TRANSIENT THERMOELASTIC ANALYSIS OF DRY … · machine design, Vol.5(2013) No.4, ... of contact used in ANSYS software; single contact, ... the amount of the penetration. Lower values

machine design, Vol.5(2013) No.4, ISSN 1821-1259 pp. 141-150

*Correspondence Author’s Address: Technische Universität Hamburg-Harburg, Institut G-2/Amp/ Denickestraße 17 (Gebäude L), 21073 Hamburg-Germany, [email protected]

Original scientific paper

TRANSIENT THERMOELASTIC ANALYSIS OF DRY CLUTCH SYSTEM Muhammad MUMTAZ JAMIL AKHTAR 1, * - Oday I. ABDULLAH 1 - Josef SCHLATTMANN 1

1 Department of System Technology and Mechanical Design Methodology, Hamburg University of Technology, Germany

Received (26.08.2013); Revised (14.11.2013); Accepted (16.11.2013) Abstract: The high thermal stresses, generated between the contacting surfaces of clutch system (pressure plate, clutch disc and flywheel) due to the frictional heating during the slipping, are considered to be one of the main reasons of clutch failure for contact surfaces. A finite element technique has been used to study the transient thermoelastic phenomena of a dry clutch system. The effect of sliding speed on contact pressure distribution, temperature field and heat flux generated along the frictional surfaces is investigated. Analysis has been completed using two dimensional axisymmetric model to simulate the clutch system. ANSYS software has been used to perform the numerical calculation in this paper. Key words: Dry friction, clutch disc, FEM, thermoelastic behavior, temperature field. 1. INTRODUCTION A clutch system is one of the most important components of a vehicle that plays a vital role in the transmission of power and control of motion from one component to another. The main task of the clutch is to connect and disconnect the driver (engine) and the driven (gearbox), and assist a gentle engagement [1]. During the engagement of clutch, pressure plate pushes the clutch disc towards the flywheel to bring it in contact with the flywheel and slipping occurs between the contact surfaces. At the beginning of engagement slipping occurs between the contact surfaces of the clutch system, as a result of this slipping heat is generated and the surface temperature increases gradually to higher values. In some cases temperature exceeds the maximum temperature limit of the material and eventually leads to premature failure [2]. Al-Shabibi and Barber [3] investigated an alternative method to solve the thermoelastic contact problem with frictional heat generation. Two-dimensional axisymmetric finite element model built to study the temperature field and pressure distribution of two sliding disks. Constant and varying speeds were considered in this analysis. The results show that the initial temperature is shown to be crucial since it represents the particular solution, which can have quite irregular form, this situation is especially true when the system operates above the critical speed. Lee et al. [4] analyzed the effects of three load conditions of thermal loading, centrifugal force and contact pressure of diaphragm spring on pressure plate of a clutch system. The results show a significant effect of thermal loading and contact pressure that suggested an increase in the thickness of pressure plate to enhance the thermal capacity of pressure plate so that the thermal stresses may be reduced. Zhang et al. [5] used Matlab/Simulink to build the model and find the temperature field during the engagement of wet clutches in hydrodynamic machineries. Two

dimensional heat conduction model was used to calculate the temperature distribution along the axial and radial direction on the sliding interface between the contact surfaces. The results have shown a good agreement with the experimental work. Zagrodzki [6] studied the frictional heating in sliding systems and the effect of sliding speed on the stability of the system when the sliding speed exceeds the critical value. Finite element model was used to investigate the transient thermoelastic process, spatial discretization and modal superposition is presented. Constant sliding speed was performed in this analysis. The transient solution includes both of homogenous part (corresponding to the initial condition) and non-homogenous part (represents the background process). The results show that the important parameters which contribute in the background process are the nominal process equivalent to uniform pressure distribution in isothermal case and the other is the pressure variation caused by geometric imperfection or by design features. Shahzamanian et al. [7] studied the transient and contact analysis of functionally graded (FG) brake disk. The coulomb contact friction is considered between the pad and the brake disc. It was found that the contact pressure and contact total stress increases with an increase in the contact stiffness factor. Gao and Lin [8] used a transient finite element technique to analyze the temperature fields in a solid rotor of a brake system with appropriate thermal boundary conditions. Effects of moving heat source (pad) with a relative sliding speed variation were considered. The results show that the operating characteristics of the brake have potential effects on the surface temperature distribution and the maximum contact temperature. Grzes [9] performed a transient thermal analysis of disc brake in single brake application to examine the effect of the angular velocity and the contact pressure on temperature field of disc brake. A parabolic heat conduction equation for two-dimensional model was used

