Existing research methods of contact interaction and stress-strain state of complex structural elements are analyzed. The main elements of hydraulic transmissions in tank transmissions are ball pistons that are connected to the toroidal running surface of the stator ring. Important parameters of these elements are the ratio of the radii of the piston and the cross-section of the running track. The studied regularities indicate the optimal range of radii ratios, which ensures minimum contact pressure and stress. Taking into account the elastic-plastic deformation of the materials of the contacting parts, in particular the surface layers, is important for recommendatory decisions. Patterns of influence on the characteristics of strength and performance of the investigated structures of varied parameters have been revealed. Accordingly, in each specific case, it is possible to develop recommendations for the justification of progressive technical solutions of certain structures according to the mentioned criteria. Ball pistons in connection with the toroidal running surface of the stator ring are decisive for strength and durability of the hydraulic transmission elements of promising tank transmissions. In particular, important parameters are the radii ratio of the piston, on the one hand, and on the other, of the cross section of the treadmill. Despite the traditionally existing approaches and efforts to bring the shapes of the contacting surfaces of conjugated bodies as close as possible, the work established regularities that contradict such solutions.
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