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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.

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Asma Masoumi, received her Ph.D. in Mechanical Engineering in 2012, from the doctorate school of "High Mechanics and Automotive Design and Technology", University of Modena and Reggio Emilia, Italy. Her Ph.D. thesis was focused on nonlinear dynamics and stability of the planetary gearboxes under supervision of Prof. Francesco Pellicano.

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