A large number of mechanical methods, machine tools, tools and materials for machining the rack determines the wide possibilities in ensuring the formation of the parameters of the surface layer of the latter and determines their operational properties. Therefore, the question of ensuring the operational properties of gear rails, depending on the parameters of the state of the surface layer of rails, is urgent. In order to successfully solve this problem, the theoretical aspects of the relationship between the parameters of the state of the surface layer of rails and the processes of their processing are considered.In contrast to the known researches, which provided for revealing the general aspects of connection of certain parameters of the state of the surface layer of rails with the conditions of their processing, the authors suggested the expediency of considering the dependence of the system of parameters of the state of the surface layer, which determine the operational properties of the gear rails with the conditions of their processing. This relationship is expressed in the mathematical dependencies that underlie the development of algorithms and programs. As a consequence, one of the main tasks of the calculation of optimal machining processes is automated, taking into account the provision of the necessary state parameters of the surface layer of gear rails, based on their operational properties. To confirm this direction, the fundamental scientific provisions of the theory of geometric three-dimensional modeling of interconnected processes of removal of allowance and formation during cutting are developed.
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