An exact solution for two-dimensional, full transient, and steady periodic heat conduction in an electromagnetic bearing is obtained. Classical methods are used to obtain an analytical expression for the temperature distribution that arises from power dissipated in the pole windings. Among the key findings is the need for cooling in the immediate neighborhood of the bearing support due to the relatively large thermal resistance of the supporting structure. The results presented prove the existence of large temperature gradients in the bearing in both the radial and circumferential directions. This demands the need for a fine mesh when performing the commonly used nodal-network thermal analysis. Conditions are described under which the temperature distribution is independent of the frequency of the time-dependent current supplied to the poles. For these cases the problem reduces to steady state, and the solution is given. A peak circumferential temperature difference of about 55°C in the bearing is possible under certain conditions that are discussed. Attention to proper thermal design is critical to reduce the dimensional distortion of the bearing caused by thermal expansion. The effects of thermal expansion can range from catastrophic, should the shaft come in contact with the bearing, to an undesirable change in the force and dynamic control characteristics caused by a variation in the critical shaft-to-bearing clearance, which is of the order of a fraction of a millimeter.

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