The function of displacements of external contour points of a friction pair hub that could provide minimization of stress state of a hub was determined on the basis of minimax criterion. The problem is to decrease stress state at that place where it is important. The rough friction surface model is used. To solve a problem of optimal design of friction unit the closed system of algebraic equations is constructed. Increase of serviceability of friction pair parts may be controlled by

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... eering methods, in particular by geometry of triboconjugation elements. Minimization of maximum circumferential stress on contact surface of friction unit is of great importance in the design stage for increasing the serviceability of friction pair. The obtained function of displacements of the hub's external contour points provides the serviceability of friction pair elements. The calculation of friction pair for oil-well sucker-rod pumps is considered as an example.