Abstract

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error.

1.
Liu
,
S. T.
, 1988, “
Curvilinear Cylindrical Gears
,”
Gear Technol.
0743-6858,
5
(
3
), pp.
8
12
.
2.
Dai
,
Y.
,
Ariga
,
Y.
, and
Nagata
,
S.
, 1999, “
Study on a Cylindrical Gear With Curved Tooth Traces
,”
Mech. Mach. Theory
0094-114X,
6
, pp.
2337
2342
.
3.
Tseng
,
R. T.
, and
Tsay
,
C. B.
, 2001, “
Mathematical Model and Undercutting of Cylindrical Gears With Curvilinear Shaped Teeth
,”
Mech. Mach. Theory
0094-114X,
36
, pp.
1189
1202
.
4.
Tsay
,
C. B.
, 1988, “
Helical Gears With Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis and Stress Analysis
,”
ASME J. Mech. Des.
0161-8458,
110
(
4
), pp.
484
491
.
5.
Litvin
,
F. L.
, and
Fuentes
,
A.
, 2004,
Gear Geometry and Applied Theory
, 2nd ed.,
Cambridge University Press
,
New York
.
6.
Litvin
,
F. L.
, 1989,
Theory of Gearing
,
NASA Publication
,
Washington, DC
.
7.
Litvin
,
F. L.
,
Zhang
,
J.
, and
Handschuh
,
R. F.
, 1988, “
Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis, Part 1: Basic Concepts, Generation of the Pinion Tooth Surface by a Surface by a Plane
,”
ASME J. Mech. Des.
0161-8458,
110
, pp.
337
342
.
8.
Litvin
,
F. L.
,
Zhang
,
J.
, and
Handschuh
,
R. F.
, 1988, “
Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis, Part 2: Generation of the Pinion Tooth Surface by a Surface of Revolution
,”
ASME J. Mech. Des.
0161-8458,
110
, pp.
343
347
.
9.
Litvin
,
F. L.
, and
Kim
,
D. H.
, 1997, “
Computerized Design, Generation and Simulation of Meshing of Modified Involute Spur Gears With Localized Bearing Contact and Reduced Level of Transmission Errors
,”
ASME J. Mech. Des.
0161-8458,
119
, pp.
96
100
.
10.
Litvin
,
F. L.
,
Lian
,
Q.
, and
Kapelevich
,
A. L.
, 2000, “
Asymmetric Modified Spur Drives: Reduction of Noise, Localization of Contact, Simulation of Meshing and Stress
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
188
, pp.
363
390
.
11.
Litvin
,
F. L.
,
Fuentes
,
A.
,
Gonzalez-Perez
,
I.
,
Carvenali
,
L.
,
Kawasaki
,
K.
, and
Handschuh
,
R. F.
, 2003, “
Modified Involute Helical Gears: Computerized Design, Simulation of Meshing and Stress Analysis
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
192
, pp.
3619
3655
.
12.
Litvin
,
F. L.
,
Gonzalez-Perez
,
I.
,
Fuentes
,
A.
,
Hayasaka
,
K.
, and
Yukishima
,
K.
, 2005, “
Topology of Modified Surfaces of Involute Helical Gears With Line Contact Developed for Improvement of Bearing Contact, Reduction of Transmission Errors, and Stress Analysis
,”
Math. Comput. Model.
,
42
, pp.
1063
1078
.
13.
Tseng
,
J. T.
, and
Tsay
,
C. B.
, 2006, “
Undercutting and Contact Characteristics of Cylindrical Gears With Curvilinear Shaped Teeth Generated by Hobbing
,”
ASME J. Mech. Des.
0161-8458,
128
(
3
), pp.
634
643
.
14.
Litvin
,
F. L.
, and
Tsay
,
C. B.
, 1985, “
Helical Gears With Circular Arc Teeth: Simulation of Conditions of Meshing and Bearing Contact
,”
ASME J. Mech. Des.
0161-8458,
107
, pp.
556
564
.
15.
Tsay
,
C. B.
, and
Fong
,
Z. H.
, 1989, “
Tooth Contact Analysis for Helical Gears With Pinion Circular Arc Teeth and Gear Involute Shaped Teeth
,”
ASME J. Mech. Des.
0161-8458,
111
, pp.
278
284
.
16.
Simon
,
V.
, 2005, “
Optimal Tooth Modifications in Hypoid Gears
,”
ASME J. Mech. Des.
0161-8458,
127
(
4
), pp.
646
655
.
17.
Wang
,
W. S.
, and
Fong
,
Z. H.
, 2008, “
A Dual Face-Hobbing Method for the Cycloidal Crowning of Spur Gears
,”
Mech. Mach. Theory
0094-114X,
43
, pp.
1416
1430
.
18.
2009, Website information for Klingelnberg Arcon© cutter head for spiral bevel gear, http://www.klingelnberg.info/en/produkte/arcon.phphttp://www.klingelnberg.info/en/produkte/arcon.php
You do not currently have access to this content.