An elliptical gear drive, whose rotation axis coincides with its geometric center, is simulated using generation with a rack cutter. The mathematical model of an elliptical gear based on the theory of gearing and gear generation mechanism is also developed. Owing to its complex geometry, the profile of elliptical gears may exhibit tooth undercutting, and pointed teeth. In addition, tooth undercutting of an elliptical gear based on the developed mathematical model of the elliptical gear and the theory of gearing is also investigated. Pointed teeth usually appear on the major axis of the gear elliptical pitch curve. Moreover, a geometric relation is developed and applied to prevent the pointed teeth appearing on elliptical gears. Furthermore, a computer simulation program is developed to generate the tooth profile of elliptical gears without tooth undercutting and pointed teeth. Various numerical examples illustrate the effectiveness of the computerized design process.

Issue Section:
Technical Papers
Keywords:
rotating bodies, CAD, mechanical contact, design engineering
Topics:
Gears
1.
Miller
,
F. H.
, and
Young
,
C. H.
,
1945
, “
Proportions of Elliptic Gears for Quick Return Mechanism
,”
Prod. Eng. (N.Y.)
,
16
(
7
), pp.
462
–
464
.
2.
Chironis, N. P., 1967, Gear Design and Application, McGraw-Hill, New York.
3.
Bernett
,
T.
,
1967
, “
Elliptical Gears for Irregular Motion
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
,
89
(
6
), pp.
33
–
39
.
4.
Katori
,
H.
,
Yokogawa
,
K.
, and
Hayashi
,
T.
,
1994
, “
A Simplified Synthetic Design Method of Pitch Curves Based on Motion Specifications for Noncircular Gears
,”
Trans. Jpn. Soc. Mech. Eng., Ser. A
,
60
(
570
), pp.
668
–
674
.
5.
Tong
,
S. H.
, and
Yang
,
C. H.
,
1998
, “
Generation of Identical Noncircular Pitch Curves
,”
ASME J. Mech. Des.
,
120
(
2
), pp.
337
–
341
.
6.
Freudenstein
,
F.
, and
Chen
,
C. K.
,
1991
, “
Variable-Ratio Chain Drives with Noncircular Sprockets and Minimum Slack-Theory and Application
,”
ASME J. Mech. Des.
,
113
, pp.
253
–
262
.
7.
Emura
,
T.
, and
Arakawa
,
A.
,
1992
, “
A New Steering Mechanism Using Noncircular Gears
,”
JSME Int. J., Ser. III
,
35
(
4
), pp.
604
–
610
.
8.
Kuczewski
,
M.
, 1988, “Designing Elliptical Gears,” Mach. Des., , Aprilpp. 166–168.
9.
Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice-Hall, New-Jersey.
10.
Chang
,
S. L.
,
Tsay
,
C. B.
, and
Wu
,
L. I.
,
1996
, “
Mathematical Model and Undercutting Analysis of Elliptical Gears Generated by Rack Cutter
,”
Mech. Mach. Theory
,
31
(
7
), pp.
879
–
890
.
11.
Pedrero
,
J. I.
,
Artes
,
M.
, and
Garcia-Prada
,
J. C.
,
1996
, “
Determination of the Addendum Modification Factors for Gears with Pre-established Contact Ratio
,”
Mech. Mach. Theory
,
31
(
7
), pp.
937
–
945
.
12.
Liou
,
C. H.
,
Lin
,
H. H.
,
Osward
,
F. B.
, and
Townsend
,
D. P.
,
1996
, “
Effect of Contact Ratio on Spur Gear Dynamic Load With No Tooth Profile Modifications
,”
ASME J. Mech. Des.
,
118
, pp.
439
–
443
.
13.
Bair
,
B. W.
, and
Tsay
,
C. B.
,
1998
, “
ZK-Type Dual-Lead Worm and Worm Gear Drives: Contact Teeth, Contact Ratios and Kinematic Errors
,”
ASME J. Mech. Des.
,
120
(
3
), pp.
422
–
428
.
14.
Litvin, F. L., 1989, Theory of Gearing, NASA Reference Publication RP-1212, Washington D.C.
15.
Wu, X., Wang, S., and Yang, A., 1991, “Non-Circular Gear CAD/CAM Technology,” 8th World Congress on the Theory of Machines and Mechanisms, Prague, Czechoslovakia, pp. 391–394.
Copyright © 2002
 by ASME
You do not currently have access to this content.