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RESEARCH PAPERS

Geometric Design Using Hypotrochoid and Nonundercutting Conditions for an Internal Cycloidal Gear

[+] Author and Article Information
Yii-Wen Hwang1

Department of Mechanical Engineering, National Chung-Cheng University, 168 San-Hsing, Ming-Hsiung, Chia-Yi 621, Taiwan, R.O.C.imeywh@ccu.edu.tw

Chiu-Fan Hsieh

Department of Mechanical Engineering, National Chung-Cheng University, 168 San-Hsing, Ming-Hsiung, Chia-Yi 621, Taiwan, R.O.C.d9143002@ccu.edu.tw

1

Corresponding author.

J. Mech. Des 129(4), 413-420 (Apr 22, 2006) (8 pages) doi:10.1115/1.2437806 History: Received November 24, 2005; Revised April 22, 2006

This paper uses the theory of gearing to derive the mathematical model of an internal cycloidal gear with tooth difference. Whereas the outer rotor profile is based on a curve equidistant to a hypotrochoidal (or extended hypocycloid) curve, the inner rotor design generally depends upon type of use—e.g., when used as a speed reducer, it is a pin wheel. Therefore, this analysis proposes designs for both a gerotor and a speed reducer. Specifically, for an inner rotor used as a gerotor pump, it outlines a mathematical model to improve pump efficiency and derives a dimensionless equation of nonundercutting. For the speed reducer, it develops and demonstrates with numerical examples, a feasible design region without undercutting on the tooth profile or interference between the adjacent pins.

Copyright © 2007 by American Society of Mechanical Engineers
Topics: Design , Rotors , Equations , Gears
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Figures

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Figure 1

Traditional design of gerotors

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Figure 17

Undercutting and interference example of Case 1 for speed reducer

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Figure 16

Design result of Case 3 of speed reducer

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Figure 15

Design result of Case 2 of speed reducer

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Figure 14

Design result of Case 1 of speed reducer

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Figure 13

Feasible design region for m=3 and N=10

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Figure 12

Feasible design region for m=2 and N=10

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Figure 11

Feasible design region for m=1 and N=10

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Figure 10

Feasible design region of gerotor

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Figure 9

Undercutting example of Case 2 for gerotor

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Figure 8

Design result of Case 2 for gerotor

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Figure 7

Design result of Case 1 for gerotor

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Figure 6

The tooth top and tooth bottom radii of the outer rotor for m=2

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Figure 5

The tooth top and tooth bottom radii of the outer rotor for m=1

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Figure 4

Coordinate system for generating inner rotor

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Figure 3

Applied coordinate system

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Figure 2

Generation of the extended hypocycloidal curve

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