This paper demonstrates a unified approach to analyze linear vibration of rotating machines with arbitrary geometry and complexity. In this formulation, the rotating machine consists of three components: a rotating part (rotor), a stationary part (stator or housing), and multiple bearings. The rotor is assumed axisymmetric and spinning at constant speed. Moreover, the rotor and the housing have arbitrary geometry and complexity. The bearings connecting the rotor and housing could be rolling-element bearings or hydrodynamic bearings. The paper consists of three major sections: mathematical modeling, integration with finite element analysis (FEA), and experimental verification. For the mathematical modeling, a stationary rotor with free boundary conditions is first discretized to obtain its normal vibration modes and modal parameters. In the meantime, the housing with its actual boundary conditions (but no bearings) is also discretized. The discretization can be achieved, for example, through FEA to accommodate arbitrary and complex geometry of the rotor and the housing. Because these vibration modes are complete, modal response of each mode can serve as a generalized coordinate to describe vibration of the actual spinning rotor and housing system. With these generalized coordinates, gyroscopic effects of the spinning rotor can be derived through material derivatives for a ground-based observer. As a result, application of Lagrange equation leads to a set of gyroscopic equations of motion with constant coefficients. These coefficients, however, contain complicated volume integrals of the mode shapes and their spatial derivatives. Therefore, algorithms are developed to calculate these coefficients explicitly from FEA. For the experimental verification, a ball-bearing spindle carrying a cylinder closed at one end is used to validate the mathematical model. Frequency response functions of the spindle/cylinder system are measured for spin speed ranging from 0 to 6000 rpm. Natural frequencies measured from the experiments agree very well with the theoretical predictions from the unified approach up to 2 kHz.
Skip Nav Destination
Article navigation
April 2005
Technical Papers
A Unified Approach to Analyze Vibration of Axisymmetric Rotating Structures with Flexible Stationary Parts
Chaw-Wu Tseng, Mechanical Engineer,,
Chaw-Wu Tseng, Mechanical Engineer,
Western Digital Corporation, San Jose, California 95138
Search for other works by this author on:
Jr-Yi Shen, Mechanical Engineer,,
Jr-Yi Shen, Mechanical Engineer,
Hitachi Global Storage Technologies, San Jose, California 95193
Search for other works by this author on:
Hyunchul Kim, Graduate Student,,
Hyunchul Kim, Graduate Student,
Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2600
Search for other works by this author on:
I. Y. Shen, Professor,
I. Y. Shen, Professor,
Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2600
Search for other works by this author on:
Chaw-Wu Tseng, Mechanical Engineer,
Western Digital Corporation, San Jose, California 95138
Jr-Yi Shen, Mechanical Engineer,
Hitachi Global Storage Technologies, San Jose, California 95193
Hyunchul Kim, Graduate Student,
Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2600
I. Y. Shen, Professor,
Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2600
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 20, 2003; final revision, April 13, 2004. Associate Editor: R. Parker.
J. Vib. Acoust. Apr 2005, 127(2): 125-138 (14 pages)
Published Online: May 3, 2005
Article history
Received:
April 20, 2003
Revised:
April 13, 2004
Online:
May 3, 2005
Citation
Tseng, C., Shen, J., Kim, H., and Shen, I. Y. (May 3, 2005). "A Unified Approach to Analyze Vibration of Axisymmetric Rotating Structures with Flexible Stationary Parts ." ASME. J. Vib. Acoust. April 2005; 127(2): 125–138. https://doi.org/10.1115/1.1857917
Download citation file:
Get Email Alerts
Cited By
Boundary-Element Analysis of the Noise Scattering for Urban Aerial Mobility Vehicles: Solver Development and Assessment
J. Vib. Acoust (October 2024)
Related Articles
A Linearized Theory on Ground-Based Vibration Response of Rotating Asymmetric Flexible Structures
J. Vib. Acoust (June,2006)
Reduction of Noise Effects for In Situ Balancing of Rotors
J. Vib. Acoust (June,2005)
Influence of Multiphysical Effects on the Dynamics of High Speed Minirotors—Part I: Theory
J. Vib. Acoust (June,2010)
Mode Evolution of Cyclic Symmetric Rotors Assembled to Flexible Bearings and Housing
J. Vib. Acoust (October,2009)
Related Proceedings Papers
Related Chapters
Unbalance
Fundamentals of Rotating Machinery Diagnostics
Research Tools
Bearing Dynamic Coefficients in Rotordynamics: Computation Methods and Practical Applications
Summary and Conclusions
Bearing Dynamic Coefficients in Rotordynamics: Computation Methods and Practical Applications