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Multistage planetary gear transmission system has been widely utilized in engineering practice due to the salient characteristics, such as high bearing load and large speed ratio. This paper addresses a two-stage planetary gearbox and establishes a system coupling torsional dynamical model which considers the time-varying mesh stiffness, friction forces, and interstage coupling factors. Meanwhile, the friction and lubrication states are classified to comprehensively analyze the calculation of friction coefficients under different conditions. Considering the time-varying influence of friction on the tooth surface under the condition of fluid lubrication, the vibration response under parametric excitation is solved by a numerical method. A multistage planetary transmission test bench is built in the back-to-back form so as to test the vibration of the two-stage planetary gearbox. It shows that the simulation results of the dynamical model are consistent with the test data. Consideration of the calculation of friction on the tooth surface and the friction coefficients is helpful for the establishment of the more accurate dynamical model and lays the foundation for the structural design, fault diagnosis, and dynamic optimization of the multistage planetary gear transmission system.

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Planetary gearboxes are very prone to failure when they are used in low-speed and heavy-load conditions for a long time. Due to the strong background noise in the industrial field and the signal decay in the process of fault signal transmission, the weak fault characteristics of planetary gearbox are submerged by noise and difficult to extract and identify. Aiming at this problem, an improved chaos detection method for weak signal frequency recognition is proposed. In this paper, the maximum weighted kurtosis is selected as the fitness function, and the Aquila Optimizer (AO) algorithm is used to find the optimal modal number K and penalty factor α of variational modal decomposition (VMD). According to the grey relational degree (GRD), the inherent modal function (IMF) containing rich fault features is selected to reduce the noise of the original signal. Further, a double-coupled Duffing oscillator equation is constructed, and a quantitative criterion for chaotic oscillator phase transition based on the standard deviation weighted average Euclidean distance (WAED) is proposed. Based on the reverse detection method, the sideband growth of the most sensitive IMF after standardization is detected to judge the health state of the planetary gearbox. Detecting the fault characteristic frequency in the most sensitive IMF after normalization and Hilbert transform processing based on the forward detection method to judge the fault type of the planetary gearbox. The effectiveness of proposed method is verified by simulation and experiment. The results show that the proposed method successfully identifies the weak fault characteristics of planetary gearbox, which fully shows that this method has excellent diagnosis effect for planetary gearbox faults with rich frequency fault characteristics, and provides a new method for the diagnosis and identification of weak faults of planetary gearbox in engineering practice.