Skip to main content
SpringerLink
Log in

A new dynamic balancing method of spindle based on the identification energy transfer coefficient

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

A new vector matching balance method (VMBM) based on the identification of energy transfer coefficient of spindle rotor system (ETCSRS) is proposed in this paper. This method only needs to extract the original vibration signal of the spindle to compute the spindle rotor system unbalanced vector, and the calculation accuracy depends on the identification precision of ETCSRS. The initial parameters of bearings were calculated by applying Newton-Raphson algorithm based on the quasi-static mechanics analysis of rolling bearings. Through establishing the FEA model of spindle, the structural parameters of the rotor shaft system are obtained and modified by modal correction method. First, the principle of VMBM is verified on a Bentley rotor test bench at different rotating speeds. Second, the verification experiment of VMBM on a high-speed spindle is carried out. Furthermore, the VMBM has a better performance than the influence coefficient method (ICM). The method proposed in this paper is very suitable for on-line dynamic balancing, since it greatly improves the balance efficiency.

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

Similar content being viewed by others

Abbreviations

M:

Mass matrix

C:

Damping matrix

G:

Gyroscopic matrix

S :

Displacement vector of the system

F:

Generalized force

u:

Unbalanced vector

r:

Unbalanced response

φ :

Lag angle

β :

Weighted influence coefficient matrix

Q:

Balance vector

A:

Vibration response vector

Fa :

Axial load

Fr :

Radial load

My :

The external bending moment

δa :

Axial displacement

δr :

Radial displacement

θ:

Relative dip angle

α:

The initial contact angle

Ri :

Radius of the distribution circle

δij :

Contact deformations of the balls

δej :

Contact deformations of the rings

λj :

Control parameters of the grooves

Kr :

Radial stiffness

δ:

Bearing inner race displacement

M1 :

The mass of the finite element model

K1 :

The stiffness of the finite element model

C1 :

The damping of the finite element model

M2 :

The mass of the experimental modal test

K2 :

The stiffness of the experimental modal test

C2 :

The damping of the experimental modal test

References

  1. S. Chowdhury and R. K. Yedavalli, Dynamics of belt-pulley-shaft systems, Mechanism and Machine Theory, 98 (2016) 199–215.

    Article  Google Scholar 

  2. L. Zhang, T. Wang, G. Wang and S. Tian, Hybrid dynamic modeling and analysis of a ball-screw-drive spindle system, Journal of Mechanical Science and Technology, 31 (10) (2017) 4611–4618.

    Article  Google Scholar 

  3. W. Shan, X. Chen, Y. He and J. Zhou, A novel experimental research on vibration characteristics of the running highspeed motorized spindles, Journal of Mechanical Science and Technology, 27 (8) (2013) 2245–2252.

    Article  Google Scholar 

  4. G. Fu, J. Fu and H. Shen, Numerical solution of simultaneous equations based geometric error compensation for CNC machine tools with workpiece model reconstruction, International Journal of Advanced Manufacturing Technology, 86 (5–8) (2016) 2265–2278.

    Article  Google Scholar 

  5. H. Cao, X. Zhang and X. Chen, The concept and progress of intelligent spindles: A review, International Journal of Machine Tools & Manufacture, 112 (2017) 21–52.

    Article  Google Scholar 

  6. J. P. Spagnol, H. Wu and K. Xiao, Dynamic response of a cracked rotor with an unbalance influenced breathing mechanism, Journal of Mechanical Science and Technology, 32 (1) (2018) 57–68.

    Article  Google Scholar 

  7. L. Qu, X. Liu, G. Peyronne and Y. Chen, The holospectrum: A new method for rotor surveillance and diagnosis, Mechanical Systems & Signal Processing, 3 (3) (2003) 255–267.

    Article  Google Scholar 

  8. Y. Zhang, X. Mei, M. Shao and M. Xu, An improved holospectrum-based balancing method for rotor systems with anisotropic stiffness, Proceedings of Institution of Mechanical Engineers Part C — Journal of Mechanical Engineering Science, 227 (2) (2013) 246–260.

    Article  Google Scholar 

  9. P. Gnielka, Modal balancing of flexible rotors without test runs: An experimental investigation, Journal of Sound and Vibration, 90 (2) (1983) 157–172.

    Article  Google Scholar 

  10. P. G. Morton, Modal balancing of flexible shafts without trial weights, Proceedings of the Institution of Mechanical Engineers C, Mechanical Engineering Science, 199 (1) (1985) 71–78.

