Vibration modes of planetary gears with unequally spaced planets and an elastic ring gear

The highly structured modal properties of planetary gears having diametrically opposed planets and an elastic ring gear are illustrated and mathematically proved in this work. Two types of modes are found: rotational and translational modes. The properties of each mode type are given mathematically. A rule for how the modes of planetary gears having equally spaced planets evolve as the planets deviate to diametrically opposed is presented and discussed.