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Research Papers

Stability Analysis of a Three-Ball Automatic Balancer

[+] Author and Article Information
Chung-Jen Lu1

Department of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Road Section 4, Taipei 10617, Taiwan, R.O.C.cjlu@ntu.edu.tw

Chia-Hsing Hung

Department of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Road Section 4, Taipei 10617, Taiwan, R.O.C.

1

Corresponding author.

J. Vib. Acoust 130(5), 051008 (Aug 14, 2008) (7 pages) doi:10.1115/1.2948415 History: Received June 04, 2007; Revised April 01, 2008; Published August 14, 2008

Ball-type automatic balancers can effectively reduce the vibrations of optical disk drives due to the inherent imbalance of the disk. Although the ball-type automatic balancer used in practice consists of several balls moving along a circular orbit, few studies have investigated the dynamic characteristics of ball-type balancers with more than two balls. The aim of this paper is to study the dynamic characteristics of a three-ball automatic balancer. Emphasis is put on the effects of the number of balls on the stability of the perfect balancing positions—the equilibrium positions where the disk is perfectly balanced. A theoretical model of an optical disk drive packed with a three-ball automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange’s equations. Closed-form formulas for the equilibrium positions are presented. The stability of the perfect balancing positions is checked with the variations for a pair of design parameters. Stable regions of the perfect balancing positions in the parameter plane of a three-ball balancer are identified and compared with those of a two-ball balancer.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the ABS-rotor system and corotating reference frame

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Figure 2

Variation of the real parts of eigenvalues with the rotational speed for a perfect balancing position of a three-ball balancer with η=0.4

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Figure 3

Variation of the equilibrium positions with the rotational speed for η=0.2

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Figure 4

Stable region of r̃11 at η=0.2 for various values of ζb

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Figure 5

Variation of the equilibrium positions with the rotational speed for η=0.4

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Figure 6

Responses starting from two different sets of initial conditions for η=0.4 and Ω=2

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Figure 7

Comparison of the stable regions of r̃=0 for the three-ball (solid) and two-ball (dashed) balancers at ηtotal=1.2

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Figure 8

Radial vibrations of the two-ball and three-ball balancers at point B in Fig. 7 for ζb=0.1

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Figure 9

Comparison of the stable regions of r̃=0 for the two-ball and three-ball balancers at ηtotal=2.4

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