15 parametric optimization of surface roughness in … · parametric optimization of surface...

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME

125

PARAMETRIC OPTIMIZATION OF SURFACE ROUGHNESS IN TURNING

INCONEL718 USING TAGUCHI METHODS AND ITS PREDICTION BY

REGRESSION ANALYSIS

Prasad.K.K1

, Dr. D. Chaudhary2

1Professor, Department of Mechanical Engineering, GNDEC, Bidar, Karnataka, India.

2Professor & Head, Department of Mechanical Engineering, GNDEC, Bidar, Karnataka, India.

ABSTRACT

Machining is a complex process wherein many variables are involved which are having a

bearing on the quality of the end products. Surface roughness is one of the most specified quality

characteristics which affect the functional behavior of parts. An excellent surface finish significantly

improves fatigue strength, corrosion resistance, creep life and also affects several other functional

attributes. There are controllable parameters like cutting speed, feed, depth of cut, nose radius and

uncontrollable parameters like machine tool vibration, tool wear, workmaterial flaws etc which are

having a telling influence on the quality of machined components.

There are objectives like surface roughness and tool life which imposes conflicting

requirement on parameters, so optimization of parameters assumes greater importance in machining.

In addition, there is a need for tools that will allow the prediction of quality characteristics in

advance to maximize the gain from machining operations.

The turning being the most widely used machining process, this work focused on parametric

optimization of surface roughness while turning components on CNC lathe. Since the effect of the

parameters on resulting surface roughness have not been quantified yet particularly when machining

difficult-to-machine materials like INCONEL718 super alloy using uncoated carbide turning inserts,

this work concentrated on those aspects. The experiment was performed based on L27 Taguchi

Orthogonal Arrays and optimal parameter setting was determined using Signal-to-Noise (S/N) ratio,

Lower-The-Better criterion. The significance of the parameters was determined by employing

Analysis of Variance (ANOVA) and the mathematical modeling and prediction of the surface

roughness is accomplished by Multiple Regression Analysis (MRA). The result obtained indicates

that Taguchi method is capable of optimizing process parameters in turning process and the

mathematical model obtained as a result of regression analysis can be reliably used for the prediction

of surface roughness.

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING

AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)

ISSN 0976 – 6359 (Online)

Volume 4, Issue 4, July - August (2013), pp. 125-137 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com

IJMET

© I A E M E



126

KEY WORDS: Surface roughness, optimization, Taguchi methods, Multiple Regression analysis

(MRA), Inconel718

1. INTRODUCTION

Machining is a term that covers a large collection of manufacturing processes designed to

remove unwanted maternal usually in the form of chips, from a workpiece to give the desired

geometry, size and finish specialized to fulfill design requirements. Almost every manufactured

product has components that require machining, often to great precision [1]

The overall value of a product and its acceptance by the customer is typically determined by

its performance with respect to multiple measures like how closely they adhere to set product

specifications for length, width, diameter, surface finish and reflective properties. Surface finish is

one of the most important quality measures that manufacturers must be able to control. Surface

roughness of machined components depends on many factors. Some of these factors can be

controlled and some cannot. Controllable process parameters include cutting speed, feed, depth of

cut, tool geometry (ie, nose radius, rake angle etc). Other factors such as vibrations of tool,

workpiece and machine tool, tool wear, variability of work material and tool material etc cannot be

controlled easily are called noise factors.[2]

Surface roughness refers to the relatively closely spaced or fine surface irregularities mainly

in the form of feed marks left by the cutting tool on the machined surface [3]. It plays a very

important role in the performance of turned workpiece as a good quality turned surface significantly

improves fatigue strength, corrosion resistance and creep life. Surface roughness also affects several

functional attributes of parts such as contact causing surface friction, wearing, light reflection, heat

transmission, ability of holding and distributing lubricant, load bearing capacity and resistance to

fatigue. [4]

