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Research Papers

An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears

[+] Author and Article Information
A. Artoni1

 Ohio State University, 201 West 19th Avenue, Columbus, OH 43210alessio.artoni@ing.unipi.it

M. Kolivand, A. Kahraman

 Ohio State University, 201 West 19th Avenue, Columbus, OH 43210

1

Corresponding author.

J. Mech. Des 132(1), 011010 (Dec 31, 2009) (9 pages) doi:10.1115/1.4000645 History: Received June 19, 2009; Revised October 20, 2009; Published December 31, 2009; Online December 31, 2009

Loaded transmission error (LTE) is one of the primary sources of gear noise and vibration. While ease-off topography has been shown to be powerful in improving the contact properties of a gear drive, its optimization to minimize LTEs has been an open problem in the gear literature. Through the formulation of an appropriate nonlinear optimization problem, this study proposes a novel methodology to systematically define optimal ease-off topography to simultaneously minimize LTEs and contact pressures, while concurrently confining the loaded contact pattern within a prescribed allowable region on the tooth surface to avoid any edge- or corner-contact condition. Effectiveness of this optimization is presented using a face-milled and a face-hobbed hypoid gear examples. These example analyses reveal particularly promising results that feature both a drastic reduction in LTE and an appreciable decrease in the maximum contact stress. Although the method is employed here for hypoid gears, its intrinsically systematic formulation enables straightforward applicability to any kind of gears. The methodology presented in this work can be a useful aid for gear engineers to determine optimal ease-off topographies without having to rely on time-consuming trial-and-error approaches or on a priori subjective judgments.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 6

Comparison of contact pressure distributions on the gear tooth of (a) the initial FM design with (b) 5C design and (c) 14C design. Pinion torque is 250 N m. (Black frame: PCA. White frame: ACA.)

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Figure 7

Sensitivity of the FM 14C design to pinion torque. The top figure compares the rms values of LTE of basic and 14C designs. Contact pressure distributions of the 14C design at selected torque values are shown below with the corresponding maximum contact pressure values.

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Figure 8

The ease-off surfaces of (a) initial design, (b) 5C design, and (c) 14C design of the example FH hypoid gear pair

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Figure 9

Comparison of the LTE function of the initial FH design with those of the 5C and 14C optimized designs. Pinion torque is 170 N m.

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Figure 10

Comparison of contact pressure distributions on the gear tooth of (a) the initial FH design with (b) 5C design and (c) 14C design. Pinion torque is 170 N m. (Black frame: PCA. White frame: ACA.)

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Figure 11

Sensitivity of the FH 14C design to pinion torque. The top figure compares the rms values of LTE of basic and 14C designs. Contact pressure distributions of the 14C design at selected torque values are shown below with the corresponding maximum contact pressure values.

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Figure 1

Conceptual flowchart of the employed LTCA model

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Figure 2

An example of (a) the ease-off surface and (b) the corresponding ease-off topography on the PCA

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Figure 3

Flowchart of the employed optimization algorithm

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Figure 4

The ease-off surfaces of (a) initial design, (b) 5C design, and (c) 14C design of the example FM hypoid gear pair

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Figure 5

Comparison of the LTE function of the initial FM design with those of the 5C and 14C optimized designs. Pinion torque is 250 N m.

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