A matrix model of the axle vibration of a piezoelectric motor

In this work, a matrix model of the axle vibration of a piezoelectric motor is proposed. The stator of this motor is composed of a thin piezoelectric membrane and a steel axle fitted at the center of the membrane. The rotor c onsists of a cylinder-shaped permanent magnet, pressed in contact with the other end of the axle by means of the magnetic forces. A travelling wave is excited in the membrane by using four electrodes and four, properly delaye d, driving signals. The rotating flexural displacement of the membrane prod uces a wide precessional motion of the axle. In this way, a continuous slip ping takes place between the axle and the rotor, and therefore, a torque is transmitted to the rotor. In this paper, the precessional motion of the ax le is modeled as the composition of two transverse vibrations belonging to two perpendicular planes passing through the axle. The axle, vibrating in i ts transverse mode, is modeled as a two-port system: the input is the bendi ng moment supplied by the membrane, and the output is the transverse force at the terminal end of the axle. With this model, we have computed the tras mission transfer function as a function of frequency, and the transversal d isplacement along the axle at its resonance frequency. The computed results are in reasonable agreement with experimental interferometric measurements carried out on a prototype. (C) 2000 Elsevier Science B.V. All rights rese rved.