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Student Number 89343001 Author Ming-Chang Wu(吳明昌) Author's Email Address s9343001@cc.ncu.edu.tw Statistics This thesis had been viewed 1995 times. Download 656 times. Department Mechanical Engineering Year 2005 Semester 2 Degree Ph.D. Type of Document Doctoral Dissertation Language zh-TW.Big5 Chinese Title Variational Upper-Bound for Upset Forging of Rings and Its Comparison with FEM Solution Date of Defense 2006-06-30 Page Count 210 Keyword natural boundary condition neutral surface upset forging of ring variational upper-bound method Abstract ABSTRACT

The objective of this thesis is to verify the validity of the variational upper-bound(VUB) method in analysis of upset forging of rings. The effect of natural boundary conditions and geometrical shape of the neutral surface on the upper-bound solution would be investigated in this project as well. As for the upper-bound method on the theoretical analysis of upset forging of rings, the most research interests concentrate on the kinematically admissible velocity field for a lower upper-bound solution of energy dissipation. The analytical result could provide some important reference for the metal forming process. However, a large gap exists between the theoretical prediction on deformation behavior and the experimental results. Therefore, in this research work, a variational upper-bound (VUB) method is used. It is the method that determines an upper-bound solution using variational calculus. Consequently, in addition to the kinematically boundary condition, a set of natural boundary conditions (NBCs) can be derived theoretically and can be applied to approximate the solution. These NBCs were found to affect the upper-bound solution of energy dissipation as well as the pattern of metal deformation significantly.

The other objective of this thesis is to investigate the effect of the geometrical shape of the neutral surface, since the results of experiment and FEM has shown that the neutral surface of the upset forging of ring is not a cylindrical shape as was assumed in the upper-bound solution. For this purpose, the radius of the neutral surface, which was assumed as a constant, will be assumed as a function of higher order in analysis. It is expected that the solution determined in this manner should be improved.

In order to verify the validity and applicability of the present method, the result obtained in this research proposal will be compared and discussed with FEM solution, and also experimentally verified by the bulged profiles of upset disks and rings, and the calibration curves which indicate the relation between the decrease in minimum internal diameter of upset rings and the reduction under different interfacial friction conditions. The result proves that while considering the neutral surface as a function form and satisfying the natural boundary conditions, not only the calibration curves and bulged profiles in upset ring will be influenced, but also the forming energy will be improved.Table of Content 目 錄

頁次

摘要I

誌謝V

目錄VI

圖表說明X

符號索引XVI

第一章 緒論1

1-1 前言1

1-2 文獻回顧2

1-3 研究動機及方法16

1-4 論文架構20

第二章 基本理論介紹21

2-1 上界限法原理21

2-2 流函數理論23

2-3 上界限流函數法27

第三章 圓環鍛粗加工之變分上界限解析30

3-1 問題定義30

3-2 基本假設31

3-3 流函數場及速度場的性質31

3-4 上界限成形功率消耗33

3-4-1 塑性變形區的功率消耗33

3-4-2 摩擦界面的功率消耗34

3-4-3 圓環鍛粗加工總功率消耗35

3-5 平衡方程式及自然邊界條件36

3-6 變分上界限解41

第四章 結果與討論43

4-1 流函數模式對解的影響及其解的驗證44

4-1-1 流函數的模式44

4-1-2 速度場的建立44

4-1-3 應變率場的建立45

4-1-4 上界限解46

4-1-5 實驗驗證47

(一) 校正曲線的實驗驗證(Calibration curve)47

(二) 圓盤桶脹輪廓的實驗驗證48

(三) 圓環桶脹輪廓的實驗驗證50

4-1-6 理論計值的討論51

(一) 速度場的比較51

(二) 等效塑性應變場的比較51

(三) 摩擦條件與半高度縮減率對變形場的影響52

(四) 摩擦條件與半高度縮減率對成形能量的影響53

4-2 自然邊界條件對圓環鍛粗的影響54

4-2-1 實驗驗證59

(一) 校正曲線的實驗驗證(Calibration curve)59

(二) 圓盤桶脹輪廓及成形負荷的實驗驗證60

(三) 圓環桶脹輪廓的實驗驗證62

4-3 非線性模式之中立面對圓環鍛粗的效應62

4-3-1 流函數的模式63

4-3-2 速度場的建立63

4-3-3 應變率場的建立64

4-3-4 上界限解66

4-3-5 實驗驗證68

(一) 校正曲線的實驗驗證(Calibration curve)68

(二) 圓盤桶脹輪廓的實驗驗證70

(三) 圓環桶脹輪廓的實驗驗證71

4-3-6 理論計值的討論72

(一) 速度場的比較72

(二) 等效塑性應變場的比較73

(三) 摩擦條件與半高度縮減率對變形場的影響73

(四) 摩擦條件與半高度縮減率對成形能量的影響74

第五章 結論與建議76

5-1 結論76

5-2 建議79

參考文獻122

附錄Ａ 變分的推導(對流函數場)138

附錄B 自然邊界條件的轉換158

附錄C 變分的推導(對速度場)163

附錄D 有限元素軟體MARC簡介176Reference 參考文獻

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