

Youyu Liu, Jiang Han, Lian Xia, Xiaoqing Tian: 701 Hobbing Strategy and Performance Analyses of Linkage Models for

Non-Circular Helical Gears Based on Four-Axis Linkage

Roman Moravčík, Mária Štefániková, Roman Čička, Ľubomír Čaplovič, Karin Kocúrová, Roman Šturm:

709 Phase Transformations in High Alloy Cold Work Tool Steel

Virginija Gylienė, Vytautas Ostaševičius: 716 Modeling and Simulation of a Chip Load Acting on a Single Milling Tool Insert

Nikola Suzić, Branislav Stevanov, Ilija Ćosić, Zoran Anišić, Nemanja Sremčev: 724 Customizing Products through Application of Group Technology:

A Case Study of Furniture Manufacturing

Shpetim Lajqi, Stanislav Pehan: 732 Designs and Optimizations of Active and Semi-Active Non-linear

Suspension Systems for a Terrain Vehicle

Sebhi Amar, Osmani Hocine, Rech Joel: 744 Tribological Behaviour of Coated Carbide Tools during Turning of Steels

with Improved Machinability

Journal of Mechanical Engineering - Strojniški vestnik

12 year 2012 volume 58 no.

Strojniški vestnik Journal of Mechanical Engineering