Modeling the wear of Polyamide 66 using artificial neural network

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Modeling the wear of Polyamide 66 using artificial neural network

A. Abdelbary ⇑, M.N. Abouelwafa, I.M. El Fahham, A.H. HamdyMechanical Eng. Dept., Faculty of Eng., Alexandria University, Alexandria, Egypt

a r t i c l e i n f o

Article history:Received 2 March 2012Accepted 4 May 2012Available online 15 May 2012

Keywords:A. PolymersE. MechanicalE. Wear

a b s t r a c t

Recently, Artificial Neural Networks (ANNs) have emerged as a good candidates to mathematical wearmodels, due to their capabilities of nonlinear behavior, learning from experimental data and generaliza-tion. In the present paper the potential of using neural networks for the prediction of sliding wear prop-erties of polymer was investigated using a measured dataset of 42 independent reciprocating slidingwear tests of Polyamide 66. The polymer was tested under various testing conditions such as applied load(constant and fluctuating), existence of surface crack and sliding media. Five different feed-forward (ff)neural network models were examined in order to find the optimum model that simulates the wearunder such parameters. The optimized ANN was utilized to predict the wear rates of new input param-eters, which were not tested. The quality of prediction was good when comparing the predicted and realtest values. Finally, the proposed ANN was applied to four data sets adopted from previous works to eval-uate its accuracy. The ANN showed good accuracy for the simulation and acceptable values of predictedwear rates. The results indicated that the well-trained neural network model is quite effective for predic-tion of wear response of materials within and beyond the experimental domain.

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1. Introduction

In the field of Tribology, very complex and highly non linearphenomena are involved. Wear of material –particularly of poly-mers– originates from multiple sets of complex interactions onmacroscopic and microscopic scale between surfaces that are inmechanical contact. These interactions depend on the materials,geometrical and tribological characteristics of the surfaces andsliding conditions, e.g. load, temperature, lubricating conditions,type of contact, etc [1].

Simulation of tribological properties generally involves thedevelopment of mathematical models derived from experimentaldata. Numbers of these models were derived to simulate wearbehavior of materials under limited conditions. However, no un-ique model generalized to express wear properties of polymers,especially under fluctuating loading condition.

Recently, Artificial Neural Networks (ANNs) have emerged asgood candidates to such models, due to their capabilities of nonlin-ear behavior, learning from experimental data and generalization[2]. The pioneering investigations of neural network (NN) tech-niques to predict tribological parameters have been presented byHatching’s group [3] and Jones et al. [4]. Subsequently, a lot ofworkers [5–14] investigated the potential on neural networks topredict and analyze the wear behavior under various parameters.

In the simulation of wear tests, known sliding properties of rub-bing material are input to the NN model and the expected wear re-sponses of the virtual case are calculated. The principle benefit ofneural network modeling compared to other approaches is in itscapability for accurate predictions when significant non-linearityand hysteresis are present simultaneously. The latter is not easyto attain with conventional curve fits. Furthermore, the neural net-works will readily handle irregular or random inputs [1].

Several articles [5–10] illustrated that the prediction accuracyof NN models was satisfactory, but the dependence of it on thenumber of training data indicates that the accuracy could be fur-ther improved by expanding the experimental database for net-work training. On the other hand, a well-trained neural networkprovides more useful data from a relatively limited database ob-tained by experiments. Lots of techniques have introduced to im-prove the predictive capabilities of the artificial neural networkby automatically identifies the optimal size of the network or byincreasing available datasets. The optimization of artificial neuralnetwork configuration is not an easy task; it was studied by manyresearchers [6–8]. However, there is lack of definite rules or meth-ods to attain a most appropriate configuration of the ANN, whichsignificantly determines the performance of network. The parame-ters of the network itself, including architecture of the hiddenlayer, training algorithm, etc., can only be optimized mainly bycomparisons between practical instances at present. By expandingthe number of training datasets and further optimizing the ANNconfiguration, the predictive accuracy would be improved [6]. Inmost cases, a simple structure of hidden layer including several

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⇑ Corresponding author. Tel.: +20 1 001 5857 18; fax: +20 3 592 1853.E-mail addresses: [email protected] (A. Abdelbary), Ibrahim.elfahham@a-

lexu.edu.eg (I.M. El Fahham).

