基于多尺度下塑性指数模型的结合面接触刚度计算方法

Calculation method for contact stiffness of contact surface based on multi-scale plastic index model

螺栓连接结合面的接触特性是影响机械系统动静态特性的关键。当结合面处于振动疲劳状态时,会导致阻尼增大和共振频率减小,因此建立精确的栓接结合面接触模型对研究整个机床的动态特性有着十分重要的意义。结合Greenwood和Williamson给出的塑性指数表达式、统计学的粗糙度参数和分形参数,建立了与微凸体频率序数相关的塑性指数模型,从而根据塑性指数得到微凸体弹性-弹塑性-塑性变形的临界频率序数,并基于赫兹接触理论,通过对不同频率区间内微凸体的积分得到整个结合面的接触载荷和接触刚度。最后,通过有限元仿真与试验相结合共同验证了理论模型的正确性,证明该理论模型具有较强的工程应用价值。

Contact characteristics of bolt connection contact surface are the key to affect dynamic and static characteristics of mechanical system.When a contact surface is in vibration fatigue state,it can cause increase in damping and decrease in resonance frequency.Therefore,establishing an accurate contact model of bolted contact surface is of great significance to study dynamic characteristics of the whole machine tool.Here,combined with the plastic index expression,statistical roughness parameters and fractal parameters given by Greenwood and Williamson,a plastic index model related to frequency ordinal number of micro-convex body was established.According to the plastic index,the critical frequency ordinal number of elastic-elastoplastic-plastic deformation of micro-convex body was obtained.Based on Hertz contact theory,the contact load and contact stiffness of the whole contact surface were obtained through integrating the micro-convex body within different frequency intervals.Finally,the correctness of the theoretical model was verified through the combination of finite element simulation and tests.It was shown that the theoretical model described above has stronger engineering application value.