An analytical model to study the frequency response of ultrasonic welding transducers

Abstract

This paper develops an analytical 3D model of ultrasonic welding transducers. The presented model investigates the effects of the workpiece's stiffness and material properties on transducers' frequency response and mode shape. Longitudinal and lateral vibration is taken into account in the model. To analyze the forced vibration of the transducer, the effect of piezoelectric and excitation electrical fields are considered. The structural damping is considered as an imaginary Young's modulus. For validation of the model, a transducer, booster, and horn with specific dimensions and physical properties is modeled in ANSYS software. Its resonant frequency is compared with the mathematical model. Then, the system is fabricated for experimental tests. The resonant frequency in the analytical model, simulation, and experimental test is achieved, 19,208, 19,280 , and 19,203 Hz, respectively. There is a 0.02% error between the analytical model and the experimental test. The Anti-resonant frequency in the analytical model is 19265 Hz which has a 0.02% error with the experiment (19,270 Hz). The admittance at a resonant frequency in the analytical model is 0.01755 mS which has a 0.2% error with the experiment (0.0176 mS). The mechanical quality factor of the transducer and its vibration amplitude is calculated by the developed analytical model according to the mechanical properties of the components.