    Article  Google Scholar 

  11. R. Ramlau and J. Niebsch, Imbalance estimation without test masses for wind turbines, Journal of Solar Energy Engineering, 131 (1) (2009) 284–289.

    Article  Google Scholar 

  12. X. Li, L. Zheng and Z. Liu, Balancing of flexible rotors without trial weights based on finite element modal analysis, Journal of Vibration & Control, 19 (3) (2012) 461–470.

    Article  Google Scholar 

  13. S. Chowdhury and R. K. Yedavalli, Dynamics of low speed geared shaft systems mounted on rigid bearings, Mechanism and Machine Theory, 112 (2017) 123–144.

    Article  Google Scholar 

  14. Y. Li, X. Chen, P. Zhang and J. Zhou, Dynamics modeling and modal experimental study of high speed motorized spindle, Journal of Mechanical Science and Technology, 31 (3) (2017) 1049–1056.

    Article  Google Scholar 

  15. H. Cao, B. Li and Z. He, Finite element model updating of machine-tool spindle systems, Journal of Vibration and Acoustics, 135 (2) (2013) 24–503.

    Article  Google Scholar 

  16. S. Chowdhury and R. K. Yedavalli, Vibration of high speed helical geared shaft systems mounted on rigid bearings, International Journal of Mechanical Sciences, 142–143 (2018) 176–190.

    Article  Google Scholar 

  17. G. F. Bin, L. D. He, J. J. Gao and L. B. Li, High-speed dynamic balancing method for low pressure rotor of a large steam turbine based on modal shape analysis, Journal of Vibration & Shock, 32 (14) (2013) 87–91.

    Google Scholar 

  18. H. Wang, J. Gong and G. Chen, Characteristics analysis of aero-engine whole vibration response with rolling bearing radial clearance, Journal of Mechanical Science and Technology, 31 (5) (2017) 2129–2141.

    Article  Google Scholar 

  19. Y. Li, H. Cao, L. Niu and X. Jin, A general method for the dynamic modeling of ball bearing-rotor systems, Journal of Manufacturing Science and Engineering, 137 (2) (2015) 021016.

    Article  Google Scholar 

  20. M. Yakout, A. Elkhatib and M. G. A. Nassef, Rolling element bearings absolute life prediction using modal analysis, Journal of Mechanical Science and Technology, 32 (1) (2018) 91–99.

    Article  Google Scholar 

  21. Y. Li, X. Chen, P. Zhang and J. Zhou, Dynamics modeling and modal experimental study of high speed motorized spindle, Journal of Mechanical Science and Technology, 31 (3) (2017) 1049–1056.

    Article  Google Scholar 

  22. Z. Liu, S. Ma, L. Cai, T. Guo and Y. Zhao, Timoshenko beam-based stability and natural frequency analysis for heavy load mechanical spindles, Journal of Mechanical Science and Technology, 26 (11) (2012) 3375–3388.

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Science and Technology Major Project of China (Grant Number 2015Z X04005001 and 2017ZX04013001).

Author information

Authors and Affiliations

  1. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710048, China

    Xialun Yun, Xuesong Mei & Gedong Jiang

  2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Xialun Yun, Xuesong Mei & Gedong Jiang

  3. Shaanxi Key Laboratory of Intelligent Robots, Xi’an Jiaotong University, Xi’an, 710049, China

    Xuesong Mei

  4. School of Mechanical Electronical Engineering, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China

    Baomin Wang

Authors
  1. Xialun Yun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xuesong Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gedong Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Baomin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuesong Mei.

Ethics declarations

The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

Recommended by Associate Editor Hyeong-Joon Ahn

Xialun Yun is a Doctor of Xi’an Jiaotong University. His research mainly includes high speed spindle machining technology and high speed spindle on — line dynamic balance technology. In recent years, he has published 5 papers and apply for more than 20 invention patents.

Xuesong Mei is a Professor of Xi’an Jiao Tong University and the Head of Shaanxi Key Laboratory of Intelligent Robots. His research interests include finishing machining, CNC technology and laser manufacturing technology. In recent years, he has edited 2 monographs in the field of machine tool manufacturing and published more than 200 papers and authorized more than 40 invention patents.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yun, X., Mei, X., Jiang, G. et al. A new dynamic balancing method of spindle based on the identification energy transfer coefficient. J Mech Sci Technol 33, 4595–4604 (2019). https://doi.org/10.1007/s12206-019-0607-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-019-0607-4

Keywords

Search

Navigation