Nonlinear dynamics of spiral bevel gears: Bearing flexibility and clearance effects

This work investigates the nonlinear behavior of a spiral bevel gear system while accounting for bearing flexibility and bearing clearances, which are often neglected in simplified dynamic models. As the main novelty of the present research, the proposed model introduces nonlinear bearing-clearance functions into a seven-degree-of-freedom translational-torsional dynamic model. The developed dynamical model took into account the effects the time-varying mesh stiffness (MS), geometric transmission error (GTE), tooth backlash, and nonlinear bearing clearance. The governing equations are solved numerically using an implicit high-order Runge-Kutta scheme, GearDyns-SBG, validated against Harmonic Balance Method solutions. Modal analysis is performed to investigate the influence of bearing stiffness (ranging from 0.35 to 3.5 GPa) on the natural frequencies of the system. The system response was analyzed using amplitude-frequency curves, bifurcation diagrams, Poincare maps, time-series analyses, FFT spectrum diagram, and recurrence quantification analysis. The results showed that bearing flexibility generally reduces the vibration level of the dynamic transmission error compared to a rigidly supported single-degree-of-freedom model, while simultaneously introducing richer nonlinear phenomena. Indeed, intermediate bearing stiffness values are shown to promote dynamic instabilities, whereas increasing bearing clearance (from 0.001 up to 0.01 mm) leads to lower vibration amplitudes but more unstable responses by a drop in determinism from DET = 98.2 % to DET = 36.9 % and a recurrence rate as low as RR = 0.06 % for the case with 0.007 mm bearing clearance.