Nonlinear characteristics of a multi-degree-of-freedom spur gear system with bending-torsional coupling vibration

The paper deals with bending-torsion coupling response of spur gear system due to its complex excitations. Based on the Bartelmus model, a multi-degrees-of-freedom lumped parameter dynamic model of a one-stage gear system, which includes gear mesh stiffness fluctuations, transmission errors, gear backlash and torque loads, is established. Considering the misalignment of gear root circle and base circle, an improved mesh stiffness model is applied to calculate the time-varying mesh stiffness by simplifying the gear tooth as a cantilever beam on the root circle. Based on these equations of gear system, the dynamic orbits of the bending-torsion coupling system are observed using bifurcation diagrams plotted with the frequency ratio and torsional stiffness as control parameters. Meanwhile the dynamic properties of the gear system are identified from the time domain response diagrams, phase plane diagrams, Poincare maps and amplitude-frequency spectrums of the gear system. The numerical results show that the system exhibits a diverse range of periodic, sub-harmonic, and chaotic motion with the coupling effects of bending and torsional vibrations. The results provide us a further understanding about vibration generation mechanisms and work status of the spur gear system.