Nonlinear vibration of the spiral bevel gear considering the axial and radial shaft misalignments

In a spiral bevel gear, noise and vibration cause malfunctioning, the same as the other gear types. In reality, some conditions, misalignment for instance, contribute to intensify the destructive effect of the factors on the dynamic behavior of a gear pair which might even lead to chaos. In this paper, the nonlinear dynamics of a spiral bevel gear pair with different misalignment conditions is deeply investigated. Axial misalignment, radial misalignment and combination of these two types are three cases of misalignments which are considered in the study. In order to illustrate the dynamic behavior, a nonlinear differential equation with time-varying mesh stiffness is solved by numerical integration based on the Runge-Kutta method. The dynamic response of the considered nonlinear system with time-varying parameters is illustrated by means of time responses, phase portraits, bifurcation diagrams and Poincaré maps. Results show that, among the considered three cases, the spiral bevel gear with axial misalignment is the worst destructive case; chaos, period doubling and multi-period responses are observable for this case. It is interesting that the chaotic responses for the case which possesses both types of misalignments are less likely with respect to the case with axial misalignment only.

Keywords:

Spiral bevel gear , Nonlinear dynamics , Misalignment , Transmission error , Gear mesh stiffness