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標題: 含非線性軸承齒輪聯結雙旋轉複合材料軸主振動響應之探討
Studies of the Primary resonance of Gear-Coupled Composite Shafts supported by nonlinear bearings.
作者: 洪維澤
Hung, Wei-Che
關鍵字: 非線性軸承;nonlinear bearing;齒輪聯結;Gear-Coupled
出版社: 機械工程學系所
引用: 參考文獻 1. S. V. Neriya, R. B. Bhat, and T. S. Sanker, “Effect of Coupled Torsion-Flexural Vibration of a Geared Shaft System on the Dynamic Tooth Load,” The Shock and Vibration Bulletin, part 3, Vol. 54, 1984, pp. 67-75. 2. S. V. Neriya, R. B. Bhat, and T. S. Sanker, “Coupled Torsional-Flexural Vibration of a Geared Shaft System Using Finite Element Analysis,” The Shock and Vibration Bulletin, part3, Vol. 55, 1985, pp. 13-25. 3. H. N. Özgüvent, “A Non-linear Mathematical Model For Dynamic Analysis of Spur Gears including Shaft and Bearing Dynamics,” Journal of Sound and Vibration, 145(2), 1991, pp. 239-260. 4. A. Kahraman, H. N. Özgüvent, and D. R. Houser, “Dynamic Analysis of Geared Rotors by Finite Elements,” Journal of Mechanical Design, Vol. 114, September 1992, pp. 507-514. 5. 張哲榮,齒輪轉子軸承系統動態特性之研究,博士論文,成功大學航空太空工程學系,1996 6. R. Maliha, C. U. Dogruer, and H. N. Özgüvent, “Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Function,” Journal of Mechanical Design, Vol. 126, May 2006, pp. 534-541. 7. T. Yamamoto, Y. Ishida, and K. Aizawa, “ On the Subharmonic Oscillations at Unsymmetrical Shafts,” Bulletin JSME, Vol. 22, 1979, pp. 164-173. 8. T. Yamamoto, Y. Ishida, T. Ikedam and M. Yamada, “ Subharmonic and Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Rotor,” Bulletin JSME, Vol. 24, 1981, pp. 192-199. 9. L. Cveticanin, “ Resonant Vibrations of Nonlinear Rotors,” Mechanism and Machine Theory, Vol. 30, 1995, pp. 581-588. 10. Z. Ji and J. W. Zu, “ Method of Multiple Scales for Vibration Analysis of Rotor-Shaft Systems with Non-Linear Bearing Pedestal Model,” Journal of Sound and Vibration, Vol. 218(2), 1998, pp. 293-305. 11. 彭文彬,複材旋轉軸非線性振動之研究,碩士論文,中興大學機械工程學系研究所,2002 12. 詹政川,承受持續外激力旋轉軸振動之主動控制,碩士論文,中興大學機械研究所, 1996 13. 陳鄭貴,複合材料旋轉軸之動態響應與其震動控制之探討,碩士論文,中興大學機械工程學系研究所,1998 14. 吳慶頤,正齒輪聯結雙旋轉複合材料軸振動特性之探討,碩士論文,中興大學機械工程學系研究所,2007 15. 蔡家偉,複合材料軸-圓盤系統振動特性之探討,碩士論文,中興大學機械工程學系研究所,2005 16. C. W. Bert, and C. D. Kim, “Whirling of Composite-Material Driveshafts Including Bending-Twisting Coupling and Transverse Shear Deformation,” Journal of Vibration and Acoustics, Vol. 117, 1995, pp. 17-21.
實例中首先探討忽略軸承非線性勁度的情形,此時之系統為線性。本文中使用模態疊加法,分析比較此旋轉軸系統在特定轉速下,齒輪間具聯結效應與無聯結效應(km=0, cm=0)時的暫態響應。接著納入軸承的非線性勁度,運用模態分析法及多尺度擾動法對非線性有限元素運動方程進行解耦(decouple),再求出軸系統在共振頻率附近運轉時軸之振幅與轉速關係。利用此關係式,探討不同的軸承非線性勁度值、複材軸的疊層角度、齒輪間耦合勁度與阻尼等因素對振幅與轉速關係的影響。
由實例分析中發現含非線性軸承勁度之雙複合材料軸系統在轉速接近共振頻率時,齒輪間具聯結效應時的振福會比未考慮齒輪間聯結效應(km=0, cm=0)時低,非線性的特性也比較不明顯,也發現非線性勁度(kn)值、耦合勁度(km)值或耦合阻尼(cm)值越大,振幅會越小。

The main objective of this thesis is to study the nonlinear vibration behavior of two composite shafts coupled by spur gears operating at or near the system’s critical speed. In the developed model, the gears and disk mounted on the shafts are treated as rigid bodies. A spring and a viscous damper are used to simulate the elastic deformation of and the friction between the meshing teeth of the spur gears. And by employing a spinning composite flexible shaft theory, a finite element system model that contains double spinning composite shafts coupled by spur gears is derived.
In the studied examples, first, the non-linear stiffness of bearings is omitted. The system hence is linear, and the modes superposition method is used to analyze and compare the transient dynamic responses for systems with or without the gear coupling effect. Next, the nonlinear stiffness of bearings is included. The nonlinear finite element equations are then decoupled and solved by an approach combining the modal analysis and the multiple-scale perturbation methods. An explicit expression of the amplitude vs. the rotational speed of the system spinning at a speed close to its bending mode or coupled mode frequency is derived. The analyses are carried out for different nonlinear stiffness of bearings, lamination angles of composite, and the coupled stiffness and viscous damping of meshing gears.
It is found from the examples being analyzed when system spinning at a speed at or near its resonance frequency, the amplitude of the system which considering the coupling effect of meshing gears is smaller than that without such an effect, and the nonlinear characteristics of response of the former system also becomes less obvious. The analyses also indicate that the amplitude is smaller when the value of nonlinear stiffness of bearings, the couple stiffness or the couple damping of meshing gears becomes larger.
其他識別: U0005-2308201214452200
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