Elechtromechanical Modeling and Vibration Analysis of a Coupled Hydroturbine-Generator Set at Different Speeds Considering the Gyroscopic Effect

Subject Areas : Renewable energy

Mohammad Farokhpour ¹ (Islamic Azad University Najafabad Branch)
Ali Soleimani ² (Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University)

Received: 2022-08-02 Accepted : 2022-12-01 Published : 2022-12-01

Keywords: Chaos, vibrations, Gyroscopic effect, Generator, Imbalance mass, Arcuate whirl, hydroturbine,

Abstract :

Vibrations in rotating equipment are inevitable phenomena and its analysis is necessary and useful to study the condition of the equipment. In a coupled hydroturbine-generator set, the vibrations are caused by the dynamic forces of both machines. Due to the coupling of the turbine and the generator the vibration analysis of each machine separately can not reveal all the phenomena and dynamic behaviors. The change in speed and torque of the turbine and the generator affect each other, so the results of the coupling analysis are closer to reality. In this paper, dynamic modeling of the generator-turbine coupling set is performed and the governing equations of the system are solved using numerical methods in MATLAB software. For more accurate modeling and analysis of the system, the rotational speed of the shaft is considered as variable. The gyroscopic effect and arcuate whirl are also included in the modeling of the set. The frequencies in the vibrations of the set are extracted and the dynamic phenomena related to each are identified. The results show that new dynamic and vibrational phenomena in this system. Also, considering that imbalance mass is never zero, the resulting force is considered in the modeling and the effect of the amount of imbalance mass is also studied and analyzed. Due to the nonlinearity of the governing equations, the analysis of vibrations using phase plane diagrams shows that in some operating conditions, the vibration behavior is chaotic, which can be used in the processing of experimental signals.

References:

[1] B.B. Xu, D.Y. Chen, H. Zhang, C. Li, J. Zhou, "Shaft mis-alignment induced vibration of a hydraulic turbine generating system considering parametric uncertainties", Journal of Sound and Vibration, vol. 435, pp. 74-90, Nov. 2018 (doi: 10.1016/j.jsv.2018.08.008).

[2] Z. Song, Y. Liu, P. Guo, J. Feng, "Torsional vibration analysis of hydro-generator set considered electromagnetic and hydraulic vibration resources coupling", International Journal of Precision Engineering and Manufacturing, vol. 19, no. 7, pp. 939-945, July 2018 (doi: 10.1007/s12541-018-0111-2).

[3] J.J. Perez-Loya, C.J.D. Abrahamsson, U. Lundin, "Electromagnetic losses in synchronous machines during active compensation of unbalanced magnetic pull", IEEE Trans. on Industrial Electronics, vol. 66, no. 1, pp. 124-131, April 2018 (doi: 10.1109/tie.2018.2827991).

[4] C. Trivedi, "A review on fluid structure interaction in hydraulic turbines: A focus on hydrodynamic damping", Engineering Failure Analysis, vol. 77, pp. 1-22, July 2017 (doi: 10.1016/j.engfailanal.201­7.02.­0­2­1).

[5] O. Giannini, "Unstable transient response of gyroscopic systems with stable eigenvalues", Mechanical Systems and Signal Processing, vol. 75, pp. 1-10, June 2016 (doi: 10.1016/j.ymssp.2016.01.008).

[6] X. H. Zeng, H. Wu, J. Lai, Y. Yu, "The effect of wheel set gyroscopic action on the hunting stability of high-speed trains", Vehicle System Dynamics, vol. 55, no. 6, pp. 924-944, June 2017 (doi: 10.1080/00423114.20­17.129­3833).

[7] H. Ma, H. Li, X. Zhao, H. Niu, B. Wen, "Effects of eccentric phase difference between two discs on oil-film instability in a rotor–bearing system", Mechanical Systems and Signal Processing, vol. 41, no. 1-2, pp. 526-545, Dec. 2013 (doi: 10.1016/j.ymssp.2013.05.006).

