本研究之主要的目的是利用有限元素法，針對機車的碟式剎車盤，在剎車時期之溫度與接觸壓力，進行一系列的模擬分析。本文是利用有限元素套裝軟體Mentat＆MARC的繪圖功能與各項參數之設定，來建立出碟剎之有限元素模型，以進行碟剎之動態與接觸問題的分析。然後再根據分析後的結果，針對三維實體模型、二維軸對稱模型之碟盤溫度、壓力與應力分佈，分別加以探討與比較。最後則利用此分析之趨勢結果，作為改善機車碟式剎車盤之依據。

The main purpose of this study is to simulate and analyze the temperature and contact pressure of the disc brake plate of a motorcycle during braking by the finite element method. By utilizing the software package Mentate and Marc which are signified with drawing and construction of the brake model to do the analysis of thermal and contact problem. In accordance with the result of analysis, the researcher discussed and compared the three-dimensional model and the two dimensional axial symmetrical model for the temperature, pressure and stress distribution of the brake. Finally, the researcher made some suggestions for the improvement of the mechanism of disc brake plate of a motorcycle.

第一章 緒論……………………………………………………………1
1-1 前言………………....……………….……………………1
1-2 研究主題..…………..……………..…….………………2
1-3 文獻回顧…………………..….……..……………………3
1-3-1 碟式剎車分析方面……………..…………………3
1-3-2 接觸理論分析方面…………………………………4
1-4 組織與架構………………..……....…….………………6
第二章 理論分析……………………….……………….…..………7
2-1 前言……………….…..……………..……………………7
2-2 摩擦理論..…………...……………..……………………7
2-3 溫度與熱應力之分析理論…………….…..………………9
2-3-1 溫度分析………………………..…….….……10
2-3-2 熱應變分析…..………………..………………14
2-4 動態與非線性的分析…………….....…………………17
2-4-1 動態分析理論……………………..……………17
2-4-2 有限元素中接觸問題的情形…..….…….……19
第三章 有限元素模型…………………………………………………21
3-1 前言………………....……………….…….……………21
3-2 基本假設..…………..……………..……………………21
3-3 有限元素模型的建立……..….……..……………….…22
3-4 本文使用元素之形式說明..……....……..……………23
3-5 邊界與初始條件………....……....…….….…………23
3-6 材料性質…………………..……....…….………….…24
第四章 結果分析與討論.………………..……………….…………25
4-1 前言……………….…..……………….…………………25
4-2 結果分析與討論……...……………..….………………25
第五章 結論與建議……..………….…….……………….…………29
5-1 前言……………….…..……………..……….…………29
5-2 綜合結論……...…………..………..………….………29
5-3 未來研究方向與建議.……..………..…….……………30
參考文獻…………………………………….………………………….45

1、R. Limpert, “Temperature and Stress Analysis of Solid-rotor Disc Brake”, The University of Michigan, Ph. D thesis, 1972.

2、R. Limpert, “The thermal performance of automotive disc brake”, SAE Paper 750873, 1975.

3、A. E. Sisson, “Thermal analysis of vented drake rotor”, SAE Paper 780352, 1978.

4、A. J. Day, P. R. J. Harding, and T. P. Newcomb, ”A finite element approach to drum brake analysis”, Proc, Instn. Mech. Engrs., Vol.193, pp.401-406, 1997.

5、A. J. Day and P. R. J. Harding, ”Performance variation of cam operated drum brakes braking of road vehicles”, I Mech E Conf., paper C10/83, pp 60-77, 1983.

6、P. R. Harding and J. B. Wintle, “Flexural effects in disc brake pads”, Proc, Instn. Mech. Engrs., Vol. 192, pp.287-294, 1984.

7、A. J. Day, P. R. J. Harding, and T. P. Newcomb, ”Combined Thermal and Mechanical Analysis of Drum Brakes”, Proc, Instn. Mech. Engrs., Part E,Vol.198 ,No.15 , pp. 287-294, 1984.

8、Farzad Samie and David C. Sheridan, ”Contact analysis for a passenger car disc brake”, SAE Paper 900005, 1990.

9、M. Tirovic and A. J. Day, ”Disc brake interface pressure distribution”, Proc, Instn. Mech. Engrs., Vol.25, Part D, pp.137-146, 1991.

10、T. K. Kao, J. W. Richmond and M. W. Moore, ”Computational analysis of disc pad performance”, I Mech E Conf., C44/027, pp.1-12, 1993.

11、P. Dufrenoy and D. Weichert, “Prediction of railway disc brake temperatures taking the dearing surface variations into account”, Proc, Instn. Mech. Engrs., Vol.209, Part F, pp.67-76, 1995.

12、N. Benseddiq, D. Weichert, J. Seidermann and M. Minet, “Optimization of design of railway disc drake pads”, Proc, Instn. Mech. Engrs., Vol.210, Part F, pp.51-61, 1996.

