Microsoft Word - B_43_Raczkovi_R.doc HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPRÉM Vol. 39(2) pp. 279-282 (2011) CBN TOOL LIFE PREDICTION BY ARTIFICAL NEURAL NETWORK L. RACZKOVI University of Miskolc, Department of Production Engineering, 3515 Miskolc-Egyetemváros, HUNGARY E-mail: laszlo.raczkovi@uni-miskolc.hu For economic application of CBN tools it is important to know how the tool life changes as a function of the most important technological parameters (cutting speed, feed rate, depth of cut and work piece diameter). These technological parameters have significant effects on the productivity of machining. The extended Taylor equation takes the effects of feed rate, depth of cut into account besides the cutting speed, but this equation is not valid in the whole range of cutting speed. Beyond the publicated tool life equations in the professional articles, the tool life can be determined by Artificial Neural Network (ANN). ANNs have huge flexibility and can handle different number of inputs thus they are suitable for determining tool life as a function of several cutting parameters. Keywords: Tool life, Artifical Neural Network Introduction Cubic boron-nitride was synthesized by R. H. Wentorf in 1957. It was first produced in industrial sizes in 1968. CBN tools with definite tool edge geometry have been produced since 1970’s. Due to coating processes (PVD, CVD) have appeared later the various (TiN, TiAlN, TiCN) coated cutting tools. CBN is the second hardness material after diamond. Due to its great hardness and heat resistance, CBN is suitable for machining hardened steel (>55 HRC). Nowadays the hard turning is used more widely in finish machining instead of/besides grinding. Hard turning has several benefits over grinding: higher flexibility, machining complex work pieces in one clamping, no need for coolant liquid, easy automation and better material removal rate [1]. The providing of required strict dimensional- and shape accuracy of the work piece demand high quality in cutting tools. It is a basic demand from these cutting tools to provide the quality and accuracy expectations of work piece beside long tool life. Nowadays the numerical methods are widely used to solve several different problems in engineering science. One of these numerical methods is that of the least squares, which is used to function approximation. Due to the available mathematical softwares the Artificial Neural Networks (ANNs) can be applied to approximate different types of functions using the method of least squares. The bases of ANNs were laid down by McCulloch and Pitts in 1943 [2]. Nowadays ANNs are widely used to evaluate various experimental results. In this study, ANN was created and simulated to determine tool life in case of different cutting speeds, work piece diameters, constant feed rate and depth of cut. Artificial Neural Network A model of a neuron ANNs consist of a set of hierarchically organised neurons. The neurons do the same operations parallel. Each neuron in a network is connected to a certain number of neurons, and this is usually a one-way relationship. Fig. 1 shows the structure of a neuron [3]. Figure 1: The architecture of a neuron The p1, p2, p3,…,pn inputs are connected to the neuron by w1n weights. Furthermore there is an additive part b which is called bias. Eq. (1) shows how a neuron works. n 1, n n i 1 a f ( w p b ) = = +∑ (1) The function f is the activation function of neuron. Usually it is a sigmoid type function such as tangent sigmoid, which is shown by Eq. (2). 