Muhammad Mumtaz Jamil Akhtar, Oday I. Abdullah, Josef Schlattmann: Transient Thermoelastic Analysis of Dry Clutch System; Machine Design, Vol.5(2013) No.4, ISSN 1821-1259; pp. 141-150

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to obtain the numerical simulation. The results show that both rotating speed of the disc and contact pressure with specific material properties greatly affect the disc brake temperature fields. Adamowicz and Grzes [10] studied the influence of convective heat transfer on transient temperature distribution of a real disc brake. They used finite element method technique to investigate an impact of heat transfer coefficient on heat dissipation from the solid disc rotor of a disk brake. The results show that in terms of single braking process for the specified dimensions and thermo-physical properties of materials the convective heat transfer mode doesn't allow to significantly lower the temperatures of the rotor. However, in the following release period after the braking action when the velocity of the vehicle remains on the same level, a considerable decrease of temperature has been observed. Abdullah and Schlattmann [11, 12, 13, 14 & 15] investigated the temperature field and the energy dissipated from dry friction clutch during a single and repeated engagement under uniform pressure and uniform wear conditions. They also studied the effect of pressure between contact surface when varying with time on the temperature field and the internal energy of clutch disc using two approaches heat partition ratio approach to compute the heat generated for each part individually whereas the second applies the total heat generated for the whole model using contact model. Furthermore, they studied the effect of engagement time and sliding velocity function, thermal load and dimensionless disc radius (inner disc radius/outer disc radius) on the thermal behavior of the friction clutch in the beginning of engagement. This paper presents full details to compute the temperature field and contact pressure distribution of the dry friction clutch during the beginning of engagement (sliding period). Finite element method is used to obtain the numerical simulation of transient thermoelastic behavior of a clutch system. Pressure applied during the period of engagement was assumed to be constant and the effect of convection is considered. This work shows the effect of sliding speed on the temperature field and the contact pressure distribution for the clutch system. 2. FUNDAMENTAL PRINCIPLES A friction clutch consists of pressure plate, clutch disc and flywheel as shown in Figure 1. When the clutch starts to engage the slipping will occur between contact surfaces due to the difference in the velocities between them (slipping period), after this period all contact parts are rotating at the same velocity without slipping (full engagement period). A high amount of kinetic energy is converted into heat energy at interfaces according to the first law of thermodynamics during the slipping period and the heat generated between contact surfaces will be dissipated by conduction between friction clutch components and by convection to the environment. In addition to the thermal effect due to the slipping there is another load condition which is the contact pressure between the contact surfaces. In the second period, there are three types of load conditions, thermal effect from the last period (slipping period), pressure between contact

surfaces due to the axial force of diaphragm spring and the centrifugal force due to the rotation of the contacting parts. Figure 2 shows the load conditions during the engagement cycle of the clutch system, where ts is the slipping time and T is the torque transmitted by the clutch [16].

3. FINITE ELEMENT FORMULATION This section presents the steps to simulate the contact elements of friction clutch using ANSYS software. Moreover it gives more details about the types of contact and algorithm which is used in this software.

Time

Thermal +Contact pressure

Slipping period (Transient case)

Full engagement period

(Steady-state case)

Thermal + Contact pressure+ Centrifugal effect

ts

T

Fig.2. The load conditions during the engagement cycle of the clutch

Tor

qu

e

Flywheel

Clutchdisc

Pressureplate

Fig.1. The main parts of clutch system


143

The first step in this analysis is the modeling. Due to the symmetry in the geometry (frictional lining without grooves) and boundary conditions of the friction clutch (the effect of the pressure and the thermal load due to the slipping were taken into consideration), two-dimensional axisymmetric FE model can be used to represent the contact between the clutch elements during the slipping period. The axisymmetric contact model of dry friction clutch system is shown in Figure 3. The effects of conduction as well as convection are considered in this analysis.

