有限元素法是目前最為廣泛使用的鍛造設計評估方法，但要獲得最適當之鍛造參數設計，常需多次嘗試錯誤的分析、設計修改，仍是相當耗時。為有效縮短開發時程，本研究建構了一套鍛造參數設計最佳化程序，將於電腦上進行鍛造製程模擬解析視為實驗，在眾多製程參數下，以田口實驗計畫法針對主要參數進行模擬分析規劃，獲得各參數對鍛造設計目標的最佳水準組合與影響性。對於多工程鍛造設計有道次間相互影響之效應或特殊品質要求，如果把所有因素放入鍛造設計目標，將使得最佳化參數分析變得相當複雜而不易使用。因此，本研究採用在單一主要特徵目標函數下進行分析，獲得最適當之參數組合後再進行符合品質或其他實務上之評估修正，達到兼顧品質水準及以最少的模擬次數找出最適當之製程條件與鍛模設計的目的。

　　熱鍛模具主要的失效模式是磨耗，為能更直接以模具壽命做為最佳化之目標函數，本研究完成以Archard磨耗理論為基礎，在模具硬度與模具材料之磨耗係數為溫度函數的假設下，以高溫硬度及高溫磨耗試驗建立其關係函數，並據以修正Archard磨耗理論使之適用於熱鍛模具之磨耗分析。

　　依據所建構之鍛造參數設計最佳化方法與模具磨耗預測模式，在模具磨耗最小化的目標下，實際應用於鈦合金人工髖關節髖臼杯的鍛造設計最佳化，不但成功鍛造出符合顯微組織與尺寸精度要求之產品，更得到較經驗預估還長的模具壽命。驗證了本研究建構之方法，不但能縮短設計時程，獲得最佳化的鍛造參數設計，且在設計階段即能預估模具可能之使用壽命。

　The finite element method (FEM) has been widely used to evaluate forging process design by transferring the trial-and-error design procedures from factory workshop to computer. However, to obtain optimum process parameters, it may take several times of computer simulation, which is very time consuming. This research therefore focused on shortening the process development cycle and a forging design parameter optimization model has been successfully constructed. The forging process simulations were considered as experiments. The orthogonal arrays and Taguchi method were adopted to plan and to minimize the simulation analysis. From the analysis, the optimum process conditions and the process parameters sensitivity were obtained. In the optimization procedure only one objective function was considered to simplify the analysis. Therefore, the quality requirement was considered as restriction and the optimum parameters were assessed based on the design experience.

　The die life has been used as the objective function in this research. Since majority of the forging die failure results from wear, this research therefore tackled the die life optimization based on the Archard wear theory by assuming that the die hardness and the die material wear coefficient is function of temperature. Furthermore, high temperature hardness tests and high temperature wear tests were performed to establish the relationship between the die hardness with the temperature and the wear coefficient with the temperature. A modified Archard wear model that accounts for the temperature in hot forging was proposed.

　By applying the modified Archard wear model and the proposed optimum parameter design method an optimum parameter design for forging titanium artificial hip joint accelebulum cup was obtained by minimizing the die wear objective function. This optimum design not only had a good quality conforming to the demanded microstructure and dimensional tolerance, but also had a die life longer than the estimation based on experiences. The methodology constructed in this research not only can shorten the design process but also can be used to estimate potential die life in the design stage. The proposed method is beneficial to the estimation of die cost, selection of die making method and efficient production scheduling.

1. Tang, J., W.T. Wu and J. Walters: Recent Development and Applications of Finite Element Method in Metal Forming, J. Materials Processing Technology, Vol. 46, pp.117-126, 1994

2. Roy, S., S. Ghosh and R. Shivpuri: A New Approach to Optimal Design of Multi-Stage Metal Forming Processes With Micro Genetic Algorithms, Int. J. Mach. Tools Manufact., Vol.37 No.1, pp.29-44, 1997

3. Syrcos, G.P., Die Casting Process Optimization Using Taguchi Methods, J. Materials Processing Technology, Vol.135, pp.68-74, 2003

