FREN DİSK-BALATA MEKANİZMASININ ÜÇ BOYUTLU GERİLME ANALİZİ

Abstract

Bu çalışmada bir otomobil disk fren mekanizması için üç boyutlu termoelastik gerilme analizi yapılmıştır. Disk/balata çifti için silindirik koordinatlarda ısı iletim denklemi türetilmiştir. Isı iletim denklemini balata ve disk için çözebilmek için sınır ve ilk şartlar belirlenmiştir. Balata ve disk arasındaki sürtünme katsayısı sıcaklığa ve zamana bağlıdır. Sıcaklığa ve zamana bağlı sürtünme katsayısını dikkate almak için termal analizde iteratif bir yöntem geliştirilmiştir. Hareket denklemi türetilmiş, sabit hızda giden aracın frenleme anından itibaren doğrusal olmayan şekilde yavaşlayarak durma anına ulaştığı görülmüştür. Sıcaklığın artması sürtünme katsayısında azalmaya ve durma zamanında artışa sebep olmuştur. Balata ve disk arasında sürtünme nedeniyle oluşan toplam ısı akısı hesaplanmıştır. Isı akısı balata ve disk yüzeylerine ısı paylaşım oranı düşünülerek uygulanmıştır. Silindirik koordinatlarda termoelastik gerilme-gerinim bağıntıları türetilmiştir. Bu bağıntıların denge denklemi içerisine konulması ile birlikte Navier denklemleri elde edilmiştir. Isı iletim ve Navier denklemlerinin hesaplamalı olarak çözülebilmesi için sonlu elemanlar metodu kullanılmıştır. Disk/balata çifti için sıcaklık dağılımları ve eşdeğer von-Mises gerilmeleri hesaplanmıştır. Frenleme basıncının ve balata fiziksel özelliklerinin disk/balata fren mekanizmasında oluşan sıcaklık ve eşdeğer gerilme değerlerine olan etkileri incelenmiştir. Sonuçlar balata malzemesi özelliklerinin disk/balata çifti için sıcaklık ve gerilmeleri dikkate değer ölçüde etkilediğini göstermiştir. Isı iletim katsayısı, yoğunluğu ve ısı kapasitesi yüksek olan bir balta malzemesi kullanımı disk üzerindeki gerilmeleri azaltarak aşınma ve kırılma gibi durumların önlenmesinde önemli rol oynayabilir.

Keywords

• Disk-balata mekanizması
• Sürtünme ısı üretimi
• Sonlu Elemanlar Analizi
• Sıcaklık dağılımı
• von-Mises gerilmesi

Three Dimensional Stress Analysis of a Brake Disc-Pad Mechanism

Abstract

In the present study, three-dimensional thermoelastic stress analysis is carried out for the automobile disc brake mechanism. Heat conduction equation is derived at cylindrical coordinate system for the disc/pad couple. In order to solve the heat conduction equation for the pad and disc, boundary and initial conditions are specified. The coefficient of friction between the pad and disc is temperature and time dependent. In order to take into account temperature and time dependent coefficient of friction, iterative method is developed in thermal analysis. Equation of motion is derived and it is observed that vehicle travelling at constant speed reaches the moment of stop with decelerating nonlinearly. Total heat flux due to the friction between pad and disc is calculated. Heat flux is applied to the surface of the pad and the disc considering heat partition ratio. Thermoelastic stress-strain relations are derived at cylindrical coordinates. Navier equations are obtained by substituting these relations into equations of equilibrium. In order to solve the heat conduction and Navier equations computationally, the finite element method is used. Temperature distributions and equivalent von-Mises stresses for the disc/pad couple are calculated. Influences of brake pressure and physical properties of the pad upon the values of temperature and equivalent stress are examined. Results indicate that properties of pad material lead to remarkable influence on temperature and stress for disc/pad couple. Utilization of pad material with high conductivity, density and specific heat capacity may play a significant role on avoiding wear and fracture situations by reducing stresses on the disc.

