تعیین حساسیت رفتار دینامیکی روتور به تلرانس‌های تولید با استفاده از تحلیل حساسیت کلی و روش آماری

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، دانشکده مهندسی مکانیک دانشگاه علم و صنعت ایران

2 علم و صنعت

چکیده

عدم قطعیت در پارامترها سبب می‌گردد تا سازه‌های با شرایط نامی یکسان دارای مقادیر متفاوت فرکانس‌های طبیعی و پاسخ ارتعاشی باشند. علی‌رغم اهمیت مساله ارتعاشات در توربوماشین‌ها به دلیل ماهیت دورانی آن‌ها و لزوم تعیین دقیق سرعت‌های بحرانی در این سیستم‌ها، تاکنون در زمینه بررسی حساسیت رفتار ارتعاشی سیستم‌های دوار به عدم قطعیت پارامترها مطالعه و بررسی کافی انجام نشده است. در این مقاله حساسیت کلی سرعت‌های بحرانی یک کمپرسور صنعتی نسبت به پارامترهای طراحی آن محاسبه شده است. همچنین نشان داده شده است که استفاده از روش مشتق‌گیری به عنوان روشی متداول در مراجع، تنها حساسیت محلی پارامتر را نشان می‌دهد و جهت درنظرگرفتن درجه اهمیت یک پارامتر بر روی خروجی مدل، باید حساسیت کلی پارامتر مورد بررسی قرار گیرد. در این بررسی، یک چهارچوب کلی جهت بررسی حساسیت سیستم‌های دوار صنعتی بر اساس روش تحلیل حساسیت کلی و تجزیه وردایی سوبول با به کارگیری روش مونت کارلو، ارائه شده است. در این روش عدم قطعیت موجود در پاسخ سیستم به عدم قطعیت پارامترهای آن به صورت کمی نسبت داده شده است و تحلیلی کمی را در کنار پیش بینی‌های کیفی در اختیار قرار می‌دهد. روش ارائه شده در طراحی ماشین دوار می‌تواند برای تدوین دستورالعمل‌های تلرانس‌گذاری اجزا سیستم مورد نظر مفید می‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Sensitivity Analysis of Rotor Dynamic Behavior to Manufacturing Tolerances Based on Global Sensitivity Analysis and Statistical Methods

نویسندگان [English]

  • Zahra Taherkhani 1
  • Hamid Ahmadian 2
1 School of Mechanical Engineering, Iran University of Science and Technology
چکیده [English]

Engineering structures are inevitably exposed to various sources of uncertainty. The uncertainty in the parameters led to structures with identical nominal parameters having different vibrational behavior, such as different natural frequencies. Therefore, it is inevitable to consider parameter variability for a robust design. The rotational motion of turbomachinery makes vibration an important issue in their design. Therefore, it is essential to accurately determine the vibrational behavior of rotating systems and the parameters affecting them. No comprehensive experimental study is reported on the sensitivity of vibration behavior of industrial rotating systems to parameter uncertainty in the related literature. Therefore, in this paper, a powerful method of global sensitivity analysis based on variance analysis is presented using an industrial compressor sample to determine the effective parameters in its response uncertainty. The Monte Carlo simulation method is adopted to implement the global sensitivity analysis method. In this method, the uncertainty in the system response quantifiably devotes itself to the uncertainty of its parameters and provides a quantitative analysis along with qualitative predictions to the designer. The presented method in this paper can be very useful in designing rotating machinery and identifying sensitive parameters on the system response for the codification of design and manufacturing instructions, like component tolerance.

کلیدواژه‌ها [English]

