Expert Systems with Applications 36 (2009) 9645–9657

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Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Modelling of the cutting tool stresses in machining of Inconel 718 usingartificial neural networks

Abdullah Kurt *

Gazi University, Technical Education Faculty, Mechanical Education Department, Teknikokullar, 06500 Ankara, Turkey

a r t i c l e i n f o

Keywords:Inconel 718Cutting tool stressesANSYSArtificial neural network (ANN)

0957-4174/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.eswa.2008.12.054

* Tel.: +90 312 202 86 26; fax: +90 312 212 00 59.E-mail address: akurt@gazi.edu.tr

a b s t r a c t

This study covers two main subjects: (i) The experimental and theoretical analysis: the cutting forces andindirectly cutting tool stresses, affecting the cutting tool life during machining in metal cutting, are one ofvery important parameters to be necessarily known to select the economical cutting conditions and tomount the workpiece on machine tools securely. In this paper, the cutting tool stresses (normal, shearand von Mises) in machining of nickel-based super alloy Inconel 718 have been investigated in respectof the variations in the cutting parameters (cutting speed, feed rate and depth of cut). The cutting forceswere measured by a series of experimental measurements and the stress distributions on the cutting toolwere analysed by means of the finite element method (FEM) using ANSYS software. ANSYS stress resultsshowed that in point of the cutting tool wear, especially from von Mises stress distributions, the ceramiccutting insert may be possible worn at the distance equal to the depth of cut on the base cutting edge ofthe cutting tool. Thence, this wear mode will be almost such as the notch wear, and the flank wear on thebase cutting edge and grooves in relief face. In terms of the cost of the process of machining, the cuttingspeed and the feed rate values must be chosen between 225 and 400 m/min, and 0.1 and 0.125 mm/rev,respectively. (ii) The mathematical modelling analysis: the use of artificial neural network (ANN) has beenproposed to determine the cutting tool stresses in machining of Inconel 718 as analytic formulas based onworking parameters. The best fitting set was obtained with ten neurons in the hidden-layer using backpropagation algorithm. After training, it was found the R2 values are closely 1.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In order to analyse the machining process, the finite elementmethods (FEM) which based on Eulerian and the updated Lagrang-ian formulation have been developed. In recent years, numericalmodels, especially the FEM, have been drawing attention theresearchers due to computer technology and the complex codesdevelopment. Eulerian formulation in the number of the FEM mod-els at the literature was used for the modelling of the orthogonalmetal cutting. Because of Lagrangian formulation technique’s abil-ity to simulate the formation of the chip from the incipient stages tosteady-state, it was used more widespread in metal cutting. To im-prove the accuracy and the efficiency of the FEM in metal cutting,finite element techniques such as element separation criterion(Komvopoulos & Erpenbeck, 1991; Shih, 1995; Shih & Yang, 1993;Strenkowski & Caroll, 1985; Strenkowski & Mitchum, 1987; Ueda& Manabe, 1992), the modelling of the cutting tool’s wear (Shih,1995; Shih & Yang, 1993; Strenkowski & Caroll, 1985; Strenkowski& Mitchum, 1987; Ueda & Manabe, 1992), re-meshing zone (Shih &Yang, 1993), friction modelling (Komvopoulos & Erpenbeck, 1991;

ll rights reserved.

Shih, 1995; Shih & Yang, 1993; Strenkowski & Caroll, 1985; Stren-kowski & Mitchum, 1987; Ueda & Manabe, 1992) etc., was used.In the literature for metal cutting with FEM, a large part of papersdescribe the simulation results on the chip formation process dur-ing orthogonal machining (Kalhori, Lundblad, & Lindgren, 1997;Shih, 1995; Usta, 1999; Zang & Bagchi, 1994) utilizing softwaresuch as Marc, Abaqus, Deform 2D/3D, Nike, Dyne, etc. In the FEMmodels on the chip formation process, the heat and chip formation(Maekawa & Shirakashi, 1996; Mansour, Osman, Sankar, & Maz-zawi, 1973; Stevenson, Wrigt, & Chow, 1983; Strenkowski & Moon,1990; Toshimichi, Nabuhiro, & Sheng, 1991), analysis of cutting toolwear (Komvopoulos & Erpenbeck, 1991), and residual stress distri-butions (Sadat, Reedy, & Yang, 1991) were investigated.

Also, there are a lot of papers in the literature about the cuttingtool stresses in respect of the variations in the cutting parameters.Seker and Kurt (2006) have investigated the effects of the cuttingforces on the cutting tool stresses, and developed the mathematicalmodels for the cutting tool stresses (mathematical modelling of thecompressive stresses in x, y and z directions) in machining of nick-el-based super alloy Inconel 718. They measured the cutting forcesexperimentally and analysed the stress distributions on the cuttingtool by means of ANSYS software. They modelled the compressivestresses with multiple regression analysis regarding to ANSYS

Table 1The chemical composition of Inconel 718 (AMS 5663).