4. Dowey, S.J. and A. Matthews, Taguchiand TQM Quality Issues for Surface Engineered Applications, Sueface and Castings Technology, Vol.110, pp.86-93, 1998

5. Khoei, A.R., I. Masters and D.T. Gethin, Design Optimization of Aluminium Recycling Processes Using Taguchi Technique, J. of Materials Processing Technology, Vol.127, pp.96-106, 2002

6. Hsiang, S.H. and J.L. Kou, An Investigation on the Hot Extrusion Process of Magnesium Alloy Sheet, J. of Materials Processing Technology, Vol.140, pp.6-12, (2003)

7. 賴永琛, 用田口方法探討鎂合金AZ31軋延參數之影響, 逢甲大學材料與製造工程所碩士論文, 2003

8. Srinivasan, R. and A. Chaudhary: Applying Numerical Taguchi Optimization to Metal Forming, JOM, pp.22-23, 1990

9. Liou, J.H. and D.Y. Jang: Forging Parameter Optimization Considering Stress Distributions in Products Through FEM Analysis and Robust Design Methodology, Int. J. Mach. Tools Manufact., Vol.37 No.6, pp.775-782, 1997

10. Ko, D.C., D.H. Kim, B.M. Kim and J.C. Choi: Methodology of Preform Design Considering Workability in Metal Forming by Artificial Neural Network and Taguchi Method, J. Materials Processing Technology, Vol.80-81, pp.487-492, 1998

11. Ko, D.C., D.H. Kim, B.M. Kim, Application of Artificial Neural Network and Taguchi Method to Preform Design in Metal Forming Considering Workability, Int. J. Mach. Tools Manufact. Vol.39, pp.771-785, 1999

12. Kojima, H. and S. Fujikawa: Development of Forging Process Optimization System Using Wear Model, Proceedings of the 7th ICTP 1, pp.223-228, 2002

13. 黎琇瑩, 窗型模鋁擠型之三維有限元素分析與製程參數研究, 國立成功大學機械工程系碩士論文, 2004

14. 董光雄,放電加工,復文書局,1988

15. Schey, J. A., Tribology in Metalworking: Friction, Lubrication and Wear, American Society for Metals, Metals Park, Ohio, pp.483-485

16.李宜哲,陳復國，鍛造模具破損原因之探討，鍛造，pp.67-78, 1994

17. Wibom, O., J. A. Nielsen and N. Bay, Influence of Tool Temperature on Friction and Lubrication in Cold Forging of Steel, 26th ICFG Plenary Meeting, Osaka, 1993

18. Sobis, T., U. Engel and M. Geiger, A Theoretical Study on Wear Simulation in Metal Forming Processes, J. Materials Processing Technology, Vol.34, pp.233-240, 1992

19. Geiger, M. and K. Lange, Fracture Mechanics Analysis of Extrusion Dies, Annals of CIRP, Vol.40, pp.303-306, 1991

20. Lange, K., M. Knoerr and T. Altan ,A Fatigue Analysis Concept to Avoid Failure of Forging Tooling, 27th ICFG Plenary Meeting, 1994

21. Knoerr, M., K. Lange and T. Altan,Fatigue Failure of Cold Forging Tooling: Causes and Possible Solutions Through Fatigue Analysis, J. Materials Processing Technology,Vol.46,pp.57-71, 1995

22. Lange, K., L. Cser, J.A. geiger and J.A.G Kals, “ Tool Life and Tool Quality in Bulk Metal Forming”, Annals of the CIRP, Vol.41, No.2, pp.667-675, 1992

23. Rosbrook, C. and R. Shivpuri, A Computer-Aided Investigation of Heat Checking and Die Life Predictions in Die Casting Dies, 17th Int. Die Casting Congress and Exposition, pp.181-190, 1993

24. Mingxin, Z., C. Baoluo and C. Qi-gong, The Application of Statistical Model of Cleavage Kic To a Hot-Work Die Steel and Its Toughening By Double Quenching Treatment,Int. J. of Fracture Vol.64, pp.23-28, 1993

