Prediction of Chatter Stability in Turning

A new technology for predicting chatter in turning, based on simulation of the cutting process in time and frequency domains using the Nyquist diagram has been developed. The cutting process is presented as carried out in an elastic closed-loop technological machining system (TMS), taking into account the machining «by trace». The dynamic model is represented as two-degrees-of-freedom system in the direction of the longitudinal and transverse axes of coordinates. The mathematical model is built in accordance with the system approach, in the form of a block diagram of the connection of elements with transfer functions according to Laplace, is non-linear and has a fourth order. Therefore, the simulation is performed numerically using the fourth-order Runge-Kutta procedure. It is shown that when studying chatter, three groups of factors should be taken into account: tool geometry, dynamic parameters and cutting mode, which should be represented as an analogue of the material removal rate. The dynamic parameters of the system are obtained by processing the experimental weight characteristics obtained by striking the system with a special hammer. An application program that allows simulation of the process of regenerative oscillations occurrence in time domain and building the amplitude-phase characteristic of TMS in cutting has been created. The application program performs modeling based on the source data of the cutting conditions and dynamic characteristics of the system. Dynamic characteristics of the system are presented in the form of stiffness and frequency of the main harmonic along the corresponding coordinate axes. The simulation showed that the results completely coincide with the frequency analysis results of the profilogram of the actually machined part that allow recommending this technology for predicting and evaluating chatter and stability in turnin