A new hypoid gearing using a common crown rack is introduced. The proposed hypoid gear has no unloaded gear transmission error. The common crown rack is located at a neutral position between the pinion and gear blanks. An arbitrary generating surface inclined at a pressure angle is prescribed. The proposed hypoid gearing is in point contact, fulfilling a constant speed ratio along the curved line of action. The synthesis feasibility is numerically verified for the entire range of hypoid gears, including parallel-, intersecting-, and crossed-axis gear systems. The proposed hypoid gear is compared with the hypoid gear by Gleason method and the differences between the two are discussed.

Issue Section:
Design Innovation Paper
Keywords:
Design of machine elements, Design theory , Gear geometry, Kinematics, Mechanism synthesis, Design methodology
Topics:
Gears, Spiral bevel gears, Blanks

References

1.
Park
,
N.
, and
Lee
,
H. W.
,
2011
, “
The Spherical Involute Bevel Gear: Its Geometry, Kinematic Behavior and Standardization
,”
J. Mech. Sci. Technol.
,
25
(
4
), pp.
1023
–
1034
.
Google Scholar
Crossref
Search ADS
 
2.
Wildhaber
,
E.
,
1946
, “
Skew Hypoid Gears
,”
Am. Mach.
,
90
(
16
), pp.
104
–
106
.
3.
Wildhaber
,
E.
,
1946
, “
Basic Relationship of Hypoid Gears
,”
Am. Mach.
,
90
(
4
), pp.
108
–
111
.
4.
Wildhaber
,
E.
,
1946
, “
Gear Tooth Sliding
,”
Am. Mach.
,
90
(
15
), pp.
106
–
110
.
5.
Shtipelman
,
B. A.
,
1978
,
Design and Manufacture of Hypoid Gears
,
Wiley
,
Hoboken, NJ
.
6.
Stadtfeld
,
H. J.
,
1993
,
Handbook of Bevel and Hypoid Gears
, 1st ed.,
Rochester Institute of Technology
,
Rochester, NY
.
7.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
,
Gear Geometry and Applied Theory
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
, pp.
98
–
99
.
8.
Vimercati
,
M.
,
2007
, “
Mathematical Model for Tooth Surfaces Representation of Face-Hobbed Hypoid Gears and Its Application to Contact Analysis and Stress Calculation
,”
Mech. Mach. Theory
,
42
(
6
), pp.
668
–
690
.
Google Scholar
Crossref
Search ADS
 
9.
Zhang
,
J.
,
Fang
,
J.
,
Cao
,
X.
, and
Deng
,
X.
,
2007
, “
The Modified Pitch Cone Design of the Hypoid Gear: Manufacture, Stress Analysis and Experimental Tests
,”
Mech. Mach. Theory
,
42
(
2
), pp.
147
–
158
.
Google Scholar
Crossref
Search ADS
 
10.
Wang
,
P.
, and
Zhang
,
Y.
,
2013
, “
An Invariant Approach for Curvature Analysis of Conjugate Surfaces
,”
Mech. Mach. Theory
,
64
, pp.
175
–
199
.
Google Scholar
Crossref
Search ADS
 
11.
Lin
,
C.
,
Tsay
,
C.
, and
Fong
,
Z.
,
1998
, “
Computer-Aided Manufacturing of Spiral Bevel and Hypoid Gears With Minimum Surface-Deviation
,”
Mech. Mach. Theory
,
33
(
6
), pp.
785
–
803
.
Google Scholar
Crossref
Search ADS
 
12.
Litvin
,
F. L.
, and
Gutman
,
Y.
,
1981
, “
Methods of Synthesis and Analysis for Hypoid Gear-Drives of ‘Formate’ and ‘Helixform,’ Part 1. Calculations for Machine Settings for Member Gear Manufacture of the Formate and Helixform Hypoid Gears
,”
ASME J. Mech. Des.
,
103
(
1
), pp.
83
–
88
.
13.
Kolivand
,
M.
,
Li
,
S.
, and
Kahraman
,
A.
,
2010
, “
Prediction of Mechanical Gear Mesh Efficiency of Hypoid Gear Pairs
,”
Mech. Mach. Theory
,
45
(
11
), pp.
1568
–
1582
.
Google Scholar
Crossref
Search ADS
 
