Nonlinear torsional instabilities in two-stage gear systems with flexible shafts

• The present paper is focused on the torsional instabilities in a two stage gear system.
• A theoretical model is established taking account the torsional flexibility of shafts and time-varying mesh stiffness of the gears.
• Multiple scale method is applied to analyse the instability areas of the gear system for which the generalized modal coordinate is adopted.
• The result is verified by numerical calculations of the dynamic equations by Runge–Kutta method.

The present paper is focused on the torsional instabilities in a two stage gear system. A theoretical model is established taking account the torsional flexibility of the shafts and the meshing time-varying stiffness of the gears. Multiple scale method is applied to analyse the instability areas of the gear system for which the generalized modal coordinate is adopted. The result is verified by numerical calculations of the dynamic equations by Runge–Kutta method.