[8] B.B. Xu, D.Y. Chen, H. Zhang, R. Zhou, "Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit", Nonlinear Dynamics, vol. 81, pp. 1263-1274, Aug. 2015 (doi: 10.1007/s11071-015-2066-5).

[9] L.K. Zhang, Z.Y. Ma, B.W. Song, "Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull", Archive of Applied Mechanics, vol. 83, no. 6, pp. 17-830, June 2013 (doi: 10.1007/s00419-012-0719-0).

[10] T.H. Patel, M.J. Zuo, X. Zhao, "Nonlinear lateral-torsional coupled motion of a rotor contacting a viscoe­lastically suspended stator", Nonlinear Dynamics, vol. 69, no. 1-2, pp. 325-339, July 2012 (doi: 10.100­7/s­1107­1-011-0267-0).

[11] S.E. Masalegoo, A. Soleimani, "Electromechanical analysis of coupled motor-gearbox vibrations with pla­netary gears", Journal of Intelligent Procedures in Electrical Technology, vol. 14, no. 56, pp. 151-168, Feb. 2022 (in Persian) (dor: 20.1001.1.23223871.1402.14.56.8.8).

[12] J. Mostafaee, S. Mobayen, B. Vaseghi, M. Vahedi, "Dynamical analysis and finite-time fast synchronization of a novel autonomous hyper-chaotic system", Journal of Intelligent Procedures in Electrical Technology, vol. 12, no. 47, pp. 73-93, Dec. 2021 (in Persian) (dor: 20.1001.1.23223871.1400.12.3.6.6).

[13] A. Shoulaie, M. Bayati-Poudeh, G. Shahgholian, "Damping torsional torques in turbine-generator shaft by novel PSS based on genetic algorithm and fuzzy logic", Journal of Intelligent Procedures in Electrical Technology, vol. 1, no. 2, pp. 3-10, Sep. 2010 (in Persian) (dor: 20.1001.1.23223871.1389.1.2.1.2).

[14] A. Soleimani, S.E. Khadem, "Experimental fault detection of a ball bearing using chaotic behavior features of a vibration signal", Modares Mechanical Engineering, vol. 15, no. 2, pp. 289-297, April 2015 (in Persian) (dor: 20.1001.1.10275940.1394.15.2.20.8).

[15] Y. Shi, J. Zhou, "Stability and sensitivity analyses and multi-objective optimization control of the hydro-turbine generator unit", Nonlinear Dynamics, vol. 107, pp. 2245-2273, Feb. 2022 (doi: 10.1007/s11071-021-07009-7).

[16] K. Zhuang, S. Huang, X. Fu, L. Chen, "Nonlinear hydraulic vibration modeling and dynamic analysis of hydro-turbine generator unit with multiple faults", Energies, vol. 15, no. 9, Article Number: 3386, May 2022 (doi: 10.3390/en15093386).

[17] J. Li, D. Chen, G. Liu, X. Gao, K. Miao, Y. Li, B. Xu, "Analysis of the gyroscopic effect on the hydro–turbine generator unit", Mechanical Systems and Signal Processing, vol. 132, pp. 138-152, Oct. 2019 (doi: 10.1016/j.ymssp.2019.06.020).

[18] Y. Shi, J. Zhou, X. Lai, Y. Xu, W. Guo, B. Liu, "Stability and sensitivity analysis of the bending-torsional coupled vibration with the arcuate whirl of hydro-turbine generator unit", Mechanical Systems and Signal Processing, vol. 149, Article Number: 107306, Feb. 2021 (doi: 10.1016/j.ymssp.2020.107306).

[19] W. Sun, Z. Guo, "Mathematical modeling and nonlinear vibration analysis of a coupled hydro-generator shaft-foundation system", Communications in Nonlinear Science and Numerical Simulation, vol. 98, Article Number: 105776, July 2021 (doi: 10.1016/j.cnsns.2021.105776).

[20] G. Kahraman, O. Ozdemir, "Mathematical modeling of vibration failure caused by balancing effect in hydraulic turbines", Mechanics Based Design of structures and Machines, vol. 51:3, pp. 1489-1500, Jan. 2021 (doi: 10.1080/15397734.2021.1873148).