Inherent mechanism of frequency drift affected by constraint conditions for rotary piezoelectric motors

The optimum drive frequency of rotary piezoelectric motors is in the vicinity of the resonance frequency of piezoelectric vibrators. Previous studies reveal that the resonance frequency is inconstant and is drifting with the variation of constraint conditions, of which the solutions generally focused on optimizing the drive circuits and control algorithms, while the working principle and equivalent modeling about frequency drift are still indistinct. By introducing the unknown parameters including stiffness coefficients and loss factors, the equivalent physical models and mathematical derivation are investigated. Based on the measured values of the impedance characteristics, the relationship between the piezoelectric parameters and the varying constrained boundaries is discussed. Then, the introduced parameters are identified and utilized as the input parameters for modifying the traditional finite element method. The numerical results agree well with the measured values and are compared with the traditional calculation, which reveals that the identified parameters and physical models are effective for illustrating the inherent mechanism of frequency drift. In addition, the mathematical equations and numerical simulation are both analyzed for the undamped and damped vibrating system, which demonstrates that the piezoelectric motor is a small damping vibration system and the effect of the loss factor on frequency calculation can be omitted.