14.
Simon
,
V. V.
,
2011
, “
Influence of Tooth Modifications on Tooth Contact in Face-Hobbed Spiral Bevel Gears
,”
Mech. Mach. Theory
,
46
(
12
), pp.
1980
–
1998
.
Google Scholar
Crossref
Search ADS
 
15.
Simon
,
V. V.
,
2009
, “
Head-Cutter for Optimal Tooth Modifications in Spiral Bevel Gears
,”
Mech. Mach. Theory
,
44
(
7
), pp.
1420
–
1435
.
Google Scholar
Crossref
Search ADS
 
16.
Simon
,
V. V.
,
2007
, “
Computer Simulation of Tooth Contact Analysis of Mismatched Spiral Bevel Gears
,”
Mech. Mach. Theory
,
42
(
3
), pp.
365
–
381
.
Google Scholar
Crossref
Search ADS
 
17.
Simon
,
V. V.
,
1998
, “
The Influence of Misalignments on Mesh Performances of Hypoid Gears
,”
Mech. Mach. Theory
,
33
(
8
), pp.
1277
–
1291
.
Google Scholar
Crossref
Search ADS
 
18.
Dooner
,
D. B.
,
2012
,
The Kinematic Geometry of Gearing
, 2nd ed.,
Wiley
,
New York
.
19.
Radzevich
,
S. P.
,
2013
,
Theory of Gearing: Kinetics, Geometry, and Synthesis
,
CRC Press
,
Boca Raton, FL
.
20.
Phillips
,
J. R.
,
1999
, “
Some Geometrical Aspects of Skew Polyangular Involute Gearing
,”
Mech. Mach. Theory
,
34
(
5
), pp.
781
–
790
.
21.
Figliolini
,
G.
,
Stachel
,
H.
, and
Angeles
,
J.
,
2007
, “
A New Look at the Ball–Disteli Diagram and its Relevance to Spatial Gearing
,”
Mech. Mach. Theory
,
42
(
10
), pp.
1362
–
1375
.
22.
Figliolini
,
G.
,
Stachel
,
H.
, and
Angeles
,
J.
,
2015
, “
A Spatial Version of Octoidal Gears Via the Generalized Camus Theorem
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021015
.
Google Scholar
Crossref
Search ADS
 
23.
Figliolini
,
G.
,
Stachel
,
H.
, and
Angeles
,
J.
,
2015
, “
The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes
,”
ASME J. Mech. Rob.
,
7
(
1
), p.
011003
.
Google Scholar
Crossref
Search ADS
 
24.
Liu
,
C.
, and
Tsay
,
C. B.
,
2002
, “
Contact Characteristics of Beveloid Gears
,”
Mech. Mach. Theory
,
37
(
4
), pp.
333
–
350
.
Google Scholar
Crossref
Search ADS
 
25.
Phillips
,
J. R.
,
2003
,
General Spatial Involute Gearing
,
Springer
,
Berlin
.
26.
Tsai
,
S. J.
, and
Wu
,
S. H.
,
2007
, “
Geometrical Design of Conical Gear Drives With Profile-Shifted Transmission
,” 12th
IFToMM
World Congress, Besancon, France, June 18–21.
27.
Xiao
,
D.
, and
Yang
,
T.
,
1989
, “
Kinematics of Three Dimensional Gearing
,”
Mech. Mach. Theory
,
24
(
4
), pp.
245
–
255
.
Google Scholar
Crossref
Search ADS
 
28.
Abadjiev
,
V.
, and
Petrova
,
D.
,
1997
, “
Testing of the Kinematic Conjugation of the Flanks Active Surfaces of Gear-Pairs of Type Spiroid
,”
Mech. Mach. Theory
,
32
(
3
), pp.
343
–
348
.
Google Scholar
Crossref
Search ADS
 
Copyright © 2017 by ASME
You do not currently have access to this content.