# 臺灣博碩士論文加值系統

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 本文主要針對安裝誤差對於轉子系統的影響做一探討，此外並提出一創新之主動式平衡器機構，內容主要可分為三大部分。首先是以Bernoulli-Euler beam theory為理論基礎建立轉子系統之模型。在建立轉子系統模型中，針對不同的支撐條件，探討將軸承視為剛性支撐與線彈性支撐時轉子系統動態上的差異。並以理論發現在軸承剛性假設為線性彈簧時，安裝誤差對於轉子的動態影響為一不隨時間變化之外加的靜變形，也因此間接證明安裝誤差對於轉子動態的影響在於支撐剛性的非線性所引起。以上結果証明安裝誤差對於轉子的動態行為與非線性的支撐剛性有密切的關係以驗證非線性軸承模型建立的必要性。另外亦從理論的推導過程中發現，連續轉子在線彈性支撐下之渦動頻率，除了和轉子工作轉速有關外，亦與沿著轉子本身的位置有關，即代表不同部分的轉子會有不同的渦動頻率。接著是建立斜角滾珠軸承模型並推導其剛性矩陣。利用由De Mul所提出的方法，以Hertz contact theory描述斜角接觸滾珠軸承內部各滾珠的接觸剛性，進而得到滾珠軸承在各方向上的剛性矩陣，作為爾後分析搭載滾珠軸承之轉子系統的輸入。最後綜合整理了目前市面上各種主動式線上平衡機構並進而提出了一利用超音波馬達的特性之主動式線上平衡機構的驅動設計概念。
 This thesis mainly discusses the effect of misalignment on the rotor system, and also proposes a generative mechanism of the active balancing balancer. The content can be divided into three parts. In the beginning, we use Bernoulli-Euler beam theory as the foundation of the entire research to model the rotor system. After this, we discuss the difference on the dynamics of the rotor when the bearing supports are considered as the rigid or linear elastic. Besides, through the establishment of the theory, the result shows the effect of misalignment on the dynamic of the rotor is the additional static deflection when the stiffness of the bearing support is considered as linear elastic. This phenomenon also shows the effect of the misalignment on the rotor dynamic is mainly due to the nonlinear bearing stiffness and verifies the importance of the establishment of the nonlinear bearing stiffness model. The another discovery is that the whirling frequency of an continuous rotor on the linear bearing stiffness supports not only have the relation to the rotating speed of the rotor ,but also the different parts of the rotor. It means the whirling frequency of the middle part of the rotor will be different from the end part under the same rotating speed.The secondary part is the modeling of the angular contact ball bearing and derivation of the stiffness matrix. In this part we use the method proposed by De Mul et al, using the Hertz contact theory to describe the contact phenomenon happening in the angular ball bearing. And find the stiffness matrix in all direction. It can be used as the input when we want to analyze dynamic of the rotor system equipped with the ball bearings as the supports in the future. In the last part, we introduce many kinds of the online active balancing system on the market, and propose a new concept of the online active balancing system adopt the supersonic motor as the driving mechanism.
 ABSTRACT…………………………………………………………………… I摘要………………………………………………………………………… III誌謝………………………………………………………………………… IV目錄………………………………………………………………………… V圖目錄……………………………………………………………………… VII表目錄……………………………………………………………………… XI第一章　緒論……………………………………………………………… 11-1研究動機…………………………………………………… 11-2　文獻回顧………………………………………………… 21-2-1 軸承模型建立……………………………………… 21-2-2 主動式線上平衡理論……………………………… 31-3　研究內容…………………………………………………… 4第二章　線性轉子-軸承系統對於安裝誤差的動態行為……………… 62-1轉子系統模型建構………………………………………… 62-2轉子-軸承系統模型建構…………………………………… 102-3考慮安裝誤差時之轉子-軸承系統模型建構……………… 132-4彈性支撐對轉子系統的動態影響………………………… 17第三章　軸承剛性與變形公式推導……………………………………… 273-1　軸承重要幾何參數……………………………………… 273-2　系統架構………………………………………………… 303-3 滾珠接觸剛性推導……………………………………… 323-4 Hertz 接觸理論………………………………………… 383-5 軸承剛性推導…………………………………………… 41第四章　平衡方法介紹與主動式平衡系統之概念設計………………… 484-1　不平衡量的定義………………………………………… 484-1-1靜不平衡…………………………………………… 484-1-2偶不平衡…………………………………………… 494-1-3動不平衡…………………………………………… 504-1-4不平衡量的表示方法……………………………… 504-2 動平衡校正的方法 ……………………………………… 514-3　主動式平衡系統之概念與系統架構…………………… 544-3-1　主動式平衡系統之系統架構…………………… 544-3-2　平衡環之作動原理……………………………… 594-3-3　平衡環驅動機構之種類與優缺點比較………… 604-4 超音波馬達應用於主動式平衡系統之概念設計……… 644-4-1 超音波馬達之作動原理………………………… 644-4-2 超音波馬達於平衡系統中之配置……………… 684-5 如何決定平衡器所需的平衡能力……………………… 69第五章　結論與未來工作………………………………………………… 74參考文獻…………………………………………………………………… 76