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Nonlinear vibration of the spiral bevel gear with a novel tooth surface modification method

  • Farhad S. SamaniEmail author
  • Moslem Molaie
  • Francesco Pellicano


The issue of gear noise is fairly common in power transmission systems. This noise largely stems from the gear pairs vibration triggered by transmission error excitation. This is mainly caused by tooth profile errors, misalignment and tooth deflections. This research endeavors to examine nonlinear spiral bevel gears vibration with the innovative method of tooth surface modification. To design spiral bevel gears with the higher-order transmission error (HTE), the nonlinear vibration of a novel method is investigated. The meshing quality of the HTE spiral bevel gears, as the results demonstrate, sounds more suitable than of the meshing quality gears. Their design was made by means of the parabolic transmission error (PTE). The maximum time response root mean square of the HTE method decreases by 44% concerning the PTE method. The peak-to-peak of the transmission error is decreased by 35% via HTE overall frequency range. However, HTE method is not able to decrease the vibration level on all frequency ratios.


Spiral bevel gear Nonlinear dynamics Tooth surface modification Transmission error 


Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflicts of interest to this work.


  1. 1.
    Derek SJ (2003) Gear noise and vibration. CRC Press, Boca RatonGoogle Scholar
  2. 2.
    Tamarozzi T, Ziegler P, Eberhard P, Desmet W (2013) On the applicability of static modes switching in gear contact applications. Multibody Syst Dyn 30(2):209–219CrossRefGoogle Scholar
  3. 3.
    Pennestrí E, Valentini PP (2002) Dynamic analysis of epicyclic gear trains by means of computer algebra. Multibody Syst Dyn 7(3):249–264CrossRefzbMATHGoogle Scholar
  4. 4.
    Mantriota G, Pennestrì E (2003) Theoretical and experimental efficiency analysis of multi-degrees-of-freedom epicyclic gear trains. Multibody Syst Dyn 9(4):389–408CrossRefzbMATHGoogle Scholar
  5. 5.
    Kahraman A, Blankenship GW (1999) Effect of involute contact ratio on spur gear dynamics. J Mech Des 121(1):112–118CrossRefGoogle Scholar
  6. 6.
    Deng XZ, Fang ZD, Wei BY, Yang HB (2003) Analysis of meshing behavior and experiments of spiral bevel gears with high contact ratio. Hangkong Dongli Xuebao/J Aerosp Power 18(6):744–748Google Scholar
  7. 7.
    Deng X, Fang Z, Yang H, Wei B (2002) Strength analysis of spiral bevel gears with high contact ratio. Hangkong Dongli Xuebao/J Aerosp Power 17(3):367–372Google Scholar
  8. 8.
    Mu Y, Li W, Fang Z, Zhang X (2018) A novel tooth surface modification method for spiral bevel gears with higher-order transmission error. Mech Mach Theory 126:49–60CrossRefGoogle Scholar
  9. 9.
    Artoni A, Kolivand M, Kahraman A (2010) An ease-off based optimization of the loaded transmission error of hypoid gears. J Mech Des 132(1):011010CrossRefGoogle Scholar
  10. 10.
    Su J, Fang Z, Cai X (2013) Design and analysis of spiral bevel gears with seventh-order function of transmission error. Chin J Aeronaut 26(5):1310–1316CrossRefGoogle Scholar
  11. 11.
    Litvin FL, Zhang Y, Lundy M, Heine C (1988) Determination of settings of a tilted head cutter for generation of hypoid and spiral bevel gears. J Mech Transm Autom Des 110(4):495–500CrossRefGoogle Scholar
  12. 12.
    Litvin FL, Fuentes A (2004) Gear geometry and applied theory. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  13. 13.
    Litvin FL, Fuentes A, Fan Q, Handschuh RF (2002) Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears. Mech Mach Theory 37(5):441–459CrossRefzbMATHGoogle Scholar
  14. 14.
    Wildhaber E (1945) Gear tooth curvature treated simply. Am Mach 89(18):122–125Google Scholar
  15. 15.
    Fong ZH (2000) Mathematical model of universal hypoid generator with supplemental kinematic flank correction motions. J Mech Des 122(1):136–142CrossRefGoogle Scholar
  16. 16.
    Stadtfeld HJ (2000) Advanced bevel gear technology. The Gleason Works, RochesterGoogle Scholar
  17. 17.
    Yinong L, Guiyan L, Ling Z (2010) Influence of asymmetric mesh stiffness on dynamics of spiral bevel gear transmission system. Math Probl Eng 2010:124148CrossRefzbMATHGoogle Scholar
  18. 18.
    Chang-Jian CW (2011) Nonlinear dynamic analysis for bevel-gear system under nonlinear suspension-bifurcation and chaos. Appl Math Model 35(7):3225–3237MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Bonori G (2006) Static and dynamic modeling of gear transmission error, PhD Thesis, University of Modena and Reggio EmiliaGoogle Scholar
  20. 20.
    Kahraman A, Lim J, Ding H (2007) A dynamic model of a spur gear pair with friction. In: Proceedings of the 12th IFToMM World CongressGoogle Scholar
  21. 21.
    Liu G, Parker RG (2008) Nonlinear dynamics of idler gear systems. Nonlinear Dyn 53(4):345–367CrossRefzbMATHGoogle Scholar
  22. 22.
    Motahar H, Samani FS, Molaie M (2016) Nonlinear vibration of the bevel gear with teeth profile modification. Nonlinear Dyn 83(4):1875–1884CrossRefGoogle Scholar
  23. 23.
    Kahraman A, Blankenship GW (1997) Experiments on nonlinear dynamic behaviour of an oscillator with clearance and periodically time-varying parameters. J Appl Mech 64:217–226CrossRefGoogle Scholar
  24. 24.
    Bonori G (2006) Static and dynamic modeling of gear transmission error, PhD Thesis, University of Modena and Reggio EmiliaGoogle Scholar
  25. 25.
    Faggioni M, Samani FS, Bertacchi G, Pellicano F (2011) Dynamic optimization of spur gears. Mech Mach Theory 46(4):544–557CrossRefzbMATHGoogle Scholar
  26. 26.
    Bonori G, Barbieri M, Pellicano F (2008) Optimum profile modifications of spur gears by means of genetic algorithms. J Sound Vib 313(3):603–616ADSCrossRefGoogle Scholar
  27. 27.
    Nayfeh AH, Balachandran B (2008) Applied nonlinear dynamics: analytical, computational and experimental methods. Wiley, New YorkzbMATHGoogle Scholar
  28. 28.
    Kahraman A (1992) On the response of a preloaded mechanical oscillator with a clearance: period-doubling and chaos. Nonlinear Dyn 3(3):183–198CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringShahid Bahonar University of KermanKermanIran
  2. 2.Department of Engineering “Enzo Ferrari”University of Modena and Reggio EmiliaModenaItaly

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