تحلیل لنگش و پایداری روتورهای با قطر متغیر ساخته شده از مواد هدفمند تحت اثر نیروی محوری و گشتاور پیچشی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان، ایران

2 گروه مکانیک، واحد خمینی شهر، دانشگاه آزاد اسلامی، خمینی شهر، اصفهان، ایران

چکیده

در این پژوهش تحلیل های لنگش و پایداری برای روتورهای ساخته شده از مواد مدرج تابعی تحت نیروی محوری و گشتاور پیچشی بررسی شده اند. روتور بر اساس تئوری تیر تیموشنکو و با در نظر گرفتن اثرات ژیروسکوپیک مدلسازی شده است. قطر روتور و خواص مکانیکی آن در راستای طولی به صورت پیوسته تغییر می کنند و در هر تکیه گاه آن دو فنر انتقالی
و دو فنر پیچشی در نظر گرفته شده اند که قادر به مدلسازی تمامی شرایط مرزی می باشند. با استفاده از قوانین نیوتن معادلات حاکم و شرایط مرزی استخراج شده و با استفاده از روش عددی تفاضلات مربعی حل شده اند. پس از اثبات همگرایی و صحت تحلیل عددی ارائه شده، تاثیر پارامترهای مختلف مانند توان پروفیل، سرعت دورانی، مقدار و جهت نیروی محوری و گشتاور پیچشی بر روی فرکانس های پیشرو و پسرو روتور و پایداری آن بررسی شده اند. نتایج عددی نشان می دهند که افزایش توان در معادله ی تغییرات خواص، وجود نیروی محوری فشاری و گشتاور پیچشی منجر به کاهش تمامی فرکانس های پیشرو و پسرو و سرع تهای بحرانی روتور می گردند و اعمال نیروی محوری کششی نیز باعث افزایش تمامی فرکانس های پیشرو و پسرو وسرعت های بحرانی روتور می شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Whirling and Stability Analyses of FG-rotors with Variable Diameter Subjected to Axial Load and Torsional Torque

نویسندگان [English]

  • K. Torabi 1
  • H. Afshari 2
1 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran
چکیده [English]

In this paper, whirling and stability analyses of a rotor made of functionally graded
materials are investigated. The rotor is modeled based on Timoshenko beam theory and gyroscopic
effects are considered. Diameter and mechanical properties of the rotor are considered to be variable
in longitudinal direction and the rotor is considered to be subjected to axial load and torsional torque.
In order to generalization of the modeling of bearings, each of them is replaced with four springs; two
translational and two rotational acting on two perpendicular directions. Using Newton’s second law,
the set of governing equations and external boundary conditions are derived and solved numerically
using differential quadrature method (DQM). Convergence and accuracy of the presented solution are
confirmed and effect of various parameters including power index, angular velocity of spin, value and
sign of applied axial load and torsional torque on the forward and backward frequencies and stability
of the rotor are investigated. Numerical results show that all forward and backward frequencies and
therefore critical speeds decrease by increase in power law, applying axial pressure load and torsional
torque and increase by applying axial tension force.

کلیدواژه‌ها [English]

  • Non-uniform rotor
  • Whirling
  • Functionally graded materials
  • Differential quadrature method

