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Super-harmonic resonance characteristic of a rigid-rotor ball bearing system caused by a single local defect in outer raceway

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Abstract

The studies on dynamics of a fault bearing system are prevalent in recent years, however, we are studying a completely different frequency range than the one where the bearing faults are best seen. Considering a local defect on outer raceway, a two-degree-of-freedom analytical model of a rigid-rotor ball bearing system is established. Three pulse force models are introduced to simulate the local defect. The frequency domain method—harmonic balance method with alternating frequency/time domain technique (HB-AFT) is used to calculate the response in a large frequency range. By comparing the performance at different frequencies, the fault systems with different defect models and parameters reveal the super-harmonic resonances, and the reasons for this phenomenon are uncovered as well. Finally, the theoretical calculation is verified qualitatively by the experimental results, through comparing the frequency spectrums of the defective bearing rotor system to the fault-free one. Therefore, the super-harmonic resonances can be regarded as a dynamic feature. Besides, the obvious super-harmonic resonances indicate the magnification of the harmonics of the “characteristic defect frequency” for outer race in the corresponding speed regions, which may be helpful for the diagnosis of a rotor ball bearing system with a local defect.

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References

  1. Hoeprich M R. Rolling element bearing fatigue damage propagation. J Tribol, 1992, 114: 328–333

    Article  Google Scholar 

  2. McFadden P D, Smith J D. Model for the vibration produced by a single point defect in a rolling element bearing. J Sound Vib, 1984, 96: 69–82

    Article  Google Scholar 

  3. McFadden P D, Smith J D. The vibration produced by multiple point defects in a rolling element bearing. J Sound Vib, 1985, 98: 263–273

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Tandon N, Choudhury A. A theoretical model to predict the vibration response of rolling bearings in a rotor bearing system to distributed defects under radial load. J Tribol, 2000, 122: 609

    Article  Google Scholar 

  6. Choudhury A, Tandon N. Vibration response of rolling element bearings in a rotor bearing system to a local defect under radial load. J Tribol, 2006, 128: 252

    Article  Google Scholar 

  7. Rafsanjani A, Abbasion S, Farshidianfar A, et al. Nonlinear dynamic modeling of surface defects in rolling element bearing systems. J Sound Vib, 2009, 319: 1150–1174

    Article  Google Scholar 

  8. Feng N S, Hahn E J, Randall R B. Using transient analysis software to simulate vibration signals due to rolling element bearing defects. In: Proceedings of the 3rd Australian Congress on Applied Mechanics. Sydney, 2002

    Google Scholar 

  9. Sopanen J, Mikkola A. Dynamic model of a deep groove ball bearing including localized and distributed defects. Part 1: Theory. Proc Inst Mech Eng Part K J Multi-Body Dyn, 2003, 217: 201–211

    Google Scholar 

  10. Sopanen J, Mikkola A. Dynamic model of a deep-groove ball bearing including localized and distributed defects. Part 2: Implementation and results. Proc Inst Mech Eng Part K J Multi-Body Dyn, 2005, 217: 213–223

    Google Scholar 

  11. Sawalhi N, Randall R B. Simulating gear and bearing interactions in the presence of faults. Mech Syst Signal Process, 2008, 22: 1924–1951

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Sassi S, Badri B, Thomas M. A numerical model to predict damaged bearing vibrations. J Vib Control, 2007, 13: 1603–1628

    Article  MATH  Google Scholar 

  14. Cao M, Xiao J. A comprehensive dynamic model of double-row spherical roller bearing—Model development and case studies on surface defects, preloads, and radial clearance. Mech Syst Signal Process, 2008, 22: 467–489

    Article  Google Scholar 

  15. Arslan H, Akturk N. An investigation of rolling element vibrations caused by local defects. J Tribol, 2008, 130: 041101

    Article  Google Scholar 

  16. Patil M S, Mathew J, Rajendrakumar P K, et al. A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing. Int J Mech Sci, 2010, 52: 1193–1201

    Article  Google Scholar 

  17. Nakhaeinejad M, Bryant M D. Dynamic modeling of rolling element bearings with surface contact defects using bond graphs. J Tribol, 2011, 133: 011102

    Article  Google Scholar 

  18. Patel V N, Tandon N, Pandey R K. A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races. J Tribol, 2010, 132: 041101

    Article  Google Scholar 

  19. Tadina M, Boltežar M. Improved model of a ball bearing for the simulation of vibration signals due to faults during run-up. J Sound Vib, 2011, 330: 4287–4301

    Article  Google Scholar 

  20. Kankar P K, Sharma S C, Harsha S P. Vibration based performance prediction of ball bearings caused by localized defects. Nonlinear Dyn, 2012, 69: 847–875

    Article  MathSciNet  Google Scholar 

  21. Pandya D H, Upadhyay S H, Harsha S P. Nonlinear dynamic analysis of high speed bearings due to combined localized defects. J Vib Control, 2014, 20: 2300–2313

