تحلیل ارتعاشات روتور دارای اثر غیرخطی هندسی با یاتاقان پد متحرک (تیلتینگ پد)

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه خوارزمی*فنی

2 گروه مهندسی مکانیک، دانشگاه خوارزمی

3 دانشگاه خوارزمی تهران

چکیده

در این مقاله، ارتعاشات روتور پیوسته با مقطع دایروی یکنواخت که بر روی دو یاتاقان پد متحرک )تیلتینگ پد( قرار دارد مطالعه می شود. روتور الغر فرض میشود و در نتیجه، اثر تغییر شکل برشی نادیده گرفته شده است ولی اثر ژیروسکوپی لحاظ می شود )تئوری تیر ریلی(. به عالوه اثر غیرخطی هندسی ناشی از تغییر شکل بزرگ روتور در نظر گرفته می شود. بر اساس فرضیه یاتاقان کوتاه، یک مدل تحلیلی غیرخطی از یاتاقان پد متحرک که با سیال روانکاری شده و دارای جریان آرام و مغشوش می باشد مدل سازی شده است. معادالت حرکت روتور با دو یاتاقان پد متحرک که در ابتدا و انتهای آن قرار دارند استخراج می شود. به منظور گسسته سازی این معادله ها از روش گلرکین استفاده می شود. با حل عددی معادله های گسسته حاکم بر مسئله، منحنی پاسخ فرکانسی سیستم بدست می آید. با مقایسه پاسخها مشخص می شود که سیستم روتور غیرخطی-یاتاقان پد متحرک دارای دامنه کمتری نسبت به روتور خطی با یاتاقان پد متحرک می باشد. همچنین پاسخ سیستم روتور-یاتاقان پد متحرک با جریان مغشوش باعث سفتتر شدن یاتاقان و کاهش دامنه پاسخ سیستم می شود. با کاهش لزجت دینامیکی سیال، از سفتی یاتاقان کاسته م یشود و سبب افزایش دامنه پاسخ م یشود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Vibrations Analysis of a Rotor Supported by Tilting-Pad Journal Bearings with Considering of Geometric Nonlinearity

نویسندگان [English]

  • Seyed Ali Asghar Hosseini 1
  • A. Tamadon 2
  • Mahdi Zamanian 3
1 Kharazmi University
2 Department of Mechanical Engineering, Kharazmi University
3 Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, P.O. Box 15719-14911, Tehran, Iran
چکیده [English]

Vibrations of a continuous rotor with uniform circular cross section supported by two tilting-pad journal bearings at both ends are analyzed. Since the shaft is slender, shear deformation is neglected, but, gyroscopic effect is considered (Rayleigh beam theory). In addition, geometric nonlinearity due to large deformation of the rotor is considered. Based on short bearing assumption, an analytical model of a tilting-pad journal bearing with laminar and turbulence flows has been derived. Galerkin method is applied to discretize differential equations of motion. By solving discrete rotorbearing system equations, the response is obtained. For further investigation, responses of rotor-bearing system in different situations are presented. Comparing the responses of the linear and nonlinear rotor with two tilting-pad journal bearings at both ends shows that the nonlinear rotor has less amplitude than linear rotor and nonlinear rotor is closer to reality. In addition, nonlinear model has a larger natural frequency in comparison to the linear rotor. Using turbulence flow makes the bearing stiffer and have less amplitude than laminar flow. Reducing viscosity of lubricant leads to increase of amplitude of response and shows that higher viscosity make the bearing stiffer.

کلیدواژه‌ها [English]

  • Nonlinear vibrations
  • Continuous rotor
  • Tilting-pad journal bearing
  • Rayleigh beam theory
  • Short bearing assumption

