基于分形接触理论和半解析法的结合部分区域虚拟材料等效建模

doi:10.3901/JME.260240

摘要/Abstract

摘要： 为了精确表征结合部的动力学特性，考虑结合部压力非均匀分布特征，基于分形接触理论和半解析法，提出了精确的结合部分区域虚拟材料等效建模方法。首先，将结合部的接触压力等效为多项式函数，根据实际压力分布对结合部进行子区域划分，使子区域内的压力分布近似均匀；其次，考虑子区域内粗糙表面的微观形貌特征，采用W-M分形函数进行表征，对子区域内不同微凸体的弹塑性变形进行求解，为了准确计算子区域的接触刚度，开发了半解析算法，对粗糙表面发生弹塑性接触变形后的无量纲接触面积进行精确求解；接着，基于分形接触理论计算得到的子区域法向与切向接触刚度，求解出子区域等效虚拟材料参数，通过名义接触面积的加权平均，获得整个结合部的等效虚拟材料参数。最后，搭建了模态测试试验平台，并建立包含等效虚拟材料的有限元仿真模型，虚拟材料参数基于上述方法获得，并对比了压力均匀分布和不考虑结合部粗糙表面微观形貌特征的虚拟材料参数，通过试验和仿真结果分析，验证了本文所提建模方法的准确性和可靠性。

关键词: 栓接结合部, 分区域虚拟材料, 非均匀接触压力, 分形接触理论, 半解析算法

Abstract: In order to accurately characterize the dynamic performance of joint interface, a precise sub-regional virtual material equivalent modeling approach is proposed based on fractal contact theory and semi-analytical method, considering uneven contact pressure of joint interface. Firstly, the contact pressure of a joint interface is equivalent to a polynomial function, and the joint interface was divided into several sub-regions according to pressure distribution, so that the pressure within each sub-region is approximately uniform. Secondly, considering the micro morphology of the rough surface in each sub-region, W-M function is used to solve elastic-plastic deformation of asperities in sub-regions. With the purpose of accurately calculate the contact stiffness of sub-regions, a semi-analytical method is developed, so that the dimensionless contact area of rough surface under elastic-plastic deformation can be solved. Next, based on the fractal contact theory, the contact stiffness of sub-regions is calculated, and the equivalent virtual material parameters of sub-regions are derived. By weighting the nominal contact area of sub-regions, the equivalent virtual material parameters of whole joint interface are obtained. Finally, a modal test platform is built up, and a finite element model containing equivalent virtual material parameters is established. The result is compared with the equivalent virtual material parameters obtained through uniform pressure distribution and regardless of the microscopic morphology of rough surface. The accuracy and reliability of the modeling method proposed in this paper are verified through the analysis of experimental and simulation results.

Key words: bolted joint, sub-regional virtual material, uneven contact pressure, fractal contact theory, semi-analytical method

中图分类号:

TG156

赵鹏昊, 刘检华, 巩浩, 王星洁. 基于分形接触理论和半解析法的结合部分区域虚拟材料等效建模[J]. 机械工程学报, 2026, 62(5): 230-243.

ZHAO Penghao, LIU Jianhua, GONG Hao, WANG Xingjie. Sub-regional Virtual Material Equivalent Modeling of Joint Interface Based on Fractal Contact Theory and Semi-analytical Method[J]. Journal of Mechanical Engineering, 2026, 62(5): 230-243.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I5/230

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