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Research Papers

Mode Evolution of Cyclic Symmetric Rotors Assembled to Flexible Bearings and Housing

[+] Author and Article Information
Hyunchul Kim, Nick Theodore Khalid Colonnese

Department of Mechanical Engineering, University of Washington, Box 352600 Seattle, WA 98195-2600

I. Y. Shen1

Department of Mechanical Engineering, University of Washington, Box 352600 Seattle, WA 98195-2600ishen@u.washington.edu

The z axis is assumed to be the spin axis.

1

Corresponding author.

J. Vib. Acoust 131(5), 051008 (Sep 11, 2009) (9 pages) doi:10.1115/1.3147167 History: Received January 20, 2009; Revised March 27, 2009; Published September 11, 2009

This paper is to study how the vibration modes of a cyclic symmetric rotor evolve when it is assembled to a flexible housing via multiple bearing supports. Prior to assembly, the vibration modes of the rotor are classified as “balanced modes” and “unbalanced modes.” Balanced modes are those modes whose natural frequencies and mode shapes remain unchanged after the rotor is assembled to the housing via bearings. Otherwise, the vibration modes are classified as unbalanced modes. By applying fundamental theorems of continuum mechanics, we conclude that balanced modes will present vanishing inertia forces and moments as they vibrate. Since each vibration mode of a cyclic symmetric rotor can be characterized in terms of a phase index (Chang and Wickert, “Response of Modulated Doublet Modes to Travelling Wave Excitation,” J. Sound Vib., 242, pp. 69–83; Chang and Wickert, 2002, “Measurement and Analysis of Modulated Doublet Mode Response in Mock Bladed Disks,” J. Sound Vib., 250, pp. 379–400; Kim and Shen, 2009, “Ground-Based Vibration Response of a Spinning Cyclic Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects,” ASME J. Vibr. Acoust. (in press)), the criterion of vanishing inertia forces and moments implies that the phase index by itself can uniquely determine whether or not a vibration mode is a balanced mode as follows. Let N be the order of cyclic symmetry of the rotor and n be the phase index of a vibration mode. Vanishing inertia forces and moments indicate that a vibration mode will be a balanced mode if n1,N1,N. When n=N, the vibration mode will be balanced if its leading Fourier coefficient vanishes. To validate the mathematical predictions, modal testing was conducted on a disk with four pairs of brackets mounted on an air-bearing spindle and a fluid-dynamic bearing spindle at various spin speeds. Measured Campbell diagrams agree well with the theoretical predictions.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

An asymmetric rotor supported by a stationary housing via bearings

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Figure 2

Free-body diagram of the rotor after it is assembled to a housing via bearings

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Figure 3

Mode shapes of a circular disk with four pairs of brackets; low-frequency range

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Figure 4

Mode shapes of a circular disk with four pairs of brackets; high-frequency range

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Figure 5

Schematic of the experimental setup

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Figure 6

Cross sections of rigid hub, ball-bearing motor, and fluid-dynamic bearing motor

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Figure 7

Campbell diagram of the disk-bracket rotor on the air-bearing spindle

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Figure 8

Campbell diagram of the disk-bracket rotor on the fluid-dynamic bearing spindle

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