280 2 ( x ) 2 f(x ) 1 1 e− ⋅ = − + (2) Multi-layered ANNs A neural network consists of three different layers at least. The first is called the input layer. This layer contains those neurons which transfer the input signal to the network. The second is the hidden layer. The neurons which carry out the real processing belong to this layer. A network has one or more hidden layers. The third (or last) layer is the output layer. The neurons in this layer transfer the information to the outside. The tasks of these neurons are same as that of the neurons in the hidden layer. The structure of a multi-layered feed-forward neural network is shown by Fig. 2 [3]. Figure 2: Structure of a multi-layered neural network Multi-layered feed forward neural networks can be used for function fitting. These networks are using back- propagation training algorithm. During the training, the network changes the values of weights and biases according to the error function. The aim of ANN training is to minimize the error function E, which is shown by Eq. (3) [4]. n 2 i i i 1 1 E a t 2 = = −∑ (3) where: ai – the i-th output value, ti – the i-th target value, n – number of outputs, E – the mean square error. The i-th net input of k+1-th layer can be calculated by Eq. (4) ∑ = +++ += s j k i k j k ji k i bawn 1 11 , 1 (4) where: ni k+1 – the i-th net input of k+1-th layer, wij k+1 – the weight between the j-th neuron of previous layer and the i-th neuron of subsequent layer, aj k – the j-th output of k-th layer, bi k+1 – the i-th bias of k+1-th layer. The i-th output of k+1-th layer can be calculated by Eq. (5). )( 111 +++ = ki kk i nfa (5) where: fk+1 – the activation function of k+1-th layer. Before training the network is initialized by random weights and biases. Each weights and biases are updated during training using Eq. (6) which is known as the back-propagation delta rule [4]. 1 1 1 + + + −= ∂ ∂ −=Δ kj k ik ij k a w E wij δαα (6) where: α – the learning rate, which defines the step length of each iteration in the negative gradient direction, δj k+1 – the backpropagated error at the j-th neuron in the k+1-th layer, ai k – the i-th output of k+1 layer. The value of δj k+1 is different, depending on that, whether the k+1-th layers is an output layer or a hidden layer. If the k+1-th layer is an output layer [4]: ))(1( 1111 j k j k j k j k j taaa −−= ++++δ (7) If the k+1-th layer is a hidden layer [4]: ∑ = +++++ −= m i k i k ij k j k j k j waa 1 22111 )1( δδ (8) Determining tool life by Artifical Neural Network In this paper the experimental data set given in [5,6] is used to design a neural network model which predicts tool life according to given range of feed rate, depth of cut, workpiece diameter and cutting speed. The applied technological parameters, which were used for training is shown in Table 1. The ANN used for modelling tool life is a two layered feed-forward network with 35 neurons in the hidden layer and 1 neuron in the output layer. The network was made using Matlab R2009 software. The activation function in hidden layer is a sigmoid type and in the output layer it is linear. The network was trained with 108 data points according to Table 1 and simulated with 27 data points. A data point contains the feed rate, the depth of cut, the workpiece diameter and the cutting speed. The applied cutting parameters to simulate ANN were the following: - depth of cut ap=0.15 mm, - feed rate f= 0.05 mm/rev., - cutting speed vc=11–120 m/min, - workpiece diameter d= 45, 75, 100 mm. 281 Table 1: Technological parameters for training the network Feed rate f mm/rev. Depth of cut ap mm Workpiece diameter d mm Cutting speed vc m/min 0.025 0.125 0.050 0.250 0.10 0.10 0.15 0.25 45 0.025 0.125 0.050 0.250 0.10 0.10 0.15 0.25 75 0.025 0.125 0.050 0.250 0.10 0.10 0.15 0.25 100 11,20,29,40,50,68,92,105,120 The back-propagation learning algorithm has been used with ‘trainlm’ training function. This training function is based on Levenberg-Marquardt nonlinear least squares method. As a result of the simulation the calculated tool life and the deviations between measured and calculated tool life are summarized in Table 2. It can be seen, the maximal deviation between measured and calculated tool life is 58%, but it occurs at very small value thus it is not significant. Fig. 3 shows the results of simulation. The correlation R between the outputs of ANN and the measured tool life values can be seen in Fig. 3a. The simulated data set is different in feed rate and depth of cut from the data set of training. The value of correlation R=0.99029 is very close to 1 which means a