Modelling of autoresonant control of an ultrasonic transducer for machining applications

The main purpose of this research is an investigation into the different strategies for the autoresonant control of an ultrasonic transducer. Numerical simulations were considered as the most appropriate method for analysis and a Matlab-Simulink computer model of a non-linear ultrasonic vibrating system with the possibility of autoresonant control was developed. The controlled system consists of two modules, the first of which is an electromechanical model of the ultrasonic transducer comprising a piezoelectric transducer and a step concentrator. The second module simulates influence from the machining process. The coefficients of the electromechanical model were calculated through an identification process based on the real measurement of the ultrasonic transducer's vibrations. The validity of the computer model of the ultrasonic vibrating system has been confirmed experimentally. 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 excitation, transformation and amplification of the control signal from a feedback sensor. Stability of the control is sustained by additional regulation of an amplification ratio by the use of a local negative feedback. The model allows the exercise 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 signals proportional to 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 completed investigation revealed the advantages and drawbacks of each of these control strategies. The results of the simulation are presented and discussed. To validate the results obtained through numerical simulations, a prototype of an autoresonant control system was developed and manufactured. For all the listed control strategies the machining experiments have been conducted with the control system. Experiments confirmed the results of the simulation.