  • Rotor dynamics
  • Global Sensitivity Analysis
  • Monte Carlo
  • Uncertainty
  • model updating
[1] J.E. Mottershead, M. Friswell, Model updating in structural dynamics: a survey, Journal of sound and vibration, 167(2) (1993) 347-375.
[2] C. Mares, J. Mottershead, M. Friswell, Stochastic model updating: part 1—theory and simulated example, Mechanical systems and signal processing, 20(7) (2006) 1674-1695.
[3] J. Mottershead, C. Mares, S. James, M. Friswell, Stochastic model updating: part 2—application to a set of physical structures, Mechanical Systems and Signal Processing, 20(8) (2006) 2171-2185.
[4] W.-X. Ren, H.-B. Chen, Finite element model updating in structural dynamics by using the response surface method, Engineering structures, 32(8) (2010) 2455-2465.
[5] H.-P. Wan, W.-X. Ren, Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel, Journal of Structural Engineering, 141(6) (2015) 04014164.
[6]  A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity analysis in practice: a guide to assessing scientific models, Wiley Online Library, 2004.
[7] Z. Kala, Sensitivity assessment of steel members under compression, Engineering Structures, 31(6) (2009) 1344-1348.
[8] J. Rohmer, E. Foerster, Global sensitivity analysis of large-scale numerical landslide models based on Gaussian-Process meta-modeling, Computers & geosciences, 37(7) (2011) 917-927.
[9] I.M. Sobol, Sensitivity analysis for non-linear mathematical models, Mathematical modelling and computational experiment, 1 (1993) 407-414.
[10]  W. Becker, J. Oakley, C. Surace, P. Gili, J. Rowson, K. Worden, Bayesian sensitivity analysis of a nonlinear finite element model, Mechanical Systems and Signal Processing, 32 (2012) 18-31.
[11] N.A. Husain, H.H. Khodaparast, H. Ouyang, Parameter selection and stochastic model updating using perturbation methods with parameter weighting matrix assignment, Mechanical Systems and Signal Processing, 32 (2012) 135-152.
[12] H.-P. Wan, Z. Mao, M.D. Todd, W.-X. Ren, Analytical uncertainty quantification for modal frequencies with structural parameter uncertainty using a Gaussian process metamodel, Engineering Structures, 75 (2014) 577-589.
[13] G. Steenackers, P. Guillaume, Finite element model updating taking into account the uncertainty on the modal parameters estimates, Journal of Sound and vibration, 296(4-5) (2006) 919-934.
[14] S. Marino, I.B. Hogue, C.J. Ray, D.E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, Journal of theoretical biology, 254(1) (2008) 178-196.
[15] S.-E. Fang, W.-X. Ren, R. Perera, A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation, Mechanical Systems and Signal Processing, 33 (2012) 83-96.
[16] A.C. Balbahadur, A thermoelastohydrodynamic model of the Morton effect operating in overhung rotors supported by plain or tilting pad journal bearings, Virginia Tech, 2001.
[17] M. Lalanne, G. Ferraris, Rotordynamics prediction in engineering, Wiley, 1998.
[18] G. Genta, Dynamics of rotating systems, Springer Science & Business Media, 2007.
[19] Zahra Taherkhani, Hamidreza Pourtaba, Geometry Effects in Tilting-Pad dynamic Coefficients and Critical Speeds of a Rotor, in:  Preceding in The Biennial International Conference on Experimental Solid Mechanics (X-Mech 2016). 2016.
[20] A. Tamer, P. Masarati, Periodic stability and sensitivity analysis of rotating machinery, in:  Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, Springer, 2015, pp. 2059-2070.
[21] S. Yan, R. Sievert, Vibration sensitivity of large turbine generator shaft trains to unbalance, in:  Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, Springer, 2015, pp. 3-14.
[22] T. Leister, C. Baum, W. Seemann, Sensitivity of computational rotor dynamics towards the empirically estimated lubrication gap clearance of foil air journal bearings, PAMM, 16(1) (2016) 285-286.
[23] F.A. Lara-Molina, A.A. Cavalini Jr, E.H. Koroishi, V. Steffen Jr, Sensitivity analysis of flexible rotor subjected to interval uncertainties, Latin American Journal of Solids and Structures, 16(4) (2019).
[24] D. Xie, Y. Yang, S. Gao, J. Guo, Sensitivity Analysis on the Dynamic Characteristics of a 1000 MW Turbo-Generator Rotor, in:  Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, Springer, 2015, pp. 1841-1852.
[25] S. Asadi, V. Berbyuk, H. Johansson, Global Sensitivity Analysis of High Speed Shaft Subsystem of a Wind Turbine Drive Train, International Journal of Rotating Machinery, 2018 (2018).
[26] L. Urbiola-Soto, Multivariate Response Rotordynamic Modeling and Sensitivity Analysis of Tilting Pad Bearings, Journal of Engineering for Gas Turbines and Power, 140(7) (2018).
[27] R. Khatri, D.W. Childs, An experimental study of the load-orientation sensitivity of three-lobe bearings, Journal of Engineering for Gas Turbines and Power, 137(4) (2015).
[28] Y. Ma, Z. Liang, M. Chen, J. Hong, Interval analysis of rotor dynamic response with uncertain parameters, Journal of Sound and Vibration, 332(16) (2013) 3869-3880.
[29] E.H. Koroishi, A.A. Cavalini Jr, A.M. de Lima, V. Steffen Jr, Stochastic modeling of flexible rotors, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 34(SPE2) (2012) 574-583.
[30] N. Wang, D. Jiang, H. Xu, Dynamic characteristics analysis of a dual-rotor system with inter-shaft bearing, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 233(3) (2019) 1147-1158.
[31] M.H. Jalali, M. Ghayour, S. Ziaei-Rad, B. Shahriari, Dynamic analysis of a high speed rotor-bearing system, Measurement, 53 (2014) 1-9.
[32] I.y.M. Sobol', Global sensitivity indices for the investigation of nonlinear mathematical models, Matematicheskoe modelirovanie, 17(9) (2005) 43-52.
[33] R.d.O. Teloli, S. da Silva, T.G. Ritto, G. Chevallier, Bayesian model identification of higher-order frequency response functions for structures assembled by bolted joints, Mechanical Systems and Signal Processing, 151 (2021) 107333.
[34] N.C. Tyminski, H.F. de Castro, Application of Bayesian inference to unbalance identification in rotors, in:  Proceedings of the 9th IFToMM international conference on rotor dynamics, Springer, 2015, pp. 711-721.
[35] J.W. Hall, L.J. Manning, R.K. Hankin, Bayesian calibration of a flood inundation model using spatial data, Water Resources Research, 47(5) (2011).
[36] E.T. Jaynes, Probability theory: The logic of science, Cambridge university press, 2003.
[37] J.L. Beck, L.S. Katafygiotis, Updating models and their uncertainties. I: Bayesian statistical framework, Journal of Engineering Mechanics, 124(4) (1998) 455-461.
[38] E.T. Jaynes, Prior probabilities, IEEE Transactions on systems science and cybernetics, 4(3) (1968) 227-241.