Measurement 46 (2013) 1521–1529
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Optimisation of machining parameters for turning operations based on response surface methodology Ashvin J. Makadia a,⇑, J.I. Nanavati b,1 a Darshan Institute of Engineering and Technology, Gujarat Technology University, At. Hadala, Rajkot-Morbi Highway, Nr. Water Sump, Rajkot 363 650, Gujarat, India b Faculty of Engineering and Technology, MS University, Kalabhavan, Baroda 390 001, Gujarat, India
a r t i c l e
i n f o
Article history: Received 12 January 2012 Received in revised form 9 November 2012 Accepted 11 November 2012 Available online 5 December 2012 Keywords: Response surface methodology Surface roughness Optimisation
a b s t r a c t Design of experiments has been used to study the effect of the main turning parameters such as feed rate, tool nose radius, cutting speed and depth of cut on the surface roughness of AISI 410 steel. A mathematical prediction model of the surface roughness has been developed in terms of above parameters. The effect of these parameters on the surface roughness has been investigated by using Response Surface Methodology (RSM). Response surface contours were constructed for determining the optimum conditions for a required surface roughness. The developed prediction equation shows that the feed rate is the main factor followed by tool nose radius influences the surface roughness. The surface roughness was found to increase with the increase in the feed and it decreased with increase in the tool nose radius. The verification experiment is carried out to check the validity of the developed model that predicted surface roughness within 6% error. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Surface roughness is one of the most important requirements in machining process, as it is considered an index of product quality. It measures the finer irregularities of the surface texture. Achieving the desired surface quality is critical for the functional behaviour of a part. Surface roughness influences the performance of mechanical parts and their production costs because it affects factors, such as friction, ease of holding lubricant, electrical and thermal conductivity, geometric tolerances and more. The ability of a manufacturing operation to produce a desired surface roughness depends on various parameters. The factors that influence surface roughness are machining parameters, tool and work piece material properties and cutting conditions. For example, in turning operation the surface ⇑ Corresponding author. Mobile: +91 09426429122; fax: +91 02822 293008. E-mail addresses:
[email protected] (A.J. Makadia), jinanavati@ hotmail.com (J.I. Nanavati). 1 Mobile: +91 09825027274. 0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2012.11.026
roughness depends on cutting speed, feed rate, depth of cut, tool nose radius, lubrication of the cutting tool, machine vibrations, tool wear and on the mechanical and other properties of the material being machined. Even small changes in any of the mentioned factors may have a significant effect on the produced surface [1]. Therefore, it is important for the researchers to model and quantify the relationship between roughness and the parameters affecting its value. The determination of this relationship remains an open field of research, mainly because of the advances in machining and materials technology and the available modeling techniques. In machinability studies investigations, statistical design of experiments is used quite extensively. Statistical design of experiments refers to the process of planning the experiments so that the appropriate data can be analysed by statistical methods, resulting in valid and objective conclusions [2]. Design methods such as factorial designs, response surface methodology (RSM) and taguchi methods are now widely use in place of one factor at a time experimental approach which is time consuming and exorbitant in cost.
