In this report the system of differential equations of troppy is obtained and analyzed. Troppy is the phenomenon of residual surface waveform damages formation as the result of nonstationary deformation process in the region of contact interaction of the solid/solid elements of an active system. From theoretical point of view troppy phenomenon represents, for example, the result of stability loss of a roller’s motion on a shaft. Motion stability loss is characterized by self-excitation of oscillations in the system and accompanied by elastoplastic deformation of bodies in the contact area.

In this work method of controlling wear-fatigue damages is obtained.

A non-traditional approach to setting and solving contact problems and the analysis of complex stressed state of roller/shaft active system is presented in this paper.