Purely rotational model and vibration modes of compound planetary gears

This study develops a rotational degree of freedom model of general compound planetary gears. The model clarifies the conflicting gear mesh deflection expressions in prior research. For systems with identical, equally spaced planet trains in each stage, all vibration modes are classified into one of two types: overall modes and planet modes. In overall modes, all planet trains in the same planet set move identically. In planet modes, only one planet set has motion, and the motion of each planet train in this planet set is a scalar multiple of that of the arbitrarily chosen first planet train in this set. These structured vibration properties are analytically proven in this study.