本研究的目的為利用塑性力學之切片法及數值分析之有限差分法來推導一套數學模式，並建立電腦程式來計算管材液壓膨脹成形之特性。考慮黏滯模式與滑動模式建立此數學模式來預測圓管於正方形模具及長方形模具中液壓膨脹之成形壓力及厚度分佈。黏滯模式是假設管材與模具接觸後，其接觸元素即不再產生變形。而滑動模式則是管材與模具間之接觸元素會隨著成形過程中之應力變化而持續產生變形。管材膨脹成形之有限元素模擬採用商業程式軟體“DEFORM”來完成。
另外實驗是以退火過之鋁合金AA 6063進行液壓膨脹實驗。將實驗後所得之成形壓力、隅半徑及厚度分佈之結果，與解析值做一比較，來驗證本數學模式之適用性。在本文中將有系統地討論模具幾何形狀、管材材料性質、模具和管材間之摩擦係數等加工參數對成形壓力、隅半徑、管材與模具之接觸長度及厚度分布等膨脹結果之影響。

The objective of this study uses the plasticity theory of the slab method and the numerical analysis of the finite difference method to construct a mathematical model. And a computer program will be developed to evaluate the quality of the tubes formed by hydraulic expansion. Considering sticking and sliding modes, a mathematical model is proposed to predict the forming pressure needed to hydroform a circular tube into square and rectangular cross-sections and the thickness distribution of the product. In the sticking friction mode, it is assumed that the elements after contact with the die do not move or slide. Whereas, in the sliding friction mode, the element in contact with the die will continue to deform with the stress variation in the subsequent forming process. A series of FE simulations on tube expansion by a commercial FE code“DEFORM”have been carried out.
In addition, the experiment employing aluminum alloy AA 6063 that has been annealed to proceed the hydraulic expansion experiment. The comparisons between analysis and the result of forming pressure, corner radius and thickness distribution by experiment are verified the validity of this mathematical model. The effects of the forming parameters such as the die geometry, the material property of the tube, friction coefficient between the die and tube, etc., upon the expansion results, such as the forming pressure, corner radius, the tube contact distance with the die, thickness distribution after expansion, etc., are systematically discussed.

中文論文摘要………………………………………………………Ⅰ
英文論文摘要………………………………………………………Ⅱ
目錄…………………………………………………………………Ⅲ
圖表目錄……………………………………………………………Ⅴ
符號說明……………………………………………………………Ⅷ
第一章 緒論…………………………………………………………………1
1-1 前言……………………………………………………………………1
1-2 管材液壓膨脹成形技術之介紹………………………………………2
1-3 管材液壓膨脹成形之文獻回顧………………………………………3
1-4 本研究之目的…………………………………………………………4
1-5 本論文之架構…………………………………………………………5
第二章 圓管液壓膨脹成形之數學解析與有限元素模擬………….7
2-1 解析模式之基本假設…………………………………………………7
2-1-1 座標系之定義…………………………………………………..7
2-1-2 基本組成方程式………………………………………………..7
2-2圓管於正方形模具膨脹成形之數學模式…………………………….9
2-2-1 黏滯模式………………………………………………………..9
2-2-2 滑動模式………………………………………………………13
2-3圓管於長方形模具膨脹成形之數學模式…………………………...19
2-3-1 黏滯模式………………………………………………………19
2-3-2 滑動模式………………………………………………………20
2-4 有限元素模擬………………………………………………………..23
第三章 解析結果與討論…………………………………………………35
3-1 解析模式與有限元素法之比較……………………………………..35
3-2 摩擦係數對成形壓力之影響………………………………………..37
3-3 摩擦係數對厚度分佈之影響………………………………………..37
3-4 模具長度對成形壓力之影響………………………………………..37
3-5 應變硬化指數對成形壓力之影響…………………………………..38
3-6 不同管材對成形壓力之影響………………………………………..38
3-7 不同管材對厚度分佈之影響………………………………………..38
3-8 非等向性r值對成形壓力之影響……………………………………39
第四章 圓管液壓膨脹成形之實驗......………………………………...39
4-1 實驗目的……………………………………………………………..51
4-2 實驗設備……………………………………………………………..51
4-3 實驗步驟……………………………………………………………..52
4-3-1 實驗前管材之處理……………………………………………52
4-3-2 拉伸試驗………………………………………………………52
4-3-3 環壓試驗………………………………………………………53
4-3-4 液壓膨脹實驗…………………………………………………54
4-3-5 實驗後管材之處理……………………………………………54
4-4 解析結果與實驗結果之比較………………………………………..55
4-4-1不同模具長度對成形壓力之比較…………………………….55
4-4-2不同模具長度對厚度分佈之比較…………………………….56
第四章 結論…………………………...……………………………………72
5-1 研究成果概要………………………………………………………..71
5-2 今後研究之課題……………………………………………………..74
參考文獻……………………………………………………………………..75