Surface roughness is specified by the extent of deviation of the finished surface from the

ideal surface. There are different ways of representing this deviation. However arithmetic mean of

roughness or arithmetic mean deviation of roughness (Ra) is the most commonly used surface

roughness measure [5].Ra is the arithmetic mean of absolute values of the evaluation profile

deviations (yi) from the mean line and it is evaluated using the equation 1

Ra = (1/n) (∑ yi�� ----------------------- (01)

For the efficient use of machine tools optimum cutting conditions are required to be

determined because under-optimized machining conditions will result in loss of quality as well as

productivity. There are many optimization techniques employed for optimization of machining

parameters which include fussy logic, genetic algorithms, Taguchi techniques, response surface

methodology, Ant colony optimization, Artificial Neural Networks etc. A detailed review of

optimization techniques can be observed in the article mentioned in reference [6].

This work used Taguchi techniques for achieving optimization because of the simple reason

that it enables multiple complex properties to be optimized at minimal cost. Taguchi Design of

Experiments (DoE) methods incorporate Orthogonal Arrays (OA) to minimize the number of

experiments required to determine the effect of process factors upon the performance characteristics.

This approach allows a statically sound experiment to be completed while investigating a minimum

number of possible combinations of factors. Using this approach the goal can be accomplished in a

timely manner and at a reduced cost with results comparable to full factorial experiment [7].



127

2. MATERIAL AND METHODS

2.1 MATERIAL: INCONEL718

Machining of Nickel based super alloys is a challenging task due to more reasons than one.

But it is worth to take up these challenges since these alloys are very popular in the industry due to

their superior properties. They have excellent high temperature strength, high corrosion and

oxidation resistance as well as resistance to thermal fatigue, thermal shock, creep and erosion

[8].Among Nickel based alloys, Inconel718 is the most widely employed construction material in the

aerospace industry, in particular in hot sections of gas turbine engines. Due to high shear strength,

low thermal conductivity, tendency to form Built Up Edge (BUE), chemical reaction tendency at

high temperatures, and high abrasive carbide particles in the micro structure and work hardening

tendency, this alloy is classified under the category of difficult to machine material. During

machining process, the interaction between the tool and workpiece causes severe plastic deformation

in the local areas of the workpiece, and intense friction at the tool work interface resulting in

excessive tool wear, low productivity and high power consumption [9].

2.2 Taguchi method

Taguchi philosophy provides two tenets (1) reduction in variation (improved quality) of a

product or process which represents a lower loss to society, and (2) the proper development of a

strategy that intentionally reduce variation.[10]

Taguchi method is an experimental technique which is useful in reducing the number of

experiments dramatically by using Orthogonal Arrays and also tries to minimize the effects of factors

out of control. The greatest advantage of Taguchi method is to decrease the experimental time, to

reduce the cost and to find out the significant factors in a shorter time period.

The most reliable of Taguchi techniques is the use of parameter design, which is an

engineering method for product or process design that focuses on determining the parameter (factor)

settings producing the best levels of a quality characteristics (performance measure) with minimum

variations[11].

Taguchi converts the objective function values to Signal-to-Noise ratio (S/N ratio) to measure

the performance characteristics of the levels of control factors. [9].The S/N ratio takes both the mean

and variability into account. In its simplest form, the S/N ration is the ratio of the mean (signal) to

the standard deviation (noise).[12]

The S/N ratio depends on the criteria of the quality characteristics to be optimized.

Depending upon the type of quality characteristics to be optimized, there are three important types of

S/N ratios defined. They are

(a) Smaller- the- Better Type (STB)

--------------------------- (02)

(b) Larger-the-Better Type (LTB)

------------------- (03)



128

(c) Nominal-the-Best,

------------------------- (04)

Where yi is the measured response in ith

run, ‘n’ is the number of observations in a row. � is

the average of the observed data and s2 is the variance.

Since minimum surface roughness value is desirable, Smaller - the- Better Type of quality

characteristics is used (Eqn - 2). [11-13]

Analysis of Variance (ANOVA) is used to determine the statistical significance of the control

parameters. The optimum combination of cutting parameters is determined with the help of main

effect plots.

