Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives

[+] Author and Article Information
Paul C.-P. Chao1

Department of Mechanical Engineering,  Chung-Yuan Christian University, Chung-Li, Taiwan 320pchao@cycu.edu.tw

Cheng-Kuo Sung, Hui-Chung Leu

Department of Power Mechanical Engineering,  National Tsing-Hua University, Hsinchu, Taiwan 300


Corresponding author.

J. Tribol 127(4), 845-856 (May 26, 2005) (12 pages) doi:10.1115/1.2032992 History: Received October 18, 2004; Revised May 26, 2005

This study is devoted to evaluating the performance of an automatic ball-type balance system (ABB) installed in optical disk drives (ODDs) with consideration of the rolling friction between the balancing balls and the ball-containing race of the ABB. Research has been conducted to study the performance of the ABB by investigating the nonlinear dynamics of the system; however, the model adopted to describe the rolling friction between the balancing balls and their race was a simple stick-slip type, which does not reflect the realistic contact dynamics, leading to an inaccuracy in predicting ABB performance. In this study, a complete dynamic model of the ABB including a detailed rolling friction model for the balls based on Hertzian contact mechanics and hysteresis loss is established. The method of multiple scales is then applied to formulate a scaled model to find all possible steady-state ball positions and analyze stabilities. It is found that possible steady-state residing positions of the ball inside the race are multiple and form continuous ranges. Numerical simulations and experiments are conducted to verify the theoretical findings, especially for the rolling friction model. The obtained results are used to predict the level of residual vibration, with which the guidelines on dimension design and material choices of the ABB are distilled to achieve desired performance.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Mathematical model of the rotor-stator-ABB system

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Figure 2

(a) Ball contact with race flange; (b) applied pressure of ball contact area along the X-axis; (c) applied pressure of ball contact area along the Y-axis

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Figure 3

Hysteresis loop for elastic material subjected to reversing stresses on ball and race

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Figure 4

Actions of forces and accelerations on the balancing balls: (a) free body diagram; (b) accelerations

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Figure 5

Illustration for four types of steady-state positions for a pair of balancing balls

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Figure 6

Stability diagram of mass ratio (mM) versus operation speed ratio (ωωn) for type I solution (a) assuming rolling friction moment Mf=1.225×10−11(Nm), (b) assuming rolling friction moment Mf=0.245×10−11(Nm)

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Figure 7

(a) Responses of the pair of balls converged to type I solution; (b) residual vibration in the radial direction

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Figure 8

Ball-residing ranges of type I solutions with respect to race material factor at (a) p=2; (b) p=5

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Figure 9

Photo of experiment components for identifying rolling friction

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Figure 10

Schematics for rolling friction identification: (a) three-dimensional view; (b) side view; (c) preliminary setup

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Figure 11

(a) Free body diagram of the moving plate; (b) free body diagram of the ball between the moving and base plates

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Figure 12

(a) Photo of experiment setup for investigating ball responses; (b) aluminum, copper, and steel circular races; (c) the parallel-beam structure supporting the rotor-disk-ABB system

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Figure 13

(a) Measured and theoretical ball-residing positions in steel race; (b) the corresponding photo; (c) measured residual vibration level

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Figure 14

(a) Measured and theoretical ball-residing positions with copper race; (b) the corresponding photo; (c) measured residual vibration level

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Figure 15

(a) Measured and theoretical ball-residing positions with aluminum race; (b) the corresponding photo; (c) measured residual vibration level




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