Electro-dynamics, micro-actuation and design of arc stators in an ultrasonic curvilinear motor

Driving mechanisms basically deliver two fundamental motions, i.e., linear and curvilinear motions. A piezoelectric laminated circular arc can serve as a curvilinear arc stator to deliver curvilinear motion on a spherical surface. This study is to evaluate ultrasonic vibration characteristics and microscopic membrane/bending actuation forces of piezoelectric actuators laminated on a curvilinear circular arc. Mathematical model and governing equations of circular arcs bonded with piezoelectric actuator patches are derived, followed by analysis of actuator control forces and moments and micro-control actions in the modal domain. A study of vibration characteristics is conducted to design an optimal actuator configuration, e.g., size and location. Then, distributed control forces and micro-control actions of the curvilinear arc stator are analyzed with respect to key design parameters (i.e., arc radius, arc thickness and actuator thickness). Study of stator vibration behavior clearly suggests an optimal actuator size and location to efficiently excite the desirable ultrasonic natural mode dominated by the micro-bending control action.