Simulation of 20MoCr130 steel drilling process and some mathematical models determined

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1 Simulation o 2oCr13 steel drilling process and some mathematical models determined ihaiela Iliescu, Aurelian Vlase, Doru Bardac Abstract Very important materials, with lot o application in automotive, aircrat, medical products, large consumer goods, etc industries, are the stainless steels. achining is oten necessary while manuacturing parts made o these steels and drilling is a widely used procedure. This paper presents new mathematical models o drilling axial orce and torque - obtained as result o simulation, experimental research and regression analysis, carried out on 2oCr13 stainless steel samples. Graphs, as well as urther application o the obtained models are, also, shown. Keywords simulation, drilling, axial orce, torque, model. I. INTRODUCTION T was in the early o 2 th century that, stainless steels were I discovered and, nowadays, their application ields are various and challenging. Primarily used or their corrosion resistance, all o them have a minimum o 1.5% o chromium. This component (chromium, Cr) has great ainity or oxygen, and orms a very thin ilm o chromium oxide on the surace o the steel, at molecular level, this layer being passive, tenacious and sel-renewing [9]. Some important characteristics o stainless steels can be stated as: high corrosion resistance to various chemical agents, ire, heat resistance, impact resistance, hygiene, impressive good look [7]. Consequently, application ields are that o: automotive, aircrat, naval, oil and gas industries, medical products, large consumer goods, ood production Usually, required shape, dimensions and surace roughness o the stainless steel part can be obtained by machining. These materials are very tough, with low thermal conductivity and thus, while machining, sever wear o the cutting tool appear, as well as, high value cutting orces [6]. Because o their high prices, it is necessary to do researches on stainless steels machinability, in order to optimize the machining process, meaning, having high productivity and low costs o parts. The values o cutting orce and torque are representative machinability parameters, meaning the higher the values, the lower this characteristic is [3]. anuscript received April 15, 29: Revised version received ***. ihaiela Iliescu is with the anuacturing Department, POLITEHNICA University o Bucharest, zip code 642, ROANIA (corresponding author:: ; iomi@clicknet.ro). Aurelian Vlase, is with the anuacturing Department POLITEHNICA University o Bucharest (bvlase@yahoo.com). Doru Bardac, is with the anuacturing Department POLITEHNICA University o Bucharest (doru@bardac.net). Speciic literature presents some relationships regarding variables o the machining process involving orce and torque but, when experimentally checking them, one can notice high dierence (o the modeled ones) rom the real obtained values [2], [4]. That is why, it has been considered useul to determine adequate new models o some machinability parameters, or a widely industrial used Romanian stainless steel 2oCr13. When a stainless steel part is designed with holes o same, or various dimensions and precisions, oten a machining procedure, like drilling, is necessary. Cutting orce, specially axial one, and cutting torque, are important parameters (output variables) o the drilling process that can oten be used or its optimization. Simulation, experiments and regression analysis are presented urther by this paper, all o them carried out in order to determine new mathematical models o axial cutting orce and torque in drilling 2oCr13 stainless steel. II. RESEARCH ETHODOLOGY In order to experimentally determine a mathematical relationship o variables speciic to a machining process, there has to be mentioned, both the independent and the dependent ones [1]. Ater doing that, the dependence relation type must be settled and, correspondingly, the appropriate experiments design established. For a more precise and adequate study, simulation o the drilling process is worth to be done. Thus, there could be noticed eventual mistakes such as used cutting tool, hole s position within the part, whole s depth, etc. The mathematical relations, regarding axial cutting orce, in drilling stainless steel materials, presented by most o the articles and books dealing with this problem, are o the type: x F x y = C D a [Nm] (2) F y F = C D a F [N] (1) where: F is the axial component o the cutting orce; the drilling torque; D the diameter o the drilling tool, [mm]; a cutting eed, o the drilling tool, [mm/rot]; x F, y F, x, y - polytropic exponents; C F, C - constants. Once the values o exponents and constants known, experiments were carried out. Issue 2, Volume 3, 29 17

