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研究生:陳昆霖
研究生(外文):Kwin-Lin Chen
論文名稱:彈性滑塊曲柄機構之動態響應
論文名稱(外文):Dynamic Response of a Flexible Connecting Rod
指導教授:陳振山陳振山引用關係
指導教授(外文):Jen-San Chen
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:英文
論文頁數:31
中文關鍵詞:彈性滑塊曲柄機構動態響應
外文關鍵詞:flexible connecting roddynamic response
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過去深入研究彈性滑塊曲柄機構的研究者有很多,求解方式的不同來自於不同的軸向力假設,這些解法大致可以區分如下 : (1)假設軸向力只為時間函數,軸向力由假設彈性連接桿為剛體運動求得,(2) 利用積分軸力平衡方程式獲得軸力,將軸力代入側向位移平衡方程式,求解側向位移,(3)假設軸力是正比於軸向應變。為了檢查上述假設的正確性,本文假設軸向力正比於Lagrangian strain推導運動方程式,低轉速與高轉速時使用不同的無因次化法,讓無因次化的位移階次為一。連接桿細長比是方程式中的一個小的參數,利用此一參數次數大小比較方程式中各項的大小。依此做法檢查先前那些假設,我們發現那些假設只能滿足曲柄轉速很低的情況。換言之,當曲柄轉速趨近於第一個彎矩自然頻率時,因為那些假設都忽略了Lagrangian strain中的非線性項,所以那些假設的結果都高估了此一機構的動態嚮應值。
Previous researches on the dynamic response of a flexible connecting rod can be categorized by the ways the axial load in the rod is being formulated. The axial load may be assumed to be (1) dependent only on time and can be obtained by treating the rod as rigid, (2) related to the transverse displacement by integrating the axial equilibrium equation, and (3) proportional to linear strain. This paper examines the validity of these formulations by first deriving the equations of motion assuming the axial load to be proportional to the Lagrangian strain. In order for the dimensionless displacements to be in the order of O(1), different nondimensionalization schemes have to be adopted for low and high crank speeds. The slenderness ratio of the connecting rod arises naturally as a small parameter with which the order of magnitude of each term in the equations of motion, and the implication of these simplified formulations can be examined. It is found that these formulations give satisfactory results only when the crank speed is low. On the other hand when the crank speed is comparable to the first bending natural frequency of the connecting rod, these simplified formulations overestimate considerably the dynamic response because terms of significant order of magnitude are removed inadequately.
1. Introduction 1
2. Equation of Motion 5
2—1 Equation of Motion 5
3. Numerical Results 8
3—1 Low Crank Speed 8
3—1—1 Linear Strain Simplification 10
3—1—2 Axial Load by Integrating Axial Equilibrium
Equation 11
3—1—3 Time-Dependent-Only Axial Load
Simplification 12
3—1—4 Runge-Kutta Simulation 13
3—2 High Crank Speed 15
3—2—1 Linear Strain Simplification 17
3—2—2 Axial Load by Integrating Axial Equilibrium
Equation 17
3—2—3 Time-Dependent-Only Axial Load
Simplification 18
3—2—4 Runge-Kutta Simulation 18
3—3 Accuracy of One-Mode Approximation 20
4. Summary and Discussion 21
Reference 22
Figure Legend 24
References
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