Stability research of multistage gear transmission system with crack fault

The sub-harmonic resonance phenomenon exists in multistage gear transmission system. Collision motion leads the sub-harmonic resonance instability, which brings harm to system stability. So investigating instability conditions of sub-harmonic resonance and effects of fault on stability have important significance on controlling system stability. From the point of view of nonlinear dynamics, dimensionless dynamical equations of multistage gear transmission system which contains a two-stage fixed-axis gear and a one-stage planetary gear are established. The bifurcation diagrams of system are obtained. By the changing of Poincaré section analyze the evolution process of sub-harmonic resonance and instability conditions. The changes of sub-harmonic resonance and system stability are studied under fixed-axis gear tooth crack fault state in different clearance. The study has important significance for operational prediction of system.