13、Y. Zhang, R. Chen, R. He and B. Shen, ”Investigation of tribological properties of brake shoe materials—phosphorous cast irons with different graphite morphologies”, Wear, Vol. 166, No. 2, pp. 179-186, 1993.

14、M. Nakazawa, O. Isobe, S. Takahashi and Y. Watanabe, “Braking force distribution control for improved vehicle dynamics and brake performance”, Vehicle System Dynamics, Vol.24, No. 4-5, pp. 413-426, 1995.

15、A. Francavilla and O.C.Zienkiewicz, “A Note On Numerical Computation of Elastic Contact Problem”, Int. J. Num. Mech. Engng, Vol. 9, pp.913-924, 1975.

16、T. D. Sachdeva, C. V. Ramakrishnan and R. Natarnjan, ”A Finite Element Method for The Elastic Contact Problem”, Trans. ASME Journal Num. Engng. Industry., Vol. 103, pp. 456-461, 1981.

17、G. R. Johnson, “High Velocity Impact Calculation in Three Dimension”, Trans. ASME J. Engng. Industry., Vol. 44, pp. 95-106, 1977.

18、N. Okamoto and M. Nakazawa, “Finite Element Incremental Contact Analysis with Various Frictional Conductions”, Int. Journal Num. Meth. Engng. , Vol. 14, pp. 337-357, 1979.

19、G. R. Johnson, “Dynamic Responsion of Axisymmetric Solids Subjected to Impact and Spin”, AIAA Journal, Vol.17, No.9, pp.975-979, 1979.

20、K. J. Bathe and A. Chaudhary, “A Solution Method for Planar and Axisymmetric Contact Problems”, Int. Journal Num. Meth. Engng., Vol. 21, pp. 65-88, 1985.

21、H. Parisch, “A Consistent Tangent Stiffness Matrix for Three Dimensional Non-Linear Contact Analysis”, Int. Journal Num. Meth. Engng., Vol. 28, pp. 1803-1812, 1989.

22、J. E. Mottershead, S. K. Pascoe and R. G. English, “A General Finite Element Approach for Contact Stress Analysis”, Int. Journal Num. Meth. Engng., Vol. 33, pp. 765-779, 1992.

23、N. Chandrasekaran, W. E. Haisler and R. E. Goforth, ”A Finite Element Solution Method for Contact Problems with Friction”, Int. Journal Num. Meth. Engng., Vol. 24, pp. 477-495, 1987.

24、Y. Kanto and G. Yagawa, ”A Dynamic Contact Buckling Analysis by The Penalty Finite Element Method”, Int. Journal Num. Meth. Engng., Vol. 29, pp. 755-774, 1990.

25、S. Ghosh, “Arbitrary Lagrangian-Eulerian Finite Element Analysis of Large Deformation in Contacting Bodies”, Int. Journal Num. Meth. Engng., Vol. 33, pp. 1891-1925, 1992.

26、J. C. Simo and T. A. Lanrsen, ”An Augrmented Largrangian Treatment of Contact Problem Involving Friction”, Computers & Structures, Vol. 42, No.1, pp. 97-116, 1992.

27、F. Paris, A. Foces and J. A. Garrido, “Application of Boundary Element Method to Solve Three-Dimensional Elastic Contact Problem without Friction” Computers & Structures, Vol. 45, No.1, pp. 19-33, 1992.

28、A. Gaknaya, D. Lambert and A. Cardou, “A Boundary Element and Mathematical Programming Approach for Frictional Contact Problems”, Computers & Structures, Vol. 42, No.3, pp. 341-353, 1992.

29、W. H. Chen and T. C. Chen, ”Boundary Analysis for Contact Problems with Friction”, Computers & Structures, Vol. 45, No.3, pp.431-438, 1992.

30、Z. H. Zhong, Finite Element Procedures for Contact-Impact Problems, Oxford University Press Inc., New York, 1993.

31、O. C. Zienkiewicz, The Finite Element Method, McGraw-Hill, New York, pp. 120-124, 1997.

32、T. R. Chandrupatla and A. D. Belegundu, Introduction to Finite Elements in Engineering, second edition, Prentice-Hall International, Inc.

33、Bathe, Finite Element Procedures, Prentice-Hall International, Inc.

34、Joseph, Edward and Shigley, “Mechanical Engineering Design”, fifth edition.
35、R. Limpert, “Brake design and safety”, SAE, U.S.A. ,1992.

36、K. H. Huebner, E. A. Thornton and T. G. Byrom, The Finite Element Method for Engineers, third edition, Wiley-Interscience, John Wiley & Sons, Inc.

37、E. B. Becker, G. F. Carey and J. T. Oden, Finite Elements, An Introduction, Vol. 1, 新月出版社.