多滾珠自動平衡系統之動態特性

The Dynamic Characteristics of Multi-Ball Automatic Balancers

洪嘉興(Chia-Hsing Hung)

指導教授 ： 盧中仁

國立臺灣大學/工學院/機械工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.00074

摘要

在抑制因光碟片偏心量所引起之振動上，滾珠型自動平衡裝置被廣泛地應用於光碟機系統。雖然在實際應用上，光碟機使用在軌道上自由移動的數顆滾珠，但關於滾珠型自動平衡系統動態特性之研究，尚侷限於分析雙滾珠系統。本論文的目的在於分析三滾珠系統之動態特性，針對碟片偏心量被完全抵銷情況下，討論滾珠平衡位置的穩定性。在建立三滾珠自動平衡系統的光碟機理論模型後，使用Lagrange’s equations 推導運動方程式，求出滾珠平衡位置之閉合解(closed-form formulae)，並分別利用Routh criterion, center manifold theorem及數值積分方法，來判別系統在平衡位置附近之局部穩定性。藉由比較三滾珠系統及雙滾珠之穩定區域，詳細探討滾珠數量對自動平衡效能的影響。最後將簡單說明滾珠型自動平衡系統之全域動態特性，並呈現數種週期性解的結果。

關鍵字

滾珠型自動平衡系統 ； 偏心振動 ； 三滾珠

並列摘要

Ball-type automatic balancers are widely employed in the optical disk drive industry to reduce the vibrations due to the inherent imbalance of the optical disk. Although ball-type automatic balancers currently used in practice consists of several balls moving freely along a circular orbit, no studies have investigated the dynamic characteristics of ball-type balancers with more than two balls. This paper aims at studying the dynamic characteristics of a three-ball automatic balancer. Emphasis is made on the stability of the equilibrium positions of the balls 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 formulae for the equilibrium positions are presented. Local stability of the equilibrium positions is investigated by the Routh criterion, center manifold theorem and numerical evaluation. By comparing the stability regions of a three-ball balancer to those of a two-ball balancer, the effects of the number of balls on the performance of automatic balancer are studied in details. Finally, the global dynamical characteristics of ball-type balancers are investigated, several types of periodic solutions are identified.

並列關鍵字

ABS ； ball-type automatic balancer ； imbalance vibration ； three-ball type

參考文獻

[10] 曾恩祥, 2004,“雙滾珠自動平衡機構的動態特性,”台灣大學碩士論文

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