Abstract
Purpose
The effect of an asymmetric transversal section on the rotor vibration behavior has recently acquired great interest, mainly due to the expansion in the usage of this type of rotor as well as the lack of effective balancing methods. In this work, an integrated method for Balancing Asymmetric Rotor-Bearing Systems is presented.
Methods
The proposed method consists in using the advantages of the conventional modal balancing (modal masses array) and then combining it with the methodology of parameter algebraic identification; the latter allows identifying both the magnitude as well as the angular position of the unbalance at low rotor speed regardless the nominal speed, preventing the system from operating at a critical speed. The proposed algebraic identifier requires the rotor vibration response as input data, instead of the vibration response produced by trial masses required in the conventional balancing methods. Likewise, the use of active balancing disks (ABDs) is proposed for rotor balancing.
Results
The identification of the unbalance parameters and their angular position was numerically validated by considering that the rotor operates at (a) constant speed and (b) variable speed at different angular velocities with lineal coast up. The proposed methodology was used to numerically balance a multiple degree-of-freedom rotor with unequal principal moments of inertia of the shaft transverse section and discrete unbalance, achieving a reduction of more than 95% in the vibration amplitude of the rotor in resonance for four vibration modes. The numerical results showed that a single trial balancing run is required to balance the asymmetric rotor-bearing system in situ.
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References
Ikeda T, Murakami S (1999) Dynamic response and stability of a rotating asymmetric shaft mounted on a flexible base. Nonlinear Dyn 20:1–19. https://doi.org/10.1023/A:1008302203981
Ganesan R (2000) Effects of bearing and shaft asymmetries on the instability of rotors operating at near-critical speeds. Mech Mach Theory 35:737–752. https://doi.org/10.1016/S0094-114X(99)00038-5
Kang Y, Hwang W-W (1996) Influence of bearing damping on instability of asymmetric shafts—Part I. Stabilizing and destabilizing effects. Int J Mech Sci 38:1349–1358. https://doi.org/10.1016/0020-7403(96)87213-4
Kang Y, Lee Y-G (1996) Influence of bearing damping on instability of asymmetric shafts—Part II. Mode veering Int J Mech Sci 38:1359–1365. https://doi.org/10.1016/0020-7403(96)00028-8
Kang Y, Lee Y-G (1997) Influence of bearing damping on instability of asymmetric shafts—Part III. Disk effects Int J Mech Sci 39:1055–1065. https://doi.org/10.1016/S0020-7403(97)00006-4
Wettergren HL, Olsson K-O (1996) Dynamic instability of a rotating asymmetric shaft with internal viscous damping supported in anisotropic bearings. J Sound Vib 195:75–84. https://doi.org/10.1006/jsvi.1996.0404
Ferfecki P, Zaoral F, Zapoměl J (2019) Using floquet theory in the procedure for investigation of the motion stability of a rotor system exhibiting parametric and self-excited vibration. Strojnícky časopis - J Mech Eng 69:33–42. https://doi.org/10.2478/scjme-2019-0027
Zheng Z, Xie Y, Zhang D, Ye X (2019) Effects of stator stiffness, gap size, unbalance, and shaft’s asymmetry on the steady-state response and stability range of an asymmetric rotor with rub-impact. Shock Vib 2019:1–11. https://doi.org/10.1155/2019/6162910
Bharti SK, Sinha A, Samantaray AK, Bhattacharyya R (2020) The Sommerfeld effect of second kind: passage through parametric instability in a rotor with non-circular shaft and anisotropic flexible supports. Nonlinear Dyn 100:3171–3197. https://doi.org/10.1007/s11071-020-05681-9
Ishida Y, Liu J (2010) Elimination of unstable ranges of rotors utilizing discontinuous spring characteristics: an asymmetrical shaft system, an asymmetrical rotor system, and a rotor system with liquid. J Vib Acoust 132:0110111–0110118. https://doi.org/10.1115/1.4000842
Ghasabi SA, Arbabtafti M, Shahgholi M (2020) Time-delayed control of a nonlinear asymmetrical rotor near the major critical speed with flexible supports. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2020.1715230
Fan Y-H, Chen S-T, Lee A-C (1992) Active control of an asymmetrical rigid rotor supported by magnetic bearings. J Franklin Inst 329:1153–1178. https://doi.org/10.1016/0016-0032(92)90009-6
Brahem M, Chouchane M, Amamou A (2020) Active vibration control of a rotor bearing system using flexible piezoelectric patch actuators. J Intell Mater Syst Struct 31:1284–1297. https://doi.org/10.1177/1045389X20916804
Lai T, Liu J (2020) Active vibration control of a rotor-bearing-actuator system using robust eigenvalue placement method. Meas Control 53:531–540. https://doi.org/10.1177/0020294019836125
Taylor HD (1940) Critical speed behavior of unsymmetrical shafts. J Appl Mech 7:A71–A79. https://doi.org/10.1115/1.4009017
