Mathematical models of tool life and surface roughness for turning operation through response surface methodology

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1 Journal of Scientific & Industrial Research Vol. 66, March 2007, pp Mathematical models of tool life and surface roughness for turning operation through response surface methodology Hari Singh 1, * and Pradeep Kumar 2 1 Mechanical Engineering Department, National Institute of Technology, Kurukshetra Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee Received 22 September 2005; revised 03 October 2006 Mathematical models of tool life and surface roughness have been developed for turning En24 steel with titanium carbide coated tungsten carbide inserts. Response surface methodology (RSM) has been applied for developing the models in the form of multiple regression equations correlating dependent parameters, tool life and surface roughness, with cutting speed, feed rate and depth of cut, in a turning process. The second order response surface was found suitable for present work. The central composite rotatable design was used to plan the experiment. Keywords: Carbide inserts, En24 steel, Experimental design, RSM, Surface roughness, Tool life IPC Code: G09B25/02 Introduction En24 is an alloy steel having: iron, 95-96; carbon, ; nickel, ; chromium, ; vanadium, 0.09; molybdenum, ; silicon, ; manganese, ; sulphur, 0.05; and phosphorus, 0.05%. Physical and mechanical properties of En24 steel are 1 : hardness, BHN; tensile strength, N/mm 2 ; melting point, 1500 C; density, 7840 kg/m 3 ; thermal conductivity, 41.9 W/m- C; and Young s Modulus, 207x10 9 N/m 2. Typical uses of En24 steel include automobile main shafts, axle shafts, push rods, studs, differential shafts, mandrel for tube production, gun barrels, various parts of machine tools such as spindle gears, power transmission gears, etc 1,2. Properties of En24 steel like low specific heat, tendency to get strain hardened and diffusion between tool and work material give rise to certain problems in its machining such as large cutting forces, high cutting tool temperatures, poor surface finish and built-up-edge formation, thereby making material difficult to machine 3-5. Shaw & Nakayama 4 recommended a cutting speed of 25 m/min with HSS tools and 165 m/min with carbide tools based on a depth of cut of 2.5 mm and a feed value of 0.25 mm/rev. Sarmah 5 *Author for correspondence hsingh_nitk@rediffmail.com found that the multi layer coated insert Widalon TK 15 with Al-O-N as the surface layer gives improved tool life and better surface finish at 247 m/min in spite of the insert experiencing high rake face temperature and stresses. TiC coated single layer insert TG was reported best flank wear resistant and TK 15 best crater wear resistant. Lo & Chen 6 studied the tool life in DC. hot machining of En24 steel using carbide tool in the speed range of m/min using response surface methodology (RSM). Kalnth et al 7 recommended an optimum heating current of 200 amperes for machining En24 steel at 80 m/min. Dearnley & Trent 8 found the flank and rake face wear rates of coated tools 10 to 100 times less than that of an uncoated carbide tool. Dearnley 9 found the aluminium oxide coating most resistant to rake face wear, being stable at elevated temperature, and titanium carbide coating as flank face wear resistant. Bose et al 10 concluded that coated tools with positive rake and in built chip breaker cause reduction of cutting forces and cutting temperature resulting in improved surface finish. A little research has been conducted to obtain mathematical models of machining characteristics for difficult to machine materials using response surface designs This paper attempts to obtain mathematical models of tool life (TL) and surface roughness (SR) for turning En 24 steel with titanium carbide coated carbide inserts using RSM.