مراجع

[1] Y. Ishida, T. Yamamoto, Linear and Nonlinear Rotordynamics, a Modern Treatment with Applications, Wiley-VCH, 2012.
[2] F. Ocvirk, Short-bearing approximation for full journal bearings, NACA Report 2808, 1952.
[3] J.W. Lund, Spring and damping coefficients for the tilting pad journal bearing, ASLE Transactions, 7 (1964) 342–352.
[4] F.K. Orcutt, The steady state and dynamic characteristics of the tilting pad journal bearing in laminar and turbulent flow regimes, ASME Journal of Lubrication Technology, 89 (1967) 392–404.
[5] C.W. Ng and C.H.T. Pan, A linearized turbulent lubrication theory, Journal of Basic Engineering, 87 (1965) 675–682.
[6] J.C. Nicholas, E. J. Gunter, P.E. Allaire, Stiffness and damping coefficients for the five-pad tilting-pad bearing, ASLE Transactions, 22 (1979) 113–124.
[7] G.J. Jones and F.A. Martin, Geometry effects in tilting-pad journal bearings, ASLE Transactions, 22 (1979) 227–244.
[8] G. Capone, Orbital motions of rigid symmetric rotor supported on journal bearings, Mecc. Ital., 199 (1986) 37–46 (in Italian).
[9] E.P. Okabe, K.L. Cavalca, Rotordynamic analysis of systems with a non-linear model of tilting pad bearings, in: Seventh International Conference on Rotor Dynamics (IFToMM), Austria, Vienna, 2006.
[10] E.P. Okabe, K.L. Cavalca, Rotordynamic analysis of systems with a non-linear model of tilting pad bearings including turbulence effects, Nonlinear Dynamics 57 (2009) 481–495.
[11] Y. Wang,Y. Gao, Y. Cui and Z. Liu, Establishment of Approximate Analytical Model of Oil Film Force for Finite Length Tilting Pad Journal Bearings, International Journal of Rotating Machinery, Article ID 531209 (2015) 1-11.
[12] M. Li et al, Rotor Dynamics Behavior of Tilting Pad Bearing Supported Turbo-Expander Considering Temperature Gradient, Journal of Computational and Nonlinear Dynamics, 11(2) (2015) 1-16.
[13] M. Chaab, S. Glavatskihac, Nonlinear dynamic behaviour of vertical and horizontal rotors in compliant liner tilting pad journal bearings: Some design considerations, Tribology International, 82 (2015) 142-152.
[14] E.P. Okabe, Analytical model of a tilting pad bearing including turbulence and fluid inertia effects, Tribology International, 114 (2017) 245-256.
[15] A. CerdaVarelaa, I. FerreiraSantos, Component level study of an actively lubricated LEG Tilting Pad Bearing: Theory and experiment, Tribology International, 120 (2018) 115-126.
[16] Y. Wu, K. Feng, Y. Zhang, W. Liu, W. Li, Nonlinear dynamic analysis of a rotor-bearing system with porous tilting pad bearing support, Nonlinear Dynamics 94 (2018) 1391–1408.
[17] B.R. Nichols, R.L. Fittro and C.P. Goyne, Steady-State Tilting-Pad Bearing Performance Under Reduced Oil Supply Flow Rates, Journal of Tribology, 140(5) (2018) 1-8.
[18] L. San Andrés, B. Koo and M. Hemmi, A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Toward Understanding the Onset of Low Frequency Shaft Motions,
Journal of Engineering for Gas Turbines and Power, 140(5) (2018) 1-14.
[19] Y. Ishida, I. Nagasaka, T. Inoue, S. Lee, Forced Oscillations of a Vertical Continuous Rotor with Geometric Nonlinearity, Nonlinear Dynamics, 11 (1996) 107-120.
[20] Z. Ji, 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, 218 (1998) 293–305.
[21] N. Shabaneh, J.W. Zu, Nonlinear dynamic analysis of a rotor shaft system with viscoelastically supported bearings, Journal of Vibration and Acoustics, 125 (2003) 290–298.
[22] S.A.A. Hosseini, S.E. Khadem, Analytical solution for primary resonances of a rotating shaft with stretching nonlinearity, International Journal of Mechanical Engineering Science, 222 (2008) 1655-1664.
[23] S.E. Khadem, M. Shahgholi, S.A.A. Hosseini, Two-mode combination resonances of an in-extensional rotating shaft with large amplitude, Nonlinear Dynamics, 65 (2011) 217-233.
[24] S.A.A. Hosseini, S.E. Khadem, Free vibration analysis of a rotating shaft with nonlinearities in curvature and inertia, Mechanism and Machine Theory, 44 (2009) 272–288.
[25] M. Moradi Tiaki, S.A.A. Hosseini, M. Zamanian, Nonlinear forced vibrations analysis of overhung rotors with unbalanced disk, Archive of Applied Mechanics, 86 (2015) 797–817.
[26] G. Capone, M. Russo, R. Russo, Dynamic characteristics and stability of a journal in a non-laminar lubrication regime, Tribology International, 20 (987) 255–260.
[27] S. S. Rao, Vibration of continuous systems, John Wiley & Sons, Inc., 2007.
[28] T. Someya, Journal-Bearing Data Book, Springer-Verlag, Berlin Heidelberg GmbH., 2013.
نشریه مهندسی مکانیک امیرکبیر
دوره 52، شماره 1
فروردین 1399
صفحه 141-154

فایل ها

هم رسانی

ارجاع به این مقاله

آمار