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研究生:林俊燁
論文名稱:彈性機構含支點力動態系統之探討
指導教授:陳精一陳精一引用關係
指導教授(外文):Ching I Chen
學位類別:碩士
校院名稱:中華大學
系所名稱:機械與航太工程研究所
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:2001
畢業學年度:89
語文別:中文
論文頁數:99
中文關鍵詞:拉格蘭日乘子法阮奇-庫特法亞當斯法勁度效應限制方程式
外文關鍵詞:Lagrange''s Multiplier MethodRunge-Kutta MethodAdams-Moulton MethodStiffness EffectConstraint Equation
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本篇論文主要針對兩種不同的動態系統作討論,以了解彈性連桿機構在運動時,系統的位移、速度、加速度、橫向變形以及接點的作用力各項參數的變化情形。
首先針對一個鋼製的旋轉彈性單連桿作探討,將作用時間分成三個區段,不同的時間區段,施加不同的驅動扭力,因其扭力為一個指定的數值,故可簡化運動方程式的求解過程,先利用拉格蘭日乘子法來推導方程式,再配合系統的限制條件,組成一個微分代數方程式,再對系統作數值分析,使用阮奇-庫特法得到前四組解,再利用這四組解代入亞當斯法,以求得相對應於其餘時間點的解,由此可得系統的各項參數值,再將剛體所得的數據和彈性體所得的數據作一比較,可得其差異量為加速度最大,速度次之,位移最小。速度及加速度較大的原因為高勁度效應,而加速度的變異量會最大的原因為慣性力的作用。
接下來則針對鋁製彈性四連桿作討論,其桿件三僅考慮橫向變形的彈性體,其餘兩桿件為剛體,其桿件二為一固定的角速度旋轉,觀察系統在運動時,各項參數的變化情形,其所得結果和彈性單連桿的結果相類似,可將所得數據代回限制方程式中,以檢視其直接積分所產生的偏離誤差。
The main objective of this paper is to study the displacement, velocity, acceleration, transverse deformation, and the reaction forces at the joints for two different dynamic systems, which are composed of moving elastic linkages.
The first system considered in this study is a flexible rotating steel beam. Three different kinds of driving torques were applied to the system at three different time intervals. At each interval, the torque can be fully prescribed so that the solving procedure for the equations of motion can be simplified. The equations were derived using the Lagrange’s multiplier method. A system of governing differential algebraic equation can then be obtained in combining these equations and the constraint conditions. To solve this system of equations numerically, Runge-Kutta method was first used to get the solutions at the first four time points. The solutions at the rest time points were then solved using Adams-Moulton method. The various parameters of the dynamic system can thus be obtained so that the responses from rigid and elastic bodies can be compared. It was found that the differences are biggest in acceleration, second in velocity, and the smallest in displacement. The main reason for higher difference in velocity and acceleration may come from the high stiffness effect. The reason for the highest variation in acceleration may result from inertial forces.
The second dynamic system considered in this study is a flexible rotating four-bar linkage of aluminum. The third link was only allowed to have transverse deformations. The rest two links were considered to be rigid. The second link was considered to rotate at constant angular velocity. The numerical results were found to be similar to those of the previous system. These results can be substitute back to the original constraint equations so that the deviation errors induced in direct integration can be evaluated.
中文摘要………………………………………………………………..Ⅰ
英文摘要………………………………………………………………..Ⅲ
誌謝……………………………………………………………………..Ⅳ
目錄………………………….………………………………………….Ⅴ
圖目錄………………………….…….…………………………………Ⅶ
表目錄………………………….…………………………………… XII
第一章緒論……….…………….………………………….………1
1.1 前言……………….………………………………………...1
1.2 文獻回顧………….………………………….……………..3
第二章彈性動力分析方法…….……… ……...…………………7
2.1 前言……….…………….……………………………......7
2.2 運動方程式.…………….…………………………………..8
2.3 運動方程式的求解……….…………….………………...17
第三章彈性單連桿之動態模型的探討…………….….…………23
3.1 前言……….……...……………………………………… 23
3.2 理論分析….………………...…………………………….24
3.3 數值結果….………………...…………………….………36
3.4 結論……….……...……………………………………….49
第四章彈性四連桿之動態系統的探討……………………………50
4.1 前言……….……...……………………………………….50
4.2 理論分析….……...……………………………………….51
4.3 數值結果….……...……………………………………….65
4.4 結論……….……...……………………………………….95
第五章結果與討論…….…….……………………………………96
參考文獻……………………….…….…………………………………98
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2. Erdman, A.G., Sandor, G.N., “Kinematic Synthesis of a Geared-Five-Bar Function Generator”, Journal of Engineering for Industry, 93B, no. 1, pp. 157-164, February 1971.
3. Badlani, M., and Kleinhenz, W., “Dynamic Stability of Elastic Mechanisms”, Journal of Mechanical Design, 101, no. 1(January 1979), pp. 149-153.
4. Kalaycioglu, S., Bagci, C., “Determination of the Critical Operating Speeds of Planar Mechanisms by the Finite Element Method Using Planar Actual Line Elements and Lumped Mass Systems”, Journal of Mechanical Design, Vol. 101, pp. 210-223, April 1979.
5. A. Aannaque, S. Garvey, M. Bennouna and J. Penny, “Operation of a Four-Bar Mechanism Above Several Critical Speeds”, Transactions of the ASME, Vol. 118, April 1996.
6. Fengfeng X.I., Rosario, S., “Effect of Dynamic Balancing on Four-Bar Linkage Vibrations”, Mech. Mach. Theory, Vol. 32, No. 6, pp. 715-728, 1997.
7. Jungkeun, R., Adnan, A., “Dynamic Response of a Revolute Joint with Clearance”, Mech. Mach. Theory, Vol. 31, No. 1, pp. 121-134,1996.
8. B. Fallahi, “An Enhanced Computational Scheme for the Analysis of Elastic Mechanisms”, Computers & Structure, Vol. 62, No. 2, pp. 369-372, 1997.
9. D.J. Zhang and R.L. Huston, “On Dynamic Stiffening of Flexible Bodies Having High Angular Velocity”, MECH. STRUCT. & MACH., 24 (3), 313-329 (1996).
10.陳升高, “空間撓性連桿組之彈性動力分析”, 國立清華大學碩士論文, June 1991.
11.方亮彬, “撓性連桿機構之動態響應分析”, 國立清華大學碩士論文, June 1993.
12.林宏毅, “近似定轉速比平面四連桿機構之合成”, 國立清華大學碩士論文, June 2000.
13.黃仁聖, “連桿機構的動態合成─於機車後懸吊系統的應用”, 國立清華大學碩士論文, June 1997.
14.Chia-Ou Chang, “Dynamic Analysis and Optimal Design of Mechanical Systems with Constraint Violation Stabilization Method, ”PhD. Thesis, University of Iowa, Mechanical Engineering Department, 1984.
15.Ching I Chen, V.H. Mucino and C. C. Spyrakos, "Flexible Rotating Beam: Comparative Modeling of Isotropic and Composite Material Including Geometric Nonlinearity", J. of Sound and Vibration, Vol. 178(5), pp. 591-605, 1994.
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