Demand for large-sized spiral bevel gears has increased in recent years and a trend expected to continue. The large-sized spiral bevel gears with equi-depth teeth are usually manufactured based on Klingelnberg cyclo-palloid system. In this paper, the tooth contact pattern of large-sized spiral bevel gears in this system are investigated analytically and experimentally. First, the tooth contact pattern and transmission errors of such gears are analyzed. The analysis method is based on simultaneous generations of tooth surface and simulations of meshing and contact. Next, the large-sized spiral bevel gears are manufactured and the tooth contact pattern of these gears is investigated experimentally. Moreover, the real tooth surfaces are measured using a coordinate measuring machine and the tooth flank form errors are detected using the measured coordinates. It is possible to analyze the tooth contact pattern of the spiral bevel gears with consideration of the tooth flank form errors expressing the errors as polynomial equations. Finally, the influence of alignment errors due to assembly on the tooth contact pattern is also investigated analytically and experimentally. These analyzed results were compared with experimental ones. As a result, the two results showed a good agreement.

1.
Davis
,
J. R.
, 2005,
Gear Materials, Properties, and Manufacture
,
ASM International Technical Books Committee
,
USA
, pp.
92
99
.
2.
Wildhaber
,
E.
, 1945, “
Basic Relationships of Bevel Gears
,”
Am. Mach.
0002-9858,
90
, pp.
99
102
.
3.
Vogel
,
W. K.
, 1959, “
The Importance of Tooth Form for Spiral Bevel Gears
,”
Machinery
,
94
, pp.
135
138
.
4.
Baxter
,
M. L.
, 1962, “
Effect of Misalignment on Tooth Action of Bevel and Hypoid Gears
,”
ASME
Paper No. 61-MD-20.
5.
Gleason Works
, 1978, “
Understanding Tooth Contact Analysis
,” Paper No. SD3139A, New York.
6.
Krenzer
,
T. J.
, 1981, “
Tooth Contact Analysis of Spiral Bevel and Hypoid Gears Under Load
,” SAE Technical Paper No. 810688.
7.
Huston
,
R. L.
,
Lin
,
Y.
, and
Coy
,
J. J.
, 1983, “
Tooth Profile Analysis of Circular-Cut Spiral Bevel Gears
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
105
, pp.
132
137
.
8.
Winter
,
H.
, and
Paul
,
M.
, 1985, “
Influence of Relative Displacements Between Pinion and Gear on Tooth Root Stresses of Spiral Bevel Gears
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
107
, pp.
43
48
.
9.
Litvin
,
F. L.
,
Tsung
,
W.
,
Coy
,
J.
, and
Heine
,
C.
, 1987, “
Method for Generation of Spiral Bevel Gears With Conjugate Gear Tooth Surface
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
109
, pp.
163
170
.
10.
Zhang
,
Y.
,
Litvin
,
F. L.
, and
Handschuh
,
R. F.
, 1995, “
Computerized Design of Low Noise Face-Milled Spiral Bevel Gears
,”
Mech. Mach. Theory
0094-114X,
30
, pp.
1171
1178
.
11.
Litvin
,
F. L.
,
Wang
,
A. G.
, and
Handschuh
,
R. F.
, 1998, “
Computerized Generation and Simulation of Meshing and Contact of Spiral Bevel Gears With Improved Geometry
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
158
, pp.
35
64
.
12.
Fuentes
,
A.
,
Litvin
,
F. L.
,
Mullins
,
B. R.
,
Woods
,
R.
, and
Handschuh
,
R. F.
, 2002, “
Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears
,”
ASME J. Mech. Des.
0161-8458,
124
, pp.
524
532
.
13.
Tsai
,
Y. C.
, and
Chin
,
P. C.
, 1987, “
Surface Geometry of Straight and Spiral Bevel Gears
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
109
, pp.
443
449
.
14.
Fong
,
Z. H.
, and
Tsay
,
B. C.
, 1991, “
A Study on the Tooth Geometry and Cutting Machine Mechanisms of Spiral Bevel Gears
,”
ASME J. Mech. Des.
0161-8458,
113
, pp.
346
351
.
15.
Gosselin
,
C. J.
, and
Cloutier
,
L.
, 1993, “
The Generating Space for Parabolic Motion Error Spiral Bevel Gears Cut by the Gleason Method
,”
ASME J. Mech. Des.
0161-8458,
115
, pp.
483
489
.
16.
Davidov
,
Y.
