Research on fractal model of normal contact stiffness for mechanical joint considering asperity interaction

Abstract

The normal contact stiffness of mechanical joint has immediate impact on dynamic characteristics and machining precision of machine tools. A fractal contact stiffness model considering the effect of asperity interaction is proposed in this paper. On the basis of elastic theory, the deformation of a given asperity is deduced. The relationship between contact stiffness, normal load and contact area is derived from Hertz contact theory and fractal theory. The effect of asperity interaction on contact stiffness is studied by comparing with fractal model. The fractal smoothness is defined from relation between fractal parameters and surface roughness. It is concluded that with the increase of the fractal dimension D and the decrease of fractal roughness parameter G, the contact stiffness of the joint increases, and the effect of asperity interaction becomes greater. The fractal smoothness also affects the normal contact stiffness and the effect of surface smoothness can be offset by the asperity interaction. Experiment shows that the proposed model is more in line with the actual load-stiffness relationship. The model reveals the factors that affect stiffness of the joint, which can provide a theoretical basis for improving the rigidity and precision of integrated machineries.