Ensuring the stability of machining when using end mills

Abstract

This paper reports a new approach to ensuring the stability of the end milling process, due to vibration-free cutting modes, which are determined from the stability lobes diagram of the dynamic machining system. An application program for automatic calculation of the stability lobes diagram in the coordinates «mill spindle speed – feed» has been developed, which is a tool for the technologist-programmer when designing control program for numerically controlled machines. The mathematical model underlying the application program represents a dynamic machining system as a single-mass system with two degrees of freedom, covered by negative feedback in the direction of two coordinates. The trailing machining is represented as positive feedback loops with a delay function in each. The mathematical model is given in the form of state variables, which allows applying numerical modeling methods to determine both transient and frequency responses. The software developed includes a separate module for automatic design of the stability lobes diagram whose algorithm uses the features of the location of the Nyquist diagram on the complex plane. Since the functioning of the developed program requires a priori information about the dynamic parameters of the machining system, a procedure for their experimental identification is presented. The stiffness of the machining system in two coordinates was determined with the help of a dynamometer, and the frequency responses were determined by the impulse response function, which was obtained with an impact hammer. The research results were confirmed experimentally both by computer simulation and milling on a machine tool and could be recommended for determining the cutting mode at end milling