Element % Element %

C 0.012–0.06 Co max. 1.0Cr 17–19 O max. 0.0025Fe 16–19 Mn 0.06–0.10Ni 52–55 Si 0.06–0.09Mo 2.8–3.15 P 0.01–0.015S max. 0.001 B 0.003–0.005Mg max. 0.003 Cu 0.03–0.05Nb 5.20–5.55 Ca 0.005–0.01Ti 0.75–1.15 Pb 0.00005–0.0001Al 0.35–0.65 Bi 0.00005–0.00001Ta max. 0.1 Se 0.00005–0.0001

Table 2The test parameters.

Workpiece material Inconel 718 (AMS 5663)

Cutting tool SNGN 120712 T01020 (KY 4300)Modulus of elasticity (E, GPa) 400 (Casto et al., 1999)Poisson’s ratio (m) 0.23 (Casto et al., 1999)

Tool holder CSRNR 2525 M12Modulus of elasticity (E, GPa) 210.7 (Lin & Lo, 1998)Poisson’s ratio (m) 0.28 (Lin & Lo, 1998)

Cutting parametersCutting speed (V, m/min.) 225, 300, 350, 400, 500Feed rate (f, mm/rev.) 0.05, 0.075, 0.1, 0.125, 0.15Depth of cut (a, mm) 1, 2

9646 A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657

stress results depending on the cutting forces and the chip–toolcontact area, and showed that the model results had good agree-ment with the ANSYS stress results. The effects of the feed rateon the cutting tool stresses in machining of Inconel 718 wereinvestigated by Kose, Kurt, and Seker (2008). They showed thatthe stresses on the ceramic insert increase with the increase ofthe feed rate, and the feed rate is the most relevant cutting param-eter affecting cutting tool stresses. They found that the cuttingtool’s stresses were influenced by the feed force and the passiveforce values in comparison to the primary cutting force value. Kurtand Seker (2005) also investigated the effects of three differentdepth of cut (0.1, 0.2 and 0.4 mm) on the cutting tool stresses (nor-mal, shear and von Mises stress) in machining of Al 2007 alumin-ium alloy orthogonally. In their FEM models, the primary cuttingforce and passive force on the cutting tool were applied as normaland tangential surface load on the rake and flank face by takinginto account chip-tool contact length. The finite element analysisresults showed that the normal stress in y-direction and shearstress in xy-plane decrease from tool tip to chip-tool contact lengthand their distributions are similar to Lee, Liu, and Lam (1995) andZorev’s (1963) normal and shear stress distributions. On the otherhand, the stresses on the contact surfaces between the insert andthe tip seat in the cutting tool were investigated by Wikgren(2001) using SNMG 120408-PM grade cutting tool (Sandvik,H10F) and SS2230 steel.

Nickel-based super alloy Inconel 718 which is most noted fortheir outstanding strength and corrosion resistance (particularlyat high temperatures), is known to be among the most difficult-to-cut materials. In point of the poor machinability of nickel-basedsuper alloys, especially of Inconel 718, are as follows (Dudzinskiet al., 2004): a major part of their strength is maintained duringmachining due to their high-temperature properties. This super al-loy is very strain rate sensitive and readily work-harden, causingfurther tool wear. The highly abrasive carbide particles containedin the microstructure cause abrasive wear. The poor thermal con-ductivity leads to high cutting temperatures up to 1200 �C at therake face. Nickel-based super alloys have high chemical affinityfor many tool materials leading to diffusion wear. Welding andadhesion of nickel alloys onto the cutting tool frequently occurduring machining causing severe notching as well as alteration ofthe tool rake face due to the consequent pull-out of the tool mate-rials. Due to its high strength, the cutting forces reach high values,excite the machine tool system and may generate vibrations whichcompromise the surface quality. In terms of the machinability ofInconel 718 by the generation of the new cutting tools; the cuttingtool wear, temperature distribution, high speed machining and thecutting tool geometries etc. subjects have drawn attention (El-Wardany, Mohammed, & Elbestawi, 1996; Elbestawi, El-Wardany,Di, & Min, 1993; Kitagawa, Kubo, & Maekawa, 1997; Li, He, Wang,& Wang, 2002; Narutaki, Yamane, Hayashi, & Kitagawa, 1993).

