基于分形理论的平面磨削粗糙表面接触刚度的研究

Study on Contact Stiffness of Rough Surface by Grinding Plane Based on Fractal Theory

为了更加准确地预测平面磨削表面的接触刚度,本文提出一种基于分形理论接触刚度的计算方法。采用分形表面对砂轮的表面形貌进行表征,结合机床运动学与切削理论,实现了平面磨削表面形貌的仿真,并采用有限元方法对平面磨削仿真表面进行接触分析。最后探讨了砂轮表面形貌参数分形维数与尺度系数对平面磨削粗糙表面接触刚度的影响。仿真结果显示,平面磨削表面接触刚度的数值随着接触压力的增大而逐渐增大,两者之间呈现非线性关系并且不同分形参数下的变化趋势相同;在相同接触压力的条件下,平面磨削表面接触刚度随分形维数的增大而逐渐增大,随着尺度系数的增加而逐渐减小。

In order to predict the contact stiffness of surface grinding more accurately,a new method based on fractal theory is proposed.Fractal surface was used to characterize the surface morphology of grinding wheel.Combined with kinematics and cutting theory of machine tool,the surface morphology of plane grinding was simulated,and the contact analysis of the simulated surface of plane grinding was carried out by using finite element method.Finally,the influence of fractal dimension and scale coefficient of grinding wheel surface morphology parameters on contact stiffness of surface roughness in plane grinding was discussed.The simulation results showed that the value of the contact stiffness of the grinding surface increased with the increase of the contact pressure,and the relationship between them was nonlinear and the variation trend was the same under different fractal parameters.Under the same contact pressure,the contact stiffness of the grinding surface increased with the increase of fractal dimension and decreased with the increase of scale coefficient.