臺灣博碩士論文加值系統

在金屬成形過程中，如何將模擬的過程更接近實際的情形，而藉由此模擬架構，讓我們能對金屬成形的結果有更大的把握，是我們努力的目標。本文以鍛粗為例，鍛粗工件與模具的接觸面摩擦現象一直是被關心討論的問題，本文的重點為如何決定在鍛粗成形過程中其摩擦係數的變化，以逆問題求解未知參數的概念，並以實驗量測值為基準，選用數值最佳化Levenberg-Marquardt Method，加上特定限制函數與收斂準則，配合軸對稱熱彈塑有限元素法，逆解在鍛粗成形過程中摩擦係數的變化，並以微觀角度對此摩擦係數變化做一說明。
藉由本文逆向演算架構，可得到更為接近實際情況的物理現象，以期使整個鍛粗成形過程更為完整。本文針對不同幾何尺寸、不同材料及不同加工溫度做一案例說明，針對軟鋼冷鍛（以實驗量測的負荷為基準）、鉬金屬溫鍛（以實驗量測的負荷為基準）、以及AISI1015冷鍛（以實驗量測的溫度為基準）為例，分別逆解其鍛粗過程中摩擦係數的變化，並觀察工件模擬之應力分佈、溫度分佈、以及外形變化情形，皆與其他文獻所觀察的現象相吻合，可進一步驗證本文以負荷或溫度逆算摩擦因子的合理性。

A simulation framework that allows the simulation process to approximate the realistic metal formation process is presented in this paper. The framework gives us better control of the results of metal formation─the goal in this paper. The case of upsetting was discussed in this paper as the friction of the upsetting workpiece and die contact interface has always been an issue of considerable concern. This paper focused on how to determine the variation of the friction coefficient during the upsetting formation process, the concept of solving unknown parameters by means of inverse problem, and the selection of the Levenberg-Marquardt numerical optimization Method based on the experimental data. The variation of the friction coefficient was calculating the upsetting formation process inversely by means of a specific constraining function and convergence criterion, plus axial symmetrical thermo-elastic-plastic finite element method. The variation of friction coefficient was then explained in a micro perspective.
As a result of the inverse calculation framework, physical properties that better approximate the realistic conditions were obtained, which presented a more comprehensive upsetting formation process. A case study featuring different geometric dimensions, different materials and different machining temperatures was presented. Specifically, mild steel cold upsetting (based on the experimental load), Molybdenum metal warm upsetting (based on the experimental load) and AISI1015 cold upsetting (based on the experimental temperature) were studied to observe the variation of friction coefficient during the upsetting process, the distribution of stress and temperature during workpiece simulation and appearance changes. The phenomena observed in this paper were found to be an exact match of those observed in previous studies. The findings prove that the use of load or temperature to the inverse calculation of the friction factor presented in this paper is a reasonable approach.

目 錄
誌 謝I
中文摘要II
ABSTRACTIII
圖表索引VI
1 第一章 緒論1
1.1 逆問題簡介1
1.2 研究動機與背景3
1.3 文獻回顧5
1.4 本文架構7
2 第二章 軸對稱熱彈塑有限元素法簡介8
2.1 基本假設8
2.2 軸對稱熱彈塑應力-應變關係矩陣的建立9
2.2.1 彈性範圍內之變形9
2.2.2 塑性範圍內的變形10
2.2.3 邊界摩擦力的處理15
2.3 大變形之應變、應變率、應力和應力率15
2.3.1 應變及應變率15
2.3.2 應力及應力率17
2.4 熱彈塑大變形-大應變的統御方程式19
2.4.1 有限元素法模式21
2.5 荷重修正矩陣及摩擦修正矩陣24
2.5.1 荷重修正矩陣24
2.5.2 摩擦修正矩陣29
2.6 熱源及熱傳方程式30
2.6.1 熱源30
2.6.2 有限差分之熱傳方程式32
3 第三章 逆向演算法介紹35
3.1 最佳化方法35
3.2 數值最佳化概述36
3.3 定義目標函數及限制函數38
3.4 鍛粗軸對稱熱彈塑有限元素逆算流程39
4 第四章 實例探討與說明45
4.1 定義模擬邊界條件45
4.2 模擬參數之輸入46
4.2.1 軟鋼之鍛粗（以負荷為基準逆算）46
4.2.2 MOLYBDENUM的溫間鍛粗（以負荷為基準逆算）59
4.2.3 AISI1015之鍛粗（以溫度為基準逆算）73
4.2.4 摩擦現象說明85
5 第五章 結論與建議86
5.1 結論86
5.2 建議88
參考文獻89

1.Tikhonov,A.N. and Arsenin, V. Y., “Solution of Ill-posed Problems,” V. H. Winston and Sons, Washington, D.C.（1977）.
