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The expected life of a gear is important parameter especially for the gears to secure of the mechanics of it. Related to this importance, fatigue failure is one of the most seen failures occurred on gears working under cyclic loads. It is not possible to eliminate fatigue failure effects but it is possible to reduce by appropriate materials selection and design criteria. Due to demand for gears with higher load-carrying capacity and increased fatigue life, it is important to determine the fatigue strengths of the gears. In this study, forward extrusion method with cosine and tapered profile dies is carried out to obtain gear-like products. The products are then tested under cyclic loads to determine the fatigue life. The results obtained from the experiments are used as inputs in developing the ANN models. Different ANN models are developed for cosine curved and straight tapered profiles to obtain the best models. A comparative analysis is performed in order to evaluate the accuracy of the developed models, in terms of statistical measurements (R², MSE, MAE). Results revealed that proposed ANN models for both cosine curved and tapered profiles are able to predict the fatigue life of the gear-like profiles. © 2016, National Institute of Science Communication and Information Resources (NISCAIR). All rights reserved.
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Indian Journal of Engineering & Materials Sciences
Vol. 23, August 2016, pp. 239-246
Fatigue life modeling of gear like products using ANN
Önder Ayera*, Sedat Bingölb, Tahir Altinbalika & Hıdır Yankı Kiliçgedikb
aDepartment of Mechanical Engineering, Trakya University, Edirne, Turkey
bDepartment of Mechanical Engineering, Dicle University, Diyarbakır, Turkey
Received 2 September 2015; accepted 2 August 2016
The expected life of a gear is important parameter especially for the gears to secure of the mechanics of it. Related to this
importance, fatigue failure is one of the most seen failures occurred on gears working under cyclic loads. It is not possible to
eliminate fatigue failure effects but it is possible to reduce by appropriate materials selection and design criteria. Due to
demand for gears with higher load-carrying capacity and increased fatigue life, it is important to determine the fatigue
strengths of the gears. In this study, forward extrusion method with cosine and tapered profile dies is carried out to obtain
gear-like products. The products are then tested under cyclic loads to determine the fatigue life. The results obtained from
the experiments are used as inputs in developing the ANN models. Different ANN models are developed for cosine curved
and straight tapered profiles to obtain the best models. A comparative analysis is performed in order to evaluate the accuracy
of the developed models, in terms of statistical measurements (R2, MSE, MAE). Results revealed that proposed ANN
models for both cosine curved and tapered profiles are able to predict the fatigue life of the gear-like profiles.
Keywords: fatigue, Gear forming, ANN, Extrusion
As defined by the AGMA gears are machine elements
that transmit motion between axis and plane. In the
design of a machine element which subjected to
cyclic loading such as gears there are several
requirements that must be met. Engineers have been
working for years on the development of advanced
materials and manufacturing methods, in order to
design gears with stronger teeth especially the failure
problem of gears. There are a lot of different material
and design parameters to consider when determining
the number of loading cycles needed for fatigue crack
to appear. As known, two types of stresses can change
in gear pair in the course of power transmission:
(i) bending stress and (ii) surface contact stress. On
the other hand, two types of teeth damage can occur
on gear when it is subjected to cyclic loads: gear
pitting and tooth breakage1. The determination of the
maximum stresses in a loaded gear tooth is
complicated by the variation in magnitude and
direction of the load on the tooth during contact and
by the shape of the tooth, since it has varying width
and is joined to the body of the gear by a fillet2-4. In
general, the strength of a tooth gradually increases
from the tip to root of the tooth.
Many studies have been carried out on the topic of
fatigue problem of gears. Sraml and Flaskel5 used
Hertzian theory for the computational modeling of
contact fatigue damage initiation. They also used
FEM to specify the number of stress cycles needed for
the primary fatigue damage to happen. Fredette and
Brown6 attempted to reduce the stresses around a gear
root tooth by drilling holes along the axis of a gear
segment. Results revealed that it is possible to
improve the strength and durability of a gear with the
addition of design features in critical areas. Sankar
and Nataraj1 investigated the change in bending
strength of a spur gear by replacing its trochoidal fillet
with a circular root fillet. Finite element simulations
were conducted on standard and modified spur gears
using ANSYS software in purpose to determine the
change in the strength of tooth as well as minimize
the failure in the spur gear. A stress-strain analysis
in the framework of FEM was conducted by
Krumberger et al.7 in order to analyze the gear crack
propagation. The process was divided into two
periods; crack initiation and crack propagation.
