滾滑動元件在反覆接觸載重下之彈塑性有限元素分析

Elastic-Plastic Finite Element Analysis of Rolling Elements under Repeatedly Contact Loading

何泓儒(Hung-Ru Ho)

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(2016年)

摘要

本研究是以彈塑性有限元素分析方法滾滑動元件在反覆接觸載重下之彈塑性變形。研究方法是以四邊形元素建立有限元素分析模型，並移動赫茲接觸應力模擬反覆滾滑動接觸過程。彈塑性有限元素分別採用Prager線性運動硬化模式與Chaboche的非線性運動硬化模式，模擬金屬材料之運動硬化行為，並以回映演算法作為材料降伏後之應力修正。為驗證有限元素分析結果之準確性，本研究分別以懸臂樑受對稱載重下之彈塑性變形和二維彈性接觸問題為例，將數值計算結果與ANSYS和解析解分析結果相互比較，並得到相當吻合的比較結果。研究結果顯示，Prager線性硬化模式因不具有飽和的特性，導致無法模擬棘輪效應，而 Chaboche模式擁有回復項較能夠模擬棘輪效應。以Chaboche模式模擬接觸元件之循環塑性變形結果顯示，彈性安定區在不同大小之接觸載重下均維持塑性變形區一半的深度。摩擦係數會增加表面的塑性變形，然而對於塑性變形的深度及彈性安定區的影響則相對較小。安定性分析結果顯示，剪應變棘輪率隨載重週期增加而遞減，而遞減速率隨接觸載重增加而遞增。此外，無因次化之最大等效應力隨載重增加而減少，而隨摩擦係數增加而逐漸增加。

關鍵字

塑性力學 ； 有限元素法 ； 非線性運動硬化模式 ； 回映演算法 ； 反覆滾滑動接觸 ； 安定性

並列摘要

The research present a finite element method to analyze elastic-plastic deformation of rolling elements under repeatedly contact loading. The finite element model is composed of four-node quadrilateral plane elements, and moving Hertzian contact stress used to simulate repeatedly rolling contact process. The Prager linear hardening model and Chaboche nonlinear model are used respectively in the elastic-plastic finite element analysis to simulate kinematic hardening behaviors of metals, and return mapping algorithm is used for the correction of stresses to yield surface. To verify the accuracy of the finite element results, numerical solutions of a cantilever beam under reversed loading and a two-dimension elastic contact problem are compared and shown a good agreement with ANSYS and analytical solutions. The results show that Prager model cannot be used to simulate ratchetting behavior for lack of a recall terms while Chaboche model is more effective to simulate cyclic deformation of materials under repeatedly contact loading. In the simulation of cyclic plastic deformation of contact components using Chaboche model, the results show that the elastic shakedown area remains at half-depth of plastic zone regardless the magnitude of contact loading. Friction coefficient may increase plastic deformation at contact surface but has limited effect on the depth of plastic zone and shakedown area. In shakedown analysis, the ratchetting rate of shear strain decreases with increasing number of contact cycles and the reduction rate increases with increasing magnitude of contact loading. In addition, the dimensionless maximum equivalent stress decreases with increasing magnitude of contact loading but increase with increasing coefficient of friction.

並列關鍵字

plasticity ； finite element method ； nonlinear kinematic hardening model ； return mapping algorithm ； repeatedly rolling/sliding contact ； shakedown

參考文獻

1. Bower, A., & Johnson, K. (1989). The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact. Journal of the Mechanics and Physics of Solids, 37(4), 471-493.

2. Merwin, J., & Johnson, K. (1963). An analysis of plastic deformation in rolling contact. Proceedings of the Institution of Mechanical Engineers, 177(1), 676-690.

3. Johnson, K. (1995). Contact mechanics and the wear of metals. Wear, 190(2), 162-170.

4. Bower, A., & Johnson, K. (1991). Plastic flow and shakedown of the rail surface in repeated wheel-rail contact. Wear, 144(1), 1-18.

5. Hills, D., & Ashelby, D. (1982). The influence of residual stresses on contact-load-bearing capacity. Wear, 75(2), 221-239.