Abstract
In the previous work by the authors (Oh et al. (1998)), it was shown that in order for the model of an interacting spur gear pair to conserve energy, the dependence of the mesh stiffness on the mean rotation must be included in deriving the equations of motion. A quadratic nonlinearity arises from the dependence of the mesh stiffness on the mean rotation, even under the assumption of small deflection. This nonlinearity ensures conservation of energy. In this study, the stability of the steady-state response of interacting spur gears, both for the new equation of motion (EOM) and the classical EOM, is investigated. The map for periodic orbits is determined and a linearized stability analysis is performed. Once the stability is determined, the comparison between the classical and the new EOM is made for a primary, a secondary sub-harmonic, and super-harmonic resonances. The frequency-amplitude curve from direct simulation is compared to the stability analysis. The effect on the stability by the nonlinear jump term is shown, as well as by the variable time. The effect of damping and the magnitude of the applied torque on the stability is shown.
