Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension
The authors carry out a numerical analysis of nonlinear dynamics of a spur gear system. For the linear suspension, the dynamics is chaotic for low values of the damping coefficient. Increasing this coefficient, yields a six-fold periodic motion. For a gear system with nonlinear suspension, the behaviour is generically chaotic. However, in different windows of damping coefficient, there appears a periodic motion. Beyond a certain value of the coefficient, the system shows an inverse period-doubling bifurcation. In the standard analysis, the only used control parameter is the rotation speed. From this study, it is evident that knowing the rotational speed and the damping coefficient for which the dynamics is chaotic, one can avoid these and ensure a smooth running of the spur gear system. The coupled equations for the angular displacement of two spur gears are solved using the usual fourth-order Runge-Kutta method. Various measures of chaos, like e.g. the Lyapunov exponent, the correlation dimension and Poincaré sections, are studied to validate the conclusions.
scientific article; zbMATH DE number 5838179