Chaotic Characteristic Analysis of Planetary Gear Transmission System Under Multi-coupling Factor Considering Thermal Effect

PurposePlanetary gears generate a lot of heat during the meshing transmission process, which results in thermal deformation of the gear teeth and affects the nonlinear dynamic characteristics of the system. It is valuable to study the influence of the thermal effect on the chaotic characteristics of planetary gear systems.MethodBased on the law of thermal deformation, considering the temperature effect and multiple nonlinear factors, including the coupling effects of time-varying meshing stiffness, meshing error, and gear backlash, a nonlinear dynamics model of the planetary gear system is established. The system's differential equation is derived from the gear system dynamics theory and solved using the Runge-Kutta method. The impact law of temperature, time-varying stiffness coefficient, and damping ratio changes on the bifurcation features of the planetary gear system is studied by combining the maximum Lyapunov exponent diagram, bifurcation diagram, time domain diagram, phase diagram, Poincare diagram, and spectrogram.ResultsThe planetary gear system exhibits chaotic and rich bifurcation characteristics under the coupling effect of multiple nonlinear factors. With the increase in temperature, the system experiences a kinematic process of chaos-four period-two period-single period. As the time-varying stiffness coefficient changes, the system exhibits chaotic, three-periodic, and two-periodic motion states. The effect of the engagement damping ratio change on the nonlinear characteristics of the system is significant when the value of the temperature is in the range of 0 < increment T < 68 & DEG;C.ConclusionThe chaotic motion of the system is weakened under higher temperature and larger damping ratio, which has an obvious effect on improving the system's stability. The pertinent conclusions can be used as future references for gear system development.

Automated summary

This study investigates the influence of thermal effect and multiple nonlinear factors on the chaotic characteristics of planetary gear systems. The results show that the chaotic motion of the system is weakened under higher temperature and larger damping ratio, which has a significant effect on improving the system's stability. These findings provide important references for the development of gear systems.