Study on the normal contact stiffness of the fractal rough surface in mixed lubrication

In this paper, an elastic interface model is developed to theoretically analyze the contact stiffness of a mixed lubrication surface where the solid and the lubricant contacts have to-be-determined contributions to the whole contact stiffness. The interfacial contact stiffness is composed of the solid contact stiffness and the lubricant contact stiffness, in which the two components are associated with each other via the equivalent thickness of lubricant. Based on the combination of two widely acknowledged ultrasonic measurement models and the Taylor approximating equation, the derivation of the lubricant contact stiffness is mostly affected by the material properties and the equivalent thickness of lubricant, and the equivalent thickness is determined by the solid contact properties under the mixed lubrication condition. Results of the mathematical analysis show that the contact stiffness of the mixed lubrication surface is larger than that of the dry rough surface due to the presence of lubricant. The interfacial contact stiffness of the mixed lubrication is obviously affected by the surface topography and the lubricant property. The proportions of contact stiffness contributed from the solid part and the lubricant part are varying with the contact area and the surface topography. Model predictions are compared with experiment results to verify the accuracy of proposed model. The analysis of the interfacial contact stiffness involved in mixed lubrication provides a theoretical basis for the performance prediction of machine tools, and might be useful to elucidate the contact properties by ultrasonic pulse probing in real engineering applications.