Mathematical Modeling of the Device for Radial Vibroturning

The structural and design scheme of the hydropulse device for radial vibration cutting with a built-in pulse generator (PPG) is considered. Based on the structural scheme of the device, scientifically substantiated structure of assumptions and representation of a hydraulic link (hereinafter HL) in the form of a Kelvin-Voigt body dynamic models of the hydropulse drive of the device for direct and return moves of the consolidated masses which interact with an HL through transfer numbers are constructed. Four simple dynamic models are presented, based on which D'Alembert principle is based on the mathematical model of the hydro-impulse drive of the device in the form of differential equations of motion of masses, conditions of unambiguity, which cause restrictions on the displacement of this energy carrier. By replacing the variables in the original differential equations of mass with new variables, these differential equations are reduced to the form of classical nonlinear differential equations of the second order, describing the forced oscillations of the masses under the action of variable oscillations of the amplitude of linear deformations of the HL during the operating cycle, and also the natural circular frequencies of the hydropulse drive of the device are established and analyzed.