Stability Analysis of a Single-Ball Automatic Balancer

[+] Author and Article Information
Chung-Jen Lu

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

J. Vib. Acoust 128(1), 122-125 (Sep 07, 2005) (4 pages) doi:10.1115/1.2149398 History: Received August 05, 2004; Revised September 07, 2005

Under proper working conditions, a ball-type automatic balancer can effectively reduce the imbalance vibrations of an optical disk drive. The proper working conditions can be determined by a stability analysis of the equilibrium states of the nonlinear system formed by the rotating disk, balancer, and suspension system. Several attempts have been made to study the stability of the equilibrium states numerically in some finite regions of the relevant parameter space. This paper in contrast analytically investigates the stability characteristics of the equilibrium states. A theoretical model of an optical disk drive packed with an automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange’s equations and closed-form formulas for the equilibrium positions are presented. Finally, general guidelines on the stability of the equilibrium states are proposed.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Schematic diagram of the ball-type automatic balancer, rotating disk and equivalent suspension system

Grahic Jump Location
Figure 2

Rotating coordinates system



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