In the past years, regression analysis were the most commonand popular modelling technique for prediction. However recently,the ANN availing engineering applications more viable attracts thepotential users. Therefore, the use of ANN for modelling and predic-tion purposes is becoming increasingly popular in the recent years(Karatas�, Sözen, Arcaklıoglu, & Erguney, in press; Sözen, Akçayol, &Arcaklıoglu, 2006; Sözen & Arcaklıoglu, 2007a, 2007b; Sözen, Ar-caklıoglu, & Tekiner, in press; Sözen, Gülseven, & Arcaklıoglu,2007; Sözen, Menlik, & Ünvar, 2008). The use of ANN in metal cut-ting attracts researchers’ attention, especially subjects of tool wear(Filice, Micari, Settineri, & Umbrello, 2007; Ghosh et al., 2007; Luo,Cheng, Holt, & Liu, 2005; Panda, Chakraborty, & Pal, 2008; Özel, Kar-pat, Figueira, & Davim, 2007; Özel & Nadgir, 2002), optimization ofmachining parameters (Mukherjee & Ray, 2006; Muthukrishnan &Davim, 2009; Umbrello, Ambrogio, Filice, & Shivpuri, 2007; Umb-rello, Ambrogio, Filice, & Shivpuri, 2008), and surface roughness

(Basheer, Dabade, Joshi, Bhanuprasad, & Gadre, 2008; Benardos &Vosniakos, 2002; Benardos & Vosniakos, 2003; Lu, 2008; Risbood,Dixit, & Sahasrabudhe, 2003; Özel et al., 2007). ANNs are especiallyuseful for prediction problems where mathematical formulae andprior knowledge on the relationship between inputs and outputsare unknown.

In this paper, the effects of the variations in the cutting param-eters (cutting speed, feed rate and depth of cut) on the cutting toolstresses (normal, shear and von Mises) during the machining ofnickel-based super alloy Inconel 718 was investigated. The cuttingforces were measured experimentally. The stress distributions onthe cutting tool were analysed by finite element method usingANSYS (Kurt, 2006). Due to the experimental work costs are veryhigh and required time to compute stresses is very long, the artifi-cial neural network (ANN) model is developed for all of the cuttingtool stresses in machining of Inconel 718.

2. Materials and methods

2.1. The measurement of cutting forces

In the cutting tests, nickel-based super alloy Inconel 718 (AMS5663) with hardness of 40–45 HRC was used as workpiece mate-rial. The chemical composition of Inconel 718 is shown in Table 1.

Whisker reinforced ceramic inserts (Al2O3 + SiCw) with an ISOdesignation SNGN 120712 T01020 (Kennametal, KY 4300 grade)were used in the cutting tests. The inserts were mounted on a toolholder with an ISO designation, CSRNR 2525 M12 (Takimsas). Cut-ting tests were carried out on a JOHNFORD T35 CNC lathe. In total50 tests were carried out without a coolant and five different cut-ting speeds and feed rates, and two different depths of cut wereused during the measurement of cutting forces. The cuttingparameters used in the experiments are shown Table 2. The prin-cipal cutting force (FC), the feed force (Ff) and the passive/radialforce (Fp) were measured by Kistler piezoelectric dynamometerType 9257B.

A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657 9647

2.2. FEM model of the cutting tool

The distribution of stresses on the cutting tool was analysed byANSYS based on the FEM using the cutting forces (FC, Ff and Fp) mea-sured during the machining. In order to reduce the calculation time

Fig. 1. The solid and the finite elem

V=225 m/min

0

100

200

300

400

500

600

700

800

0.05 0.075 0.125 0.1 0.15

f (mm/rev)

(N)

The depth of cut 1 mm 2 mm

FC

Ff

Fp

FC

Ff

Fp

V=350 m/min

0

100

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0.05 0.075 0.125 0.1 0.15

f (mm/rev)

(N)

The depth of cut 1 mm 2 mm

FC

Ff

Fp

FC

Ff

Fp

V=500 m/

0

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0.05 0.075 0.

f (mm

(N)

The depth of cut1 mm 2 mm

FC

Ff

Fp

FC

Ff

Fp

Fig. 2. The cutting forces in respect of the

in the analysis; the tool holder was modelled 50 mm length and theclamping components (clamp, shim, shim screw, etc.) to clamp theinsert were neglected in the model. The process of the cutting toolmodelling, by taking into account geometric properties of the cut-ting tools (rake angle, inclination angle, nose radius, chamfer angle,

ent models of the cutting tools.

V=300 m/min

0

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Fp

FC

Ff

Fp

V=400 m/min

0

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f (mm/rev)

(N)

The depth of cut1 mm 2 mm

FC

Ff

Fp

FC

Ff

Fp

min

125 0.1 0.15

/rev)

variations in the cutting parameters.

9648 A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657

clearance angles, etc.), was carried out by the solid model made upon Mechanical Desktop 6 Power Pack and than sent to ANSYS in ‘‘.iges”format. During the modelling of the cutting tools, the chip–tool con-tact length (lc, indirectly the chip–tool contact area, AC) was also

a b

Fig. 3. Three dimensional stress state.

Fig. 4. Stress distributions (a) rx, (b) ry, (c) rz, (d) sxy,

taken into account as well illustrated in literature (Kurt & Seker,2005; Seker & Kurt, 2006; Toropov & Ko, 2003a, 2003b, 2005). Thechip–tool contact areas (AC) are 2.0308 and 8.0561 mm2 for thedepth of cuts 1 and 2 mm, respectively.

