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Research Papers

Parametric Study of Meshing Characteristics With Respect to Different Meshing Rollers of the Antibacklash Double-Roller Enveloping Worm Gear

[+] Author and Article Information
Xingqiao Deng

Jinge Wang

 School of Mechanical Engineering and Automation,  Xihua University, P.R. 610039 Chinawangjg@mail.xhu.edu.cn

M. F. Horstemeyer

 Mississippi State University, Mississippi State, MS 39762mfhorst@cavs.msstate.edu

K. N. Solanki

 School for Engineering of Matter, Transport, and Energy,  Arizona State University, Tempe, AZ 85287kns3@cavs.msstate.edu

Junfu Zhang

 School of Mechanical Engineering and Automation,  Xihua University, P.R. 610039 Chinazhang_junfu@126.com

J. Mech. Des 134(8), 081004 (Jul 24, 2012) (12 pages) doi:10.1115/1.4006829 History: Received August 26, 2011; Accepted April 18, 2012; Published July 24, 2012; Online July 24, 2012

Roller shapes play a very critical role in the performance of antibacklash double-roller enveloping hourglass worm (ADEHW) gears; however, their influence is seldom reported in the literature. Based on the theories of differential geometry and gear meshing, this paper presents generic models of meshing characteristics for ADEHW gears, including both the contact curve and the tooth profile. We present different meshing functions and their derivatives with respect to each drive type and their associated roller shapes. We also compare the effects of contact curve, tooth profile, tooth undercutting, lubrication angle, induced normal curvature, and autorotation angle in order to design the most optimal tooth profile for the ADEHW gear. Finite element analysis was also conducted in order to minimize the contact stresses as a function of the roller type. Our results show that a spherical roller has the smallest value among the three available meshing roller shapes but is the most difficult design to procure. A cylindrical roller, however, incurs the greatest contact stress.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Construction diagram of the worm wheel. Part #3 is the roller that will be analyzed as one of three shapes: cylindrical, conical, or spherical

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Figure 2

Location of coordinate systems applied in the parameter study

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Figure 3

The movable coordinate system of the (a) cylindrical roller, (b) conical roller, and (c) spherical roller

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Figure 12

The autorotation angle for the ADEHW gearing with the cylindrical rollers as the largest, while the autorotation angle for the spherical roller is the smallest

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Figure 13

Hobbing machine and corresponding custom-made auxiliary equipment

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Figure 14

Schematic of tooth profile manufacturing processes for (a) troughing on the worm gear, (b) grinding on the worm gear, and (c) grinding by a ball-end grinder

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Figure 15

The tooth profiles of the worm gears produced with the (a) cylindrical, (b) conical, and (c) spherical rollers

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Figure 16

Contact von Mises stress analysis showing (a) the experimental results and the finite element simulation results for cylindrical roller, (b) the finite element mesh used in the analysis, (c) the von Mises stress in the worm gear, and (d) the maximum von Mises stress in the worm roller

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Figure 17

Contact stress comparison with respect to the rotational angle ϕ2 for the conical, cylindrical, and spherical rollers

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Figure 4

Relations of the vector radii for the differential geometry theory used in the parametric analysis

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Figure 5

Contact curves for the (a) cylindrical roller, (b) conical roller, and (c) spherical roller

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Figure 6

The undercutting function Γ values from Eq. 20 of the drive with different center distance A for the (a) cylindrical roller, (b) conical roller, and (c) spherical roller

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Figure 7

The undercutting function Γ values varying with i12 for the (a) cylindrical roller, (b) conical roller, and (c) spherical roller

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Figure 8

The undercutting function Γ values varying with R or β for the (a) cylindrical roller, (b) conical roller, and (c) spherical roller

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Figure 9

The undercutting function Γ values varying with u for the (a) cylindrical roller, (b) conical roller, and (c) spherical roller

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Figure 10

The change of the curvature with respect to the rotational angle ϕ2 for the three rollers, showing that the cylindrical and conical rollers changed curvature but the spherical roller remained fairly constant

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Figure 11

The lubrication angle for the conical roller and cylindrical roller increase as the planet worm gear rotational angle ϕ2 increases, and the lubrication angle for the spherical roller decreases as the planet worm gear rotational angle ϕ2 increases

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