There are three basic types of contact used in ANSYS software; single contact, node-to-surface contact and surface-to-surface contact. Surface-to-surface contact is the most common type of contact used for bodies that have arbitrary shapes with relative large contact areas. This type of contact is most efficient for bodies that experience large values of relative sliding such as block sliding on a plane or sphere sliding within a groove [17]. Surface-to-surface contact is the type of contact assumed in this analysis because of the large areas of clutch elements in contact. The elements used for contact elastic model in this analysis are:

“PLANE13” used for all elements of the clutch system (flywheel, clutch disc, and pressure plate).

“CONTA172” used for contact surfaces that are the upper and lower surfaces of clutch disc.

“TARGE169” used for the target surfaces that are the lower surface of flywheel and the upper surface of pressure plate.

Figure 4 shows the schematic details of all elements that have been used in contact analysis. The element used for transient thermal model (heat conduction and convection is considered) is PLANE55. Higher values of contact stiffness will decrease the amount of penetration, but can lead to ill-conditioning of the global stiffness matrix and convergence difficulties. The stiffness relationship between contact and target surfaces will decide the amount of the penetration.

Lower values of contact stiffness can lead to a certain amount of penetration and facilitate convergence of the solution. The contact stiffness for an element of area A is calculated using the following formula [18]:

dAfefF Tiikn (1)

Where f is the shape function and e is the elastic restraining stiffness and is dependent on the material properties. The default value of the contact stiffness factor FKN is 1 and it is appropriate for bulk deformation. If bending deformation dominates the solution, a smaller value of FKN = 0.1 is recommended. There are five different algorithms used for surface-to-surface contact type, Augmented Lagrange method is used in this analysis to obtain the contact distribution between the contact surfaces of clutch system. This algorithm is an iterative penalty method. The constant traction (pressure and frictional stresses) are augmented during equilibrium iterations so that the final penetration is smaller than the allowable tolerance. This method usually leads to a better conditioning and is less sensitive to the magnitude of the constant stiffness. The contact force (pressure) between two contact bodies is:

pnn xkF (2)

Where Fn is the contact force, kn is the contact stiffness, xp is the distance between the two existing nodes or separate contact bodies (penetration or gap) and is Lagrange multiplier component (Figure 5). The axisymmetric finite element models (elastic and thermal) of friction clutch system with boundary conditions are shown in Figures 6 & 7. In Figure 7, h is the flow of heat to the environment due to convection and Qgen.f, Qgen.c and Qgen.p are the

Fig.3. The Contact model for clutch system

Axial Cushion

Flywheel

Pressure plate

The frictional lining r

z

Conta172Plane13Targe169

Flywheel

Pressure plate

Clutch disc

Fig.4. Elements used in contact analysis of friction clutch (No. of elements=2084)

Fn

xp kn

Fig.5. The contact stiffness between two contact bodies


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amounts of heat flux generated in flywheel, clutch disc and pressure plate respectively.

A mesh sensitivity study was done to choose the optimum mesh from computational accuracy point of view. The full Newton-Raphson with unsymmetric matrices of elements used in this analysis assuming a large-deflection effect. In all computations for the friction clutch model, material has been assumed a homogeneous and isotropic material and all parameters and material properties are listed in Table 1. Analysis is conducted by assuming there are no cracks in the contact surfaces. In modeling of contact problems, a special attention is required because the actual contact area between the contacting bodies is usually not known beforehand. In contact problems, unlike other boundary problems, nodes on the contact surface do not have prescribed displacements or tractions. Instead, they must satisfy two relationships: (1) Continuity of normal displacements on the contact surface (no overlap condition of contact area) (2) Equilibrium conditions (equal and opposite tractions) Even if the contacting bodies are linear materials, contact problems are nonlinear because the contact area does not change linearly with the applied load. Accordingly, iterative or incremental schemes are needed to obtain accurate solutions of contact problems. The iterations to obtain the actual contact surface are finished when all of these conditions are met [19].

