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RESEARCH PAPERS

Mathematical Model and Characteristic Analysis of Elliptical Gears Manufactured by Circular-Arc Shaper Cutters

[+] Author and Article Information
Biing-Wen Bair1

Department of Mechanical Engineering, National United University, 1 Lien Da, Kung-Ching Li, Miao Li, Taiwan 36003, Republic of Chinabairwen@nuu.edu.tw

Chien-Fa Chen, Shih-Fa Chen, Chung-Yi Chou

Department of Mechanical Engineering, National United University, 1 Lien Da, Kung-Ching Li, Miao Li, Taiwan 36003, Republic of China

1

Corresponding author.

J. Mech. Des 129(2), 210-217 (Jan 23, 2006) (8 pages) doi:10.1115/1.2406091 History: Received August 21, 2005; Revised January 23, 2006

A circular-arc elliptical gear drive with convex (or concave) tooth profiles, which is used in an oil pump with a larger pumping volume, was simulated by using circular-arc shaper cutters with concave (or convex) tool profiles. Mathematical models of circular-arc elliptical gears, based on the theory of gearing and the gear generation mechanism, were also developed. The generated elliptical gear drive has a convex–concave tooth profile contact. Because of its complex geometry, the profile of circular-arc elliptical gears may exhibit tooth undercutting, and pointed teeth. Pointed teeth usually appear on the major axis of the elliptical pitch curve. A geometric relation was developed and applied to prevent the pointed teeth on the elliptical gears. A larger pressure angle at major axis and circular-arc radius can eliminate tooth undercutting and increase its tooth thickness at the addendum circle for small teeth. Moreover, a computer simulation program was developed to generate the tooth profile of circular-arc elliptical gears without tooth undercutting and pointed teeth.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Gears
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References

Figures

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Figure 1

Normal section of a rack cutter Σp for generating the driving shaper cutter

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Figure 2

Kinematic relationship between the shaper cutter and the generated gear

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Figure 3

Tangent line of the ellipse

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Figure 4

Normal section of a rack cutter Σg for generating the driven shaper cutter

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Figure 5

Driving circular-arc elliptical gear with tooth undercutting and pointed teeth

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Figure 6

Driven circular-arc elliptical gear with tooth undercutting and pointed teeth

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Figure 7

Driving circular-arc elliptical gear without tooth undercutting and pointed teeth

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Figure 8

Driven circular-arc elliptical gear without tooth undercutting and pointed teeth

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Figure 9

Driving circular-arc elliptical gear for Rp=350mm and ψn=26deg

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Figure 10

Driven circular-arc elliptical gear for Rg=5000mm and ψn=26deg

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