, 1998, “
General Idea of Generating Mechanism and Its Application to Bevel Gears
,”
Mech. Mach. Theory
0094-114X,
33
, pp.
505
515
.
17.
Handschuh
,
R. F.
, and
Bibel
,
G. D.
, 1999, “
Experimental and Analytical Study of Aerospace Spiral Bevel Gear Tooth Fillet Stresses
,”
ASME J. Mech. Des.
0161-8458,
121
, pp.
565
572
.
18.
Lelkes
,
M.
,
Márialigeti
,
J.
, and
Play
,
D.
, 2002, “
Numerical Determination of Cutting Parameters for the Control of Klingelnberg Spiral Bevel Gear Geometry
,”
ASME J. Mech. Des.
0161-8458,
124
, pp.
761
771
.
19.
Simon
,
V.
, 2007, “
Computer Simulation of Tooth Contact Analysis of Mismatched Spiral Bevel Gears
,”
Mech. Mach. Theory
0094-114X,
42
, pp.
365
381
.
20.
Kato
,
S.
, and
Akamatsu
,
T.
, 1982, “
Measuring Method of Hypoid Gear Tooth Profiles
,” SAE Technical Paper No. 810105.
21.
Krenzer
,
T. J.
, and
Knebel
,
R.
, 1983, “
Computer Aided Inspection of Bevel and Hypoid Gears
,” SAE Technical Paper No. 831266.
22.
Litvin
,
F. L.
,
Zhang
,
Y.
,
Kieffer
,
J.
, and
Handschuh
,
R. F.
, 1991, “
Identification and Minimization of Deviations of Real Gear Tooth Surfaces
,”
ASME J. Mech. Des.
0161-8458,
113
, pp.
55
62
.
23.
Litvin
,
F. L.
,
Kuan
,
C.
,
Wang
,
J. C.
,
Handschuh
,
R. F.
,
Masseth
,
J.
, and
Maruyama
,
N.
, 1993, “
Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurement
,”
ASME J. Mech. Des.
0161-8458,
115
, pp.
995
1001
.
24.
Lin
,
C. Y.
,
Tsay
,
C. B.
, and
Fong
,
Z. H.
, 1998, “
Computer-Aided Manufacturing of Spiral Bevel and Hypoid Gears With Minimum Surface Deviation
,”
Mech. Mach. Theory
0094-114X,
33
, pp.
785
803
.
25.
Gosselin
,
D.
,
Nonaka
,
T.
,
Shiono
,
Y.
,
Kubo
,
A.
, and
Tatsuno
,
T.
, 1998, “
Identification of the Machine Settings of Real Hypoid Gear Tooth Surfaces
,”
ASME J. Mech. Des.
0161-8458,
120
, pp.
429
440
.
26.
Townsend
,
D. P.
, 1991, “
The Design, Manufacture and Application of Gears
,”
Dudley’s Gear Handbook
,
2nd ed.
,
McGraw-Hill
,
New York
, pp.
20.42
20.45
.
27.
Fort
,
P.
, 1980, “
Computer Aided Design, Manufacturing and Inspection System for Spiral Bevel Gears
,”
ASME
Paper No. 80-C2/Det-127.
28.
Kawasaki
,
K.
,
Tamura
,
H.
, and
Nakano
,
Y.
, 1994, “
A Method for Inspection of Spiral Bevel Gears in Klingelnberg Cyclo-Palloid System
,”
Proceedings of the 1994 International Gearing Conference
, Newcastle Upon Tyne, UK, pp.
353
358
.
29.
Kawasaki
,
K.
, and
Tamura
,
H.
, 1998, “
Duplex Spread Blade Method for Cutting Hypoid Gears With Modified Tooth Surface
,”
ASME J. Mech. Des.
0161-8458,
120
, pp.
441
447
.
30.
Litvin
,
F. L.
, and
Fuentes
,
A.
, 2004,
Gear Geometry and Applied Theory
, 2nd ed.,
Cambridge University Press
,
Cambridge
, pp.
98
101
.
31.
Fan
,
Q.
,
DaFoe
,
R. S.
, and
Swangaer
,
J. W.
, 2008, “
Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears
,”
ASME J. Mech. Des.
0161-8458,
130
, p.
072601
.
32.
Stadtfeld
,
H. J.
, 1993, “
Handbook of Bevel and Hypoid Gears, Calculation, Manufacturing and Optimization
,” Rochester Institute of Technology, RIT, pp.
9
12
.
You do not currently have access to this content.