應用質量重置法於可調平面連桿組之最佳動態平衡

Optimum Dynamic Balancing of Adjustable Planar Linkages by Mass Redistribution

鄧巧梅(Chiao-Mei Teng)

指導教授 ： 劉霆

國立臺灣大學/工學院/機械工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.02102

摘要

本研究應用質量重置法，針對可視為由四連桿前後串聯而成之串聯型平面可調n連桿，進行動態平衡最佳化，以權衡改善所有調整狀態之各項動力性能。首先，以向量閉迴路方程式分析串聯型平面n連桿之各桿件運動性質，再以牛頓─尤拉運動方程式，由輸出端反向遞迴演算，依序推導各接頭作用力與驅動扭矩，而後，列出可調平面連桿組的動力性能最佳化問題與評估動力性能改善成效之無因次指標，再以固定輸入轉速、固定樞軸位置可調整的一組可調六連桿與可調八連桿為例，分別對於無負載與外加負載的情形，最佳化其動力性能，驗證本研究之可行性。為考慮負載之影響，僅與慣性相關之搖撼力、搖撼力矩，本研究則以更能直接代表機架狀況之機架合力、機架合力矩取代，範例結果顯示，各調整狀態之軸承力、可調樞軸力、驅動扭矩、機架合力與機架合力矩，皆可獲得改善。此外，本研究亦討論質量性質與外加負載以閉迴路為單位往輸入端影響之特性，以及最佳化時考慮負載之重要性，整體而言，若外加負載相對於各慣性力與力矩明顯較大，較難以改變桿件質量性質的方式改善連桿組的動力性能。本研究結果可應用於串聯型平面可調n連桿之質量性質設計，亦探究其動力特性，助於連桿機構動態平衡之研究，並對於日後可調連桿組於實務上之發展有所助益。

關鍵字

質量重置法 ； 平面可調n連桿 ； 動態平衡 ； 最佳化 ； 搖撼力 ； 搖撼力矩

並列摘要

This study presents the optimum dynamic balancing of adjustable planar n-bar linkages, which is considered a series of 4-bar linkages, for the trade-off of dynamic performance improvement between every adjustment state by mass redistribution. First, the kinematics is analyzed using the vector loop closure equations. Subsequently, joint forces and driving torque are formulated in sequence using Newton-Euler equations of motion. They are calculated reversely and recursively, and the driving torque is last determined. Then, the optimization problem for improving the dynamic performances is posed. Finally, two examples, including an 6-bar and 8-bar linkages with constant drive speed and adjustable fixed pivots, are given to demonstrate the feasibility of this study. Two situations which are with and without external loads are involved in both examples. In order to take the effect of external loads into account, the frame status is evaluated by the frame force and moment instead of shaking force and shaking moment in this study. The result of examples shows that the bearing forces, adjustable pivot forces, driving torque, frame force and moment are improved in every state. This study could be applied to the design of mass properties of serial planar n-bar linkages, and promote the research on dynamic balancing and the practical application of adjustable linkages.

並列關鍵字

dynamic balancing ； adjustable planar n-bar linkages ； mass redistribution ； optimization ； shaking force ； shaking moment

參考文獻

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