Simulations were done by variable loading in order to
determine the life of the spur gear. In another study,
Krumberger et al.8 determined the cycles needed for
fatigue crack in a thin-rim gear to appear on the basis
of FEM analysis. Mohanty9 has used analytical
method for the calculation of the load sharing of HCR
spur gears. A detailed investigation on contact
stresses in spur gears has been carried out by
——————
*Corresponding author (E-mail: onderayer@trakya.edu.tr)
240 INDIAN J ENG. MATER. SCI., AUGUST 2016
Thirumurugan and Muthuveerappan10 by conducting a
single point loaded FEM model. The effect of
different FE models and certain gear parameters were
analyzed in order to determine
the load sharing ratio and the stresses. Li11 used
FEM to investigate the tooth contact strength of spur
gears for different contact ratios and addendums.
Contact analyses were conducted based on the LSR
(load shearing ratio) using a mathematical
programming method.
In practice, gears usually work under dynamic
loads. Because of this, a localized damage can cause a
tooth breakage, which most often leads to a total gear
failure. The failure analysis based on stress-life
diagram is most widely used method for gear design
applications. Fatigue life diagrams can be used to
show the behavior of a material under various
conditions. Obtaining such information requires a
large number of experiments. Artificial Neural
Networks (ANNs) may be used in predicting fatigue
life of gears beforehand thus reducing the number of
experiments needed. The use of ANN in predicting a
wide range of material properties and forming
methods has been investigated by several researchers.
These researchers have used ANN models to estimate,
forming loads37-38, fatigue life diagrams12-20, flow
curves21-27, as well as bending properties28-33, wear
loss and surface properties34-36 of various types of
materials and methods. Genel15 attempted to predict
the fatigue life properties of steels using tensile
material data. It was pointed out that it is possible to
make fairly good predictions using ANN. Lee et al.18
developed an ANN model for the estimation of the
fatigue damage based on the experimental results.
Results revealed that by use of ANN, fatigue damage
can be estimated with relative ease. Mohanty et al.19
applied ANN for fatigue life estimation of two
different aluminum alloys. It was observed that
predicted results for both alloys were in agreement
with the experiments. Junior et al.20 demonstrated the
generalization capability of ANNs in building life
diagrams by using a few S-N curves.
In the light of the above mentioned studies, it can
be seen that the use of ANN in modeling of various
types of materials and forming methods became
widespread. However, it should be noticed herein
that, to the authors’ best knowledge, a predictive
ANN model for fatigue life prediction of gear like
products has not been studied in the literature and is
the subject of current study. In this study; the cyclic
loads were applied on the products which were
produced by forward extrusion with cosine and
tapered profile dies with different die land lengths to
determine the fatigue strength. The experimental
fatigue stress values of each product were measured
and recorded. Later on, possibility of using ANNs for
the lifetime predictions of gear like products was
investigated by conducting networks with different
configurations using the data derived from the
experiments that were carried out using different
sample types. The excellent capabilities of ANNs in
fitting the experimental stress-life curves were also
evaluated.
Methodology
In this study, gear like profiles were produced by
forward extrusion with two different die profiles;
cosine curved and straight tapered. Samples were
tested under variable stresses and experimental results
for selected parameters were recorded per sample
giving a total of 96 data to analyze. Using the data
available, ANN models were developed for fatigue
life prediction. Then, ANN results were compared
with the experimental results. Having sufficient data
available can be particularly helpful in understanding
how well the network is performing. Flowchart for the
present study is given in Fig. 1.
Fig. 1—Flowchart of the study
AYER et al.: FATIGUE LIFE MODELING OF GEAR LIKE PRODUCTS USING ANN 241
Experimental study
Al1050 material was used in the experiments.
The chemical compound of Al 1050 was given in
Table 1.
