Chatter in milling with robots with structural nonlinearity

Abstract

Stiffness and damping nonlinearities are often negligible in machine tool vibrations, but they are shown to be prominent in industrial robots that are used for milling, mainly due to the several nonlinear phenomenon that occur in the robot’s revolute joints. In this paper, a 2DOF nonlinear vibratory model is presented to study regenerative chatter in robotic milling. The presented model includes cubic stiffness and damping terms to account for the robot’s structural nonlinearities. The machining forces are represented by a combination of periodic forces and delayed vibration terms; the former is generated by the feed motion of the tool and the later by chip regeneration. Furthermore, the machining force model is non-smooth due to (a) periodic entrance and exit of the cutting edges to and from the cutting region, and (b) loss-of-contact at high-amplitude oscillations. The dynamics in the presented model is therefore described by a set of nonlinear Delay Differential Equations with periodic coefficients and non-smooth forces. Numerical continuation with smoothing techniques is used to determine the combinations of spindle speed and axial depth of cut at which the forced periodic vibrations go through secondary Hopf or period doubling bifurcations, causing chatter in the milling process. A KUKA robotic arm with milling end-effector is used as a case study. The presented analysis shows that feedrate, which has no effect on chatter in machine tools with linear dynamics, alters the stability of vibrations in milling systems with nonlinear structural dynamics. Nonlinear systems’ stiffness and damping depend on vibration amplitude. Since feedrate directly influences the amplitude of forced vibrations, the nonlinear system’s damping and stiffness and consequently its chatter stability changes by feedrate.