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  1. 1. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401393 | P a g eExpert modeling and multi objective optimization of laser trepandrilling of titanium alloy sheet1. Md Sarfaraz Alam*, 2Md Tabish Haque1,2,3Motilal Nehru National Institute of Technology, Allahabad-211004, Uttar Pradesh, IndiaABSTRACTNowadays laser machining became anattractive machining process for difficult to cutmaterials like ceramics, composites and superalloys. Titanium alloys specially Ti-6Al-4V(grade 5) is most widely used for differenttechnologically advanced industries due to theirsuperior performance characteristics such ashigh strength and stiffness at elevatedtemperatures, high strength to weight ratio,high corrosion resistance, fatigue resistance, andability to withstand moderately hightemperatures without creeping. Laser trepandrilling (LTD) being a thermal and non contactnature and having the ability to produce microdimensions with required level of accuracy.However laser drilled holes are inherentlyassociated with a number of defects like noncircularity of hole, spatter thickness and holetaper. The present paper investigate the lasertrepan drilling(LTD) process performanceduring trepanning of titanium alloy (Ti-6Al-4V)by modeling and simultaneous optimization ofthree important performance challenges such ashole taper (HT), circularity at entrance(CIRentry) and circularity at exit (CIRexit). Ahybrid approach of artificial neural network(ANN)-genetic algorithm (GA) and greyrelational analysis (GRA) has been proposed formulti-objective optimization. The verificationresults are in the close agreements with theoptimization results.Keywords: ANN, GA, GRA and LTD.1. INTRODUCTIONThe laser drilling process is one of themost widely used thermal energy based non-contact type advance machining process which canbe applied across a wide range of materials.Nowadays laser drilling is finding increasinglywidespread application in the industries. Laserbeam machining is based on the conversion ofelectrical energy into light energy and then intothermal energy to remove the material from workpiece. The material removal process is by focusinglaser beam onto the work material for melting andvaporizing the unwanted material to create a hole.CO2 laser drilling has been widely used inindustries because of its high production rate andabilities on rapidly varying holes size, drillingholes at shallow angle, and drilling hard-to-workmaterial such as high strength materials, ceramicand composite. Laser drilled holes are inherentlyassociated with a number of defects. Noncircularity of hole, spatter thickness, and hole taperare some defects associated with laser drilling. As aresult, the quality of the drilled holes is the mainissue in the laser drilling process. There are twotypes of laser drilling: trepan drilling andpercussion drilling. Trepan drilling involves cuttingaround the circumference of the hole to begenerated, whereas percussion drilling is carriedout by utilizing a focused laser spot to heat, meltand vaporize the target material such that a desiredhole is formed through the work piece with norelative movement of the laser or work material[1,2]. Fig. 1 shows a schematic of laser beamdrilling [2]Fig. 1: Schematic of laser beam drilling
  2. 2. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401394 | P a g eA Number of researchers have performed theexperimental studies to investigate into the processof laser percussion drilling by considering somesignificantly affecting factors/ process parameters,without applying any scientifically designedexperimentation technique, further analyzing theimpact of every parameter on observed processperformance characteristics. Tongyu and Guoquan,[3] performed a study to investigate the relationshipof laser beam parameters (energy, power, pulsewidth, pulse frequency) with the hole geometricalquality characteristics and to find feasibility of highcarbon steel to investigate the heat affected zone inlaser drilling. Laser percussion drilling of aluminaceramics was investigated by Kacar et al, [4] todetermine the effect of peak power (2-11 kw) andpulse duration (0.5-7 ms) on geometrical featuresof drilled holes such as diameter at entrance andexit, crater (Initial