کاهش بهینه ارتعاشات سیستم شفت-دیسک-پره انعطاف پذیر با استفاده از مجموعه چاه های غیرخطی انرژی روی دیسک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، دانشکده مهندسی مکانیک و انرژی، دانشگاه شهید بهشتی، تهران، ایران

2 گروه طراحی کاربردی دانشکده مهندسی مکانیک و انرژی دانشگاه شهید بهشتی

3 استادیار، دانشکده مهندسی مکانیک و انرژی، دانشگاه شهید بهشتی، تهران، ایران

4 استادیار، گروه تجهیزات دوار مکانیکی، پژوهشگاه نیرو، تهران، ایران

چکیده

در این مقاله کاربرد چاه غیرخطی انرژى در کاهش غیرمستقیم ارتعاشات  پرههاى سیستم شفت-دیسک-پره  انعطافپذیر نمونه توربین بخارى واقعی با نصب روى دیسک بررسی  می شود. ٧٣ مجموعه هفت عددى پره متصل به هم در شراد به دور دیسک نصب  شدهاند. از تحلیل المان محدود مدل متقارن  چرخهاى شفت-دیسک-پره براى استخراج مدهاى طبیعی و نمودار فرکانسی استفاده  می شود. مدل  چرخهاى شامل یک مجموعه  هفت پرهاى و برشی از دیسک-شفت است. براى دومین مد فرکانسی ترکیبی که مد خمشی دوم شفت و سوم دیسک-پره است، مدل کاهش مرتبه ٢ درجه آزادى با قابلیت  مدلسازى  نرمشوندگی فرکانسی سیستم شناسایی  می شود. چاه غیرخطی انرژى که شامل یک جرم کوچک، فنر الزاماً غیرخطی و میرایی خطی است روى این مدل در محل جرم مودال دیسک-شفت نصب  می شود. براى حل معادلات غیرخطی سیستم از حل عددى به روش رانگ-کوتا استفاده و پارامترهاى ضریب سفتی و میرایی براى حداقل سازى دامنه ارتعاش پره بهینه  میگردد. نتایج تحلیل، وقوع پاسخ مدوله قوى در  بازهاى حول رزونانس و کاهش مطلوب دامنه ارتعاش پره را نشان  میدهد. سیستم به سفتی غیرخطی حساس است و در ضریب سفتی بزرگ و یا  میراییهاى کوچک، انشعابی زین اسبی در نزدیک رزونانس ایجاد و امکان پاسخ نوسانی ساده دامنه بزرگ وجود خواهد داشت.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Optimal Vibration Reduction of the Flexible Shaft-Disk-Blades System Using a Set of Nonlinear Energy Sink

نویسندگان [English]

  • Jafar Aghayari 1
  • pedram safarpour 2
  • Abbas Rahi 3
  • saeed bab 4
1 PhD Candidate, Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, Tehran, Iran
2 Faculty of Mechanical & Energy Engineering,Shahid Beheshti University
3 Assistant professor, Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, A.C., Tehran, Iran
4 Department of Mechanical Rotary equipment, Niroo Reseach Institute, Tehran, Iran
چکیده [English]

In this paper, the application of nonlinear energy sinks for indirect vibration reduction of the blades in a flexible shaft-disk-blades system of a real steam turbine is conducted. 37 packets of seven-connected blades are mounted on the disk. The cyclic symmetric finite element analysis is employed to perform frequency analysis of this system. For the 11th mode, which is a combination of the second bending mode of shaft and the third bending mode of disk-blades, a two degrees of freedom reduced order model is identified. Nonlinear energy sinks with a small mass, an essential nonlinear stiffness and a linear damping are installed on the reduced order model in the anti-node position of the disk. The Runge-Kutta method is used to solve the nonlinear equations of motion numerically. Optimum stiffness and damping of the absorbers are determined to minimize the vibration amplitude of the blades. The results show that the occurrence of strongly modulated response around the resonance leads to the desired vibration reduction of the blades. If the absorbers have large nonlinear stiffness or low damping, a saddle-node bifurcation and a wide island is appeared in the negative detuning frequencies, and the blade could experience large amplitude periodic oscillation.

