本研究是使用有限元素法分析兩圓柱間的共形滾動接觸(conformal rolling contact)問題。首先推導出運動關係式(kinematic relations)，並將節點應力的接觸條件轉換為節點位移的多點拘束條件，並且加入有限元素法系統中求解。本研究所發展出之方法將可求出共形靜態接觸下接觸區域大小及接觸區域內的應力分佈，並求出正向摩擦接觸下的應力分佈與滾動接觸情況下之節點力分佈。

In this thesis the rolling contact problem between two closely conforming elastic bodies are analyzed by the finite element method. The kinematic relation between two conforming bodies in rolling contact is derived. The kinematic relation and the stress contact conditions are transformed into multiple point constraints for nodal displacements. Upon imposing these constraints into the finite element system equations, the nodal displacements and stresses may satisfy all contact conditions. This technique may be used to obtain the contact length, and tangential as well as normal stresses in the contact region during static and rolling contact of two conforming bodies.

目錄

中文摘要	I 
英文摘要	II
目錄	III
圖目錄	IV

第1章 研究計畫之背景及目的	1
第2章 共形滾動接觸之運動關係	6
第3章 共形滾動接觸條件	11
第4章 以多點拘束條件處理共形滾動接觸條件	18
第5章 以多點拘束條件處理節點力接觸條件	25
第6章 分析程序	28
第7章 結果與討論	33
第8章 結論	35
參考文獻	42

圖目錄

圖1 圓柱與圓孔間的共形滾動接觸	1
圖2 二維彈性圓柱體模型	6
圖3 以尤拉座標表示之模型	6
圖4 接觸區域放大圖	7
圖5 極座標示意圖	9
圖6 接觸區域運動示意圖	11
圖7 圓孔與插銷的半徑關係圖	12
圖8 接觸區元素放大圖	14
圖9 接觸區中的上下兩元素	18
圖10 有限元素分析模型	28
圖11 插銷與孔洞間的網格	31
圖12 接觸區的細分網格	31
圖13 接觸半角 示意圖及接觸區域內節點之角度 	32
圖14 正向無摩擦接觸的正向力與接觸半角的關係	36
圖15 正向無摩擦接觸的應力與接觸半角的關係	37
圖16 μ=0.22時正向摩擦接觸的正向應力與側向應力分佈	38
圖17 μ=0.40時正向摩擦接觸的正向應力與側向應力分佈	39
圖18 μ=0.66時正向摩擦接觸的正向應力與側向應力分佈	40
圖19 共形滾動接觸下正向力與側向力的分佈	41

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