Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact

C. Spitas, V. Spitas

Research output: Contribution to journalArticle

20 Citations (Scopus)


The current technological state-of-the-art utilises modified gear profiles, which are in part non-conjugate and therefore cannot be analysed using standard conjugate contact theory. Existing non-conjugate mathematical models require the solution of a system of implicit equations, typically with significant computational effort and need for careful monitoring of solution stability, convergence and selection of initial values. This paper derives a modified form for the fundamental gear meshing equations, which are reduced analytically to a single scalar equation, resulting in improved solution speed and stability. The solution is verified in benchmark tests using real gear geometries.

Original languageEnglish
Pages (from-to)2162-2171
Number of pages10
JournalApplied Mathematical Modelling
Issue number10
Publication statusPublished - Oct 1 2008



  • Direct analytical solution
  • Gear mesh analysis
  • Non-conjugate contact

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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