結合雙系統配置與配重塊之四連桿組最佳動態平衡

Abstract

本研究以配重塊平衡法為基礎，欲結合複製機構平衡概念之雙系統配置，針對四連桿組以最少的配重塊達成動態平衡。本文先以向量迴路法與D’Alembert原理建立平面四連桿之運動及動力模型，並針對軸向之軸承分布，計算機台座之軸承受力。接著，採用固定於桿件上之配重塊，以最佳化方法計算各配重塊之質量與位置，並比較目標函數為無因次化最大搖撼力與搖撼力矩之總和以及達成標準最大搖撼力與搖撼力矩之配重塊質量，其最佳解對於系統動力特性的效果。結果顯示前者不容易同時達成複數動力特性之最佳化，而後者之最佳解可以降低振動至標準值並減少配重塊質量。最後，針對雙系統配置討論不同輸入轉速方向、不同擺放方向以及不同相角差下的動態平衡效果。根據分析結果可以分成兩類別，兩者主要差異在於搖撼力矩。進而利用此特性，結合最佳化配重平衡，可以使系統搖撼力與搖撼力矩下降至標準值，同時更進一步減少配重塊的質量。本研究使用簡單之雙系統配置進行初步的平衡，再以最佳化配重塊配置，使系統添加最少的配重塊即可達成所需的動態平衡，此研究成果應有助於動態平衡之研究與實務上之應用。

This study is going to combine the dual-system which is similar to the duplicate mechanism and counterweights to achieve the dynamic balancing of four-bar linkage with the lightest counterweights. This paper is starting with constructing the kinematic model and the dynamic model of a planar four-bar linkage by the vector loop closure equations and D’Alembert’s principle, and focus on the axial arrangement of the bearings to analyze the bearing forces. Then, the counterweights mounted on the linkages are applied to balance the system. The differences between two object functions of optimizing the counterweights, one is the non-dimensional total of shaking force and shaking moment and the other is the total mass of the counterweights which can balance the system to a standard level, are shown in this study. The result shows that the latter is easier to lower the specific dynamic properties and decrease the mass applied. Finally, this study discusses the balancing effects of different settings of the dual-systems. According to the result, the settings can be classified into two categories and the main difference between the two is the shaking moment. With this property, the combination of dual-system settings and optimal counterweights can lower the shaking force and the shaking moment and decrease the mass of counterweights even more. This study could be applied in practice and promote the research on the dynamic balancing.