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Previously, most published studies show the tendency to seek effect of cutting conditions like cutting speed, feed rate and depth of cut on surface roughness as well as less number of trials (Table 1). Present study seeks to find out the effect of above parameters and cutting geometry such as tool nose radius on the surface roughness value and 81 number of experiments. Thiele and Melkote [3] had used a three-factor complete factorial design to determine the effects of work piece hardness and cutting tool edge geometry on surface roughness and machining forces. These models concluded that the effect of the two-factor interaction of the edge geometry and work piece hardness on the surface roughness is also found to be important. Mital and Mehta [4] have conducted a survey of surface prediction models developed and factors influencing the surface roughness. They have developed the surface finish models for aluminium alloy 390, ductile cast iron, medium carbon leaded steel, medium carbon alloy steel 4130, and inconel 718 for a wide range of machining conditions defined by cutting speed, feed and tool nose radius. They concluded that cutting speed, feed and tool nose radius have a significant effect on the surface roughness. Sundram and Lambert [5,6] have developed the mathematical models for predicting the surface roughness of AISI 4140 steel during the fine turning operation using both TiC coated and uncoated tungsten carbide throw away tools. Noordin et al. [7] studied the application of response surface methodology in describing the performance of coated carbide tools when turning AISI 1045 steel. They concluded that feed was the most significant factor that influences the surface roughness, however (SECA)2 and (feed SECA) also provide contribution for the surface roughness. Suresh et al. [8] have developed a surface roughness prediction model for turning mild steel using a response surface methodology to produce the factor effects of the individual process parameters. Surface roughness prediction model has been optimised by using genetic algorithms (GAs). The Taguchi method was used by [9,16,17] to find the optimal cutting parameters for turning operations. The study found that feed rate and tool nose radius having highest effect. Choudhury and El-Baradie [10] revealed that cutting speed was the main influencing factor on the tool wear, followed by the feed rate and the depth of cut. Munoz and Cassier [11] developed mathematical model for surface roughness for different types of steel such as AISI 1020, AISI 1045 and AISI 4140. They found that surface finish improves by increasing cutting speed and tool nose radius and by decreasing the feed rate. The depth of cut
does not seem to have a significant influence on surface finish. Fang and Wang [12] developed an empirical model for surface roughness using two level fractional factorial design (251) with three replicates considering work piece hardness, feed rate, cutting tool point angle, cutting speed and cutting time as independent parameters using non linear analysis. Paulo Davim [13], the cutting speed has greater influence on the roughness followed by the feed and depth of cut has no significant influence on surface roughness found by using the Taguchi method. Lee, Tarng and Jaun [14,15] have developed a system for measuring surface roughness of turned parts through computer vision system. They extracted the features of the surface image and thus predicted the surface roughness of the turned parts using the image of the turned surface and turning conditions. Petropoulos et al. [18] had used multi regression analysis and ANOVA for statistical study of surface roughness in turning of PEEK composite. The result for all three PEEK’S examined increase in feed causes significant increase in all the surface roughness, increase of cutting speed was favourable, as decreases roughness but only slightly. Nikolaos et al. [19] used 23 full factorial design for AISI 316L steel with three variables named feed, speed and depth of cut for application of femoral head. The established equation showed that the depth of cut was the main influencing factor on the surface roughness. It increased with increasing the depth of cut and feed rate respectively, but it decreased with increasing the cutting speed. Nikos [20] used Response Surface Methodology (RSM) and fuzzy logic system through the Adaptive Neuro-Fuzzy Inference System (ANFIS) for Ti6Al4 V titanium alloy. The feed rate has been verified as the most important parameter for the surface of Ti6Al4 V. The polynomial models that have been employed to predict the surface roughness produced during the Ti6Al4 V turning, only the 2FI model was successful in Ra prediction. Lalwani et al. [21] used RSM for investigations of cutting parameters influence on cutting forces and surfaces finish in hard turning of MDN250 steel and concluded that good surface roughness can be achieved when cutting speed and depth of cut are set nearer to their high level of the experimental range and feed rate is at low level of the experimental range. Mohamed Dabnum et al. [22] describe the development of surface roughness model for turning glass ceramic (MACOR) utilising design of experiment and response surface methodology and showed that the feed rate was the main influencing factor on the roughness, followed by cutting speed and depth of cut. Choudhury and EL-Baradie [23]
Table 1 Factors affecting on surface roughness and major investigators. Investigators
Nos. of trials
Major factors
Yang and Tarang [9] Chaudhary et al. [33] Noordin et al. [7] Mohamed et al. [32] Davidson et al. [31] Lalwani et al. [29] Nikos et al. [24] Nikolaos et al. [23]
09 24 16 12 17 28 32 27
Cutting Cutting Cutting Cutting Cutting Cutting Cutting Cutting
speed, speed, speed, speed, speed, speed, speed, speed,
feed feed feed feed feed feed feed feed
rate, rate, rate, rate, rate, rate, rate, rate,
depth of cut depth of cut side cutting edge angle depth of cut coolant depth of cut depth of cut depth of cut
Material used
Methodology
S 45C EN 24 T AISI 1045 steel Glass ceramic Flow formed AA6061alloy MDN250 steel Ti6Al4 V Alloy AISI 316L steel
Taguchi method Response surface Response surface Response surface Response surface Response surface Response surface Response surface
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developed surface roughness prediction model for turning of EN 24T utilising response surface methodology. The results have revealed that the effect of feed is much more pronounced than the effect of cutting speed and depth of cut on the surface roughness. However, a higher cutting speed improves the surface roughness. The aim of the present study has been, therefore to develop the surface roughness prediction model of AISI 410 steel with the aid of statistical method under various cutting conditions. By using response surface methodology and (34) full factorial design of experiment, quadratic model has been developed with 95% confidence level.
