本研究提出一套數學模式，將成形中管材外形視為橢圓薄殼曲面，藉以瞭解在管材液壓鼓脹成形過程中，薄管於開模下塑性變形之行為。此數學模式建構為，在自由鼓脹區考量管材為非均一變薄，而管材與模具間之磨擦介面可分為黏滯和滑動兩種解析模式。在黏滯模式下，一旦有管材元素接觸模具後，元素並不會發生滑移現象。然而，在滑動模式下，其將會隨成形過程而持續變形。由此數學模式探討內部壓力與鼓脹高度之關係。而各種加工因子如入模半徑、管之厚度、管長度對管直徑之比、材料性質等等對成形壓力與產品厚度分佈之影響，亦會在本研究中有系統地討論。

A mathematical model considering ellipsoidal surface for the forming tube is proposed in this work to examine the plastic deformation behavior of a thin-walled tube during tube bulge hydroforming process in an open die. In the formulation of this mathematical model, nonuniform thinning in the free bulged region and sticking and sliding friction modes between the tube and die are considered. In the sticking friction mode, the elements in contact with the die do not move or slide after contact with the die. Whereas, in the sliding friction mode, the elements in contact with the die will continue to deform plastically in the subsequent forming process. The relationship between the internal pressure and the bulge height of the tube is examined. The effects of various forming parameters such as the die entry radius, the initial thickness, the length/diameter ratio, material property, etc., upon the forming pressure and the thickness distribution of products were discussed systematically.

論文摘要 Ⅰ
目錄 II
圖表索引 Ⅳ
符號說明 Ⅵ
第一章 緒論 1
1-1 前言 1
1-2 管材液壓成形製程簡介 2
1-3 影響管材液壓成形之加工因子 3
1-4 管材液壓成形之文獻回顧 4
1-5 本研究之目的 6
1-6 本論文之架構 6
第二章 管材液壓鼓脹成形數學模式 8
2-1 解析模式之基本假設 8
2-1-1 座標系之定義 9
2-1-2 基本組成方程式 9
2-2 管材鼓脹成形之解析模式 11
2-2-1 引言 11
2-2-2 黏滯模式 11
2-2-3 滑動模式 18
第三章 解析結果與討論 33
3-1 使用Deform之有限元素模擬 33
3-1-1 Deform 2D之分析模式 34
3-2 解析結果與討論 35
第四章 結論 53
4-1 研究成果之概要 53
4-2 今後研究之課題 54
參考文獻 55
附錄A - 橢圓球薄殼曲面參數之推導 58
附錄B - 橢圓曲率半徑之推導 60
附錄C - 邊緣處厚度之推導 62

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