SIMULATION MODELING OF 2.5D MILLING DYNAMICS BY END MILLS

Abstract

A mathematical model for simulation modeling of 2.5D end milling is presented. The model takes into account the loop closed of the cutting process in the elastic machining system through the feedback in the form of elastic shifts along the coordinate axes. The dynamics of the system are represented by a single-mass model with two degrees of freedom. A block diagram of the milling process using transfer functions, which reflects the cross-links of the real machining system. It is shown that the main cause of regenerative oscillations is cutting along the trail from the previous pass. The mathematical model is compiled in state variables, which allows the use of numerical methods for simulation modeling. The linearization coefficients relate the cutting force to the feed per tooth of the mill and the cutting depth. An application program has been created that uses a time-frequency approach to modeling the 2.5D milling process. Therefore, it is possible to observe dynamic processes both in the form of transient characteristics in time and in the form of amplitude-frequency characteristics in the form of a Nyquist diagram. An application program has been created, which makes it possible to observe processes in time in an interactive mode, thanks to the built-in virtual oscilloscope. It provides the possibility of a simulation experiment to determine the influence of all the initial data of the system on the dynamics of its behavior. The results of the influence of the cutting mode for determining the boundary of stability in the coordinates of the cutting speed – feedrate are presented. It is shown that a modified stability criterion according to the parameters of the Nyquist diagram on the complex plane can be used to estimate the stability of the machining system. The created application program allows to determine the chatter-free cutting mode and in practice is an important tool for the programmer-technologist when assigning the cutting mode to the control program 2.5D milling on CNC machine.