An Approximate Analysis of the Temperature Conditions in a Journal Bearing. Part I: Theory

An analysis is presented for solving the energy equation for a journal bearing film, coupled with the heat conduction equation for the bearing sleeve. The analysis approximates the temperature profile across the film thickness by a fourth order polynomial while the circumferential temperature variation is expressed in terms of a Fourier series expansion. The solution gives the temperatures of the journal, the bearing sleeve, and the lubricant film from which the viscosity distribution can be obtained for use in solving Reynold’s equation. Because the method is quite economic in computer time it should prove useful in practical calculations of journal bearing performance.