Table 1. The properties of materials and operations

Parameters Values

Inner radius of friction material & axial cushion, ri [m] 0.06298

Outer radius of friction material & axial cushion, ro[m] 0.08721

Thickness of friction material [m], tl 0.003

Thickness of the axial cushion [m], taxi. 0.0015

Inner radius of pressure plate [m], rip 0.05814

Outer radius of pressure plate [m], rop 0.09205

Thickness of the pressure plate [m], tp 0.00969

Inner radius of flywheel [m], rif 0.04845

Outer radius of flywheel [m], rof 0.0969

Thickness of the flywheel [m], tf 0.01938

Pressure, p [MPa] 1

Coefficient of friction, μ 0.2

Number of friction surfaces, n 2

Young’s modulus for friction material, El [GPa] 0.30

Young’s modulus for pressure plate, flywheel & axial cushion, (Ep, Ef, and Eaxi), [Gpa]

125

Poisson’s ratio for friction material, 0.25

Poisson’s ratio for pressure plate, flywheel & axial cushion

0.25

Density for friction material, (kg/m3), ρl 2000

Density for pressure plate, flywheel & axial cushion, (kg/m3), (ρp, ρf, and ρaxi)

7800

Specific heat for friction material, [J/kg K] 120

Specific heat for pressure plate, flywheel & axial cushion, [J/kg K]

532

Conductivity for friction material, [W/mK ] 1

Conductivity for pressure plate, flywheel & axial cushion [W/mK]

54

Thermal expansion for friction material and steel [K-1]

12e-6

Slipping time, ts [s] 0.4

Figure 8 shows the interfaces of two adjacent subregions i and j of elastic bodies. The elastic contact problem is treated as quasi-static with standard unilateral contact conditions at the interfaces. The following constraint conditions of displacements are imposed on each interface:

,ji ww if P > 0 (3)

,ji ww if P = 0 (4)

Where P is the normal pressure on the friction surfaces. The radial component of the sliding velocity resulting from the deformations is considerably smaller than the circumferential component. Therefore, the frictional forces in radial direction on the friction surfaces are disregarded in this study [20]. Figure 8 (b) shows thermal phenomena of two adjacent subregions of bodies. The

Fig.7. FE models with the boundary conditions. (Thermal model)

r

z

Clutchdisc

Flywheel

Pressureplate

hh

h

h

Qgen.f+Qgen.c

Qgen.p+Qgen.c

Fig.6. FE model with boundary conditions (elastic model)

r

z

Pressure

Contact surfaces

Pressure plate

Clutch disc

Flywheel

Ux=0


145

interfacial thermal boundary conditions depend on the state of mechanical contact. Two unknown terms qni and qnj exist on each interface. To fully define the heat transfer problem, two additional conditions are required on each contact interface. If the surfaces are in contact, the temperature continuity condition and the heat balance condition are imposed on each interface:

ji TT , if P > 0 (5)

njnin qqqq Pr , if P > 0 (6)

Where and are the coefficients of friction and

angular sliding velocity, respectively. Using the aforementioned conditions, equations of one node from each pair of contact nodes are removed. If the surfaces are not in contact, the separated surfaces are treated as an adiabatic condition:

njni qqq 0 , if P = 0 (7)

(a) (b)

Fig.8. Contact model for (a) elastic and (b) transient thermal problem in two adjacent subregions

Fig.9. Schematic diagram of transient thermal analysis [21]

Distribution of normal pressure P in Eq. (6) can be obtained by solving the mechanical problem occurring in the clutch disc. Assume the sliding angular velocity decreases linearly with time as,

)1()(s

o t

tt , stt 0 (8)

Where ωo is the initial sliding angular velocity when the clutch starts to slip (t=0). Figure 9 shows the schematic diagram for the finite element analysis of a coupled-field problem. Two different models are prepared; one to solve the elastic contact problem to get contact pressure distribution and the other to solve the transient thermal problem considering heat conduction and convection effects to get the temperature field distribution during the sliding of a clutch. The whole period is divided into small time steps assuming the contact pressure is constant during these time steps. Output of the elastic model (contact pressure distribution) is used to define the frictional heat flux for the thermal model using eq. (6) [21].