2 SINGH & KUMAR: MATHEMATICAL MODELS OF TOOL LIFE AND SURFACE ROUGHNESS 221 Response Surface Methodology (RSM) In RSM 15, it is possible to represent independent factors in quantitative form. Then these factors can be thought of as having a functional relationship or response: Y = φ (X 1, X 2,...., X k ) ± e r (1) between the response Y and X 1, X 2,.... X k of k quantitative factors. Function φ is called response surface or response function. Residual e r measures experimental error 16. For a given set of independent variables, a characteristic surface is responded. In applying RSM, dependent parameter is viewed as a surface to which a mathematical model is fitted. For the development of regression equation, second order response surface has been assumed as: k k k = 2 bo + bi X i + bii X i + bij i= 1 i= 1 i< j= 2 Y X X ± e (2) Y contains linear, squared and cross product terms of variables X i s. Scheme based on central composite rotatable design is reported 17 to fit in second order response surfaces very accurately. Central Composite Second Order Rotatable Design In this design, standard error remains same at all the points that are equidistant from centre of the region. This criterion of rotatability can be explained as follows: Let the point (0, 0,... 0) represent centre of the region, in which the relation between Y and X is under investigation. From the results of any experiment the standard error, e r, of Y can be computed at any point on the fitted surface. This standard error will be a function of the co-ordinates X i s of the point. Due to rotatability condition, this standard error is same at all equidistant points with the distance ρ from centre of the region i.e. for all points for which 16 : X X X k 2 = ρ 2 = constant (3) A central composite rotatable design is subdivided into three parts: i) Points related to 2 k design, where k is the number of parameters and 2 is the number of levels, at which parameters are kept during experimentation. In present work, k = 3, so it results into (2 3 )= 8 experiments; ii) Extra points called star points positioned at a distance α from origin on both sides of the co-ordinate axes. For k < 5, α may be calculated by 2 k/4, whereas, for k 5, α is given by i j r Table 1 Components of central composite second order rotatable design Number of Factorial Star Center Total Value variables points points points N α K 2 k 2k n * * *Half replication α -Distance of the star points from the center 2 (k-1)/4 (Table 1). In present work, α turns out to be These points will result in 2k additional experiments. So, total additional experiments in the present work are 6; and iii) A few more points added at the centre to give roughly equal precision for response Y with a circle of radius one. For three parameters, six additional experiments need to be conducted at the origin. The total number of experiments in the present work is 8+6+6=20 (Fig. 1). Entire experimentation need not be replicated to find the error mean square, since this can be found out by replicating the centre points 15,18. Turning Process Parameters The identified process parameters affecting characteristics of turned parts are: i) Cutting tool parameters tool geometry and tool material; ii) Work piece related parameters- metallography, hardness, etc.; iii) Cutting parameters- cutting speed, feed rate, depth of cut; and iv) Environment parameters dry cutting and wet cutting Process parameters selected for study are cutting speed (A, m/min), feed rate (B, mm/rev) and depth of cut (C, mm). The following parameters were kept constant during entire experimentation: i) Tool material Widadur TG inserts; ii) Work material En 24 steel; and iii) Environment dry cutting. Ranges of selected turning process parameters (Fig. 2) were decided by conducting experiments and using one variable at a time approach 24. Experimental Procedure En24 alloy steel rods (90 mm diam, 500mm long) were turned on an H-22 centre lathe of Hindustan Machine Tools. TiC coated carbide inserts were used

3 222 J SCI IND RES VOL 66 MARCH 2007 Fig. 1 Experimental points for three variables Fig. 2 Ishikawa cause-effect diagram of a turning process

4 SINGH & KUMAR: MATHEMATICAL MODELS OF TOOL LIFE AND SURFACE ROUGHNESS 223 Table 2 Values of selected variables at different levels Variable Levels symbols A, m/min B, mm/rev C, mm Table 3 Experimental design values and average values of responses Sr. Randomized A B C TL SR No TL - Tool life, min; SR Surface roughness, ru to machine En24 steel (0.4%C) of 220 BHN. ISO designation of insert is SPUN and tool holder is CSBPR 2525 H 12. Observations (20) of TL, by measuring flank wear (width of wear land), were recorded using Large Tool Maker s microscope. For TL assessment, flank wear width was measured at an interval of 1 min and the flank wear criterion of 0.45 mm against 1 TL was applied. SR was measured for each run using a Philips roughness tester having a least count of 1 ru (0.025 µ). The levels at which the parameters were tested are given in Table 2. Experimental design values of process variables along with average values of TL and SR are given in Table 3. Results and Analysis Design Expert 7.0 software (dx7) was used for regression and graphical analysis 25. For analysis of the data, checking of goodness of fit of model is very much required. Model adequacy checking includes test for significance of regression model and on model coefficients, and test for lack of fit 26. Analysis of variance (ANOVA) is performed for this purpose. Analysis of Tool Life The fit summary recommended that linear model is statistically significant for analysis of TL. Model F- value of implies the model is significant (Table 4). There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise. Values of "Prob > F" (< ) indicate model terms are significant. In this case A, B, C are significant model terms. Values more than indicate the model terms are not significant. "Lack of Fit F-value" of 0.15 implies the Lack of Fit is not significant relative to the pure error. There is a 99.51% chance that a "Lack of Fit F-value" this large could occur due to Table 4 Analysis of variance table for tool life Source Sum of squares df Mean square F value p-value Prob > F Model < (significant) A- Cutting speed < B- Feed rate < C- Depth of cut Residual Lack of fit (not significant) Pure error Cor. Total Standard deviation = 0.53, Mean = 19.65, Coefficient of variation % = 2.69, Predicted residual error of sum of squares (PRESS) = 5.79, R 2 = , R 2 adjusted = , Predicted R 2 = , Adequate precision =

