Study of the Base Curve and Formation of Singular Points on the Tooth Profile of Noncircular Gears

[+] Author and Article Information
Héctor Fabio Riaza

Faculty of Mechanical Engineering,  Universidad Tecnológica de Pereira, Pereira, Colombiahquinte@utp.edu.co

Salvador Cardona i Foix, Lluïsa Jordi Nebot

Department of Mechanical Engineering,  Universitat Politècnica de Catalunya, Barcelona, Spain

J. Mech. Des 129(5), 538-545 (May 06, 2006) (8 pages) doi:10.1115/1.2712221 History: Received September 22, 2005; Revised May 06, 2006

The base circle of a circular gear is concentric with the pitch circle and tangent to the action line. However, in a noncircular gear the base curve is not known a priori and not easy to determine. In this study, the base curves of noncircular gear wheels are obtained as the geometrical locus of the singular points on the involute tooth profile. Singular points—points from which a second involute branch begins to form on the tooth profile—restrict the allowable tooth height and allow the minimum number of teeth required to be estimated. We discuss the influence of the curvature radius of the pitch curve on the allowable tooth height and present an example to illustrate the proposed method.

Copyright © 2007 by American Society of Mechanical Engineers
Topics: Gears , Wheels
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Figure 6

Formation of singular points: (a) generation process and (b) vector representation of the components of dOJ and dJP

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Figure 7

Singular points of tooth profile

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Figure 8

Influence of curvature radius of pitch curve about allowable tooth height

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Figure 10

Driving and driven gear wheels

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Figure 11

Pitch curve curvature radius

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Figure 12

Base curve, singular points, and generation of a second involute branch along tooth profile

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Figure 13

Allowable tooth height

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Figure 1

Pitch curve evolute, pitch curve, and tooth profile (4)

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Figure 2

Base curve obtained as the envelope curve to the action lines (6)

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Figure 3

Graphical application of the Euler-Savary theorem (8)

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Figure 4

Coordinates systems

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Figure 5

Tangent and normal vector of pitch curve



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