Extra machinability modeling Modeliranje povečane obdelovalnosti Miha Kovačič1, 2 *, Matej Pšeničnik2 1ŠTORE STEEL, d. o. o., Store, Slovenia 2University of Nova Gorica, Laboratory for Multiphase Processes, Nova Gorica, Slovenia Corresponding author. E-mail: Miha.Kovacic@store-steel.si Received: December 17, 2008 Accepted: June 06, 2009 Abstract: The steels with extra machinability are made according to special technological process. It depends on several parameters, particularly on the steel chemical composition, whether the steel will meet the criterion of extra machinability. By special test it is established whether the steel has extra machinability or not. In our researches the prediction of machinability of steels, depending on input parameters, was performed by logistic regression and genetic programming. The research shows that genetic programming model performs better. The best model developed during the simulated evolution was practically verified. Izvleček: Jekla s povečano obdelovalnostjo so izdelana s posebnim tehnološkim postopkom. Povečana obdelovalnost jekla je odvisna od mnogih parametrov, predvsem pa od kemične sestave. Obdelovalnost jekla se določa na podlagi posebnega preizkusa. V naši raziskavi smo za napovedovanje obdelovalnosti jekla uporabili logistično regresijo in genetsko programiranje. Rezultati kažejo, da se bolje obnese metoda genetskega programiranja. Rezultati modela so bili preizkušeni v praksi. Key words: steel, extra machinability, modeling, logistic regression, genetic programming Ključne besede: jeklo, povečana obdelovalnost, modeliranje, logistična regresija, genetsko programiranje Introduction In general, tool steels are divided into ordinary steels and steels with extra machinability. These two groups differ in the technology of steel manufacture, which influences the steel properties during machining processes (e. g. turning, milling). In case of steel with extra machinability it is possible to reach much higher resistance of cutting tools even with higher cutting speeds, therefore the price of such steels is 10 % higher on the average than the price of the ordinary steel.[1] The steels with improved machinabili-ty retain all good qualities of ordinary steels their advantage being that they allow machining at 25-50 % higher cutting speeds, 4-6 times lower tool wear and 30 % reduction of machining cost.[1] In case of steel with extra machinabi-lity the molten metal is treated with calcium, which improves their machining properties. Instead of aluminium oxides the steel with extra machina-bility contains calcium aluminates of 2-20 |im size which are of regular forms and uniformly scattered. In this steel the calcium aluminates have sulphide surface. The heat in the cutting zone softens the sulphide surface and ensures the cutting tool to have lubrication effect. As a result, the tool wear in lower and higher machining speeds are allowed.[1] The test of the steel machinability is preformed according to the technological standard ISO 3685.[2] The test process is demanding and time-consuming. As long as the data on machina-bility are not known, the steel cannot be included in the further technological process. If the steel does not reach the degree of extra machinability it is considered to be ordinary steel. The steel machinability is influenced particularly by the chemical composition. As there are several chemical elements in the steel its machinability is hard anticipate and predict. In addition, also other technological parameters change, which additionally make the steel machinability prediction difficult. In the paper prediction of steel machinability by logistic regression and genetic programming was used. The both methods were also compared. Prediction of machinability of steel helps to avoid time-consuming and expensive testing of steel machinability and to contribute to improvement of the material flow in the production process. Test of tool resistance Appropriateness of steel with extra machinability is verified by parameter v15 which is prescribed for each grade of time t = 22.6 min, within which tool steel. wear takes place, v15 amounts to: The parameter v15 is the speed of cutting of the tool which is worn out within 15 min. The tool wear is prescribed. The test of tool resistance is preformed on a CNC lathe. That test is carried out for each batch. The batch is the quantity of steel cast as a whole in the steelworks. The mass of one batch is 52 000 kg. Each batch is identified by its identification number. The steel sample for finding out the ma-chinability must have the diameter of at least 60 mm and the minimum length of 500 mm. After machining (turning) without cooling, within time t (approximately fifteen minutes) and with selected speeds, the wear of the cutting insert is measured under a microscope (Figure 1). The tip of the insert (VBB) may be worn out for not more then 0.30 mm and the entire insert edge (V ) ° v BB max/ for not more than 0.60 mm. Afterwards, the parameter v15 is calculated by Taylor's equation:[3] v • tn = C (1) where v is cutting speed, t is cutting time, n is constant depending on tool material (insert). Constant n for ceramic inserts is 0.25. v-i"=vI5-15" (2) Vt 0.25 = v15-15 -0.25 0.25 v15=v- v15 = 330 150.25 22.60'25 15 0.25 = 365.6 m /min BB max Figure 1. Side wear of the insert Experimental background The data were collected in the period of 13 months in the factory Štore Steel Ltd. from Slovenia. The most influencing parameters are the sample diameters and the chemical elements (calcium, oxygen and sulphur) necessary for production of steel with extra machinability. 