If the first order model demonstrates any statistical lack of fit, a second order model can then be developed.
2. Postulation of the surface roughness model
In this study, cutting experiments are planned using 3 level full factorial experimental design. Machining tests are conducted by considering four cutting parameters: cutting speed (v), feed rate (f), depth of cut (d), and tool nose radius (r). Total 34 = 81 cutting experiments are carried out. Low-middle-high level of cutting parameters in cutting space of three level full factorial experimental design are shown in Table 2. Ranges of cutting parameters are selected based on shop floor. All the experiments were carried out on Jobber XL model made by Ace design, CNC lathe machine with variable spindle speed 50–3500 RPM and 7.5 KW motor drive was used for machining tests. Surface finish of the work piece material was measured by Surf test model No. SJ-400 (Mitutoyo make).The surface roughness was measured at three equally spaced locations around the circumference of the work pieces to obtain the statistically significant data for the test. In the present work, the work piece material was the AISI 410 steel. This material has good wear and corrosion resistance and used for the manufacturing of nozzle, valve parts and impeller of submersible pump. A mechanical property of the material
A popular model [1] to estimate the surface roughness with a tool having none zero radius is:
Ra ¼
0:032f 2 r
ð1Þ
where Ra is the surface roughness (lm), f is the feed rate (mm/rev), r is the tool nose radius (mm). To borrow the Taylor’s tool life equation in metal cutting, a functional relationship between surface roughness and the independent variables under investigation could be postulated by: m
q
Ra ¼ cf r n v p d
ð2Þ
where Ra is the surface roughness, c the constant, f the feed rate (mm/rev), r the tool nose radius (mm), v the cutting speed (m/min), d the depth of cut (mm), m, n, p, q are the constant that are to be derived. A logarithmic transformation can be applied to convert the non linear form of Eq. (2) into the following linear form:
lnðRa Þ ¼ lnc þ m lnf þ n lnr þ p lnv þ q lnd
ð3Þ
This is one of the data transformation methods used in empirical model building. Eq. (3) can be rewritten as a linear model:
g ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4
^ ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4 þ b12 x1 x2 þ b13 x1 x3 y þ b14 x1 x4 þ b23 x2 x3 þ b24 x2 x4 þ b34 x3 x4 þ b11 x21 þ b22 x22 þ b33 x23 þ b44 x24
ð6Þ
A second order empirical regression model is required when the true response function is non linear and unknown. 3. Experimental work
Table 2 Input parameters and their levels. Sr. no.
Parameters
Level 1
Level 2
Level 3
1 2 3 4
Cutting speed (v), m/min Feed (f), mm/rev Depth of cut (d), mm Tool nose radius (r), mm
220 0.1 0.3 0.4
250 0.15 0.6 0.8
280 0.2 0.9 1.2
ð4Þ
where g is the true value of surface roughness on logarithmic scale. For simplicity Eq. (4) can be written as:
^ ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4 y
ð5Þ
^ is the predicted surface roughness value after logwhere y arithmic transformation and b0, b1, b2, b3 and b4 are estimates of the parameters b0, b1, b2, b3, b4 respectively. With the experimental data, the analysis consisted of estimating these four parameters for a first order model.
Table 3 Mechanical properties of AISI 410 steel. Material properties
AISI 410 steel
Physical density Mechanical hardness, Rockwell B Tensile strength, ultimate Tensile strength, yield Elongation of break Modulus of elasticity
7.74 g/cm3 99 HRB 510 Mpa 310 Mpa 25% 200 Gpa
Table 4 Model summery statistics. Source
Standard deviation
R2
Adj. R2
Pred. R2
PRESS
Linear 2FI Quadratic
0.130411 0.114851 0.067053
0.9476 0.9626 0.9880
0.9449 0.9572 0.9854
0.9407 0.9528 0.9825
1.46332 1.16464 0.43136
Suggested
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Table 5 Estimated regression coefficients for roughness (Ra). Term
Coeff.