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neurons has an adequate capability to model the problems. How-ever, the more complex the nonlinear relation between input andoutput is, the more training data are required. Nevertheless, thedetermination of best neuron number is case dependent. The pre-diction quality increases in a certain range with an increase in neu-rons, but it may deteriorate when the neuron number exceeds thesaturation value [8].

Studying sliding wear and friction of polymeric composite usingANN was introduced [1] to investigate the effect of the so-calledsecondary parameters (mechanical and thermo-mechanical prop-erties), on sliding wear and friction. They used two datasets in-cluded the material compositions (volume fraction of matrix,fillers, reinforcing agents and lubricants), the testing conditions(pressure and sliding speed) as well as mechanical and thermo-mechanical properties of polyphenylene sulfide (PPS) compositesas input parameters; the output parameters were the tribologicalproperties (specific wear rate and friction coefficient). The predic-tive quality results for the wear performance were improved whentensile modulus and strain were used as input along with materialcomposition and testing conditions. It was established that somesecondary parameters exert great influence on the predictionquality.

Lada et al. [14] evaluated over 400 different network configura-tions by systematically varying both the number of hidden layers(between 1 and 2) and the number of neurons in the hidden layer(between 1 and 20) in order to introduce optimum network archi-tectures that simulate the wear of polyphenylene sulfide (PPS) ma-trix composites. Each network was trained with 80–90% of the dataand then tested by the other 10–20% of the data. This procedurewas repeated 200 times. The performance of each network was as-sessed in terms of the mean relative error. The networks thatyielded the lowest mean relative error were chosen subsequentlyfor modeling the sliding friction and wear properties of the PPScomposites. They demonstrated that it is possible to develop a neu-ral network model that is able to learn from examples presented toit and construct proper fitting function that correctly reproducesnot only the characteristic tribological properties for these exam-ples but is also able to interpolate correctly for unseen cases fromthe same knowledge domain.

Velten et al. [5] extended the earlier work done by Jones et al. [4]to predict and analyze the wear behaviour of short fiber reinforcedpolymeric bearing materials using three-layer feed-forward neuralnetwork. They used a higher number of input variables characteriz-ing the materials and the experimental conditions (compressivestrength, compression modulus, contraction to failure, tensilestrength, strain to failure, impact strength, environmental testingtemperature, starting load, average load, and average velocity).Empirical and phenomenological equations of ferreting wear werestudied to select parameters to model the wear of PA46-compos-ites. It was stated that the quality of predictions based on artificialneural networks usually increases with increasing available datasets, and also there are still many possibilities to optimize the net-work construction with respect to its performance. Similar conclu-sion was also suggested by Jiang et al. [6,8].

Kranthi and Satapathy [10] applied the ANN approach to predictthe dry sliding wear of epoxy based composites under different testconditions within and beyond the experimental domain. In thisstudy they derived optimal settings of the control factors for min-imization of specific wear rate. Sliding velocity, normal load andfiller content were taken as the three input parameters wherethe outer layer of the network had only one neuron to representspecific wear rate. Comparison between the experimental valuesand the ANN predicted results for the specific wear rates of poly-mer composites indicated that the error in ANN prediction lies inthe range of 0–8% which establishes the validity of the neuralcomputation.

