一种考虑微凸体接触角分布的结合面侧接触分形模型  

A Fractal Model for Lateral Contact of Joint Considering Contact Angle Distribution Between Asperities

作　　者：王世军[1] 刘鑫 范凌松 崔圣奇 李鹏阳[1] WANG Shijun;LIU Xin;FAN Lingsong;CUI Shengqi;LI Pengyang(School of Mechanical and Precision Instrument Engineering,Xi’an University of Technology,Xi’an 710048,China)

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048

出　　处：《西安交通大学学报》2023年第12期190-200,共11页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(52075439);陕西省区域创新能力引导计划资助项目(2022QFY01-01);西安市科技计划资助项目(2020KJRC0072)。

摘　　要：针对以往分形模型中忽略微凸体侧向接触和接触角度分布来源的问题,提出了一种考虑微凸体之间接触角分布的结合面接触刚度的侧接触分形模型。通过轮廓显微镜采集了接触表面的轮廓,采用三点峰方法将表面轮廓模型化,获得了相邻微凸体之间的水平距离及高度差的数据。利用功率谱密度法进行分析,发现相邻微凸体之间的水平距离和高度差均具有分形规律。根据所发现的分形规律,推导出两个微凸体相互接触时接触角的分布函数规律,然后采用分形理论建立了结合面的侧接触模型。基于这个模型,通过数值仿真,研究了分形参数、塑性指数、法向载荷系数及接触方式对结合面法向、切向接触刚度的影响。结果表明:无量纲切向接触刚度随着分形维数、塑性指数及法向载荷系数的增大而增大,随着无量纲分形尺度参数的增大而减小。对比有限元分析及模态试验的结果,发现二者最大相对误差为4.32%,相较LZT模型精度提高了46.8%,说明所提模型能够比较准确地预测结合面的接触刚度。Aiming at the problem that the lateral contact and the source of contact angle distribution between asperities are ignored in the existing fractal models,a lateral fractal model of contact stiffness of joint considering the contact angle distribution between asperities was proposed.The profile of the contact surfaces was obtained by the profile microscope,and the surface profiles were modeled by the three-point peak method to obtain the data of the horizontal distance and height difference between adjacent asperities.The analysis results based on power spectral density method show that the horizontal distances and height differences between adjacent asperities have fractal laws.According to the discovered fractal law,the distribution function law of contact angle is derived when two asperities contact with each other,then the contact stiffness model of joint is established by the fractal theory.Based on this model,the effects of fractal parameters,plastic index,normal load coefficient,and contact mode on the normal and tangential contact stiffness were studied through the numerical simulation.The results indicate that the dimensionless tangential contact stiffness increases with the fractal dimension,plastic index,and normal load coefficient,while decreases as the fractal scale parameter increases.Comparing the results of finite element analysis and modal experiment,it is found that the absolute value of the maximum relative error is 4.32%,and the accuracy is 46.80%higher than that of the LZT model,which illustrates that this model can accurately predict the contact stiffness of joint.

关 键 词：侧接触 接触角分布 分形模型 接触刚度 

分 类 号：TH113.1[机械工程—机械设计及理论]