A FRACTAL MODEL OF CONTACT BETWEEN THREE-DIMENSIONAL ROUGH SURFACES WITH SUPERPOSED ASPERITIES

Abstract A fractal model of contact between three-dimensional rough surfaces with superposed asperities is developed based on fractal theory. The superposed asperity is established by prioritized frequency index, prioritized ridge and prioritized radius of single asperity, respectively. It is found that the profile of superposed asperity established by prioritized ridge method does coincide with profile simulated by Weierstrass-Mandelbrot function. The relations between contact area and contact load for each layer of a single superposed asperity in elastic, elastoplastic, fully plastic deformation are given, respectively. The relations between real contact area and total contact load for rough surface are obtained by asperity size distribution function. The results show that the mechanical properties of a single superposed asperity depend on that of each single layer asperity in superposed asperity. The mechanical properties of rough surface depend on that of a single superposed asperity. A superposed asperity which is overlapped by a lot of single asperities has N layers asperities. As only elastic deformation takes place in each layer asperity, the rough surface appears elastic characteristic. As only fully plastic deformation takes place in asperities ranging from the first to N-1th layer, the rough surface appears fully plastic characteristic. As only elastic deformation takes place in asperities ranging from the first to I1th layer, only elastoplastic deformation takes place in asperities ranging from the I1+1th to I2th layer, only fully plastic deformation takes place in asperities ranging from the I2+1th to N-1th layer, a transition from fully plastic, elastoplastic to elastic contact mode takes place in rough surface. A comparison of the present model with the other models is given to verify the rationality of the present model.