Modeling of Gear Transmissions Dynamics in Non-stationary Conditions

  • Fakher ChaariEmail author
  • Mohamed Haddar
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Dynamic behavior of gear transmissions running under non-stationary operating conditions is extremely different from that operating in stationary conditions. The main feature that makes this difference is the variability of speed. Three main cases where it is possible to observe speed variation: start-up, shut down and time varying loading conditions. In this chapter, these three regimes will be discussed using dynamic modeling of gear transmission. Both amplitude and frequency modulations are observed in vibration signatures. The case study of wind turbine transmission is presented at the end of the chapter showing clearly this phenomenon.


Gear transmission Non-stationary operating conditions Amplitude and frequency modulation 


  1. Bartelmus W (1992) Vibration condition monitoring of gearboxes. Mach Vib 1:178–189Google Scholar
  2. Bartelmus W (2001) Mathematical modelling and computer simulations as an aid to gearbox diagnostics. Mech Sys Sig Proc 15:855–871Google Scholar
  3. Bartelmus W, Zimroz Z (2009a) Vibration condition monitoring of planetary gearbox under varying external load. Mech Syst Sig Proc 23:246–257Google Scholar
  4. Bartelmus W, Zimroz Z (2009b) A new feature for monitoring the condition of gearboxes in non-stationary operating conditions. Mech Syst Sig Proc 23:1528–1534Google Scholar
  5. Bartelmus W, Chaari F, Zimroz R, Haddar M (2010) Modelling of gearbox dynamics under time varying non-stationary operation for distributed fault detection and diagnosis. Eur J Mec A/Sol 29:637–646CrossRefGoogle Scholar
  6. Chaari F, Fakhfakh T, Haddar M (2006) Simulation numérique du comportement dynamique d’une transmission par engrenages en présence de défauts de denture. Méc Ind 6:625–633CrossRefGoogle Scholar
  7. Chaari F, Baccar W, Haddar M (2008) Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission. Eur J Mec A/Sol 27:691–705CrossRefzbMATHGoogle Scholar
  8. Chaari F, Fakhfakh T, Haddar M (2009) Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. Eur J Mec A/ Sol 27:461–468CrossRefGoogle Scholar
  9. Chaari F, Bartelmus W, Zimroz R, Fakhfakh T, Haddar M (2012) Gearbox vibration signal amplitude and frequency modulation. Sh Vib 19:635–652CrossRefGoogle Scholar
  10. Chaari F, Abbes MS, Rueda FV, del Rincon AF, Haddar M (2013) Analysis of planetary gear transmission in non-stationary operations. Front Mec Eng 8:88–94CrossRefGoogle Scholar
  11. DNV, RISO (2002) Guidelines for design of wind turbines, 2nd edn. Det Norske Veritas, CopenhagenGoogle Scholar
  12. Hugues JH (1993) Contribution à l’étude dynamique lors du démarrage de chaines cinématiques à engrenages entraînés par moteur éléctrique, PhD, INSA Lyon, FranceGoogle Scholar
  13. Khabou MT, Ksentini O, Jarraya A, Abbes MS, Chaari F, Haddar M (2014) Influence of disk brake friction on the dynamic behaviour of a directly coupled spur gear transmission. Mult Mod Mat Str 10 (in press)Google Scholar
  14. Khabou MT, Bouchaala N, Chaari F, Fakhfakh T, Haddar M (2011) Study of a Spur Gear Dynamic Behavior in Transient Regime. Mec Sys Sig Pro 25:3089–3101CrossRefGoogle Scholar
  15. Randall RB (1982) A new method of modelling gear faults. J Mech Des 104:259–267Google Scholar
  16. Sika G, Velex P (2008) Analytical and numerical analysis of gears in the presence of engine acyclism. ASME J Mech Des 130:1–6CrossRefGoogle Scholar
  17. Velex P (1988) Contribution à l’analyse du comportement dynamique de Réducteurs à engrenages à axes parallèles. PhD INSA Lyon, FranceGoogle Scholar
  18. Walha L, Fakhfakh T, Haddar M (2009) Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash. Mech Mach Th 44:1058–1069CrossRefzbMATHGoogle Scholar
  19. Wright D (2005) Class Notes on Design and Analysis of Machine Elements. The University of Western Australia, Department of Mechanical and Materials Engineering, Crawley, Perth, AustraliaGoogle Scholar
  20. Zimroz R, Urbanek J, Barszcz T, Bartelmus W, Millioz F, Martin N (2011) Measurement of instantaneous shaft speed by advanced vibration signal processing—application to wind turbine gearbox. Met Meas Syst 18:701–712Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.National School of Engineers of SfaxSfaxTunisia

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