This paper discusses the kinematic characteristics of lapping process and the main parameters of the process. It was determined that the influencing degree of technological parameters to the forming surface and processes. It was projected the construction of the lapping head for processing of internal cylindrical surfaces, scheme of the lapping operation and graphic description of the forces influencing. The relationships between the axial, radial and tangential cutting forces and the effect of the combined force thereof are determined in order to ensure the necessary surface pressure. During the analysis geometric and mathematical relationships were obtained. The extracted analytical expressions can be realized by further experimental researches and can be used in engineering calculations of technological parameters of processing by lapping. Angular velocity, friction force, linear velocity, also the length of the tactile curve and the radius of the part can be considered the main kinematic and dynamic parameters of the process that the formation of the surface, also the course of the process depends on these parameters. Depending on the kinematic parameters, the wear nature of the tool changes and this changes the linear and angular velocities, which have a significant impact on the accuracy, quality and productivity of processing. When examining the technological capabilities of the process, the nature of the movement between the part and the grinding tool, also changes in cutting speed are often considered as a main factor. Analytical expressions were obtained to determine the main parameters of the process, taking into account the kinematic characteristics of the friction process. These expressions can be used in engineering calculations and allow to determine the optimal values of the processing mode. In order to obtain the required micrometric surface cleanliness and measurement accuracy, correlation relationships were established between the main parameters of the process, equations of the equilibrium system of shear forces were compiled and analytical expressions were obtained based on the analysis of kinematic and dynamic properties of the system.
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