146 batches were made. Out of them 125 were adequate. If the batch is adequate this means when parameter v15 in the individual batch exceeds With cutting speed v = 330 m/min and the prescribed value ^ for that batch. The prescribed value of parameter v15 = 85.61 %. The number of each steel depends on the grade of steel. Conse- grade specimens and the average chem- quently, during that period the success ical composition and prescribed v15 for of production of steels was 21/146 steel grade is presented in Table 1. Table 1. The number of each steel grade specimens and average chemical composition and prescribed v Steel grade Number of specimens w(Ca)/% w(O)/% w(S)/% v15/(m/min) 16MnCrS5 2 0.0305 0.034 0.0275 410 C45 139 0.0293 0.0462 0.0270 360 C50 2 0.0235 0.0145 0.021 360 C15 1 0.029 0.019 0.028 450 St70.2 2 0.03 0.0375 0.029 360 The experimental data and extra machinability suitability are presented in Table 2. If the batch of steel is adequate then it is marked with logical variable 1 and with 0, if it is not. Table 2. The experimental data # Batch number Steel grade Sample diameter w(Ca)/% w(O)/% w(S)/% V15 Prescribed V15 Extra machinability 1 36968 C45 19.0 0.024 0.019 0.031 327 360 0 2 37101 16MnCrS5 60.0 0.026 0.044 0.027 453 410 1 3 37236 C50 70.0 0.026 0.005 0.022 308 360 0 4 37237 C50 70.0 0.021 0.024 0.02 346 360 0 143 37322 C45 70.0 0.027 0.018 0.025 261 250 1 144 37358 C45 70.0 0.033 0.042 0.028 452 450 1 145 37359 C45 70.0 0.029 0.044 0.022 459 450 1 146 37360 C45 68.0 0.033 0.046 0.025 438 410 1 Extra machinability modeling Evaluation of models were determined by Bayesian analysis (true positive TP, true negative TN, false positive FP, false negative FN) applying sensitivity SENS = TP/(TP+FN), specificity SPEC = TN/(FP+TN), positive predictive value PP V= TP/(TP+FP) and negative predictive value NPV = TN/(FN+TN). The higher are values of mentioned parameters the better model fits to experimental data. According to the logistic regression results the logistic mathematical model for extra machinability is: (3) p ' lg 1 -p = 0.058 cp + 123.607 • w{ca) + +101.616 • w(0) + 326.759 w(iS)-18.537 where p is the probability of steel not being extra machinability steel. If the probability p was lower then 0.5, then the extra machinability was denoted as 1 otherwise as 0. The parameters in the mathematical models for extra machinability are denoted as: • $ - sample diameter • w(Ca)/% - mass fraction of calcium • w(O)/% - mass fraction of oxygen • w(S)/% - mass fraction of sulphur Logistic regression modeling The most important results of logistic regression are presented in Table 3. The logistic regression model sensibility is 0.976, specificity 0.524, positive predictive value 0.924, negative predictive value 0.786 and test efficiency 0.911. Genetic programming modeling Genetic programming is probably the most general evolutionary optimization method.[4-6] The organisms that undergo adaptation are in fact math- Table 3. Logistic regression results Parameter B S. E. Wald df Sig. Exp(B)

)- 2.32712 1.11863 -(p + w(0)-w(5)- 1.70735 2.32712 --+ w(0) +- M.O) w(0) + w(S) J w(0)(2.32712+w(5')) the greatest permissible depth in creation of population 6, the greatest permissible depth after the operation of crossover of two organisms 10 and the smallest permissible depth of organisms in generating new organisms 2. Genetic operations of reproduction and crossover were used. For selection of organisms the tournament method with tournament size 7 was used. We have developed 100 independent civilizations of mathematical models for prediction of extra machinability. Only one out of 100 is presented in eq. 4 (page 343) With sensibility of 1, specificity 0.810, positive predictive value 0.969, negative predictive value 1 and test efficiency 0.973. Conclusions Due to their specific properties if compared with ordinary steels, the steels with extra machinability will represent a growing share on the market. Their advantage over the remaining steels, in particular, is that they can be machined at higher machining speeds and that they assure smaller cutting tool wear. In researches two approaches were used for predicting the steel machin-ability - logistic regression and genetic programming. Evaluation of models was determined by Bayesian analysis. The logistic regression model was obtained with sensibility 0.976, specificity 0.524, positive predictive value 0.924, negative predictive value 0.786 and test efficiency 0.911. The best genetic programming model (out of 100) performed better with sensibility of 1, specificity 0.810, positive predictive value 0.969, negative predictive value 1 and test efficiency 0.973. Out of 146 values the best model wrongly predicts 4 values; it means that its reliability is 97.26 %. In case of all 4 wrong predictions the model predicts that the steel has appropriate machinability, while in fact it does not have it. Research has shown that by using the genetic programming method for prediction of appropriateness of the steel machinability it is possible to establish efficient planning and optimizing of production, to reduce the costs of researches and the handling changes and, finally, to increase satisfaction of the buyers due to shorter delivery times. The future researches will be focused on testing the mathematical model and optimizing the chemical composition. The prognosis is optimistic. References [1] www.store-steel.si (2009). [2] ISO 3685:1993, Ed. 2, Tool-life test- ra ing with single-point turning tools. [3] Galante, G., Lombardo, A., Passan-nanti A., Tool-life modeling as a stochastic process, International journal of machine tools and manufacture, 1998, 38, 1361-1369. [6] [4] Kovacic, M., Brezocnik, M., Turk, R. (2005): Modeling of hot yield stress curves for carbon silicion steel by genetic programming. Materials and manufacturing processes, Vol. 20, 1-10. Kovacic, M., Uratnik, P., Brezocnik, M., Turk, R. (2007): Prediction of the bending capability of rolled metal sheet by genetic programming. Materials and manufacturing processes, Vol. 22, 634-640. Koza, J. R. (1999): Genetic programming III. Morgan Kaufmann, San Francisco, 1154 p.