2 It could be noticed that the same values o cutting tool s diameter and cutting eed but, dierent values o cutting speed resulted in various values o axial orce and torque. That it why, it was assumed that the that the parameter not mentioned by relations (1) and (2), meaning cutting speed should play an important role in drilling axial orce and torque prediction. As consequence o the above mentioned, there are experienced other mathematical models o axial cutting orce and torque, where one more independent variable appear, that is cutting speed v [mm/rot]. So, the new, original proposed mathematical models are: x y z F F = C D F a v v [N] (3) F x y = C D a v [Nm] (4) z Fig. 1 Isy-CA selecting cutting tool where: v is peripheral rotational speed o the drilling tool, usually mentioned as cutting speed [m/min]; z v, z - polytropic exponents; For obtaining the constants and polytropic exponents values, relations (3) and (4) must be o linear type and, so, by logarithm their linear expressions are: lg F = lgcf lg D + yf lg a + zf lg v (5) lg = lg C + x lg D + y lg a + z lg v (6) Fig. 2 Isy-CA hole axis position III. SIULATION OF THE DRILLING PROCESS When a part is designed so that includes holes, it is important to have good accuracy o their axes position. So, whenever possible, simulation o the drilling process must be done, in order to avoid errors o involved holes position, length and diameter. For the studied material and process, there has been carried out simulation, considering rectangular shape samples, each o them with our holes, all o them being, in act, used in experiments. The sotware used or simulation was isy-ca, which is speciic to Isel-automation manuacturing systems [8]. It operates under Windows and is made o two parts: Isy-CA CAD part (or designing and modeling parts 2D or, 3D) Isy-CA CA part (or machining on CNC machinetools with 3, 3.5 or 5 axes); So, some images o the drilling process simulation can be seen in: - igure 1 or selecting cutting tool type, - igure 2 or hole axis position, - igure 3 or phases o the simulated drilling a. sample beore drilling b. sample while drilling the second whole c. sample ater drilling. b. c. a. Fig. 3 Isy-CA drilling simulation Issue 2, Volume 3, 29 18

3 IV. ATHEATICAL ODELS Obtaining the new mathematical models proposed implies, irst, experiments and, ater that, constants and polytropic exponents determination, as well as regression analysis. A. Experiments There were carried out experiments under specially designed conditions, meaning: drilling process simulation, experimental stand components; established variation ields and values o studied variables; certain experiments designs; regression analysis techniques. So, the machine tool was a drilling machine, coded GC 32D 3. whose electric motor had 3,5 kw power. Its table dimensions were (mm) and the main spindle had a no. 4 orse cone. Possible rotational speed range values o the drilling tool were 7 14 [rot/min], with 12 geometrical ratio levels variation and possible cutting eed values were.12;.2;.32;.5 [mm/rot]. There has been used a cooling/lubricating luid, 2% P emulsion. Cutting tools were helix drilling ones, made o Rp5 material and having Rockwell hardness no. 62. The edge angle was o 2 χ =14 and the diameter values considered were: Φ 1 = 8 ; Φ 2 = 12 ; Φ 3 = 14 [mm] As or the drilling experimental conditions, they were according to R137/2-69 Standard, type A. Adequate measuring o axial cutting orces and torques, in drilling, involved the design and manuacture o a special rotational device, acting as a dynamometer. Its most important element is represented by an elastic sleeve, on which there were attached our resistive transducers, each inclined by 45 with respect to horizontal and vertical axes. The exit cables o this device were connected to an IEI type electronic bridge which, was coupled to a data acquisition system, using the graphical programming LabVIEW sotware. see Figure 4. The studied material was 2oCr13, its chemical structure being presented in Table 1, while its mechanical characteristics are mentioned by Table 2 C o Ni Cr n Si S P Tensile Strength, R m [N/mm 2 ] Table 2 echanical Characteristics Flow Strength, R 2 [N/mm 2 ] Relative Elongation δ Hardness, HB Images o the designed stand, taken while experimenting are Fig.3 Drilling experiments shown in igure 5. An example o the obtained graphic, or all drilling orce s components, as well as or the power involved by the process is presented in Figure 6. Fig.4 LabVIEW graphical program Table 1 Chemical Structure Fig.6 LabVIEW data acquisition drilling orce s components Issue 2, Volume 3, 29 19

