New Statistical Models of Cutting Tool Wear and Cutting Speed in Turning 20MoCr130 Stainless Steel

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1 New Statistical Models of Cutting Tool Wear and Cutting Speed in Turning MoCr13 Stainless Steel MIHAIELA ILIESCU, AURELIAN VLASE Manufacturing Department POLITEHNICA University of Bucharest Splaiul Independentei no. 313 Street, District no. 6, zip code 64 ROMANIA Abstract: - Special materials, with very good mechanical characteristics and special look, are represented by the stainless steels. Parts made of these materials are used in special and various industrial fields but, most of the times need machining. Because of the fact that turning is a very important machining procedure and that, special conditions are needed for obtaining optimum machined surface characteristics, this paper deals with aspects involved by the way statistical models of cutting tool wear and cutting speed in turning MoCr13 stainless steel were obtained.. Further application of the obtained models are also, mentioned. Key-Words: - cutting tool wear, cutting speed, turning, stainless steel, statistical model 1 Introduction Stainless steels represent very important materials, because of their good corrosion resistance to powerful agents, their possible use into high temperature conditions and to efficient energy saving systems [, 5]. So, they are used into various fields, starting with chemistry, food, energetic and reaching automotive, spatial etc. industries. Turning is widely used in manufacturing stainless steel parts and, due to the their high hardness, cutting tool is severe worn out, if not correct machining parameters values are settled. The specific literature presents some theoretical data, regarding cutting tool wear in turning stainless steel but, if checking them into real manufacturing conditions, one can notice poor concordance to the eperimental observations. A Romanian stainless steel, MoCr13, have been submitted to competent research, so as to get new statistical models of the variables specific to turning manufacturing process. So, this paper points the steps carried out, in order to determine statistical models of cutting tool wear and cutting speed, in turning MoCr13 steel. There are mentioned the variables considered, their values, the eperiment design and, finally, after regression analysis, the statistical models obtained. First, it was obtained the model of cutting tool wear and, then, out of it, the cutting speed model could be determined. Graphs, corresponding to the obtained models are, also, plotted and some further application of them are mentioned. Research Methodology The eperimentally determining of a machining process variables relationship involves the setting of, both, independent variables (inputs) and dependent variable (output) [1]. Then, the dependence relation type must be established and, consequently, the eperiments carried out. The model of cutting tool wear, in turning stainless steel materials, presented by most of the specific literature dealing with this problem, is: y z w VB = CVBt f v τ [mm] (1) where: VB is the cutting tool wear parameter; t the cutting depth, [mm]; f cutting feed, []; v cutting speed, [m/min];, y, z, w - polytropic eponents; C VB - constant. Once the eperiments carried out, the values of polytropic eponents,, y, z, and of C VB constant can be calculated and so, the relation (1) would be completely determined [4]. When checking, thus theoretically calculated values (by introducing real values of the independent variables) with the corresponding eperimentally obtained ones, there could be notice not to good adequacy. For obtaining the constant and polytropic eponents values, relations (1) has to be of linear type and, so, by logarithm its linear epressions is: lgvb = lgcvb + lgt + y lg f + z lg v + wlg τ () ISSN: ISBN:

2 3 Mathematical Models Determining the new mathematical model can be done first, by eperiments and, second, by specific calculi for constants and ploytropic eponents values. 3.1 Eperiments Eperiments were carried out under specially designed conditions. The machine tool was a SN 4 lathe, whose electric motor had 7,5 kw power. Possible rotational speed range values of the main spindle were 1 15 [rot/min], with geometrical ratio levels variation and possible cutting feed values [], 3 geometrical ratio levels variation. There has been used a cooling/lubricating fluid, % P emulsion. Turning tool used had carbide removable plate, M, whose cutting geometry implied the nose radius, r =1. 5 mm and α = 8, γ = angles. The studied material was MoCr13, its chemical structure being presented in Table 1, while its mechanical characteristics are mentioned by Table. Image of the designed eperimental stand, is presented by figure 1, while the wear of cutting and its measurement on Carl Zeiss microscope are shown in Figure. Fig.1 Eperimental stand C Table 1 Chemical Structure. Mo Ni Cr Mn Si S P Table Tensile Strength, R m [N/mm ] Mechanical Characteristics. Flow Strength, R [N/mm ] Relative Elongation δ Hardness, HB Fig. Cutting tool wear measuring ISSN: ISBN:

