滾珠平衡系統週期解的數值分析和實驗驗證

Abstract

滾珠型自動平衡機構在適當的工作條件下，可因應不同的偏心量，自動調整滾珠的平衡位置而大幅降低偏心振動，因此廣泛的應用於轉子系統上。然而，當轉速高於系統自然頻率時，滾珠有時無法定位於完全平衡位置上，而是繞著碟片作週期性的旋轉或是來回振盪運動，此時系統伴隨有劇烈的振動量。由於旋轉週期解無法由現有的數值方法直接求得，本文使用新發展的Modified Incremental Harmonic Balance法探討各種形式的週期解，求取週期解在Ω-η平面上的存在區域及其穩定性，並分析各參數的影響，最後進行實驗驗證。

Under proper working conditions, a ball-type automatic balancer can adjust the positions of its balls according to the imbalance of the rotor and significantly reduces the rotational vibrations. As a consequence, ball-type automatic balancers are widely applied to rotor systems. However, when the rotational speed is above the natural frequency of the system, the balls may not settle to the perfect balancing positions but keep circulating or oscillating around the disk and result in large vibrations. Moreover the rotary periodic motions can’t be determined by the existing numerical methods used for the detection of periodic solutions. In this study, we employed the modified incremental harmonic balance method to analyze all kind of periodic motions, obtain the existence regions in the η-Ω plane and determine the corresponding stability. Then a comprehensive parametric study was performed and the results were verified experimentally.