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Effects of tooth crack on vibration responses of a profile shifted gear rotor system

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Abstract

Considering the effects of profile shift and tooth crack, Time-varying mesh stiffness (TVMS) is determined based on an analytical model and the result accuracy is also verified by Finite element (FE) model. Then, by introducing TVMS into the FE model of a gear rotor system, the combined effects of profile shifted gear pair under positive, negative and zero gear transmission conditions and tooth crack on the system vibration responses are analyzed. The time-domain waveform, frequency spectrum and instantaneous energy at a constant rotational speed are used to indicate the crack feature, and the amplitude frequency response is adopted to display the crack-induced response change. The results show that different modification conditions have great influences on the TVMS due to the change of contact ratio and tooth thickness. The sideband frequency and instantaneous energy both can be adopted to diagnose the tooth crack and evaluate crack levels, and the latter is more sensitive than the former. The amplitude frequency responses of profile shifted gear under small crack condition show slight change compared with those of normal gear, and the change of acceleration is more obvious than that of displacement.

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References

  1. S. X. Jia and I. Howard, Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations, Mechanical Systems and Signal Processing, 20 (2) (2006) 332–349.

    Article  Google Scholar 

  2. J. D. Wang and I. Howard, Finite element analysis of high contact ratio spur gears in mesh, J. of Tribology, 127 (3) (2005) 469–483.

    Article  Google Scholar 

  3. J. F. Li, M. T. Xu and S. Y. Wang, Finite element analysis of instantaneous mesh stiffness of cylindrical gears (with and without flexible gear body), Communications in Numerical Methods in Engineering, 15 (8) (1999) 579–587.

    Article  MATH  Google Scholar 

  4. J. D. Wang and I. Howard, The torsional stiffness of involute spur gears, Proceedings of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 218 (2004) 131–142.

    Google Scholar 

  5. T. Lin, H. Ou and R. F. Li, A finite element method for 3D static and dynamic contact/impact analysis of gear drives, Computer Methods in Applied Mechanics and Engineering, 196 (9) (2007) 1716–1728.

    Article  MATH  Google Scholar 

  6. S. Zouari et al., Three-dimensional analyses by finite element method of a spur gear: effect of cracks in the teeth foot on the mesh stiffness, J. of Failure Analysis and Prevention, 7 (6) (2007) 475–481.

    Article  Google Scholar 

  7. X. H. Tian, Dynamic simulation for system response of gearbox including localized gear faults, M.Sc. Thesis, University of Alberta, Edmonton, Alberta, Canada (2004).

    Google Scholar 

  8. X. J. Zhou et al., Time-varying meshing stiffness calculation and vibration analysis for a 16dof dynamic model with linear crack growth in a pinion, Journal of Vibration and Acoustics, 134 (2012) 011011–111.

    Article  Google Scholar 

  9. F. Chaari, T. Fakhfakh and M. Haddar, Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness, European J. of Mechanics-A/Solids, 28 (3) (2009) 461–468.

    Article  MATH  Google Scholar 

  10. Z. G. Chen and Y. M. Shao, Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth, Engineering Failure Analysis, 18 (8) (2011) 2149–2164.

    Article  Google Scholar 

  11. Z. G. Chen and Y. M. Shao, Dynamic features of a planetary gear system with tooth crack under different sizes and inclination angles, Transactions of the ASME-Journal of Vibration and Acoustics, 135 (3) (2013) 031004–1-12.

    Article  Google Scholar 

  12. Z. G. Wan et al., An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack, Engineering Failure Analysis, 42 (2014) 157–177.

    Article  Google Scholar 

  13. X. H. Liang, M. J. Zuo and M. Pandey, Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set, Mechanism and Machine Theory, 76 (2014) 20–38.

    Article  Google Scholar 

  14. Z. G. Chen and Y. M. Shao, Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack, Mechanism and Machine Theory, 62 (2013) 63–74.

    Article  Google Scholar 

  15. O. D. Mohammed, M. Rantatalo and J. Aidanpaa, Improving mesh stiffness calculation of cracked gears for the purpose of vibration-based fault analysis, Engineering Failure Analysis, 34 (2013) 235–251.

    Article  Google Scholar 

  16. Y. Pandya and A. Parey, Failure path based modified gear mesh stiffness for spur gear pair with tooth root crack, Engineering Failure Analysis, 27 (2013) 286–296.

    Article  Google Scholar 

  17. A. F. del Rincon et al., A model for the study of meshing stiffness in spur gear transmissions, Mechanism and Machine Theory, 61 (2013) 30–58.

    Article  Google Scholar 

  18. A. F. del Rincon et al., Gear transmission dynamic: Effects of tooth profile deviations and support flexibility, Applied Acoustics, 77 (2014) 138–149.

