Research on continuous smooth exponential model of elastic-plastic contact and normal contact stiffness of rough surface

A novel approximate exponential analytical model of asperity elastic-plastic contact is developed. The proposed model can solve the problem of discontinuous, leap and unsmooth contact load and contact area in three separated phases, i. e. perfectly elastic phase, elastic-plastic phase and fully plastic phase, and can also deal with the problem of non-monotone of average contact pressure in the elastic-plastic phase. The analytical model between the contact stiffness or contact pressure of rough surface and the real contact area in the three phases is further established by the fractal theory. The dimensionless normal contact stiffness Kn* and dimensionless normal contact load Fn* are obtained. The influences of fractal dimension D, plastic index Φ and dimensionless fractal roughness parameter G* on Kn* or Fn* are simulated and analyzed, and the change of Kn* with Fn* is also simulated and analyzed. The results show that Kn* and Fn* increase with increasing dimensionless real contact area Ar*; the increasing rate of Kn* and Fn* are enhanced with the increase of Φ or decrease of G*. The increasing rate of Fn* decreases first and then increases with D, while the increasing rate of Kn* shows an exponential increase. Kn* increases with Fn*. When D changes from 1.1 to 1.9, the increasing rate of Kn* increases first and then decreases with Fn*. When D>1.51, the value of Kn*/Fn* obviously increases with the decrease of G*. The natural frequencies of the dumbbell model are calculated by the normal contact stiffness model and compared with the experimental one, verifying the accuracy of the proposed model. © 2016, Editorial Office of Journal of Xi'an Jiaotong University. All right reserved.