4 Exp. No. Cutting Tool Diameter, D [mm] Cutting Feed Table 3 Experimental results Rotational Speed n [rot/min] Cutting Speed v [m/min] Axial Cutting Force, Drilling Torque [Nm] where: n is the rotational speed o the machine tool s main spindle v n = 1 [rot/min] πd Experimental values obtained or the axial orce and torque, in drilling 2oCr13 stainless steel are shown in Table 3. B. Obtaining First athematical odels Based on the experimental results, and on research methodology mentioned, the equation systems necessary or models determination are as ollows: lg 2282 = lgcf lg8 + yf lg.12 + zv lg14.7 lg 2976 = lgcf lg8 + yf lg.2 + zv lg14.7 lg1998 = lgcf lg8 + yf lg.12 + zv lg lg 3522 = lg CF lg12 + yf lg.12 + zv lg 21.1 (7) lg 4.97 = lgc + x lg8 + y lg.12 + z lg14.7 lg 6.68 = lgc + x lg8 + y lg.2 + z lg14.7 lg 4.43 = lgc + x lg8 + y lg.12 + z lg lg 9.54 = lgc + x lg12 + y lg.12 + z lg 21.1 (8) By solving the equations systems, the values o constants, C F, C and polytropic exponents, x F, y F, x, y are obtained [7]. Knowing that the initial dependence relationships were exponential ones, and the ones used in solving are obtained rom the irst ones, by logarithm, the inal mathematical models o the axial cutting orce and torque, in drilling 2oCr13 stainless steel are: 1.35,52.28 F = 87D a v [N] (9) 1.85,58.24 =.684D a v [Nm] (1) Graphs o the axial orce and torque variances, on some o the considered variables (cutting eed, a, and cutting tool diameter, D) are shown in Figure 7 and, respectively, Figure 8. [Nm] ,5,1,15,2,25,3, v = 2 m/min v = 2 m/min D = 14 mm D = 12 mm D = 8 mm D = 14 mm D = 12 mm D = 8 mm,5,1,15,2,25,3,35 Fig.7 Axial orce, F, and torque variation,, on cutting eed, a Issue 2, Volume 3, 29 11

5 6 5 a =.12 m/rot 4 v = 14,7 [m/min] v = 39,56 [m/min] D [mm] v = 21,1 [m/min] In each case, there have been established (based on previous experiments) variation intervals and number o experimental values. For a more eicient and precise analysis, there has been used a special sotware DOE KISS, student version [4]. Considering the number o independent variables studied (3) and the sotware version available, there have been done experiments, according to a Full Factorial Design, each variable with two variation levels. As needed [5], [6], coded variable values had to be considered so, relationship o natural, z j, to coded, x j, is given by relation: zmin + zmax z j x 2 j =, j =1,2, 3 (11) zmax zmin 2 [Nm] a =.12 m/rot v = 39,56 [m/min] v = 14,7 [m/min] D [mm] v = 21,1 [m/min] Fig.8 Axial orce, F, and torque variation,, on cutting tool diameter, D As relations (9) and (1) were obtained by solving classical equation systems our unknown parameters and our equations, one can think o trying to improve the obtained mathematical models. That is i, changing one o the equations in systems (7) and, respectively, (8), by considering another experimental results rom Table 3 experiment number 5 or, 6, dierent values or the constants and polytropic exponents should be obtained. C. Obtaining Second athematical odels Regression analysis represents a more adequate tool or determining mathematical models representing relationship o the studied variables. So, the dependent variable (output) is considered to be axial cutting or or torque, while independent variables (inputs) are cutting tool diameter, cutting speed and cutting eed. Real and coded values o inputs are presented in table 4 while, the applied experiment design is shown in table 5. As result o all the above mentioned, relation (1) can be customized or each o the independent variables considered, thus obtaining: = z 2.16 x ; x 2 = z ; x 3 = z (12) Cutting tool diameter, D [mm] Cutting eed, Cutting speed, v [m/min] Table 4 Independent variables values Real, z j Coded, x j Table 5 Full actorial experiment design Experience number x 1 x 2 x Issue 2, Volume 3,

6 Experimental results, or cutting orce and torque values, are presented in table 6. It should be mentioned that each experience has been repeated ive times, these involving that replicates number equals ive. Results o regression analysis, carried out with DOE KISS sotware, are shown in igure 9: a. or axial cutting orce, b. or torque. It must be mentioned that regression coeicients whose P (2 Tail) values are higher than.5, are considered to have no signiicant inluence on the output variable. Experience number Table 6 Experimental results values Axial orce, Torque, [N m] a. or axial cutting orce b. or torque Fig.9 DOE KISS sotware Regression analysis results Issue 2, Volume 3,

