Skip to main content
SpringerLink
Log in

Effects of Localized Defects of Gear-Shaft-Bearing Coupling System on the Meshing Stiffness of Gear Pairs

  • Original Paper
  • Published:
Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Gear-shaft-bearing systems are commonly used in transmission mechanisms of modern industry. Because of the coupling relationship of the gear pair system and the bearing system, complex vibration signals will be generated when there are localized defects on the transmission system, which makes the defect diagnosis more difficult. Thus, for explaining the vibration signals, a model of gear-shaft-bearing coupling system with 36 DOFs is established. In the proposed model, the model of gear pair with spalling defects and the model of ball bearing with localized defects are combined, and the center distance error and misalignment of the shafts caused by the displacement of bearings’ inner raceways are used as a connection, then the coupling relationship between the gear pair system and the bearing system is established, and the changing laws of the meshing stiffness are studied. The results show that the decrease of meshing stiffness will also be excited by the center distance error and the misalignment angle caused by system vibration. And when there are localized defects on the gear and bearing, the sudden change of actual center distance and misalignment angle will be caused, which results in a further reduction in the meshing stiffness of the gear pair as the failure zone is loaded and a short time after the failure zone. There are obvious signs of the coupling relationship between gears and bearings on the vibration spectrogram of the gear-shaft-bearing. When there is a single defect on the gear pair or bearing, the defect frequencies of the gear pair and bearing can be found at the same time on the spectrogram. Finally, the established model and the analysis of the results are verified by experiments. The established model is closer to engineering practice, and it provides a theoretical basis for fault diagnosis of rotating machinery.

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
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Hu Z, Tang J, Zhong J, Chen S (2016) Frequency spectrum and vibration analysis of high speed gear-shaft system with tooth root crack considering transmission error excitation. Eng Fail Anal 60:405–441

    Article  Google Scholar 

  2. del Rincon AF, Viadero F, Iglesias M, de-Juan A, Garcia P, Sancibrian R (2012) Effect of cracks and pitting defects on gear meshing. Proc Inst Mech Eng C: J Mech Eng Sci 226(11):2805–2815

    Article  Google Scholar 

  3. Jiang H, Shao Y, Mechefske CK (2014) Dynamic characteristics of helical gears under sliding friction with spalling defect. Eng Fail Anal 39:92–107

    Article  Google Scholar 

  4. Hu Z, Tang J, Zhong J, Chen S, Yan H (2016) Effects of tooth profile modification on dynamic responses of a high speed gear-shaft-bearing system. Mech Syst Signal Process 76–77:294–318

    Article  Google Scholar 

  5. Liu J, Zhao W, Liu W (2019) Frequency and vibration characteristics of high-speed gear-shaft-bearing system with tooth root crack considering compound dynamic backlash. Shock Vib 2019:1–19

    Google Scholar 

  6. Ma H, Zeng J, Feng R, Pang X, Wang Q, Wen B (2015) Review on dynamics of cracked gear systems. Eng Fail Anal 55:224–245

    Article  Google Scholar 

  7. Howard I, Jia SX (2001) The dynamic modeling of a spur gear in mesh including friction and a crack. Mech Syst Signal Process 15(5):831–853

    Article  Google Scholar 

  8. Parey A, El Badaoui M, Guillet F, Tandon N (2005) Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect. J Sound Vib 294(3):547–561

    Article  Google Scholar 

  9. Wan Z, Cao H, Zi Y, He W, He Z (2014) An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-shaft system with tooth root crack. Eng Fail Anal 42:157–177

    Article  Google Scholar 

  10. Ma R, Chen YS (2012) Research on the dynamic mechanism of the gear system with localized crack and spalling failure. Eng Fail Anal 26:12–20

    Article  Google Scholar 

  11. Liang X, Zhang H, Liu L, Zuo MJ (2016) The influence of tooth pitting on the mesh stiffness of a pair of external spur gears. Mech Mach Theory 106:1–15

    Article  Google Scholar 

  12. Chaari F, Baccar W, Abbes MS, Haddar M (2007) Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission. Eur J Mech-A/Solids 27(4):691–705

    Article  MATH  Google Scholar 

  13. Wu S, Cheng HS (1993) Sliding wear calculation in spur gears. J Tribol 115(3):493–500

    Article  Google Scholar 

  14. Chen ZG, Shao YM (2013) Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack. Mech Mach Theory 62:63–74

    Article  Google Scholar 

  15. Chen ZG, Shao YM (2015) Dynamic features of planetary gear train with tooth errors. Proc Inst Mech Eng C: J Mech Eng Sci 229(10):1769–1781

    Article  Google Scholar 

  16. Ma H, Zeng J, Feng RJ (2016) An improved analytical method for mesh stiffness calculation of spur gears with tip relief. Mech Mach Theory 98:64–80

    Article  Google Scholar 

  17. Liu J, Liu S, Zhao W, Zhang L (2019) Dynamic characteristics of spur gear pair with dynamic center distance and backlash. Int J Rotat Mach 2019:1–9

    Google Scholar 

  18. Zhang J, Liu XZ (2015) Effects of misalignment on surface wear of spur gears. Proc Inst Mech Eng Part J: J Eng Tribol 229(9):1145–1158

    Article  Google Scholar 

  19. McFadden PD, Smith JD (1984) Model for the vibration produced by a single point defect in a rolling element bearing. J Sound Vib 96(1):69–82

    Article  Google Scholar 

  20. McFadden PD, Smith JD (1985) The vibration produced by multiple point defect in a rolling element bearing. J Sound Vib 98(2):263–273