5 224 J SCI IND RES VOL 66 MARCH 2007 noise. Non-significant lack of fit is good. Predicted R 2 of is in reasonable agreement with the adjusted R 2 of Adequate precision measures signal to noise ratio. A ratio more than 4 is desirable; ratio of indicates an adequate signal. This model can thus be used to navigate design space. Normal probability plot of residuals for TL (Fig. 3) shows that residuals are falling on a straight line, which means the errors are normally distributed. Final response equation in terms of coded factors is given as: TL = * A -0.88* B * C (4) The final response equation in terms of actual factors is given as: TL = * Cutting speed * Feed rate * Depth of cut (5) The developed response surface, within the experimental region, is as: TL = v f d ± (6) where TL = tool life, min; v = cutting speed, m/min; f = feed, mm/rev; d = depth of cut, mm. Analysis for Surface Roughness (SR) The fit summary recommended that the linear model is statistically significant for analysis of SR. Model F-value of implies the model is significant (Table 5). There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise. Values of "Prob > F" (< ) indicate model terms are significant. In this case, A, B, C are significant model terms. The "Lack of Fit F-value" of 0.22 implies the Lack of Fit is not significant relative to the pure error. There is a 98.39% chance that a "Lack of Fit F-value" this large could occur due to noise. Non-significant lack of fit is good. The predicted R 2 of is in reasonable agreement with adjusted R 2 of Adequate precision measures the signal to noise ratio. A ratio more than 4 is desirable; ratio of indicates an adequate signal. This model can thus be used to navigate design space. Normal probability plot of the residuals for SR (Fig. 4) indicates that residuals are falling on a straight line, indicating that the errors are normally distributed. The final response equation in terms of coded factors is given as: SR = * A * B * C (7) The final response equation in terms of actual factors is given as: SR= * Cutting speed * Feed rate * Depth of cut (8) Fig. 3 Normal probability plot residuals for tool life Fig. 4 Normal probability plot residuals for surface roughness

6 SINGH & KUMAR: MATHEMATICAL MODELS OF TOOL LIFE AND SURFACE ROUGHNESS 225 Table 5 Analysis of variance table for surface roughness Source Sum of squares df Mean square F value p-value Prob > F Model < (significant) A- Cutting speed B- Feed rate < C- Depth of cut Residual Lack of fit (not significant) Pure error Cor. Total Standard deviation = 5.11, Mean = 95.50, Coefficient of variation % = 5.35, Predicted residual error of sum of squares (PRESS) = , R 2 = , R 2 adjusted = , Predicted R 2 = , Adequate precision = The developed response surface within the experimental region is as: SR = 3112 v f d 0.34 ± (9) where SR = surface roughness, ru; v = cutting speed, m/min; f = feed, mm/rev; and d = depth of cut, mm. The predicted values of TL ( min) and SR ( ru) in this case study are similar to reported values 27 of TL (20.19 min) and SR (81.38 ru) at 95 % confidence level. The results thus compare well with the present case study through RSM. Limitations of the Case Study The results of this case study are valid for En 24 steel and selected process variables and their specified range. Any extrapolation must be confirmed through further experimentation. Conclusions Models developed in this study can be used to predict tool life of titanium carbide coated tungsten carbide inserts and surface roughness obtainable for turning En 24 alloy steel provided process variables are within the specified range. The predicted values of the tool life and surface roughness are min and ru respectively. The effect of process variables on tool life and surface roughness can be further ascertained by plotting the developed models. References 1 Mottram R A & Woolman J, The Mechanical and Physical Properties of the British Standard EN Steels, 1st edn, vol 2, EN 21-EN 39 (Pergamon Press, Oxford) 1966, Robert R B, Metallic Materials, Specification Hand Book (McGraw-Hill, New York) 1968, Komanduri R, Schroeder T, Hazra J, von Turkovich B F & Flom D G, Catastrophic shear instability in high speed machining of AISI 4340 steels, Trans ASME, J Eng Ind, 104 (1982) Nakayama K & Shaw M C, Machining High Strength Materials, Annals of CIRP, 15 (1967) Sarmah B P, Some investigations into performance of CVDcoated indexable carbide inserts in machining of difficult to machine materials, Ph D Thesis, Mech. and Ind Engg Dept, University of Roorkee, Roorkee, India, Lo K C & Chen N N S, Prediction of tool life in hot machining of alloy steels, Int J Prod Res, 15 (1977) Kalnth G S, Sachdeva S C & Choudhary A P, An Experimental investigation into hot machining of En 24 steel, Proc AIMTDR Conf (IIT Bombay, Mumbai) 1978, Dearnley P A & Trent E M, Wear Mechanism of Coated Carbide Tools, Metal Technology, 9 (1982) Dearnley P A, Rake and flank wear mechanism of coated and uncoated carbide tools, ASME Trans, J Engg Mat & Technol, 107 (1985) Bose et al, Improved performances of coated carbide tools with positive rake and in-built chip breaker, Power Metallurgy Int, 17 (1985) Lambert B K & Taraman K, Development and utilization of a mathematical model of a turning operation, Int J Prod Res, 11 (1973) Taraman K, Multi-machining output multi-independent variable turning research by response surface methodology, Int J Prod Res, 12 (1974) Hassan G A & Suliman S M A, Experimental modelling and optimization of turning medium carbon steel, Int J Prod Res, 28 (1990) El Baradie M A, Surface roughness model for turning grey cast iron (154 BHN), Proc Instn Mech Engrs, 207 (1993) Cochran G & Cox G M, Experimental Design (Asia Publishing House, New Delhi) 1962, Box G E P & Hunter J S, Multifactor experimental design, J Ann Math Stat, 28 (1957) Box G E P, Hunter W G & Hunter J S, Statistics for Experimenters (Wiley, New York) 1978, Draper N R, Center points in second order response surface designs, Technometrics, 18 (1982)

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