Research on nonlinear characteristics of herringbone planetary gear transmission system considering temperature effect

Herringbone gear planetary gear transmission system has the advantages of high contact ratio and high bearing capacity and is widely used in various heavy load fields. However, the gear generates a large amount of heat during the meshing transmission, which affects the nonlinear dynamic characteristics of the system. In this paper, the various nonlinear factors are considered, including time-varying meshing stiffness, engagement damping, backlash, and engagement error. A nonlinear dynamic model of the herringbone planetary gear system considering temperature effects is established by using the lumped-parameter method. The nonlinear vibration differential equation of the system is solved by using the Runge–Kutta method. The impact law of temperature and engagement damping ratio changes on the bifurcation features of the herringbone planetary gear system is studied by combining the maximum Lyapunov exponent diagram, bifurcation diagram, time domain diagram, phase diagram, Poincare diagram, and spectrogram. And the chaos phenomenon of the system is analyzed and controlled by using a non-feedback control method with the external periodic signal. The result shows that with the change of temperature rise and meshing damping ratio, the system exhibits the kinematics response of chaotic, multi-period, and single-period. Higher temperature rise (∆ T > 64 °C) and larger engagement damping ratio ( ξ > 0.122) can make the gear system enter stable periodic motion. The chaotic motion region of the system is effectively controlled to the periodic motion orbit by introducing the periodic signal feedback controller. The relevant conclusions can provide a theoretical basis for the optimal design of the dynamic structure stability of herringbone planetary gear.