Abstract
When rotor systems operate near resonance points, the amplitudes of the system become very large. Therefore, the dynamic characteristics of the system are determined by various nonlinearities that depend on the displacements. In this paper, the nonlinear forces caused by the fluid-film of the squeeze-film damper (SFD) and the cubic nonlinearity of the system are considered as sources of nonlinearity in the rotor systems. In addition, no matter how precisely the rotor system is manufactured, there will certainly exist some faults; therefore, such faults should be reflected in the system model, in order to accurately analyze the dynamic behavior of the system. In this paper, cubic nonlinearity and nonlinearity in SFD is together considered in the rotor systems with initial bow and used to study the dynamic behavior of the system. The equation of motion of the system is solved by combining the classical incremental harmonic balance (IHB) method and the modified IHB method, and stability analysis of the solutions of rotor systems is performed using the Floquet theory. Frequency–response curves, time histories, Poincaré sections and disk-centered whirl orbits according to the change of system parameters are constructed. The calculated results can contribute to studying the response characteristics of rotor systems with an initial bow.
Similar content being viewed by others
Data availability
All data generated or analyzed during this study are included in this published article.
References
Nicholas, J.C., Gunter, E.J., Allaire, P.E.: Effect of residual shaft bow on unbalance response and balancing of a single mass flexible rotor part1: unbalance response. J. Eng. Gas. Turb. Power 98(2), 171–189 (1976)
Flack, R.D., Rooke, J.H., Bielk, J.R., Gunter, E.J.: Comparison of the unbalance responses of Jeffcott rotors with shaft bow and shaft runout. J. Mech. Des. 104, 318–328 (1982)
Parkinson, A.G., Darlow, M.S., Smalley, A.J.: Balancing flexible rotating shafts with an initial bend. AIAA J. 22(5), 683–689 (1984)
Shiau, T.N., Lee, E.K.: The residual shaft bow effect on dynamic response of a simply supported rotor with disk skew and mass unbalances. J. Vib. Acoust. Stress Reliab. Des. 111, 170–178 (1989)
Darpe, A.K., Gupta, K., Chawla, A.: Dynamics of a bowed rotor with a transverse surface crack. J. Sound Vib. 296, 888–907 (2006)
Shen, X., Jia, J., Zhao, M.: Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow. Arch. Appl. Mech. 78, 225–240 (2008)
Song, G.F., Yang, Z.J., Ji, C., Wang, F.P.: Theoretical–experimental study on a rotor with a residual shaft bow. Mech. Mach. Theory 63, 50–58 (2013)
Chen, Y., Kuo, C.: Dynamic analysis of a geared rotor-bearing system with translational motion due to shaft deformation under residual shaft bow effect. MATEC Web Conf. 119, 01014 (2017)
Chen, Y.: Effect of residual shaft bow on the dynamic analysis of a double-stage geared rotor-bearing system with translational motion due to shaft deformation. Adv. Mech. Eng. 11(5), 1–13 (2019)
Yang, Y., Yang, Y., Ouyang, H., Li, X., Cao, D.: Dynamic performance of a rotor system with an initial bow and coupling faults of imbalance-rub during whirling motion. J. Mech. Sci. Technol. 33(10), 1–13 (2019)
Saeed, N.A.: On the steady-state forward and backward whirling motion of asymmetric nonlinear rotor system. Eur. J. Mech. A Solids 80, 103878 (2019)
Saeed, N.A., Awwad, E.M., El-Meligy, M.A., Nasr, E.A.: Sensitivity analysis and vibration control of asymmetric nonlinear rotating shaft system utilizing 4-pole AMBs as an actuator. Eur. J. Mech. A Solids 86, 104145 (2021)
Saeed, N.A., Eissa, M.: Bifurcation analysis of a transversely cracked nonlinear Jeffcott rotor system at different resonance cases. Int. J. Acoust. Vib. 24(2), 84–302 (2019)
Eissa, M., Kamel, M., Saeed, N.A., El-Ganaini, W.A., El-Gohary, H.A.: Time-delayed positive-position and velocity feedback controller to suppress the lateral vibrations in nonlinear Jeffcott-rotor system. Minufiya J. Electron. Eng. Res. 27(1), 1–16 (2017)
Ri, K., Han, W., Pak, C., Kim, K., Yun, C.: Nonlinear forced vibration analysis of the composite shaft-disk system combined the reduced-order model with the IHB method. Nonlinear Dyn. 104, 3347–3364 (2021)
Ri, K., Ri, Y., Yun, C., Kim, K., Han, P.: Analysis of nonlinear vibration and stability of Jeffcott rotor supported on squeeze-film damper by IHB method. AIP Adv. 12, 025127 (2022)
Ri, K., Jang, J., Yun, C., Pak, C., Kim, K.: Analysis of subharmonic and quasi-periodic vibrations of a Jeffcott rotor supported on a squeeze-film damper by the IHB method. AIP Adv. 12, 055328 (2022)
