Mechanical stability of high-speed planetary gears

The structured properties of the critical speeds and associated critical speed eigenvectors of high-speed planetary gears are identified and mathematically proven. Planetary gears have only planet, rotational, and translational mode critical speeds. Divergence instability is possible at speeds adjacent to critical speeds, and whether or not it occurs is determined using a perturbation method. Numerical results verify the critical speed locations and the stability near these critical speeds. Flutter instabilities occur at extremely high speeds, and these are investigated numerically for each mode type.