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Research Papers: Power Transmissions and Gearing

Internal Gear Strains and Load Sharing in Planetary Transmissions: Model and Experiments

[+] Author and Article Information
Avinash Singh1

Advanced Power Transfer, GM Powertrain, General Motors Corporation, 30240 Oak Creek Drive, Wixom, MI 48393avinash.singh@gm.com

Ahmet Kahraman

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

Haris Ligata

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

1

Corresponding author.

J. Mech. Des 130(7), 072602 (May 20, 2008) (10 pages) doi:10.1115/1.2890110 History: Received April 24, 2007; Revised November 28, 2007; Published May 20, 2008

This paper presents results of a comprehensive experimental and theoretical study to determine the influence of certain key factors in planetary transmissions on gear stresses and planetary load sharing. A series of tests are conducted on a family of planetary gear sets, and strains are recorded at various locations on the outer diameter and gear tooth fillet of the ring gear. Pinion position errors are introduced as a representative key manufacturing tolerance, and the resultant changes in the planetary behavior are observed. The experimental data are compared to the predictions of a state-of-the-art multibody contact analysis model—Gear System Analysis Modules (GSAM). This model is capable of including the influences of a number of system-level variables and quantifying their impact on gear strains. The model predictions are shown to compare well with the measured strain at the ring gear outer diameter and tooth fillet. GSAM predictions of planet load sharing are then used to quantify the influence of tangential pinhole position errors on three-, four-, five-, and six-planet test gear sets. These predictions also agree well with the planet load sharing experiments presented in a companion paper.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Stress , Gears , Errors , Gages
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Figures

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Figure 1

Schematic showing locations of strain gages on the test ring gear

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Figure 2

GSAM model of the five-pinion test gear set

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Figure 3

Ring gear loads under forward (positive ẽc1) and reverse loadings (negative ẽc1)

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Figure 4

Location of strain gages on the ring gear: (a) root fillet gage and (b) OD hoop gage

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Figure 5

Hoop strain measured by a typical OD and root fillet strain gage at Location A under forward loading (tooth bending portion not shown)

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Figure 6

Hoop strains measured by four OD hoop gages under forward loading

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Figure 7

Gage and pinion locations

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Figure 8

Hoop strains measured by OD hoop gages under forward and reverse loadings: (a) Gage A, (b) Gage B, (c) Gage C, and (d) Gage D

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Figure 9

(a) Gage location—forward loading, (b) gage location—reverse loading, (c) strain gage measured data—forward loading, and (d) strain gage measured data—reverse loading

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Figure 10

Experimental strain curve showing peak to peak variation—four pinion, no error condition: (a) reversed loading, Fillet Gage A3 and (b) forward loading, Hoop Gage A4

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Figure 11

GSAM predicted strains at four OD hoop gage locations—forward loading

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Figure 12

GSAM predicted hoop strains at OD hoop gage locations under forward and reverse loadings: (a) Gage A, (b) Gage B, (c) Gage C, and (d) Gage D

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Figure 13

(a) GSAM predicted fillet strain under forward loading for varying profile locations. Close-up view of the (b) peak bending stress and (c) peak hoop stress portion.

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Figure 14

(a) GSAM predicted fillet strain under reverse loading for varying profile locations. (b) Close-up view of the peak compressive bending stress portion and (c) gear tooth profile showing sprof.

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Figure 15

Strain curves at the OD and fillet locations under forward and reverse loadings: (a) experiment and (b) GSAM predicted

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Figure 16

GSAM predicted load sharing pattern under positive error: (a) four planets, (b) five planets, and (c) six planets

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Figure 17

GSAM predicted load sharing pattern for a seven-pinion variant with +70μm error

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Figure 18

Comparison of experimental and GSAM predicted loads: (a) four planets, (b) five planets, and (c) six planets

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