Skip to main content
SpringerLink
Log in

Nonlinear dynamic force transmissibility of a flywheel rotor supported by angular contact ball bearings

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The dynamic force transmissibility (DFT) of aerospace flywheel rotor system (FRS) supported by angular contact ball bearings (ACBBs) is examined in this paper. The influence of combined loads and contact angle variation is considered in the Sjovall formula to accurately solve the load distribution and nonlinear stiffness of ACBB. Subsequently, the lateral vibration model of FRS is established by considering the nonlinear stiffness characteristics of ACBB. The DFT of the system is solved via harmonic balance method and arc length continuation, and the stability of the results is determined. Numerical integration and dynamic tests are utilized to verify the accuracy of harmonic balance results. Based on the proposed model, the effects of rotor unbalance excitation, axial preload, and rotor damping on the DFT of the system are discussed. The soft-stiff transition phenomenon is observed in terms of the varying supporting stiffness of ACBB wherein deformation is measured under axial preload. The value of rotor unbalanced mass determines the nonlinear characteristics of FRS. The results provide an important reference for dynamic performance evaluation and vibration isolation device design of aerospace FRS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Miller, D.W., Weck, O.L. Uebelhart, S.A., Grogan, R., Basdogan, I.: Integrated dynamics and controls modeling for the Space Interferometry Mission (SIM), IEEE Aerospace Conference, Big Sky, MT, USA, March 10-17, pp. 2089-2102 , (2001)

  2. Miller, S.E., Kirchman, P., Sudey, J.: Reaction wheel operational impacts on the goes jitter environment. AIAA Guidance, Navigation and Control Conference and Exhibit, Hilton Head, South Carolina, AIAA 2007-6736 (2007)

  3. Kim, Y.K., Koo, J.H., Kim, K.S.: Vibration isolation strategies using magneto-rheological elastomer for a miniature cryogenic cooler in space application. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montreal, ON, pp. 1203-1206 , (2010)

  4. Pong, C.M., Smith, M.W., Knutson, M.W., Lim, S., Murphy, S.D.: One-arcsecond line-of-sight pointing control on exoplanetsat, a three-unit cubesat. Advances in the Astronautical Sciences 141, 11–35 (2011)

    Google Scholar 

  5. Han, Q., Wang, T., Ding, Z., Xu, X., Chu, F. Magnetic equivalent modeling of stator currents for localized fault detection of planetary gearboxes coupled to electric motors. IEEE Transactions on Industrial Electronics 68, 2575–2586 (2021)

  6. Masterson, R.A., Miller, D.W. Development and validation of empirical and analytical reaction wheel disturbance models. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, St. Louis MO., pp. 1-10 , (1999)

  7. Narayan, S.S., Nair, P.S., Ghosal, A.: Dynamic interaction of rotating momentum wheels with spacecraft element. Journal of Sound and Vibration 315(4–5), 970–984 (2008)

    Article  Google Scholar 

  8. Zhang, Z., Aglietti, G.S., Zhou, W.: Microvibrations induced by a cantilevered wheel assembly with a soft-suspension system. AIAA Journal 49(5), 1067–1079 (2011)

    Article  Google Scholar 

  9. Zhou, W.Y., Aglietti, G.S., Zhang, Z.: Modelling and testing of a soft suspension design for a reaction/momentum wheel assembly. Journal of Sound and Vibration 330(18–19), 4596–4610 (2011)

    Article  Google Scholar 

  10. Zhang, Z., Aglietti, G.S., Ren, W.: Coupled microvibration analysis of a reaction wheel assembly including gyroscopic effects in its accelerance. Journal of Sound and Vibration 332(22), 5748–5765 (2013)

    Article  Google Scholar 

  11. Luo, Q., Li, D., Zhou, W.: Studies on vibration isolation for a multiple flywheel system in variable configurations. Journal of Vibration and Control 21(1), 105–123 (2015)

    Article  Google Scholar 

  12. Wei, Z., Li, D., Luo, Q., Jiang, J.: Modeling and analysis of a flywheel microvibration isolation system for spacecrafts. Advances in Space Research 55(2), 761–777 (2015)

