Dynamics of spiral bevel gear rattling system

A non-smooth spiral bevel gear rattling model with backlash was established by considering input shaft angle excitation and normal transmission error. Based on the Poisson´s impact law, the oblique-impact process was analyzed in which friction was considered between gear teeth, and the relation between the pre-impact state and the post-impact one was obtained. Selecting the tooth face as the Poincaré section, the Poincaré map was constructed, and a calculation method of Lyapunov exponents presented by using the local map method to avoid calculating the Jacobian at the impact points. An example was given to validate the above calculation method. The results show that with increase in forcing amplitude, the motion state of the gear rattling system change from single-sided tooth impact to double-sided tooth impact. The spectrums of the largest Lyapunov exponents are calculated in a large range of parameters.