Modeling of the wear of surface cracked polymer was presentedby Helmy [13]. The aim of his work was to design and study thefeasibility of neural network model that simulate the wear ofPMMA under different working conditions, such as sliding distancecrack angle relative to sliding direction, crack length and contactarea, using four different feed-forward (ff) neural network models.All networks showed good accuracy for the simulation. In metals,surface damage due to fatigue wear was also modeled using ANNs[15]. The basic wear model was considered under the macroscopicpoint of view and combined rolling and sliding actions were recog-nized to be effective for surface deterioration. Influence of running-in initial transient phase as well as influence of mild to severe tran-sitions was considered in neural network model. It was concludedthat the reliability of the method strongly depends on the reliabil-ity of the adopted physical model. A valuable feature of the net-work is the strength of its learning capability with respect tonew data. Based on the aforesaid, the applications of ANNs the fieldof Tribology are still in their basic stages, which mean that theinvestigations of the implementation possibilities in differentmaterial research areas and the improvements of the predictivequalities are still matters for further research.

In the present work, artificial neural network approach was ap-plied to study the wear of Polyamide 66 under different conditions.Systematic parameters study were carried out using ANN in orderto predict the wear rates of the polymer under such conditions ofloading parameters, existence of surface crack, sliding media. Thenetwork was trained based on experimental data obtained fromprevious studies [16,17]. The designed ANN model was tested witha group of data not included in the training dataset to evaluate thenetwork strength.

2. Neural network application

2.1. Experimental data set

Two datasets were used in the present application. The first one(dataset I) for the dry sliding wear contained a (23) independentdata measurements and the second one (dataset II) for wet slidingconditions contained a (14) independent data measurements. Bothdatasets included the testing conditions (loading parameters andsurface crack parameters) while the output parameter was thewear rate WR. Tables 1 and 2 give an overview of input and outputdata used for the ANN approach. The selection of input and outputparameters used in the ANN can be expressed as following schemeof NN as illustrated in Fig. 1.

(a) Applied load (F): The choice of this parameter was due to itseffect on wear of polymeric materials, it represents bothconstant and fluctuating applied load (F). It is important tonote that the value of (F) in fluctuating load tests will bethe mean value of the load cycle (Fmean).

(b) Load ratio (R): The effect of load ratio (R) was obviouslydetected in the wear tests performed under cyclic loadingconditions. The governing equation of this parameter isgiven by:

R ¼ Fmin=Fmax ð1Þ

In constant load tests, this parameter will equal to unity, i.e.R = 1

(a) Cyclic loading frequency (f): This parameter is directly relatedto the time dependent nature of loading condition. It is clearthat under constant loading condition, the value of (f) will beequal to zero.

A. Abdelbary et al. / Materials and Design 41 (2012) 460–469 461


(b) Number of surface cracks (nc): Such parameter is very easy tobe evaluated on the wear test. Although there is very fewtests considered the number of surface cracks, but it wasfound that it has a significant effect on wear rate underdry sliding condition. Also, it is clear that for uncracked poly-mer, the value of (nc) will be equal to zero.

(c) Fluid film thickness (ho): This parameter will be introduced tothe second dataset. It refers to the type of lubricant condi-tion (boundary or hydrodynamic). The governing equationwas introduced by Lancaster [18]:

dcrit ¼ 2:73h23o

Fgv

� �12

ð2Þ

where dcrit is the critical wear scar diameter (m), ho the fluid filmthickness at the trailing edge of the pin (m), g the viscosity of thelubricant fluid (Ns/m2), v the sliding speed (m/s), and F is the ap-plied force (N).

(a) Linear wear rate (WR): This parameter can be calculated fromthe wear curve using Equation (3) for both the running-inand steady state portions on the wear curve.

WR ¼ VX

mm3=m ð3Þ

where V is the volume loss (mm3) and X is the sliding distance (m).

2.2. ANN configuration

In order to find a general NN configuration, five feed-forwardANNs consist of 3, 4 and 5 layers were introduced, as shown inTable 3. The NNs are trained by the group of data presented inTables 1 and 2 using MATLAB 7.0 Software. Levenberg Marqurdittraining method was applied until a normalized mean squarederror between the measured data and that obtained from theANN was minimal.

3. Training and evaluation

The polymer tested in our present study was Polyamide 66 rub-bing on steel counterface of arithmetic roughness value,Ra � 0.3 lm. The results of a (42) dry and wet tribological weartests were collected. Experimental data of a (36) tests were se-lected as training data of neural network, and the residuals wereused to verify the predicted results.

