Control of Regenerative Self-Excited Vibrations in the Milling Process

Abstract

The problem of the occurrence and rapid suppression of vibrations arising in the process of milling using robot arm is considered. It is assumed that the tool (cutter) is connected with the robot by an elastic suspension, which is used for the force sensation of the robot. Based on the mathematical model of regenerative self-excited vibrations (chattering), the simulation of the system "robot-tool-work surface" was carried out. The tool moves evenly along the work surface with a given pressure on it. The cutter is pressed using the position-force control algorithm based on two PID-controllers with coordinate and force feedbacks. It provides the necessary axial depth of cut. Uniform movement along the work surface is carried out using the velocity control algorithm based on PID-controller with velocity feedback. It provides the required tool feed. Several authors have experimentally and analytically shown that in the process of milling "on the track" unstable regenerative self-oscillations can occur. Track remains on the machined surface during the previous cutter tooth pass. Chattering is a deterrent to increase productivity which mainly depends on rotation speed of cutter and the axial depth of cut. In this paper we consider the possibility of promptly detecting the onset of unstable auto-oscillations from the amplitude spectrum of the sensor readings of the horizontal forces of interaction between the instrument and the work surface. The amplitude spectrum is obtained using the fast Fourier transform, which allows to promptly determine the beginning of unstable processes in system. The subsequent decrease of the axial depth of cut (within one to two percent) almost completely stabilizes the cutting process. This paper proposes a variant of adaptation contour for the robot vertical movement control system based on the allowable change of the axial depth of cut.