Research On Contact Performance Of Three Dimensional Fractal Surface

Contact problems are widely existed in the mechanical engineering fields. All the micro-contact surfaces are not absolutely smooth, and contact surfaces are actually a series of different sizes asperities contact, leading the real contact area far less than the nominal contact area, making the smaller real contact area to bear a larger contact load, resulting in the contact surface of the accelerated failure. In order to improve the bearing capacity and the fatigue life of contact surfaces, based on fractal geometry theory and contact mechanics, this paper studies the contact characteristics of the rough surface considering the influence of the asperities range.In order to study the characteristics of elastoplastic rough surface. Weierstrass Mandelbrot function is adopted to simulate two dimensional and three dimensional fractal rough surface firstly. Simulation results shows: as the fractal dimension increasing, the rough surfaces are meticulous; as the characteristic length scale of the surface increasing, the height of rough surfaces are enhanced, but the shape of the profile curve hardly changed.Secondly, a modified two-variable Weierstrass-Mandelbrot function is adopted to simulate three-dimensional fractal rough surface. The conditions of existence of elastic deformation, elastoplastic deformation and fully plastic deformation of the single asperity are derived. The relations between size distribution function for all level asperities and size distribution function for each level asperity are given. Then the relations between the total contact load and the real contact area have been obtained. The results show: the mechanical properties of the rough surface depend on the minimum level asperity and sequential six levels asperities. Other levels asperities have little effect on the mechanical properties of the whole rough surface. When the minimum level and sequential six levels are less than elastic critical level, the rough surface appears to be elastic property; When the minimum level and sequential six levels are more than the second elastoplastic critical level, the rough surface appears to be of inelastic property.Thirdly, based on two variable Weierstrass-Mandelbrot function, elastoplastic superposition contact model of three dimensional fractal rough surface, combining the cumulative size-distribution of islands, is established and gets the geometric parameters of asperities Then the relations between the total contact load and the real contact area have been obtained. The results show: the critical contact areas are related to the number of superimpositions asperities. The height of the asperity and the radius of curvature of the peak are reduced as the number of asperity increases. A transition from elastic, elastoplastic to fully plastic contact model takes place in this order and agrees with classical Hertz contact model.When the number of superimpositions asperities is more, the rough surface appears to be of inelastic property. When the number of superimpositions asperities is small, the rough surface appears to be of elastic property. Therefore, the reasons for the plastic deformation to the elastic deformation of the rough surface are analyzed.Finally, surface topography of rough surface was measured by Leica DCM 3D and the contact performance test rig of rough surface was designed. The test results are compared with the fractal model, and the mechanical model is proved to be reasonable and correct by contact experiment.