Since heavier gases exert larger effects on rotordynamic stability, stability evaluation is important in developing or designing high-pressure compressors. To evaluate the rotor stability during operation, an excitation test using a magnetic bearing is the most practical method. In stability analysis, labyrinth seals can produce significant cross-coupling forces, which particularly reduce the damping ratio of the first forward mode. Therefore, forward modes should be distinguished from backward modes in the excitation test. One method that excites only the forward modes, not the backward modes (and vice versa), is the use of a rotating excitation. In this method, the force is simultaneously applied to two axes to excite the rotor in circular orbits. Two trigonometric functions, i.e., cosine and sine functions, are used to generate this rotation force. Another method is the use of a unidirectional excitation and a mathematical operation to distinguish the forward whirl from the backward whirl. In this method, a directional frequency response function that separates the two modes in the frequency domain is obtained from four frequency response functions by using a complex number expression for the rotor motion. In this study, the latter method was employed to evaluate the rotor stability of a high-pressure compressor. To obtain the frequencies and damping ratios of the eigenvalues, the curve fitting based on system identification methods, such as the prediction error method, was introduced for the derived frequency response functions. Firstly, these methods were applied to a base evaluation under a low-pressure gas operation, in which the stability mainly depends on the bearing property. Using the obtained results, the bearing coefficients were estimated. Next, the same methods were applied to stability evaluations under high-pressure gas operations. The destabilizing forces were also estimated from the test results and compared with the calculation results.

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Characteristics of natural frequencies of an impeller and an equivalent disc were investigated in high-density gas to develop a method for predicting natural frequencies of centrifugal compressor impellers for high-density gas applications. The equivalent disc had outer and inner diameters equal to those of the impeller. We expected that natural frequencies would decrease with increasing the gas density because of the added-mass effect. However, we found experimentally that some natural frequencies of the impeller and the disc in high-density gas decreased but others increased. Moreover, we observed, under high-density condition, some resonance frequencies that we did not observe under low-density condition. These experimental results cannot be explained by only the added-mass effect. For simplicity, we focused on the disc to understand the mechanism of the behavior of natural frequencies. We developed a theoretical analysis of fluid-structure interaction considering not only the mass but also stiffness of gas. The analysis gave a qualitative explanation of the experimental results. In addition, we carried out a fluid-structure interaction analysis using the finite element method. The behavior of natural frequencies of the disc in high-density gas was predicted with errors less than 6%.

Active magnetic bearing (AMB) systems are intrinsically unstable but stabilized by feedback control. In order to evaluate objectively the stability, a standard criterion is necessary. One of the indices for stability evaluation is a maximum gain of sensitivity functions. Radial positions of the rotor are regulated by four-axis control, that is, a radial system needs to be treated as a multi-input multi-output (MIMO) system. One of general criteria for evaluating the stability of a MIMO system is a maximum singular value of a sensitivity function matrix, which needs 16 matrix elements for calculation. It is, however, easier to regard each control axis as an independent single-input single-output (SISO) system and it can be evaluated by just four sensitivity functions. ISO/DIS 14839-3 will employ this concept. This paper discusses the stability evaluation as a SISO system with parallel/conical mode separation or side-by-side treatment, and a MIMO system using maximum singular value, also these differences. In addition to this, a conversion from the usual x,y-axis form to forward/backward form is proposed and the stability is evaluated for the system in the converted form. For experimental evaluation, a test rig diverted from a high-speed turbo compressor rated at 180kW was used. The transfer functions were measured by exciting the system with swept signals at rotor standstill and at 30,000r/min rotational speed. For stability limit evaluation, the control loop gain was increased or a phase lag was inserted in the control loop to lead the system to be nearby unstable intentionally. Using these test results, the differences among the evaluation manners are discussed.

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