Dynamic Modelling of Planetary Gearboxes with Cracked Tooth Using Vibrational Analysis

  • Imthiyas ManarikkalEmail author
  • Faris Elasha
  • Dina Shona Laila
  • David Mba
Conference paper
Part of the Applied Condition Monitoring book series (ACM, volume 15)


Planetary gearboxes failure has been a major problem in systems reliability, hence condition monitoring of this component is essential. In order to identify faults, a dynamic model of the gearbox is presented taking into account backlash and tooth cracks. Newtonian equations of motion developed for a planetary gear is solved and modal analysis for solving the lumped parametric differential equations of modelled single stage planetary gearbox is adopted to observe the vibrational responses and to compare with existing literature. This work focuses primarily on the effects of stiffness and damping. The eigenvalue problem has been solved to measure the natural frequencies and amplitude of the system. Parametric studies using stiffness and damping results indicate significant changes in vibrational signals when there is a crack present on tooth. Simulation results also show the relation between increment in backlash and high frequency responses in the resultant vibration.


Gearbox Vibration Dynamic modelling Crack Stiffness Damping 


  1. 1.
    Feng Z, Zuo M (2013) Fault diagnosis of planetary gearboxes via torsional vibration signal analysis. Mech. Syst. Signal Process. 36(2):401–421MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bartelmus W, Zimroz R (2009) A new feature for monitoring the condition of gearboxes in non-stationary operating conditions. Mech. Syst. Signal Process. 23(5):1528–1534CrossRefGoogle Scholar
  3. 3.
    Bartelmus W (2001) Mathematical modelling and computer simulations as an aid to gearbox diagnostics. Mech. Syst. Signal Process. 15(5):855–871CrossRefGoogle Scholar
  4. 4.
    Jia S, Howard I, Wang J (2003) The dynamic modeling of multiple pairs of spur gears in mesh, including friction. J. Rotating Mach. 9(6):437–442CrossRefGoogle Scholar
  5. 5.
    Aski FS, Mirparizi M, Samani FS, Hajabasi MA (2014) Vibration behavior optimization of planetary gear sets. Propul. Power Res. 3(4):196–206CrossRefGoogle Scholar
  6. 6.
    He S, Jia Q, Chen G, Sun H (2015) Modeling and dynamic analysis of planetary gear transmission joints with backlash. Int. J. Control Autom. 8(2):153–162CrossRefGoogle Scholar
  7. 7.
    Liang X, Zuo MJ, Hoseini MR (2014) Understanding vibration properties of a planetary gear set for fault detection. In: International conference on prognostics and health management, Cheney, WA, USA, pp 1–6Google Scholar
  8. 8.
    Inalpolat M, Kahraman A (2008) Dynamic modelling of planetary gears of automatic transmissions. Accessed 15 Dec 2017Google Scholar
  9. 9.
    Sawalhi N, Randall R (2006) Simulation of the vibrations produced by extended bearing faults in gearboxes. In: First australasian acoustical societies conference, Christchurch, New ZealandGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Imthiyas Manarikkal
    • 1
    Email author
  • Faris Elasha
    • 1
  • Dina Shona Laila
    • 1
  • David Mba
    • 2
  1. 1.Faculty of EECCoventry UniversityCoventryUK
  2. 2.Faculty of TechnologyDe Montford UniversityLeicesterUK

Personalised recommendations