摘要
为了获得粗糙表面点接触的力学特性,提高接触元件的承载能力,采用Weierstrass-Mandelbrot函数生成了三维粗糙球形表面,建立了粗糙球形表面与一刚性平面接触的分形力学模型,推导出不同接触区域上各个频率指数的微凸体的截断面积密度分布函数,获得了真实接触面积与总接触载荷的解析表达式,得到了接触半宽上的接触压力分布。计算结果表明:微凸体的频率指数范围直接影响粗糙球形表面的接触力学性质;当最小频率指数n_(min)与临界弹性频率指数n_(ec)满足n_(min)+5≤n_(ec)时,粗糙球形表面在整个接触过程中呈现弹性变形性质,当最小频率指数n_(min)与临界弹塑性频率指数n_(epc)满足n_(min)>n_(epc)时,粗糙球形表面在整个接触过程中呈现非弹性变形性质;粗糙球形表面的接触半宽主要由基圆确定,对于相同比例的下压量,接触压力峰值与最小频率指数成正比;在弹性变形与弹塑性变形阶段,接触压力在接触区域中心达到最大,向接触区域边缘方向递减,在完全塑性变形阶段,接触压力在整个接触区域近似均匀分布。
To investigate mechanical properties of point contact between rough surfaces and improve the bearing capacity of contact component, the Weierstrass-Mandelbrot function is used to simulate a three-dimensional sphere-based fractal rough surface, and then a mechanical model of contact between a sphere-based fractal rough surface and a rigid plane is developed. The truncated size distributions for asperities with different frequency indexes in different contact zones are derived. The relation between real contact area and total contact load is obtained, and the contact pressure distribution on the contact half width is obtained. The results show that the mechanical properties of sphere-based fractal rough surface are mainly affected by the range of frequency index. When the relation between the minimum frequency index nmin and the elastic critical frequency index nec is nmin+5≤nec, the sphere-based fractal rough surface exhibits elastic property in a complete contact process. When the relation between the nmin and the elasto-plastic critical frequency index nepc is nmin>nepc, the sphere-based fractal rough surface exhibits inelastic property during the entire contact process. The value of contact half width of the sphere-based fractal rough surface mainly depends on the radius of base circle. With the same ratio of interference, the peak contact pressure is proportional to the value of the minimum frequency index. In elastic and elasto-plastic deformation process, the contact pressure reaches the maximum at the center of contact zone, and decreases from center to edge of the contact zone. In plastic deformation process, the contact pressure exhibits approximately uniform distribution in whole contact zone.
作者
原园
张利华
徐颖强
YUAN Yuan;ZHANG Lihua;XU Yingqiang(College of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi'an 710048, China;School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China)
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2019年第5期176-186,共11页
Journal of Xi'an Jiaotong University
基金
基金项目:国家自然科学基金资助项目(51475364
51105304)
关键词
粗糙球形表面
分形
微凸体
接触
频率指数
sphere-based rough surface
fractal
asperity
contact
frequency index
