Research Papers: Design of Direct Contact Systems

A Gear Load Distribution Model for a Planetary Gear Set With a Flexible Ring Gear Having External Splines

[+] Author and Article Information
Yong Hu, Ahmet Kahraman

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

David Talbot

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: talbot.11@osu.edu

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 30, 2018; final manuscript received September 17, 2018; published online January 11, 2019. Assoc. Editor: Hai Xu.

J. Mech. Des 141(5), 053301 (Jan 11, 2019) (12 pages) Paper No: MD-18-1604; doi: 10.1115/1.4041583 History: Received July 30, 2018; Revised September 17, 2018

In order to accurately predict ring gear deformations and to investigate the effects of ring gear flexibility on quasi-static behaviors of planetary gear sets, a complete load distribution model of planetary gear sets having flexible ring gears will be formulated here based on the baseline model proposed by the same authors (Hu, Y., Talbot, D., and Kahraman, A., 2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 053302). Direct comparisons to published experiments are provided to assess the accuracy of the proposed load distribution methodology. Example analyses with flexible ring gear rims are performed indicating that ring gear flexibility could influence gear mesh-level and planetary gear set system-level behaviors. Influence of spline supporting a ring gear is also investigated revealing that positions of planet branches with respect to external splines could influence ring deflections and resultant gear mesh load distributions.

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Fig. 1

(a) A three-node circular beam element, and (b) finite element model of a ring gear segment

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Fig. 2

External spline tooth l¯ splits the element l between ring gear tooth l and (l + 1) into two elements

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Fig. 3

Definition of contact point m in the local circular coordinate system of tooth l of the ring gear and the global coordinate system of the planetary gear set

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Fig. 4

Measured and predicted radial ring gear deflection ΔR of the three-planet gear set for ring gears having (a) Γ = 0.058, (b) Γ = 0.084, and (c) Γ = 0.112 at Ts=1000 N·m

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Fig. 5

Ring gear deflections of the gear set of Table 1 with Γ=0.058 under Ts=1000 N·m: (a) N = 3, (b) N = 4, (c) N = 5, and (d) N = 6 (radial rim deflections are magnified 200×)

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Fig. 6

(a) Peak contact stress of the sun-planet meshes versus Γ, and (b) maximum contact stress distribution over the line of action for a rigid ring as well as ring gears having Γ = 0.0543, 0.0373 and 0.0237

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Fig. 7

(a) Peak contact stress of the ring-planet meshes versus Γ, and (b) maximum contact stress distribution over the line of action for a rigid ring as well as ring gears having Γ = 0.0543, 0.0373, and 0.0237

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Fig. 8

(1) Deformed ring gear and (2) contact stress [MPa] distribution within plane of action of all gear meshes at multiple positions (a,b,c,d)

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Fig. 9

Maximum contact pressures of sun-planet 1 and ring-planet 1 meshes with respect to carrier rotation spanning three consecutive splines

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Fig. 10

Load sharing of (a) a four-planet gear set and (b) a five-planet gear set with rigid (dashed lines) and flexible (solid lines) ring gear with respect to Ts under E1=70μm and other Ei=0



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