Studies on Estimation Methods of Stability Criteria for Rotor Levitated by Active Magnetic Bearing Applied to Advanced Rotating Machinery

我们开发了一系列软件来分析主动磁轴承悬浮转子的稳定性和稳态强迫响应。通过数值分析，我们认识到当改变磁轴承的控制增益时，系统稳定性在一个阈值处突然变化。在软件开发的同时，我们完成了一个小型磁轴承转子测试装置。通过改变实验装置的控制参数，使转子从稳定区逐渐接近不稳定区，然后测量稳定裕度指标（灵敏度函数最大增益、灵敏度函数最大奇异值、增益裕度、相位裕度、阻尼比、稳定裕度距离），将控制系统划分为4个区；A区是系统足够稳定的区域，B区是长期连续运行的可行区域，C区是机器通常被认为不能长期连续运行的区域，D区是机器通常被认为会造成破坏的区域。此外，在实验中，当控制器增益改变时，稳定裕度变小，接近从一定增益开始迅速产生不稳定振动的发生区。将分析结果与实验结果进行比较，观察两者在稳定性极限上的差异。从分析方法和实验两方面考虑了产生差异的原因。在分析中，对其进行了修正，以便能够正确地评估控制系统稳定性的转轴内部阻尼。在实验方面，测量了4×4维的灵敏度函数矩阵，计算了灵敏度函数矩阵的最大奇异值。结果证实了灵敏度函数矩阵最大奇异值的计算过程是复杂的，并且灵敏度函数的最大增益、相位裕度和增益裕度随系统稳定性的变化而变化。因此，我们证实了可以使用灵敏度函数矩阵的最大增益、相位裕度和增益裕度等简单的估计方法来估计AMB系统的稳定性，而不是使用复杂的灵敏度函数矩阵的最大奇异值。《旋转机械设计人员磁力轴承指南（日文）》翻译成英文出版（Touka Syobou/Japan Publications Trading Co., Ltd）。此外，指南的一部分被采纳为日本提案ISO/TC108（振动与冲击）/SC2（机器振动）/WG7（磁轴承）part 4（磁轴承设计指南）。少

We have developed a series of software analyzing stability and steady forced response of a rotor levitated by active magnetic bearings. According to the numerical analysis, we recognize that the system stability changes suddenly at a threshold when changing control gains of the magnetic bearings. In parallel to the software development, we have completed a small magnetic bearing-rotor testing device. The control parameter of this experimental device is changed so that the rotor is gradually brought close to an unstable region from a stable area, and then stability margin indexes (a maximum gain of sensitivity function, a maximum singular value of sensitivity function, a gain margin, a phase margin, a damping ratio, stability margin distance ) are measured to classify the control system in 4 zones; zone A in which the system is sufficiently stable, zone B which is a long-term continuous-running feasible region, zone C in which machines normally considered unsatisfactory for long term co … More ntinuous operation, and zone D in which machines are normally considered to cause damage. Moreover, also in the experiment, when controller gain is changed, it becomes clear that a stability margin becomes small and approaches occurrence zone of unstable vibration generating rapidly from a certain gain value. When the analytical result is compared with the experimental result, the difference between two results is observed in the stability limit. The cause of the difference is considered from both sides of the analyzing method and the experiment.In the analysis, it is corrected so that internal damping of the rotating shaft which will govern system stability can be evaluated correctly. Moreover, in respect of the experiment, the sensitivity function matrix of 4×4 dimensions is measured, and the maximum singular value of the sensitivity function matrix is calculated. As a result, we confirm that calculation process of the maximum singular value of sensitivity function matrix is complicated and the maximum gain of sensitivity function maximum, the phase margin, and the gain margin change in same manner according to change of the system stability. Therefore we confirmed that the AMB system stability can be estimated by using easy estimation methods such as the maximum gain of sensitivity function matrix, the phase margin, and the gain margin instead of usage of the complicated maximum singular value of the sensitivity function matrix."The magnetic bearing guidebook for rotating machine designers (in Japanese)" was translated into English and published (Touka Syobou/Japan Publications Trading Co., Ltd.). Furthermore, a part of the guidebook were adopted as the Japanese proposal of ISO/TC108 (vibration and impact)/SC2 (vibration of a machine)/WG7(magnetic bearing) Part 4 (magnetic bearing design guideline). Less