Research Papers: Design of Direct Contact Systems

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

[+] Author and Article Information
N. Leque

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: nicholas.leque@pw.utc.com

A. Kahraman

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

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 17, 2015; final manuscript received December 15, 2016; published online January 16, 2017. Assoc. Editor: Qi Fan.

J. Mech. Des 139(3), 033302 (Jan 16, 2017) (11 pages) Paper No: MD-15-1830; doi: 10.1115/1.4035554 History: Received December 17, 2015; Revised December 15, 2016

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional (3D) formulation of N planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all the three types of manufacturing errors, namely, constant errors such as carrier pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation, and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

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Grahic Jump Location
Fig. 1

(a) A sun-planet pi pair, (b) a ring-planet pi pair (a left-handed planet gear is shown (β>0)), and (c) a carrier-planet pi pair

Grahic Jump Location
Fig. 2

Eccentricity errors for each gear and the carrier (adapted from Ref. [11])

Grahic Jump Location
Fig. 7

Variation of Li with rotation of planets with respect to carrier for (a) configuration H, (b) configuration I, and (c) configuration J, all at Ts=200 N⋅m

Grahic Jump Location
Fig. 6

(a) Variation of Li with Ts for configurations E–F in Table 2 for et1=50 μm and (b) variation of (Li)max with et1 at Ts=200 N⋅m for the same configurations

Grahic Jump Location
Fig. 5

(a) Variation of Li with Ts for configurations A–D in Table 2 for ec1=50 μm and (b) variation of (Li)max with ec1 at Ts=200 N⋅m for the same configurations

Grahic Jump Location
Fig. 4

Variation of Li of (a) in-phase, (b) sequentially phased, (c) counter-phased helical planetary gear sets, (d) in-phase, (e) sequentially phased, and (f) counter-phased spur equivalents of the same gear sets

Grahic Jump Location
Fig. 3

Comparison of the predicted load sharing factors Li to the experiments of Ligata et al. [3] for a range of sun torques Ts with carrier pin hole error: (a) ec1=35 μm and (b) ec1=70 μm



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