Nonlinear dynamic analysis and chaos control of multi-freedom semi-direct gear drive system in coal cutters

Under the nonlinear influence, the nonlinear oscillation of the semi-direct gear drive system (SDGDS) in coal cutters will happen, which will cause the system unstable. To solve this unstable problem, a multiple degrees of freedom (MDOF) nonlinear dynamic model of a gear pair is set up using mass centralized method, with both gear meshing features including time-varying mesh stiffness, mesh damping, backlash and dynamic transmission errors and nonlinear coupling effect such as radial clearance of ball bearing being taken into account. After the application of dimensionless treatment, the system is calculated using Runge-Kutta method. Meanwhile, the main parameters which may cause chaos and bifurcation are studied, for example, exciting frequency, radial clearance of ball bearing and mesh stiffness ratio. Then, the kinematic phase diagram, the Poincare map, the largest Lyapunov exponent chart as well as the bifurcation diagram are presented with different parameters. Furthermore, a chaos control method by means of proportion integral (PI) is proposed within a selected reasonable range. The results demonstrate that different parameters can lead to the occurrence of different chaotic behavior. It is also found that the chaotic control method suggested in this paper may not only reduce the area of chaos sufficiently but also suppress the chaotic phenomenon effectively. Besides, as there exists many nonlinear parameters, the study of parameters will lay a profound theoretical basis and practical significance for the improvement of the system stability and the optimization of the system parameters.