Abstract This work examines the vibration instability regarding the out-of-plane bending of an annular rotor of axial-flux permanent magnet (PM) motors. An analytical model is built up in magnetic-load-synchronous frame, where the magnetic load is rotating with the rotor at the same speed, and the rotor-fixed support and rotation stiff of the annular and web are included. By using the synchronous frame, a governing equation of motion without time-variant coefficients is developed. Based on this model, the eigenvalues are formulated through conventional vibration theory. The dependence of mechanical-magnetic parameters such as the vibration wavenumber, magnet count and rotation speed on the vibration instability is examined. The stable and unstable regions are estimated by the closed-form transition curves, and further the position, shape and size of unstable regions are predicted by the transition curves expressed by mechanical-magnetic parameters. The results verify the divergent instability always exists regardless of the combinations of the wavenumber and magnet count, but the flutter instability can occur or be eliminated. The rules governing the occurrence or elimination are presented. The damping effect on vibration instability is also examined. Main results are demonstrated by numerical calculations.

中文翻译：

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轴向磁通永磁电机同步载荷作用下环形转子的机磁耦合振动失稳

摘要 这项工作研究了轴向磁通永磁 (PM) 电机环形转子平面外弯曲的振动不稳定性。在磁载荷同步坐标系中建立了磁载荷与转子同速旋转的分析模型，包括转子固定支撑和环和腹板的旋转刚度。通过使用同步坐标系，开发了一个没有时变系数的运动控制方程。基于这个模型，特征值是通过传统的振动理论来制定的。检查了机械-磁参数（例如振动波数、磁体数量和旋转速度）对振动不稳定性的依赖性。稳定和不稳定区域由封闭形式的过渡曲线估计，进一步的位置，不稳定区域的形状和大小由机械-磁参数表示的过渡曲线预测。结果证明无论波数和磁体数的组合如何，发散不稳定性始终存在，但颤振不稳定性可以发生或消除。介绍了控制发生或消除的规则。还检查了对振动不稳定性的阻尼效应。通过数值计算证明了主要结果。还检查了对振动不稳定性的阻尼效应。通过数值计算证明了主要结果。还检查了对振动不稳定性的阻尼效应。通过数值计算证明了主要结果。