Prediction and suppression of inconsistent natural frequency and mode coupling of a cylindrical ultrasonic stator

Abstract

Inconsistent frequency and mode coupling are primary concerns of ultrasonic motors. These modal properties are influenced by motor features, including piezoelectric ceramics, stator teeth, or other supports attached on a stator. While this influence is understood intuitively and has been studied numerically, they have not been clarified analytically. This work develops the analytical model of the example cylindrical stator and uses it to study the influence of the features on the modal properties. In this model, the stator is considered as a thin ring with equally spaced features. The analytical solution of the model is obtained by using the direct perturbation analysis, which connects the feature number and the wave number with the modal properties, and naturally provides an effective means to achieve the coincident frequency and suppress or even eliminate the predominant mode coupling only by optimizing the combination of the two numbers. Simulation results are well consistent with the analytical conclusions. The main feature of this work is that a quick and quantitative understanding of the effects of deviation from the perfect cylindrical stator is obtained. In addition, the derived analytical results contribute to the applications of common ultrasonic motor design choices. Furthermore, while the terminology of a cylindrical stator is used in this work, the analysis method applies for other stators, such as the disc-like or linear stator.

Single Source Hybrid Drive for Multi-Functional Ultrasonic Motor

“…Although the rectangular prism stator and a through-shaft mobile element provide a compact design, mode coupling as the drive method of the motor limits its use when the motor is subjected to unpredicted conditions. These unpredicted conditions affect the resonance frequency of the coupled modes [35]. Since mode coupling is obtained at a specific frequency where the resonance frequencies of two modes match, shifting resonance frequencies of the modes in different directions abolish the driving conditions.…”

Dual-mode frequency splitting elimination of ring periodic structures via feature shifting

“…37 A further search throughout the existing studies implies: (1) most researchers employed the perturbation method but the deviation from the axisymmetry can be remarkable. (2) Some examined the splitting in the context of unshifted standard structures, 5,6,9,[12][13][14][21][22][23] with the exception of Fox et al 3,10,15 and Parker et al 18,27,39 Since symmetry is normally a primary concern in practice, research on general symmetric topologies is necessary. (3) Most researchers focused on the splitting for one wavenumber only, but Fox et al 3 aimed at two at the expense of the symmetry.…”

Analytical Treatment With Rigid-Elastic Vibration of Permanent Magnet Motors With Expanding Application to Cyclically Symmetric Power-Transmission Systems

“…The frequency splitting and mode contamination are key issues discussed in the existing literature available on this subject [18][19][20][21][22][23][24][25][26]. Wickert and colleagues [18][19][20][21] studied disk-shaped periodic structures using the perturbation method, and found that if the feature number N is even, the contaminated wave orders on the n base wave number can be defined as those m satisfying the criterion jn6mj ¼ N, 2N, 3N,… for repeated modes, and m ¼ N, 2N, 3N,… for splitting modes.…”

“…Wu and Parker [22] studied ringshaped structures by using the perturbation and Galerkin analysis and obtained the corresponding splitting and contamination criteria. Using the perturbation idea [18][19][20][21], authors of this work dealt with the modal behaviors of cylindrical ultrasonic stators [25]. Kumar and Krousgrill [26] also examined these on the basis of disk-shaped ultrasonic stators.…”

“…Further, many-to-many correspondence can be formed due to the temporal harmonics in excitation and spatial ones in mode shape. Even so, one can examine the harmonic vibration to predict the overall response using such principle as well as the available criteria on frequency splitting and mode contamination [18][19][20][21][22][23][24][25][26]. Note that, since the structural periodicity should be included to identify precise predictions, the proposed method needs to be further developed to manage this change.…”