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RESEARCH PAPERS

Express Model for Load Sharing and Stress Analysis in Helical Gears

[+] Author and Article Information
Raynald Guilbault

Department of Mechanical Engineering, École de Technologie Supérieure, Montréal, Canada H3C 1K3

Claude Gosselin, Louis Cloutier

Department of Mechanical Engineering, Laval University, Québec, Canada G1K 7P4

J. Mech. Des 127(6), 1161-1172 (Nov 29, 2004) (12 pages) doi:10.1115/1.1992509 History: Received August 21, 2003; Revised November 29, 2004

The performance of a gear set is strongly influenced by the manufacturing and assembly quality. Therefore, detailed analyses at the design stage, where the effects of expected assembly and manufacturing errors can be simulated, are crucial. At an early design stage, when contact conditions are addressed, the widely used finite element method (FEM) may still result in unwanted computing time. The paper presents an Express model developed to serve as a fast design tool offering fine simulation and a high precision level. The model establishes load sharing, fillet stresses and pressure distribution along the contacting surfaces of meshing helical gear teeth. The calculations combine the finite strip method with a pseudo-three-dimensional (3D) model of the tooth base solved with finite differences to calculate tooth bending deflexion and fillet stresses. The accuracy of the procedure is demonstrated through 3D FEM models. A contact cell discretization completes the model. This very fast and accurate approach gives the contact pressure distributions resulting from the roll-slide motion of mating teeth. An analysis of a helical gear set in two different assembly positions reveals the effects of edge contact, and exhibits the influence of tooth stiffness reduction near tooth corners.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Finite strip of a rectangular plate, (b) spur gear tooth

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Figure 2

Cross section of thick plate deformation

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Figure 4

Stress concentration factor (Kf) and shear stress derivative

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Figure 5

Tooth taper beam model

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Figure 6

Tooth-base model

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Figure 7

Model boundary conditions

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Figure 8

FDM boundary types

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Figure 9

Mesh density transition

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Figure 10

FDM irregular mesh

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Figure 11

Minimum principal stress (compression)

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Figure 12

Maximum shear stress (compression)

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u displacement (compression)

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Figure 14

v displacement (compression)

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Figure 15

Displacement-stress model of a helical gear tooth

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Figure 16

Load cases and results position

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Figure 17

Displacement and tooth fillet stress - spur gear tooth (a) Displacement in the neutral plane (b) Minimum principal stress (compressive side) (c) Maximum principal stress (tensile side)

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Figure 18

Displacement and tooth fillet stress - helical gear tooth. (a) Displacement in the neutral plane (b) Minimum principal stresses (compressive side)

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Figure 19

Pressure cells in contact plane

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Figure 20

Equivalent deformation of surfaces made with the same material

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Figure 21

Release of free boundary. (a) Half-space condition, (b) free boundary corrected.

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Figure 22

Contact pressure distribution—spur gear

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Figure 23

Contact lines of the helical gear set

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Figure 24

Contact pressure distribution—Case A

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Figure 25

Maximum pinion fillet stress—Case A

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Figure 26

Maximum pinion shear stress—Case A

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Figure 27

Contact pressure distribution—Case B

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Figure 28

Maximum pinion fillet stress—Case B

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Figure 29

Maximum pinion shear stress—Case B

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