    Article  Google Scholar 

  13. Jones, A.B.: A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. Journal of Basic Engineering 82(2), 309–320 (1960)

    Article  Google Scholar 

  14. Bai, C., Zhang, H., Xu, Q.: Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system. Nonlinear Dynamics 53, 173–190 (2008)

    Article  Google Scholar 

  15. Cui, L., Zhang, J.: Nonlinear vibration and stability analysis of a flexible rotor supported on angular contact ball bearings. Journal of Vibration and Control 20(12), 1767–1782 (2014)

    Article  Google Scholar 

  16. Zhang, J., Fang, B., Hong, J., Wan, S., Zhu, Y.: A general model for preload calculation and stiffness analysis for combined angular contact ball bearings. Journal of Sound and Vibration 411, 435–449 (2017)

    Article  Google Scholar 

  17. Zhang, J., Fang, B., Zhu, Y., Hong, J.: A comparative study and stiffness analysis of angular contact ball bearings under different preload mechanisms. Mechanism and Machine Theory 115, 1–17 (2017)

    Article  Google Scholar 

  18. Zhang, J., Fang, B., Hong, J., Zhu, Y.: Effect of preload on ball-raceway contact state and fatigue life of angular contact ball bearing. Tribology International 114, 365–372 (2017)

    Article  Google Scholar 

  19. Li, X., Yu, K., Ma, H., Cao, L., Luo, Z., Li, H., Che, L.: Analysis of varying contact angles and load distributions in defective angular contact ball bearing. Engineering Failure Analysis 91, 449–464 (2018)

    Article  Google Scholar 

  20. Xu, K., Wang, B., Zhao, Z., Zhao, F., Kong, X., Wen, B.: The influence of rolling bearing parameters on the nonlinear dynamic response and cutting stability of high-speed spindle systems. Mechanical Systems and Signal Processing 136, 106448 (2020)

    Article  Google Scholar 

  21. Wang, H., Han, Q., Zhou, D.: Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings. Mechanical Systems and Signal Processing 85, 16–40 (2017)

    Article  Google Scholar 

  22. Wang, H., Han, Q., Luo, R., Qing, T.: Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports. Journal of Sound and Vibration 406, 124–145 (2017)

    Article  Google Scholar 

  23. Sjovall, H.: The load distribution within ball and roller bearings under given external radial and axial load. Tekniks Tidskrift Mek. 9, 97–102 (1933)

    Google Scholar 

  24. Zhou, W., Li, D., Lu, Q., Liu, K.: Analysis and testing of microvibrations produced by momentum wheel assemblies. Chinese Journal of Aeronautics 25(4), 640–649 (2012)

    Article  Google Scholar 

  25. Harris, T., Kotzalas, M.: Rolling Bearing Analysis. Taylor & Francis, Boca Raton (2007)

    Google Scholar 

  26. Liu, J., Tang, C., Wu, H., Xu, Z., Wang, L.: An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing. Mechanism and Machine Theory 142, 103597 (2019)

    Article  Google Scholar 

  27. Rao, J.S.: Rotor dynamics. John Wiley & Sons, New York (1983)

    Google Scholar 

  28. Heidari, H., Safarpour, P.: Optimal design of support parameters for minimum force transmissibility of a flexible rotor based on \(\rm H\mathit{}_{\infty }\) and \(\rm H\mathit{}_2\) optimization methods. Engineering Optimization 50(4), 671–683 (2018)

    Article  MathSciNet  Google Scholar 

  29. Ma, Y., Liang, Z., Wang, H., Zhang, D., Hong, J.: Theoretical and experimental steady-state rotordynamics of an adaptive air film damper with metal rubber. Journal of Sound and Vibration 332, 5710–5726 (2013)

    Article  Google Scholar 

  30. Ribeiro, E.A., Pereira, J.T., Bavastri, C.A.: Passive vibration control in rotor dynamics: Optimization of composed support using viscoelastic materials. Journal of Sound and Vibration 351, 43–56 (2015)

