Fast unconditionally stable 2-D analysis of non-conjugate gear contacts using an explicit formulation of the meshing equations

C. Spitas, V. Spitas

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Computerised analysis of the contact of gear teeth is currently dependent on numerical solution techniques involving implicit multi-equation systems. These present inherent convergence problems when the initial values are not close enough to the real solution and require significant computational effort. Here a comprehensive new solution is presented using a modified form for the fundamental gear meshing equations in two dimensions. This formulation allows the analytical reduction of the system of meshing equations to a single scalar equation, which is solved using a fast unconditionally stable numerical method. The need for careful determination of initial values for the numerical solution is eliminated and test runs on real gear geometries verify solution accuracy, stability and speed. Application of the algorithm to profile-modified involute gears and Geneva-type mechanisms and related results are shown.

Original languageEnglish
Pages (from-to)869-879
Number of pages11
JournalMechanism and Machine Theory
Volume46
Issue number7
DOIs
Publication statusPublished - Jul 2011
Externally publishedYes

Fingerprint

Gears
Gear teeth
Numerical methods
Geometry

Keywords

  • Contact analysis
  • Geneva gears
  • Initial value selection
  • Modified involute gears
  • Non-conjugate contact
  • Numerical stability
  • Transmission error

ASJC Scopus subject areas

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

Cite this

Fast unconditionally stable 2-D analysis of non-conjugate gear contacts using an explicit formulation of the meshing equations. / Spitas, C.; Spitas, V.

In: Mechanism and Machine Theory, Vol. 46, No. 7, 07.2011, p. 869-879.

Research output: Contribution to journalArticle

@article{da713638ed044607a790c1ae37d9c30f,
title = "Fast unconditionally stable 2-D analysis of non-conjugate gear contacts using an explicit formulation of the meshing equations",
abstract = "Computerised analysis of the contact of gear teeth is currently dependent on numerical solution techniques involving implicit multi-equation systems. These present inherent convergence problems when the initial values are not close enough to the real solution and require significant computational effort. Here a comprehensive new solution is presented using a modified form for the fundamental gear meshing equations in two dimensions. This formulation allows the analytical reduction of the system of meshing equations to a single scalar equation, which is solved using a fast unconditionally stable numerical method. The need for careful determination of initial values for the numerical solution is eliminated and test runs on real gear geometries verify solution accuracy, stability and speed. Application of the algorithm to profile-modified involute gears and Geneva-type mechanisms and related results are shown.",
keywords = "Contact analysis, Geneva gears, Initial value selection, Modified involute gears, Non-conjugate contact, Numerical stability, Transmission error",
author = "C. Spitas and V. Spitas",
year = "2011",
month = "7",
doi = "10.1016/j.mechmachtheory.2011.02.010",
language = "English",
volume = "46",
pages = "869--879",
journal = "Mechanism and Machine Theory",
issn = "0374-1052",
publisher = "Elsevier",
number = "7",

}

TY - JOUR

T1 - Fast unconditionally stable 2-D analysis of non-conjugate gear contacts using an explicit formulation of the meshing equations

AU - Spitas, C.

AU - Spitas, V.

PY - 2011/7

Y1 - 2011/7

N2 - Computerised analysis of the contact of gear teeth is currently dependent on numerical solution techniques involving implicit multi-equation systems. These present inherent convergence problems when the initial values are not close enough to the real solution and require significant computational effort. Here a comprehensive new solution is presented using a modified form for the fundamental gear meshing equations in two dimensions. This formulation allows the analytical reduction of the system of meshing equations to a single scalar equation, which is solved using a fast unconditionally stable numerical method. The need for careful determination of initial values for the numerical solution is eliminated and test runs on real gear geometries verify solution accuracy, stability and speed. Application of the algorithm to profile-modified involute gears and Geneva-type mechanisms and related results are shown.

AB - Computerised analysis of the contact of gear teeth is currently dependent on numerical solution techniques involving implicit multi-equation systems. These present inherent convergence problems when the initial values are not close enough to the real solution and require significant computational effort. Here a comprehensive new solution is presented using a modified form for the fundamental gear meshing equations in two dimensions. This formulation allows the analytical reduction of the system of meshing equations to a single scalar equation, which is solved using a fast unconditionally stable numerical method. The need for careful determination of initial values for the numerical solution is eliminated and test runs on real gear geometries verify solution accuracy, stability and speed. Application of the algorithm to profile-modified involute gears and Geneva-type mechanisms and related results are shown.

KW - Contact analysis

KW - Geneva gears

KW - Initial value selection

KW - Modified involute gears

KW - Non-conjugate contact

KW - Numerical stability

KW - Transmission error

UR - http://www.scopus.com/inward/record.url?scp=79955064735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955064735&partnerID=8YFLogxK

U2 - 10.1016/j.mechmachtheory.2011.02.010

DO - 10.1016/j.mechmachtheory.2011.02.010

M3 - Article

VL - 46

SP - 869

EP - 879

JO - Mechanism and Machine Theory

JF - Mechanism and Machine Theory

SN - 0374-1052

IS - 7

ER -