Static loading of rotating shafts can yield substantial temperatures in the shaft due to heat generated from material damping. It has been recently observed that such a situation in electric generators can lead to insulation failures and machine outages. The hysteretic model for material damping was used to yield the heat generation in the elastic deformation range. The heat conduction equation was solved in the cylindrical shaft with surface cooling. Analytical solutions were obtained and expressions for the maximum temperatures and the maximum surface temperatures were computed and tabulated for design purposes. It is shown that substantial temperatures can develop in shafts at high speeds of rotation even at moderate static loads.

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