Thus, the solid models of the cutting tools, with taken into con-sideration the chip–tool contact area, shown in Fig. 1, were devel-oped according to the chip–tool contact length and the depth ofcuts. The material models for the ceramic insert and the tool holderwere shown in Table 2 (modulus of elasticity and Poisson’s ratiowere 400 GPa and 0.23 for the ceramic insert, and 210.7 GPa and0.28 for the tool holder). SOLID92, three-dimensional 10-node tet-rahedral structural solid with a quadratic displacement behaviourand well suited to model irregular meshes (such as produced fromvarious CAD/CAM systems), was used as the element type for thecutting tools in the FEM model. The mesh density was selected

(e) re (V = 225 m/min, a = 2 mm, f = 0.15 mm/rev).

A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657 9649

too dense (smartsize = 3) in the chip–tool contact areas and sparse(smartsize = 5) in the other parts of the cutting tool (Fig. 1). Thecontact pairs were also applied between cutting tool and the seatsurface of the tool holder (3-D 8-node surface-to-surface contactelement CONTA174 for the insert and 3-D target segmentTARGE170 for the tool holder). In term of the solutions generatedby ANSYS; 10237 (11931 nodes) and 26550 (29663 nodes) ele-ments were used for CSRNR 2525 tool holder and SNGN 120712T01020 ceramic insert, respectively.

In spite of the clamping components (clamp, shim screw, etc.)were neglected in the solid model, the clamping forces applied tothe insert by the clamping system were taken into considerationin the analysis. The clamping forces were applied to the clamp-to-insert contact zone as the nodal force, force/on nodes (Fig. 1).The cutting forces were applied to nodes in the chip–tool contactareas (shaded area in Fig. 1) as follows: the primary cutting forcewas applied as triangular surface load throughout the chip–toolcontact length. The feed force (+x direction) and the passive force(�y direction) were applied to nodes in the contact areas in thefeed direction of the cutting tool and workpiece as the nodal force.

In order to reduce the calculation time in the analysis, some ofassumptions were performed as follows: the weight of the toolholder and the insert are neglected. The inserts used in the analysisare new and unused (sharp). The vibrations and temperatures oc-curred in the metal cutting are neglected in the analysis. The staticanalysis solution method was used. As a boundary condition forconstraint, the degree of freedom of the nodes (nodal displace-ments) in the area to mount the tool holder to the dynamometer,on the tool holder mounting length, was selected zero in all direc-tions (nodal displacements = 0).

2.3. Artificial neural network (ANN)

ANN is a system loosely modeled on the human brain. The brainconsists of a large number of neurons, connected with each otherby synapses. These networks are called as natural neural network(Sözen & Arcaklıoglu, in press). The ANN is a simplified mathemat-ical model of a natural neural network. It is a directed graph wherea vertex corresponds to a neuron and an edge to a synapse (Ander-son & McNeill, 1992). Different ANN models have been proposedsince its conception in the 1940s, but the multi- layer perception(MLP) is the most widely used. These layered networks have beenapplied to various problems such as pattern recognition, predic-tion, and function approximation (Haykin, 1994). There are differ-

Bias

Bias

FfFCaV f

Fig. 5. ANN arc

ent learning algorithms. A popular algorithm is the back-propagation algorithm, which have different variants. The goal ofany training algorithm is to minimize the global error such asmean root-mean-square (RMS), mean absolute percentage error(MAPE) and R2. The error for hidden-layers is determined by prop-agating back the error determined for the output layer. These er-rors are explained as follows:

RMS ¼ ð1=pÞX

j

jtj � ojj2 !1=2

ð1Þ

MAPE ¼ o� to� 100 ð2Þ

R2 ¼ 1�P

jðtj � ojÞ2PjðojÞ2

!ð3Þ

3. Stresses on the cutting tools

3.1. The experimental and theoretical analysis

The cutting forces measured by the cutting tests according to onthe change in the feed rate value are shown in Fig. 2. In general, thecutting forces increase with the increase of the feed rate for all thecutting speed and the depth of cut. In all of the cutting experi-ments, the primary cutting force (FC) was measured too higherthan other cutting forces. The measured cutting force values forthe depth of cut 2 mm are higher than in the depth of cut 1 mm.Especially for the depth of cut 1 mm, the feed force (Ff) and the pas-sive/radial force (FP) are nearly equal for all the cutting speed andthe depth of cut.

