Normal contact stiffness model for fractal surfaces considering scale dependence and friction behavior

The normal contact stiffness on rough surfaces has a significant impact on the interfacial dynamic characteristics of mechanical joints. Based on the fractal geometry theory, this work improves the contact stiffness modeling by considering the complete contact characteristics of multiple asperities and frictional factor. First, to include the property that the critical contact areas of asperities are scale-dependent, the model for the contact stiffness is formed on each scale and the relationship between total stiffness and load on rough surfaces is obtained by the summation of all length scale asperities. Second, friction factor is taken into account in the revised normal contact stiffness model, where a contact friction coefficient is introduced into the equation to incorporate the effects of friction force. Moreover, the influences of fractal dimension D and fractal roughness G on normal contact stiffness and friction coefficient are investigated. Through the comparison of numerical and experimental results, the revised model is shown to be more reasonable and presents higher consistency of the stiffness versus load curve than the original model. It is therefore concluded that a complete and more accurate model for normal contact stiffness is proposed in this work with precise modeling of scale-dependent contact characteristics and friction behavior taken into account, which is critical for exact estimation of rigidity of contact surfaces in industrial applications.