Non-linear modeling of gear drive dynamics incorporating intermittent tooth contact analysis and tooth eigenvibrations

Emmanouil Sakaridis, Vasilios Spitas, Christos Spitas

Research output: Journal PublicationArticlepeer-review

32 Citations (Scopus)


In this paper the effect of the of individual tooth inertia on spur gear dynamics is investigated. A lumped element model is developed, in which tooth and gear inertial properties are decoupled, incorporating meshing position and load dependent meshing stiffness and backlash. A novel methodology for tooth contact analysis, which examines the instantaneous motion of individual teeth, completes the model. The dynamic response of a single-stage drivetrain is examined using both linear and non-linear analysis. Linear analysis demonstrates that, apart from tooth eigenfrequencies, high frequency coupled motion of gear tooth and gear hub DOFs occurs. Non-linear simulation is conducted for a range of operating conditions. Results show that tooth-inertia related vibration modes have noteworthy effects, especially in scenarios involving gears with low tooth numbers or low load. These include the presence of high frequency constituents in the dynamic transmission error, which promote contact loss and chaotic motion, without having a noticeable spectral signature in the transmission output and the reduction in the average number of contacting teeth at low loads, because of tooth eigenvibrations. These results indicate that modeling of individual tooth dynamics in the aforementioned scenarios is important.

Original languageEnglish
Pages (from-to)307-333
Number of pages27
JournalMechanism and Machine Theory
Publication statusPublished - Jun 2019
Externally publishedYes


  • Chaotic motion
  • Gear dynamics
  • Tooth contact analysis
  • Tooth eigenvibrations
  • Transmission error

ASJC Scopus subject areas

  • Bioengineering
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications


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