A dataset of measurement results were divided into a trainingdataset and a test dataset. The training dataset was used to adjustthe weights of all the connecting nodes until the desired error levelis reached. Thereafter, the network performance is evaluated byusing the test dataset. The quality of the prediction can normallyby characterized by the root mean square error (RMSE) of the

Table 1Database I, input and output parameters of dry wear tests.

Test No. Input parameters Output parameters

F (N) Fmax (N) R f (Hz) nc WRrunning-in � 10�4 mm3/m WRs.state � 10�4 mm3/m

1 90 90 1 0 0 22.2 13.22a 90 90 1 0 1 24.9 14.83 135 135 1 0 0 38.1 18.14 135 135 1 0 1 45.5 30.75 90 90 1 0 3 34.9 25.26 90 170 0.06 1.50 0 22.4 15.87 90 170 0.06 1.50 0 27.3 22.18 90 170 0.06 1.50 1 46.6 30.19 90 135 0.33 1.50 0 23.2 1610 90 135 0.33 1.50 0 24.7 14.711a 90 135 0.33 1.50 1 33.7 22.412 90 110 0.64 1.50 0 25.0 18.613 90 110 0.64 1.50 0 25.0 19.914 90 110 0.64 1.50 1 24.4 20.415 70 135 0.07 1.50 0 14.0 7.616 70 135 0.07 1.50 0 14.0 8.517 70 135 0.07 1.50 1 32.9 23.918 90 110 0.64 0.75 0 19.2 14.619 90 110 0.64 0.75 1 21.0 15.820 90 170 0.06 0.75 0 30.5 14.721 90 170 0.06 0.75 1 22.4 14.622 90 110 0.64 0.25 0 27.7 19.823 90 110 0.64 0.25 1 37.9 29.824 90 170 0.06 0.25 0 21.4 13.725a 90 170 0.06 0.25 1 29.1 21.826 90 170 0.64 0.25 3 43.2 29.7

a Data used to test the NN performance.

Table 2Database II, input and output parameters of wet wear tests.

TestNo.

Input parameters Output parameters

F(N)

Fmax

(N)R f

(Hz)nc ho

(lm)WR � 10�4

(mm3/m)

27 90 90 1 0 0 0.24 90.428 90 90 1 0 1 0.24 81.029 135 135 1 0 0 0.20 95.730a 135 135 1 0 1 0.20 10131 90 110 0.64 1.50 0 0.22 79.232 90 110 0.64 1.50 1 0.22 60.533 90 170 0.06 1.50 0 0.17 54.934 90 170 0.06 1.50 1 0.17 52.335 90 110 0.64 0.75 0 0.22 81.136a 90 110 0.64 0.75 1 0.22 70.937 90 170 0.06 0.75 0 0.17 58.138 90 170 0.06 0.75 1 0.17 60.239 90 110 0.64 0.25 0 0.22 73.240 90 110 0.64 0.25 1 0.22 98.241 90 170 0.06 0.25 0 0.17 43.242a 90 170 0.06 0.25 1 0.17 58.5


462 A. Abdelbary et al. / Materials and Design 41 (2012) 460–469


Input layer Output layer

Hidden layer/s

- Load parameters(F, Fmax, R, f )

- Sliding condition (ho)

- Surface crack (nc)

Wear rate (WR)

Fig. 1. Schematic representation of the ANN.

Measured Wear Rates, WR x10-4 mm3/m0 10 20 30 40 50

Measured Wear Rates, WR x10-4 mm3/m0 10 20 30 40 50

0

10

20

30

40

50

0

10

20

30

40

50

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

(a) (b)Fig. 2. Comparison between the measured and predicted running-in wear rate of the (a) training and (b) test dataset, dry sliding. Input: F, R, f, nc and Output: WRrunning-in.

