在眾多型式的自動平衡裝置中，滾珠型自動平衡裝置具有構造簡單、組裝方便而且平衡效果佳的優點，但此系統中仍有一些不確定的因子存在，這些因子即為本研究中主要探討的對象。研究過程中是以光碟機系統為載具，對於應用在光碟機上之滾珠型自動平衡裝置進行探討。首先建立整個系統的數學模型，並且推導出系統的運動方程式及滾珠本身之運動方程式。接著針對含有兩顆滾珠時的數學模式進行穩定度分析，進而依據穩定度分析以找出合適的設計參數。經由穩定度分析與實驗結果顯示，滾珠到達最佳的平衡位置才能使自動平衡裝置發揮平衡減振的效果，然後藉著穩定度分析所找出的合理參數來設計滾珠型自動平衡裝置，以改善光碟機系統因動不平衡所造成之振動。

In many kinds of the automatic balancers, the ball balancer has the advantages of simple in construction, easily to assemble and high capacity to compensate automatically for the unbalance of a rotor above the critical speed. However, experimental results show that the ball balancer applied to the optical-disk drive has the characteristic of low consistence in locating the balls at right positions. To understand the reasons for low consistence, a mathematical model is first constructed for the purpose of theoretically investigating the dynamic behaviors of the foundation and balancing balls. Therefore, the positions of the balls at steady state can be predicted. Herein, the steady state indicates that the speed of the spindle motor runs constantly and there is no relative motion between balls and the balancer. Then, the method of multiple scale is employed to analyze the stability of the balancer with two balls at steady state. Finally, an experimental setup is constructed to examine the correctness of the mathematical model and computer simulation of the steady-state solutions and their stability. Good agreement has been obtained. This research also leads to several design guidelines for the ball balancer in improving the consistence of ball positions and, therefore, reducing vibration resulting from unbalance of the rotor.

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