3 Ep. No. Sample Diameter, D [mm] Cutting Depth t [mm] Table 3 Eperimental results Cutting Rotational Cutting Speed Feed Speed s [] n [rot/min] Machining Time τ [min] Wear where: n is the rotational speed of the machine tool s main spindle πnd v = [m/min] 1 Eperimental results are shown in Table 3, where, one can also notice, the values of the turning parameters, for each eperience. The samples were cylindrical ones, with various diameter values and, the turning procedure was eterior cylindrical one, at constant speed.. Obtaining Mathematical Models Based on the eperimental results, and on research methodology mentioned, the equation system necessary for models determination is: lg.41 lg.917 lg1.645 lg.177 lg.11 = lg C VB + lg.5 + y lg.1 + z lg w lg 8 = lg C VB + lg.5 + y lg. + z lg w lg 8 = lg C VB + lg.5 + y lg.1 + z lg w lg 8 = lg C VB + lg.5 + y lg.1 + z lg11. + w lg 8 = lg C VB + lg.5 + y lg.1 + z lg w lg1 (3) By solving the equations systems [4], the values of C VB constants, and polytropic eponents,, y, z, w are obtained. As the initial dependence relationship was eponential one, and the ones used in solving were obtained from the first one, by logarithm, the final mathematical model of the cutting tool wear, in turning MoCr13 stainless steel is: VB = t f v τ [mm] (4) The durability criterion, is the value of VB parameter and, for stainless steels turning, it is recommended the value of VB =, 7 mm. From relation (4), one can get the mathematical formula of the cutting speed, in turning MoCr13 stainless steel, that is: 6.9 v = [m/min] (5) T t f Graphs of the cutting tool wear and cutting speed variances, on some of the considered variables are shown in Figure 4 and, respectively, Figure ,5 3,5 1,5 1,5 t =.5 mm; τ = 1 min v = 15.5 m/min; τ = 1 min f =.36 f =. f =.1,1,,3,4,5,6 t [mm] Fig.4 Cutting tool wear, VB, variation, on turning parameters f =.36 f =. f =.1 ISSN: ISBN:

4 t =.5 mm T = 8 min,5,1,15,,5,3 f [] t =.5 mm Model given by relation (4) was obtained solving classical equation systems five unknown parameters and five linear equations, so, one can think of trying to improve it, because of the fact that if, changing one of the equations in system (3), by considering another eperimental values different values for the constant and polytropic eponents should be obtained. That is why, another eperimental data set was studied, meaning, it was considered a full factorial two level eperiment design (with 8 runs) [3] Table 4 Full Factorial Design Eperiments Structure Its structure is presented in Table 4, where, j ( j =1,,3) represents the coded independent variable value. It is -1, for minimum real value and, it is +1, for maimum real value. As for variables considered to significantly influence the cutting tool wear (based on real eperience and the previously obtained mathematical model), they were: cutting speed, v; cutting feed, s and cutting depth, t see table 5. The machining time, τ was the one corresponding to the durability criterion studied, meaning, it was about, 8 minutes long. Run f =.1 f =. f =.8 t =.4 mm T [min] Fig.5 Cutting speed, v, variation, on turning parameters Table 5 Real and coded values of the independent variables studied Cutting Speed Cutting Feed Cutting Depth [m/min] [] [mm] v ( ) 1 f ( ) t ( ) 3 (-1) (+1) (-1) (+1) (-1) (+1) Table 6 Eperimental values Run VB [mm] ISSN: ISBN:

