Abstract: According to spur gear pair of laboratorial gearbox, a dynamic model with time-varying mesh stiffness, nonlinear clearance and transmission error is established, and its nonlinear dynamic mechanism is also researched. The dynamic response of gear model is analyzed under primary resonance and 1/2 sub-harmonious resonance by means of averaging method, and shows the effect of crack evolvement on mesh stiffness and dynamic characteristic of gear system. The vibration features of gear pair with cracked failure are analyzed by amplitude frequency curve, time domain, phase contrail, Poincare mapping and frequency spectrum. Singularity theory analysis shows the relation between crack extents as well as the internal force formed by transmission error and the dynamic bifurcation of gear system, which indicates different bifurcation under different crack extent and transmission error. At last, mechanism research results are proved by the vibration characteristic of fault signals measured on gearbox experiment, which supply a theory base to crack fault diagnosis of gearbox.

Key words: 1/2 sub-harmonious resonance, Cracked failure, Gear system, Primary resonance, Singularity theory