Random Vibration Analysis For Impellers Of Centrifugal Compressors

The impellers of centrifugal compressors, also known as the working wheels, are the only components that provide work on the air in the compressors. Impellers are loaded by aerodynamic force of fluctuate pressure in operations. Therefore, it is necessary to investigate strength problem for impellers in the case of pneumatic pulsate loadings. Extracting the pneumatic pressure based on its time history data from the viewpoint of time domain and carrying out transient analysis often requires solutions of differential equation, which leads to time consuming multiple load-step and unreliable numerical results. Due to the unsteady and pulsate nature of flow field, pressure on the surface of the impeller is to some extent stochastic. Hence, it is applicable to transform the original problem into a random vibration problem and solve it through the Pseudo-Excitation method. With the Pseudo-Excitation method algebraic equations can be formulated through the Fourier transformation, and highly accurate solutions can be obtained at the cost of much less computational time. Additionally, the power spectrum and the spectral moments of the response in the frequency domain can be determined, which is beneficial to the subsequent reliability analysis.The main work of this thesis can be summarized as follows:First, the basic knowledge of random vibration is provided. The eigenvalue of the random variable is reviewed in terms of probability, time domain and frequency domain focusing on the properties of normal distributed random variables. The applicability, advantages and disadvantages of the common methods for power spectrum estimation are discussed.Second, the Pseudo-Excitation method is introduced to analyze the random vibration of impellers of compressors. The Pseudo-Excitation method is efficient and accurate in random vibration analysis method, but it cannot be directly applied in the existing finite element software. In this paper, a secondary development is made by the author to combine the Pseudo-Excitation method with the module of harmonic response of finite element software Ansys through Ansys/APDL command flow. A simple model is constructed to obtain analytical solutions using the Pseudo-Excitation method compared with the numerical solutions of Ansys harmonic response for the cases of single point excitation, one dimensional multiple excitation and multi-dimensional, multiple point excitations, respectively. It is found that the relative error of the presented method is under0.01and the accuracy is acceptable, which validates the application of this method and push forward the advances of the Pseudo-Excitation method to compressor engineering. Third, a practical example is shown for random vibration analysis for a centrifugal impeller through the aforementioned method. Considering numerical accuracy and computational efficiency, harmonic response analysis is carried out on a single sector of the impeller with rotational symmetry. Load is applied on910nodes to determine the highly stressed area which is most prone to fatigue damage.Finally, the most commonly adopted method is introduced for reliability analysis in random vibration. The impeller’s reliability is solved at rated speed by a second order moment method. The impeller’s average stress increases with the rising speed, and both the index of reliability and the failure probability are increased. The computation of reliability index lays a foundation for solving the exceedance probability of stress and fatigue analysis of impellers.