Simulation of Vibrations in Real Time Plane Milling with Spindle Speed Correction

Abstract

In milling the hard-to-machine materials vibrations (chatter) often arise from the high cutting forces if a technological system is insufficiently rigid. The main way to suppress these vibrations is to increase a stiffness of the mounting system of the tool and the work-piece to be machined. However, sometimes this method doesn’t lead to desirable result because of high values of intrinsic pliability of the tool and the work-piece. Currently, there are more complicated methods to ensure milling process quality. Among them there are three main groups: mathematical simulation of milling process dynamics and computation of processing parameters which provide high quality of machined surface, low level of vibrations and static deflections of a tool and a work-piece; introduction of the active vibration suppression devices into machine tool design; such devices include a vibration sensor, a feedback circuit, and an actuator which induces kinematic or force action on the oscillatory system; control of processing parameters, mainly of rotation frequency for minimizing the amplitudes of vibrations. The paper studies one of the 3 rd group methods. There is a suggestion to process a signal of vibrational accelerations in real time and detect a chatter onset. If the chatter has been detected its frequency is to be identified, and the new value of rotation speed is set: where Ω – rotation frequency, rot/s; p – the tool eigenfrequency value identified during processing, Hz; z – mill tooth number; i – positive integer number; e<1 – small positive parameter. In the current research it is assumed that e = 0,2. The formula has been chosen because at the rotation frequency axis where tooth pass frequency is slightly less than the eigenfrequency divided by the integer value there are stable zones of dynamics in the milling process. The study shows a developed model of the plane milling dynamics. It includes a dynamic model of the tool, a model of cutting forces, and geometrical models of cutting edges and work-piece surface. The model is used to study an impact of described control system on the milling process dynamics. Simulations were performed for different values of rotation frequency, and two cases were considered: without and with control. Analysis of the simulations showed that the developed control system provides considerable reduction of vibration amplitudes when milling.