# 臺灣博碩士論文加值系統

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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[1] Badlani, M., and Kleninhenz, W., “Dynamic Stability ofElastic Mechanism,” ASME Journal of Mechanical Design,Vol. 101, pp.149-153, pp. 1979.[2] Badlani, M., and Midha A, “Member Initial CurvatureEffects on the Elastic Slider-Crank Mechanism Response,”ASME Journal of Mechanical Design, Vol.104, pp.159-167,1982.[3] Badlani, M., and Midha A, “Effect of Internal MaterialDamping on the Dynamics of a Slider-Crank Mechanism,”ASME Journal of Mechanism, Transmission, and Automation inDesign, Vol.105, pp.452-459, 1983.[4] Chu, S.C., and Pan, K.C., “Dynamic Response of a HighSpeed Slider-Crank Mechanism With an Elastic ConnectingRod,” ASME Journal of Engineering for Industry, Vol. 97,pp542-550, 1975.[5] Fung, R.-F., and H.-H. Chen, “Steady-State Response ofthe Flexible Connecting Rod of a Slider-Crank MechanismWith Time-Dependent Boundary Condition,” Journal of Soundand Vibration, Vol. 199, pp.237-251, 1997.[6] Hsieh, S.R., and Shaw S.W., “The Dynamic Stability andNonlinear Resonance of a Flexible Connecting Rod : SingleMode Model,” Journal of Sound and Vibration, Vol. 170,pp.25-49, 1994.[7] Jasinski, P.W., Lee, H.C., and Sandor, G.N., “Stabilityand Steady-State Vibrations in a High Speed Slider-CrankMechanism,” ASME Journal of Applied Mechanics, Vol.37,pp.1069-1076, 1970.[8] Jasinski, P.W., Lee, H.C., and Sandor, G.N., “Vibrationsof Elastic Connecting Rod of a High Speed Slider-CrankMechanism,” ASME Journal of Engineering for Industry,Vol.93, pp.636-644, 1971.[9] Midha, A., Erdman., A.G., and Frohrib, D.A., “FiniteElement Approach to Mathematical Modeling of High SpeedElastic Linkages,” Mechanism and Machine Theory, Vol.13,pp.603-618., 1978.[10] Nagarajan S., and Turcic, D.A., “General Methods ofDetermining Stability and Critical Speeds for ElasticMechanism Systems,” Mechanism and Machine Theory, Vol.25,No.2, pp.209-223, 1990.[11] Neubauer, A.H., Cohen, R., and Hall, A.S., “An AnalyticalStudy of the Dynamics of an Elastic Linkage,” ASMEJournal of Engineering for Industry, Vol., pp., 1966.[12] Tadjbakhsh, I.G., “Stability of Motion of Elastic PlanarLinkages With Application to Slider Crank Mechanism,”ASME Journal of Mechanical Design, Vol.104, pp.698-703,1982.[13] Tadjbakhsh, I.G., and Younis, C.J., “Dynamic Stability ofthe Flexible Connecting Rod of a Slider Crank Mechanism,”ASME Journal of Mechanism, Transmission, and Automation inDesign, Vol.108, pp.487-496, 1986.[14] Viscomi, B.V., and Ayre, R.S., “Nonlinear DynamicResponse of Elastic Slider-Crank Mechanism,” ASME Journalof Engineering for Industry, Vol.93, pp.251-262, 1971.[15] Zhu, Z.G., and Chen Y., “The Stability of the Motion of aConnecting Rod,” ASME Journal of Mechanism, Transmission,and Automation in Design, Vol. 105, pp.637-640, 1983.
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 1 彈性滑塊曲柄機構之動態實驗與分析

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