The lumped parameter method is used to establish the “translation torsion” coupling dynamic model of the two-stage speed increasing planetary gear system. The bifurcation diagram and the maximum Lyapunov exponent spectrum of the system varying with the excitation frequency are obtained. The chaotic state of the system is quantitatively analyzed and verified by the correlation dimension
(1) By changing the dimensionless excitation frequency, the Poincare section shows the characteristics of fixed point, discrete point and attractor, which indicates that there are periodic, quasi periodic and chaotic states in the system, and that the simultaneous existence of backlash and time-varying meshing stiffness and other factors will make the two-stage planetary gear system appear extremely rich nonlinear dynamic characteristics. When the rotational speed is small, the system is in chaotic state, and there are both unilateral and bilateral shocks in the system; with the increase of rotational speed, the system appears periodic motion, the bilateral shocks disappear, and the system vibration tends to be stable. The main ways of the system entering into chaos are boundary shock and quasi periodic.
（2） With the increase of backlash, the vibration space between meshing pairs of gear system increases, and the ratio of chaotic interval and periodic interval increases. It is more difficult to avoid the chaotic interval in engineering, and the degree of chaos increases. The system begins to appear super chaotic interval, and the system vibration is more unpredictable. From the point of view of restraining chaos, reducing backlash can make the system reduce chaos and enter periodic motion as soon as possible.
(3) When the backlash is small and the meshing is good, the bifurcation diagram of the system has a long steady state, which indicates that the system can keep regular periodic motion for a long time It is difficult for the system to return to periodic or quasi periodic state (near the zero line of curve regression), which indicates that it is difficult for the system to keep periodic motion for a long time, but alternate quasi periodic and chaos and chaos for a long time.