A multi-scale normal contact modeling of mechanical joint surfaces considering macro-meso-microscopic geometric parameters

The normal contact stiffness of the bolted joint surface is a key parameter for machine performance. In this paper, a multi-scale fractal contact model considering macro-meso-micro of machine surfaces is proposed to characterize the normal contact behavior of bolted joint surfaces with multi-scale topography. Firstly, an improved single-asperity contact model is proposed to characterize the contact mechanics of asperities under angular deviation, positional deviation, and micro-slip deformation. Secondly, considering the meso-scale waviness characteristics of the mechanical surface, the waviness deformation coefficient is introduced to establish the coupling relationship between waviness and the number of asperity contacts, and the contact area distribution density function is modified. Further, a multi-scale fractal contact model covering macro-meso-micro is constructed by integrating the macro-scale shape function, meso-scale waviness, and micro-scale topography through fractal theory. Finally, the accuracy of the model is verified with experimental data: the accuracy of the proposed model is confirmed by comparing the consistency between the previous theoretical model and the experimental modal values (with a maximum relative error of less than 8%). This paper also analyzes the effects of different surface topographies, macroscopic geometric deviation, different preload force and waviness deformation coefficient on the joint surface characteristics. This model provides theoretical guidance for the optimization design of the mechanical surface topography.