25. Jeong, D. J., D. J. Kim, J. H. Kim, B. M. Kim and T. A. Dean, Effects of Surface Treatments and Lubricants for Warm Forging Die Life, J. Materials Processing Technology,Vol.113, pp.544-550, 2001

26. Iwama, T. and Y. Morimoto, Die Life and Lubrication in Warm Forging, J. of Materials Processing Technology, Vol.71, pp.43-48, 1997

27. Lange, K., A. Hettig and M. Knoerr, Increasing Tool Life in Cold Forging Through Advanced Design and Tool Manufacturing Techniques, J. of Materials Processing Technology, Vol.35, pp.495-513, 1992

28. Nagao, Y., M. Knoerr and T. Altan, Improvement of Tool Life in Cold Forging of Complex Automotive Parts, J. of Materials Processing Technology, Vol.46, pp.73-85, 1994

29. Geiger, M., M. Hansel and T. Rebhan, Improving the Fatigue Resistance of Cold Forging Tools by FE Simulation and Computer Aided Die Shape, Proc. Instn. Mech. Engrs., Vol.206, pp.143-150, 1992

30. Li, G., X. Li and J. Wu, Study of the Thermal Fatigue Crack Initial Life of H13 and H21 Steels, J. of Materials Processing Technology, Vol.74, pp.23-26, 1998

31. Kim, H. Y., J. J. Kim and N. Kim, “Physical and Numerical Modeling of Hot Closed-die Forging to Reduce Forging Load and Die Wear”, J. of Materials Processing Technology, Vol.42, pp.401-420, 1994

32. 江昌勇, 模具的失效分析, 模具工業, No.12, pp.8-11, 1996

33. Cser, L. and M. Geiger, A Generalized Life-Time Model for Cold Extrusion Tools, Annals of the CIRP, Vol.40, No.1, pp.299-301, 1991

34. Tekkaya, A.E., A. Sonsoz and K. Lange, Life Estimation of Extrusion Dies, Annals of the CIRP Vol.44, No.1, pp.231-234, 1995

35. Kim, T. H., B. M. Kim and J.C. Choi, Prediction of Die Wear in The Wire-Drawing Process, J. of Materials Processing Technology, Vol.65, pp.11-17, 1997

36. Cser, L., and M. Geiger, Simulation of Tool Life Cycle, 26th ICFG Plenary Meeting,Osaka, 1993

37. Lange, K., L. Cser, J.A. Geiger, J.A.G. Kals and M. Hansel, Tool Life and Tool Quality in Bulk Metal Forming, Proc. Instn Mech. Engrs., Vol 207, pp.223-239, 1993

38. Nepershin, R.I., A.G. Kazantsev and V.V. Klimenov, Evalution of Forging-Die Life Based On Formation of Low-Cycle Thermo-mechanical Fatigue Cracks, J. of Machinery Manufacture and Reliability, No.5, pp.102-108, 1991

39. Lange, K., L. Cser, J.A. Geiger and J.A.G. Kals, Tool Life and Tool Quality in Bulk Metal Forming, Annals of the CIRP, Vol.41, No.2, pp.667-675, 1992

40. Motomura, M. and T. Ohashi, Development of Risk Analyzer for Cold Forging Die Life with Fuzzy Language Computations, J. of the JSTP Vol.35, No.405, pp.1183-1188, 1994

41. Cser, L. and A. Csoma, Knowledge Based System for Life Estimation of Cold Forging Tools, 29th ICFC Plenary Meeting, 1996

42. Lee, Y. C. and F. K. Chen, Fatigue Life of Cold-forging Dies with Various Values of Hardness, Journal of Materials Processing Tech., Vol.113, pp.539-543, 2001

43. Rong, H. and O. Tsuda, Creep Life Prediction of Isothermal Forging Dies, KOBELCO TECHNOLOGY REVIEW, No.17, pp.58-60, 1994

44. Painter, B., R. Shivpuri and T. Altan, Prediction of Die Wear During Hot-extrusion of Engine Valves, Journal of Materials Processing Technology, Vol. 59, pp.132-143, 1996

45. Bariani, P. F., G. A. Berti, and R. Guggia, Wear in Hot and Warm Forging：Design and Validation of an New Laboratory Test, Annals of the CIRP, Vol.45, No.1, pp.249-253, 1996