Measured Wear Rates, WR x10-4 mm3/m Measured Wear Rate, WR x10-4 mm3/m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Pred

icte

d W

ear R

ates

, WR

x10

-4 m

m3 /m

(a) (b)Fig. 3. Comparison between measured and predicted steady state wear rate of the (a) training and (b) test dataset, dry sliding. Input: F, R, f, nc and Output: WRsteady state.



predicted values from the real measured data. The smaller the(RMSE) of the test dataset the higher is the predictive quality.The coefficient of determination B (also called R2) were calculatedand introduced on the figures to evaluate ANNs quality, defined by:

B ¼ 1�PM

i¼1ðoðPÞðiÞ � oðiÞÞ2PM

i¼1ðoðiÞ � oÞ2ð4Þ

where o(P)(i) is the ith predicted property characteristic, o(i) is themeasured value, O is the mean value of o(i), and M is the numberof test data. The coefficient B describes the fit of the ANN outputvariable curve. Higher B coefficients indicate an ANN with betteroutput approximation capabilities. To avoid any artificial influencein selecting the test data, a random technique was applied in theselection process.

4. Application of the ANN

The 7-[20 10 10]3-1 ANN was employed to plot Figs. 9 and 10 inorder to predict number of WR values that were not included in theexperimental work. Virtual F and Fmean values were used as inputparameters and the predicted WRs were the output.

Measured Wear Rate, WR x10-4 mm3/m Measured Wear Rate, WR x10-4 mm3/m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

(a) (b)Fig. 4. Comparison between the measured and predicted steady state wear rate of the (a) training and (b) test dataset, dry sliding. Input: F, R, f, nc, WRrunning-in and Output:WRsteady state.

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m


Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

(a) (b)Fig. 5. Comparison between the measured and predicted wear rate of the (a) training and (b) test dataset, wet sliding. Input: F, R, f, nc, ho and Output: WRsteady state.

Table 3Configuration of ANNs used in wear rates prediction.

Conditions NN Neurons type

I/P Hidden O/P

Dry sliding {4 [25]1 1} tan-sigmoid tan-sigmoid pure-linearWet sliding {5 [25]1 1} tan-sigmoid tan-sigmoid pure-linearGeneral NN {5 [40]1 1} tan-sigmoid pure-linear pure-linear

{5 [20 5]2 1} tan-sigmoid pure-linear pure-linear{7 [20 10 10]3 1} tan-sigmoid pure-linear pure-linear



5. Discussion

Particularly in our present case, we aimed to introduce an ANNmodel that has the capability of predicting the wear rate of poly-mer considering different input parameters such as; applied load,sliding condition, and surface defect. Factors affecting the perfor-mance of the desired ANN will be discussed in the present section.

5.1. Effect of input parameters

Not only the training algorithm, but also the configuration has astrong influence on the NN predictive quality [11]. Based on Leven-berg–Marquardt (LM) algorithm, various ANN constructions wereemployed in modeling the effect of transverse surface crack on

the wear rate of polyamide, as shown in Table 3. The choice of LMalgorithm was due to its faster training especially with moderatesize networks. A simple two ANN configurations {4-[25]1-1} and{5-[25]1-1} have been introduced to predict the wear rate of surfacecracked polymer in dry and wet sliding conditions respectively. Thefirst ANN was chosen for predicting the wear rate in dry slidingbased on the input parameters (F, R, f, and nc). On the other hand,the second ANN was employed to predict the wear rate in wet slid-ing based on the input parameters (F, R, f, nc, and ho). Figs. 2–8 pres-ent the predicted wear rates for training and test datasets.

In fact, the above NN configurations sometimes gave good out-put results with high predictive quality, i.e. about 30% of the B-val-ues were in the range of 0.95–0.99. However, the results were notstable, which means when repeating the random selection of test


Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

(a) (b)Fig. 6. Comparison between the measured and predicted wear rate of the (a) training and (b) test dataset, dry and wet sliding. Input: F, R, f, nc, ho and Output: WRrunning-in orWRsteady state.