Keywords

• Disc-pad mechanism
• Frictional heat generation
• Finite Element Analysis
• Temperature distribution
• von-Mises stress

References

1. Adamowicz, A., Grzes, P., 2011, “Analysis of disc brake temperature distribution during single braking under non-axisymmetric load”, Applied Thermal Engineering, 31, 1003-1012.
2. Akhtar, M.M.J., Abdullah, O.I., Schlattmann, J., 2013, “Transient Thermoelastic analysis of dry clutch system”, Machine Design, 5(4), 141-150.
3. ANSYS Inc., 2016, “ANSYS Basic Analysis Procedure Guide, Release 17.1”, Canonsburg, PA, USA.
4. Belhocine, A., 2017, “FE prediction of thermal performance and stresses in an automotive disc brake system”, International Journal of Advanced Manufacturing Technology, 89, 3563-3578.
5. Belhocine, A., Abu Bakar, A., Bouchetara, M., 2014, “Structural and contact analysis of disc brake assembly during single stop braking event”, American Journal of Mechanics and Applications, 2(3), 21-28.
6. Belhocine, A., Abu Bakar, A., Bouchetara, M., 2016, “Thermal and structural analysis of disc brake assembly during single stop braking event”, Australian Journal of Mechanical Engineering, 14(1), 26-38.
7. Belhocine, A., Bouchetara, M., 2012a, “Thermal analysis of a solid brake disc”, Applied Thermal Engineering, 32, 59-67.
8. Belhocine, A., Bouchetara, M., 2012b, “Thermomechanical modelling of dry contacts in automotive disc brake”, International Journal of Thermal Sciences, 60, 161-170.

