• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.12
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• pp.874-880
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• 2015

This paper presents the vibration analysis of a deploying beam with spin when the beam has a time-dependent spinning speed. In the previous studies for the deploying beams with spin, the spinning speed was time-independent. However, it is more reasonable to consider the time-dependent spinning speed. The present study introduces the time-dependent spinning speed in the modeling. The Euler-Bernoulli beam theory and von Karman nonlinear strain theory are used together to derive the equations of motion. After the equations of motion are transformed into the weak forms, the weak forms are discretized. The natural frequency and dynamic response are obtained. The effect of the time-dependent spinning speed on the dynamic response is studied.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.411-428
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• 2022

This paper presents the Campbell diagram analysis of the rotordynamic system using the full order model (FOM) and the reduced order model (ROM) techniques to determine the critical speeds, identify the stability and reduce the computational time. Due to the spin-speed-dependent matrices (e.g., centrifugal stiffening matrix), several model order reduction (MOR) techniques may be considered, such as the modal superposition (MS) method and the Krylov subspace-based MOR techniques (e.g., Ritz vector (RV), quasi-static Ritz vector (QSRV), multifrequency quasi-static Ritz vector (MQSRV), multifrequency/ multi-spin-speed quasi-static Ritz vector (MMQSRV) and the combined Ritz vector & modal superposition (RV+MS) methods). The proposed MMQSRV method in this study is extended from the MQSRV method by incorporating the rotational-speed-dependent stiffness matrices into the Krylov subspace during the MOR process. Thus, the objective of this note is to respond to the question of whether to use the MS method or the Krylov subspace-based MOR technique in establishing the Campbell diagram of the shaft-disc-blade assembly systems in three-dimensional (3D) finite element analysis (FEA). The Campbell diagrams produced by the FOM and various MOR methods are presented and discussed thoroughly by computing the norm of relative errors (ER). It is found that the RV and the MS methods are dominant at low and high rotating speeds, respectively. More precisely, as the spinning velocity becomes large, the calculated ER produced by the RV method is significantly increased; in contrast, the ER produced by the MS method is smaller and more consistent. From a computational point of view, the MORs have substantially reduced the time computing considerably compared to the FOM. Additionally, the verification of the 3D FE rotordynamic model is also provided and found to be in close agreement with the existing solutions.

• Tribology and Lubricants
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• v.39 no.6
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• pp.268-272
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• 2023

This study explores the characteristics of tilting pad journal bearings used in the high-speed rotating shaft systems of centrifugal compressors. A centrifugal compressor is a high-speed rotating machine that is widely used to compress gases or vapors employed in various industrial applications. It transfers the centrifugal force of a fast-spinning impeller to the fluid and compresses it under high pressure. Many high-speed rotating shaft systems, which require high stability, use tilting pad journal bearings. The characteristics of these bearings can vary depending on several properties, and identifying the appropriate characteristics is essential to optimize the design on a case-to-case basis. In this study, the authors perform a time-dependent analysis of the properties of tilting pad journal bearings and the rotordynamics of the rotating shaft system using COMSOL Multiphysics software. Specifically, the authors analyze the characteristics of the tilting pad journal bearings by performing a parametric sweep using parameters such as pad clearance, maximum tilting angle, preload, number of pads, and pad pivot offset. The authors then use the results of the bearing-characteristics analysis to evaluate the vibration of the rotating shaft and verify its operation within a desirable range. The understanding gained from this study will allow us to determine the optimal properties of these bearings and the limiting operational speed using COMSOL Multiphysics software.