Nonlinear dynamics analysis of multifactor low-speed heavy-load gear system with temperature effect considered

Low-speed and heavy-load gears generate a lot of heat during meshing transmission, which leads to thermal deformation of the gears and affects the transmission performance of the gear system. It is of great significance to explore the influence law of temperature effects on the nonlinear dynamics of the gear system. Based on the principle of thermal deformation, taking into account the temperature effect and nonlinear parameters, including time-varying meshing stiffness, tooth side clearance as well as comprehensive errors, a nonlinear dynamic model of the gear system of spur cylindrical gear system is established. The Runge–Kutta method is used for numerical solution, the effect of temperature variation and time-varying stiffness coefficient on the bifurcation characteristics of the gear system is analyzed by combining bifurcation diagram, maximum Lyapunov index diagram, phase diagram and Poincare section diagram. The results show that the gear system exhibits complex nonlinear dynamics with the consideration of temperature effects, including four states of single-fold periodic motion, multi-fold periodic motion, and bifurcation and chaotic motion. The influence of temperature variation on the nonlinear characteristics of the gear system is closely related to the value of the time-varying stiffness coefficient. The effect of temperature variation on the bifurcation characteristics of the system is obvious when the value of the time-varying stiffness coefficient s is in the range of 0.4 < s < 0.8. The relevant conclusions can provide references for the design of gear systems under special working conditions.