Heat propagation due to torsional vibration of shafts

Torsional vibration 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. In the study reported here forced torsional vibration is assumed, and both lumped mass and continuous systems are considered. The hysteretic model for material damping is used to yield the heat generation in the elastic deformation range and an elastoplastic material is assumed in the plastic range. The heat conduction equation is solved for a cylindrical shaft with surface cooling. Closed form solutions and expressions for the maximum temperatures and the maximum surface temperatures are obtained and tabulated for design purposes. It is shown that substantial temperatures can develop in shafts undergoing torsional vibration.