مراجع

[1] G. Genta, Dynamics of rotating systems, Springer Sciencem & Business Media, 2007.
[2] R. Grybos, The effect of shear and rotary inertia of a rotor at its critical speeds, Archive of applied mechanics, 61(2)(1991) 104-109.
[3] S. Choi, C. Pierre, A. Ulsoy, Consistent modeling of rotating Timoshenko shafts subject to axial loads, Journal of vibration and acoustics, 114(2) (1992) 249-259.
[4] Y.-G. Jei, C.-W. Lee, Modal analysis of continuous asymmetrical rotor-bearing systems, Journal of Sound and Vibration, 152(2) (1992) 245-262.
[5] F. Sturla, A. Argento, Free and forced vibrations of a spinning viscoelastic beam, Journal of vibration and acoustics, 118(3) (1996) 463-468.
[6] J. Melanson, J. Zu, Free vibration and stability analysis of internally damped rotating shafts with general boundary conditions, Journal of vibration and acoustics, 120(3)(1998) 776-783.
[7] O. Jun, J. Kim, Free bending vibration of a multi-step rotor, Journal of sound and vibration, 224(4) (1999) 625-642.
[8] M. Mohiuddin, Y. Khulief, Coupled bending torsional vibration of rotors using finite element, Journal of Sound and Vibration, 223(2) (1999) 297-316.
[9] W. Kim, A. Argento, R. Scott, Free vibration of a rotating tapered composite Timoshenko shaft, Journal of Sound and Vibration, 226(1) (1999) 125-147.
[10] S. Karunendiran, J. Zu, Free vibration analysis of shafts on resilient bearings using Timoshenko beam theory, Journal of vibration and acoustics, 121(2) (1999) 256-258.
[11] N. Shabaneh, J.W. Zu, Dynamic analysis of rotor–shaft systems with viscoelastically supported bearings, Mechanism and machine theory, 35(9) (2000) 1313-1330.
[12] T. El-Mahdy, R. Gadelrab, Free vibration of unidirectional fiber reinforcement composite rotor, in, Academic Press, 2000.
[13] F.A. Raffa, F. Vatta, Equations of motion of an asymmetric Timoshenko shaft, Meccanica, 36(2) (2001)201-211.
[14] U. Gu, C. Cheng, Vibration analysis of a high-speed spindle under the action of a moving mass, Journal of sound and vibration, 278(4-5) (2004) 1131-1146.
[15] M. Behzad, A. Bastami, Effect of centrifugal force on natural frequency of lateral vibration of rotating shafts, Journal of sound and vibration, 274(3-5) (2004) 985-995.
[16] G. Sheu, S.-M. Yang, Dynamic analysis of a spinning Rayleigh beam, International Journal of Mechanical Sciences, 47(2) (2005) 157-169.
[17] J. Banerjee, H. Su, Dynamic stiffness formulation and free vibration analysis of a spinning composite beam,Computers & structures, 84(19-20) (2006) 1208-1214.
[18] S. Hosseini, S. Khadem, Free vibrations analysis of a rotating shaft with nonlinearities in curvature and inertia, Mechanism and Machine theory, 44(1) (2009) 272-288.
[19] B.G. Bazehhour, S.M. Mousavi, A. Farshidianfar, Free vibration of high-speed rotating Timoshenko shaft with various boundary conditions: effect of centrifugally induced axial force, Archive of Applied Mechanics, 84(12) (2014) 1691-1700.
[20] H. Afshari, M. Irani, K. Torabi, Free whirling analysis of multi-step Timoshenko rotor with multiple bearing using DQEM, Modares Mechanical Engineering, 14(10)(2014) 109-120.
[21] M. Irani, A. Mohebbi, H. Afshari, Longitudinal-Torsional and Two Plane Transverse Vibrations of a Composite Timoshenko Rotor, (2016).
[22] K. Torabi, H. Afshari and H. Najafi, Whirling analysis of axial-loaded multi-step Timoshenko rotor carrying concentrated masses, Journal of solid mechanics, 9(1)(2017) 138-156.
[23] K. Torabi, H. Afshari, Exact solution for whirling analysis of axial-loaded Timoshenko rotor using basic functions, Engineering Solid Mechanics, 4(2) (2016) 97-108.
[24] R. Bellman, B. Kashef, J. Casti, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of computational physics, 10(1) (1972) 40-52.
[25] C.W. Bert, S.K. Jang, A.G. Striz, Two new approximate methods for analyzing free vibration of structural components, AIAA journal, 26(5) (1988) 612-618.
[26] C. Bert, M. Malik, Free vibration analysis of tapered rectangular plates by differential quadrature method:a semi-analytical approach, Journal of Sound and Vibration, 190(1) (1996) 41-63.
[27] C.W. Bert, M. Malik, The differential quadrature method for irregular domains and application to plate vibration, International Journal of Mechanical Sciences, 38(6) (1996) 589-606.
[28] C.W. Bert, M. Malik, Differential quadrature method in computational mechanics: a review, Applied mechanics reviews, 49(1) (1996) 1-28.
[29] C.W. Bert, W. Xinwei, A.G. Striz, Differential quadrature for static and free vibration analyses of anisotropic plates, International Journal of Solids and Structures, 30(13) (1993) 1737-1744.
[30] C. Bert, X. Wang, A. Striz, Convergence of the DQ method in the analysis of anisotropic plates, in, Academic Press, 1994.
[31] T. Kaneko, On Timoshenko's correction for shear in vibrating beams, Journal of Physics D: Applied Physics, 8(16) (1975) 1927.
[32] H. Afshari, A. Pouretemad, K. Torabi, Whirling analysis of non-uniform Timoshenko rotors subjected to axial load and torsional torque, in: 6th conference on rotating equipment in oil & power industries, Shahid Beheshti conference center, Tehran, Iran, 2014.
[33] H. Du, M. Lim, R. Lin, Application of generalized differential quadrature method to structural problems, International Journal for Numerical Methods in Engineering, 37(11) (1994) 1881-1896.
[34] H. Du, M. Lim, R. Lin, Application of generalized differential quadrature to vibration analysis, Journal of Sound and Vibration, 181(2) (1995) 279-293.
نشریه مهندسی مکانیک امیرکبیر
دوره 49، شماره 4
اسفند 1396
صفحه 759-772

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