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TECHNICAL PAPERS

The Synthesis of Elliptical Gears Generated by Shaper-Cutters

[+] Author and Article Information
Giorgio Figliolini

DiMSAT, University of Cassino, G. Di Biasio 43, 03043 Cassino (Fr), ITALYe-mail: figliolini@unicas.it

Jorge Angeles

Dept. of Mechanical Engineering & CIM, McGill University, 817 Sherbrooke St., Montreal, Quebec H3A 2K6, Canadae-mail: angeles@cim.mcgill.ca

J. Mech. Des 125(4), 793-801 (Jan 22, 2004) (9 pages) doi:10.1115/1.1631573 History: Received May 01, 2002; Revised April 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
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References

Figures

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Pitch curves of the elliptical gears and their rack
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Pitch curves and their evolute for rA=200 mm and n1=2: a) convex profile for rB=150 mm; b) convex profile for rB=100 mm; c) concave profile for rB=50 mm and n1=2; d) rack for the same parameters as c)
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Pitch curves and their evolute for rA=200 mm and n1=3: a) convex profile for rB=180 mm; b) convex profile for rB=155.55 mm; c) concave profile for rB=100 mm and n1=3; d) rack for the same parameters as c)
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Geometric model of the shaper-cutter
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Pure-rolling motion of the pitch circle PS of the shaper-cutter on the pitch curve P1 the pinion 1
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Elliptical gears for n1=n2=1,N1=N2=31,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20: a) α1=0 deg; b) α1=45 deg; c) α1=90 deg. The code produces: C=66 mm,m=2.07 mm,L1=L2=201.46 mm and: a) α2=0 deg; b) α2=−79.28 deg; c) α2=−126.87 deg.
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Prototype of the elliptical pair of gears of Fig. 6: a) α1=0 deg; b) α1=45 deg; c) α1=90 deg
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Elliptical gears for n1=1,n2=2,N1=31,N2=62,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−34.93 deg, c=96.19 mm,m=2.07 mm,L1=201.46 mm,L2=402.92 mm.
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Elliptical gears for n1=1,n2=3,N1=31,N2=93,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−22.25 deg, c=126.98 mm,m=2.07 mm,L1=201.46 mm,L2=604.38 mm.
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Elliptical gears for n1=1,n2=4,N1=31,N2=124,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−16.31 deg, c=157.94 mm,m=2.07 mm,L1=201.46 mm,L2=805.84 mm.
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Elliptical pinion-rack for n1=1,N1=31,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code yields Yr*=22.54 mm and m=2.07 mm.
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Elliptical pinion-rack for n1=3,N1=93,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=30 deg. The code yields Yr*=19.81 mm and m=0.83 mm.
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Zoom-in of the elliptical pinion-rack of Fig. 12
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Elliptical gears for n1=2,n2=3,N1=62,N2=93,rA=74 mm,rB=52 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−35.54 deg, c=156.70 mm,m=2.06 mm,L1=401.74 mm,L2=602.61 mm.
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Tooth profiles of elliptical gears for n1=1,N1=15,rA=44 mm,rB=22 mm, ϕ=10 deg, Ns=20 (undercutting)
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Tooth profiles of elliptical gears for n1=1,N1=15,rA=44 mm,rB=22 mm, ϕ=40 deg, Ns=20 (overcutting)

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