In this study, the impact of misalignments on root stresses of hypoid gear sets is investigated experimentally and theoretically. An experimental set-up designed to allow operation of a hypoid gear pair under loaded quasi-static conditions with various types of tightly controlled misalignments is introduced. These misalignments include the position errors (V and H) of the pinion along the vertical and horizontal directions, the position error (G) of the gear along its axis, and the angle error (γ) between the two gear axes. For example, face-hobbed hypoid gear pair from an automotive axle application is instrumented via a set of strain gauges positioned at the roots along the faces of multiple teeth to measure root strains within a range of input torque. These root strain measurements at different V, H, G, and γ values are presented. A computational model is also proposed to predict the root stresses of face-milled and face-hobbed hypoid gear pairs under various loading and misalignment conditions. The model employs an automated finite elements mesh generator based on a predefined template for a general and computationally efficient treatment of the problem. Model predictions are compared to measurements at the end to assess the accuracy of the model and describe the measured sensitivities.

References

1.
Alban
,
L. E.
, 1985,
Systematic Analysis of Gear Failures
,
American Society for Metals
,
Metals Park, OH
.
2.
McIntire
,
W. L.
,
Malott
,
R. C.
, and
Lyon
,
T. A.
, 1967, “
Bending Strength of Spur and Helical Gear Teeth
,”
Presented at the Semi-Annual Meeting of the American Gear Manufacturers Association
,
Chicago, IL
.
3.
Kawalec
,
A.
,
Wiktor
,
J.
, and
Ceglarek
,
D.
, 2006, “
Comparative Analysis of Tooth-Root Strength Using ISO and AGMA Standards in Spur and Helical Gears with FEM-Based Verification
,”
ASME J. Mech. Des.
,
128
(
5
), pp.
1141
1158
.
4.
Chen
,
Y.-C.
, and
Tsay
,
C.-B.
, 2002, “
Stress Analysis of Helical Gear Set With Localized Bearing Contact
,”
Finite Elem. Anal. Des.
,
38
, pp.
707
723
.
5.
Guibault
,
R.
,
Gosselin
,
C.
, and
Cloutier
,
L.
, 2005, “
Express Model for Load Sharing and Stress Analysis in Helical Gears
,”
ASME J. Mech. Des.
,
127
(
6
), pp.
1161
1172
.
6.
Litvin
,
F. L.
,
Chen
,
J. S.
,
Lu
,
J.
, and
Handschuh
,
R. F.
, 1996, “
Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis
,”
ASME J. Mech. Des.
,
118
(
4
), pp.
561
566
.
7.
Clapper
,
M. L.
, and
Houser
,
D.
,
A Boundary Element Procedure for Predicting Helical Gear Root Stresses and Load Distribution Factors
(94FTM6 American Gear Manufacturers Association, AGMA Technical Papers, 1994).
8.
Gagnon
,
P.
,
Gosselin
,
C.
, and
Cloutier
,
L.
, 1996, “
Analysis of Spur, Helical, and Straight Bevel Gear Teeth Deflection by Finite Strip Method
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
421
426
.
9.
Guingand
,
M.
,
Vaujany
,
J. P.
, and
Icard
,
Y.
, 2004, “
Fast Three-Dimensional Model Quasi-Static Analysis of Helical Gears Using the Finite Prism Method
,”
ASME J. Mech. Des.
,
126
(
6
), pp.
1082
1088
.
10.
Richard
,
E. D.
,
Echempati
,
R.
, and
Ellis
,
J.
, 1998, “
Design and Stress Analysis of Gears using the Boundary Element Method
,”
DETC98/PTG-5791, 1998 ASME DETC Power Transmission and Gearing Conference
,
Atlanta, GA
.
11.
Sfakiotakis
,
V. G.
,
Vaitsis
,
J. P.
, and
Anifantis
,
N. K.
, 2001, “
Numerical Simulation of Conjugate Spur Gear Action
,”
Comput. Struct.
,
79
(
12
), pp.
1153
1160
.
12.
Vijayakar
,
S. M.
,
Busby
,
H. R.
, and
Houser
,
D. R.
, 1987, “
Finite Element Analysis of Quasi-Prismatic Bodies Using Chebyshev Polynomials
,”
Int. J. Numer. Methods Eng.
