Modelling of Autoresonant Control of Ultrasonic Transducer for Machining Applications
Modelling of autoresonant control of a loaded ultrasonic transducer is presented. Investigation of different control strategies is discussed. 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 system controlled 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. Coefficients of the electromechanical model were calculated through an identification process based on the real measurement of the ultrasonic transducer’s vibration. 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 model allows exercise and comparison of different control strategies based on the feedback signal proportional to the displacement of the end of the concentrator (mechanical feedback) or on the signals proportional to the electrical characteristics of the piezoelectric transducer (electrical feedback). 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 control strategies being modelled the machining experiments have been conducted with the control system. The results of simulation correlate well with experiments.