    Article  Google Scholar 

  22. Bogdevičius M, Skrickij V. Investigation of dynamic processes in ball bearings with defects. Solid State Phenom, 2013, 198: 651–656

    Article  Google Scholar 

  23. Wang F, Jing M, Yi J, et al. Dynamic modelling for vibration analysis of a cylindrical roller bearing due to localized defects on raceways. J Multi-Body Dyn, 2015, 229: 39–64

    Google Scholar 

  24. Liu J, Shao Y, Lim T C. Vibration analysis of ball bearings with a localized defect applying piecewise response function. Mech Mach Theory, 2012, 56: 156–169

    Article  Google Scholar 

  25. Liu J, Shao Y. A new dynamic model for vibration analysis of a ball bearing due to a localized surface defect considering edge topographies. Nonlinear Dyn, 2015, 79: 1329–1351

    Article  Google Scholar 

  26. Liu J, Shao Y, Zhu W D. A new model for the relationship between vibration characteristics caused by the time-varying contact stiffness of a deep groove ball bearing and defect sizes. J Tribol, 2015, 137: 031101

    Article  Google Scholar 

  27. Liu J, Shao Y. Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges. J Sound Vib, 2017, 398: 84–102

    Article  Google Scholar 

  28. Moazen Ahmadi A, Petersen D, Howard C. A nonlinear dynamic vibration model of defective bearings—The importance of modelling the finite size of rolling elements. Mech Syst Signal Process, 2015, 52-53: 309–326

    Article  Google Scholar 

  29. Niu L, Cao H, He Z, et al. Dynamic modeling and vibration response simulation for high speed rolling ball bearings with localized surface defects in raceways. J Manuf Sci Eng, 2014, 136: 041015

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Singh S, Köpke U G, Howard C Q, et al. Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model. J Sound Vib, 2014, 333: 5356–5377

    Article  Google Scholar 

  32. Sawalhi N, Randall R B. Vibration response of spalled rolling element bearings: Observations, simulations and signal processing techniques to track the spall size. Mech Syst Signal Process, 2011, 25: 846–870

    Article  Google Scholar 

  33. Petersen D, Howard C, Prime Z. Varying stiffness and load distributions in defective ball bearings: Analytical formulation and application to defect size estimation. J Sound Vib, 2015, 337: 284–300

    Article  Google Scholar 

  34. Cui L, Zhang Y, Zhang F, et al. Vibration response mechanism of faulty outer race rolling element bearings for quantitative analysis. J Sound Vib, 2016, 364: 67–76

    Article  Google Scholar 

  35. Singh S, Howard C Q, Hansen C H. An extensive review of vibration modelling of rolling element bearings with localised and extended defects. J Sound Vib, 2015, 357: 300–330

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Sunnersjö C S. Varying compliance vibrations of rolling bearings. J Sound Vib, 1978, 58: 363–373

    Article  Google Scholar 

  38. Harris T A, Kotzalas M N. Essential Concepts of Bearing Technology. Boca Raton, Florida: CRC Press, 2006

    Book  Google Scholar 

  39. Bai C, Zhang H, Xu Q. Subharmonic resonance of a symmetric ball bearing-rotor system. Int J Non-Linear Mech, 2013, 50: 1–10

    Article  Google Scholar 

  40. Fukata S, Gad E H, Kondou T, et al. On the radial vibration of ball bearings: Computer simulation. Trans Japan Soc Mech Eng C, 1984, 50: 1703–1708

    Article  Google Scholar 

  41. Zhang Z, Chen Y, Cao Q. Bifurcations and hysteresis of varying compliance vibrations in the primary parametric resonance for a ball bearing. J Sound Vib, 2015, 350: 171–184

    Article  Google Scholar 

  42. Zhang Z Y, Chen Y S, Li Z G. Influencing factors of the dynamic hysteresis in varying compliance vibrations of a ball bearing. Sci China Tech Sci, 2015, 58: 775–782

    Article  Google Scholar 

  43. Jin Y, Yang R, Hou L, et al. Experiments and numerical results for varying compliance contact resonance in a rigid rotor-ball bearing system. J Tribol, 2017, 139: 041103

    Article  Google Scholar 

  44. Igarashi T, Hamada H. Studies on the vibration and sound of defective rolling bearings. First report: Vibration of ball bearings with one defect. Bull JSME, 1982, 25: 994–1001

    Article  Google Scholar 

  45. Tandon N, Choudhury A. A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribol Int, 1999, 32: 469–480

    Article  Google Scholar 

  46. Tandon N, Nakra B C. Technical article practical articles in shock and vibration technology: Vibration and acoustic monitoring techniques for the detection of defects in rolling element bearings—A review. Shock Vib Digest, 1992, 24: 3–11

    Article  Google Scholar 

  47. Yong G, QinKai H, FuLei C. A vibration model for fault diagnosis of planetary gearboxes with localized planet bearing defects. J Mech Sci Technol, 2016, 30: 4109–4119