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m


(a) (b)

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Fig. 7. Determination of the measured and predicted wear rate for the test dataset for different NN configurations, dry and wet sliding. Input: F, R, f, nc, ho and Output:WRrunning-in or WRsteady state.



datasets once more, the quality could be even very poor. Moreover,the predicted wear rates of the test dataset were relatively

different from the measured values, as shown in Figs. 2b and 3b.The reason for the unstable quality of the simple ANN was notclear, but one should always consider that ANN is inspired by

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Measured Wear Rate, WR x10-4 mm3/m

Fig. 8. Determination of the measured and predicted wear rate of the test datasetfor the final general ANN, dry and wet sliding. Input: F, Fmax, R, f, nc, ho, WRrunning-in

and Output: WRsteady state.

Static Load F, N

Wea

r Rat

e W

R, x

10-4

mm

3 /m

Fig. 9. Application of NN in predicting WR under different values of static loads.

Table 5Data adopted from Ref. [13] and used to evaluate the predictive accuracy of the present ANN.

Test Area of contact(mm2)

Crack angle(deg.)

Crack length(mm)

WR (measured)(�10�4 mm3/m)

Original ANN Present ANN

WR (predicted)(�10�4 mm3/m)

Error(%)

WR (predicted)(�10�4 mm3/m)

Error(%)

1 139 0 0 10.7 10.8 0.93 10.7 02 63.5 0 0 47.5 48.5 2.10 47.57 0.153 63.5 90 0 28.5 28.2 �1.05 23.4 �17.894 127 0 100 40.0 40.0 0 40.3 0.755 127 90 100 11.2 11.1 �0.89 11.2 06 127 0 6 48.7 43.2 �11.29 48.7 07 127 0 10 44.1 42.9 �0.03 43.7 �0.918 127 0 12 40.9 42.8 4.65 42.4 3.669 127 0 13 42.4 42.8 0.94 41.9 �1.18

10 127 0 14 41.2 42.7 3.64 41.5 0.7311 127 0 15 42.4 42.6 0.47 41.2 �2.8312 127 0 16 41.1 42.6 3.65 41.0 �0.2413 127 90 6 27.3 21.8 �20.15 23.37 �14.3914 127 90 10 23.0 21.5 �6.52 23.37 �1.61

Average error (arithmetic mean) (%) 4.03 3.17


Test Slidingvelocity(cm/s)

Load(N)

Fillercontent(wt.%)

Slidingdistance(m)

Specific WR (measured)(�10�5 mm3/Nm)

Original ANN Present ANN

Specific WR (predicted)(�10�5 mm3/Nm)

Error(%)

Specific WR (predicted)(�10�5 mm3/Nm)

Error(%)

1 42 5 0 252 21 228 5.55 220 1.852 42 10 5 504 172 157 �8.72 170 �1.163 42 15 10 756 25 27 8.00 30.00 20.004 84 5 0 756 202 216 6.92 200 �0.995 84 10 5 252 178 161 �9.55 180 1.126 84 15 10 504 309 291 �5.82 310 0.327 126 5 0 504 197 204 3.55 200 1.528 126 10 5 756 352 382 8.52 350 �0.579 126 15 10 252 207 227 9.66 210 1.45




our biological neural system. In human beings, someone can learnvery fast and catch the right solution even only if a little informa-tion is available [12]. It was suggested that increased number of in-put parameters and training epochs may resulted in improving theANN performance [19].

In order to enhance the performance of the NN of dry slidingwear, running-in wear rate (WRrunning-in) dataset were added tothe input parameters. Fig. 4 shows the comparison between themeasured and predicted wear rates for the training and test data-sets. The present NN indicated higher coefficient of determination(B = 0.999) as well as better WR prediction of test datasets, asshown in Fig. 4(b), which agree with the previous suggestion aboutthe effect of the input size. It was stated that the higher the percent-age of B P 0.9 is, the better is the quality [9]. It is important to notethat the above issue was applied only on the dry sliding case be-cause in wet sliding there were no running-in wear phase. So,ANN in wet sliding still has poor performance in predicting testdataset, as shown in Fig. 5(b). To find a general NN which can pre-dict the wear of surface cracked polymer under different types ofloading and sliding conditions, the datasets I and II were collectedas input parameters in {5-[40]1-1} configuration, as shown inFig. 6(a). Note that the lubrication parameter (ho) in dry tests wasequal to zero value. Predicted WRs of this NN showed relatively


