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Mathematical Problems in Engineering
Volume 2018, Article ID 5368294, 18 pages
Research Article

Study on the Load-Sharing Characteristics of an Aeronautical II-Stage Five-Branching Planets Gear Train Based on the Loaded Tooth Contact Analysis

1School of Mechatronic Engineering, Xi’an Technological University, Xi’an 710021, China
2College of Mechanical and Electrical Engineering, Northwestern Polytechnical University, Xi’an 710072, China

Correspondence should be addressed to Dong Hao; moc.anis@enafoahgnod

Received 27 December 2017; Accepted 28 February 2018; Published 11 April 2018

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2018 Dong Hao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aeronautical two-stage five-branching planets gear train is widely used in the internal decelerator of aeroengines and the main decelerator of helicopters. In order to study the load-sharing characteristics of the aeronautical two-stage five-branching planets gear train, a static load-sharing calculation model for this system is established. The loaded tooth contact analysis method is introduced in the static load-sharing calculation model, and the time-varying meshing stiffness condition of each gear pair is obtained. According to the characteristics of the whole system’s power flow closed-loop characteristics, the twist angle deformation coordination condition of the system is established, which includes installation error, manufacturing error, and floating factor. Using the equivalent meshing error theory, the error of the gear manufacturing and the installation error of the system are analyzed. At the same time, the floating meshing error caused by the change of the meshing side gap caused by the floating of the sun gear and the inner ring gear is considered. The moment balance condition of the sun gear based on the floating of the spline gap is established. Combined with the coordination condition of torsion angle deformation, the torque of each gear pair is obtained. The load-sharing coefficient of the system is further calculated. The influence of the manufacturing error, the installation error, and the floating amount on the load-sharing coefficient is analyzed. The results show that the load-sharing coefficient of each planets gear varies with time when the manufacturing error and installation error alone affect the load-sharing characteristic. The sun gear floating can obviously improve the load-sharing performance. The correctness of the theoretical algorithm is verified by experiments. A new method of calculating the load-sharing characteristics of this system is put forward, which provides a theoretical basis for determining the load-sharing coefficient, reasonable allocation, and control tolerance on the design.