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.

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%.

In designing an impeller for centrifugal compressors, it is important to predict the natural frequencies accurately in order to avoid resonance caused by pressure fluctuations due to rotor-stator interaction. However, the natural frequencies of an impeller change under high-density fluid conditions. The natural frequencies of pump impellers are lower in water than in air because of the added mass effect of water, and in high-pressure compressors the mass density of the discharge gas can be about one-third that of water. So to predict the natural frequencies of centrifugal compressor impellers, the influence of the gas must be considered. We previously found in the nonrotating case that some natural frequencies of an impeller decreased under high-density gas conditions but others increased and that the increase of natural frequencies is caused by fluid-structure interaction, not only the added mass effect but also effect of the stiffness of the gas. In order to develop a method for predicting natural frequencies of centrifugal compressor impellers for high-density gas applications, this paper presents experimental results obtained using a variable-speed centrifugal compressor with vaned diffusers. The maximum mass density of its discharge gas is approximately 300 kg/m3. The vibration stress on an impeller when the compressor was speeding up or slowing down was measured by strain gauges, and the natural frequencies were determined by resonance frequencies. The results indicate that for high-density centrifugal compressors, some natural frequencies of an impeller increased in high-density gas. To predict this behavior, we developed a calculation method based on the theoretical analysis of a rotating disk. Its predictions are in good agreement with experimental results.

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.

In designing an impeller for centrifugal compressors, it is important to predict the natural frequencies accurately in order to avoid resonance caused by pressure fluctuations due to rotorstator interaction. However, the natural frequencies of an impeller change under high-density fluid conditions. The natural frequencies of pump impellers are lower in water than in air because of the added mass effect of water, and in high-pressure compressors the mass density of the discharge gas can be about one-third that of water. So to predict the natural frequencies of centrifugal compressor impellers, the influence of the gas must be considered. We previously found in the non-rotating case that some natural frequencies of an impeller decreased under high-density gas conditions but others increased and that the increase of natural frequencies is caused by fluid-structure interaction, not only the added mass effect but also effect of the stiffness of the gas. In order to develop a method for predicting natural frequencies of centrifugal compressor impellers for high-density gas applications, this paper presents experimental results obtained using a variable-speed centrifugal compressor with vaned diffusers. The maximum mass density of its discharge gas is approximately 300 kg/m3. The vibration stress on an impeller when the compressor was speeding up or slowing down was measured by strain gages, and the natural frequencies were determined by resonance frequencies. The results indicate that for high-density centrifugal compressors, some natural frequencies of an impeller increased in high-density gas. To predict this behavior, we developed a calculation method based on the theoretical analysis of a rotating disc. Its predictions are in good agreement with experimental results.