Test Load (N) Sliding distance (m) Wight loss (measured) (g) Original ANN Present ANN

Wight loss (predicted) (g) Error (%) Wight loss (predicted) (g) Error (%)

1 10 62.8 0.16 0.17 6.25 0.1603 0.192 20 62.8 0.23 0.24 4.35 0.2309 0.393 10 188.4 0.26 0.25 �3.84 0.2600 04 20 188.4 0.38 0.36 �5.26 0.3801 0.035 8 125.6 0.20 0.21 5.00 0.2003 0.156 22 125.6 0.35 0.34 �2.86 0.3480 �0.577 15 36.8 0.21 0.21 0 0.2037 �3.008 15 214.4 0.31 0.30 �3.22 0.3099 �0.039 15 125.6 0.24 0.24 0 0.2468 2.80


Wea

r Rat

e WR, x

10-4

mm

3 /m

Cyclic Load Fmean, N

Fig. 10. Application of NN in predicting WR under different values of mean loads,(f = 1.5 Hz, R = 0.06).


Test Input parameters Output WR (x10�4 mm3/m)

F (N) Fmax (N) R f (Hz) Measured Predicted Error (%)

1 35 35 1 0 3.50 3.50 02 70 70 1 0 3.70 3.68 0.543 90 90 1 0 5.70 5.92 �3.864a 105 105 1 0 6.10 5.52 9.515 40 75 0.06 0.38 6.00 5.99 0.176 70 105 0.33 0.38 5.39 5.09 5.577 90 125 0.44 0.38 9.00 9.03 �0.338 105 140 0.50 0.38 6.30 6.29 0.179 150 185 0.62 0.38 4.05 4.32 �6.6710 70 105 0.33 0.70 5.25 5.19 1.1411a 90 125 0.44 0.70 13.5 13.47 0.2212 70 105 0.33 1.38 7.42 7.45 0.4013 90 125 0.44 1.38 15.30 15.31 0.0714 90 105 0.71 0.70 5.40 5.93 �9.8115 90 112 0.61 0.70 5.67 5.82 �2.6516 90 150 0.20 0.70 3.60 3.64 �1.1117 90 175 0.03 0.70 5.40 5.47 �1.3018 90 112 0.61 1.38 5.85 5.69 2.7419 90 150 0.40 1.38 5.94 5.59 5.8920a 90 175 0.03 1.38 5.49 6.10 �11.11

Average error (arithmetic mean) 3.16%




lower performance (B = 0.961), as shown in Fig. 6(b). We suggestedthat the ANN configuration should be adapted in order to get betterprediction quality.

5.2. Effect of ANN configuration

In order to investigate the effect of NN configuration on the net-work performance, two ANNs model, {5-[20 5]2-1} and {7-[20 1010]3-1}, with two and three hidden layers, respectively, wereemployed. Predicted data showed that the response of the NNwas improved by increasing the number of hidden layers, as shownin Fig. 7. It seems that the complex ANN configuration (three layersNN) was more convenient in predicting the wear behavior of

polymer that has a very complex relationship with the inputparameters. Or simply we can say that in designing NN, the com-plexity of the network configuration should be selected in the lightof the input parameters size. This issue was suggested in studyingthe influence of ANN structure on the predicted data of Polyamidecomposites wear [6].

Finally, the {7-[20 10 10]3-1} ANN was introduced to predict thewear rates while the maximum load (Fmax) and running-in wear(WRrunning-in) rate were used as an input parameters. Excellent per-formance (B = 1) was obtained specially in predicting the test data,as shown in Fig. 8. It is suggested that the predictive quality of theNN can be further improved by enlarging the input training data-sets and by optimizing the network construction. A well trained

Measured Wear Rate, WR x10-4 mm3/mMeasured Wear Rate, WR x10-4 mm3/m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

Pred

icte

d W

ear R

ate,

WR

x10

-4 m

m3 /m

(a) (b)Fig. 11. Measured and predicted wear rate of the (a) training and (b) test dataset, dry sliding of PA66 against stainless steel counterface at 0.25 m/s sliding velocity. Adoptedfrom Ref. [21].

