Abstract: To overcome the shortcoming that the calculation efficiency of the ordinary method is low in the flywheel rotor shape optimization, adopting the optimal control theory, brief analytic expressions of the optimal rotor shapes are gained directly based on analyzing the effects of rotating speed on the rotor shapes and dividing it into low, medium and high speed intervals. Through comparing the optimal shapes of the isotropic solid and hollow rotors at low, medium and high speed respectively, variations of the shapes with the rotating speed are revealed. The results indicate that at low rotating speed, the optimal shape of the flywheel rotor has a characteristic of “inner thin, outer thick” along the radial direction, at medium rotating speed, the optimal shape is “inner thick, outer thin”, and at high rotating speed, it is “inner and outer thick, middle thin”. At low rotating speed, the optimal shapes of the solid and hollow rotors are similar. However, at medium and high rotating speed, the hollow rotor optimal shape does not have constant stress arc as well as the one of the solid rotor. Because of containing the constant stress arc in the optimal shape, the solid rotor energy storage performance is better than the hollow one.

Key words: Flywheel rotor, Optimal control, Shape optimization