کلیدواژه‌ها [English]

  • Flexible shaft-disk-blades
  • Nonlinear energy sink
  • Cyclic symmetry
  • Frequency diagram
  • Strongly modulated response

مراجع

[1] G. Óttarsson, Dynamic modeling and vibration analysis of mistuned bladed disks. (١٩٩٤).
[2] D. J. Mead, Wave propagation and natural modes in periodic systems: I. Mono-coupled systems. Journal of Sound and Vibration,40(1) (1975) 1-18.
[3] B. J. Olson, S. W. Shaw, & C. Pierre, Order-tuned vibration absorbers for a rotating flexible structure with cyclic symmetry. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference-DETC2005 (1) (2005) 2475-2484.
[4]  G. Genta, Dynamics of rotating systems , Springer Science & Business Media, 2007.
[5] B. Zhou, F. Thouverez, & D. Lenoir, Vibration reduction of mistuned bladed disks by passive piezoelectric shunt damping techniques. AIAA journal, (2014).
[6] S. Gozen, B. J. Olson, S. W. Shaw, & C. Pierre, Resonance suppression in multi-degree-of-freedom rotating flexible structures using order-tuned absorbers. Journal of Vibration and Acoustics, 134(6) (2012) 61016.
[7] B. Bergeot, S. Bellizzi, & B. Cochelin, Analysis of steady-state response regimes of a helicopter ground resonance model including a non-linear energy sink attachment. International Journal of Non-Linear Mechanics, 78 (2016) 72–89.
[8] B. Zhou, F. Thouverez, & D. Lenoir, Essentially nonlinear piezoelectric shunt circuits applied to mistuned bladed disks. Journal of Sound and Vibration, 333 (9) (2014) 2520–2542.
[9] M. Singh, SAFE Diagram-A Dresser-Rand Evaluation Tool For Packeted Bladed Disc Assembly. Technology Report Dresser-Rand Company, TP025, (1984).
[10] V. Kharyton, C. Gibert, L. Blanc, & F. Thouverez,Elements of Dynamic Characterization of a Bladed Disk by Using the Tip-Timing Method Under Vacuum Conditions. ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition,  (2011) 1127–1135.
[11] P. Polach, Evaluation of the suitability of the bladeddisk design regarding the danger of the resonant vibration excitation. Engineering Mechanics, 18(3–4) (2011) 181–191.
[12] A. P. I. Std, ٦١٢ Special Purpose Steam Turbines for Petroleum. Chemical and Gas Industry Services, (n.d.).
[13] Y.-J. Chiu, X.-Y. Li, Y.-C. Chen, S.-R. Jian, C.H. Yang, & I.-H. Lin, Three methods for studying coupled vibration in a multi flexible disk rotor system. Journal of Mechanical Science and Technology,  31 (11) (2017) 5219–5229.
[14] S. Bab, S. E. Khadem, & M. Shahgholi, Lateralvibration attenuation of a rotor under mass eccentricity force using non-linear energy sink. International Journal of Non-Linear Mechanics, 67(2014) 251–266.
[15] B. Bergeot, S. Bellizzi, & B. Cochelin, Passivesuppression of helicopter ground resonance using nonlinear energy sinks attached on the helicopter blades. Journal of Sound and Vibration, 392 (2017)41-55.
[16] B. Mokrani & A. Preumont, A numerical and experimental investigation on passive piezoelectric shunt damping of mistuned blisks. Journal of Intelligent Material Systems and Structures, (2017) 1045389X17721023..
[17] S. M. Schwarzendahl, J. Szwedowicz, M. Neubauer, L. Panning, & J. Wallaschek, On blade damping technology using passive piezoelectric dampers. ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, (2012) 1205–1215.
