On the normal contact stiffness and contact resonance frequency of rough surface contact based on asperity micro-contact statistical models

Contact stiffness is an important parameter for describing the interface characteristics in many engineering applications. In this paper, five different statistical micro-models including the Greenwood-Williamson (GW), Zhao-Maietta-Chang (ZMC), Kogut-Etsion (KE), Jackson-Green (JG) and Brake are employed to predict the normal contact stiffness for rough surface contact. It is found that the expressions of contact stiffness obtained using the statistical micro-models are very complex and the direct relationship between the contact stiffness and normal load is not available. Accordingly, an explicit approximated expression for contact stiffness is established in terms of normal load based on the results of numerical simulations. The normal contact stiffness as a function of normal load can be approximated using a power law, in which the coefficient and power are related to surface roughness parameters, material properties as well as nominal contact area. The close agreement between the predicted results and full numerical simulations verify the accuracy of the established explicit expression. The contact stiffness calculated using the predictive expressions are also compared with available experimental results from both ultrasonic method and contact resonance method. Further, the explicit expression of contact resonance frequency for rough surface contact with respect to the normal load is also provided, which can be used to evaluate the contact resonance frequency. The predicted contact resonance frequency is also validated through comparing with experimental results.