Combined finite element-normal mode expansion methods for ultrasonic motor modeling

Ultrasonic motors (USM) have been widely studied in the past decade. To promote industrial applications, systematic approaches for their development and scaling laws are necessary. The proposed numerical modeling technique combines the finite element method (FEM) and the normal mode expansion method. To use these methods, three different steps have to be considered: (i) construction of a finite element mesh of the USM taking into account the 3D piezoelectric effect, (ii) derivation of the electromechanical circuit representation and computation of the transient process with stick-slip effects between the stator and the rotor, (iii) analysis of the motor behavior using finite element post-processors. Essential results such as electrical admittance and force factor for the USM as well as load characteristics have been obtained. This approach has been applied to two different motors: a traveling wave and a mode conversion USM. Experimental results are compared to numerical results and prove the method's versatility