In order to explain three-dimensional stress state, a cube wasused (Fig. 3). The stress results were interpreted with respect toFig. 3a and b: stress signed ‘‘+” and ‘‘�” was showed the formrþx ;rþy ;rþz ; sþxy; sþyz; sþxz and r�x ;r�y ;r�z ; s�xy; s�yz; s�xz, respectively. Nor-mal stresses and shear stresses were showed by symbol r and s,respectively: rþx ;rþy ;rþz and r�x ;r�y ;r�z pointed out the tensionaland the compressive stresses in x, y, z axis, respectively. sþxy; sþyz; sþxz

and s�xy; s�yz; s�xz pointed out the maximum shear stresses and theminimum shear stresses, respectively. re pointed out von Misesstress (or effective stress) (Fig. 3).

Analyses were carried out for all 50 cutting experiments accord-ing to the stated loading condition. Fig. 4 shows the stress distribu-tions for the cutting speed 225 m/min, the feed rate 0.15 mm/rev,

Output layer

Hidden layer

Input layer

Fp AC

hitecture.

9650 A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657

and the depth of cut 2 mm. The critical zone in terms of the cuttingtool wear for the cutting speed 225 m/min, the feed rate 0.15 mm/rev, and the depth of cut 2 mm, is determined as being equal to thedepth of cut on the base cutting edge of the cutting tool (Fig. 4e).

Generally, for all the cutting speeds, it is shown that all normalstress values are increase in parallel to the increase of the cuttingspeed regardless of the depth of cut. The highest value of the ten-sional normal stress compound in x-direction ðrþx Þ is 1128.1 MPafor the cutting speed 500 m/min, the feed rate 0.15 mm/rev, and

0.050.075

0.10.125

0.15

225

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f (mm/rev)V (m/min)

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σ x (M

Pa)

σ z (M

Pa)

σ y (M

Pa)

+

+

+

--

-

Fig. 6. ANSYS vs. ANN resu

the depth of cut 2 mm. The highest values for tensional rþy andrþz are 912.19 MPa and 1225.9 MPa at the depth of cut 2 mm forV = 225 m/min, f = 0.15 mm/rev and V = 500 m/min, f = 0.15 mm/rev, respectively. r�x ;r�y ;r�z compressive stresses are increase inparallel to the increase of the depth of cut, but the variation ofr�z is small than the other normal stress compounds. The compres-sive stresses for all tests may be lined up with respect to it is mag-nitude as r�x ;r�y ;r�z . The highest r�x ;r�y ;r�z stresses are 6006.5,3585.8, and 910.36 MPa, respectively, for the cutting speed

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σ x (M

Pa)

σ z (M

Pa)

σ y (M

Pa)

lts (normal stresses).

A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657 9651

500 m/min, the feed rate 0.15 mm/rev, and the depth of cut 2 mm.When tension stress is compared to compressive stress, in gener-ally, it may be said that rx and ry stresses are more active as com-pressive stress. It also was observed that all of the maximum shearstresses increase in parallel at increasing of the feed rate for all thecutting speed and the depth of cut. The highest values for the max-imum shear stresses on the xy and xz planes ðsþxy; sþyzÞ were ob-tained at the cutting speed 500 m/min, the feed rate 0.15 mm/

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τ xy (M

Pa)

+ -

τ yz (M

Pa)

+ -

τ xz(

MP

a)

+ -

Fig. 7. ANSYS vs. ANN res

rev, and the depth of cut 2 mm (2779.1 and 2113.5 MPa, respec-tively). The highest value of the minimum shear stresses on theyz plane ðs�yzÞwas obtained as 1451.7 MPa at the same cutting con-ditions. Also von Mises stresses (re) increase at increasing of thefeed rate. Especially for the depth of cut 2 mm, the feed rate hassignificant effect on von Mises stresses. For the cutting speed225 m/min, re stress increased approximately 380 MPa at thedepth of cut 1 mm, but it had an increase of 1352 MPa at the depth

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τ xy (M

Pa)

τ yz (M

Pa)

τ xz(

MP

a)

ults (shear stresses).

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f (mm/rev)V (m/min)

ANSYS (a=1 mm)

ANN (a=1 mm)

ANSYS (a=2 mm)

ANN (a=2 mm)

TEST

σ e (M

Pa)

Fig. 8. ANSYS vs. ANN results (von Mises stresses).

9652 A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657

of cut 2 mm. The increasing in the cutting speed results in an in-crease in von Mises stresses. The effect of the feed rate on vonMises stresses can be clearly viewed for the cutting speed 500 m/min. von Mises stresses results show that the highest stress value(7294.8 MPa) occurs again for the cutting speed 500 m/min, thefeed rate 0.15 mm/rev, and the depth of cut 2 mm (for furtherinformation about normal stresses (tension, r+, and compressive,r�), shear stresses (signed ‘‘+” and ‘‘�”), and von Mises stressesin respect of the variations in the cutting parameters, see Figs. 6–8).

