Study of temperature fields in a ball bearings bodies under boundary conditions of the third kind

Abstract

The reliability of the rolling bearing body directly affects the continuity and duration of operation of industrial equipment. Ball bearings are often used in centrifugal pumps of thermal power plants and water supply systems. Overheating and subsequent failure of such bearings lead to failure of pumping equipment. To avoid such breakdowns, it is necessary to study the thermal processes inside the rolling elements, which can lead to their deformation and destruction. In this paper, the problems of non-stationary heat transfer inside rolling bodies (spherical bodies) are considered. An analytical solution of the problem in dimensionless values of temperatures and coordinates is obtained on the basis of Fourier and Bubnov-Galerkin methods under boundary conditions of the third kind. The solution of such a problem requires the use of an extensive mathematical apparatus, so special software tools such as Mathcad and MatLab were used in the work. So solving the problem analytically in dimensionless quantities is convenient because it allows you to scale the results to all such objects without reference to a specific rolling body. As a result, the solution is obtained in the form of a power polynomial that does not contain special functions.