# Dynamic response of Spur Planetary Gear System

The number of planetary gears is n = 3, the comprehensive meshing error amplitude is e = 10 μ m, and the rated power of the drive motor is 11kw. The above specific parameters are substituted into the non dimensional nonlinear differential equations. By solving the nonlinear dynamic differential equations of the system, the required images of the displacement and speed in the steady state of the system can be obtained, so as to understand the dynamic response of each component in the transmission system. Because it is aimed at the dynamic response of the rotor, the given dynamic characteristics take the radial X direction of the rotor as an example. When the material of the seal is C / C composite material, and the rotor speed n is different, the time domain and frequency domain diagram of the rotor’s dimensionless vibration displacement are given. In order to facilitate the subsequent application, the specific frequency value is marked in the figure.

As shown in the figure, the time domain response of the radial vibration displacement of the rotor at different speeds and the calculated radial vibration characteristics of the rotor are shown in the figure. AI, Bi, CI and di represent the I (I = 1, 2, 3) times of the rotor rotation frequency when the rotor speed n is 3000, 6000, 9000 and 12000r / min, respectively. It can be seen from the figure that the vibration displacement fluctuation of the rotor presents a relatively regular periodic change, and with the increase of the speed, the vibration displacement of the rotor generally increases; the corresponding frequency response shows that the main frequency components affecting the system vibration are the rotor rotation frequency and its frequency doubling harmonics. Although the variation of the vibration displacement of the rotor is very small, and it is basically in the micron level, it may cause the rotor instability and affect the sealing performance of the seal. Therefore, a clear understanding of the dynamic characteristics of the rotor is very important for the stability of the rotor operation and the sealing performance of the system.

Through the independent analysis of the transmission system and the rotor system, the transmission and rotor system are integrated. Through the corresponding treatment, the dynamic model of the sealed rotor system considering the gear meshing characteristics is established, and the dynamic differential equation of the system is given. MATLAB is used to analyze the dynamic characteristics of the system Using Runge Kutta numerical integration method, the dynamic characteristics of the rotor at different speeds are solved. The corresponding time domain and frequency domain response curves are given and analyzed briefly.

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