Dynamics modeling for the ultrasonic machining tool using a data-driven approach and a D-RBFNN

Ultrasonic machining presents several advantages over traditional CNC machining tools, including reduced cutting force and minimized friction between the cutting tool and workpiece. However, due to its complexity, it can be challenging to model the system's behavior accurately. In particular, it is crucial to identify the nominal air cutting system dynamics and associated parameters regularly during the warm-up stage to ensure successful practical machining processes. Therefore, this paper aims to describe mathematical models of the ultrasonic machining system, which consists of a driving circuit part and mechanical part. By using the driving input voltage, circuit output and the displacement of the cutting tool, the associated transfer functions can be constructed by using the autoregressive with extra input (ARX) together with a proper system order reduction. To improve prediction accuracy, a directional radial basis function neural network (D-RBFNN) is proposed to fit the nonlinear dynamics of the cutting tool, which can capture forward/backward nonlinear behaviors of the machine tools. The proposed modeling algorithm enables monitoring of the ultrasonic machine tool's status during the warm-up stage within a short time to prevent possible anomalies during practical machining. Experiments demonstrate that the method accurately captures transient circuit dynamics and predicts good mechanical cutting tool output.