Autoresonant control strategies of loaded ultrasonic transducer for machining applications

Abstract

A computer model of a nonlinear ultrasonic vibrating system with the possibility of autoresonant control is presented. The system 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. Calculation of the coefficients of the electromechanical model was based on the parameters of a real ultrasonic transducer and the process of calculation is explained in detail in the paper. The validity of the created model of the ultrasonic vibrating system has been confirmed experimentally. Further, a 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. The first one is based on the feedback signal proportional to the displacement of the end of the concentrator (mechanical feedback). The two other types of control are based on the electrical characteristics of the piezoelectric transducer (electrical feedback). One of these strategies uses the current in the piezoceramic rings as the control signal (current feedback). The last control strategy takes into account both the current and the power of the piezoelectric transducer (power feedback). The results of the simulation are presented and discussed.