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5

Frequency of cyclic load f, Hz0 0.5 1 1.5 2 2.5

Frequency of cyclic load f, Hz

Wea

r Rat

e WR

, x10

-4 m

m3 /m

2

4

6

8

10

12

Wea

r Rat

e WR, x

10-4

mm

3 /m

(a) (b)Fig. 12. Application of the proposed ANN in predicting the relation between wear rate (WR) and the frequency of the applied cyclic load (f). (a) Relation between frequency ofthe cyclic load and the measured wear rates as presented in Refs. [20,21]. (b) Relation between frequency of the cyclic load and the corresponding wear rates (measured andpredicted data using the proposed NN).



ANN is expected to be very helpful for optimum design of poly-meric materials, in particular tribological applications. When intro-ducing load parameters (F or Fmean, f, R), surface cracks (nc), as inputparameters to a suitable ANN, acceptable values of running-inwear rates were predicted, as shown in Figs. 9 and 10. This success-ful prediction could be of benefit to reduce the number of tribo-experiments and could be used to enlarge the dataset.

In order to evaluate the accuracy of the proposed ANN in light ofprevious literatures, the {7-[20 10 10]3-1} ANN was applied tothree data sets adopted from Refs. [10,13,20]. The results are col-lected and presented in Tables 4–7 respectively. The average valuesof error were reduced significantly (more than 20% reduction in theerror values) when applied the present ANN compared to the ori-ginal ones, as shown in Tables 4–6.

Moreover, the proposed network showed an acceptable accu-racy (3.16% average error) in predicting wear rates (WR) of thesame polymer sliding against stainless steel counterface and sub-jected to constant and cyclic load in dry condition [21,22] as shownin Table 7 and Fig. 11. The application of the NN results in improv-ing the curve fitting of the relation between the wear rate and thefrequency (f) of the applied cyclic load, as presented in Fig. 12(a,b).About (5%) increase in R-squared value was obtained by introduc-ing seven additional predicted (WR) values using seven virtual loadfrequencies (f) within and beyond the experimental domain. Thisissue illustrates the advantage of ANN in saving of time and costfor researchers and strengthens the application of the ANNmodeling.

It was reported that once a well-trained ANN model has beenobtained, new data can be predicted without performing too many,long lasting experiments. The developed model is able to constructproper fitting function that correctly reproduces not only the char-acteristic tribological properties for these examples but is also ableto interpolate correctly for unseen cases from the same knowledgedomain [9,14,23]. We believe that, using a suitable dataset and se-lected neural architectures, a good trained ANN can be generalizedto model the wear phenomena under any virtual conditions.

6. Conclusions

The current study elucidates that the use of feed-forward neuralnetworks to simulate experiments with parametric design strategyis effective and efficient to predict the sliding wear response ofpolyamide under different test conditions within and beyond theexperimental domain. Probably, the same holds true for other neu-ral network architectures.

Acceptable predicted values of wear rates were obtained byintroducing load parameters, sliding condition, lubrication param-eter, existence of surface crack and running-in wear rate as inputdata to a suitable ANN. The performance of the network was gov-erned by the size of input parameters and the NN configuration.Successful introducing of ANNs in tribological applications couldbe of benefit to reduce the number of tribo-experiments as wellas estimating the actual life time of bearing components. TheANN technique can make a more efficient utilization of the rela-tively limited experimental databases, which means a considerablesaving of time and cost for both research and production. It allows

systematic parametric studies on computer for materials optimiza-tion since more distinct dependencies of the mechanical and wearcharacteristics on the compositions and working conditions can beobtained according to the predicted results.

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Modeling the wear of Polyamide 66 using artificial neural network

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