cavity before getting throughhole) diameter and hole taper angle. The craterdiameter and the hole exit diameters showsproportional changes with the Pulse duration andpeak power, although, the entrance hole diameterdo not changes much with them. The reason theyfound, after morphological investigation with thehelp of optical microscope that the resolidifiedmaterial at the entrance side increases with theincrease in pulse duration and peak power, whichultimately reduces the entrance hole diameter evenafter larger crater diameter. Also due to the samereason there is a decrease in taper angle at the sameconditions, which further becomes negative forhigher values of process parameters. Ghoreishi etal. [5] investigated the relationships and parameterinteractions between laser peak power, laser pulsewidth, pulse frequency, number of pulses, assistgas pressure and focal plane position on the holetaper and circularity in laser percussion drilling ofstainless steel and mild steel. The central compositedesign was employed to plan the experiments inorder to obtain required information. The processperformance was evaluated in terms of equivalententrance diameter, hole taper and hole entrancecircularity. They found that the pulse frequencyhad a significant effect on the hole entrancediameter and hole circularity in drilling stainlesssteel unlike the drilling of mild steel, where thepulse frequency had no significant effect on thehole characteristics. Benyounis and Olabi [6] did acomprehensive literature review of the applicationsof design of experiments, evolutionary algorithmsand computational networks on the optimization ofdifferent welding processes through mathematicalmodels. According to their review of variousliteratures, they were of the opinion that there wasconsiderable interest among the researchers in theadaption of response surface methodology (RSM)and artificial neural net- work (ANN) to predictresponses in the welding process. For a smallernumber of experimental runs, they noted that RSMwas better than ANN and genetic algorithm (GA)in the case of low order non-linear behavior of theresponse data. In the case of highly non-linearbehavior of the response data, ANN was better thanother techniques. They also observed that theTaguchi approach of S/N ratio might lead to non-optimal solutions with less flexibility and theconducting of needless experiments. Some recentattempts have been made to control the laser drilledhole taper through the development of drillingtechniques [7, 8]. Ng and Li [9] assessed the effectof laser peak power and pulse width on the holegeometry repeatability in Nd:YAG laser percussiondrilling of 2 mm thick mild steel sheets. Thirty-fiveholes were drilled and analyzed for each set ofidentical laser parameters. They found that higherpeak power and shorter pulse width gave betterhole geometry repeatability. The circularity of theentrance hole ranged from 0.94 to 0.87, and wasfound to correlate with repeatability.Titanium and its alloys are most widelyused for different technologically advancedindustries such as aerospace, marine, chemical,food processing and medical due to their superiorperformance characteristics such as high strengthand stiffness at elevated temperatures, high strengthto weight ratio, high corrosion resistance, fatigueresistance, and ability to withstand moderately hightemperatures without creeping [10]. The Ti-6Al-4Vis an alloy (grade 5) of Ti, has extensively used inaerospace, marine, chemical processing, medicaland automobile sectors for making differentcomponents such as airframes, fastenercomponents, vessels, cases, hubs, forgings, boneplates, rods, expendable ribs cages, finger and toereplacements, spinal fusion cages and dentalimplants, pistons and piston rings. Ti and its alloyscannot be cut easily by conventional cuttingmethods due to their improved mechanicalproperties, poor thermal conductivity, low elasticmodulus and high chemical affinity at elevatedtemperatures. Due to the poor thermal conductivityof these alloys, the heat generated during thecutting cannot dissipated properly which resultsvery high temperature at the tool–work pieceinterface and melting of the tool tip. Thus adverselyaffects the tool life. Ti is chemically reactive atelevated temperatures due to which the toolmaterial either rapidly dissolves or chemicallyreacts during the cutting process, resultingpremature tool life [11]. The low elastic modulus ofTi alloys permits greater deflection of workpieceduring machining and complexity of the machiningincreases. While machining the Ti alloys, thecontact length between the tool and chip has beenfound very small due to which high cuttingtemperatures and high cutting stresses areconcentrated near the tool tip which results themelting of tool tip and finally tool life reduces. Dueto the thermal plastic instability, the shear strains in
