The Research On The Contact Between Rough Surfaces Based On Fractal Theory

From the macroscopic point of view,the surface of mechanical parts seems smooth,but at the microscopic scale,these surfaces are actually rough and uneven,which results in that the actual contact area of two parts' surfaces squeezed with each other is much smaller than the nominal contact area observed from the macroscopic scale and that the load is borne only by the actual contact area.With the increase of contact load,the partial surface is easy to collapse,which will not only lead to the increase of friction resistance and energy loss between the contact surfaces,but also directly affect the transmission,processing,measurement and assembly accuracy of some precision instruments which have high requirements on structure and processing.Therefore,the study of contact mechanics characteristics and mechanism of rough surfaces has important practical significance for avoiding and solving the actual engineering problems mentioned above.On the basis of fractal geometry theory,the contact mechanics problems of two-dimensional and three-dimensional rough surfaces are modeled.Weierstrass-Mandelbrot(W-M)function is used to characterize and simulate morphology of the equivalent two-dimensional and three-dimensional rough surfaces(interface)related to fractal dimension D,fractal roughness G and frequency index n of asperity.The analytical expressions of mechanical properties including contact interference,contact area,contact load and contact stiffness of a single asperity and the whole contact interface during the contact between two rough surfaces are obtained through theoretical deduction.Then the numerical solutions of the theoretical results in present models are compared with the representative research conclusions and experimental results in this field to verify the feasibility and rationality of the theoretical models.(1)On the basis of fractal geometry theory and W-M function,the morphology of two-dimensional and three-dimensional rough surface are simulated and characterized.The physical meanings of fractal dimension D,fractal roughness G and frequency index of asperity n are respectively elucidated.Then how morphology of rough surfaces change with these three parameters are analyzed,and the fundamental reasons for the changes are expounded.The analyses show that the larger the fractal dimension,the smaller the fractal roughness and the smaller the frequency index of asperity correspond to the smoother surface morphology(2)The problem of contact between two rough surfaces is transformed into the problem of contact between an equivalent rough surface(interface)and a rigid smooth plane.Starting with a single asperity,its mechanical mechanism of elastic,elastic-plastic and plastic deformation in the process of contact is deduced based on fractal theory and classical contact mechanics.The distribution rule of asperities is revised reasonably,and the area distribution function of asperity corresponding to each frequency index is deduced.The analytical expressions of contact load and true contact area during the whole contact process are obtained,and the correlation between them is analyzed and explained.The analyses show that in the present model where the size distribution functions of asperities are modified,unit area on interfaces actually bear a higher contact load than that in the previous model(3)Based on fractal theory and classical contact mechanics theory,combining the normal contact stiffness corresponding to the elastic,elastic-plastic and plastic deformation of a single asperity with the revised asperities' truncation area distribution function,the modified three-dimensional normal contact stiffness model of rough surfaces is established through rigorous mathematical deduction.The analytical solutions of normal contact load and normal contact stiffness of the three-dimensional equivalent rough surface(interface)are obtained by substituting the values of fractal dimension D,fractal roughness G and related material parameters into theoretical expressions and through MATLAB programming.Finally,the numerical results of normal contact load and normal contact stiffness of interface are obtained.The influences of fractal parameters D,fractal roughness G,frequency index of asperities n and normal contact load Fr on normal contact stiffness of interface are respectively analyzed.The analysis results show that the normal contact stiffness increases with the increase of fractal dimension,the decrease of fractal roughness,the decrease of frequency index and the increase of normal contact load(4)The surface morphology of two groups of test specimens with different grinding roughness from the same production batch are measured by Leica DCM 3D white light interferometer.On the basis of the measurement data,the actual fractal dimension D and fractal roughness G of each specimen's surface and the equivalent surface(interface)were calculated through structural function method.The material parameters and calculated fractal parameters D and G of the specimens are substituted into the analytical solution to obtain the theoretical numerical solution.Then a normal loading test device is designed and installed,and two groups of test specimens are installed to implement this loading experiment.The experimental data of normal contact surface pressure and normal displacement directly output from the data acquisition system are recorded and collated.Finally,the rationality and application scope of the theoretical model are analyzed by comparing and analyzing the two results.Compared with the experimental results,the theoretical model in this paper has better adaptability in practical situation.