Analyses of the ceramic cutting insert made after the cuttingexperiments show that the highest cutting tool wear may be occurat the distance equal to the depth of cut on the base cutting edge of

rþx ¼1

1þ e�ð�0:1323�F1�1:2949�F2þ2:3202�F3�0:1361�F4�0:4726�F5�0:8911�F6�6:1122�F7þ5:364

rþy ¼1

1þ e�ð�2:7401�F1�6:9103�F2þ6:7309�F3þ3:5864�F4�6:1363�F5�2:0115�F6þ5:0066�F7þ0:866

rþz ¼1

1þ e�ð�1:6971�F1�1:4258�F2þ1:8009�F3�2:0906�F4�3:4941�F5þ2:8879�F6�1:7072�F7þ3:501

sþxy ¼1

1þ e�ð5:5977�F1�0:6556�F2�4:3353�F3þ7:2282�F4�0:8674�F5�0:4761�F6�6:4609�F7�0:1679�

sþyz ¼1

1þ e�ð2:4589�F1�5:0055�F2�3:386�F3þ3:1604�F4�4:2882�F5þ1:0205�F6þ3:3803�F7þ2:4083�F

sþxz ¼1

1þ e�ð�1:2369�F1�1:1946�F2þ1:9977�F3�1:4304�F4þ0:3041�F5�0:3823�F6�4:489�F7�1:8487�

re ¼1

1þ e�ð2:7396�F1�0:8016�F2þ5:9375�F3þ3:5912�F4�0:9952�F5�0:2844�F6�5:7673�F7þ2:3908�F

r�x ¼1

1þ e�ð4:1115�F1�0:9804�F2�1:6629�F3þ5:3972�F4þ0:0067�F5�0:5784�F6�5:1742�F7�0:3727�

r�y ¼1

1þ e�ð2:908�F1�0:5195�F2�1:2668�F3þ3:8217�F4�5:13�F5�0:7212�F6�2:9902�F7þ1:1715�F8þ

r�z ¼1

1þ e�ð�1:0329�F1�1:5357�F2þ7:5405�F3�1:6108�F4�0:8181�F5�6:6672�F6�7:0688�F7þ3:851

s�xy ¼1

1þ e�ð�0:0668�F1�0:5064�F2þ1:2967�F3þ0:0575�F4�2:1739�F5�0:4926�F6�4:4223�F7þ2:991

s�yz ¼1

1þ e�ð4:0411�F1þ0:3254�F2þ3:6262�F3þ5:198�F4�6:8704�F5�1:0984�F6�5:022�F7þ1:2504�F8þ

s�xz ¼1

1þ e�ð1:5462�F1�0:848�F2þ4:9161�F3�1:8481�F4�2:4873�F5�0:0858�F6�3:0012�F7þ1:5014�F

the cutting tool, in parallel with von Mises stress results for thecutting speed 500 m/min, the feed rate 0.15 mm/rev, and the depthof cut 2 mm (Fig. 4e). Thence, this wear mode will be almost suchas the notch wear, and the flank wear on the base cutting edge andgrooves in relief face.

3.2. Application results of ANN

The selected different ANN structures are shown in Fig. 5. Var-iant of the algorithm used in the study is scaled conjugate gradient(SCG) with 10 neurons. Inputs and outputs are normalized in the(�1, 1) range. Neurons in input layer have no transfer function.Each input is multiplied by a connection weight. In the simplestcase, products and biases are simply summed, then transformedthrough a transfer function to generate a result, and finally the out-put obtained. Logistic sigmoid (logsig) transfer function has beenused. The transfer function used:

f ðzÞ ¼ 11þ e�z

ð4Þ

where z is the weighted sum of the input.Computer program has been performed under MATLAB in order

to use different algorithms and different neurons in the ANN. In-puts for the ANN are cutting speed (V), feed rate (f), depth of cut(a), the principal cutting force (FC), the feed force (Ff), the radialforce (Fp), and the chip–tool contact area (AC); outputs are thestress compounds (rþx , rþy , rþz , sþxy, sþyz, sþxz, r�x , r�y , r�z , s�xy, s�yz, s�xz,and re). Fig. 5 shows the single hidden-layer ANN architectureused in our application.

The cutting tool stresses in machining of Inconel 718 are deter-mined as analytic formulas in Eqs. (5)–(17) by using artificial neu-ral network (ANN) based on working parameters. The newformulas of the output as the best algorithm SCG with 10 neuronsis given Eqs. (5)–(17).

