Prediction method for the fundamental radial mode of multi-mode motors

Ultrasonic motors often use a combination of vibration modes to create the elliptical vibration field desired for motion. The efficiency of multi-mode motors is maximised when the various modes are complementary to each other. However, design optimisation is not straightforward, as multiple mode coupling can lead to catastrophic failure of the intended mechanism. The paper presents a method for the theoretical optimisation of ultrasonic motors that employ a radial mode and a bending mode. The method is based on a finite element approach to estimate the radial mode frequency that is best matched to a bending mode frequency derived from an analytical formula. The proposed method overcomes the dimensional limitations of formulae currently available for the calculation of radial frequencies of piezoceramic rings. This approach has been applied to motor designs of different materials and dimensions, and has been shown to provide a useful tool for decreasing the amount of speculation and maximising the efficiency of multi-mode motor designs.