Gyroscopic Effects in a Vibratory System

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Abstract
An analytical investigation is made to determine the influence on a vibrating elastic system of a high speed rotating element. A fundamental condition for the presence of any gyroscopic effect is that the vibration be such as to produce a tilt of the spin vector of the rotor. Equations are derived showing (a) that if precession be prevented, no gyroscopic effects are present, and (b), that if precession be permitted, the gyroscopic action contributes a force opposed to the tilt, and proportional to the angle of tilt, in effect increasing the stiffness of the elastic system. Calculations based on an arbitrarily chosen rotor intended to approximate a typical small motor armature indicate that this additive spring force is small, and that the increase in natural frequency caused by the added stiffness is exceedingly small—on the order of 0.1 percent—in the case where the precessional motion is not restrained.

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