9�F8�0:2013�F9�2:5397�F10�1:888Þ ð5Þ

�F8þ3:5641�F9�1:034�F10�3:5476Þ ð6Þ

7�F8�2:0258�F9�1:791�F10þ1:5205Þ ð7Þ

F8þ7:0464�F9�2:1686�F10þ6:1648Þ ð8Þ

8þ2:9851�F9�0:8356�F10þ1:6138Þ ð9Þ

F8�1:4753�F9�3:2417�F10þ8:947Þ ð10Þ

8þ3:4982�F9�2:5331�F10�3:1765Þ ð11Þ

F8þ5:2103�F9�2:4636�F10þ4:3061Þ ð12Þ

3:6654�F9�1:1224�F10þ4:3398Þ ð13Þ

5�F8�0:8046�F9�3:8289�F10þ5:9102Þ ð14Þ

3�F8þ0:0405�F9�3:2349�F10þ4:7216Þ ð15Þ

5:1132�F9�1:2332�F10þ0:91Þ ð16Þ

8�1:9367�F9�1:8951�F10þ2:0603Þ ð17Þ

Tabl

e3

The

wei

ghts

betw

een

inpu

tla

yer

and

hidd

enla

yer

for

scg1

0.

iC 1

iC 2

iC 3

iC 4

iC 5

iC 6

iC 7

iC 8

i

10.

3509

�18

.613

32.

1635

�1.

7965

�10

.428

1�

0.35

7813

.811

70.

3625

2�

0.02

210.

1004

�4.

2188

�0.

2546

�8.

6506

6.20

40�

1.57

774.

6662

30.

8052

6.48

024.

3011

4.79

322.

8684

2.20

301.

8379

3.53

774

�1.

6874

1.56

29�

1.93

1617

.961

62.

2312

9.21

06�

4.97

58�

6.71

625

0.00

14�

0.00

54�

2.20

920.

1588

1.76

18�

3.99

230.

3667

1.97

306

0.01

17�

0.00

424.

3290

�2.

0432

2.77

010.

0279

�0.

3857

�0.

2820

70.

0042

0.02

56�

3.58

310.

1085

�2.

0701

�1.

6467

�6.

7930

9.16

548

6.27

423.

4063

�2.

3149

0.74

245.

4766

1.13

80�

0.03

493.

9512

91.

7420

�1.

3703

�2.

4687

�19

.084

4�

1.88

96�

8.66

530.

5882

7.98

6510

0.07

870.

3375

4.65

73�

0.93

73�

7.91

11�

0.81

649.

5156

0.94

30 Table 4Values for normalization.

Inputs Divided by Outputs Multiplied by

V Divided by 600 rþx Multiplied by 1200f Multiplied by 6 rþy Multiplied by 1000a Divided by 10 rþz Multiplied by 1500FC Divided by 1000 sþxy Multiplied by 3000Ff Divided by 700 sþyz Multiplied by 1000Fp Divided by 500 sþxz Multiplied by 2500Ac Divided by 10 re Multiplied by 8000

r�x Multiplied by 7000r�y Multiplied by 4500r�z Multiplied by 1000s�xy Multiplied by 500s�yz Multiplied by 1600s�xz Multiplied by 700

A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657 9653

where; Fi can be calculated according to Eq. (18). The formulas forthe prediction of the cutting tool stresses (Eqs. (5)–(17)) is depen-dent on working parameters as seen in Eq. (19).

Fi ¼1

1þ e�Eið18Þ

where Ei is given Eq. (19), which is working parameters.

Ei ¼ C1i � V þ C2i � f þ C3i � aþ C4i � FC þ C5i � Ff þ C6i � Fp

þ C7i � AC þ C8i ð19Þ

The constants (Cij) in Eq. (19) are given Table 3. The input andoutput values in network need normalizing according toTable 4.

Figs. 6–8 present the simulated results versus the cutting toolstresses in machining of Inconel 718 experimental data for thetesting database. Deviations between experimental results andtheoretical results are very small for each parameter and negligi-ble. Figs. 6–8 show the model’s ability to predict the cutting toolstresses values at different working parameters for Inconel 718.As seen from results ANN can be use the determination the cut-ting tool stresses. From this correlation and statistical test, it isevident that the model was successful in predicting the experi-mental data of the cutting tool stresses values. This shows theimportance of the artificial neural network to determine the cut-ting tool stresses. Table 5 and Figs. 9–11 show the performanceof ANN. The statistical error values for these approaches are givenTable 5.

4. Results and discussion

The cutting tests on the Inconel 718 workpiece, using SNGN120,712 T01020 ceramic cutting insert (KY 4300 grade), and the re-sults of the ANSYS stress analysis are as follows:

– Although the resultant force for metal cutting is approximatelythe same for all the tests, the cutting tool’s stresses were influ-enced by the feed force and the passive force values in compar-ison to the primary cutting force value in the machining ofInconel 718.

– The stresses on the ceramic insert increase with the increase ofthe feed rate.

– In respect of the depth of cut 2 mm, there is an inverse relation-ship between an increase in the cutting speeds and the stressvalues in the depth of cut 1 mm.

