The global dynamics of a herringbone planetary gear system under stochastic excitations are analyzed, Specifically, excitation parameters following a normal distribution are generated via the Box-Muller transformation, while the Largest Lyapunov Exponent (LLE) and cell mapping spatial discretization are jointly applied to the system’s global analysis. The results show that periodic subdomains are intricately nested at the boundaries of the chaotic subdomain and with the higher-periodic enclosed by the lower-periodic in the parametric solution domain, quasi-periodic motion occurs in the sun gear speed range of 5200, 6000 r/min. In addition, lower periodic subdomains (e.g. P1 and P2) typically exhibit regular borders, increasing the damping ratio above 0.15 or reducing the backlash below 0.08 can weaken the vibration response, meanwhile, a P13 basin of attraction is validated at the 0, 0 state cell. Stochasticity induces chaos to erode periodic subdomains across their boundaries and with numerous scattered chaotic cells evolving into the P2 and P1 regions, enhancing the stochasticity of damping ratio or backlash significantly impairs high-speed vibration stability, and stochasticity acting on backlash more easily induces scattered chaotic cell distribution in the state space. These findings could help optimize the dynamic parameter design of gear systems and thereby mitigate their vibrations.
Lin et al. (Sat,) studied this question.
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