2.Zantev, V. K., Markov, V. F. and Skugarev, V. P., “Application of Inverse Heat Conduction problems in Experimental Investigations of Heat Exchange of Casting Units of Furnaces, “ Journal of Engineering Physics, Vol. 45, No. 5, pp.1318-1322, Nov.（1983）.
3.Huang C. H., Ju T. M. and Tseng A. A., “The Estimate of Surface Thermal Behavior of the Working Roll in Hot Rolling Process,” Int. J. Heat Mass Transfer. Vol. 38, No. 6, pp. 1019-1031（1995）.
4.Karstein. Sorli, and Inge M. Skaar, ”Monitoring the Wear-Line of a Melting Furnace,” Inverse Problems in Engineering: Theory and Practice 3rd Int. Conference on Inverse problems in Engineering June 13-18, Port Ludlow, WA, USA（1999）.
5.Lin, J., “Inverse Estimation of the Tool-Work Interface Temperature in End Milling,” International Journal of Machine Tools & Manufacture Vol. 35, No. 5, pp. 751-760（1995）.
6.Park K. C. and Felippa Carlos A., “A Flexibility-based Inverse Algorithm For Identification of Substructural and Joint properties,” AMD-Vol. 228, Computational Methods for Solution of Inverse Problems in Mechanics, ASME, pp.11-22（1998）.
7.Shiro Kubo, Koji Fukumoto, and Kiyotsugu Ohji, “An Application of the Mollification Method to Estimation of Governing Equation of Field Problem From Noisy Observations”, Inverse Problems in Engineering：Theory and Practice, ASME, pp. 246（1998）.
8.張三木,”預估鍛造過程中表面摩擦係數的變化”,國立成功大學碩士論文（1997）.
9.Lin S. Y., ”An Investigation of Die-Workpiece Interface Friction During the Upsetting Process,” Journal of Materials Processing Technology, Vol. 54, pp. 239-248（1995）.
10.Sparrow, E. M., Haji-Sheikh A. and Lundgern, T. S. “The Inverse Problem in Transient Heat Conduction,” J. Appl. Mech., Vol. 86e, pp. 369-375（1964）.
11.Alifanov, O. M., “Solution of an Inverse Problem of Heat Conduction by iteration method,” Journal of Eng. Phys., Vol. 26, No. 4, pp. 471-476（1974）.
12.Trujillo D. M., “Application of Dynamic Programming to the General Inverse Problem,” International Journal for Numerical Methods in Engineering, Vol. 12, pp. 613-624（1978）.
13.Trujillo D. M. and Busby Henry R., Practical Inverse Analysis in Engineering, CRC Press, Boca Raton, New York（1997）.
14.Beck, J. V., “Surface Heat Flux Determination Using an Integral Method,” Nucl. Eng. Dec., Vol. 7, pp. 170-178（1968）.
15.Alifanov, O. M. and Mikhailov, V. V., ”Solution of the Nonlinear Inverse Thermal Conductivity Problem by the Iteration Method,” High Temperature, Vol. 35,No. 6, pp. 1501-1506（1978）.
16.Beck, J, V., Blackwell, B. and Haji-Sheikh, A., ”Comparison of Some Inverse Heat Conduction Methods Using Experimental Data,” International Journal of Heat and Mass Transfer, Vol. 39, No. 17, pp. 3649-3657（1996）.
17.Blanc, G., Beck, J. V. and Raynaud, M., ”Solution of the Inverse Heat Conduction Problem with a Time-Variable Number of Future Temperatures,” Numerical Heat Transfer, Part B, Vol. 32, pp. 437-451（1997）.
18.Kishimoto, K., Shibuya, T., Inoue, H., and Shinbo, H., ”Inverse Analysis Related to Stress Separation in Thermoelastic Stress Analysis,” JSME International Journal. Series A, Solid Mechanics and Material Engineering（1997）.
19.Huang C. H., Ozisik M. N. and Sawaf B., “Conjugate Gradient Method for Determining Unknown Contact Conductance During Metal Casting,” Int. J. Heat Mass Transfer, Vol. 25, No 7, pp. 1799-1786（1992）.
20.Tudor Balan, Lionel Fourment, and Jean-Loup Chenot, ”Shape Optimization of the Preforming Tools in forging,” Inverse problems in Engineering：Theory and Practice, ASME（1998）.
