邊界元素法應用於微動接觸應力分析

Fretting Contact Stress Analysis by the Boundary Element Method

林祺惠(Chi-Huei Lin)

指導教授 ： 郭昌宏

國立暨南國際大學/科技學院/土木工程學系/碩士(2015年)

https://doi.org/10.6837/NCNU.2015.00098

摘要

本研究主要係應用邊界元素法於二維圓柱微動接觸應力分析。先以彈性半無限域基本解為影響函數推導表面相對位移方程式，再根據位移和接觸物幾何外形一致和黏著區相對切線位移保持定值的兩個特性推導邊界積分方程式，建構邊界元素模型並以二節點線性等參數元素將積分方程離散，最後使用半區間法和Gauss-Seidel疊代法求解接觸區域和應力分布。將上述之分析方法應用於二維圓柱赫茲接觸問題，將數值分析結果與赫茲接觸理論相比較，確認分析方法正確後，再以此方法分析微動接觸問題。首先討論圓柱微動接觸的應力分布，其次根據半區間法和Gauss-Seidel疊代法之分析結果，歸納兩種方法的優缺點和適用性，最後探討摩擦係數、切線載重之歷程、材料常數等因素對應力分布之影響。研究結果顯示邊界元素法非常適合用來分析微動接觸問題中有關切線載重反覆加載及卸載過程。施加載重前，圓柱內部von Mises應力極值位於原點座標下深度約0.7a(a為接觸半寬)；加卸載的過程中，應力極值會隨著載重大小增加而變大，且其位置會從原點座標下方約0.7a逐漸往接觸區域邊緣移動。此外，半區間法和Gauss-Seidel疊代法應用於微動接觸應力分析之結果都十分精確，不過因為不同材料圓柱微動接觸的黏著區位置變化較難預測，所以較適合以Gauss-Seidel法疊代得到其接觸應力。

關鍵字

赫茲接觸 ； 微動接觸 ； 應力分析 ； 邊界元素法 ； 半區間法 ； Gauss-Seidel疊代法

並列摘要

The research presents a boundary element method for the contact stress analysis of fretting between two cylinders. The boundary integral equations are derived based on the fundamental solutions of an elastic half-space and the linear element is used to discretize and solve the integral equation. As the contact region is unknown a priori, the iterative procedure based on the bisection and Gauss-Seidel methods is implemented respectively to determine the actual contact region and the contact pressure, and the tractions and displacements on the interfaces. Numerical solutions are obtained for the tractions on the interfaces and subsurface stresses in the cylinders, and used to study the effects of coefficient of friction, tangential load history, and material parameters on the contact stress and contact region. Numerical results show that the boundary element method is suitable to analyze the fretting contact problem. The extremum of von Mises stress is located at (0.0,−0.7a) before repeated load and unload. During the repeated load and unload, the extremum increases when the value of the load increases, and the position of the extremum moves from (0.0,−0.7a) to the border of the contact zone. The results of applying the bisection method and Gauss-Seidel method are accurate. The variation of the stick zone of the fretting contact of dissimilar material is difficult to estimated, so Gauss-Seidel method is suitable for this problem.

並列關鍵字

Hertz contact ； Fretting contact ； Boundary element method ； Bisection method ； Gauss-Seidel iterative method ； Stress analysis

參考文獻

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