Parametric Solution Domain Structures for Bifurcation and Non-Meshing Dynamic Characteristics of Straight Bevel Gear Systems

Abstract

Aimed at the coupling transition relationship between the periodic motion, the tooth surface impact, the non-meshing state and the dynamic load of straight bevel gear systems with backlash, the 2-parameter plane with respect to the time-varying meshing stiffness and the frequency ratio was built based on the cell mapping principle. Besides, the improved CPNF (continuous-Poincaré-Newton-Floquet) method was applied to solve the solution domain structure of the periodicity, impact, non-meshing and dynamic load characteristics of the system cells. The simulation results show that, there are plentiful bifurcation modes with 3 kinds of tooth surface impacts coexisting in the 2-parameter solution domain structure, including the saddle node bifurcation, the Hopf bifurcation, the period-doubling bifurcation, the catastrophe bifurcation and the period-3 bifurcation. The tooth surface impact and chaos will intensify due to increase of the time-varying meshing stiffness coefficient. The tooth surface non-meshing, the tooth back meshing and the dynamic load coefficient will exhibit mutations under the influences of the tooth impact and the periodic motion. Meanwhile, in the same domain, the tooth surface non-meshing and the tooth back meshing will weaken with the frequency ratio but heighten with the stiffness coefficient.