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Statistical analysis and modelling of an Yb:KGW femtosecond laser micro- drilling process

Femtosecond laser drilling is capable of economically drilling a number of closely located holes on micro-scale. Different characteristics or acceptance criteria like geometric and metallurgical factors are used to judge the quality of the drilled
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   Procedia CIRP 62 ( 2017 ) 275 – 280 Available online at 2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( ).Peer-review under responsibility of the scientific committee of the 10th CIRP Conference on Intelligent Computation in Manufacturing Engineeringdoi: 10.1016/j.procir.2016.06.111 ScienceDirect  10th CIRP Conference on Intelligent Computation in Manufacturing Engineering-CIRP ICME '16 Statistical analysis and modellingof an Yb:KGW femtosecond laser micro-drilling process Giuseppe Casalino a, *,Aurora Maria Losacco b ,Angela Arnesano b ,Francesco Facchini a , MaurizioPierangeli a , Cesare Bonserio b a  DMMM, Politecnico di Bari, Viale Japigia 182, Bari 70124, Italy b  Laserinn, Strada Provinciale Casamassima km 3, Valenzano70010,Italy * Corresponding author. Tel.:+39-080-5962753;fax:39-080-5962788.  E-mail address: Abstract Femtosecond laser drilling is capable of economically drillinga numberof closely located holes on micro-scale. Differentcharacteristics or acceptance criteria like geometric and metallurgical factors are used to judge the quality of the drilled holes.This paper aims to evaluate the quality of micro-holes, which were drilled by Yb:KGW laser end-pumped by high-power diodebars. The geometric factors included hole roundness, hole taper and variation in hole entrance diameter. The metallurgical factorsincluded recast layer and micro-cracks. The process parameters that most affected the hole quality were identified by the analysisof a full factorial design. Optimum hole characteristics on stainless steel sheet were studied by theANOVA analysis. ANN modelprovided better insight into the best conditions for process adjustment, making possible simultaneous optimization of multipleresponses. ©2016The Authors. Published by Elsevier B.V.Selection and peer-review under responsibility ofthe International Scientific Committee of “10th CIRP ICME Conference". Keywords: micro-drilling;Yb:kgwLaser; ANOVA; ANN. 1. INTRODUCTIONNomenclature YB:KGBYtterbium-Doped Potassium Gadolinium TungstateMZCMinimum Zone CircleIADInlet Average DiameterOADOutlet Average DiameterT TaperDInlet nominal diameterdOutlet nominal diameterfs femtosecondLaser processing of materials has proved to be an importanttool for the development of micro-feature like micro-channeland micro-hole [1, 4]. Foil micro-drilling is suitable fornumerous tasks and applications, electronic circuitry, opticalsurfaces, apertures and mechanical filters are just a fewthat canbe mentioned [5].Nanosecond lasers have been used for laser-machinedthrough-holes. Nevertheless,compared to characteristicdurations of laser radiation interaction with metals,nanosecondpulses aretoo long. The material is heated comparativelyslowly, energy has a lot of time to diffuse into the surroundingarea before the affected spot is heated enough forthe materialremoval, which produces alarge heat affected zone.Moreover, the produced plasma plume interacts with thesurface and brings about mostly negative consequences. Higherprecision and better quality beyond the limits of acommercialized nanosecond pulsed laser system have beenachieved using a cover plate [6].Picosecond lasers offer high power for industrial scalefabrication and their pulse length adapt for metal fabricationbecause the characteristic durations of lattice heating are in theregion of several to several tens of picoseconds [7].Femtosecond lasers do not yet rival picosecond systems indelivered power, but with their parameters and industrial   © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( ).Peer-review under responsibility of the scientific committee of the 10th CIRP Conference on Intelligent Computation in Manufacturing Engineering  276  Giuseppe Casalino et al. / Procedia CIRP 62 ( 2017 ) 275 – 280 robustness improving steadily,theyseem destined to reachmaturity in industry in theverynear future. In fact, thetechnical advances in femtosecond laser technology are makinglaser machining of thin metallic coatings or foils a feasiblesolution for high-quality, deep drilling.Femtosecond laser pulses provide a micromachining toolwithhigh-quality material processing and large area patterningof solids.At relatively low laser fluence, i.e. close to theablation thresholdvisible thermal ormechanical damage canhappen[8].For the smallest features and the least amount of heating andcollateral damage, pulse lengths of femtosecond are almost asefficient as their picosecond alternative, and lead to the samemorphologies inside the hole [9].A studyfor aero-components like turbine