  3. 3. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401395 | P a g ethe chips are not uniform which promotes theformation of serrated chips. These serrated chipscreate fluctuations in the cutting force (generatesvibrational forces) which are responsible for severflank wear of cutting tools [12]. Thus there is acrucial need for reliable and effective cuttingprocess for Ti and its alloys. Alternatively for thecutting of these materials advanced cuttingprocesses such as Electric discharge machining,ultrasonic machining, laser beam machining maybe used with some limitations. But for using theseadvanced cutting methods, a lot of research workhas been required so that the required objectivesmay be fulfilled by controlling different processparameters.Most of the previous works related to holedrilling used the percussion drilling process wherewith intense laser burst, the hole size was the sizeof the beam that was varied by focusing. Thepresent study focuses on the alternative trepandrilling. This paper reports the multi-objectiveoptimization of hole geometrical qualities such asHT, CIRentry and CIRexit in the pulsed Nd:YAGlaser trepanning of Titanium alloy sheet. Themotivation for the investigation is the fact thatTitanium alloys being increasingly used in differentindustries and engineers of these industries aretrying to obtain best qualities of these materials inthe laser drilling. In this investigation, Ti-6Al-4V(Titanium alloy sheet grade 5) sheet has beenselected because it is known for its exceptionalperformance characteristics and is one of themostly used Titanium alloys. Due to highermaterial costs, the Ti alloys require such type ofdrilling methods in which minimum wastage ofmaterials is obtained with satisfactory trepannedqualities. But the reported research works showthat poor qualities are obtained by use of air ornitrogen assist gases due to low thermalconductivity and high chemical reactivity atelevated temperatures. The use of costlier inertgases may further increase the cutting cost.Therefore, the aim of present research is to obtaingood quality of trepanned hole by using N2 as assistgas. ANN has been applied for the modeling of HT,CIRentry and CIRexit with the help of data obtainedby the L27 orthogonal array experimentation. Thehybrid approach of ANN, GA and GRA basedentropy measurement technique has been appliedfor modeling and multi-objective optimization ofHT, CIRentry and CIRexit. The predicted optimumresults have been verified by confirmation tests.2. EXPERIMENTAL SETUP AND DESIGNOF EXPERIMENTSThe experiments have been performed on200W pulsed Nd:YAG laser cutting system withCNC work table supplied by SIL Pune, India. Theassist gas used is Nitrogen and it is passed througha nozzle of 1 mm diameter, which remains constantthroughout the experiments. The focal length of thelens is 50 mm and the standoff distance is 1 mm.The Titanium alloy sheet (Ti-6Al-4V) of thickness1.4 mm is used as work material. The chemicalcompositions of the Ti-6Al-4V are shown in Table1. Pulse width or pulse duration, pulse frequency,assist gas pressure and cutting speed have beenselected as input process parameters (controlfactors). An exhaustive pilot experimentation hasbeen performed in order to decide the range of eachcontrol factors for complete through cutting. Thedifferent control factors and their levels are shownin Table 2. The quality characteristics or responsesselected for the analyses are HT, CIRentry andCIRexit. 