原园, 成雨, 张静. 基于分形的三维粗糙表面弹塑性接触力学模型与试验验证[J]. 工程力学, 2018, 35(6): 209-221. DOI: 10.6052/j.issn.1000-4750.2017.02.0106
引用本文: 原园, 成雨, 张静. 基于分形的三维粗糙表面弹塑性接触力学模型与试验验证[J]. 工程力学, 2018, 35(6): 209-221. DOI: 10.6052/j.issn.1000-4750.2017.02.0106
YUAN Yuan, CHENG Yu, ZHANG Jing. FRACTAL BASED ELASTOPLASTIC MECHANICS MODEL FOR CONTACT WITH ROUGH SURFACE AND ITS EXPERIMENTAL VERIFICATION[J]. Engineering Mechanics, 2018, 35(6): 209-221. DOI: 10.6052/j.issn.1000-4750.2017.02.0106
Citation: YUAN Yuan, CHENG Yu, ZHANG Jing. FRACTAL BASED ELASTOPLASTIC MECHANICS MODEL FOR CONTACT WITH ROUGH SURFACE AND ITS EXPERIMENTAL VERIFICATION[J]. Engineering Mechanics, 2018, 35(6): 209-221. DOI: 10.6052/j.issn.1000-4750.2017.02.0106

基于分形的三维粗糙表面弹塑性接触力学模型与试验验证

FRACTAL BASED ELASTOPLASTIC MECHANICS MODEL FOR CONTACT WITH ROUGH SURFACE AND ITS EXPERIMENTAL VERIFICATION

  • 摘要: 基于分形几何理论,利用双变量的Weierstrass-Mandelbrot函数模拟三维分形粗糙表面,建立了三维分形粗糙表面弹塑性接触模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定了粗糙表面上各等级微凸体的面积分布密度函数,获得了总接触载荷和真实接触面积之间的关系式。计算结果表明:单个微凸体的临界接触面积与其尺寸相关,随着微凸体等级的增大,微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与经典的赫兹模型保持一致。粗糙表面的力学性能仅与最小等级及后续的6个等级微凸体相关,其余微凸体基本上对整个粗糙表面的力学性能影响很小。最后对粗糙表面的接触力学性能进行了试验测试,验证了该模型的合理性与正确性。

     

    Abstract: Based on fractal geometrical theory, an elastoplastic contact mechanics model for three-dimensional fractal rough surfaces has been established. A modified two-variable Weierstrass-Mandelbrot function is adopted to simulate a three-dimensional fractal rough surface. The existing conditions of elastic deformation, elastoplastic deformation and fully plastic deformation of the single asperity are derived. The relations between size distribution function for all level asperities and size distribution function for each level asperity are developed. Then the relations between the total contact load and the real contact area have been obtained. The results show that:the critical contact areas of a single asperity are related to its geometric size. As an asperity level increases, the height and radius of curvature decrease. As the load and contact area increase, a transition from elastic, elastoplastic to fully plastic contact model takes place in this order and agrees with classical Hertz contact model. The mechanical properties of the rough surface depend on the minimum level asperity and sequential six levels asperities. Other level's asperities have little effect on the mechanical properties of the whole rough surface. Finally, the mechanical model is proved to be reasonable and correct by contact experiment.

     

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