Fractal theoretical modeling of loading contact characteristics of machine tool joint interfaces considering interaction between asperities

Based on fractal geometry theory, the influence of the interaction between asperities on the contact characteristics of mechanical joint interfaces is considered. At the same time, the two stages of elastic-plastic deformation of asperities are considered, and the elastic critical deformation of the asperity considering the interaction between asperities is obtained. Thus, a theoretical model for the contact load and contact stiffness of a single asperity at each deformation stage is established, taking into account the interaction between asperities. Further establish a fractal theoretical model for the real contact load and contact stiffness of the joint interface considering the interaction between asperities, and perform dimensionless processing. Derive the one-dimensional relationship between contact load, contact stiffness, and contact area. Through simulation analysis and comparison, it can be seen that the critical deformation of a single asperity when considering the interaction between asperities is smaller than when not considering the interaction between asperities, while the corresponding contact load and contact stiffness of asperities are greater than when not considering the interaction between asperities. By comparing the effects of different fractal dimensions on the contact load and contact stiffness of the joint interface when considering the interaction between asperities, it is found that the fractal dimension increases when considering the interaction between asperities, and the contact load and contact stiffness of the joint interface show an increasing trend.