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Analytical solution to thermal stresses of high speed PM rotor considering thermal load and heat convection

Aiming at the high speed permanent magnet (PM) rotor with the heat source, this work investigates the analytic solution to the transient temperature field and thermal stress field of the rotor, considering the influence of the forced air cooling of rotor surface on the stress field. Firstly, dimensionless formulation of the transient heat conduction equation including interior heat source is derived, where the axially non-uniform heat convection coefficient and the temperature of main flow region are equivalent to their mean values. Secondly, the Fourier integral transform method is used to solve the dimensionless heat conduction equation. Then, the obtained temperature field is loaded into the analytical solution of strength, in which three types of stress sources such as interference fit, centrifugal force and temperature gradient are included. Finally, examples are carried out to verify the analytical solutions and relative results are discussed.