Nonlinear Dynamics and Chaos in Planetary Gears

In planetary gear systems the most important source of vibrations is the parametric excitation due to the periodically time-varying mesh stiffness of each sun-planet and ring-planet gear, as the number of tooth pairs in contact changes during gear rotation. This parametric excitation causes severe vibrations when a harmonic component is in vicinity of the natural frequencies (or their linear combinations). The complex dynamics of a single-stage planetary gear system with time varying mesh stiffness and backlash is simulated using a dynamic model with three equally spaced planets. A bifurcation analysis is performed to explore the dynamic scenario (periodic, quasiperiodic and chaotic), with a special attention to symmetry breaking phenomena that are extremely interesting in planetary gears as they can cause additional imbalance-induced-stresses. Symmetry breaking in the dynamical systems may occurs in the case of chaotic response and the planetary gearbox under investigation, which is perfectly balanced for each position, can suffer of a big dynamic imbalance when chaotic regimes take place; such imbalance gives rise to alternate and unexpected high loads on bearings.