The stress-strain relationship of AA 1050 which
is a very important mechanical property of the
material was determined from compression test. It is
given as;
σ = 138ε0.156 MPa … (1)
Billets were cut into sections from the bar, each 45
mm in length. Then, the diameter of the billets was
machined to 28 mm. The container has an inner
diameter of 28.2 mm and outer diameter of 60 mm.
The punch was made from the same material and has
the diameter of 28 mm.
Two different transition geometries, cosine curved
and straight tapered dies, with four and six teeth
profiles were used in the present study. Punches,
containers and billets were cut out using CNC
machine. The dies were made by wire-cut EDM
machine due to their geometrical complexity. Dies
and other tools were made from 1.2344 DIN hot
worked tool steel and hardened to 54 HRc.
Photographical view of the experimental set up were
given in Fig. 2. The hydraulic press used in the
experiments is a 150 metric ton press having a
constant ram speed of 5 mm/s. Before the
experiments, all the billets were cleaned using acetone
in order to provide the similar friction conditions.
Photographical view of the extruded part can also be
seen in Fig. 2. Cosine and straight tapered die
transition profiles with three different die land length
which were 15, 20, 25 mm. respectively were used in
the forward extrusion experiments.
INSTRON 8501 Universal Test Machine was used
for the experiments in this study. Upper and lower
apparatus were machined from 1.2344 steel, hardened in
oil and tempered to 52Rc for fatigue tests. Experimental
setup of fatigue tests can be seen in Fig. 3.
Loading effect on the machine parts is related with
the location of the applied force. Total bending load
for gears occurs in the dedendum. Resultant stress
(Wbend) value is given in Eq. (2);
 =
=∗
… (2)
and expressed in Eq. (3).
 =ğ
ğ … (3)
Moment value according to gear geometry can be
expressed as in Eq. (4);
 = 5.133 ∗  (4)
So resultant fatigue bending stress on the gear can
be written as:
 =(∗
)
∗ … (5)
hmin and y values of each gear is measured and
recorded for accurate calculations.
Load is given schematically in Fig. 4 and can be
defined as Ft=F/2 for tooth and it is forced to be bent
and fractured. Moreover, fatigue stress occurs at a
critical point near dedendum, hence determination of
the loading point has a great importance to analyze
the experiments.
Table 1—Chemical compound of AA 1050 aluminum.
Si Fe Cu Mn Mg Zn V Ti Pb Al
0.158
0.291
0.012
0.005
0.012
0.018
0.01
0.008
0.005
Balance
Fig. 2—Experimental die setup and extrusion products
Fig. 3—Experimental setup of fatigue tests
Fig. 4—
Schematical view of loads on gears for fatigue test
(a)
detailed view of loading, (b) 4 teeth gear loading and
(c) 6 teeth gear loading
242 INDIAN J ENG. MATER. SCI., AUGUST 2016
Loading to gears is carried out by the movement of
Instron 8501 Universal Test Machine’s jaws. A force
couple on the gears is manifested by means of an
implemented Ft force. The distance between this force
couples is calculated as 18.2 mm in 4 teeth gears and
as 20 mm in 6 teeth gears. By opening two channels
on the upper loading apparatus in the testing set two
pins with 2 mm diameter are attached to these
channels. In this way, the force couple is made to
affect through a single distributed loading line on the
gears sensitively.
Development of the ANN modeling
Different learning rules can be used in order to
improve the ANNs’ performance. Back propagation is
a common algorithm for training the ANNs since it
has the advantages of being very simple and accurate.
After the network is initialized with random weights,
the method continuously updates the weights to match
the required output until the loss function is
minimized.
The results obtained from the experiments were
used for the development of the ANN models. The
inputs of the network are tooth number (N),
die bearing length (L) and stress (σ), and the only
output is fatigue life (logN). The modeling was
divided into two sections; the first ANN model is
related to the fatigue life prediction of tapered die
profile. The second ANN model is related to
the estimation of fatigue life of cosine die profile.
The structure of the developed neural networks is
given in Fig. 5.
