Abstract

Tooth bending fatigue failure is a primary design concern for gear designers in power transmission applications. Fracture of a gear tooth in operation results in overload conditions to adjacent teeth, which cascades into potential failure. Total loss of power transmission usually occurs within seconds of the primary failure. While standard constant stress amplitude fatigue evaluations are common to experimentally determine probabilistic stress–life (PSN) relationships, they do not directly measure the fatigue lives under complex, non-constant amplitude loading scenarios applied to gears in most applications. Various cumulative damage models exist to estimate fatigue life under duty cycle loading, but their accuracy is both material and stress state dependent. Most models are validated under only uniaxial stress states and for limited materials. There is a void of experimental data that would enable the evaluation of the accuracy of cumulative damage models for gear tooth bending fatigue in typical cases of carburized gear steels. This research study conducts a standard fatigue evaluation along with two sets of dual stress amplitude single tooth bending fatigue tests to empirically determine the effects of multi-stage loading. Various cumulative damage fatigue models are then employed to estimate the fatigue lives of the dual stress amplitude specimens, and the accuracy of each model is assessed.

References

1.
Fatemi
,
A.
, and
Yang
,
L.
,
1998
, “
Cumulative Fatigue Damage and Life Prediction Theories: A Survey of the State of the Art for Homogeneous Materials
,”
Int. J. Fatigue
,
20
(
1
), pp.
9
34
.
2.
Singh
,
A.
,
2001
, “
An Experimental Investigation of Bending Fatigue Initiation and Propagation Lives
,”
ASME J. Mech. Des.
,
123
(
3
), pp.
431
435
.
3.
Manson
,
S. S.
,
Freche
,
J. C.
, and
Ensign
,
C. R.
,
1967
,
Application of a Double Linear Damage Rule to Cumulative Fatigue
, Vol.
3839
,
National Aeronautics and Space Administration
.
4.
Manson
,
S. S.
, and
Halford
,
G. R.
,
1981
, “
Practical Implementation of the Double Linear Damage Rule and Damage Curve Approach for Treating Cumulative Fatigue Damage
,”
Int. J. Fract.
,
17
(
2
), pp.
169
192
.
5.
Höhn
,
B.-R.
,
Ostre
,
P.
,
Michaelis
,
K.
,
Suchandt
,
T.
, and
Stahl
,
K.
,
2000
, “
Bending Fatigue Investigation Under Variable Load Conditions on Case Carburized Gears
,”
Fall Tech. Meet. FTM AGMA
,
Cincinnati, OH
.
6.
Hectors
,
K.
, and
De Waele
,
W.
,
2021
, “
Cumulative Damage and Life Prediction Models for High-Cycle Fatigue of Metals: A Review
,”
Metals
,
11
(
2
), pp.
1
32
.
7.
Subramanyan
,
S.
,
1976
, “
Cumulative Damage Rule Based on the Knee Point of the S-N Curve
,”
J. Eng. Mater. Technol.
,
98
(
4
), pp.
316
321
.
8.
Hashin
,
Z.
, and
Rotem
,
A.
,
1978
, “
A Cumulative Damage Theory of Fatigue Failure
,”
Mater. Sci. Eng.
,
34
(
2
), pp.
147
160
.
9.
Batsoulas
,
N.
,
2016
, “
Cumulative Fatigue Damage: CDM-Based Engineering Rule and Life Prediction Aspect
,”
Steel Res. Int.
,
87
(
12
), pp.
1670
1677
.
10.
Rege
,
K.
, and
Pavlou
,
D. G.
,
2017
, “
A One-Parameter Nonlinear Fatigue Damage Accumulation Model
,”
Int. J. Fatigue
,
98
, pp.
234
246
.
11.
Kwofie
,
S.
, and
Rahbar
,
N.
,
2013
, “
