基于域扩展因子和微凸体相互作用的结合面接触刚度模型研究

结合面接触刚度直接影响了机械设备的整机动态特性，为了建立更为准确的接触刚度模型，以分形几何理论为基础，利用单一微凸体承受局部载荷时的弹性变形特性，并基于域扩展因子引入微接触截面积分布函数，推导了考虑表面微凸体相互作用影响的结合面接触刚度分形模型。为了验证所提出模型的准确性，通过三维非接触式测量，获得了试验试样的表面轮廓数据，并根据结构函数法，计算了各个试样的表面分形参数，进而将理论接触刚度与试验结果对比分析，结果表明：法向接触刚度的增长速率与粗糙面表面临界接触面积有关，临界接触面积决定了结合面内的弹性变形占比。考虑微凸体相互作用后，所提出模型的预测曲线更加符合试验中法向载荷与接触刚度的关系。

Investigation of Contact Stiffness Model for Joint Surfaces Based on Domain Expansion Factor and Asperity Interaction

The dynamic characteristics of mechanical equipment can be directly affected by the contact stiffness of joint surfaces. In order to establish a more accurate model of contact stiffness, the elastic deformation characteristics of a single asperity subjected to local load are obtained based on the fractal geometry theory. The distribution function of micro contact truncated area is introduced from the domain extension factor. The fractal model of contact stiffness considering the influence of surface asperity interaction is derived. Also, the surface profile data of the experimental samples are obtained by three-dimensional non-contact measurement to verify the accuracy of the proposed model. According to the structure function method, the surface fractal parameters of each sample are calculated, and then the theoretical contact stiffness and the experimental results are compared and analyzed. It is concluded that the growth rate of normal contact stiffness is related to the critical contact area of rough surface, and the critical contact area determines the proportion of elastic deformation in the joint. After considering the interaction of asperities, the predicted curve of the proposed model is more in line with the relationship between experimental normal load and contact stiffness.