[18] A. S. Alsuwaiyan & S. W. Shaw, Performance and dynamic stability of general-path centrifugal pendulum vibration absorbers. Journal of Sound and Vibration, 252 (5) (2002) 791–815.
[19] O. V. Gendelman, Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn. , Springer, 2001,pp. 237–253.
[20] O. Gendelman, L. I. Manevitch, A. F. Vakakis, & R. M’closkey, Energy pumping in nonlinear mechanical oscillators: Part I-Dynamics of the underlying Hamiltonian systems. Journal of Applied Mechanics, 68 (1) (2001) 34–41.
[21] O. V Gendelman, G. Sigalov, L. I. Manevitch, M. Mane, A. F. Vakakis, & L. A. Bergman, Dynamics of an eccentric rotational nonlinear energy sink. Journal of applied mechanics, 79 (1) (2012) 11012..
 [22] Y. S. Lee, F. Nucera, A. F. Vakakis, D. M. McFarland, & L. A. Bergman, Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Physica D: Nonlinear Phenomena,238 (18) (2009) 1868-1896.
[23] S. Bab, S. E. Khadem, M. K. Mahdiabadi, & M. Shahgholi, Vibration mitigation of a rotating beam under external periodic force using a nonlinear energy sink (NES). Journal of Vibration and Control, 23 (6) (2017) 1001–1025.
[24] E. Gourdon, N. A. Alexander, C. A. Taylor, C.-H. Lamarque, & S. Pernot, Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results. Journal of sound and vibration,300 (3) (2007)522–551.
[25] A. F. Vakakis, O. V Gendelman, L. A. Bergman,D. M. McFarland, G. Kerschen, & Y. S. Lee, Nonlinear targeted energy transfer in mechanical and structural systems , Springer Science & Business Media, 2008.
[26] Z. Lu, Z. Wang, Y. Zhou, & X. Lu, Nonlinear dissipative devices in structural vibration control: A review. Journal of Sound and Vibration, 423(2018) 18–49.
[27] S. Bab, S. E. Khadem, M. Shahgholi, & A. Abbasi, Vibration attenuation of a continuous rotor- blisk-journal bearing system employing smooth nonlinear energy sinks. Mechanical Systems and Signal Processing, 84 (2017) 128–157.
[28] C. Guo, M. A. AL-Shudeifat, A. F. Vakakis, L. A. Bergman, D. M. McFarland, & J. Yan, Vibration reduction in unbalanced hollow rotor systems with nonlinear energy sinks. Nonlinear Dynamics, 79(1) (2015) 527–538.
[29] Y. S. Lee, A. F. Vakakis, L. A. Bergman, D. M.McFarland, & G. Kerschen, Suppressing aeroelastic instability using broadband passive targeted energy transfers, part ١: theory. AIAA journal, 45 (3)(2007) 693.
[30] Y. S. Lee, G. Kerschen, D. M. McFarland, W. J.Hill, C. Nichkawde, T. W. Strganac, L. A. Bergman, A. F. Vakakis, L. A. Bergman, D. M. McFarland, & G. Kerschen, Suppressing aeroelastic instability using broadband passive targeted energy transfers, part ٢: experiments. AIAA journal, 45 (10) (2007)2391.
[31]  H. Guo, Y. Chen, & T. Yang, Limit cycle oscillationsuppression of ٢-DOF airfoil using nonlinear energy sink. Applied Mathematics and Mechanics, 34 (10) (2013) 1277–1290.
[32] M. A. AL-Shudeifat, Highly efficient nonlinear energy sink. Nonlinear Dynamics, 76 (4) (2014)1905–1920..
[33] ANSYS Inc. Release ١٥.٠, ANSYS Mechanical APDL Element Reference. (2013).
[34] A. Muszynska, Rotordynamics , CRC press, 2005.
[35] E. I. Rivin, Handbook on stiffness & damping inmechanical design , ASME Press New York, 2010.
[36] M. P. Norton & D. G. Karczub, Fundamentalsof noise and vibration analysis for engineers , Cambridge university press, 2003.
نشریه مهندسی مکانیک امیرکبیر
دوره 52، شماره 12
اسفند 1399
صفحه 3425-3444

فایل ها

هم رسانی

ارجاع به این مقاله

آمار