    Article  Google Scholar 

  21. Tandon N, Choudhury A (1997) An analytical model for the prediction of the vibration response of rolling element bearings due to localized defect. J Sound Vib 205(3):275–292

    Article  Google Scholar 

  22. Ho D, Randall RB (2000) Optimization of bearing diagnostic techniques using simulated and actual bearing fault signals. Mech Syst Signal Process 14(5):763–788

    Article  Google Scholar 

  23. Liu J, Shao Y (2018) An improved analytical model for a lubricated roller bearing including a localized defect with different edge shapes. J Vib Control 24(17):3894–3907

    Article  MathSciNet  Google Scholar 

  24. Patil MS et al (2010) A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing. Int J Mech Sci 52(9):1193–1201

    Article  Google Scholar 

  25. Yang JX, Cao CF (2007) Model for dynamic characteristics produced by inner race local defect in ball bearing system and its simulation. J Zhejiang Univ (Eng Sci) 41(4):551–555 (in chinese)

    Google Scholar 

  26. Behzad M, Bastami AR, Mba D (2011) A new model for estimating vibrations generated in the defective rolling element bearings. J Vib Acoust 133(4):041011

    Article  Google Scholar 

  27. Niu L, Cao H, He Z (2014) Dynamic modeling and vibration response simulation for high speed rolling ball bearings with localized surface defects in raceways. ASME J Manuf Sci E 136(4):041015

    Article  Google Scholar 

  28. Niu L, Cao H, He Z (2015) A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects. J Sound Vib 357:207–232

    Article  Google Scholar 

  29. Wang FT, Jing MQ, Yi J (2015) Dynamic modelling for vibration analysis of a cylindrical roller bearing due to localized defects on raceways. Proc I Mech E Part K: J Multi-body Dyn 229(1):39–64

    Google Scholar 

  30. Sawalhi N, Randall RB (2008) Simulating gear and bearing interactions in the presence of faults. Mech Syst Signal Process 22(8):1924–1951

    Article  Google Scholar 

  31. Sawalhi N, Randall R (2008) Simulating gear and bearing interactions in the presence of faults. Mech Syst Signal Process 22(8):1952–1966

    Article  Google Scholar 

  32. El-Thalji I, Jantunen E (2015) A summary of fault modelling and predictive health monitoring of rolling element bearings. Mech Syst Signal Process 60–61:252–272

    Article  Google Scholar 

  33. Mohammed OD, Rantatalo M (2016) Dynamic response and time-frequency analysis for gear tooth crack detection. Mech Syst Signal Process 66–67:612–624

    Article  Google Scholar 

  34. Saxena A, Parey A, Chouksey M (2015) Effect of shaft misalignment and friction force on time varying mesh stiffness of spur gear pair. Eng Fail Anal 49:79–91

    Article  Google Scholar 

  35. Park S, Kim S, Choi JH (2018) Gear fault diagnosis using transmission error and ensemble empirical mode decomposition. Mech Syst Signal Process 108:262–275

    Article  Google Scholar 

  36. Jia SX, Howard I (2006) Comparison of localized spalling and crack damage from dynamic modeling of spur gear vibrations. Mech Syst Signal Process 20:332–349

    Article  Google Scholar 

  37. Sainsot P, Velex P, Duverger O (2004) Contribution of gear body to tooth deflections—a new bidimensional analytical formula. J Mech Des 126:748–752

    Article  Google Scholar 

  38. Tian XH (2004) Dynamic simulation for system response of gearbox including localized gear faults. Master’s thesis, University of Alberta

  39. Cheng H, Zhang Y, Lu W, Yang Z (2019) Research on ball bearing model based on localized defects. SN Appl Sci 1(10):1–10

    Article  Google Scholar 

  40. Zhao Z, Yin X, Wang W (2019) Effect of the raceway defects on the nonlinear dynamic behavior of rolling bearing. J Mech Sci Technol 33(6):2511–2525

    Article  Google Scholar 

Download references

Acknowledgements

The work described in this paper was fully supported by a grant from the National Natural Science Foundation of China (No. 51905001), Wuhu Science and Technology Projects (No. 2020yf53), and Scientific Research Project of Anhui Polytechnic University (No. Xjky019201904).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Anhui Polytechnic University, Beijing Middle Road, Wuhu, Anhui, 241000, People’s Republic of China

    Peng Dai, Jianping Wang, Shuping Yan, Benchi Jiang & Fengtao Wang

  2. Anhui New R&D Institutions of Human-Machine Interaction and Collaboration, Wuhu, Anhui, People’s Republic of China

    Peng Dai, Jianping Wang, Shuping Yan, Benchi Jiang & Fengtao Wang

  3. Anhui Key Laboratory of Advance Numerical Control and Servo Technology, Wuhu, Anhui, People’s Republic of China

    Peng Dai, Jianping Wang, Shuping Yan, Benchi Jiang & Fengtao Wang

  4. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, People’s Republic of China

    Linkai Niu

Authors
  1. Peng Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianping Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuping Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Benchi Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fengtao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Linkai Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianping Wang.

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

Dai, P., Wang, J., Yan, S. et al. Effects of Localized Defects of Gear-Shaft-Bearing Coupling System on the Meshing Stiffness of Gear Pairs. J. Vib. Eng. Technol. 10, 1153–1173 (2022). https://doi.org/10.1007/s42417-022-00435-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42417-022-00435-w

Keywords

Search

Navigation