    Article  Google Scholar 

  19. D. G. Lewicki and R. Ballarini, Effect of rim thickness on gear crack propagation path, Journal of Mechanical Design, 119 (1997) 88–95.

    Article  Google Scholar 

  20. D. G. Lewicki, Gear crack propagation path studiesguidelines for ultra-safe design, Journal of the American Helicopter Society, 47 (1) (2002) 64–72.

    Article  MathSciNet  Google Scholar 

  21. Y. Pandya and A. Parey, Simulation of crack propagation in spur gear tooth for different gear parameter and its influence on mesh stiffness, Engineering Failure Analysis, 30 (2013) 124–137.

    Article  Google Scholar 

  22. F. Q. Zhao, Z. G. Tian and Y. Zeng, Uncertainty quantification in gear remaining useful life prediction through an integrated prognostics method, IEEE Transactions on Reliability, 62 (2013) 146–159.

    Article  Google Scholar 

  23. H. Ma et al., Time-varying mesh stiffness calculation of cracked spur gears, Engineering Failure Analysis, 44 (2014) 179–194.

    Article  Google Scholar 

  24. W. Bartelmus, Mathematical modelling and computer simulations as an aid to gearbox diagnostics, Mechanical Systems and Signal Processing, 15 (5) (2001) 855–871.

    Article  Google Scholar 

  25. O. D. Mohammed, M. Rantatalo and J.-O. Aidanpää, Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis, Mechanical Systems and Signal Processing, 54–55 (2015) 293–305.

    Article  Google Scholar 

  26. O. D. Mohammed, M. Rantatalo, J.-O. Aidanpää and U. Kumar, Vibration signal analysis for gear fault diagnosis with various crack progression scenarios, Mechanical Systems and Signal Processing, 41 (1) (2013) 176–195.

    Article  Google Scholar 

  27. S. Wu, M. Zuo and A. Parey, Simulation of spur gear dynamics and estimation of fault growth, J. of Sound and Vibration, 317 (3) (2008) 608–624.

    Article  Google Scholar 

  28. F. K. Omar, K. A. F. Moustafa and S. Emam, Mathematical modeling of gearbox including defects with experimental verification, J. of Vibration and Control, 18 (2012) 1310–1321.

    Article  Google Scholar 

  29. H. Ma et al., Fault feature analysis of a cracked gear coupled rotor system, Mathematical Problems in Engineering (2014) Article ID 832192.

    Google Scholar 

  30. Y. M. Hu et al., Transient meshing performance of gears with different modification coefficients and helical angles using explicit dynamic FEA, Mechanical Systems and Signal Processing, 25 (5) (2011) 1786–1802.

    Article  Google Scholar 

  31. H. Ma et al., Effects of tip relief on vibration responses of a geared rotor system, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228 (7) (2014) 1132–1154.

    Google Scholar 

  32. Z. H. Ye, Z. H. Lan and M. R. Smith, Mechanisms and machine theory, Higher Education Press (2001).

    Google Scholar 

  33. Y. M. Zhang et al., Dynamic analysis of three-dimensional helical geared rotor system with geometric eccentricity, JMST, 27 (11) (2013) 3231–3242.

    Google Scholar 

  34. H. Ma et al., Fault features analysis of cracked gear considering the effects of the extended tooth contact, Engineering Failure Analysis, 48 (2015) 105–120.

    Article  Google Scholar 

  35. S. Loutridis, Damage detection in gear systems using empirical mode decomposition, Engineering Structures, 26 (2004) 1833–1841.

    Article  Google Scholar 

  36. Y. P. Cheng and T. C. Lim, Dynamics of hypoid gear transmission with nonlinear time-varying mesh characteristics, ASME Journal of Mechanical Design, 125 (2) (2003) 373–382.

    Article  Google Scholar 

  37. A. Kahraman and G. W. Blankenship, Effect of involute tip relief on dynamic response of spur gear pairs, ASME J.of Mechanical Design, 121 (2) (1999) 313–315.

    Article  Google Scholar 

Download references

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Correspondence to Hui Ma.

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Recommended by Editor Yeon June Kang

Hui Ma is a professor at the school of Mechanical Engineering and Automation, Northeastern University, China. His research interests include rotor dynamics and fault diagnosis.

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Ma, H., Feng, R., Pang, X. et al. Effects of tooth crack on vibration responses of a profile shifted gear rotor system. J Mech Sci Technol 29, 4093–4104 (2015). https://doi.org/10.1007/s12206-015-0903-6

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  • DOI: https://doi.org/10.1007/s12206-015-0903-6

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