Ri, K., Jong, Y., Yun, C., Kim, K., Han, P.: Nonlinear vibration and stability analysis of a flexible rotor-SFDs system with cubic nonlinearity. Nonlinear Dyn. 109, 1441–1461 (2022)
Li, J., Wang, W., Xia, Y., Zhu, W.: The soft-landing features of a micro-magnetorheological fluid damper. Appl. Phys. Lett. 106, 014104 (2015)
Versaci, M., Cutrupi, A., Palumbo, A.: A magneto-thermo-static study of a magneto-rheological fluid damper: a finite element analysis. J. Latex Class Files 14(8), 1–10 (2015)
Sun, S., Yang, J., Li, W., Deng, H., Du, H., Alici, G.: Development of a novel variable stiffness and damping magnetorheological fluid damper. Smart Mater. Struct. 24, 085021 (2015)
Guo, H., Żur, K.K., Ouyang, X.: New insights into the nonlinear stability of nanocomposite cylindrical panels under aero-thermal loads. Compos. Struct. 303, 116231 (2023)
Guo, H., Ouyang, X., Żur, K.K., Wu, X., Yang, T., Ferreira, A.J.M.: On the large-amplitude vibration of rotating pre-twisted graphene nanocomposite blades in a thermal environment. Compos. Struct. 282, 115129 (2022)
Guo, H., Ouyang, X., Yang, T., Żur, K.K., Reddy, J.N.: On the dynamics of rotating cracked functionally graded blades reinforced with graphene nanoplatelets. Eng. Struct. 249, 113286 (2021)
Guo, H., Ouyang, X., Żur, K.K., Wu, X.: Meshless numerical approach to flutter analysis of rotating pre-twisted nanocomposite blades subjected to supersonic airflow. Eng. Anal. Bound. Elem. 132, 1–11 (2021)
Guo, H., Du, X., Żur, K.K.: On the dynamics of rotating matrix cracked FG-GPLRC cylindrical shells via the element-free IMLS-Ritz method. Eng. Anal. Bound. Elem. 131, 228–239 (2021)
Eyvazian, A., Sebaey, T.A., Żur, K.K., Khan, A., Zhang, H., Wong, S.H.F.: On the dynamics of FG-GPLRC sandwich cylinders based on an unconstrained higher-order theory. Compos. Struct. 267, 113879 (2021)
Guo, H., Yang, T., Żur, K.K., Reddy, J.N.: On the flutter of matrix cracked laminated composite plates reinforced with graphene nanoplatelets. Thin Wall Srtuct. 158, 107161 (2021)
Babaei, H., Kiani, Y., Żur, K.K.: New insights into nonlinear stability of imperfect nanocomposite beams resting on a nonlinear medium. Commun. Nonlinear Sci. 118, 106993 (2023)
Kumar, A., Das, S.L., Wahi, P., Żur, K.K.: On the stability of thin-walled circular cylindrical shells under static and periodic radial loading. J. Sound Vib. 527, 116872 (2022)
Kiani, Y., Żur, K.K.: Free vibrations of graphene platelet reinforced composite skew plates resting on point supports. Thin Wall Srtuct. 176, 109363 (2022)
Tiwari, R.: Rotor Systems Analysis and Identificaiton. CRC Press, New York (2018)
He, J.H.: Hamilton’s principle for dynamical elasticity. Appl. Math. Lett. 72, 65–69 (2017)
Ri, K., Han, P., Kim, I., Kim, W., Cha, H.: Nonlinear forced vibration analysis of composite beam combined with DQFEM and IHB. AIP Adv. 10, 085112 (2020)
Kim, K., Ri, K., Yun, C., Kim, C., Kim, Y.: Analysis of the nonlinear forced vibration and stability of composite beams using the reduced-order model. AIP Adv. 11, 035220 (2021)
Taylor, D.L., Kumar, B.: Nonlinear response of short squeeze film dampers. ASME J. Lubr. Technol. 102(1), 51–58 (1980)
Inayat-Hussain, J.I., Kanki, H., Mureithi, N.W.: On the bifurcations of a rigid rotor response in squeeze-film dampers. J. Fluids Struct. 17(3), 433–459 (2003)
Heidari, H., Ashkooh, M.: The influence of asymmetry in centralizing spring of squeeze film damper on stability and bifurcation of rigid rotor response. Alex. Eng. J. 55(4), 3321–3330 (2016)
Zhao, J.Y., Linnett, I.W.: Stability and bifurcation of unbalanced response of a squeeze film damped flexible rotor. J. Tribol Trans. ASME 116, 361–368 (1994)
Zhao, J.Y., Linnett, I.W., Mclean, L.J.: Unbalance response of a flexible rotor supported by a squeeze film damper. J. Vib. Acoust. 120(1), 32–38 (1998)
Zhu, C.S., Robb, D.A., Ewins, D.J.: Analysis of the multiple-solution response of a flexible rotor supported on non-linear squeeze film dampers. J. Sound Vib. 252(3), 389–408 (2002)
Inayat-Hussain, J.I.: Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs. Chaos Soliton Fract. 39(2), 519–532 (2009)
Krack, M., Gross, J.: Harmonic Balance for Nonlinear Vibration Problems. Springer, Berlin (2019)
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics. Wiley, New York (1995)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Han, Y., Ri, K., Yun, C. et al. Effect of nonlinearities on response characteristics of rotor systems with residual shaft bow. Nonlinear Dyn 111, 16003–16019 (2023). https://doi.org/10.1007/s11071-023-08716-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-023-08716-z