21.洪茂人,”熱鍛製程變形與熱傳的逆向分析,”國立成功大學機械工程學系碩士論文（1998）.
22.Lee, C. H. and Kobayashi S., “Analyses of Axisymmetric Upsetting and Plane-Strain Side-Pressing of Solid Cylinders by the Finite Element Method,” J. Engng. Ind. Vo1.93, pp.445-454（1971）.
23.McMeeking, R. M. and Rice J. R., “Finite Element Formulation for Problem of Large Elastic-Plastic Deformation,” Int. J. Solids Struct. Vol. 11, pp.601-616（1975）.
24.Pillinger, I., P. Hartley, C. E. N. Sturgess and G. W. Rowe, ”Finite- Element Modelling of Metal Flow in Three-Dimensional Forming,” Int. J. Numer. Meth. Engng. Vo1.25, pp.87-97（1988）.
25.Rebelo, N. and Kobayashi S., “A Coupled Analysis of Viscoplastic Deformation and Heat Transfer-I,” Int. J. Mech. Sci. Vo1. 22, pp. 699-705（1980）.
26.Rebelo, N. and Kobayashi S., “A Coupled Analysis of Viscoplastic Deformation and Heat Transfer-II,” Int. J. Mech. Sci Vo1. 22, pp. 707-718（1980）.
27.Male, A. T. and Cockcroft, M.G., “A Method for the Determination of the Coefficient of Friction of Metals Under Conditions of Bulk Plastic Deformation,” J. Inst. Met., Vol. 93, pp. 38-46（1964-65）.
28.Avitzur, B. and Sauerwine, F., ”Limit Analysis of Hollow Disk Forging,” Trans. ASME. J. Eng. Ind., Vol. 100, pp. 340-346（1978）.
29.Depierre, V. and Gurney, F., “A Method for Determination of Constant and Varying Friction Factors During Ring Compression Tests,” Trans. ASME. J. Lubr. Technol., Vol. 96, pp. 482-488（1974）.
30.Xu, W. L., Rao, K. P., Watanabe, T., and Hua, M. “Analysis of Ring Compression Using Artificial Neural Network,” J. Mater. Process. Technol., Vol. 44, pp.301-308（1994）.
31.Rao, K. P. and Xu, W. L., “Neural Evaluation of Friction and Flow Stress Adaptive to Ring Geometry,” JSME. Int. J. ：Series A, Vol. 38, No. 4, pp. 506-514（1995）.
32.Hwang, S. M. and Kobayashi, S., “A Note on Evaluation of Interface Friction in Ring Tests,” Proc. Of the 18th MTDR Conference, pp. 193-196（1977）.
33.Yamada, Y., “Visco-elasticity Plasticity,” Baifukan, Japan（1980）.
34.Rao S. S., “The Finite Element Method in Engineering”, Pergamon Press Inc., U.S.A.（1982）.
35.Holman J. P., ”Heat Transfer,” McGraw-Hill, New York（1981）.
36.Dennis J. E., JR. and Schnabel Robert B., “Numerical Methods for Unconstrained Optimization and NonLinear Equations,” Prentice-Hall, Inc., Englewood Cliffs, New Jersey（1988）.
37.Schnur D. S. and Zabaras Nicholas, ”An Inverse Method For Determining Elastic Material Properties And A Material Interface,” International Journal for Numerical Methods in Engineering, Vol. 33, pp. 2039-2057（1992）.
38.Ravi V. and Jennings A. A., “Penetration Model Parameter Estimate From Dynamic Permeablity Measurements,” Soil Sci. Soc. Am. J., Vol. 54（1990）.
39.Marquardt, D. W., “An Algorithm for the Estimate of Non-Linear Parameter,” Soc. Ind. Appl. Maths., pp. 431-441（1963）.
40.Shirakaashi, T., K. Maekawa and E. Usui, “Flow Stress of Low Carbon Steel at High Temperature and Strain Rate,” Bull. Japan Soc. Prec. Engng. Vol. 17, pp. 167-172（1983）.
41.Thiebaut C., Bonnet C., and Morey J.M., ”Evolution of the Friction Factor of a Molybdenum Workpiece During Upsetting Tests at Different Temperature,” Journal of Materials Processing Technology, vol. 77, pp. 204-205（1998）.
42.Lahoti G. D. and Altan T., “Prediction of Temperature Distribution in Axisymmetric Compression and Torsion,” Journal of Engineering Materials and Technology, pp.113-120（1975）.
43.Moore D. F., “Principles and Application of Tribology,” Oxford, New York, Pergamon Press（1975）.