1 mm diameter holes are made with tworepetitions for the each experimental run. The holediameters at the entrance and exit were measured atsix orientations at an interval of 300. Diameters aremeasured by using optical microscope with 10Xmagnification supplied by Radical instruments,India. The HT, CIRentry and CIRexit were calculatedby following formula:Hole taper     tdd exitfentrancef  ,(Since α =tan α, for small value of α) Where(df) entrance and (df) exit are mean Feret’s diameters atthe entrance and exit, respectively and (t) is thedrilled hole depth.Circularity at entry/exitwhere (df) Min and (df) Max are minimum andmaximum Feret’s diameters at entrance or exit sideof drilled hole.The total number of experiments can besubstantially reduced with the help of a welldesigned experimental plan without affecting theaccuracy during the experimental study of anymanufacturing process. Taguchi have suggestedthat it is better to make the process robust ratherthan equipments and machinery just by nullifyingthe effects of variations through selection ofappropriate parameter level. Taguchi has suggestedproperly designed experimental matrices known asorthogonal arrays (OAs) to conducts theexperiments. In this present research work fourcontrol factors with three levels of each have beenconsidered. Hence experiments can be performed
  4. 4. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401396 | P a g eby using simplest L9 OA. But authors have selected L27 OA for high resolution factor [13].Table 1: Composition of titanium alloy sheet (grade-5) (% volume)Table 2: Control factors and their levels3. METHODOLOGY3.1. ARTIFICIAL NEURAL NETWORK (ANN)ANN is information processing paradigminspired by biological nervous systems like ourbrain. In neural network a large number of highlyinterconnected processing elements (neurons) areworking together. Like people, they learn fromexperience. In a biological system, learninginvolves adjustments to the synaptic connectionsbetween neurons; the same is true for ANNs [14].In the network, each neuron receives total inputfrom all of the neurons in the preceding layer as(1)Where the total or net input and N isare the numbers of inputs to the rth neuron in theforward layer. is the weight of the connectionto the qth neuron in the forward layer from the rthneuron in the preceding layer , is the inputfrom the rth neuron in the preceding layer to theforward layer and the bias to qth neuron . Aneuron in the network produces its output ( )by processing the net input through an activationfunction Ғ , such as log sigmoid function and purelinear function chosen in this study as below(2)&(3)In calculation of connection weights, oftenknown as network training, the weights are givenquasi-random initial values. They are theniteratively updated until converges to the certainvalue using the gradient descent method. Gradientdescent method updates weights so as to minimizethe mean square error between the network outputand the training data set. For simultaneousoptimization of more than one qualitycharacteristics, sometimes it is desirable tonormalize the quality characteristics. So thetraining data set, i.e. the experimental values ofquality characteristics have been normalized usingfollowing formula:(4)Where the normalized value of the kthresponse is during ith observation, is themaximum value of for the kth response.3.2. GENETIC ALGORITHM (GA) FOROPTIMIZATIONGenetic algorithms (GA) are the globaloptimization technique which is quite suitable fornon-linear optimization problems. GA is based onthe Darwin’s principle of “survival of fittest” .Thealgorithm starts with the creation of randompopulation. The individual with best fitness areselected to form the mating pair and then the newpopulation is created through the process of cross-over and mutation. The new individuals are againtested for their fitness and this cycle is repeateduntil some termination criteria are satisfied [14].3.3 GREY RELATIONAL ANALYSIS (GRA)A common difficulty with multi-objectiveoptimization is the appearance of an objectiveconflict; none of the feasible solution allowssimultaneous optimal solution for all objectives.The individual optimal solutions of each objectiveare usually different. To get the solution of multi-objective optimization problem, using classicalmethods, all the objectives are converted intosingle objective function. There are many methodsof transforming multi-objective optimizationproblem into single objective optimization problemand objective weighting