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Research Papers

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

[+] Author and Article Information
M. Kolivand1

 Ohio State University, 201 West 19th Avenue, Columbus, OH 43210kolivand.1@osu.edu

A. Kahraman

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

1

Corresponding author. Present address: American Axle and Manufacturing Inc.

J. Mech. Des 132(7), 071004 (Jun 09, 2010) (8 pages) doi:10.1115/1.4001722 History: Received September 28, 2009; Revised April 27, 2010; Published June 09, 2010; Online June 09, 2010

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Gears , Errors
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References

Figures

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Figure 1

Construction of the ease-off, action, and Q surfaces

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Figure 2

Graphical demonstration of the procedure for updating the ease-off surface for surface deviations

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Figure 3

Graphical demonstration of the procedure to compute unloaded TCA: (a) the gear projection plane, ease-off, and Q surfaces; (b) instantaneous contact curve, contact line, and unloaded transmission error

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Figure 4

Theoretical contact curves of an example hypoid gear pair (a) on the drive-side and (b) on the coast side

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Figure 5

Example local deviation surfaces for the gear and pinion tooth surfaces of a face-milled hypoid gear pair

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Figure 6

Ease-off update for the example deviation shown in Fig. 5: (a) three-dimensional view of the projection plane; ℜ¯, ℜ, Q¯, and Q surfaces, and contour plots of (b) ℜ¯, (c) ℜ, and (d) the change in the ease-off topography

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Figure 7

Predicted unloaded tooth contact patterns of (a) theoretical and (b) deviated surfaces of the example face-milled gear pair for σ=6 μm

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Figure 8

Transmission error curves of the theoretical and deviated surfaces of the example face-milled gear pair (a) at no load and (b) at a pinion torque of 200 Nm.

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Figure 9

Predicted maximum contact pressure distributions of (a) the theoretical and (b) the deviated surfaces of the example face-milled gear pair at a pinion toque of 200 N m

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Figure 10

Measured global tooth surface deviations of the example face-hobbed hypoid gear set: (a) deviation of the pinion tooth surfaces, (b) deviation of gear tooth surfaces, and ((c) and (d)) contour plots of these deviations in the active tooth regions

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Figure 11

(a) Theoretical ease-off topography, (b) updated ease-off topography only with the pinion surface deviations, (c) updated ease-off topography only with the gear surface deviations, and (d) updated ease-off topography with both pinion and gear surface deviations of the example face-hobbed hypoid gear pair

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Figure 12

Predicted unloaded tooth contact patterns of (a) theoretical and (b) deviated surfaces of the example face-hobbed gear pair for σ=6 μm

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Figure 13

Transmission error curves of the theoretical and deviated surfaces of the example face-hobbed gear pair (a) at no load and (b) at a pinion torque of 200 N m

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Figure 14

Predicted maximum contact pressure distributions of (a) the theoretical and (b) the deviated surfaces of the example face-hobbed gear pair at a pinion torque of 200 N m

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