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The investigation of planetary gear dynamics including dynamic modeling and dynamic response analysis is a crucial approach in vibration reduction of industrial power transmission systems. In this paper, the nonlinear, time-varying dynamic model of a spur planetary gear system under consideration of the translational and rotational motions is investigated. The three subsystems for sun-planet, ring-planet and planet-carrier are analyzed subsequently, and the dynamic equations of the system are obtained. Moreover, different planet phasing and spacing configurations can be described by means of this model. In addition, the dynamic response is investigated by the multiple-scale method. First, the analytical solutions of the primary, superharmonic and subharmonic resonances are obtained. Then the frequency amplitude curves of different resonance modes are compared and the influence of some parameters on the vibration amplitude is studied. Meanwhile, the accuracy of the analytical solutions is evaluated by the numerical integration simulations. The results show that the frequency-amplitude curves of the primary and superharmonic resonance are similar in shape, the three solutions coexist, and the types of unstable solutions and stable solutions are identical. Furthermore, the softening nonlinearity of the subharmonic amplitude-frequency curve is more obvious under the three-dimensional model. This research is an important development of three-dimensional dynamic modeling and vibration prediction of planetary gears, and also improves the efficiency and accuracy of dynamic response calculation.

Accurate fruit tree models are essential for canopy volume measurement work, we build an orchard mobile robot platform and develop a fruit tree model reconstruction algorithm based on it, optimize the LIDAR Odometry specifically for the orchard environment, fuse the LIDAR Odometry, Inertial Measurement Unit (IMU), Global Navigation Satellite System (GNSS) sensor information and loop closure detection in the form of factors to add factor maps for back-end optimization to reconstruct the orchard map model, use the sliding window method to process in real time The fused information and narrowed the range where the tree trunks are located for two times of line surface feature matching, and the point cloud data are processed to get the fruit tree model. In order to make the point cloud distribution of the reconstructed model uniform, the robot also needs to match a specific walking route, and use the Hough transform and K-Means clustering algorithm to extract the linear-circular-linear walking route autonomously according to the tree row arrangement. The experimental results show that the error of the map model is less than 0.160 m, and the correlation coefficient R2 and root-mean-square error (RMSE) of the canopy model for volume measurement are 0.984 and 0.102 m3, respectively. The collected LiDAR data based on the robotic platform meets the requirement of fruit canopy volume calculation.