300

400

500

600

700

800

900

1000

1100

300 400 500 600 700 800 900 1000 1100

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa)

x+σ

Training data

Testing data

1500

2200

2900

3600

4300

5000

5700

6400

1500 2200 2900 3600 4300 5000 5700 6400

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa) Training data

Testing data

xσ

250

350

450

550

650

750

850

950

250 350 450 550 650 750 850 950

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa)

y+σ

Training data

Testing data

1000

1450

1900

2350

2800

3250

3700

1000 1450 1900 2350 2800 3250 3700

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa) Training data

Testing data

yσ

400

500

600

700

800

900

1000

1100

1200

1300

400 500 600 700 800 900 1000 1100 1200 1300

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa)

z+σ

Training data

Testing data

475

550

625

700

775

850

925

475 550 625 700 775 850 925

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa)

Training data

Testing data

zσ

Fig. 9. The performance of ANN (normal stresses).

Table 5The statistical error values.

Output Training data Testing data

RMS R2 MAPE RMS R2 MAPE

rþx 0.005182 0.999904 0.511668 0.00422 0.999922 0.945444rþy 0.004981 0.999892 0.800388 0.009387 0.999489 1.825894rþz 0.00509 0.999886 0.96822 0.006319 0.999769 1.401075sþxy 0.004619 0.999919 0.494808 0.00428 0.999917 1.069269sþyz 0.004795 0.999853 0.964464 0.003631 0.999873 0.739667sþxz 0.003344 0.999959 0.539465 0.005328 0.999871 1.182814re 0.003575 0.999954 0.496114 0.002971 0.999961 0.69195r�x 0.002591 0.999973 0.477138 0.004131 0.999915 1.01595r�y 0.003497 0.99995 0.562041 0.006458 0.999812 1.239776r�z 0.006189 0.999906 0.821088 0.009149 0.999794 1.29199s�xy 0.003448 0.999963 0.467795 0.004927 0.999911 0.868266s�yz 0.004019 0.999949 0.457704 0.007215 0.999823 1.408554s�xz 0.003348 0.999952 0.558552 0.006705 0.999769 1.556545

9654 A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657

700

1000

1300

1600

1900

2200

2500

2800

700 1000 1300 1600 1900 2200 2500 2800

ANSYS stress results (MPa)

AN

N s

tres

s re

sults

(M

Pa)

xy+τ

Training data

Testing data

150

200

250

300

350

400

450

150 200 250 300 350 400 450

ANSYS stress results (MPa)

AN

N s

tres

s re

sults

(M

Pa)

xyτ

Training data

Testing data

200

300

400

500

600

700

800

200 300 400 500 600 700 800

ANSYS stress results (MPa)

AN

N s

tres

s re

sults

(MP

a)

yz+τ

Training data

Testing data

450

600

750

900

1050

1200

1350

1500

450 600 750 900 1050 1200 1350 1500

ANSYS stress results (MPa)

AN

N s

tres

s re

sult

s (M

Pa)

yzτTraining data

Testing data

750

1000

1250

1500

1750

2000

2250

750 1000 1250 1500 1750 2000 2250

ANSYS stress results (MPa)

AN

N s

tres

s re

sults

(M

Pa)

xz+τ

Training data

Testing data

175

225

275

325

375

425

475

525

575

175 225 275 325 375 425 475 525 575

ANSYS stress results (MPa)

AN

N s

tres

s re

sults

(M

Pa)

xzτTraining data

Testing data

Fig. 10. The performance of ANN (shear stresses).

2000

2700

3400

4100

4800

5500

6200

6900

7600

2000 2700 3400 4100 4800 5500 6200 6900 7600

ANSYS stress results (MPa)

AN

N s

tres

s re

sults

(MP

a)

eσTraining data

Testing data

Fig. 11. The performance of ANN (von Mises stresses).

A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657 9655

– In terms of the cost of the process of machining, the cuttingspeed and the feed rate value must be chosen between 225and 400 m/min, and 0.1 and 0.125 mm/rev, respectively.

– As a result of the cutting tool’s stress analysis, especially fromvon Mises stress distributions, in terms of the cutting tool wear,the ceramic cutting insert may be possible worn at the distanceequal to the depth of cut on the base cutting edge of the cuttingtool (actually, the ceramic insert worn at this distance in cuttingtests (Kurt, 2006). Thence, this wear mode will be almost such asthe notch wear (groove), and the flank wear on the base cuttingedge and grooves in relief face.

– The results of validation and comparative study indicate thatthe ANN based estimation technique for the cutting toolstresses.

– This study confirms the ability of the ANN to predict the cuttingtool stresses.

– The results indicate that the ANN model seems promising forevaluation powder flow in the known working parameters.

9656 A. Kurt / Expert Systems with Applications 36 (2009) 9645–9657

Acknowledgements

The author would like to thank Gazi University (Project Code:07/2002–13) and The State Planning Organisation (Project Code:2002K120250–05) for providing financial support for the project.Also, the author would like to thank Assoc. Prof. Dr. Adnan Sozenand Assoc. Prof. Dr. Erol Arcaklioglu for critically reviewing the ori-ginal manuscript and application of ANN.

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