2.3 MULTIPLE REGRESSION ANALYSIS (MRA)

The objective of multiple regression analysis is to construct a model that explains as much as

possible, the variability in a dependent variable, using several independent variables. The model fit is

called regression model, is usually a linear model, though sometimes non linear models such as log-

linear models are also constructed. To include interaction terms, the following model is used in this

investigation.

Yi = ß0 + ß1 x1 + ß2 x2 +.....+ ßm xm + ß12 x1x2 + ß13x1x3 +....+ ß1m x1 xm + �.---(05)

Where Yi is the dependent variable and X1 …………… Xm are the independent variables � is the error

term. The coefficients, ß0,, ß1……………ß m , ß12, ß13……… ß1m are constants.[14]

The fitted model can be utilized to estimate the values of the responses.

3. EXPERIMENTAL

3.1 Work Material and Tool Turning experiment was performed on CNC lathe with Inconel 718 rod of 25mm diameter

and 100mm length (Fig.1) using uncoated carbide turning insert of Sandvik Coromant make (Fig.2)

with ISO specification numbers as given below.

1. CNMG12 04 04-QM H13A

2. CNMG12 04 08-QM H13A

3 CNMG12 04 12-QM H13A

FIG. 1 INCONEL718 FIG.2 UNCOATED CARBIDE WORKPIECE MATERIAL TURNING INSERT



129

3.2 MEASUREMENT OF SURFACE ROUGHNESS

In this investigation, surface roughness (Ra) is measured by MITUTOYO SJ210 SURF

TEST, a stylus type profilometer (Fig3) and its specifications are given in table 1. Each surface is

characterized by the average surface roughness Ra value. The cut off length λc and the sampling

number (N) are selected as 0.8mm and5 respectively, and travel length selected is 4mm. In total four

different measurements in the scan direction are taken on the textured surface. The average of those

four measurements is used to find out the ultimate Ra values.

Table1. Specifications of SURFTEST SJ-210

FIG 3. SURFTEST SJ-210

Portable Surface Roughness Tester

Sl.No. Details Values

1 Measurement Range 360µm

2 Stylus Diamond

3 Tip radius 5 µm

4 Measuring Force 4mN

5 Ditector range 21mm

6 Transverse speed 0.25mm/s(measurement)

1mm/s(return)

7 Resolution 0.0016 µm



130

4. SELECTION OF STANDARD ORTHOGONAL ARRAY AND ITS CONSTRUCTION

4.1 Basis for Selection of Orthogonal Array

Before constructing an orthogonal array, the following requirements must be defined:

• Number of factors to be studied

• Number of levels for each factor

• Specific 2-factor interactions to be estimated

4.2 COUNTING DEGREES OF FREEDOM The first step in constructing an Orthogonal Array to fit a specific case study is to count the

total degrees of freedom which tell the minimum number of experiments that must be performed to

study all the chosen control factors. To begin with, one degree of freedom is associated with the

overall mean regardless of the number of control factors to be studied. In general, the number of

degrees of freedom associated with a factor is equal to one less than the number of levels for that

factor. The degrees of freedom associated with interaction between two factors are given by the

product of the degrees of freedom for each of the two factors. A suitable OA is selected based on the

Degree of freedom [13]

4.3 EXPERIMENTAL DESIGN Number of parameters = 4

Number of levels for each parameters = 3

Total degree of freedom (DOF) for 4 parameters = 4× (3-1) = 8

Number of interactions considered (AXB), (AXD), and (BXD)

Degree of freedom for interactions= 3X2X2=12

Therefore Minimum number of experiment = Total DOF for parameters +1

= 20 + 1

Minimum number of experiment = 21

L27(3)13

orthogonal array of Taguchi is selected.

