Asma Masoumi - PhD Student, University of Modena and Reggio Emilia, Modena, Italy
Francesco Pellicano - Associate Professor, University of Modena and Reggio Emilia, Modena, Italy
Farhad Sheykh Samani - Assistant Professor, Shahid Bahonar University of Kerman, Kerman, Iran

Planetary gear vibrations produce dynamic loads, cause reduction in the structural life time and generate noise. The main source of vibration is due to the parametric excitation introduced by the periodically time-varying mesh stiffness of each sun-planet and ring-planet gear meshing stiffness fluctuation. A strong interaction between noise and dynamic transmission error (DTE) has been clearly proved. This study presents a full model to simulate the dynamic behavior of a single-stage planetary gear system with backlash. The generic nature of the formulation allows the analysis of a planetary gear set with any number of planets. This dynamic model considers time varying mesh stiffness and backlash, for all sun-planets and ring-planets meshes and bearing compliance. In the present model each element (the sun gear, planets, carrier and the ring gear) has three degrees of freedom; two transverse and one rotational, giving a total of eighteen degrees of freedom for the case studywith three planets. The linear averaged equations of motion are solved to obtain the natural frequencies and the nonlinear equations of motion are solved numerically to study the effect of time-varying stiffness and backlash. The proposed model is employed to describe the nonlinear behavior of a planetary gearsystem.

planetary gear, nonlinear dynamics,transmission error, backlash