應用於三維可變形彈性物體接觸分析之有限元素網格研究

Abstract

本研究主要是針對在使用有限元素法處理接觸問題時，如何有效的建立網格系統，期望能以較有效率的方法進行模擬分析。研究中首先將具有解析解的三維圓球赫茲接觸問題建立有限元素分析模型，分別以局部加密､不同網格類型比較以及節點對應建立網格系統進行測試，將各項測試結果與理論解作比較，探討模擬結果的趨勢。並針對數值解的部分，以一收斂性判別準則判斷何時數值解已足夠準確。以此建立整個接觸問題模擬分析的流程。最後再以直齒漸開線錐形齒輪為載具，調整其網格密度，使用上述模擬分析流程對接觸區正向應力作模擬分析，以確立整套流程應用的可行性，期能在往後應用於真實狀況下的接觸分析。

This research is mainly aimed at how to construct suitable mesh system when conducting 3D elastic contact problems with Finite Element Method in a more efficient way. In the beginning, a three-dimensional Hertz contact problem with two spheres was considered. The Hertz analytical solution was used as a basis for the comparisons with different mesh systems characterized as “localized element density”, “mesh systems of different types” and “touched nodes on the contact surfaces”. The tendencies of these results were discussed and the most suitable mesh system was decided. Meanwhile, the convergence criterion concerning with strain energy was adopted to determine when the mesh system was dense enough to obtain accurate solution for problems without an analytical solution. Incorporated this criterion with FEM, a complete procedure was built, which can determine the suitable mesh systems used in common contact analysis. Finally, a straight beveloid gear pairs contact problem was taken as a realistic example, by comparing the normal stress in contact area for different mesh density, the usability of the procedure was verified.