Optimization of Numerical Modeling and System Design for Automatic Multi-ball Balancers

滾珠型自動平衡裝置具有在高於系統自然振頻的轉速下平衡振動的能力，因此在不定負荷的旋轉機械中具有廣泛的應用，然而仍有系統性能表現不一致性的缺點存在。本研究以多滾珠自動平衡裝置之暫態行為特性為指標，嘗試改善一致性不佳的問題，首先以Lagrange理論推導系統運動方程式；並藉由赫茲接觸理論所建構之接觸模型建立滾珠與滾珠之間、滾珠與軌道之間的接觸關係；同時以庫倫摩擦模型模擬滾珠與軌道間之摩擦行為，此模型經由與彈性體軌道壁、軌道阻尼模型及滾珠純滑動模型之比較以驗證其適用性。而模擬結果顯示滾珠初始位置的集中程度會影響到系統的收斂時間；較大的摩擦力雖然可以減少系統的收斂時間，但卻會加劇系統的振動量；此外，隨著滾珠數目的增加，可以同時改善系統的收斂時間與殘留振動量。Being capable of balancing vibration when speeds exceed system natural frequency, the automatic multi-ball balancer has been widely used in rotary machinery with variable unbalanced mass. However, it still suffers from inconsistent performance in operations. By investigating transient behaviors, this research aims to reduce inconsistency of this system. The equations of motion are derived by the Lagrange approach, and the Hertz contact theory is used to model contacts between balls and balls to the race. Coulomb friction is employed to simulate friction between balls and race. These models are justified by comparisons with flexible race wall, traditional damping and pure sliding ball models. According to the simulations, initial positions of balls will affect the system convergent time, and higher friction results in shorter convergent time and larger vibration. Moreover, increasing the number of balls can reduce both the convergent time and vibration for the system.口試委員會審定書...i謝...ii文摘要...iii文摘要...iv錄...v一章 緒論...1.1 研究背景與動機...1.2 文獻回顧...3.3 研究方法與流程...8.4 論文架構...9例...10二章 研究方法及理論...13.1 前言...13.2 系統運動方程式之建構法則...13.2.1 D’Alembert 原理...13.2.2 Lagrange 方程式...14.3 碰撞接觸理論...15.3.1 離散模型...15.3.2 連續模型...16.3.3 模型比較與討論...22.4 庫倫摩擦理論...24例...26三章 系統模型之建立...30.1 前言...30.2 系統概述...30.3 系統模型之建構...32.3.1 系統運動方程式...32.3.2 接觸模型之建構...35.3.3 庫倫摩擦模型之建構...39.4 模型之驗證與比較...41.4.1 系統參數設定...41.4.2 剛體與彈性體軌道壁...44.4.3 滾動與滑動...47.4.4 摩擦與軌道阻尼液...48格...51例...53四章 系統暫態模擬與分析...60.1 前言...60.2 分析指標...60.3 滾珠初始位置之影響...61.4 摩擦力之影響...66.5 滾珠數目之影響...68.6 系統設計的最佳化...72格...74例...79五章 結論與建議...88.1 綜合結論...88.2 未來展望與研究方向...89amp;#63851;考文獻...91錄一 彈性變形與塑性變形公式之推導...100例...103錄二 系統變數之二階微分方程式...10