單滾珠自動平衡裝置之碰撞特性分析

Abstract

自動平衡裝置具有在高於系統自然頻率的大範圍轉速下平衡偏心振動的能力，因此在變動負荷的旋轉機械中具有廣泛的應用，然而系統性能表現的不一致是其主要的缺點。本研究主要探討單滾珠自動平衡裝置的暫態碰撞行為，以Lagrange方程式推導系統的暫態運動方程式，並結合Hertz接觸理論與有限元素分析模型建立滾珠與軌道壁之碰撞模型。其後再針對不同的系統參數進行敏感度分析。由分析結果可知主軸最高加速度及等效定子質量對系統的收斂時間有較大的影響；系統等效阻尼係數與等效定子質量對最大振幅的影響較大；而滾珠與承載盤軌道之間的碰撞現象，則主要受軌道黏滯液阻尼係數的影響。此外，也藉由統計的方式分析收斂時間與最大振幅對不同滾珠初始角度位置之分佈情形，期望據此可以作為設計與改良系統不一致性時的參考。

Automatic ball balancers have been widely used in rotating machinery with different imbalance due to the capability of balancing vibration at speeds higher than the system natural frequency. However, it also suffers from performance inconsistency in applications. Transient contact behaviors of the single-ball balancer are investigated in this research by Lagrange approach. The equations of motion for transient analysis are derived, and the contact model for collisions between the ball and the race is established by the Hertz theory and finite element analysis. According to the sensitivity analysis of system parameters, the maximum angular acceleration of the spindle motor and mass of the stator are found influential to the convergent time, and the system damping and mass of the stator have a strong effect on the largest amplitude of system vibration. The race damping dominates the number of collisions. The consistency of system performance is investigated by the variation of convergent time and largest vibration amplitude subject to various initial conditions of the ball. The results are hoped to be useful for system design and improvement.