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

Abstract

The phasing effect of the slot/magnet combination on rigid-elastic vibration is addressed by incorporating the cyclic symmetry of permanent magnet (PM) motors. Expanding research is also carried out to achieve more general findings in rotary power-transmission systems widely available in practical engineering. To these aims, model-free analysis is used to deal with the effect via superposition treatment. The results imply that the vibration induced by temporal-spatial excitation can be classified into rotational, translational, and balanced modes, all of which have rigid and elastic vibrations having specific base and/or contaminated deflections, and the elastic vibration can be of the standing, forward traveling, and backward traveling waves. These modes can be suppressed or excited depending on whether particular algebraic relationships are satisfied by slot/magnet combination, excitation order, and base and contaminated wave numbers. Since the analysis is independent of any models, specified magnetic force, and rigid-elastic vibration, analytical results regarding the expected relationships can be naturally created due to the structural and force symmetries of the PM motors. Because of this, similar results can be found for other rotary systems basically consisting of a rotary rotor and a stationary stator both having equally-spaced features, apart from the PM motors, typically including the turbine machines having fluid field and planetary gears with a mechanical contact. As an engineering application, the proposed method can serve as a fundamental tool when predicting or even suppressing the possible excitations associated with particular vibration modes in the mechanical and electrical designs of the symmetric systems. The superposition effect and analytical predictions are verified by the finite element method and strict comparisons against those from disk-shaped structures in an existing study.

Magnetically induced rotor vibration in dual-stator permanent magnet motors

“…It needs to be noted that some of these results, especially the rigid and elastic vibration for n¼ 0 and 71, are scattered in the literature, such as a recent paper [35]. Whether they are excited or not depends on the forcing terms on the right hand side, like those in motor, gear and other cyclically symmetric power-transmission systems [11,12,14,24,27]. …”

“…Motivated by the similarities between power-transmission systems [23][24][25][26][31][32][33], authors of this work proposed superposition and modulation methods to deal with the typical rigid-elastic vibrations of conventional motors [11,12]. Also authors employed the superposition method to address the typical vibration by incorporating cyclic symmetry [27]. This method is mathematically effective, and it can find application in dual-stator motors, though it cannot quantitatively present more results.…”

Analiza drgań własnych płyt pierścieniowych z otworami mimośrodowymi

“…W publikacjach [5][6][7][8][9][10][11]13] wykorzystano właściwości cyklicznej symetrii układów (płyt kołowo-symetrycznych, kół zębatych i innych) w procesie ana-348 S. Noga lizy ich drgań poprzecznych. Z kolei w pracach [2,4,12] analizowano drgania poprzeczne płyt kołowych z różnymi przypadkami niejednorodności geometrii (otwory przelotowe, dodatkowe pierścienie, zgrubienia na obrzeżach itp.).…”

“…Podejście takie pozwoli na znaczne zmniejszenie rozmiaru modeli MES. Efektywność tego rodzaju modeli w porównaniu do pełnych modeli omówiono szerzej w pracach [5,7,[9][10][11]13]. W rozważanym przypadku do opracowania modeli z cykliczną symetrią wykorzystuje się segment (rys.…”

Driver Model Based on Mechanical Traveling Wave Principle

“…Figure 5. The contact model between the elastic layer and friction layer considering shear deformation [10][11][12][13][14][15][16] Friction layer between the elastic layer and output shaft is the key part to drive the output shaft. Considering the stiffness of elastic layer is larger than that of friction layer, it is supposed that friction layer hasdeformed while elastic layer has no deformation, and the elastic layer has the waveform shape.…”