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Research Papers

Modal Analysis of Double-Helical Planetary Gears With Numerical and Analytical Approach

[+] Author and Article Information
Zhaohua Sheng

State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha 410083, China
e-mail: zhsheng@csu.edu.cn

Jinyuan Tang

State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha 410083, China
e-mail: jytangcsu_312@163.com

Siyu Chen

State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha 410083, China
e-mail: chsy1324@csu.edu.cn

Zehua Hu

State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha 410083, China
e-mail: zhhucsu@csu.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 19, 2014; final manuscript received August 4, 2014; published online November 7, 2014. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 137(4), 041012 (Apr 01, 2015) (17 pages) Paper No: DS-14-1081; doi: 10.1115/1.4028788 History: Received February 19, 2014; Revised August 04, 2014

The vibration modal properties of double-helical planetary gear (DHPG) system with three-dimensional motion are investigated with a combined use of numerical and analytical approach in this paper. The lumped-parameter model of the DHPG considering stiffness coupled between the left gear and the right gear is developed. Load-sharing with journal bearings is accepted in this planetary gear system, so that four stiffness coefficients can be applied to describe the dynamic behavior between the planet gear and the carrier. The model has three planar degrees of freedom for the carrier and an added axial degree of freedom for all gears, considering the effect of axial dynamic forces. The vibration equations are obtained according to Lagrange equation. A modal type distribution map is plotted initially to simplify modal classification. With the application of this modal type distribution map, all vibration modes are categorized distinctly into three essentially different types of modes including planet mode (PM), rotational-axial mode (RAM), and planer-translational mode (PTM). Unique characteristics of these vibration modes, such as, eigenvalue number, multiplicity of natural frequencies and deflection relations, are deduced and proved analytically. For each type of vibration modes, the reduced-order eigenvalue problems are derived.

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References

Figures

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Fig. 5

(a) Force analysis of the nth planet gear when the DHPG begins to work and (b) geometry and dynamic model of hydrodynamic journal bearing

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Fig. 4

Dynamic model of the nth ring-planet gear pair and its coordinates in isometric view

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Fig. 3

Dynamic model of the nth sun-planet gear pair and its coordinates in isometric view

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Fig. 2

Dynamic model of the DHPG and its system coordinates in transverse direction. Note: superscript L, R hided, such as, xc represents xcL(R), the rest remains the same.

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Fig. 1

(a) Solid model of DHPG and (b) inner structure with left ring hided

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Fig. 8

Mode shapes at (a) 4767 Hz and (b) 6788 Hz. The left- and right-side views show the translations in ζ direction and rotations of the left and right planet gears, respectively; the front view shows the axial motions of planet gears. Only moved planet gears are colored to emphasize the behavior.

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Fig. 6

Modal type distribution map of the DHPG with five planet gears

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Fig. 7

Modal type distribution maps of the DHPG with (a) 3, (b) 4, (c) 6, and (d) 7 planet gears

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Fig. 9

Mode shapes at (a) 1780 Hz and (b) 3165 Hz. The left- and right-side view show the translations and rotations of the left and the right planet gears, respectively, and rotations of the central components; the front view shows the axial motion of all gears. All moved gears are colored to emphasize this behavior.

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Fig. 10

Mode shapes at 2816 Hz. The left- and right-side view show the translational deflections in x, y directions of the central components, and ζ, η directions of the planet gears, respectively; the front view shows the axial deflections of all components.

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