7 Based on regression analysis results there were obtained second mathematical models, or axial cutting orce and torque, as shown by relations (13) and, respectively, (14). F = x x x x1 x x1 x x2 x3 (13) = x x2.6625x x1 x x1 x x2 x3 (14) a. or axial cutting orce Pareto chart o coeicients, meaning the graph that points out how strong the inluence o each independent variables, as well as their interactions, on the dependent variable is, can be noticed in igure 1, a. or axial cutting orce, b. or torque. x 1 x 2 x 1x 2 b. or torque x 1 x 3 x 3 x 1 x 2 x 1 x 2 x 2x 3 a. or axial cutting orce Fig.11 DOE KISS sotware - arginal means There are also presented graphs that evidence the level o output variation, or each input variables extreme values (minimum and maximum) considered. These graphs are called arginal eans see igure 11, a. or axial cutting orce, b. or torque. Further processing o relations (13) and (14), when considering relation (12), results in mathematical relationships where real variables values are considered and, not coded ones as presented below. So, there were obtained the models expressed by relations (15) and (16): x 1 x 3 x 2 x 3 x 3 b. or torque F = D a v D a D v a v [N] (15) x 1 x 2 x 3 Fig.1 DOE KISS sotware Pareto charts o coeicients = D a.13v 2.823D a +.5D v +.297a + v [Nm] (16) Issue 2, Volume 3,

8 [Nm] D = 14 mm v = 26,82 m/min,5,1,15,2,25 D = 14 mm v = 26,82 m/min D = 8 mm D = 11 mm,5,1,15,2,25 D = 11 mm D = 8 mm Fig.12 Graphs o axial orce, F, and torque,, variation on cutting eed, a Based on the above obtained models, there have been plotted out graphs o axial cutting orce and torque variation, on cutting eed see igure 12. Study on machinability aspects o a requently used stainless steel, 2oCr13, is presented by the article. The dependent variables (outputs) considered are the axial cutting orce and the torque, the process being drilling. There were carried out experiments under specially designed conditions, meaning: drilling process simulation, experimental stand components; established variation ields and values o studied variables; certain experiments designs; regression analysis techniques. All mathematical models determined, have proved to be adequate, and evidenced similar inluence o independent variables (inputs) on the output. Better modeling o axial orce and torque is considered to be obtained by regression the analysis, as it allows evidencing both the inluence o each input, as well as the inluence o their interactions. Once determined, the considered models were urther checked, by more experiments or dierent values o the parameters. All the experimentally obtained results were in good concordance with the mathematically predicted values. Further research should be developed so as, to implement the obtained mathematical models, into an automated optimization system.o the manuacturing process. Also, some other inputs o the drilling process could be considered and, even, more process characteristics (cutting tool wear, power consumption, surace roughness) models determined. REFERENCES [1] Iliescu., Vlădăreanu L, Statistic odels o Surace Roughness ET 4 etallized Coating in Grinding anuacturing System, 12 th WSEAS International Conerence on Systems, pag , ISSN , Greece, July, 28 [2] Hsu-Hwa Chang, Chih-Hsien Chen, Use o Response Surace ethodology and Exponential Desirability Functions to Paper Feeder Design, WSEAS TRANSACTIONS on APPLIED and THEORETICAL ECHANICS Issue 9, Volume 2, September 27, ISSN: [3] Ghionea A., Vlase A, Ghionea I, Wear Evaluation o Cutting Edge and Cutting Speed in Drilling Process o Some anganese Steel, Proceedings o 18 th International DAAA Symposium ISSN , Austria, 27 [4] Premrov, Dobrila P, Bedenik B., Ŝpacapan I., Slip odeling in Timber-Framed Walls with Wood-Based or Fiber-Plaster Sheathing Board, WSEAS TRANSACTIONS on APPLIED and THEORETICAL ECHANICS Issue 9, Volume 2, September 27, ISSN: [5] ontgomery D, Runger G, Applied Statistics and Probability or Engineers, John Wiley & Sons, Inc., 23 [6] Stephen S., Schmidt, Robert G, Laungy, Understanding Industrial Design Experiments, Air Academy Press* Associates, USA, 25 [7] Vlase I, Contribution to Determining o Some Indexes or Quantiying the Stainless Reractory Steels achinability, Doctoral Thesis, 22. V CONCLUSION Stainless steels represent important materials, whose application ields has known a high extend, specially because o special characteristics, such as: high corrosion resistance to various chemical agents, ire, heat resistance, impact resistance, hygiene, impressive good look As consequence, they are expensive materials and research on their machinability is worth to be done, in order to optimize the machining process, meaning, having high productivity and high precision with low costs o parts. Representative element o any material s machinability can be considered to be the cutting orce and torque, specially [2] [1] [8] Isel-automation Catalogue, 27 [9] www. stainless-steel-world.net, accessed april, 29 when drilling process is involved. Issue 2, Volume 3,