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

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

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.

Document ID

19970018108

Acquisition Source

Legacy CDMS

Document Type

Reprint (Version printed in journal)

Authors

Date Acquired

September 6, 2013

Publication Date

September 1, 1996

Subject Category

Report/Patent Number

Meeting Information

Meeting: Power Transmission and Gearing

Location: San Diego, CA

Country: United States

Start Date: October 6, 1996

End Date: October 9, 1996

Accession Number

97N20188

Funding Number(s)

Distribution Limits

Public

Work of the US Gov. Public Use Permitted.

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