airfoilindicated acomplete absence of any melting, recast layers, heat-affectedzones or microcracks close to the femtosecond lasermicromachining of single crystal superalloys [10].In fact, laser drilling has become the accepted economicalprocess for drilling thousands of closely space holes instructures such as aircraft wings and engine components [11].Femtosecond laser(fs)pulseprovidesthemodification of surface or bulk of a transparent material with micrometerprecision. A tightlyonecan deposit energy into a transparentmaterial through high-order nonlinear absorption, producing3D-localized material ablation either on the surface or in thebulk [12].In micro-hole drilling and cutting usingfs fiber laser (1030nm wavelength and 750-fs pulse duration), no crack orcollateral thermal damage was observed for both hard and softtissue [13]. Even if femtosecond laser material processing athigh laser fluences has provided a practical tool for highquality, deep drilling of metals,explanations supportingadvantages of femtosecond lasers have to be given yet.Moreover, femtosecond lasers should be able to drill smallerholes than it is possible with other conventional techniques likewire EDM, punching, broaching, and to do this job with thesame speed or faster [14].Commercially available femtosecond laser sources, likeTi:sapphire based systems, allow to drill high quality holes but,unfortunately, the processing speed is still too low for manyindustrial applications. This disadvantage can be overcomebythe newregenerativeamplified solid state laser sources,providing much higher average powers and repetition rates.[15]. At this point, the full power of the ultrafast ytterbium-doped fiber CPA system achieves high quality holes, evenwithout shielding gas [16].Also double pulsed has been applied to bimetal micro-drilling and has been proven to be a good tool in controlling theablation process [17].Some parameters like the pulse duration of the applied lasersource influence, the micro-drilling process of metals[18].Therefore, the quality of a drilled hole in laser drilling dependson the right choice of the process parameters.Entry and exitcircularityand taper are very important attributes whichinfluence thedrillquality [19].The design of experiments (DOE) isadequate to studyseveral process factors and their interactions complexity inorder to solve problems bymeans of statistical analysis [20].Multi-objective optimization of hole characteristics duringpulsed Nd:YAG laser microdrilling of gamma-titaniumaluminide alloy sheet was performed usingbotha centralcomposite design (CCD) and response surface methodology(RSM) [19]. Precise modeling of stainless steel Nd:YAG laserpercussion drilling was achieved by generalized neural network regression. This method permitted to adjust input parameters of the process in multipurpose and single purpose optimizationmodes [22].Grey relational optimization approach combined with fuzzymethodology determined the optimum process parameters,which minimizes HAZ and hole circularity and maximizesmaterial removal rate in a Pulsed Nd:YAG laser micro-drillingin high carbon steel within existing resources [23].As reported in main theoretical and experimental studies inthe literature [24],the removal of material by means of ultrashort laser pulses (ps, fs) substantially occurs throughdifferent mechanisms than ms and ns regimeslaser processessince the thermal contribution is extremely reduced due to thepulse duration less than the timeof electron-photon relaxation(0.5 ÷ 50 ps).Fluence below 10 J/ cm 2 and"gentle ablation" regimeproduces high-precision micro machiningusing femtosecondlaser pulses. In fact, higher fluences, i.e. under a "strongablation" regime, inducealterations and irregularities, whichcompromise the quality of the holewith results comparable tothose obtained by means of nanosecond lasers.In this paper,thedesign of experiment andtheartificialneuralnetworkswere used to create a statistical modelforfslasermetal foil micro drilling.Tests were carried out onstainless steel 303 sheets with 0.17 mm thicknessusing aYb:KGW femtosecond laser. A micro-hole array of 81 holeswas drilled with 27 combinations of laser parameters, whichwere the pulse frequency, the pulse width, and the laser power.The quality of the drilled holes was assessed by means of the analysis of the variance of inlet and outlet averagediameters (IAD and OAD) and taper (T).The recast layer and micro-crackwere detectedandanalyzedby optical and scanning electron microscopy (NikonMicroscope and ZEISS EVO 40 XVP SEM).Neural networksaimedtomapping the process parametersand holefeatures usingLevenberg–Marquardtoptimization[25, 26]. ANNtook as input the statistical significant processparameters, which warranted a better converging and errorperformance. 