A transfer function is necessary to translate the
input signals to output signals. The choice of the
transfer function in ANNs is of great importance to
their performance however there isn’t a strict rule for
selecting transfer function. The selection depends
mostly on experience. In this study, two transfer
functions, Tanh Axon and Sigmoid Axon, were used
to introduce nonlinearity into the network. An ANN
structure with the feed-forward neural networks was
used to estimate the fatigue life of tapered and cosine
gear. The total experimental data (48 samples for
tapered profile and 48 samples for cosine profile) was
randomized and divided into two categories named
training subsets (80% of total data) and testing subsets
(20% of total data). The ideal transfer function and
the number of neurons and hidden layers should be
found through a trial and error method. In the
selection of best network structure, the measurements
(R2, RMSE, MAE) were used as the performance
criteria between the ANN predicted and the
experimental values. The effect of different network
structures and training algorithms on the ANN models
is presented in Table 2.
As shown in Table 2, the network structure with 12
neurons (Model 3) provided fairly good prediction
results for the tapered profile and the network
structure with 14 neurons (Model 9) produced the best
Fig. 5—Neural network structure for fatigue life estimation
Table 2—Statistical values of all the performed ANN models.
ANN Models of Tapered Profile
Algorithm
Function Neuron Number
MSE MAE R2
M1 TanhAxon LM 4 0.135 0.318 0.678
M2 TanhAxon LM 8 0.128 0.295 0.799
M3 TanhAxon LM 12 0.032 0.153 0.946
M4 TanhAxon Momentum 6 0.039 0.169 0.935
M5 SigmoidAxon LM 8 0.065 0.215 0.898
M6 SigmoidAxon Momentum 16 0.052 0.198 0.907
ANN Models of Cosine
Profile
Algorithm
Function Neuron Number
MSE MAE R2
M7 TanhAxon LM 6 0.036 0.124 0.898
M8 TanhAxon LM 12 0.022 0.085 0.982
M9 TanhAxon LM 14 0.002 0.030 0.999
M10 TanhAxon Momentum 4 0.015 0.113 0.982
M11 SigmoidAxon LM 8 0.034 0.114 0.901
M12 SigmoidAxon Momentum 14 0.029 0.095 0.924
AYER et al.: FATIGUE LIFE MODELING OF GEAR LIKE PRODUCTS USING ANN 243
performance for cosine die profile in terms of
statistical criterions (R2, MSE, MAE). In particular,
exceptional agreement was obtained adopting the
LM algorithm. Furthermore, changes in the
transfer function also impact the model estimation
capabilities. In this regard, relatively better
responses were provided by TanhAxon functions.
Considering these results and disregarding small
variations, it can be said that, as far as the fatigue life
prediction is regarded, the models offer fairly strong
performance.
Results and Discussion
Since the gears are subjected to variable stresses by
general operating conditions, they carry out their
duties under continuous fatigue effect. In this study, a
test type which affects the gear and determines the
resistance of the gear as a result of one-way bending
fatigue procedure is used to determine the resistance
of manufactured gear parts against the fatigue. The
conducted experiment is extremely suitable with
regards to determining the effects of parameters such
as production method, material geometry and material
to the resistance of the product. In order to determine
the fatigue resistances of the gears, implemented
stress values must be known or calculated.
Implemented stress values on the gear in the
conducted test are given in Table 3.
Effect of die transition profile and die land length
In order to compare fatigue strengths of 4 and 6
teeth parts, implemented stress values were equal in
the experiments for each test. At the moment any
damage occurred on the gears the experiments were
stopped, number of cycles is noted and then following
Wohler curves were obtained for each product
separately and diagrams were concluded and the best
fatigue resistant die set was chosen for which die land
length is 15 and die transition profile is cosine for
both 4 and 6 teeth gears.
4 teeth products were obtained by using dies
having cosine dies with 15, 20 and 25 mm die land
length and experimented on fatigue test. When
graphics were examined together, it can be seen
that fatigue strength values are extremely close to
in each other in logarithmic scale. By the increase of
die land length the fatigue strength decreases even if
by a little.
Experiments were conducted by using also 4 teeth
but tapered dies having different die land lengths and
selecting appropriate stress values. When the results
were examined, very close results attract the attention.
However, it can also be seen that parts with shorter
die land lengths have a little bit better fatigue
strength.
