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Shock and Vibration
Volume 2017 (2017), Article ID 9864959, 18 pages
Research Article

Three-Dimensional Modeling and Structured Vibration Modes of Two-Stage Helical Planetary Gears Used in Cranes

1School of Mechanical Engineering, Shandong University, Jinan, China
2Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, Shandong University, Ministry of Education, Jinan, China
3Weichai Power Co., Ltd., Weifang, China

Correspondence should be addressed to Yong Wang; moc.361@368ywem

Received 9 September 2016; Revised 26 November 2016; Accepted 22 December 2016; Published 27 February 2017

Academic Editor: Francesco Ripamonti

Copyright © 2017 Lina Zhang 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 dynamic investigation of helical planetary gears plays an important role in structure design as the vibration and noise are perceived negatively to the transmission quality. With consideration of the axial deformations of members, the gyroscopic effects, the time-variant meshing stiffness, and the coupling amongst stages, a three-dimensional dynamic model of the two-stage helical planetary gears is established by using of the lumped-parameter method in this paper. The model is applicable to variant number of planets in two stages, different planet phasing, and spacing configurations. Numerical simulation is conducted to detect the structured vibration modes of the equally spaced systems. Furthermore, the unique properties of these vibration modes are mathematically proved. Results show that the vibration modes of the two-stage helical planetary gears can be categorized as five classes: the rigid body mode, the axial translational-rotational mode, the radical translational mode, and the 1st-stage and the 2nd-stage planet mode.