SE Coeff.
T
P
Constant Cutting speed (v) Feed (f) Depth of cut (d) Nose radius (r) Speed speed Feed feed Depth of cut depth of cut Nose radius nose radius Cutting speed feed Cutting speed depth of cut Cutting speed nose radius Feed depth of cut Feed nose radius Depth of cut nose radius
0.11407 0.05481 0.50981 0.04407 0.4100 0.0837 0.11241 0.01185 0.12259 0.02528 0.01472 0.01194 0.01417 0.0950 0.00556
0.022351 0.009125 0.009125 0.009125 0.009125 0.015805 0.015805 0.015805 0.015805 0.011176 0.011176 0.011176 0.011176 0.011176 0.011176
49.844 6.007 55.871 4.830 44.931 5.296 7.112 0.750 7.757 2.262 1.317 1.069 1.268 8.501 0.497
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.456 0.000 0.027 0.192 0.289 0.209 0.000 0.621
is given in Table 3. In this study, ceramic inserts (supplied by Ceratizit) were used. Inserts with ISO code TNMG160404 EN-TMF, TNMG 160408 EN-TM and TNMG 160412 EN-TM with different nose radius (60° triangular shaped inserts) were used. The inserts were mounted on a commercial tool. The procedure of experimental scheme is shown in Fig. 8.
4. Result and discussion The analysis of variance (ANOVA) was applied to study the effect of the input parameters on the surface roughness. Table 4 gives the statistics for the model summery. It reveals that the quadratic model is the best appropriate model. So, for further analysis this model was used. Table 5 gives the Estimated Regression Coefficients of surface Roughness for uncoded units. The value ‘‘p’’ for the model is less than 0.05 which indicates that the model terms are significant, which is desirable as it indicates that the terms in the model have a significant effect on the response. From response surface Eq. (7), the most significant factor on the
surface roughness is feed rate. The next contribution on surface roughness is nose radius and cutting speed. Further, it is seen that the R2 value is 0.9880 and the Adj. R2 is 0.9854. The predicted R2 value 0.9825 is in reasonable agreement with Adj. R2 value. The R2 value in this case is high and close to 1, which is desirable. In order to understand the turning process, the experimental results were used to develop the mathematical models using response surface methodology (RSM). In this work, a commercially available software package (MINITAB 14) was used for the computation work. The proposed quadratic model was developed from the above functional relationship using RSM method.
Ra ¼ 5:32260 0:0475792v þ 31:1315f 0:208642d 1:75949r þ 0:00009v 2 2
44:9630f 2 0:131687d þ 0:7662204r 2 0:0168519v f þ 0:00163580v d þ 0:000995370v r þ 0:94444fd 457000fr 0:0462963dr
Fig. 1. Main effect plots of surface roughness (Ra).
ð7Þ
A.J. Makadia, J.I. Nanavati / Measurement 46 (2013) 1521–1529
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Fig. 2. Interaction plots of surface roughness (Ra).
Eq. (7) gives the prediction model for the surface roughness in terms of actual factors. It reveals that surface roughness increases with increasing feed rate and decreases with increasing tool nose radius. Surface finish improves with increasing cutting speed. However, depth of cut has no significant effect on the surface roughness (Fig. 1) The adequacy of the modal has been investigated by the examination of residuals. The residuals, which are the difference between the respective observed response and the predicted response are examined using normal probability plots of the residuals and the plots of the residuals versus the predicted response. If the model is adequate, the points
on the normal probability plots of the residuals should form a straight line. On the other hand the plots of the residuals versus the predicted response should be structure less, that is, they should contain no obvious pattern. The normal probability plots of the residuals and the plots of the residuals versus the predicted response for the surface roughness values are shown in Figs. 3 and 4. It revealed that the residuals generally fall on a straight line implying that the errors are distributed normally. Fig. 4 revealed that they have no obvious pattern and unusual structure. This implies that the model proposed is adequate and there is no reason to suspect any violation of the independence or constant variance assumption [7].
Fig. 3. Normal probability plot of residual for surface roughness data.
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Fig. 4. Plot of residual vs. fitted surface roughness values.