5. CONSTRUCTION OF ORTHOGONAL ARRAYS

5.1 Factors with codes and Levels

Table2. Parameter combinations for Experiment with four factors and three levels for INCONEL

718 using uncoated carbide tool [15-17]

Parameters/Factors

Levels

1 2 3

Speed(A) m/min 25 30 35

Feed(B) mm/rev 0.08 0.1 0.12

Depth of cut(C) mm 0.15 0.35 0.55

Nose radius(D)mm 0.4 0.8 1.2



131

6. FACTOR ASSIGNMENTS ON L27 ORTHOGONAL ARRAY

TABLE3. Factor Assignments For INCONEL 718 and Experimental Results

TOOL: UNCOATED CARBIDE CNMG120404-QM H13A, CNMG120408-QMH13A,

CNMG120412-QM H13A

Expt.N0.

Column numbers and factor assignments Ra

Measured

S/N Ratio

Ratio

Ra predicted

1 2 3 5 6 8 9

A B

A*B D A*D B*D C µm �(dB) µm

1 25 0.08

1 0.4 1 1

0.15 0.559 5.0518 0.57984

2 25 0.08 1 0.8 2 2 0.35 0.448 6.9744 0.44355

3 25 0.08 1 1.2 3 3 0.55 0.317 9.9788 0.30297

4 25 0.1 2 0.4 1 2 0.35 0.767 2.3041 0.77100

5 25 0.1 2 0.8 2 3 0.55 0.636 3.9309 0.63245

6 25 0.1 2 1.2 3 1 0.15 0.463 6.6884 0.47157

7 25 0.12 3 0.4 1 3 0.55 0.955 0.3999 0.96199

8 25 0.12 3 0.8 2 1 0.15 0.782 2.1359 0.80314

9 25 0.12 3 1.2 3 2 0.35 0.641 3.8628 0.66482

10 30 0.08 2 0.4 2 1 0.35 0.591 4.5683 0.59534

11 30 .008 2 0.8 3 2 0.55 0.461 6.7260 0.45702

12 30 0.08 2 1.2 1 3 0.15 0.288 10.8122 0.29666

13 30 0.1 3 0.4 2 3 0.55 0.78 2.1581 0.77954

14 30 0.1 3 0.8 3 2 0.15 0.607 4.3362 0.61188

15 30 0.1 3 1.2 1 1 0.35 0.64 3.8764 0.51254

16 30 0.12 1 0.4 2 3 0.15 0.926 0.6678 0.89889

17 30 0.12 1 0.8 3 1 0.35 0.785 2.1026 0.78319

18 30 0.12 1 1.2 1 2 0.55 0.654 3.6884 0.67028

19 35 0.08 3 0.4 3 1 0.55 0.605 4.3649 0.61090

20 35 0.08 3 0.8 1 2 0.15 0.431 7.3105 0.45281

21 35 0.08 3 1.2 2 3 0.35 0.29 10.7520 0.31426

22 35 0.1 1 0.4 3 2 0.15 0.751 5.0518 0.72345

23 35 0.1 1 0.8 1 3 0.35 0.609 6.9744 0.60828

24 35 0.1 1 1.2 2 1 0.55 0.479 9.9788 0.49462

25 35 0.12 2 0.4 3 3 0.35 0.928 2.3041 0.91236

26 35 0.12 2 0.8 1 1 0.55 0.798 3.9309 0.82207

27 35 0.12 2 1.2 2 2 0.15 0.625 6.6884 0.64060



132

7. RESULTS AND DISCUSSION

7.1. Analysis Using MINITAB Software After machining work pieces, response values were noted down (Table3) and with the help

of MINITAB14 software optimum levels of control factors determined based on S/N ratios. ANOVA

was performed to find out the influence of various factors on objective functions. Multiple

Regression Analysis (MRA) was performed to construct mathematical models and to estimate Ra.

Experiments were conducted on INCONEL718 based on L27 Orthogonal Array using uncoated

carbide turning insert.

