基于分形理论的齿面微观形态接触特性分析

Contact Characteristics Analysis of Tooth Surface Microscopic Morphology Based on the Fractal Theory

如何有效计算结合面的接触刚度以及分析结合面刚度对整体结构动态特性的影响,是机械结构研究的重要课题之一。目前更多的是简单地将分形理论应用于结合面刚度计算分析,难以全面地对微观形态接触特性进行分析。因此,亟待提出齿面接触刚度计算的新方法,对微观形态接触特性进行分析。基于W-M(Weierstrass-Mandelbrot)函数构建了齿面微观结合面三维实体模型,考虑粗糙度对刚度的影响,提出了一种基于分形维数D和齿面粗糙度的粗糙表面轮廓分形表征新方法;探讨了微凸体接触变形机制,揭示了接触刚度随微凸体变形而变化的规律。研究表明,在同一粗糙度的微观结合面中,当微凸体变形到同一水准时,分形维数D越大,其接触刚度越大;在同一分形维数、不同粗糙度的结合面中,结合面的粗糙度越小,接触刚度越大。

How to effectively calculate the contact stiffness of the joint surface and analyze the influence of the joint surface stiffness on the dynamic characteristics of the overall structure is one of the important subjects in the study of mechanical structures.However,at present,the fractal theory is simply applied to the calculation and analysis of the joint surface stiffness,and it is difficult to comprehensively analyze the microscopic contact characteristics.Therefore,it is urgent to propose a new method to calculate the contact stiffness of the tooth surface and to analyze the microscopic contact characteristics.Based on the W-M(Weierstrass-Mandelbrot)function,a three-dimensional solid model of the microcosmic joint surface of the tooth surface was constructed,and a new method for fractal representation of the rough surface profile based on the fractal dimension D and the tooth surface roughness was proposed,considering the influence of roughness on the stiffness.The contact deformation mechanism of asperities was discussed,and the law of contact stiffness changing with the deformation of asperities was revealed.The research shows that in the same roughness of the micro-joint surface,when the asperity deforms to the same level,the larger the fractal dimension D is,the greater the contact stiffness will be.In the joint surface with the same fractal dimension and different roughness,the smaller the roughness of the joint surface is,the greater the contact stiffness will be.