A Fatigue Driving Stress Approach to Damage and Life Prediction Under Variable Amplitude Loading
,”
Int. J. Damage Mech.
,
22
(
3
), pp.
393
404
.
12.
Zhu
,
S. P.
,
Hao
,
Y. Z.
,
de Oliveira Correia
,
J. A. F.
,
Lesiuk
,
G.
, and
de Jesus
,
A. M. P.
,
2019
, “
Nonlinear Fatigue Damage Accumulation and Life Prediction of Metals: A Comparative Study
,”
Fatigue Fract. Eng. Mater. Struct.
,
42
(
6
), pp.
1271
1282
.
13.
Aeran
,
A.
,
Siriwardane
,
S. C.
,
Mikkelsen
,
O.
, and
Langen
,
I.
,
2017
, “
A New Nonlinear Fatigue Damage Model Based Only on S-N Curve Parameters
,”
Int. J. Fatigue
,
103
, pp.
327
341
.
14.
Basquin
,
O. H.
,
1910
, “
The Exponential Law of Endurance Tests
,”
Am. Soc. Test. Mater. Proc.
,
10
, pp.
625
630
.
15.
SAE International Surface Vehicle Recommended Practice
,
1997
, “Single Tooth Gear Bending Fatigue Test,” SAE Stand. J1619.
16.
Hong
,
I. J.
,
Kahraman
,
A.
, and
Anderson
,
N.
,
2021
, “
An Experimental Evaluation of High-Cycle Gear Tooth Bending Fatigue Lives Under Fully Reversed and Fully Released Loading Conditions With Application to Planetary Gear Sets
,”
ASME J. Mech. Des.
,
143
(
2
), p.
023402
.
17.
Hong
,
I. J.
,
Kahraman
,
A.
, and
Anderson
,
N.
,
2020
, “
A Rotating Gear Test Methodology for Evaluation of High-Cycle Tooth Bending Fatigue Lives Under Fully Reversed and Fully Released Loading Conditions
,”
Int. J. Fatigue
,
133
, p.
105432
.
18.
Hong
,
I.
,
Teaford
,
Z.
, and
Kahraman
,
A.
,
2021
, “
A Comparison of Gear Tooth Bending Fatigue Lives from Single Tooth Bending And Rotating Gear Tests
,”
Forsch im Ingenieurwesen
,
86
, pp.
259
271
.
19.
2016
, Windows-LDP, Load Distribution Program, The Gear and Power Transmission Research Laboratory, The Ohio State University, Columbus, OH.
20.
ISO
. ISO 6336-6:2006(En), Calculation of Load Capacity of Spur and Helical Gears – Part 6: Calculation of Service Life Under Variable Load.
21.
Curà
,
F.
,
2016
, “
ISO Standard Based Method for Calculating the In-Operation Application Factor KA in Gears Subjected to Variable Working Conditions
,”
Int. J. Fatigue
,
91
, pp.
459
465
.
22.
Nejad
,
A. R.
,
Gao
,
Z.
, and
Moan
,
T.
,
2014
, “
On Long-Term Fatigue Damage and Reliability Analysis of Gears Under Wind Loads in Offshore Wind Turbine Drivetrains
,”
Int. J. Fatigue
,
61
, pp.
116
128
.
23.
Dixon
,
W. J.
, and
Mood
,
A. M.
,
1948
, “
A Method for Obtaining and Analyzing Sensitivity Data
,”
J. Am. Stat. Assoc
,
43
(
241
), pp.
109
126
.
24.
Engler-Pinto
,
C. C.
,
Lasecki
,
J. V.
,
Frisch
,
R. J.
,
Dejack
,
M. A.
, and
Allison
,
J. E.
,
2005
, “
Statistical Approaches Applied to Fatigue Test Data Analysis
,”
SAE Tech. Pap
,
114
, pp.
422
431
.
25.
Müller
,
C.
,
Wächter
,
M.
,
Masendorf
,
R.
, and
Esderts
,
A.
,
2017
, “
Accuracy of Fatigue Limits Estimated by the Staircase Method Using Different Evaluation Techniques
,”
Int. J. Fatigue
,
100
, pp.
296
307
.
26.
Nelson
,
W.
,
1984
, “
Fitting of Fatigue Curves With Noncontant Standard Deviation to Data with Runouts
,”
J. Test. Eval.
,
12
(
2
), pp.
69
77
.
27.
Pollak
,
R. D.
, and
Palazotto
,
A. N.
,
2009
, “
A Comparison of Maximum Likelihood Models for Fatigue Strength Characterization in Materials Exhibiting a Fatigue Limit
,”
Probabilistic Eng. Mech.
,
24
(
2
), pp.
236
241
.
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