Modeling and predictive control of chatter instabilities in single point turning.

Abstract

Based on the concept of long range prediction in the context of self-tuning control theory, a generalized predictive kinetic energy controller (GPKEC) suitable for applications to high speed machining processes is developed. A three dimensional lumped mass model capable of representing both tool and workpiece dynamics in a single point turning operation on a lathe machine is first developed to accurately reflect their interactions in a machining process. Based on the linearized uncoupled one dimensional model for the machining dynamics and noting that feed can effectively be used to control the unstable machine-tool dynamics, a single-input single-output (SISO) discrete time predictive control law (GPKEC) is derived by minimizing the predicted incremental kinetic energy of the cutting process. The instantaneous feed is used as the control variable of this controller which is calculated using the feedback of instantaneous displacement of the tool tip in the feed direction. It is observed from the simulation results that the proposed GPKEC controller is capable of suppressing the unstable and marginally stable system dynamics in their incipient stages, even in the presence of uncertain disturbances. The GPKEC strategy is also found to be robust against modeling or estimation errors. In order to verify the simulation results, a number of experimental runs are carried out. An estimate of acceleration signal, instead of displacement, in the feed direction is used as feedback signal due to practical reasons. A servomotor, which is connected to the main feed drive shaft through a high performance timing (HPT) belt, has been used to control the instantaneous feed of a cutting process. It is observed that there has been a good agreement between the experimental and simulation results. The experimental results show that the GPKEC strategy can effectively suppress the chatter vibration in a machining process. It is also observed from experimental results that the proposed controller is robust against overparametrization, estimation errors, uncertain inputs, system noise, and even against changes in the system dynamics.