Modelling of time-varying meshing stiffness under tooth wear condition for nonlinear dynamics in compound planetary gear set

Under tooth profile wear condition, with running time increasing, the tooth chord length of the gear tooth is thinner and the tooth profile is not involute profile any more, which results in the changes in amplitude and fluctuation of time-varying meshing stiffness. In this work, in order to reveal the influence of tooth profile wear on time-varying meshing stiffness, an analytical model for calculating the time-varying meshing stiffness under tooth wear condition is built and incorporated with a “translational-rotational” dynamic model of compound planetary gear set. Poincare section, the phase trajectory and bifurcation diagram are employed for analysis of periodic and chaotic motion. The results indicate that, tooth wear accumulation result in the reduction in the amplitude of meshing stiffness at the meshing region of double-pair teeth, but makes no difference in meshing stiffness for the meshing region of single-pair teeth. In order to avoid the system being in Chaos motions, under large tooth wear condition, the input speed should be avoided away from 3700 r/min-6725 r/min, so as to keep the system in a stable periodic motion state.