Background

Switched reluctance motor (SRM) generates considerable radial magnetic force during its running, which is much larger than the tangential magnetic force. The radial magnetic force interacts with the vibration displacement of the stator/rotor such that the coupled vibration causes a widespread concern in the industry.

Purpose

By building the stator/rotor coupled vibration model of SRM under the action of complex radial magnetic forces, the coupled vibration response of the motor could be quickly and effectively calculated. Furthermore, it has become a reality to summarize the response law of stator/rotor coupled vibration and superharmonic resonance.

Methods

An analytical model of the stator/rotor coupled vibration in a 12/8-pole SRM excited by complex radial magnetic force is built with a finite element method (FEM). Each radial magnetic force applied onto the stator teeth and the magnetic resultants of the rotor are strictly derived via intermediate variables that vary with the rotational angle. The stator/rotor vibration response at the rated speed is numerically simulated, and its main characteristics both in time and frequency domain are also discussed in detail.

Results and Conclusions

The vibration of the stator exhibits dominant square deformation due to four orthogonal teeth being excited simultaneously. The eccentric rotor causes the radial magnetic force of a single stator tooth to fluctuate so that the vibration of the stator is transferred from square deformation to the coexistence of oval and square deformation. In addition, by solving the coupled vibration at different speeds cyclically, the corresponding speed when the stator or rotor has a superharmonic resonance could be found, which is more effective than existing commercial software. Using only the basic technical parameters of SRM, this proposed analytical model can be used to quickly evaluate the radial coupled vibration of the stator/rotor. Most importantly, the model can conveniently study the effects of other operating parameters on coupled vibrations and guide the selection of appropriate parameters.

中文翻译：

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开关磁阻电机径向耦合振动与超谐共振的解析模型

背景

开关磁阻电动机（SRM）在其运行过程中会产生相当大的径向磁力，该径向磁力远大于切向磁力。径向磁力与定子/转子的振动位移相互作用，从而耦合振动引起了业界的广泛关注。

目的

通过在复杂径向磁力作用下建立SRM的定子/转子耦合振动模型，可以快速有效地计算出电动机的耦合振动响应。此外，总结定子/转子耦合振动和超谐共振的响应定律已成为现实。

方法

利用有限元方法（FEM）建立了由复杂径向磁力激发的12/8极SRM中定子/转子耦合振动的解析模型。施加到定子齿上的每个径向磁力以及转子的磁合量都是通过随旋转角度变化的中间变量严格得出的。对额定转速下的定子/转子振动响应进行了数值模拟，并详细讨论了其在时域和频域的主要特性。

结果与结论

定子的振动表现出主要的方形变形，这是因为四个正交齿同时被激励。偏心转子使单个定子齿的径向磁力发生波动，从而使定子的振动从正方形变形传递到椭圆形和正方形变形的并存状态。另外，通过周期性地解决不同速度下的耦合振动，可以找到定子或转子超谐共振时的相应速度，比现有的商用软件更有效。仅使用SRM的基本技术参数，此建议的分析模型可用于快速评估定子/转子的径向耦合振动。最重要的是，