參考文獻
[1] F. Dohmann and Ch. Hartl, “Hydroforming-a method to manufacture light-weight parts, ” Journal of Material Processing Technology, Vol.60 (1996), pp.669-676.
[2] F. Dohmann and Ch. Hartl, “Tube hydroforming: research and practical application,” Journal of Material Processing Technology, Vol.71 (1997), pp.174-186.
[3]日本塑性加工學會, “Хшみйиルみт⑦ヲ—管材ソ二次加工シ製品設計—,” ヵ①Ю社, p.65-90 (1992).
[4] M. Ahmetoglu, and T. Altan, “Tube hydroforming: state-of-the-art and future trends,” Journal of Materials Processing Technology, Vol.98(2000), pp.25-33.
[5] S. Fuchizawa, “Influence of Plastic Anisotropy on Deformation of Thin-walled Tubes in Bulge Forming,” Advanced Technology of Plasticity, Vol.Ⅱ(1987), pp.727-732.
[6] S. Fuchizawa and M. Narazaki, “Analysis of Bulge Deformation of Thin Tube with Cylindrical Die –Hydrostatic Tube Bulging with Closed DieⅠ-, Journal of JSTP, Vol.30, no.336, pp.116-122 (1989-1)
[7] S. Fuchizawa and M. Narazaki, “Bulge Deformation of Thin Copper Tube with Cylindrical Die –Hydrostatic Tube Bulging with Closed DieⅡ-, Journal of JSTP, Vol.30, no.339, pp.520-525 (1989-4)
[8] D. M. Woo and A. C. Lua, “Plastic Deformation of Anisotropic Tubes in Hydraulic Bulging,” Journal of Engineering Materials and Technology, Vol.100(1978), pp.421-425.
[9] S. Fuchizawa and M. Narazaki, “Bulge Test for Determining Stress-Strain Characteristics of Thin Tubes,” Advanced technology of plasticity 4th ICTP, pp.488-493, (1993).
[10] T. Sokolowski, K. Gerke, M. Ahmetoglu and T. Altan, “Evaluation of tube formability and material characteristics: hydraulic bulge testing of tubes,” Journal of Material Processing Technology, Vol.98 (2000), pp.34-40.
[11] T. Yoshida and Y. Kuriyama, “Effects of Material Properties and Process Parameters on Deformation Behavior of Tube Hydroforming,” Innovations In Tube Hydroforming Technology, June 13-14, (2000).
[12] M. Koç and T. Altan, “Prediction of forming limits and parameters in the tube hydroforming process,” International Journal of Machine Tools ＆Manufacture (2002), Vol.42, pp.123-138.
[13] M. Amino and K. Manabe, “Prediction of Wall Thickness Distribution in Tube Hydroforming by FEM Simulation,” The Proceedings of the 48nd Japanese Joint Conference for the Technology of Plasticity (1997), pp.373-374.
[14] K. Manabe and M. Amino, “Influence of Plastic Anisotropy on Tubular Hydroformed Component,” The Proceedings of the 49nd Japanese Joint Conference for the Technology of Plasticity (1998), pp.303-304.
[15] K. Manabe and M. Amino, “Effects of Process Parameters and Material Properties on Deformation Process in Tube Hydroforming,” Advances in Materials Processing and Technologies, Vol.1(1998), pp.523-530.
[16] K. Manabe, M. Amino and S. Nakamura, “FE Analysis on Local Thinning and Fracture Phenomenon in Hydroforming of Tubular Components,” Advanced Technology of Plasticity, Vol.Ⅱ(1999), Proceedings of the ICTP, pp.1229-1234.
[17] S. Fuchizawa, K. Satou, K. Itoga, A.Shirayori and M.Navazak,” Effect of Lubrication on Deformation Behavior of Tube in Hydraulic Bulging with Square Die,” The Proceedings of the 51nd Japanese Joint Conference for the Technology of Plasticity (2000), pp.361-362.
[18] S. Fuchizawa, Y. Ikeda, A. Shirayori and M. Narazake, “Effect of Lubrication on Deformation Behavior of Tube in Hydraulic Bulging with Square Die( Report),” The Proceedings of the 52nd Japanese Joint Conference for the Technology of Plasticity (2001), pp.19-20.
[19] M. Fukumura, K. Suzuki, K. Uwai, S. Toyoda, Q. Yu and M. Shiratori, “Friction Effect Dependence on the Die Shape During the Tube Hydroforming Process,” The Proceedings of the 52nd Japanese Joint Conference for the Technology of Plasticity (2001), pp.17-18.
[20] K. Yamada, H. Mizukoshi and H. Okada, “Mechanical Properties of Aluminum Alloy Tubes for Hydroforming-Second report: estimation of anisotropic parameters-, The Proceedings of the 51nd Japanese Joint Conference for the Technology of Plasticity (2000), pp.349-350.
[21] M. Miellnik, Metalworking Science and Engineering, McGraw-Hill, Inc, (1993), pp.38-50.
[22] R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, (1950), pp.317-340.
[23] F. P. Beer and E. R. Johnston, Mechanics of materials, 2nd edition, McGraw-Hill, Inc, (1992), pp.377-379.
[24] W. Johnson and P. B. Mellor, Engineering Plasticity, Ellis Horwood Ltd., (1985), pp.201-210.
[25] 金重勳,“機械材料,＂復文書局 (1994)
[26] “Standard Methods of Tension Testing Wrought and Cast Aluminum- and Magnesium-Alloy Products [Metric],” Annual Book of ASTM Standards Section 3, Vol03.01, pp.60-70.
[27] C.H. Lee and T. Altan, “Influence of Flow Stress and Friction Upon Metal Flow in Upset Forging of Rings and Cylinders,” Journal of Engineering for Industry (1972), pp.775-782.
[28] J. B. Hawkyard and W. Johnson, “An Analysis of the Changes in Geometry of a Short Hollow Cylinder During Axial Compression,” International Journal of Mechanical Sciences, Vol.9(1967), pp.163-182.
[29] M. Metcalf and J. Reid, Fortran 90 explained, (1990), Oxford University Press.
[30] R. L. Burden and J. D. Faires, Numerical Analysis, seventh edition, (2001), Brooks/Cole.