4. RESULTS AND DISCUSSIONS Transient thermoelastic analysis of a dry friction clutch is carried out to investigate the effect of relative sliding velocities on contact pressure distribution and temperature field during the slipping period of a clutch system. Series of computation have been conducted using four different initial sliding angular velocities (75, 150, 225 and 300 rad/s). The effects of conduction and convection are considered in transient thermal analysis. Figures 10-17 show the contact pressure distribution of both sides of the clutch disc (flywheel side and pressure plate side) using different initial sliding angular velocities at selected time intervals. Approximately the same behavior of contact pressure distribution can be seen for both sides of the clutch disc. The contact pressure values increase when the sliding speed increases. The maximum values of contact pressure occur at a sliding velocity of 300 rad/s. The values of contact pressure grow with the time and maximum values of contact pressure during the slipping period occur near the inner radius when the slipping period almost approaches to an end and the system is near to enter the full engagement period. The maximum values of contact pressure are found to be 2.73 MPa and 2.84 MPa for the flywheel side and pressure plate side respectively. Figures 18-25 illustrate the variation of the heat flux with disc radius of both sides of clutch disc (flywheel side and pressure plate side) for different sliding velocities at selected time steps. It can be noted that the trend of heat flux with the disc radius for both sides of the clutch disc is approximately similar.


146

Fig.10. Contact pressure distribution at flywheel side with ωo=75 rad/s




Fig.14. Contact pressure distribution at pressure plate side with ωo=75 rad/s



147

Heat flux is proportional to the sliding speed and higher values of heat flux occur at higher sliding speeds. It can be observed that the location of maximum value of heat flux shifts from outer radius towards the near of inner radius with the time. Reason for these results is the higher amount of heat flux occurring at the start of the slipping period (with maximum sliding speed) and as time passes, pressure distribution changes due to the thermal deformation in the clutch disc. The maximum values of the heat flux are found to be 7.45 MW/m2 and 7.46 MW/m2 at sliding speed=300 rad/s for the flywheel and pressure plate side respectively. Figures 26-29 show the variation of temperature with time for different locations at the surfaces of clutch disc {inner radii at the flywheel and pressure plate sides (rif & rip), mean radii at the flywheel and pressure plate sides (rmf & rmp) and outer radii at the flywheel and pressure plate sides (rof & rop)}. It can be seen that the maximum values of temperature occur at the mean radius for both sides of

Fig.19. Heat flux distribution at flywheel side with ωo=150 rad/s






148

Fig.26. Temperature distribution at different radii locations with ωo=75 rad/s


Fig.22. Heat flux distribution at pressure plate side with ωo=75 rad/s





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the clutch disc and the minimum values occur at the outer radius of the clutch. The maximum values of the temperature are found to be 446.8 K and 447 K at ωo=300 rad/s on the flywheel and pressure plate sides respectively. Also, it can be noted that the temperature rises with the time from its initial value to attain the maximum value near the middle of the slipping period and finally decreases to the final temperature at the end of the slipping period. Figure 30 demonstrates the variation of the maximum temperature with time for different angular sliding speeds. The maximum value of the temperature is found to be 465.4 K with ωo=300 rad/s. 5. CONCLUSIONS In this paper, the solution of the transient homogeneous thermoelastic analysis of the clutch system during the

beginning of engagement (slipping period) has been performed. A two dimensional axisymmetric finite element model was built to obtain the contact pressure distribution and temperature field distribution of the clutch system (flywheel, clutch disc and pressure plate). It can be seen that the values of contact pressure and temperature field are proportional to the sliding speed. It’s necessary to take into consideration the maximum limit of the sliding velocity of friction material because when the sliding speed between the contact surfaces exceeds the maximum limit, a high amount of heat will be generated at the contact surfaces and this situation will lead to rapidly increase the rate of wear and clutch failure in short time. This study presents a valuable design tool to investigate the effect of thermoelastic phenomena of the clutch system behaviour during the beginning of its engagement.




Fig.30. Maximum temperature history curves with different sliding velocities


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Approach, 5th ed. 5-Maxwell Drive, Clifton Park, NY 12065-2919, USA: Delmar, Cengage Learning, 2009.

[2] O.I. Abdullah, J. Schlattmann, A.M. Al-Shabibi, "Stresses and Deformations Analysis of a Dry Friction Clutch System," Tribology in Industry, vol. 35, no. 2, pp. 155-162, 2013.

[3] Abdullah M. Al-Shabibi and James R. Barber, "Transient Solution of the Unperturbed Thermoelastic Contact Problem," Journal of Thermal Stresses, vol. 32, no. 3, pp. 226-243, February 2009.

[4] Choon Yeol Lee, Il Sup Chung, Young Suck Chai, "Finite Element Analysis of an Automobile Clutch System," Key Engineering Materials, vol. 353-358, pp. 2707-2711, September 2007.