method is one of thepopular methods. In objective weighting method,multi-objective functions are combined into oneoverall objective function by assigning differentweigh to different objective [15]. Thedetermination of weight is a critical aspect, whichsometimes is decided by designer’s experience orsome mathematical techniques. In this study, theGRA coupled with entropy measurement technique[16] has been used to find the weight of eachquality characteristics for multi-objectiveAl Fe Sn V Ti6.22 0.187 0.56 3.35 89.6Symbol Factors Level 1 Level 2 Level 3X1 Pulse width (ms) 0.8 1.2 1.6X2 Pulse frequency (Hz) 13 17 21X3 Gas pressure (kg/cm2) 6 8 10X4 Trepanning speed (mm/s) 0.1 0.2 0.3
  5. 5. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401397 | P a g eoptimization. The working of the GRA and entropymeasurement technique has been explained withthe help of block diagram in Fig. 2.Fig. 2: Block diagram for GRA and Entropy measurement techniqueThe normalized value of the quality characteristics have been calculated using Eqs. (4), and have been shown inthe Fig.3.4. MODELINGThe optimal neural network architectureused for normalized hole taper (NHT), normalizedcircularity at entry (NCIRentry) and normalizedcircularity at exit (NCIRexit) is shown in Fig. 4. Thenetwork for all three NHT, NCIRentry and NCIRexitconsists of one input, one hidden and one outputlayer. The input and output layers have four andone neuron respectively. The neurons in input layerare corresponded to Pulse width, Pulse frequency,Gas pressure and Trepanning speed. Output layercorresponds to NHT, NCIRentry and NCIRexit. Thehidden layer has five neurons in case of all. Theactivation function used for the hidden layer andoutput layer was log sigmoid and pure linearrespectively. In this work, a commercially availablesoftware package MATLAB was used for thetraining of ANN .The values of the weights, andbiases, after network getting fully trained areshown in the Table 3 for all the NHT, NCIRentry andNCIRexit. 3 5 7 9 11 13 15 17 19 21 23 25 27NormalizedvaluesExperiment NumberExperimental values for NHTExperimental values forNCIRentryExperimental values forNCIRexitInput layerHidden layerX1X2X3X4Output layerwqr bqNHT/ NCIRentry/NCIRexitNormalization ofdataCalculation of greyrelational coefficientCalculation of the sum of thegrey relational coefficientEvaluation of thenormalized coefficientCalculation of the entropy ofeach quality characteristicsCalculation of the sumof entropyCalculation of the weight ofeach quality characteristicFig. 4: Architecture of artificial neural network for NHT, NCIRentryand NCIRexitFig. 3: Normalized values of quality characteristics
  6. 6. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401398 | P a g eTable 3: Final values of Weights and Biases for NHT, NCIRentry and NCIRexitSo, in the mathematical form, the ANN model forNMRR can be represented as follows:NHT/NCIRentry/NCIRexit (5)Where and corresponded to weight andbias to output layer and is the net input to theoutput layer from hidden layer and it is given by,q=1, 2… 5The results of the experimental data and neuralnetwork predicted data for NHT, NCIRentry andNCIRexit have been compared in the Table 4. It isevident that ANN prediction is in good agreementwith the experimental results. It is found that ANNwith mean square error of 0.000037%, 0.0000186%and 0.000125% respectively, appears to constitutea workable model for predicting the characteristicsunder given set of input parameters for LTD.The values of , , and are shown in Table 3.I: Experiment No. II: Pulse width III: Pulse frequency IV: Gas pressureV: Trepanning speed VI: Experimental Hole taper VII: Experimental Circularity VIII:Experimental Circularityat entry at exitIX: ANN predicted Hole taper X: ANN predicted Circularity XI: ANN predicted Circularity XII: % errorin prediction ofat entry at exit Hole taperXIII: % error in prediction of XIV: % error in prediction ofCircularity at entry Circularity at exitTable 4: Comparison of ANN predicted result with the experimental result for NHT, NCIRentry and NCIRexitI II III IV V VI VII VIII IX X XI XII XIII XIV1 0.500 0.619 0.600 0.333 0.433 0.914 0.966 0.433 0.914 0.952 0.055 0.005 1.4682 0.500 0.619 0.800 0.667 0.736 0.927 0.942 0.736 0.927 0.952 0.051 0.005 1.0963 0.500 