A new approach for the computerized simulation of load distribution in mismatched spiral bevel gears with point contact is presented. The loaded tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line (Simon, 2006, Mech. and Machine Theory, in press), which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming the usually applied elliptical contact area. The bending and shearing deflections of gear teeth, the local contact deformations of mating surfaces, gear body bending and torsion, the deflections of supporting shafts, and the manufacturing and alignment errors of mating members are included. The tooth deflections of the pinion and gear teeth are calculated by the finite element method. As the equations governing the load sharing among the engaged tooth pairs and load distribution along the tooth face are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. By using this program the load and tooth contact pressure distributions, the angular displacements of the driven gear and the stresses in the pinion and gear teeth are calculated. The influence of design data and transmitted torque on load distribution parameters and fillet stresses is investigated and discussed.

1.
Handschuh
,
R. F.
, 1997, “
Recent Advances in the Analysis of Spiral Bevel Gears
,”
Proceedings, MTM’97 International Conference on Mechanical Transmissions and Mechanisms
,
Tianjin, pp.
635
641
.
2.
Litvin
,
F. L.
, and
Zhang
,
Y.
, 1991, “
Local Synthesis and Tooth Contact Analysis of Face-Milled Spiral Bevel Gears
,” NASA, CR-4342 (AVSCOM TR-90-C-028).
3.
Argyris
,
J.
,
Fuentes
,
A.
, and
Litvin
,
F. L.
, 2002, “
Computerized Integrated Approach for Design and Stress Analysis of Spiral Bevel Gears
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
191
, pp.
1057
1095
.
4.
Huston
,
R. L.
, and
Coy
,
J. J.
, 1982, “
Surface Geometry of Circular Cut Spiral Bevel Gears
,”
ASME J. Mech. Des.
0161-8458,
104
, pp.
743
748
.
5.
Kawasaki
,
K.
,
Tamura
,
H.
, and
Iwamoto
,
Y.
, 1999, “
Klingelnberg Spiral Bevel Gears with Small Spiral Angles
,”
Proceedings, 4th World Congress on Gearing and Power Transmissions
,
Paris, pp.
697
703
.
6.
Lin
,
C.-Y.
, and
Tsay
,
C.-B.
, 1996, “
Mathematical Model of Spiral Bevel and Hypoid Gears Manufactured by the Modified Roll Method
,”
Mech. Mach. Theory
0094-114X,
32
, pp.
121
136
.
7.
Gosselin
,
C.
,
Shiono
,
Y.
,
Kagimoto
,
H.
, and
Aoyama
,
N.
, 1999, “
Corrective Machine Settings of Spiral-Bevel and Hypoid Gears with Profile Deviations
,”
Proceedings, 4th World Congress on Gearing and Power Transmissions
,
Paris, pp.
543
555
.
8.
Lin
,
C.-Y.
,
Tsay
,
C.-B.
, and
Fong
,
Y.-H.
, 1998, “
Computer-Aided Manufacturing of Spiral Bevel and Hypoid Gears with Minimum Surface-Deviation
,”
Mech. Mach. Theory
0094-114X,
33
, pp.
785
803
.
9.
Stadtfeld
,
H. J.
, 1999, “
The Universal Motion Concept for Bevel Gear Production
,”
Proceedings, 4th World Congress on Gearing and Power Transmissions
,
Paris, pp.
595
607
.
10.
Lelkes
,
M.
,
Márialigeti
,
J.
, and
Play
,
D.
, 2002, “
Numerical Determination of Cutting Parameters for the Control of Klingelnberg Spiral Bevel Gear Geometry
,”
Adv. Microelectron.
,
124
, pp.
761
771
.
11.
Wilcox
,
L. E.
, 1981, “
An Exact Analytical Method for Calculating Stresses in Bevel and Hypoid Gear Teeth
,”
Proceedings, International Symposium on Gearing and Power Transmissions
,
Tokyo, Vol.
II
, pp.
115
121
.
12.
Gosselin
,
C.
,
Cloutier
,
L.
, and
Nguyen
,
Q. D.
, 1995, “
A General Formulation for the Calculation of the Load Sharing and Transmission Error Under Load of Spiral Bevel and Hypoid Gears
,”
Mech. Mach. Theory
0094-114X,
30
, pp.
433
450
.
13.
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
.
14.
Falah
,
B.
,
Gosselin
,
C.
, and
Cloutier
,
L.
, 1998, “
Experimental and Numerical Investigation of the Meshing Cycle and Contact Ratio in Spiral Bevel Gears
,”
Mech. Mach. Theory
0094-114X,
33
, pp.
21
37
.
15.
Linke
,
H.
,
Haase
,
A.
,
Hünecke
,
C.
,
Hutschenreiter
,
B.
, and
Trempler
,
U.
, 1999, “
A New Methodology for the Calculation of the Geometry, the Contact Pattern and the Gear Load Capacity of Bevel Gears
,”
Proceedings, 4th World Congress on Gearing and Power Transmissions
,
Paris, pp.
623
634
.
16.
Fuentes
,
A.
,
Litvin
,
F.
,
Mullins
,
B.
,
Woods
,
R.
, and
Handschuh
,
2002, “
Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears
,”
ASME J. Mech. Des.
0161-8458,
124
, pp.
524
532
.
17.
Fang
,
Z.
, and
Wei
,
B.
, 2004, “
Loaded Tooth Contact Analysis for Spiral Bevel Gears Considering Edge Contact
,”
Proceedings, 11th World Congress in Mechanism and Machine Science
,
Tianjin, pp.
838
842
.
18.
Simon
,
V.
, 2000, “
Load Distribution in Hypoid Gears
,”
ASME J. Mech. Des.
0161-8458,
122
, pp.
529
535
.
19.
Simon
,
V.
, 2006, “
Computerized Simulation of Tooth Contact Analysis of Mismatched Spiral Bevel Gears
,”
Mech. Mach. Theory
0094-114X, in press.
20.
Litvin
,
F. L.
, 1994,
Gear Geometry and Applied Theory
,
Prentice–Hall
, Englewood Cliffs, NJ.
21.
Kubo
,
A.
, 1981, “
Estimation of Gear Performance
,”
Proceedings International Symposium on Gearing and Power Transmissions
,
Tokyo, Vol.
II
, pp.
201
206
.
22.
Simon
,
V.
, 2004, “
FEM Stress Analysis in Spiral Bevel Gears
,”
Proceedings 11th International Conference on Tools ICT-2004
,
Miskolc, pp.
147
152
.
23.
Cornell
,
R. W.
, 1981, “
Compliance and Stress Sensitivity of Spur Gear Teeth
,”
ASME J. Mech. Des.
0161-8458,
103
, pp.
447
459
.
24.
Gosselin
,
C.
,
Gagnon
,
P.
, and
Cloutier
,
L.
, 1998, “
Accurate Tooth Stiffness of Spiral Bevel Gear Teeth by the Finite Strip Method
,”
ASME J. Mech. Des.
0161-8458,
120
, pp.
599
605
.
25.
Litvin
,
F.
,
Fuentes
,
A.
, and
Hayasaka
,
K.
, 2006, “
Design, Manufacture, Stress Analysis, and Experimental Tests of Low-Noise High Endurance Spiral Bevel Gears
,”
Mech. Mach. Theory
0094-114X,
41
, pp.
83
118
.
You do not currently have access to this content.