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)

Abstract

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
Volume32
Issue number10
DOIs
Publication statusPublished - Oct 2008
Externally publishedYes

Fingerprint

Meshing
Gears
Two Dimensions
Analytical Solution
Contact
Stability and Convergence
Scalar
Monitoring
Mathematical Model
Benchmark
Mathematical models
Geometry
Form

Keywords

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

ASJC Scopus subject areas

  • Computational Mechanics
  • Control and Systems Engineering
  • Control and Optimization

Cite this

Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact. / Spitas, C.; Spitas, V.

In: Applied Mathematical Modelling, Vol. 32, No. 10, 10.2008, p. 2162-2171.

Research output: Contribution to journalArticle

@article{dac421d667ed4709a44b5f4898f97733,
title = "Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact",
abstract = "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.",
keywords = "Direct analytical solution, Gear mesh analysis, Non-conjugate contact",
author = "C. Spitas and V. Spitas",
year = "2008",
month = "10",
doi = "10.1016/j.apm.2007.07.007",
language = "English",
volume = "32",
pages = "2162--2171",
journal = "Applied Mathematical Modelling",
issn = "0307-904X",
publisher = "Elsevier",
number = "10",

}

TY - JOUR

T1 - Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact

AU - Spitas, C.

AU - Spitas, V.

PY - 2008/10

Y1 - 2008/10

N2 - 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.

AB - 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.

KW - Direct analytical solution

KW - Gear mesh analysis

KW - Non-conjugate contact

UR - http://www.scopus.com/inward/record.url?scp=44649188559&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44649188559&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2007.07.007

DO - 10.1016/j.apm.2007.07.007

M3 - Article

VL - 32

SP - 2162

EP - 2171

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 10

ER -