[5] Jin-Le Zhang, Biao Ma, Ying-Feng Zhang and He-Yan Li, "Simulation and Experimental Studies on the Temperature Field of a Wet Shift Clutch during one Engagement," in International Conference of Computational Intelligence and Software Engineering (CiSE), IEEE, 2009.

[6] Przemyslaw Zagrodzki, "Thermoelastic Instability in Friction Clutches and Brakes-Transient Modal Analysis Revealing Mechanisms of Excitation of Unstable Modes," International Journal of Solids and Structures, vol. 46, pp. 2463–2476, 2009.

[7] M.M. Shahzamanian, B.B. Sahari, M. Bayat, Z.N. Ismarrubie and F. Mustapha, "Transient and Thermal Contact Analysis for the Elastic Behavior of Functionally Graded Brake Disks Due to Mechanical and Thermal Loads," Journal of Materials & Design, vol. 31, no. 10, pp. 4655–4665, 2010.

[8] Gao C.H. and Lin X.Z., "Transient Temperature Field Analysis of a Brake in a Non- axisymmetric Three Dimensional Model," Journal of Materials Processing Technology, vol. 129, pp. 513-517, 2002.

[9] Piotr Grzes, "Finite Element Analysis of Disc Temperature During Braking Process," Acta Mechanica et Automatica, vol. 3, no. 4, pp. 36-42, 2009.

[10] Adam Adamowicz and Piotr Grzes, "Three Dimensional FE Model of Frictional Heat Generation and Convective Cooling in Disc Brake," CMM-2011-Computer Methods in Mechanics , 2011.

[11] Oday I. Abdullah and Josef Schlattmann, "The Effect of Disc Radius on Heat Flux and Temperature Distribution in Friction Clutches," Journal of Advanced Materials Research, vol. 505, pp. 154-164, 2012.

[12] Oday I. Abdullah and Josef Schlattmann, "Finite Element Analysis of Dry Friction Clutch with Radial and Circumferential Grooves," in Proceeding of World Academy of Science, Engineering and Technology Conference, Paris, 2012, pp. 1279-1291.

[13] Oday I. Abdullah and Josef Schlattmann, "Effect of Band Contact on the Temperature Distribution for Dry Friction Clutch," in Proceeding of World Academy of Science, Engineering and Technology Conference, Berlin, 2012, pp. 167-177.

[14] Oday I. Abdullah and Josef Schlattmann, "The Correction Factor for Rate of Energy Generated in the Friction Clutches under Uniform Pressure Condition," Journal of Advances in Theoretical and Applied Mechanics, vol. 5, no. 6, pp. 277 – 290, 2012.

[15] Oday I. Abdullah and Josef Schlattmann, "Finite Element Analysis of Temperature Field in Automotive Dry Friction Clutch," Journal of Tribology in Industry, vol. 34, no. 4, pp. 206-216, 2012.

[16] Oday I. Abdullah, Josef Schlattmann and Abdullah M. Al-Shabibi, "Transient Thermoelastic Analysis of Multi-disc Clutches," in Proceedings of 9th Arnold Tross Colloquium, Hamburg, June 2013.

[17] ANSYS Contact Technology Guide, "ANSYS Release 11.0 Documentation," ANSYS Inc,.

[18] Mohr GA, "A Contact Stiffness Matrix for Finite Element Problems Involving External Elastic Restraint ," Journal of Computers & Structures, vol. 12, no. 2, pp. 189–191, August 1980.

[19] A.A. Becker, The Boundary Element Method in Engineering. New York: McGraw-Hill, 1992.

[20] P. Zagrodzki, "Analysis of Thermomechanical Phenomena in Multi-disc Clutches and Brakes," Journal of Wear, vol. 140, no. 2, pp. 291–308, 1990.

[21] Abdullah M. Al-Shabibi, "The Thermo-mechanical Behavior in Automotive Brake and Clutch Systems," in New Trends and Developments in Automotive System Engineering, Prof. Marcello Chiaberge, Ed.: InTech, January, 2011, ch.

Documents

TRANSIENT THERMOELASTIC ANALYSIS OF DRY … · machine design, Vol.5(2013) No.4, ... of contact used in ANSYS software; single contact, ... the amount of the penetration. Lower values