0.619 1.000 1.000 0.992 0.973 0.963 0.991 0.973 0.961 0.027 0.004 0.1504 0.500 0.810 0.600 0.667 0.539 0.902 0.970 0.539 0.902 0.971 0.079 0.003 0.1005 0.500 0.810 0.800 1.000 0.691 0.910 0.955 0.691 0.910 0.955 0.049 0.004 0.033Weights to hidden layer frominput layerBias tohiddenlayerWeights to output layerBias tooutputlayerNHT [122.7035 -28.3073 16.9694 -33.6773;-4.8487 -22.6453 -32.7136 -10.3398;2.8113 -2.9929 5.8978 0.53677;3.9119 3.3126 0.68229 0.29932;-2.7571 2.4243 -5.7577 -0.61036][-81.9011;58.7437;-1.1352;-4.0345;0.56399][0.33548 -0.44801 -43.5783 -2.3246 -105.1382][46.4105]NCIRentry [-3.0176 -4.1509 60.4266 -0.77578;1.0815 6.3481 1.2684 1.7164;-1.1774 -6.0712 -1.3746 -1.6547;41.2793 -1.1825 8.5567 -34.2151;5.5617 -56.9911 1.8769 2.2187][-29.6378;-8.1871;8.1269;-3.1741;51.2141][-0.094972 -4.8731 -5.0107 -0.046963 -0.074669][6.129]NCIRexit [19.7725 6.0393 -7.3166 -1.7965;0.26041 67.3029 -70.135678.0474; -45.1386185.994 64.4417 66.0488;-57.4946 0.24336 0.11946 -0.53196;20.0861 -59.1983 24.6627 -61.9418][-13.606;-9.8892;-225.056;64.2284;64.7269][-0.074678 0.047406 -0.045112 -66.1898 -0.048632][67.1431]
  7. 7. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401399 | P a g e6 0.500 0.810 1.000 0.333 0.584 0.914 0.935 0.584 0.914 0.935 0.001 0.095 0.0047 0.500 1.000 0.600 1.000 1.000 0.971 0.954 1.000 0.971 0.954 0.000 0.002 0.0438 0.500 1.000 0.800 0.333 0.703 0.902 0.904 0.704 0.902 0.906 0.038 0.001 0.2019 0.500 1.000 1.000 0.667 0.900 0.942 0.942 0.899 0.942 0.943 0.043 0.003 0.05510 0.750 0.619 0.600 0.667 0.337 0.935 0.927 0.338 0.935 0.926 0.015 0.003 0.13211 0.750 0.619 0.800 1.000 0.372 0.956 0.960 0.371 0.956 0.961 0.116 0.000 0.12112 0.750 0.619 1.000 0.333 0.437 0.957 0.901 0.437 0.958 0.901 0.002 0.069 0.00113 0.750 0.810 0.600 1.000 0.437 0.952 0.962 0.436 0.952 0.964 0.181 0.006 0.11714 0.750 0.810 0.800 0.333 0.293 0.919 0.919 0.292 0.918 0.921 0.398 0.113 0.17615 0.750 0.810 1.000 0.667 0.670 0.944 0.921 0.670 0.943 0.922 0.067 0.110 0.12016 0.750 1.000 0.600 0.333 0.555 0.937 0.884 0.555 0.937 0.884 0.038 0.002 0.00317 0.750 1.000 0.800 0.667 0.696 0.925 0.902 0.696 0.925 0.901 0.011 0.002 0.16018 0.750 1.000 1.000 1.000 0.668 0.985 0.946 0.669 0.985 0.945 0.165 0.001 0.10519 1.000 0.619 0.600 1.000 0.335 0.974 1.000 0.335 0.974 0.999 0.009 0.006 0.09020 1.000 0.619 0.800 0.333 0.517 0.961 0.947 0.518 0.960 0.947 0.179 0.061 0.00121 1.000 0.619 1.000 0.667 0.710 1.000 0.979 0.710 1.000 0.978 0.021 0.000 0.09422 1.000 0.810 0.600 0.333 0.513 0.969 0.949 0.514 0.969 0.949 0.222 0.002 0.04923 1.000 0.810 0.800 0.667 0.526 0.946 0.960 0.526 0.947 0.962 0.093 0.124 0.26724 1.000 0.810 1.000 1.000 0.834 0.980 0.967 0.834 0.980 0.968 0.006 0.010 0.10025 1.000 1.000 0.600 0.667 0.656 0.991 0.986 0.656 0.991 0.986 0.007 0.000 0.01526 1.000 1.000 0.800 1.000 0.664 0.970 0.978 0.665 0.971 0.977 0.107 0.009 0.06927 1.000 1.000 1.000 0.333 0.914 0.977 0.904 0.913 0.977 0.903 0.186 0.003 0.1525. MULTI OBJECTIVE OPTIMIZATIONUsing GRA coupled with entropymeasurement, the weight for NHT, NCIRentry andNCIRexit have been found as 0.33, 0.33 and 0.34respectively. Now the multi-objective optimizationproblem can be transformed into single objectiveoptimization problem. In the present case, both theobjective functions are of conflicting naturebecause the aim is to maximize HT the andminimize the NCIRentry, NCIRexit. Thus, theobjective function of optimization problem can bestated as below:Find: X1, X2, X3 and X4Minimize:(6)Where = 0.33, 0.33 and = 0.34 NHT,NCIRentry and NCIRexit Eq. (5) ,with range ofprocess input parameters:0.8≤ ≤1.613≤ ≤216≤ ≤100.1≤ ≤0.3The critical parameters of GA are the sizeof the population, cross-over rate, mutation rate,and number of generations. After trying differentcombinations of GA parameters, the populationsize 20, cross-over rate 0.8, mutation rate 0.01 andnumber of generation 40, have been taken in thepresent study. The objective function in Eq. (6) hasbeen solved without any constraint. Thegeneration-fitness graphics have been shown in theFig.5. The fitness function is optimized when themean curve converges to the best curve after 7generation. The corresponding values of Pulsewidth, Pulse frequency, Gas pressure andTrepanning speed have been found as1.3 ms, 17Hz, 8 kg/cm2and 0.2 mm/s.
