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Research Papers

A Closed-Form Planet Load Sharing Formulation for Planetary Gear Sets Using a Translational Analogy

[+] Author and Article Information
H. Ligata

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210

A. Kahraman1

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210kahraman.1@osu.edu

A. Singh

Advanced Power Transfer Group, General Motors Powertrain, 30240 Oak Creek Drive, Wixom, MI 48393

1

Corresponding author.

J. Mech. Des 131(2), 021007 (Jan 07, 2009) (7 pages) doi:10.1115/1.3042160 History: Received May 09, 2008; Revised October 04, 2008; Published January 07, 2009

A simplified discrete model to predict load sharing among the planets of a planetary gear set having carrier planet position errors is presented in this study. The model proposes a translational representation of the torsional system and includes any number of planets positioned at any spacing configuration. The discrete model predictions are validated by comparing them to (i) the predictions of a deformable-body planetary gear set model and (ii) planet load sharing measurements from planetary gear sets having three to six planets. A set of closed-form planet load sharing formulas are derived from the discrete model for gear sets having equally-spaced planets for conditions when all of the planets are loaded. These formulas allow, in an accurate and direct way, calculation of planet loads as a function of position errors associated with each planet.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 2

Steps to define initial configuration

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Figure 3

The 2D deformable-body model for the example four-planet gear set

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Figure 4

Comparison of Li values predicted by the models to measurements for a four-planet system as a function of Ts. (a) e1=70 μm and (b) e1=35 μm.

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Figure 5

Comparison of Li values predicted by the models to measurements for a four-planet system at Ts=1000 N m. (a) L1 and L3, and (b) L2 and L4.

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Figure 6

Comparison of Li values predicted by the models to measurements for a five-planet system with ec1=70 μm. (a) L1, (b) L3 and L4, and (c) L2 and L5.

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Figure 7

Comparison of Li values predicted by the models to measurements for a five-planet system at Ts=1000 N m. (a) L1, (b) L3 and L4, and (c) L2 and L5.

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Figure 10

Comparison of the discrete model results to (a) Eq. 18 for n=5 and e1=70 μm, e2=40 μm, e3=60 μm, e4=20 μm, and e5=50 μm and (b) Eq. 19 for n=6 and e1=70 μm, e2=20 μm, e3=30 μm, e4=−15 μm, e5=40 μm, and e6=50 μm

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Figure 1

(a) Simplified rotational planet load sharing model and (b) the equivalent translational planet load sharing model

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Figure 8

Comparison of Li values predicted by the models to measurements for a six-planet system with ec1=70 μm. (a) L1, (b) L4, (c) L3 and L5, and (d) L2 and L6.

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Figure 9

Comparison of Li values predicted by the models to measurements for a six-planet system at with Ts=1000 N m. (a) L1, (b) L4, (c) L3 and L5, and (d) L2 and L6.

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