Engineering resonance frequency charts of PZT rings of different sizes and at different clamping conditions

For developing ring type ultrasonic motors and piezoelectric transformers, the method by V. Stephenson for the computation of resonance frequency of piezoceramic rings was extended. Engineering charts of the resonance frequencies of PZT rings with different sizes and at different clamping conditions were constructed. The resonance frequencies obtained from the charts were in good agreement with the experiments. Some interesting features of the resonance frequency with respect to the ring dimensions (the outside and inside diameters, OD and ID) were found. The resonance frequency for rings with the same outside diameter decreased with decreasing OD/ID ratio. Clamping of the outer circumference of the ring reduced the resonance frequency. There was a minimum in the curve of the resonance frequency versus OD/ID, when the inside of the ring was clamped. These features provided methods to reduce the resonance frequency so as to miniaturize ultrasonic motors and other piezoelectric devices using PZT rings.