Effect of the coupling strength on the nonlinear synchronization of a single-stage gear transmission

This paper discusses a study of the synchronization phenomenon of a single-stage gear transmission. The analysis is based on numerical and experimental data. Numerical data were obtained from a 4-DOF lumped-mass model which includes the housing stiffness as a linear spring. Experimental data were acquired from a gearbox with soft housing. Both numerical and experimental data were analyzed by different signal processing techniques: the continuous wavelet transform, the phase diagram, the synchronization error diagram, the Kuramoto’s order parameter, and statistical descriptors, such as the mean value, standard deviation, and kurtosis. Statistical descriptors were used to quantify the synchronization degree. It was found that the kurtosis increases as the system becomes more synchronized. The numerical results show that if the coupling strength is sufficiently weak, there is no synchronization; if it reaches a certain threshold, the mechanical elements synchronize; and if it is too stiff, the synchronization ceases. In the case of the experimental data, results indicate a high degree of synchronization. Finally, through analysis of the power spectral density, it was found that the cyclic loading increases 40 % due to synchronization.