  8. 8. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401400 | P a g eFig. 5: The generation-fitness graphics6. DISCUSSIONAchieving a good compromise betweenobjective functions in multi-objective optimizationproblem is a big challenge due to existence ofmultiple solutions, known as Pareto-optimalsolutions. To overcome it, in the present work,weights for each quality characteristics have beencalculated first, to get optimal solution.7. CONCLUSIONSThe multi-objective optimization of lasertrepan drilling of Ti-6Al-4V using hybrid approachof artificial neural network, genetic algorithm andgrey relational analysis with entropy measurementtechnique has been done. Following conclusionshave been drawn on the basis of results obtained:(1) The developed models for HT, CIRentry andCIRexit, with mean square error of 0.000037%,0.0000186% and 0.000125% respectively, are wellin agreement with the experimental result.(2) The optimum levels of control factors are Pulsewidth, Pulse frequency, Gas pressure andTrepanning speed have been found as 1.3 ms, 17Hz, 8 kg/cm2and 0.2 mm/s respectively.(3) Validation has been performed in order toverify the result, which shows a good agreementbetween the optimized and experimental result.REFERENCES[1] A.K Dubey, V Yadava. Laser beammachining- a review. InternationalJournal of Machine Tools andManufacture 2008; 48:609–28.[2] KP Rajurkar, G Levy, A Malshe, MMSundaram, J McGeough, X Hu, RResnick, A DeSilva. Micro and nanomachining by electro-physical andchemical processes. CIRP Annals -Manufacturing Technology 2002;55(2):643–66.[3] W. Tongyu, S. Guoquan,” GeometricQuality Aspects of Nd:YAG LaserDrilling Holes”, Proceedings of 2008IEEE International Conference onMechatronics and Automation.[4] E. Kacar, M. Mutlu, E. Akman,A. Demir,L. Candan, T. Canel, V. Gunay, T.Sınmazcelik ,”Characterization of thedrilling alumina ceramic using Nd:YAGpulsed laser”, journal of materialsprocessing technology 2 0 9 ( 2 0 0 9 )2008–2014.[5] M Ghoreishi, DKY Low, L Li.Comparative statistical analysis of holetaper and circularity in laser percussiondrilling. International Journal of MachineTools and Manufacture 2002; 42(9):985–95.[6] KY Benyounis, AG Olabi. Optimizationof different welding processes usingstatistical and numerical approaches—areference guide. Advance EngineeringSoftware 2008; 39:483–96.[7] DKY Low, L Li, PJ Byrd. Taperformation and control during laser drillingin Nimonic 263 alloy. InternationalProceedings of the 33rd international
  9. 9. Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.393-401401 | P a g eMATADOR conference, Manchester,2000. p. 461–6.[8] DKY Low, L Li, PJ Byrd. Influence oftemporal pulse train modulation onmaterial ejection related process. Opticsand Lasers Engineering 2001;35(2001):149–64.[9] GKL Ng, L Li. The effect of laser peakpower and pulse width on the holegeometry repeatability in laser percussiondrilling. Optics and Laser Technology2001; 33:393–402.[10] CA Biffi, N Lecis, B Previtali, M Vedani,GM Vimercati. Fiber laser microdrillingof Titanium and its effect on materialmicrostructure. International Journal ofAdvanced Manufacturing Technology2011; 54:149–60.[11] DA Dornfeld, JS Kim, H Dechow, JHewson, LJ Chen. Drilling burr formationin Titanium alloy (Ti–6Al–4V). Annals ofCIRP 1999; 48:73–6.[12] J Kumar, JS Khamba. An experimentalstudy on ultrasonic machining of pureTitanium using designed experiments.Journal of Brazil Society of MechanicalScience & Engineering 2008; 3:231–8.[13] PJ Ross. Taguchi Techniques for QualityEngineering.2nd edition. New Delhi(India): Tata Mcgraw-Hill PublishingCompany Ltd; 1996.[14] Lamba V.K. Neuro fuzzy systems;University science press, New Delhi.2008.[15] Kalyanmoy Dev, N Srinivas.Multiobjective optimization usingnondominated sorting in geneticalgorithms. Journal of EvolutionaryComputation 1994, 2, 221-248.[16] KT Wen, CG Chang, ML You .The greyentropy and its application in weightinganalysis. IEEE International Conferenceon Systems, Man, and cybernetics 1998, 2,1842-1844.