    Article  Google Scholar 

  48. Wang T, Han Q, Chu F, et al. A new SKRgram based demodulation technique for planet bearing fault detection. J Sound Vib, 2016, 385: 330–349

    Article  Google Scholar 

  49. Zhang H, Chen X, Du Z, et al. Nonlocal sparse model with adaptive structural clustering for feature extraction of aero-engine bearings. J Sound Vib, 2016, 368: 223–248

    Article  Google Scholar 

  50. Zhang H, Chen X, Du Z, et al. Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis. Mech Syst Signal Process, 2014, 80: 349–376

    Article  Google Scholar 

  51. Epps I K. An investigation into vibrations excited by discrete faults in rolling element bearings. Dissertation of Doctoral Degree. Christchurch, New Zealand: The University of Canterbury, 1991

    Google Scholar 

  52. Antoni J, Randall R B. Differential diagnosis of gear and bearing faults. J Vib Acoust, 2002, 124: 165

    Article  Google Scholar 

  53. Randall R B, Antoni J. Rolling element bearing diagnostics—A tutorial. Mech Syst Signal Process, 2011, 25: 485–520

    Article  Google Scholar 

  54. Antoni J, Randall R B. A stochastic model for simulation and diagnostics of rolling element bearings with localized faults. J Vib Acoust, 2003, 125: 282–289

    Article  Google Scholar 

  55. Brie D. Modelling of the spalled rolling element bearing vibration signal: An overview and some new results. Mech Syst Signal Process, 2000, 14: 353–369

    Article  Google Scholar 

  56. Yang R, Jin Y, Hou L, et al. Study for ball bearing outer race characteristic defect frequency based on nonlinear dynamics analysis. Nonlinear Dyn, 2017, 90: 781–796

    Article  Google Scholar 

  57. Kim Y B, Noah S T. Stability and bifurcation analysis of oscillators with piecewise-linear characteristics: A general approach. J Appl Mech, 1991, 58: 545–553

    Article  MathSciNet  MATH  Google Scholar 

  58. Zhang Z, Chen Y. Harmonic balance method with alternating frequency/ time domain technique for nonlinear dynamical system with fractional exponential. Appl Math Mech-Engl Ed, 2014, 35: 423–436

    Article  MathSciNet  Google Scholar 

  59. Chen Y S. Nonlinear Dynamics. Beijing: Higher Education Press, 2002

  60. Sun C, Chen Y, Hou L. Steady-state response characteristics of a dual-rotor system induced by rub-impact. Nonlinear Dyn, 2016, 86: 91–105

    Article  Google Scholar 

  61. Kostek R. Analysis of the primary and superharmonic contact resonances— Part 1. J Theor Appl Mech, 2013, 51: 475–486

    Google Scholar 

  62. Perret-Liaudet J, Rigaud E. Response of an impacting Hertzian contact to an order-2 subharmonic excitation: Theory and experiments. J Sound Vib, 2006, 296: 319–333

    Article  Google Scholar 

  63. Tiwari M, Gupta K, Prakash O. Effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor. J Sound Vib, 2000, 238: 723–756

    Article  Google Scholar 

  64. Harsha S P. Nonlinear dynamic response of a balanced rotor supported by rolling element bearings due to radial internal clearance effect. Mech Mach Theory, 2006, 41: 688–706

    Article  MATH  Google Scholar 

  65. Gupta T C, Gupta K, Sehgal D K. Instability and chaos of a flexible rotor ball bearing system: An investigation on the influence of rotating imbalance and bearing clearance. J Eng Gas Turbines Power, 2011, 133: 082501

    Article  Google Scholar 

  66. Bai C, Xu Q. Dynamic model of ball bearings with internal clearance and waviness. J Sound Vib, 2006, 294: 23–48

    Article  Google Scholar 

  67. Hou L, Chen Y, Fu Y, et al. Application of the HB–AFT method to the primary resonance analysis of a dual-rotor system. Nonlinear Dyn, 2017, 88: 2531–2551

    Article  Google Scholar 

  68. Fu C, Fu D, Ou Y, et al. Rotor Dynamics and Whole Body Vibration (Aircraft Engine Design Manual. Volume 19). Beijing: Aviation Industry Press, 2000

    Google Scholar 

  69. Krämer E. Dynamics of Rotors and Foundations. Berlin Heidelberg: Springer, 1993

    Book  Google Scholar 

  70. Xie G. Vibration Mechanics. 2nd Ed. Beijing: National Defense Industry Press, 2011

    Google Scholar 

  71. Mevel B, Guyader J L. Routes to chaos in ball bearings. J Sound Vib, 1993, 162: 471–487

    Article  MATH  Google Scholar 

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Yang, R., Jin, Y., Hou, L. et al. Super-harmonic resonance characteristic of a rigid-rotor ball bearing system caused by a single local defect in outer raceway. Sci. China Technol. Sci. 61, 1184–1196 (2018). https://doi.org/10.1007/s11431-017-9155-3

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