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Research Papers

Synthesis of the Pitch Cones of N-Lobed Elliptical Bevel Gears

[+] Author and Article Information
Giorgio Figliolini

DiMSAT, University of Cassino, G. Di Biasio 43, Cassino (Fr) 03043, Italyfigliolini@unicas.it

Jorge Angeles

Department of Mechanical Engineering and CIM, McGill University, 817 Sherbrooke Street, Montreal, QC, H3A 2K6, Canadaangeles@cim.mcgill.ca

J. Mech. Des 133(3), 031002 (Feb 22, 2011) (8 pages) doi:10.1115/1.4003412 History: Received January 07, 2010; Revised December 14, 2010; Published February 22, 2011; Online February 22, 2011

A general formulation of the synthesis of the pitch cones of a pair of N-lobed elliptical bevel gears and the pitch surface of its conjugate crown-rack is proposed. In particular, two pitch cones and the pitch surface of their crown-rack are obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This formulation is implemented in MATLAB ; several significant examples are included, with circular bevel gears becoming a particular case thereof.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Axonometric view of the spherical cone

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Figure 2

The xz section of the elliptical cone

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Figure 3

The yz section of the elliptical cone

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Figure 4

Illustration of the generation of the spherical ellipse

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Figure 5

Starting configuration of three-lobed elliptical pitch cones and the pitch surface of their crown-rack

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Figure 6

General configuration of three-lobed elliptical pitch cones and their crown-rack

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Figure 7

Flow chart for the algorithm synthesis of the pitch surface

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Figure 8

Example of circular bevel gears and their crown-rack for n1=n2=1, γ1M=γ1m=30 deg, and φ1=0 deg. The code produced γ12=60 deg, γ13=120 deg, and φ2=φ3=0 deg.

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Figure 9

Example of one-lobed elliptical pitch cones and their crown-rack for n1=n2=1, γ1M=41.00 deg, γ1m=9.00 deg, and φ1=20 deg. The code produced n3=3, γ12=50 deg, γ13=115 deg, φ2=−72.93 deg, and φ3=−13.23 deg.

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Figure 10

Example of two-lobed elliptical pitch cones and their crown-rack for n1=n2=2, γ1M=53.94 deg, γ1m=16.06 deg, and φ1=35 deg. The code produces n3=4, γ12=70 deg, γ13=125 deg, φ2=−63.95 deg, and φ3=−25.06 deg.

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Figure 11

Example of three-lobed elliptical pitch cones and their crown-rack for n1=n2=3, γ1M=46.56 deg, γ1m=13.44 deg, and φ1=30 deg. The code produced n3=7, γ12=60 deg, γ13=120 deg, φ2=−48.17 deg, and φ3=−17.29 deg.

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Figure 12

Example of two- and one-lobed elliptical pitch cones and their crown-rack for n1=2, n2=1, γ1M=31.31 deg, γ1m=8.69 deg, and φ1=10 deg. The code produced n3=7, γ12=33.95 deg, γ13=110 deg, φ2=−89.80 deg, and φ3=−5.17 deg.

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Figure 13

Example of three- and five-lobed elliptical pitch cones and their crown-rack for n1=3, n2=5, γ1M=27.22 deg, γ1m=17.78 deg, and φ1=5 deg. The code produced n3=8, γ12=61.42 deg, γ13=112.50 deg, φ2=−4.05 deg, and φ3=−2.29 deg.

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