    Article  Google Scholar 

  31. Liu, J., Shao, Y., Lim, T.: Impulse vibration transmissibility characteristics in the presence of localized surface defects in deep groove ball bearing systems. Proceedings of IMechE, Part K: Journal of Multi-body Dynamics 228(1), 62–81 (2014)

    Article  Google Scholar 

  32. Al-Solihat, M.K., Behdinan, K.: Nonlinear dynamic response and transmissibility of a flexible rotor system mounted on viscoelastic elements. Nonlinear Dynamics 97(2), 1581–1600 (2019)

    Article  Google Scholar 

  33. Al-Solihat, M.K., Behdinan, K.: Force transmissibility and frequency response of a flexible shaft-disk rotor supported by a nonlinear suspension system. International Journal of Non-Linear Mechanics 124, 103501 (2020)

    Article  Google Scholar 

  34. Gu, J., Zhang, Y. Research on modeling and mechanical behaviors of matched angular contact ball bearings. Proceedings of IMechE, Part C: Journal of Mechanical Engineering Science, https://doi.org/10.1177/0954406220937038,(2020)

  35. Groll, G., Ewins, D.J.: The HBM with arc-length continuation in rotor stator contact problems. Journal of Sound and Vibration 241(2), 223–233 (2001)

    Article  Google Scholar 

  36. Fafard, M., Massicotte, B.: Geometrical interpretation of the arc-length method. Computers and Structures 46(4), 603–615 (1993)

    Article  MathSciNet  Google Scholar 

  37. Cameron, T.M., Griffin, J.H.: An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. Journal of Applied Mechanics 56(1), 149–154 (1989)

    Article  MathSciNet  Google Scholar 

  38. Knaapen, R.J.: Experimental determination of rolling element bearing stiffness. Eindhoven University of Technology, Eindhoven, The Netherlands, Ph.D.Thesis (1997)

  39. Dietl, P.: Damping and stiffness characteristics of rolling element bearings-theory and experiment. Technical University of Vienna, Ph.D.Thesis (1997)

  40. Karthick, S., Kumar, K.S., Mohan, S.: Relative analysis of controller effectiveness for vertical plane control of an autonomous underwater vehicle, pp. 1–6. Shanghai, China, IEEE OCEANS (2016)

  41. Sun, K., Liu, L., Qiu, J., Feng, G.: Fuzzy adaptive finite-time fault-tolerant control for strict-feedback nonlinear systems. IEEE Transactions on Fuzzy Systems (2020). https://doi.org/10.1109/TFUZZ.2020.2965890

  42. Sun, K., Qiu, J., Karimi, H.R., Fu, Y.: Event-triggered robust fuzzy adaptive finite-time control of nonlinear systems with prescribed performance. IEEE Transactions on Fuzzy Systems (2020). https://doi.org/10.1109/TFUZZ.2020.2979129

  43. Sun, K., Qiu, J., Karimi, H.R., Gao, H. A novel finite-time control for nonstrict feedback saturated nonlinear systems with tracking error constraint. IEEE Transactions on Systems, Man, and Cybernetics: Systems, https://doi.org/10.1109/TSMC.2019.2958072(2019)

Download references

Acknowledgements

This study was supported by the National Natural Science Foundation of China under Grant No. 11872222 and No. U1837602 and the State Key Laboratory of Tribology under Grant No. SKLT2021D11.

Author information

Authors and Affiliations

  1. Beijing Institute of Control Engineering, Beijing, 100000, China

    Duzhou Zhang, Dengyun Wu & Hong Wang

  2. The State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Qinkai Han

Authors
  1. Duzhou Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dengyun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qinkai Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qinkai Han.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, D., Wu, D., Han, Q. et al. Nonlinear dynamic force transmissibility of a flywheel rotor supported by angular contact ball bearings. Nonlinear Dyn 103, 2273–2286 (2021). https://doi.org/10.1007/s11071-021-06221-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06221-9

Keywords

Search

Navigation