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Research Papers

Vibration Analysis of a Self-Excited Vibration in a Rotor System Caused by a Ball Balancer

[+] Author and Article Information
Tsuyoshi Inoue

 Department of Mechanical Science and Engineering, School of Engineering, Nagoya University, Nagoya, 464-8603, Japaninoue@nuem.nagoya-u.ac.jp AISIN SEIKI CO., LTD., 2-1, Asahi-machi, Kariya, Aichi, 448-8650, Japaninoue@nuem.nagoya-u.ac.jp

Yukiko Ishida, Hideaki Niimi

 Department of Mechanical Science and Engineering, School of Engineering, Nagoya University, Nagoya, 464-8603, Japan AISIN SEIKI CO., LTD., 2-1, Asahi-machi, Kariya, Aichi, 448-8650, Japan

J. Vib. Acoust 134(2), 021006 (Jan 18, 2012) (11 pages) doi:10.1115/1.4005141 History: Received September 30, 2010; Revised July 17, 2011; Published January 18, 2012; Online January 18, 2012

The ball balancer has been used as a vibration suppression device in rotor systems. It has a superior characteristic that the vibration amplitude is reduced to zero theoretically at a rotational speed range higher than the critical speed. However, the ball balancer causes a self-excited vibration near the critical speed when the balls rotate in the balancer. This self-excited vibration may occur in the wide rotational speed range with a large amplitude vibration, and in such a case, escaping from it becomes difficult. In this paper, the occurrence region and the vibration characteristics of the self-excited vibration caused by the ball balancer are investigated. The nonlinear theoretical analysis is performed and a set of the fundamental equations governing the self-excited vibration is obtained. The influences of the parameters of the ball balancer, such as, the damping of the ball’s motion, the ball’s mass, and radius of the balls’ path, are explained and they are also validated experimentally.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Theoretical model

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Figure 2

Natural frequency diagram

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Figure 3

Resonance curve in the case with unbalance (e > 0): the steady state oscillation when the balls remain statically in the disk (amplitude •) and the self-excited vibration when the balls rotate in the disk (maximum value Δ and minimum value ∇ of the amplitude)

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Figure 6

Resonance curve of the ω component, Pω, in the self-excited vibration in the case with unbalance (e > 0)

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Figure 7

Vibration characteristic of the self-excited vibration in the case with unbalance (e > 0): (a) Resonance curve, (b) Angular velocity ωb

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Figure 4

Time history of the displacement x, y, and r and its spectrum diagram of the self-excited vibration at ω=1.1 in Fig. 3 (e > 0)

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Figure 5

Time history of the ball’s motion in the self-excited vibration: (a) ball angular position θb1,θb2, (b) ball angular velocity θ·b1,θ·b2

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Figure 8

Vibration characteristic of the self-excited vibration in the case with no unbalance e (e=0): (a) Resonance curve, (b) Angular velocity ωb

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Figure 9

Influence of the damping of ball’s motion cb to theself-excited vibration: (a) Resonance curve, (b) Angular velocity ωb

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Figure 10

Influence of the ball mass mb to the self-excited vibration: (a) Resonance curve, (b) Angular velocity ωb

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Figure 11

Influence of the radius of ball orbit a to the self-excited vibration: (a) Resonance curve, (b) Angular velocity ωb

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Figure 12

Influence of the gyro-effect represented by ip to the self-excited vibration: (a) Resonance curve, (b) Angular velocity ωb

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Figure 13

Experimental system: (a) Experimental setup (b) Shape of the ball’s path

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Figure 14

Time history of the displacement x, y, and r and its spectrum diagram of the self-excited vibration (data observed at ω = 801 rpm for the case without cover shown in Fig. 1)

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Figure 15

Influence of the damping of ball’s motion (a) Resonance curve of maximum amplitude (b) Resonance curve of the self-excited vibration component (c) Angular velocity of ball rotation: □, ◯ and Δ denote the self-excited vibration when the balls rotated in the disk and • denotes the steady state vibration when the balls remained statically in the disk

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Figure 16

Influence of the ball mass of ball balancer (middle radius) (a) Resonance curve of maximum amplitude (b) Resonance curve of the self-excited vibration component (c) Angular velocity of ball rotation: □, ◯ and Δ denote the self-excited vibration when the balls rotated in the disk and • denotes the steady state vibration when the balls remained statically in the disk

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Figure 17

Influence of the radius of ball’s path (a) Resonance curve of maximum amplitude (b) Resonance curve of the self-excited vibration component (c) Angular velocity of ball rotation: □, ◯ and Δ denote the self-excited vibration when the balls rotated in the disk and • denotes the steady state vibration when the balls remained statically in the disk

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