Engineering >> Mechanical Engineering

Average Temperature in a Steel Bearing During Quenching

by Ryan Gittens


Submitted : Spring 2013

In this project, the process of quenching (rapidly cooling a metal to obtain certain mechanical properties) a metal sphere was analyzed from a mathematical standpoint. Using mathematical principles covered in Calculus III, the partial differential equation relating the temperature of the sphere with respect to both radial distance and time was proven. Also, the average temperature of the sphere as a function of time was derived. This derived function was then used to solve for the time it takes a steel ball bearing of radius 0.015m to decrease from 900°C to an average temperature of 150°C. Microsoft Excel was used to solve for the time by trial and error. The resulting value was found to be approximately 4 seconds, which was within range of expectation.

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Advisors :
Gerald Hefley, Mathematics and Statistics
Scott Campbell, Chemical & Biomedical Engineering
Suggested By :
Scott Campbell