,
24
, pp.
1461
1477
.
13.
Vijayakar
,
S.
, 1991, “
A Combined Surface Integral and Finite Element Solution for a Three-Dimensional Contact Problem
,”
Int. J. Numer. Methods Eng.
,
31
, pp.
525
545
.
14.
Guibault
,
R.
,
Gosselin
,
C.
, and
Cloutier
,
L.
, 2006, “
Helical Gears, Effect of Tooth Deviations and Tooth Modifications on Load Sharing and Fillet Stresses
,”
ASME J. Mech. Des.
,
128
(
2
), pp.
444
456
.
15.
Conry
,
T. F.
, and
Seireg
,
A.
, 1973, “
A Mathematical Programming Technique for the Evaluation of Load Distribution and Optimal Modifications for Gear Systems
,”
ASME J. Eng. Ind.
,
95
, pp.
1115
1122
.
16.
Talbot
,
D.
, 2007, “
Finite Element Analysis of Geared Shaft Assemblies and Thin-Rimmed Gears
,” MS thesis, The Ohio State University, Columbus, OH.
17.
Hotait
,
M.
, and
Kahraman
,
A.
, 2008, “
Experiments on Root Stresses of Helical Gears with Lead Crown and Misalignments
,”
ASME J. Mech. Des.
,
130
(
7
), p.
074502
.
18.
Wilcox
,
L. E.
, 1981, “
An Exact Analytical Method for Calculating Stresses in Bevel and Hypoid
,”
Proceedings of International Symposium on Gearing and Power Transmissions
,
II
, pp.
115
121
.
19.
Handschuh
,
R. F.
, and
Bibel
,
G. D.
, 1999, “
Experimental and Analytical Study of Aerospace Spiral Bevel Gear Tooth Fillet Stresses
,”
ASME J. Mech. Des.
,
121
(
4
), pp.
565
572
.
20.
Vijayakar
,
S. M.
,
Calyx Hypoid Gear Model, User Manual
(
Advanced Numerical Solution, Inc.
,
Hilliard, OH
, 2004).
21.
Piazza
,
A.
, and
Vimercati
,
M.
, 2007, “
Experimental Validation of a Computerized Tool for Face Hobbed Gear Contact and Tensile Stress Analysis
,”
ASME Conference Proceedings
,
48086
, pp.
939
946
.
22.
Simon
,
V.
, 2000, “
FEM Stress Analysis in Hypoid Gears
,”
Mech. Mach. Theory
,
35
(
9
), pp.
1197
1220
.
23.
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.
,
191
(
11–12
), pp.
1057
1095
.
24.
Vecchiato
,
D.
, 2005, “
Design and Simulation of Face-Hobbed Gears and Tooth Contact Analysis by Boundary Element Method
,” Ph.D. dissertation, University of Illinois at Chicago, Chicago, IL.
25.
Litvin
,
F. L.
,
Fuentes
,
A.
, and
Hayasaka
,
K.
, 2006, “
Design, Manufacture, Stress Analysis, and Experimental Tests of Low-Noise High Endurance Spiral Bevel Gears
,”
Mech. Mach. Theory
,
41
(
1
), pp.
83
118
.
26.
Fong
,
Z.
, 2000, “
Mathematical Model of Universal Hypoid Generator with Supplemental Kinematic Flank Correction Motions
,”
ASME J. Mech. Des.
,
122
(
1
), pp.
136
142
.
27.
Fan
,
Q.
, 2006, “
Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process
,”
ASME J. Mech. Des.
,
128
(
6
), pp.
1315
1327
.
28.
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
.
29.
Zhang
,
Y.
, and
Wu
,
Z.
, 2007, “
Geometry of Tooth Profile and Fillet of Face-Hobbed Spiral Bevel Gears
,”
ASME IDETC/CIE, PTG, DETC2007-34123
,
Las Vegas, NV
.
30.
Kolivand
,
M.
, and
Kahraman
,
A.
, 2009, “
A Load Distribution Model for Hypoid Gears Using Ease-Off Topography and Shell Theory
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1848
1865
.
31.
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
.
32.
Stadtfeld
,
H. J.
, 1993,
Handbook of Bevel and Hypoid Gears
,
Rochester Institute of Technology
,
New York
.
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