9. Belhocine, A., Bouchetara, M., 2013, “Investigation of temperature and thermal stress in ventilated disc brake based on 3D thermomechanical coupling model”, Ain Shams Engineering Journal, 4, 475- 483.
10. Benslimane, A., Bouzidi, S., Methia, M., 2018, “Displacements and stresses in pressurized thick-walled FGM cylinders: Exact and numerical solutions”, International Journal of Pressure Vessels and Piping, 168, 219-224.
11. Bouchetara, M., Belhocine, A., 2014, “Thermoelastic Analysis of Disk Brakes Rotor”, American Journal of Mechanical Engineering, 2(4), 103-113.
12. Charron, F., 1943, “Partage de la chaleur entre deux corps frottants”, Publ. scient. et techn. Ministere air, 182.
13. Cho, C., Ahn, S., 2002, “Transient thermoelastic analysis of disc brake using the Fast Fourier Transform and finite element method”, Journal of Thermal Stresses, 25(3), 215-243.
14. Choi, J.-H., Lee, I., 2004, “Finite element analysis of transient thermoelastic behaviors in disc brakes”, Wear, 257, 47-58.
15. Eslami, M.R. et al., 2013, “Theory of Elasticity and Thermal Stresses”, Solid Mechanics and Its Applications, 197, DOI: 10.1007/978-94-007-6356-2 16, Springer Science+Business Media Dordrecht.
16. Fono-Tamo, R.S., 2018, “A Mathematical Model for the purpose of analysing the Thermal Stress Characteristics Of PKS-Based Brake Pad with MATLAB”, Materials Today: Proceedings, 5, 12534- 12544.
17. Grzes, P., 2014, “Numerical Analysis of Temperature Field in a Disc Brake at Different Cover Angle of the Pad”, Acta mechanica et automatica, 8(4), 185-188.
18. Grzes, P., 2018, “Finite element solution of the three-dimensional system of equations of heat dynamics of friction and wear during single braking”, Advances in Mechanical Engineering, 10(11), 1-15.
19. Grzes, P., 2019, “Maximum temperature of the disc during repeated braking applications”, Advances in Mechanical Engineering, 11(3), 1-13.
20. Guo, F., Yan, Y., Hong, Y., Li, Y., 2020, “Multiscale modeling: Prediction for thermophysical properties of needled carbon/carbon composite and evaluation of brake disk system”, Materials Today Communications, 22, 100685.
21. Jimbo Y., Mibe, T., Mihe T., Akiyama, K., Matsui H., Yoshida M., Ozawa A., 1990, “Development of High Thermal Conductivity Cast Iron for Brake Disc Rotors”, Journal of Matarials and Manufacturing SAE Transactions, 99(5), 1-7.
22. Liew, K.W., Nirmal, U., 2013, “Frictional performance evaluation of newly designed brake pad materials”, Materials and Design, 48, 25-33.
23. Mahmoudi, T., Parvizi, A., Poursaidi, E., Rahi, A., 2015, “Thermo-mechanical analysis of functionally graded wheel-mounted brake disc”, Journal of Mechanical Science and Technology, 29(10), 1-8.
24. Mumtaz Jamil Akhtar, M., Abdullah, O.I., Schlattmann, J., 2013, “Transient Thermoelastic Analysis of Dry Clutch System”, Machine Design, 5(4), 141-150.
25. Narayana, K.S., Rao, G.U., Simhachalam, D., Nagaraju, B., 2014, “Finite Element Analysis of Solid and Ventilated Disc Brake”, International Journal of Science and Research, 3(9), 875-882.
26. Shahzamanian, M.M., Sahari, B.B., Bayat, M., Ismarrubie, Z.N., Mustapha, F., 2010a, “Transient and thermal contact analysis for the elastic behavior of functionally graded brake discs due to mechanical and thermal loads”, Materials and Design, 31, 4655-4665.
27. Shahzamanian, M.M., Sahari, B.B., Bayat, B.B., Mustapha, F., Ismarrubie, Z.N., 2010b, “Finite element analysis of thermoelastic contact problem in functionally graded axisymmetric brake disks”, Composite Structures, 92, 1591-1602.
28. Söderberg, A., Andersson, S., 2009, “Simulation of wear and contact pressure distribution at the pad-to- rotor interface in a disc brake using general purpose finite element analysis software”, Wear, 267, 2243-2251.
29. Talati, F., Jalalifar, S., 2009, “Analysis of heat conduction in a disk brake system”, Heat and Mass Transfer, 45(8), 1047-109.
30. Tehrani, P.H., Talebi, M., 2012, “Stress and Temperature Distribution Study in a Functionally Graded Brake Disk”, International Journal of Automotive Engineering, 2(3), 172-179.
31. Wolff, A., 2010, “A Method to Achieve Comparable Thermal States of Car Brakes during braking on the road and on a high-speed roll-stand”, The Archives of Transport, 22(2), 10.2478/v10174-010-0016- z.
32. Yevtushenko, A.A., Adamowicz, A., Grzes, P., 2013, “Three-dimensional FE model for the calculation of temperature of a disc brake at temperature-dependent coefficients of friction”, International Communications in Heat and Mass Transfer, 42, 18-24.
33. Yevtushenko, A., Grzes, P., 2011, “Finite element analysis of heat partition in a pad/disc brake system”, Numerical Heat Transfer Part-A Applications, 59(7), 521-542.
34. Yevtushenko, A.A., Grzes, P., 2012, “Axisymmetric FEA of temperature in a pad/disc brake system at temperature –dependent coefficients of friction and wear”, International Communications in Heat and Mass Transfer, 39, 1045-1053.
35. Yevtushenko, A.A., Grzes, P., 2014, “Mutual influence of the velocity and temperature in the axisymmetric FE model of a disc brake”, International Communications in Heat and Mass Transfer, 57, 341-346.
36. Yevtushenko, A.A., Grzes, P., 2015, 3D FE model of frictional heating and wear with a mutual influence of the sliding velocity and temperature in a disc brake”, International Communications in Heat and Mass Transfer, 62, 37-44.
37. Yevtushenko, A., Kuciej, M., Topczewska, K., 2018, “Analytical model to investigate distributions of the thermal stresses in the pad and disk for different temporal profiles of friction power”, Advances in Mechanical Engineering, 10(10), 1-10.
38. Yevtushenko, A.., Kuciej, M., Topczewska, K., 2019, “Effect of the temporal profile of the friction power on temperature of a pad-disc brake system”, Journal of Theoretical and Applied Mechanics, 57(2), 461-473.
39. Zhu, Z.-C., Peng, Y.-X., Shi, Z.-Y., Chen, G.-A., 2009, “Three-dimensional transient temperature field of brake shoe during hoist’s emergency braking”, Applied Thermal Engineering, 29, 932-937.