A Computer Program for the Computation of Running Gear Temperatures Using Green's Function.

Abstract

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1996
Accession Number
ADA318138

Entities

People

  • D. P. Townsend
  • J. W. Murdock
  • L. S. Akin
  • S. Koshigoe

Organizations

  • Glenn Research Center

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Layer
  • Cartesian Coordinates
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programs
  • Finite Element Analysis
  • Gear Teeth
  • Geometry
  • Heat Flux
  • Heat Transfer
  • Helmholtz Equations
  • Integral Equations
  • Lubricants
  • Modulus Of Elasticity
  • Simultaneous Equations
  • Steady State
  • Surface Temperature

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Tribology (the study of the boundary interaction between sliding surfaces, lubrication, wear and friction).