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Abstract. At present, belt grinding is widely used in the leading branches of the national economy. The rotary belt grinding process has a complex stochastic nature, which leads to a dispersion of product quality parameters and does not allow to use all possibilities of this method, due to the lack of an adequate mathematical description of the process. The article is devoted to the development of the theoretical and probabilistic model of the rotary belt grinding process.

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The theoretical study and evaluation of stress-strain condition of the friction pair's surfaces of total hip joint prosthesis with partially regular texture on a ball head surface, depending on the values of its characteristic parameters, using finite element modeling are performed. It has allowed formulating the recommendations for dimple's spacing rationing and the extent of a surface rough site with partially regular texture, aiming to increase the prosthesis' lifespan. The problem is solved from the condition of dry or boundary lubrication. For the indicated range of nominal contact pressure in hip joint, the quantitative evaluation of allowable roughness parameters to which it is necessary to process the ball head surface for metal-on-metal and metal-on-polymer friction pairs are obtained, considering the dimple's spacing and size on the surface.

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