5 Fig.6 DOE KISS Regression analysis results Eperimentally obtained values, for cutting tool VB parameter, are presented in Table 6.and the regression analysis results, carried out with a specialized soft-ware, DOE KISS, are shown in Figure 6. Based on the above, regression model of cutting tool wear parameter, is: VB = (6) where: = v ; 63,8.19 = f ;, = t.5 (7) One can notice that all the studied variables, as well as all their interactions do have significant influence on VB wear parameter. DOE KISS, provides an Epert Optimizer which sets the input values as to minimize T values - see in figure 7.. This software enables graph plots, of answering surface, as well of Pareto Charts, the last mentioned, pointing out how strong the influence of each input, and their interactions, on the output is presented in Figure 8. Also, this software enables graph plots, of answering surface, as well of Pareto Charts, the last mentioned, pointing out how strong the influence of each input, and their interactions, on the output is presented in Figure 8. As noticed, the model predicted by relation (6) is a polynomial type one. By setting the value of VB, at a specified value (say, VB =, 7 ), the relationship of cutting speed and other turning parameters, can be obtained Graphs of the cutting tool wear variance, on some of the considered variables are shown in Figure 9. Fig.7 DOE KISS Epert Optimizer optimized inputs values, as to minimize the output value ISSN: ISBN:

6 1,4 1, 1,8,6,4 f =.8 t =.375 mm f =.1, Fig.8 DOE KISS Pareto Chart of Coefficients Fig.9 Cutting tool wear, VB, variation, on turning parameters 4 Conclusion MoCr13 stainless steels is a widely used material into various industry fields, because of its special chemical and mechanical characteristics. There are presented the steps carried out, in order to determine statistical models of cutting tool wear and cutting speed, in turning this stainless steel type. First statistical model obtained, was about the relationship of cutting tool wear parameter, VB, with turning variables: cutting depth, cutting feed, cutting speed and machining time. It is an eponential type one and, by studying it one can notice that the greatest influence is that of v variable, as long as the lowest, is that of τ. All the considered variable have a direct influence, meaning, on cutting tool wear. Cutting speed mathematical model, was determined from the VB dependence relation, by etracting the v variable, when the durability criterion, of the cutting tool, was settled to VB =.7 mm. By studying the obtained regression model, one can notice that the turning process variables studied, have indirect influence on cutting speed value, that is the higher its value, the lower should be the machining time, cutting depth or, cutting feed. The most important influence, on the dependent variable, v, is that of machining time, τ. Second statistical model of cutting tool wear parameter, VB, was obtained as result of a full factorial eperiment design. It was a polynomial type model, pointing out the fact that all studied independent variables, as well as their interactions, do significantly influence the dependent variable. The influence of cutting speed, v, and cutting feed, f, are, almost, identically and, the higher variables values, the higher, cutting tool wear value. All the above mentioned are graphically pointed out by the figures of this paper. Further research should be developed so as, to implement the obtained results statistical models, into an automated optimization system.of the manufacturing turning process. References: [1] Iliescu M., Vlădăreanu L, Statistic Models of Surface Roughness MET 4 Metallized Coating in Grinding Manufacturing System, 1 th WSEAS International Conference on Systems, pag , ISSN , Greece, July, 8 [] Grigoriu M, Gheorghiu L., Energy Efficiency Pumping Systems Improvement Method, Energetica Journal, no. /8, pag , ISSN , Bucharest, 8 [3] Montgomery D, Runger G, Applied Statistics and Probability for Engineers, John Wiley & Sons, Inc., 3 [4] Vlase A., Ocnărescu C, Bayer M., New Equations for Determining Tool Wear when Machining Polymeric Materials, Plastics Journal, nr..4, pag , ISSN 5/589, Bucharest, 7 [5] Vlase I, Contribution to Determining of Some Indees for Quantifying the Stainless Refractory Steels Machinability, Doctoral Thesis,. ISSN: ISBN: