Adaptive Neural-Network-Based Active Control of Regenerative Chatter in Micromilling

Abstract

In this paper, an active control approach using two piezoelectric actuators (PZTAs) and an adaptive controller is investigated for suppressing the two-DOF regenerative chatter in micromilling. The PZTAs are utilized as active control elements to provide force compensation for chatter suppression. First, the dynamical model of micromilling process is demonstrated. Then, an adaptive controller is developed by employing neural networks to approximate the unknown dynamics of the cutting system and the unknown bounding functions related to the time-delayed tool vibrations, and applying the Lyapunov–Krasovskii functional to aid in treating the time-delayed effect of the regenerative mechanism of chatter. By employing the developed control approach, the tool vibrations in two directions vertical to each other are successfully suppressed. Finally, simulations are presented to validate the effectiveness of the developed control approach. Note to Practitioners —The work presented here was motivated by an industrial problem of micromilling. In micromilling, chatter, known as self-excited vibrations, is one of the critical issues as it gives rise to a lot of production problems, deteriorating the machined surface finish, decreasing the machining efficiency, and has an adverse effect on tool wear and tool life. There has been tremendous work done on the investigation of chatter mechanism and chatter suppression. Appropriate upfront designs of the machine tool, fixturing, spindle, choosing appropriate tool geometric angle, and spindle speed control are the means for suppressing chatter occurrence. Recently, with the advent of piezoelectric devices, more and more attention is attracted to the application of piezoelectric actuators (PZTAs) for micromilling systems. PZTAs have the prominent characteristic of fast expansions with small response time. With an electrical voltage applied, the PZTA can expand and reach its nominal displacement on the order of microseconds and a pushing or pulling force can be excited with large accelerations, so that the position of the milling tool can be maneuvered to suppress the chatter effect. In this paper, we attempt to control the unstable regenerative chatter in micromilling by employing two PZTAs as active control elements with the developed adaptive controller, where the uncertainties of the dynamics of cutting are approximated by neural networks. The time-delayed effect of chatter is addressed by the Lyapunov–Krasovskii functional. The stability proof of the closed-loop system, the convergence analysis, and the simulations indicate the developed control approach is sensible. In the future work, we shall focus on the hysteresis effect of the PZTAs and the implementation of the developed theoretical work to a practical system.