Stability Analysis of a Planetary Gear Train Having Repeated Natural Frequencies

A Planetary gear trains (PGTs) are widely used in numerous engineering fields, such as automotive, aerospace, and wind turbines, etc. In the dynamic model of geared systems, the time-varying meshing stiffness causes parametric resonances or instability. This paper investigates the instability caused by the time changing meshing stiffness in a PGTs with three symmetrically arranged planet gears. Focus is placed on the instability related to the repeated natural frequencies. The multiple scales method is used in the analysis, and the analytical results are verified with numerical simulation based on Floquet theory.