2. Experimental set-up and procedure The experimental set-up, as reported in Fig. 1, makes use of a Yb:KGW femtosecond laser PHAROS,   = 1.03 µm withrepetition rate in the range 1 KHz–600 KHz single shot, and apulse duration in the range 300 fs–10 ps.The system can work in linear mode by using of 3 linear axesand 2 rotational axes (Aerotech, work area 1000mmx1000mm), or in scanning mode by using of a galvo scan head(Hurryscan, work area 7mmx7mm)and a beam shifting unit(WOP).This configuration allows high accuracy machining (micro-cuts, micro-holes, micro-3D structuring, micro-markings etc.)  277 Giuseppe Casalino et al. / Procedia CIRP 62 ( 2017 ) 275 – 280 in industry and science field, in terms of dimensional accuracy,presence of defects and/or alterations induced in the material asa result of interaction with the laser radiation, process times.Critical issues that satisfies:• Micrometer dimensional tolerances• Minimization of the alterations induced by the laser andthermal defects (cracks, burrs, oxidation)• Ability to control the geometric parameters (holetaper, cutdepth, inclination of the cutting edges)• Significant variation of the effects of laser-matter as af unction of thewavelength of the radiation and / or of thetemporal width of the pulses.• Minimization of process times. Fig. 1.Experimental device. Micromachining was carried out in air using the laseroperating at a repetition rate of 50-100-150 kHz anddelivering individual pulses of 220–-500-1000 fs duration, atthree different average power of 4.5-5-5.5 W, by using theBeam Scanning Unit.Each experiment was repeated threetimes for a total of 81 micro holes. Table 1 contains the levelsfor each treatment.The sample was 0.17 mm thick stainlesssteel foil (steel grade-SAE 303). Table 1. Factors and levels for eachtreatment. Figure 2 shows the simplified geometrical features of themicro hole.The roundness was evaluated with the Minimum ZoneCircle (MZC) method. In this method, two circles are usedasreference for measuring the roundness error.One circle isdrawn outside the roundness profile just as to enclose the wholeof it and the other circle is drawn inside the roundness profileso that it is just inscribed in the profile. Fig. 2.Micro-hole geometric features. The roundness error here is the differencebetween the radiusof the two circles (see figure 3). Fig. 3.Micro-holeroundness. Theinlet average diameter(IAD)andoutletaveragediameter (OAD) were calculated by the mean of the radius of the two circles for the inlet (D) and the outlet (d) diameters.The taper (T) was calculated by the ratio of the differencebetween the inlet and outlet diameters of the sections to thefoilthickness:(1) 3. Analysis of variance The adequacy of the developed mathematical models forthegeometrical featuresof the micro-drilled hole generated by theYb:KGW femtosecond laserwas evaluated by the analysis of balanced variance.Tablesfrom2to4 show the results in termsofF-ratio testand P-value.Lower than 0.05 p-valuesprove thesignificanceof the factor on the response.According to the tables of variance, the pulse frequencyissignificant for T and IAD and the pulse widthis significant onlyfor IAD and OAD. The interaction between the pulse frequencyand pulse widthis significantfor T, IAD, and OAD. FactorsLevel 1Level 2Level 3A: Pulse frequency(Hz)50100150B. Pulse width(fsec)2205001000C: Laser power (W)4.554.5  278  Giuseppe Casalino et al. / Procedia CIRP 62 ( 2017 ) 275 – 280 Table 2. ANOVA tableof resultsfor taper(T).Table 3. ANOVA tableof resultsfor inlet average diameter (IAD).SourcesDFFP-valueA29.470.000B218.160.000C20.750.639AB427.950.000BC41.210.931AC40.020.277ABC80.960.687Error54Total80Table 4. ANOVA table of resultsforoutletaverage diameter(OAD).SourcesDFFP-valueA21,250,295B222,220,000C20,230,796AB44,400,004BC41,670,170AC40,410,802ABC80,820,590Error54Total80 4. Artificial Neural Network model Approximate experimentalmodels ofthe process have beendeveloped by the generalized regressionneural networktool(GRNN).ARelationship between hole featuresand processparameterswas established under different conditions. For thisscope, the approachwas based on the adoption of threedifferentand independentnetworks. Consistently each ANNwas used in order to predict only one of geometricalparameters.Asubset as big as68% of the available experimental data,which wascomposed by 81 inputs/targets pairs,was used fortheANN training. In this phase, the synaptic weights, whichare thelinksbetween neurons,has a synaptic weight attached.Theywereupdatedrepeatedlyin order to reduce the errorbetweentheexperimental outputs andtheassociatedtargets.A subset of 16% from the same experimental sample wasadopted for validation. This phase consisting of identifying theunderlying trend of the training data subset, avoiding theoverfitting phenomenon.The training process was stopped when the error begantoincrease. In order to deal withthe overfitting problem, thetraining phase wasstopped when the mean square error (MSE)assumedvalues lower than 0.01. The remaining dataof thesame experimental sample (16%) was been used for testingtheforecast reliability of the ANN inthelearning phase.A randomstrategy was adopted for assigningtheinputs/targets pairs toeach subset. 