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

开发了一套分析主动磁轴承悬浮转子的稳定性和稳态强迫响应的软件。根据数值分析，我们认识到当改变磁悬浮轴承的控制增益时，系统的稳定性在某一阈值处突然发生变化。在软件开发的同时，完成了小型磁悬浮轴承-转子检测装置的研制。通过改变实验装置的控制参数，使转子从稳定区域逐渐接近不稳定区域，然后测量稳定裕度指标(灵敏度函数的最大增益、灵敏度函数的最大奇异值、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，系统足够稳定；B区，长期连续运行可行区域；C区，机器通常被认为长期不满意的co…更连续的操作，以及D区，在D区，机器通常被认为会造成损坏。此外，在实验中，当控制器增益改变时，稳定裕度变得很小，并且接近从某一增益值快速产生不稳定振动的发生区域。将分析结果与实验结果进行比较，发现两者在稳定极限方面存在差异。分析中从分析方法和实验两方面考虑了产生差异的原因，并在分析中进行了修正，使控制系统稳定性的转轴的内耗能得到正确的估计。在实验方面，测量了4×4维的灵敏度函数矩阵，并计算了灵敏度函数矩阵的最大奇异值。结果表明，灵敏度函数矩阵的最大奇异值的计算过程比较复杂，灵敏度函数的最大增益、相位裕度和增益裕度都随着系统稳定性的变化而变化。因此，我们证实了可以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磁悬浮轴承系统的稳定性，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轴承指南(日文)》被翻译成英文并出版(Touka Syobou/Japan Publications Trading Co.)。此外，指南的一部分被采纳为ISO/TC108(振动和冲击)/SC2(机器的振动)/WG7(磁力轴承)第4部分(磁力轴承设计指南)的日本建议。较少

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