Bishop RED, Parkinson AG (1965) Second order vibration of flexible shafts. Philos Trans R Soc London Ser A, Math Phys Sci 259:1–31. https://doi.org/10.1098/rsta.1965.0052
Matsukura Y, Inoue T, Kiso M et al (1979) Estimation of the distributing cross sectional asymmetry along the rotor axis. Bull JSME 22:491–496. https://doi.org/10.1299/jsme1958.22.491
Parkinson AG (1966) On the balancing of shafts with axial asymmetry. Proc R Soc London Ser A Math Phys Sci 294:66–79. https://doi.org/10.1098/rspa.1966.0194
Matsukura Y, Kiso M, Inoue T, Tomisawa M (1979) On the balancing convergence of flexible rotors, with special reference to asymmetric rotors. J Sound Vib 63:419–428. https://doi.org/10.1016/0022-460X(79)90684-9
Songbo, X., W. Xinghua, W. Guangming, P. Yucai, L. Rongqiang, and X. Shichang (1989) A New Balance Method for Flexible Rotors with Asymmetric Principal Stiffnesses. American Society of Mechanical Engineers, Design Engineering Division (Publication) 18:1
Shiraki K, Kanki H (1975) New field balancing method on tandem connected multi-span flexible rotor system. In: in Dynamics of Rotors (IUTAM Symposium Lyngby, Denmark, August 12–16, 1974). The Proceedings of the Symposium, pp 494–523
Kang Y, Liu C-P, Sheen G-J (1996) A modified influence coefficient method for balancing unsymmetrical rotor-bearing systems. J Sound Vib 194:199–218. https://doi.org/10.1006/jsvi.1996.0353
Kang Y, Sheen G-J, Wang S-M (1997) Development and modification of a unified balancing method for unsymmetrical rotor-bearing systems. J Sound Vib 199:349–369. https://doi.org/10.1006/jsvi.1996.0652
Kang Y, Chiang C-P, Wang C-C et al (2003) The minimization method of measuring errors for balancing asymmetrical rotors. JSME Int J Ser C 46:1017–1025. https://doi.org/10.1299/jsmec.46.1017
Colín Ocampo J, Gutiérrez Wing ES, Ramírez Moroyoqui FJ et al (2017) A novel methodology for the angular position identification of the unbalance force on asymmetric rotors by response polar plot analysis. Mech Syst Signal Process 95:172–186. https://doi.org/10.1016/j.ymssp.2017.03.028
Fliess M, Sira-Ramírez H (2003) An algebraic framework for linear identification. ESAIM Control Optim Calc Var 9:151–168. https://doi.org/10.1051/cocv:2003008
Blanco-Ortega A, Silva-Navarro G, Coln-Ocampo J et al (2012) Automatic balancing of rotor-bearing systems. Advances on analysis and control of vibrations - theory and applications. InTech
Beltran-Carbajal F, Silva-Navarro G, Arias-Montiel M (2013) Active unbalance control of rotor systems using on-line algebraic identification methods. Asian J Control 15:1627–1637. https://doi.org/10.1002/asjc.744
Arias-Montiel M, Beltrán-Carbajal F, Silva-Navarro G (2014) On-line algebraic identification of eccentricity parameters in active rotor-bearing systems. Int J Mech Sci 85:152–159. https://doi.org/10.1016/j.ijmecsci.2014.05.027
Mendoza Larios JG, Colín Ocampo J, Blanco Ortega A et al (2016) Balanceo Automático de un Sistema Rotor-Cojinete: Identificador Algebraico en Línea del Desbalance Para un Sistema Rotodinámico. Rev Iberoam Automática e Informática Ind RIAI 13:281–292. https://doi.org/10.1016/j.riai.2016.03.004
Colín Ocampo J, Mendoza Larios JG, Blanco Ortega A et al (2016) Determinación del Desbalance en Sistemas Rotor-cojinete a velocidad constante: Método de Identificación Algebraica. Ing mecánica, Tecnol y Desarro 5:385–394
Mendoza-Larios JG, Barredo E, Arias-Montiel M et al (2021) An algebraic approach for identification of rotordynamic parameters in bearings with linearized force coefficients. Mathematics 9:2747. https://doi.org/10.3390/math9212747
Lalanne M, Ferraris G (1988) Rotordynamics prediction in engineering, 2nd edn. John Wiley and Sons
Blanco-Ortega A, Beltran-Carbajal F, Favela-Contreras A, Silva-Navarro G (2008) Active disk for automatic balancing of rotor-bearing sytems. In: 2008 American Control Conference. IEEE, pp 3023–3028
Blanco-Ortega A, Beltrán-Carbajal F, Silva-Navarro G, Méndez-Azúa H (2010) Control de Vibraciones en Maquinaria Rotatoria. Rev Iberoam Automática e Informática Ind RIAI 7:36–43. https://doi.org/10.1016/S1697-7912(10)70058-3
Bishop RED, Parkinson AG (1972) On the use of balancing machines for flexible rotors. J Eng Ind 94:561–572. https://doi.org/10.1115/1.3428193
Bishop RED, Gladwell GML (1959) The vibration and balancing of an unbalanced flexible rotor. J Mech Eng Sci 1:66–77. https://doi.org/10.1243/JMES_JOUR_1959_001_010_02
Lin YH (1994) Vibration analysis of timoshenko beams transversed by moving loads. J Mar Technol 2:25–35
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Baltazar-Tadeo, L.A., Colín-Ocampo, J., Mendoza-Larios, J.G. et al. An Integrated Balancing Method for Asymmetric Rotor-Bearing Systems: Algebraic Identification, Modal Balancing, and Active Balancing Disks. J. Vib. Eng. Technol. 11, 619–645 (2023). https://doi.org/10.1007/s42417-022-00598-6
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DOI: https://doi.org/10.1007/s42417-022-00598-6