Study On The Normal Contact Stiffness Of Rough Surfaces Based On Ubiquitiform Theory

The actual machining surface is not completely fitted,which is composed of many microscopic and irregular convex or concave bodies.It is pointed out that the actual physical object is ubiquitiform rather than fractal in the ubiquitiform theory.The normal contact stiffness of rough surfaces will be studied by ubiquitiform theory.Firstly,based on the ubiquitiform theory,a generalized ubiquitiformal Sierpinski carpet is introduced to describe the size and position distribution of asperities which height satisfies Gaussian distribution on a rough surface.Using Hertz contact model to calculate the normal contact stiffness of a single asperity,in the rough surface,the analytical expression of ubiquitiformal normal contact stiffness is obtained.The results indicate that normal contact stiffness increases with the increase of ubiquitiformal complexity and the decrease of the lower bound to scale invariance.Compared with the results of the literature,the normal contact stiffness of rough surface under ubiquitiform theory is more consistent with experimental results than existing fractal and statistical methods.Secondly,in order to avoid the influence of statistical parameters ubiquitiformal results,2D and 3D ubiquitiformal W-M functions are constructed by introducing the lower bound to scale invariance δmin into the original 2D and 3D fractal W-M functions.The ubiquitiformal complexity D,characteristic scale parameter G,and the lower bound to scale invariance δmin in the ubiquitiformal W-M functions are collectively referred to as the ubiquitiformal characteristic parameters,which are scale independence.The rough surface morphologies of specific ubiquitiformal characteristic parameters are simulated by 2D and 3D ubiquitiformal W-M functions.The effects of these ubiquitiformal characteristic parameters on the rough surface morphology are analyzed.Finally,the rough surface profile is assumed to be a ubiquitiformal curve.The idea of the rough surface contact model under fractal theory is used to study the contact problem between a rough surface and smooth rigid plane through 2D and 3D ubiquitiformal W-M functions.According to the characteristic lengths of asperities in different ranges,corresponding elastic and plastic deformation criteria are given.The relationships between normal pressure and stiffness of rough surface and the real contact area are derived.The relationship curve between normal pressure and stiffness we obtained is basically consistent with the experimental results in literature.It is investigated that normal contact stiffness increases with the increase of lower bound to scale invariance and ubiquitiformal complexity.Based on ubiquitiform theory,the normal contact stiffness of rough surfaces is studied.Compared with the fractal theory,the deformation process can be described more realistically.The relevant theoretical results can provide an important theoretical basis for the design and manufacture of sophisticated instruments and precise structures.