Accession Number : ADA318138

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

Descriptive Note : Technical memo.,

Corporate Author : NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CLEVELAND OH LEWIS RESEARCH CEN TER

Personal Author(s) : Koshigoe, S. ; Murdock, J. W. ; Akin, L. S. ; Townsend, D. P.

PDF Url : ADA318138

Report Date : SEP 1996

Pagination or Media Count : 11

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.

Descriptors :   *HEAT TRANSFER, *COMPUTER PROGRAMS, *COMPUTATIONS, *GREENS FUNCTIONS, *GEARS, LINEAR SYSTEMS, TEMPERATURE, TIME DEPENDENCE, TWO DIMENSIONAL, INTEGRALS, SHAPE, EIGENVECTORS, EIGENVALUES, REGIONS, PROBLEM SOLVING, TIME, BOUNDARIES, INTEGRATION, COEFFICIENTS, INTEGRAL EQUATIONS, RUNGE KUTTA METHOD, GEAR TEETH, HELMHOLTZ EQUATIONS.

Subject Categories : Theoretical Mathematics
      Computer Programming and Software
      Machinery and Tools

Distribution Statement : APPROVED FOR PUBLIC RELEASE