Problems of Mathematical Modeling of Thermal Processes in Electric Machines

Abstract

The work is devoted to the problems that arise during the construction of mathematical models of heat transfer processes in electric machines during their operation. The electric machine is considered as a complex multilayer electromechanical system with different conditions of heat exchange between the layers, some of which have heat sources of different nature. The radial section of the machine, from a geometric point of view, has the form of a complex area consisting of circles and a 2-n petal rose. Complex system - multilayer cylinder includes movable and fixed layers with different thermophysical properties, rotating at a constant angular velocity around its axis. A mathematical model of temperature distribution in radial sections of an electric machine is constructed, which takes into account the nature of heat exchange at the interface of the structural elements of the machine. The model allows you to calculate the temperature of individual parts of an electric machine. The problem that arises during the construction of mathematical models which is the uncertainty of the conditions of heat exchange between the inner layers of the machine at an unknown temperature on the surfaces of the inner layers is considered. The mathematical model of the thermal process in an electric machine is considered as a boundary value problem for the thermal conductivity equation in a multilayer region with different thermophysical properties of the layers. A method for solving boundary value problems is proposed, which allows to solve the problem of uncertainty of heat exchange conditions between the inner layers in the multilayer region. Numerical experiments were performed and graphs of temperature distributions in an electric machine were constructed.