Parametric instability of a multi-degree-of-freedom spur gear system with friction

The instability due to parametric excitation from variable mesh stiffness in a gear pair system has been studied with the help of a six-degree-of-freedom translational-rotational model to consider the contribution of tooth sliding friction. A new harmonic balanced method based analytical technique has been developed to find instability boundaries for mesh frequency at different resonance conditions. Results are compared with a numerical method based on Floquet theory and show good agreement for mesh frequency equals to natural frequency and twice the natural frequency of the gear pair system. The effects of friction coefficients, modal damping and tooth profile modification on the stability boundaries are investigated.