The results of the computer simulation of the cutting process of gears by the power skiving method are presented. Following the kinematics of the process, a method for generating 3D geometric models of undeformed sheared layers were developed, and their parameters were analyzed. The influence of tool geometry and technological parameters on cutting conditions is investigated. The simulation results and calculation of the tangential force and torque on the tool axis and their influence on the error due to angular elastic deformation of the tool are given.

The paper presents the results of modelling and investigation of the gear cutting process using the power skiving method. The investigations are based on the developed geometrical model of undeformed chips. The approach is based on the original method of forming an integral three-dimensional model on the basis of discrete cross-sections of tool tooth in their successive positions on the cutting path, taking into account the shape and size of the gap previously formed by this tooth. The formulae for calculating the cutting force and the forces acting on the work gear and tool are derived as a function of the angular position of the cutter. The dependence of this force on the angle of tool shaft setting and the angle of inclination of gear teeth is studied. The formulae take into account how the cutting intensity changes due to the peculiarities of the kinematics of power skiving technology and the influence of the actual geometric parameters of the tool on the cutting force. Based on the obtained dependencies, a methodology has been developed for the selection of the axial feed rate and spindle set angle to ensure a compromise between the required productivity and the accuracy of the gear profile.

The paper presents the results of a simulation on a 3D model of undeformed chips and cutting forces during three-pass gear cutting using the power skiving method. At the level of individual blades and teeth in successive angular cutting positions, the main component of the cutting force and the tangential force on the cutter axis are shown. The analysis of the forces acting on a single gear tooth and the continuous cutting forces allowed the development of a methodology for the selection of rational cutting modes – the value of the axial feed, the number of passes with different cutting depths in order to ensure the minimum time consumption and to achieve the required accuracy of the gears in terms of the parameter of the permissible angular deviation of the profile of the cut gear. It is shown that, provided the required machining accuracy is ensured, higher productivity is achieved by increasing the axial feed at a lower depth of cut and increasing the number of passes, rather than by reducing the feed and increasing the depth of cut.

Today, the world's leading enterprises engaged in the manufacture of gear wheels increasingly use the Power Skiving method of cutting the gear crown on the wheel. This modern method allows you to process wheels with an external and internal crown, both spur and helical, as well as cut slots on shafts or hubs. This technology combines elements of turning and milling and ensures a very short production time. However, every year this method is increasingly improved, and in terms of its kinematics it is very complex and requires precise calculations. Determining the exact position of the tool and the workpiece at each moment of time is necessary for synchronizing movements during cutting. The principle of building an undeformed chip when cutting an internal straight-tooth crown by the Power Skiving method is shown. Section parameters for chip sections are obtained. They are the basis for modeling and calculating the values of cutting forces, friction, the necessary work that is needed to eliminate the allowance, heat flows that occur during cutting, the intensity of tool heating, temperature and wear of the tool, simulation of oscillations and dynamic processes. Complete information about the size and shape of the sheared layers, their size in different sections of the tooth at each moment of the cutting time is necessary for the description of various interrelated and interdependent deformation and contact processes. The established regularities of their continuous cyclical change during the revolution of the cutting tool are required for a comprehensive reproduction of the processes that occur during the cutting process of the toothed crown. A complex system of grapho-analytical, mathematical and computer modeling of this process has been developed for such a task. Kinematics is taken into account and the patterns of cutting-forming processes are reliably reproduced. The application of the grapho-analytical method of constructing sections for an undeformed chip is presented, which made it possible to establish its geometry and main characteristics, as well as to obtain a 3D model. Adequate models of chip formation are obtained. Quantitative estimates of parameters for slices in the process of Power Skiving are analyzed.

This paper analyzes the influence of kinetic and physical-mechanical parameters of systems on the characteristics of dynamic processes in moving one-dimensional nonlinear-elastic systems. Improved convenient calculation formulas have been derived that describe the laws of changing the amplitude-frequency characteristics of systems for both a non-resonant case and a resonant one. An important issue of studying the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear-elastic systems has not been considered in detail until now in the scientific literature. This issue relates to the vibrations of shafts in gears, pipe strings when drilling oil and gas wells, the oscillations of turbine blades and rotating turbine discs, the longitudinal vibrations of the beam as an element of structures. The main reason for this in the analytical study of dynamic processes were the shortcomings of the mathematical apparatus for solving the corresponding nonlinear differential equations that describe the laws of motion of those systems. It was found that in the case of longitudinal oscillations in the moving beam with an increase in the longitudinal speed of the medium to 10 m/s, the amplitude of the oscillation also increases by 13.5 %. However, when the longitudinal velocity of the beam is 5 m/s, the amplitude will increase by only 3 %. It is established that with the growth of the amplitude, the frequency of longitudinal oscillations decreases sharply, and if the system moves at a higher speed, for example, 20 m/s, it reduces the frequency of oscillation by about 13 %. The results reported here make it possible to assess the effect of kinetic and physical-mechanical parameters on the frequency and amplitude of oscillations. The research that involved the asymptotic method makes it possible to predict resonant phenomena and obtain engineering solutions to improve the efficiency of technological equipment.

Aim. Analyze the state of the branch of new Power skiving technology, the limits of its rational use, its advantages and disadvantages, to form the main directions of development of this method of tooth cutting and optimization of the structure and geometry of its cutting tool. Method. The research consists in the analysis of numerous works; they are devoted to a new effective method of tooth processing, systematization of scientific knowledge and practical experience, developed methods of mathematical modeling and computer simulation of the Power skiving process for its further improvement and application in the production of gear wheels. Results. The results of the analysis and systematization of data on Power skiving made it possible to identify the shortcomings of known methods and approaches to modeling and outline the main directions for their improvement. The scientific novelty and practical significance lies in the fact that, on the basis of the processed information, new approaches to the kinematical description of the process and the optimization of the geometry of cup cutters have been developed, as well as the directions for improving the Power skiving technology and the cutting tool for this method have been substantiated for the most effective use in the production of gear wheels.