4.1.ANN training and validation ThedesignoftheANN architectureconsists inidentifyingthenumber of hidden layers and the numberof neurons for eachlayer.On one hand,manyneurons can lead to memorizethetraining sets withand lost ofthe ANN’scapability togeneralise. On the other hand, a lack of neurons can inhibitappropriate pattern classification.In thiswork, a number of tests wasperformedvarying the number of hidden layers andthe numberof neurons in the hidden layer.In each case the best accuracy was achieved adopting anANNarchitecturewith two hidden layers.The number of inputnodes, hidden(for each layer), andoutput nodes for everynetwork are givenin tables5thorough 7at the line labelled“architecture”.Levenberg–Marquardtoptimization wasadopted to trainingthe ANNs. Networks 1 and 3 were trained usingthe back propagation algorithm.This method allows tominimize thesquares of the differences (  E  ) between the desirable output,identified as  y d  (t), and the predicted output  y  p (t) . ‘E’ is given bythe follow equation:   (2)Levenberg–Marquardt algorithmwas also adopted, whichblends the ‘Steepest Descent’ method and the ‘Gauss–Newton’, therefore it can converge well even if the errorsurface is much more complex than the quadratic situation;ensuring, in many cases, speed and stability.Levenberg–Marquardt algorithm can be presented as:    (3)Where  J  is Jacobian matrix,  μ is the ‘combinationcoefficient’ (always positive),  I  is the identity matrix, and e representsthe error vector.When μ  is very small (nearly zero),Gauss–Newton algorithm is used. On the other hand, when μ  isvery large, steepest descent method is used.In order to evaluate the reliability of the geometricparameters predicted by modelling, the features of the weldcomputed byANNwerecompared totheexperimentalones.For this scope, the Mean Absolute Percentage Error (MAPE)see equation 4,wascalculated.   (4) SourcesDFFP-valueA24.520.015B20.120.888C20.940.398AB410.730.000BC41.000.418AC41.290.284ABC80.430.899Error54Total80  279 Giuseppe Casalino et al. / Procedia CIRP 62 ( 2017 ) 275 – 280 Back-propagation routine was trained with the steepestdescent algorithm (eq. 3), where  Δ w(k) is the vector of weights, g(k) is the current gradient,  α (k) is the learning rate, and m isthe momentum parameter, which prevents that the algorithmconverges to a local minimum or to a saddle point. Moreover,it avoidsthe risk of minimum overshooting, which can causeinstability of the network. The learning rate and the momentumparameter are arbitrarily set to 0.01 and 0.99, respectively.The training of the network was stoppedwhen themeansquare error (MSE) assumedvalues lower than 0.01. 4.2.ANNresults and discussion Tables5 through 7displaythe results of training andvalidation for the taper, the average inlet diameter, and theaverage outlet diameter, respectively. Table 5. ANN table of results for taper (T).Table 6. ANN table of resultsfor inlet average diameter (IAD).Table 7. ANN table of results for inlet averagediameter (OAD). Sim-1 was performedregardless tothe resultsof theANOVA analysis. The pulse frequency, pulse width and taperwere the input. Otherwisefor Sim-2, Sim-3, and Sim-4,theinputwerethe significant parametersaccordingly toANOVAresults. They changed from one simulation to another. Thereason wastoassesstheeffects of statistically significantparameterson thenetworkperformance.In particular, Sim-2 was stopped at 50000 iterations andMAPE was compared with that of Sim-1. It was found thatSim-2 network, which took into account the ANOVA results,had a lower MAPE with respecttothat of the networks trainedbefore the ANOVA.Moreover, Sim-3were stopped at the same MAPE of Sim-1. Again, after ANOVA networks had a better performance interms of number of iterations that were required for a certainMAPE.Eventually, Sim-4s were trained to their ultimate MAPE. Itwas found that their MAPEs were systematically lower thanthose of Sim-1. 5. Recast layer, spatters, and micro-crack Recast layers, spatters, and microcracks commonlyaccompanylaser-drilledholes. The overall quality of laser-drilled holescan be affected by those defects.The high temperature on the work piece surfacecancausethermal damage in the edge zones which has, as a rule,anegative influence on the components life.Thiscondition istermed “the Recast Layer”[27].Figure 4 shows the macrograph of a 10-hole array. Fig.4.Hole array outlook.Fig.5.Holeentrance, hole8.Fig.6.Hole exit, hole 8.Sim-1Sim-2Sim-3Sim-4InputA,B,CA,A*BA,A*BA,A*BArchitecture3-9-3-12-10-12-10-12-10-1MAPE9,55%6,52%9,55%5,57%n°iterations50.42450.00037.00072000Sim-1Sim-2Sim-3Sim-4InputA,B,CA,B,A*BA,B,A*BA,B,A*BArchitecture3-9-12-13-9-12-13-9-12-13-9-12-1MAPE6,35%5,77%6,35%5,77%n°iterations50.75450.00028.70049600Sim-1Sim-2Sim-3Sim-4InputA,B,CB, A*BB, A*BB, A*BArchitecture3-9-12-12-4-7-12-4-7-12-4-7-1MAPE8,00%7,89%8,00%5,38%n°iterations50.21450.00042.00078000  4.1 mm 10 9 8 7 6 5 4 3 2
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