Parametric instability induced by traveling magnetic load within permanent magnet motors

Zhao, Zongci; Wang, Shiyu; Yang, Jianming; Chen, Wei

doi:10.1007/s11071-015-1909-4

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…In fact, the distortion is addressed via an axisymmetric ring stator. However, the stator is essentially a rotationally periodic structure subjected to traveling load, just like those in Ouyang (2011), Zhao and Wang (2015) and Xie et al. (2015), which can experience natural frequency splitting and mode distortion (Wang et al., 2010).…”

Section: Resultsmentioning

confidence: 99%

“…For simplicity, this work assumes that the stator has a smooth ring shape instead of a straight line. Since ring models are widely used in the existing literature (Duan et al., 2009; Wang and Sinha, 2013; Huang and Soedel, 1987; Zhao and Wang, 2015; Xie et al., 2015), this section only briefly presents the main derivation. Given the complexities of the electromechanical coupling and geometric topology, the scope is limited to the in-plane deflection under bending moment from the piezoelectric patch on a smooth thin-cylindrical stator.…”

Section: Problem Formulationmentioning

confidence: 99%

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Excitation and distortion of elastic vibration of cylindrical ultrasonic stator

Wang

Xiu

2016

Journal of Vibration and Control

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This work examines the elastic vibration of the ultrasonic stator subjected to piezoelectric bending excitation by focusing on two fundamental issues: general driving rule and vibration distortion. An elastic model of a cylindrical ultrasonic stator is developed by using Hamilton’s principle and solved by analytical approach. The results imply that a desired vibration can be aroused provided that an algebraic relation is satisfied by a suitable parameter combination. Traveling/standing wave is excited by conventional time-spatial voltage ones or even other ones. The relationships between the duty ratio of input voltage and wave distortion are identified as closed-form expression of basic parameters. The excitation’s average creates a stationary deflection but it can be neglected thanks to the sufficiently small amplitude it causes relative to that at the resonance frequency. The rotation reversion is realized by changing the duty ratio or excitation frequency but remarkable distortion and amplitude decrease occur, leading to the asymmetry between the forward and inversion. Main results are validated by the superposition approach and comparisons against the existing ones. Discussions on phasing effect and vibration distortion relative to other symmetric systems are also made. Main contributions are the general driving rule with non-π/2 time-spatial phases and explanations on vibration distortion. These are achieved via the general time-spatial phasing in cyclically symmetric power-transmission systems.

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Section: Resultsmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Excitation and distortion of elastic vibration of cylindrical ultrasonic stator

Wang

Xiu

2016

Journal of Vibration and Control

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“…For the electric stiffness, Ye et al 20,21 examined the parametric vibration aroused by the traveling bias voltages of a micro-ring. For the magnetic stiffness, Zhao and Wang 22 investigated the parametric instability induced by the magnetic load in the permanent magnet motors, and then handled the instability of a dual-ring structure. 23,24 The above studies usually employ the multiscale and Floque´t methods, and they concluded that the parametric excitations exist only for integer 2 n/N.…”

Section: Introductionmentioning

confidence: 99%

Natural frequency splitting and principal instability of rotating cyclic ring structures

Sun

Wang

Xia

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work develops an analytical method to estimate the natural frequency splitting and principal instability of the rotating cyclic ring structures. An elastic model is built up under the ring-fixed frame by using the energy method. The modeling leads to a partial differential equation with time-variant coefficient. The eigenvalue is formulated to estimate the natural frequency splitting, principal instability and their relationships. The dependence of the basic parameters on the natural frequency splitting and principal instability is demonstrated. The principal instability can occur at the splitting natural frequencies but cannot at the repeating ones. A classical problem regarding the parametric instability of the rotating ring with stationary supports and the inverse problem are examined. The results verify that the natural frequency splitting does not mean unstable for the former problem, but for the latter the splitting implies unstable. Besides, the model is transformed into the support-fixed frame and thus an equivalent time-invariant model is obtained, which is solved by using the general vibration theory. The analytical method is validated through the comparisons with the results in the open literature and especially the comparisons between the results from the two types of frames.

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