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Modeling and dynamic analysis of spiral bevel gear coupled system of intermediate and tail gearboxes in a helicopter.

Zhu, Haimin; Chen, Weifang; Zhu, Rupeng; Zhang, Li; Fu, Bibo; Lu, Xiong


Haimin Zhu

Weifang Chen

Rupeng Zhu

Li Zhang

Bibo Fu

Xiong Lu


The coupled dynamic model of the intermediate and tail gearboxes’ spiral bevel gear-oblique tail shaft-laminated membrane coupling was established by employing the hybrid modeling method of finite element and lumped mass. Among them, the dynamic equation of the shaft was constructed by Timoshenko beam; spiral bevel gears were derived theoretically by the lumped-mass method, where the effects of time-varying meshing stiffness, transmission error, external imbalance excitation and the like were considered simultaneously; laminated membrane coupling was simplified to a lumped parameter model, in which the stiffness was obtained by the finite element simulation and experiment. On this basis, the laminated membrane coupling and effects of several important parameters, including the unbalance value, tail rotor excitation, oblique tail shaft’s length and transmission error amplitude, on the system’s dynamic characteristics were discussed. The results showed that the influences of laminated membrane coupling and transmission error amplitude on the coupled system’s vibration response were prominent, which should be taken into consideration in the dynamic model. Due to the bending-torsional coupled effect, the lateral vibration caused by gear eccentricity would enlarge the oblique tail shaft’s torsional vibration; similarly, the tail rotor’s torsional excitation also varies the lateral vibration of the oblique tail shaft. The coupled effect between the eccentricity of gear pairs mainly hit the torsional vibration. Also, as the oblique tail shaft’s length increased, the torsional vibration of the oblique tail shaft tended to diminish while the axis orbit became larger. The research provides theoretical support for the design of the helicopter tail transmission system.


ZHU, H., CHEN, W., ZHU, R., ZHANG, L., FU, B. and LU, X. 2021. Modeling and dynamic analysis of spiral bevel gear coupled system of intermediate and tail gearboxes in a helicopter. Proceedings of the Institution of Mechanical Engineers, part C: journal of mechanical engineering science [online], 235(22), pages 5975-5993. Available from:

Journal Article Type Article
Acceptance Date Jan 17, 2021
Online Publication Date Apr 13, 2021
Publication Date Nov 30, 2021
Deposit Date Apr 30, 2021
Publicly Available Date Apr 30, 2021
Journal Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Print ISSN 0954-4062
Electronic ISSN 2041-2983
Publisher SAGE Publications
Peer Reviewed Peer Reviewed
Volume 235
Issue 22
Pages 5975-5993
Keywords Spiral bevel gear; Oblique tail shaft; Finite element method; Lumped mass method; Tail rotor excitation
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