good fitting of calculated values to measured values. Fig. 3b shows the tool life curves at different workpiece diameters and constant feed rate and depth of cut. Table 2: The calculated tool life values and deviations between measured and calculated tool life values Workpiece diameter, mm 45 75 100 f, mm/rev. a, mm f, mm/rev. a, mm f, mm/rev. a, mm 0.05 0.15 0.05 0.15 0.05 0.15 vc m/min Tm TANN E E% Tm TANN E E% Tm TANN E E% 11 258 270.93 -12.93 5.0 314 331.59 -17.59 5.6 325 388.56 -63.56 19,5 20 194 219.61 -25.61 13.2 236 234.51 1.48 0.6 245 257.66 -12.66 5,1 29 203 215.17 -12.17 6.0 215 225.07 -10.07 4.6 224 237.51 -13.51 6,0 40 216 210.20 5.79 2.6 227 222.42 4.57 2.0 231 234.70 -3.70 1,6 50 216 196.57 19.42 8.9 229 217.37 11.62 5.0 241 231.89 9.10 3,7 68 93 114.99 -21.99 23.6 154 176.66 -22.66 14.7 198 212.98 -14.98 7,5 92 25 25.43 -0.43 1.7 54 50.57 3.42 6.3 77 94.14 -17.14 22,2 105 14 17.80 -3.80 27.1 31 27.89 3.10 10,0 43 46.66 -3.66 8,5 120 10 15.80 -5.80 58,0 18 21.77 -3.77 20.9 26 31.49 -5.49 21,1 Tm – Measured tool life TANN – ANN predicted tool life E – deviation between measured and ANN predicted tool life E% – deviation in % 282 a) The correlation between ANN results and b) The measured and simulated tool life values at measured tool life values different workpiece diameters (f=0.05 mm/rev, ap=0.15 mm) Figure 3: The results of ANN simulation It can be seen on Fig. 3b that the characteristics of tool life curves predicted by ANN are similar to curves by specified in [6]. In [7, 8] professional articles Kundrak et al. was a new generalized tool life equation used [5].This equation is valid in the whole range of the cutting speed. The effect of changing of the workpiece diameter on tool life was published Kundrak et al. in [6]. According to this at small workpiece diameter the changing of the direction of chip flow vector is steeper than in case of greater diameters. Therefore the tool life is decreased at small workpiece diameters. Summary The aim of this paper was to determine the tool life of CBN cutting tools using Artifical Neural Network. The inputs of ANN were feed rate, depth of cut, workpiece diameter and cutting speed. These parameters have huge influence on tool life of CBN cutting tool. The predicted tool life by ANN shows good agreement with experimental results of [6]. ACKNOWLEDGEMENTS “The described work was carried out as part of the TÁMOP-4.2.1.B-10/2/KONV-2010-0001 project in the framework of the New Hungarian Development Plan. The realization of this project is supported by the European Union, co-financed by the European Social Fund.” REFERENCES 1. H. K. TÖNSHOFF, C. ARENDT, R. BEN AMOR: Cutting of Hardened Steel. CIRP Annals Manufacturing Technology, 49(2), (2000), 547–566 2. W. S. MCCULLOCH, W. PITTS, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5, (1943), 115–133 3. M. HUDSON, M. BEALE, T. HAGAN, H. DEMUTH: Neural Network Toolbox™ User’s Guide copyright 1992-2010 by The MathWorks, Inc. 4. R. ROJAS: Neural Networks, Springer-Verlag, Berlin 1996 5. J. KUNDRÁK: Determination of Tool Life in Cutting, Proc. of the tenth International Conference on Tools, ICT-2000, September 6-8, 2000. Miskolc, Hungary, pp. 205–210. (ISBN 963 661 434 2) 6. J. KUNDRÁK, V. ZUBAR: Vlijanie diametra rastchivanija na osobennosti processa rezanija, Cutting and tools in manufacturing systems, 59, 2001, 143–148 7. A. G. MAMALIS, J. KUNDRAK, M. HORVATH: Wear and tool life of CBN cutting tools, International Journal of Advanced Manufacturing Technology 20(7), (2002), 475–479 DOI: 10.1007/s001700200180 8. A. G. MAMALIS, J. KUNDRAK, M. HORVATH: On a novel tool life relation for precision cutting tools, Journal of Manufacturing Science and Engineering - Transactions of the ASME, 127(2), (2005), 328–332 DOI: 10.1115/1.1794158 << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJDFFile false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description << /CHS /CHT /DAN /DEU /ESP /FRA /ITA /JPN /KOR /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. 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