本論文研究可分成兩部分，第一部分是建立一刀軸具傾斜情形之銑削力預測模式，此模式主要是由基本切削函數、屑寬密度函數及刀具序列函數所組成。第二部份是建立一球銑刀數值積分銑削力模式，並將此模式與有限元素ANSYS結合運用在銑削製程模擬上，進而分析單自由度與雙自由度結構(刀具－工件－夾具)之銑削動態特性，研究項目包括工件－夾具結構之模態振型、剛性分析及銑削過程中工件振動位移情形。最後並將分析結果與實驗值作驗證，以確保模式與分析流程之正確性。因此藉由以上研究將提供一套完整之銑削製程分析，且透過銑削力與銑削過程中之結構振動情形預測，將可提供使用者事先掌握銑削特性。

The thesis is divided into two parts. Part 1 is to establish a model of ball-end milling force with cutter inclination. This model consists of fundamental cutting function, chip width density function and tool sequence function. Part 2 is to establish a model of ball-end milling force with numerical integration method, and combine this model with finite-element analysis software Ansys to simulate milling process. This model is then used to simulate the milling dynamics of the one-degree freedom and two-degree freedom structures. Investigations include modal analysis, static analysis, and vibration of the workpiece-fixture structure. Finally, these models are verified through the comparison with experiments. Through this research, it provides a systematic method to predict milling force and the vibration of the workpiece-fixture system.

1. W. J. Eneres, R.E. DeVor, and S. G. Kapoor, 1995, “A Dual -Mechanism Approach to the Prediction of Machining Forces,” ASME Journal of Engineering for Industry, Vol. 117, pp. 526-541.
2. I. Yellowley, 1985, “Observations on the Mean Values of Forces, Torque and Specific Power in the Peripheral Milling Process,” International Journal of Machine Tool Design and Research, Vol. 25(4), pp. 337-346.
3. A. J. P. Sabberwal, 1961, “Chip Section and Cutting Force During the Milling Operation, ” Annals of the CIRP, Vol. 10, pp. 197-203.
4. E. Budak, Y. Altintas, E. J. A. Armarego, 1996, ”Prediction of Milling Force Coefficients from Orthogonal Cutting Data,” Transactions of ASME, 118, pp. 216-224.
5. Y. Altintas, P. Lee, 1998, “Mechanics and Dynamics of Ball End Milling,” Transactions of ASME, Journal of Manufacturing Science and Engineering, 120, pp. 684-692.
6. J. J. Wang, S. Y. Liang, and W. J. Book, 1994, "Convolution Analysis of Milling Forces Pulsation," ASME Journal of Engineering for Industry, Vol. 116, pp.17-25.
7. J.-J. Wang and C.M. Zheng, 2002, “An Analytical Force Model with Shearing and Ploughing Mechanisms for End Milling,” Int. J. Machine Tool and Manufacture, Vol. 42, pp.761-771.
8. J.-J. Wang and C.M. Zheng, 2002, “Identification of Shearing and Ploughing Cutting Constants from Average Forces in Ball-End Milling,” Int. J. Machine Tool and Manufacture, Vol.42, pp.695-705.
9. J.-J. Wang and C.M. Zheng, 2003, “On-line Identification of Shearing and Plowing Constants in End Milling,” ASME, J. of Manufacturing Science and Engineering, Vol. 125, pp. 58-65.
10. W. S. Yun, J. H. Ko, D. W. Cho, and K. F. Ehmann, 2002, “Development of a Virtual Machining System, Part 2: Prediction and Analysis of a Machined Surface Error,” International Journal of Machine Tools and Manufacture, Vol. 42, pp. 1067-1615.
11. S. Y. Liang, I. Lazoglu, 2000, “Modeling of Ball-End Milling Force With Cutter Axis Inclination,” Journal of Manufacturing Science and Engineering, Vol.122, pp. 3-11.
12. S. A. Tobias, W. Fishwick, 1958, “Theory of Regenerative Machine Tool Chatter,” Engineering, London, Vol. 205.
13. F. Koenigsberger, and J. Tlusty, 1967, Machine Tool Structure-Vol.Ⅰ: Stability Against Chatter, Pergamon Press.
14. M. P. Williamson, 1985, "Finite-element analysis," Computer-Aided Engineering Journal , pp.66-69.
15. Tom Carlstedt-Duke, 1985, "The CAE workstation-how much can it do?," Computer-Aided Engineering Journal, pp.45-49.
16. C. Shin, K. F. Eman, S. M. Wu, 1989, "Experimental Complex Modal Analysis of Machine Tool Structures," ASME Journal of Engineering for Industry, Vol.111, pp.116-124.
17. K. F. Eman, K. J. Kim, 1983, "Modal Analysis of Machine Tool Structures Based on Experimental Data," ASME Journal of Engineering for Industry, Vol.105, pp.282-287.
18. N.H. Cook, 1959, “Self-excited Vibrations in Metal Cutting, ” Trans. ASME Journal of Engineering for Industry, Vol.81, pp.183.
19. J.P. Gurney, 1962, “Analysis of Two Degree of Freedom Instability in Machine Tool,” J. Mech. Eng. Sci., Vol.4, No.1, pp.53.
20. H. E. Merritt, 1965, “Theory of Self-Excited Machine Tools Chatter,” Journal of Engineering for Industry, Vol.87, pp.447-454.
21. J. Tlusty, and F. Ismail, 1983, “Special Aspects of Chatter in Milling,” Journal of Vibration, Stress, and Reliability in Design, Vol.105, pp.24-32.
22. J. Tlusty, 1986, “Dynamics of High Speed Milling,” Journal of Engineering for Industry, Vol.108, pp.59-67.
23. R. Sridhar, R. E. Hohn, and G.W. Long, 1968, “A Stability Algorithm for the General Milling Process.” Trans. ASME Journal of Engineering for Industry, pp.330-334.
24. W. A. Kline, R. E. Devor, and I. A. Shareef, 1982, “The Prediction of Surface Accuracy in End Milling.” Trans. ASME Journal of Engineering for Industry, Vol.104, pp.272-278.
25. Y. Altintas, D. Monygomery, and E. Budak, 1992, “Dynamic Peripheral Milling of Flexible Structures.” Trans. ASME Journal of Engineering for Industry, 114(2).
26. R. Sagherian, and M.A. Elbestawi, 1990, “A Simulation System for Improving Machining Accuracy in Milling.” Computer in Industry, Vol. 14, pp.293-305.
27. E. Budak, 1994, “Mechanics and Dynamics of Milling Thin Walled Structures.” Master’s thesis, University of British Columbia.
28. 張家豪, 以有限元素法探討薄葉片銑削加工之穩定性分析, 國立成功大學機械工程研究所, 八十八年碩士論文。