Fractal models of surface topography and contact mechanics

In many tribological applications, some geometrical parameters defined in Euclidean space such as the developed area, surface bearing, void and material volume are very difficult to measure independently of the unit of measurement. The values of these parameters increase when the scale of measurement is decreased. Fractal geometry can be used as an adapted space for rough morphology in which roughness can be considered as a continuous but nondifferentiable function and dimension D of this space is an intrinsic parameter to characterize the surface topography. In the first part of this work, the fractal theory is used as a mathematical model for random surface topography, which can be used as input data in contact mechanics modeling. The result shows that the fractal model is realistic and the fractal dimension can be used as an indicator of the real values of different scale-dependent parameters such as length, surfaces, and volume of roughness. In the second part, we have analyzed through experiments, the contact between fractal random surfaces and a smooth plane, the experimental results show that the fractal dimension can be used as an invariant parameter to analyse the distribution law of the contact points area.