It was determined that extrusion products of 4 teeth
parts’ fatigue strength values vary according to die
land length and transition profile. At the same die
land length values, products which were
manufactured with dies having cosine die profile have
more strength than products produced with die
products having tapered die profile. It was observed
that die transition profile in these dies produces more
deformation than tapered dies and in this case the
product’s fatigue strength increases. It is clear from
the results that best fatigue resistant product is
obtained from the cosine curved die with 15 mm die
land length and its fatigue stress-cycle curve is seen in
Fig. 6. Only one diagram was given in the study
because of the similarity of the results in the
logarithmic scale hence detailed fatigue stress-cycle
results were given in Table 4.
Likewise, 6 teeth products were produced by
forward extrusion method. Fatigue strengths of
Table 3—Applied stress and load values of fatigue tests
4 Teeth gear 6 Teeth gear
Stress (MPa) Load (kN) Load (kN)
76 -1.75±1.5 -0.950±0.700
92 -2.125±1.875 -1.125±0.875
98 -2.375±2.125 -1.250±1.000
115 -2.625±2.375 -1.375±1.125
126 -2.875±2.625 -1.500±1.250
138 -3.125±2.875 -1.625±1.375
182 -4.125±3.875 -2.125±1.875
Fig. 6—Fatigue stress-
cycle curve of 4 teeth cosine profile for 15
mm die land length
244 INDIAN J ENG. MATER. SCI., AUGUST 2016
manufactured extrusion products were examined by
using the same testing apparatus. When the obtained
results were examined; it was observed that, fatigue
cycles of damage occurrence are extremely close but
still products manufactured by using dies with shorter
land length have better fatigue strength. It is observed
from the results that for 6 teeth gear products cosine
curved die with 15 mm die land length is best die setup
for higher fatigue resistance. Products manufactured by
using dies with tapered cross have 3% less fatigue
strength than comparing to dies with cosine curved
profile. Cycle which the gear can be operated without
getting any damage also decreases inversely
proportionally with the increase of die land length.
When the fatigue strength diagrams which were
obtained for parts manufactured with cosine and
tapered dies by the four teeth forward extrusion
methods were examined, a view similar to direct
extrusion of six teeth parts can be observed. It was
observed that for cosine and taper profiled dies’
fatigue strength values are close to each other and by
the increase of die land length, the fatigue strength
values decrease too little. Detailed stress-cycle values
for fatigue test results are given in Table 4.
Regardless of the fact that fatigue life cycle values
are very close to each other in logarithmic scale, the
measured cycles are quite different between each
other. For example, when the fatigue stress value is
182 MPa, 6 teeth cosine curved die transition profile
with 15 mm. die land length gives 3.36654 when for
20 mm. the die land length, cycle in logarithmic scale
falls only 3.33746 but in the experiments, the
difference between the cycle values is 150. The
difference becomes bigger when the fatigue stress is
lower. For the same die sets when the stress was
chosen as 76 MPa, the difference between cycle
values is obtained as 82040.
