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

开发了电磁轴承悬浮转子稳定性分析和稳态受迫响应分析软件。根据数值分析，我们认识到，系统的稳定性突然改变的阈值时，改变控制增益的磁轴承。在软件开发的同时，我们还完成了一台小型磁轴承转子测试装置。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，（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）被测量以将控制系统分类为4个区域;区域A是系统足够稳定的区域，区域B是长期连续运行的可行区域，区域C是机器通常被认为不符合长期连续运行的要求的区域。 ...更多信息 连续操作和D区，机器通常被认为会造成损坏。此外，在实验中，当改变控制器增益时，清楚的是稳定裕度变小并且接近从某一增益值快速产生的不稳定振动的发生区域。当分析结果与实验结果进行比较时，在稳定性极限方面观察到两个结果之间的差异。从分析方法和实验两方面考虑了产生这种差异的原因，并在分析中进行了修正，使决定系统稳定性的转轴内阻尼得到了正确的评价。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复杂，灵敏度函数的最大增益、相位裕度和增益裕度随着系统稳定性的变化而变化。因此，我们证实，电磁轴承系统的稳定性可以估计使用简单的方法，如最大增益的灵敏度函数矩阵，相位裕度，增益裕度，而不是使用复杂的最大奇异值的灵敏度函数矩阵。“旋转机械设计者的磁轴承指南（日文）”被翻译成英文并出版（Touka Syobou/Japan Publications Trading Co.，Ltd.）。此外，该指南的一部分被采纳为ISO/TC 108（振动和冲击）/SC2（机器振动）/WG 7（磁轴承）第4部分（磁轴承设计指南）的日本提案。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