Numerical modeling and vibration control of transducer in ultrasonically assisted machining

Ultrasonic assisted machining has been applied in machining brittle and hard material. The critical problem of ultrasonic assisted machining is to get a proper adaptive controller of the ultrasonic vibration. In this paper, a numerical vibration model is established by a mass-damper-elastic component. The loading effect on dynamics of ultrasonic transducer is investigated. The transfer function of transducer is obtained and simulation calculation model is carried out in Matlab. The effects of different damper and elastic component on frequency characteristic of ultrasonic transducer are found. The PID algorithm and the H® algorithm for vibration control are established and simulated in the Matlab Simulink, and proves both PID algorithm and Hoo algorithm can achieve the accurate and fast controlling results. Finally, some experiments are carried out to verify the simulation calculation.