Modelling of autoresonant control of ultrasonic transducer for machining applications

Abstract

A computer model of a non-linear ultrasonic vibrating system with the possibility of autoresonant control is presented in this paper. The system controlled consists of two modules, the first of which is an electromechanical model of an ultrasonic transducer comprising a piezoelectric transducer and a step concentrator. The second module simulates an influence from the machining process. Coefficients of the electromechanical model and its validity were estimated through an identification process based on the experiments with a real ultrasonic transducer. Further, a numerical model of the autoresonant control of this system has been developed. The autoresonant control maintains the resonant regime of oscillation by means of positive feedback, which provides transformation and amplification of the control signal. The model allows the use and comparison of three control strategies depending on the different electrical and mechanical feedback control signals. The results from simulation and from real machining experiments under different control strategies are compared and discussed.