46. Deschaux-Beaume, F., F. Schmidt, N. Frety, J. C. Boyer and C. Levaillant, Failure Prediction for Ceramic Dies in the Hot-forging Process Using FEM Simulation, Journal of Materials Processing Technology, Vol. 75, pp.100-110, 1998

47. Kang, J.H., I.W. Park, J.S. Jae and S.S. Kang, A Study on a Die Wear Model Considering Thermal Softening: (I) Construction of the wear model, Journal of Materials Processing Technology, Vol. 96, pp.53-58, 1999

48. Kang, J.H., I.W. Park, J.S. Jae and S.S. Kang, A Study on a Die Wear Model Considering Thermal Softening: (I I) Applicatuon of the Suggested Wear Model, Journal of Materials Processing Technology, Vol. 94, pp.183-188, 1999

49. Lee, H. C., B. M. Kim and K. H. Kim, Estimation of Die Service Life in Hot Forging, Considering Lubricants and Surface Treatments, Pro. Instn. Engrs., Vol.217 Part B: J. Engineering Manufacture, pp.1011-1022, 2003

50. Morishita, H. and T. Suzuki, “鋼の熱間鍛造におけゐ磨耗と金型壽命預測”, 塑性と加工,45卷 520號, pp.22-26, 2004

51. Sheikh, A.K. and S.E. Khany, Reliability of the Wire Drawing Dies, Proc. 3rd International Symposium on Advanced Materials, pp.754-761, 1993

52. Engel, U., Prediction of Tool Failure From A Probabilistic Point of View, J. of Materials Processing Technology, Vol.42, pp.1-13, 1994

53 Engel, U., Reliability Analysis of Cold Forging Tools, Proc. of the 9th Int. Cold Forging Congress, pp.103-112, 1995

54. Engel, U., Reliability of Cold Forging Tools, 29th ICFC Plenary Meeting, 1996

55. Khany, S. E. and A. K. Sheikh, Extrusion Die Life Prediction: A Probabilistic Approach, Indian Journal of Engineering & Materials Sciences, Vol.3, pp.9-12, 1996

56. Archard J. F., Contact and Rubbing of Flat Surfaces, J. Applied Physics Vol.24, 1953

57. Lee, G. A. and Y. T. Im, Finite-element Investigation of the Wear and Elastic Deformatuion of Dies in Metal Forming, J. of Materials Processing Technology, Vol.89-90, pp.123-127, 1999

58. Doege, E., P. Groche and Th. Bobke, Application of Adhesion Theory to Friction and Wear Processes in Hot Die Forging, Advance Technology of Plasticity, Vol.1, pp.27-32, 1990

59. Jensen, M. R., F. F. Damborg, K. B. Nielsen and J. Danckert, Optimization of the Draw-die Design in Conventional Deep-drawing in Order to Minimize Tool Wear, Journal of Materials Processing Tech., Vol.83, pp.106-114, 1998

60. Kennedy, D.M. and M.S.J. Hashmi, Methods of Wear Testing for Advanced Surface Coating and Bulk Materials, J. of Materials Processing Technology, Vol. 77, pp.246-253, 1998

61. 陳怡安, 數值模擬於溫鍛模具磨耗分析之應用, 國立成功大學機械工程學系碩士論文，2001

62. 劉嘉浚, 材料磨損原理及其耐磨性, 清華大學出版社, 1993

63. 鍾清章,黃錦洲,李友錚,黃庭彬,江瑞清,林朝蒼,葉政治, 品質工程 (田口方法), 中華民國品質管制學會, 1994

64. Brunette, D.M., P. Tengvall, M. Textor and P. Thomsen, Titanium in Medicine: Material Science, Surface Science, Engineering, Biological Responses and Medical Applications, Springer-Verlag Berlin Heidelberg New York, 2001

65. 聯合骨科器材公司網站, http://www.uoc.com.tw, 2005
66. Fluhrer, J., DEFORMTM 2D Version 8.02 User’s Manual, Scientific Forming Technologies Corporation, 2004