Dynamic response analysis for non-smooth gear rattling system

For non-smooth gear rattling system, a general dynamic model with backlash consisting of two wheels with a sinusoidal driving is considered in this paper. Selecting the tooth face as the Poincaré section, the Poincaré map is 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 is given to validate the above calculation method. The results show that with increase in forcing amplitude, the motion state of the gear rattling system will change from single-sided tooth impact to double-sided tooth impact. The corresponding phase plane plots are shown. The spectrums of the largest Lyapunov exponents are calculated in a large range of parameters, and the results compared with the bifurcation diagrams obtained by means of local map method in the corresponding parameter range.