HEAT-TRANSFER IN AN ELECTROMAGNETIC BEARING

An exact solution for two-dimensional, full transient, and steady peri odic heat conduction in an electromagnetic bearing is obtained. Classi cal methods are used to obtain all analytical expression for the tempe rature distribution that arises from power dissipated in the pole wind ings. Among the key findings is the need for cooling in the immediate neighborhood of the bearing support due to the relatively large therma l resistance of the supporting structure. The results presented prove the existence of large temperature gradients in the bearing in both th e radial and circumferential directions. This demands the need for a f ine mesh when performing the commonly used nodal-network thermal analy sis. Conditions are described under which the temperature distribution is independent of the frequency of the time-dependent current supplie d to the poles. For these cases the problem reduces to steady state, a nd the solution is given. A peak circumferential temperature differenc e of about 55 degrees C in the bearing is possible under certain condi tions that are discussed. Attention to proper thermal design is critic al to reduce the dimensional distortion of the bearing caused by therm al expansion. The effects of thermal expansion can range from catastro phic, should the shaft come in contact with the bearing, to an undesir able change in the force and dynamic control characteristics caused by a variation in the critical shaft-to-bearing clearance, which is of t he order of a fraction of a millimeter.