The paper presents the results of a comprehensive study of the process of cutting helical internal grooves on the basis of computer simulation in order to establish the influence of technological parameters of cutting on the forming force. Researches of cutting of screw grooves on thinwalled steel sleeves by a cutting mandrel with various cutting speeds have been carried out. The method of processing internal screw grooves on machines with simple kinematics is presented. The dependences of the influence of cutting rates on implementation of the hidden kinematical connection are established. Graphs reflecting the dependence of the cutting rate on the angle of inclination of the cut helical groove are constructed, and a regression equation is obtained describing the dependence of the studied factors on the axial force. Ranges of cutting rates are established, allowing to provide the maximum productivity at various angles of the spiral inclination. The results of processing the experimental data of the study of the influence of tool geometrical parameters on the forming force when cutting helical grooves on the inner surface of the cylindrical shell are shown. Levels of change of factors, variance of experiment results on each of experiments are defined. The regression coefficients are calculated, the regression equation is compiled, the variance of model adequacy is estimated and adequacy of the regression equation is checked, the nature of infl uence of interaction of cutting rate parameters, front angle and the allowable allowance on the forming force is determined. Based on the results of modeling using the Maple program, a regression equation was obtained that reflects dependence of influence of factors on the axial force per tool tooth, dependence of the influence of the studied factors on the change in temperature in a cutting zone, and also constructed a temperature field reflecting the heat distribution in the processing zone on the example of one experiment. The study was performed with the financial support of the Russian Foundation for Basic Research within the research project No. 19-38-90057.

The work purpose was the investigation of dependence impact of tool geometrical parameters upon shaping effort during internal groove cutting. As a realization for the fulfillment of the helical groove processing investigation there was used a software complex based on a finite element method and a computer mathematic system. As a result of the investigations carried out there was obtained a regression equation manifesting the dependence of factors impact upon axial force falling on one tooth of the tool in the set scale of factor parameters. The scientific novelty consists in that in the paper there is considered a new method for helical groove cutting in which a shaping motion is carried out at the expense of the contact interaction of a tool and a billet performing free cutting. The investigation results obtained allowed determining the number of teeth operating simultaneously, that can be used further at cutting mode setting, and also as recommendations during designing tool design.

The existing profiles of internal screw channels are reviewed. Formulas are proposed for the static error in the channel depth due to elastic deformation of the walls of the cylindrical shell in cutting. (Shells of steel 45 and BrAZh9-4 bronze are considered.) An approach is outlined to determining the static error in machining helical channels by a mandrel with one and three cutting teeth. The error in the cutting depth is plotted as a function of the cutting speed with different wall thickness of the cylindrical shell.

The article shows the results of the solution of the direct design problem associated with the definition of the producing surface of the end mill for processing shafts with an equiaxed contour, obtained using the geometric theory of surface formation by cutting tools. The cases when the axis of the cutter and the parts intersect at a right angle and smaller angles. The results of calculation and geometric modeling of producing surfaces of such mills for the RC-profile shaft of a given size are shown. The work was carried out as part of the funding of the Grant of the President of the Russian Federation to young scientists and graduate students engaged in promising research and development in priority areas of modernization of the Russian economy, for 2018-2020 SP-591.2018.1