The effect of main factor and interactions are shown in Figs. 1 and 2. The 3D surface graphs for the surface roughness are shown in Figs. 5–7. As the model is adequate these 3D surface plots can be used for estimating the surface roughness values for the any suitable combination of the input
parameters namely feed rate, tool nose radius, cutting speed and depth of cut. It is clear from Fig. 5 that the surface roughness decreases with increasing tool nose radius. Good surface finish can be obtained for a higher tool nose radius, and depth of cut has no significant effect on the surface roughnes. Fig. 6 revealed that cutting speed improves surface roughness. Fig. 7 gives the surface graph for surface roughness at depth of cut = 0.3 mm, tool nose radius = 0.4 mm and feed rate and cutting speed varies. It indicates that surface roughness increases with increasing feed rate. One of the most important aims of experiments related to manufacturing is to achieve the desired surface roughness of the optimal cutting parameters. To end this, the response surface optimisation is an ideal technique for determination of the best cutting parameters in turning operation. Here, the goal is to minimise surface roughness (Ra). RSM optimisation results for surface parameters are shown in Fig. 9 and Table 6. Optimum cutting parameters are found to be cutting speed of 255.75 m/min, feed of 0.1 mm/rev, depth of cut of 0.3 mm and tool nose radius of 1.2 mm. The optimised surface roughness parameter is Ra = 0.2601 lm.
Fig. 5. 3D Surface graph for (Ra) at nose radius and depth of cut varies.
Fig. 6. 3D Surface graph for (Ra) at cutting speed and nose radius varies.
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Fig. 7. 3D Surface graph for (Ra) at cutting speed and feed varies.
Fig. 8. Experimental scheme.
5. Confirmation test In order to verify the accuracy of the model developed, three confirmation run experiments were performed (Table 7). The test conditions for the confirmation test were so chosen that they be within the range of the levels defined previously. The predicted values and the associ-
ated experimental values were compared. The error percentage is within permissible limits. So, the response equation for the surface roughness predicted through RSM can be use to successfully predict the surface roughness values for any combination of the feed rate, tool nose radius, cutting speed and depth of cut within the range of the experimentation performed.
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Fig. 9. Response optimisation for surface roughness parameters.
Table 6 Response optimisation for surface roughness parameters. Parameters
Ra
Goal
Minimum
Optimum conditions
v (m/min)
f (mm/rev)
d (mm)
r (mm)
255.758
0.1
0.3
1.2
Lower
Target
Upper
Pre. resp.
Desirability
0.3
0.3
2.4
0.260122
1
Table 7 Confirmation test. Sr. no.
Speed (v) (m/min)
Feed (f) (mm/rev)
Nose radius (r) (mm)
Depth of cut (d) (mm)
Experimental (Ra)
RSM Predicted (Ra)
Error (%)
1 2 3
220 260 275
0.12 0.15 0.18
0.4 0.8 1.2
0.5 0.7 0.8
1.30 0.95 0.90
1.2230 0.9170 0.8519
5.9 3.4 5.3
6. Conclusions In this paper, application of RSM on the AISI 410 steel is carried out for turning operation. A quadratic model has been developed for surface roughness (Ra) to investigate the influence of machining parameters. The results are as follows: (1) For the surface roughness, the feed rate is the main influencing factor on the roughness, followed by the tool nose radius and cutting speed. Depths of cut have no significant effect on the surface roughness. (2) It can be seen that interaction between most factors has no significant effect except feed rate and tool nose radius which have the highest influence. (3) 3D surface counter plots are useful in determining the optimum condition to obtain particular values of surface roughness. (4) Response surface optimisation shows that the optimal combination of machining parameters are
(255.75 m/min, 0.1 mm/rev, 0.3 mm, 1.2 mm) for cutting speed, feed rate, depth of cut and tool nose radius respectively. (5) Verification experiments carried out show that the empirical models developed can be used for turning of AISI-410 steel within 6% error.
Acknowledgements The author wishes to thank Mr. Mahesh Pansuriya of M/ s Unitech Engg. Pvt. Ltd., Rajkot, Gujarat, for providing help and support for the measurement of surface roughness of the work piece material for research work. References [1] G. Boothroyd, W.A. Knight, Fundamentals of Machining and Machine Tools, third ed., CRC press, Taylor & Francis Group, 2006. [2] D.C. Montgomery, Design and Analysis of Experiments, fourth ed., John Wiley & sons Inc., 1997.
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