Comparison of experimental results with ANN
In order to verify the developed ANN models, a
comparison between ANN predicted and experimental
results was performed and presented in Fig. 7. The
correlation coefficient (R2) between predicted and
experimental values of fatigue life for tapered die
profile is 0.946 and for the cosine curved die profile,
it is 0.999. The high values of R2 indicates a fine
agreement between the ANN-predicted and
experimental values of fatigue life. It can also be seen
in Fig. 8 that ANN predicted results are very close to
experimental ones. The differences between the
experimental and predicted values are reported as
graphically in Fig. 9. Maximum percentage error in
the test results of cosine curved die model is 2.95%,
meanwhile maximum error of the tapered die model is
6.41%. Likewise, right y-axes of same figures show
Table 4—Stress-cycle values of the fatigue tests
Cycles (logN)
Stress (MPa) 6 Teeth
Cosine
15 mm
6 Teeth
Cosine
20 mm
6 Teeth
Cosine
25 mm
6 Teeth
Tapered
15 mm
6 Teeth
Tapered
20 mm
6 Teeth
Tapered
25 mm
182 3.36654 3.33746 3.32139 3.35469 3.29973 3.27646
138 4.47083 4.44567 4.41191 4.43908 4.41948 4.38672
126 5.12237 4.98875 4.88995 4.77459 4.74856 4.85546
115 5.53616 5.51444 5.51284 5.51431 5.49982 5.50139
98 5.75198 5.71852 5.73632 5.71639 5.69125 5.71015
92 5.89954 5.84221 5.78511 5.87556 5.81237 5.75339
76 6.08668 6.05647 6.02628 6.04649 6.00584 5.99615
Stress (MPa) 4 Teeth
Cosine
15mm
4 Teeth
Cosine
20 mm
4 Teeth
Cosine
25 mm
4 Teeth
Tapered
15 mm
4 Teeth
Tapered
20 mm
4 Teeth
Tapered
25 mm
182 3.96993 3.89702 3.80882 3.76462 3.69706 3.65108
138 4.55524 4.53307 4.51613 4.49087 4.47150 4.45096
126 4.88990 4.99687 4.85663 4.76932 4.83272 4.63325
115 5.58857 5.58717 5.58426 5.55186 5.54083 5.52832
98 5.72146 5.73266 5.77464 5.71566 5.69664 5.66912
92 5.91849 5.89997 5.89917 5.88788 5.86889 5.82979
76 6.12004 6.10001 6.07900 6.09980 6.04927 6.02984
AYER et al.: FATIGUE LIFE MODELING OF GEAR LIKE PRODUCTS USING ANN 245
the absolute error values. The maximum absolute
error values for cosine curved model are in range of
(-0.026)-(0.112) while the maximum absolute error
values for tapered model are in range of (-0.241)-
(0.199). These small error values indicate that
predicted fatigue life results for both die profiles
match well with the experimental results.
Conclusions
Fatigue life of an extruded product is affected by a
number of critical parameters. Identifying the effects of
process parameter plays a key role in the prevention of
fatigue failure. The aim of the presented study is to
investigate the fatigue strength of the gear like
components. Additionally, fatigue strength of two
different die profiles were also estimated by using ANN.
The results obtained lead to the following conclusions:
(i) It was determined that extrusion products of 4
teeth parts’ fatigue strength values vary according
to die land length and transition profile and can be
realized that die transition profile of 4 teeth dies
produces more deformation than tapered dies and
in this case the product’s fatigue strength
increases. Similarly to this observation, for 6 teeth
products’ fatigue cycles of damage occurrence are
extremely close to 4 teeth samples but still
products manufactured by using dies with shorter
land length have better fatigue strength
Fig. 7—Comparison of ANN-
predicted and experimental values
of fatigue life for (a) cosine curved and (b) straight tapered
die
profiles
Fig. 8
Experimental and ANN predicted fatigue life results in
the test period for (a) cosine curved and (b)
straight tapered die
profile
Fig. 9—Percentage error of the
(a) cosine curved and (b) straight
tapered die profile network models
246 INDIAN J ENG. MATER. SCI., AUGUST 2016
(ii) It was also determined that for cosine and taper
profile dies’ fatigue strength values are close to
each other and by the increase of die land length,
the fatigue strength values decrease too little.
(iii) A good agreement between ANN-predicted and
experimental fatigue strength results were
obtained for different gear profiles. The R2
between predicted and experimental data was
0.946 for straight tapered die profile and 0.999 for
cosine curved profile.
(iv) The error values of the developed ANN models
are 2.95% and 6.41% for cosine curved and
straight tapered die profiles, respectively. Low
error values indicate that complex fatigue
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  • M R Jamli
  • A Ariffin
  • D Wahab
Jamli M R, Ariffin A K & Wahab D A, Expert Syst Appl, 452 (2015) 2604-2614.
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Setti S G & Rao R N, Rare Met, 33(2014) 249-257. 24 Gholamzadeh A & Taheri A K, Mech Res Commun, 36(2009) 252-259.
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  • O Ayer
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Bingol S, Ayer O & Altinbalik, Int J Adv Manuf Technol, 76 (2015) 983-992.
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Inamdar M, Date P P, Narasimhan K, Maiti S K & Singh U P, Int J Adv Manuf Technol, 16 (2000) 376-381.