Influence of the Non-linear Hertzian Stiffness on the Dynamic Behavior of Planetary Gear During Run up Condition

  • Ayoub MbarekEmail author
  • Ahmed Hammami
  • Alfonso Fernández del Rincón
  • Fakher Chaari
  • Miguel Iglesias
  • Fernando Viadero Rueda
  • Mohamed Haddar
Conference paper
Part of the Applied Condition Monitoring book series (ACM, volume 15)


Planetary gear transmissions are widely utilized in rotating machinery which is running under stationary or non-stationary conditions.

In this work, a numerical study of a planetary gear transmission is investigated in both run up the regime and stationary condition.

The non-linear dynamic behavior of a single stage planetary gear during these two regimes was studied. The non-linearity is induced by the Hertzian contact force between teeth gear and it is implemented in a torsional lumped parameter model. In addition, the gear system is excited with the motor torque variation and the fluctuation of ring-planets and sun-planets mesh stiffness during the non-stationary regime. The system equations of motion were resolved by using the implicit type numerical integration technique Newmark-β with Newton-Raphson method. The obtained numerical results approve the influence of the Hertzian stiffness on the dynamic behavior of the system, especially in the run-up regime.


Planetary gear Run-up Non-linearity Torsional model 



The authors would like to acknowledge project “Dynamic behavior of gear transmissions in non-stationary conditions”, ref. DPI2017-85390-P, funded by the Spanish Ministry of Science and Technology.

Acknowledgment to the University of Cantabria cooperation project for doctoral training of University of Sfax’s students.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ayoub Mbarek
    • 1
    • 2
    Email author
  • Ahmed Hammami
    • 1
  • Alfonso Fernández del Rincón
    • 2
  • Fakher Chaari
    • 1
  • Miguel Iglesias
    • 2
  • Fernando Viadero Rueda
    • 2
  • Mohamed Haddar
    • 1
  1. 1.Laboratory of Mechanics, Modeling and Production (LA2MP)National School of Engineers of SfaxSfaxTunisia
  2. 2.Department of Structural and Mechanical Engineering, Faculty of Industrial and Telecommunications EngineeringUniversity of CantabriaSantanderSpain

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