7.2 Taguchi Analysis: Ra versus SPEED, FEED, DOC, NR

Table4. Response Table for Signal to Noise Ratios for Ra

Smaller is better

Level SPEED FEED DOC NR

1 4.592 7.393 4.841 2.517

2 4.326 4.054 4.377 4.420

3 4.701 2.172 4.400 6.682

Delta 0.375 5.221 0.464 4.165

Rank 4 1 3 2

Table5. Analysis of Variance for S/N Ratio of Ra

Source DF SS MS F P Contribution

(%)

SPEED 2 0.668 0.334 0.375 0.493 0.31

FEED 2 125.859 62.929 70.627 0.000 57.98

DOC 2 1.231 0.6155 0.691 0.144 0.567

NR 2 78.249 39.1245 43.91 0.000 36.05

SPEED*FEED 4 0.459 0.115 0.129 0.610 0.21

SPEED*NR 4 0.231 0.06 0.067 0.723 0.17

FEED*NR 4 5.031 1.258 1.412 0.019 2.32

Error 06 5.343 0.891 01 0.41

Total 26 217.072

S = 0.667293 R-Sq = 97.54% R-Sq (adj) = 94.67%

7.3 Regression Analysis: Ra versus SPEED, FEED, DOC AND NR

The regression equation is

Ra = 0.0194 - 0.00058 SPEED + 8.62 FEED + 0.0753 DOC - 0.344 NR

+ 0.0104 SPEED*FEED - 0.000508 SPEED*NR - 0.141 FEED*NR---- (6)



133

Table6. Regression Table

Predictor Coef T P

Constant 0.01937 0.27 0.793

SPEED -0.000578 -0.36 0.725

FEED 8.6222 21.32 0.000

DOC 0.07530 1.85 0.080

NR -0.34362 -16.96 0.000

SPEED*FEED 0.010446 1.42 0.171

SPEED*NR -0.0005082 -1.01 0.327

FEED*NR -0.1414 -0.97 0.344

Analysis of Variance

Source SS F P

Regression 0.88107 106.91 0.000

Residual Error 0.02237

Total 0.90344

S = 0.0343120 R-Sq = 97.5% R-Sq (adj) = 96.6%

FIG.4. Main Effects Plot (data means) for SN ratios

Mean of SN ratios

353025

8

6

4

2

0.120.100.08

0.550.350.15

8

6

4

2

1.20.80.4

SPEED FEED

DOC NR

Main Effects Plot (data means) for SN ratios(Ra)

Signal-to-noise: Smaller is better



134

FIG.5.Interaction Plot (data means) for SN ratios

FIG.6 Comparison of Measured and Predicted Values of Ra

Table7. Optimum parameter settings

Factor Level Value

Speed (A) A3 35m/min

Feed(B) B1 0.08mm/rev

DOC(C) C1 0.15mm

NR(D) D3 1.2mm

SP EED

10

5

0

FEED

NR

1.20.80.4

0.120.100.08

10

5

0

353025

10

5

0

SPEED

35

25

30

FEED

0.12

0.08

0.10

NR

1.2

0.4

0.8

Interaction Plot (data means) for SN ratios(Ra)

S ignal-to-noise: Smaller is better



135

7.4. CONFIRMATION EXPERIMENT.

Confirmation experiment was conducted with the optimal parameter settings by taking four

trials and the results are shown in Table 8.The mean Ra value=0.286 µm

Table 8.Results of Confirmation Experiment

Factor Level Value Trial

No. Ra(µm)

Speed (A) A3 35m/min 1 0.286

Feed(B) B1 0.08mm/rev 2 0.285

DOC(C) C1 0.15mm 3 0.289

NR(D) D3 1.2mm 4 0.285

mean 0.286

When factor values are substituted in the mathematical model equation 6, it has given Ra

value =0.29 µm. The difference in surface roughness values observed is only 0.004 µm which is

negligibly small and hence the model is validated. Ra value of 0.286 µm is lower than the lowest

measured surface roughness value observed in table 3indicating optimum factor level A3B1C1D3 is

more or less satisfied

7.5. Optimization of Ra

The main effects of each parameter on Ra, are plotted on graphs shown in figure 4 for mean

values of S/N ratios for each level of control variables. These figures clearly indicates how speed,

feed, DOC and tool nose radius changes and affects the modified parameter S/N ratio. Figure shows

that, with the increase in speed, the S/N ratio initially decreases by a small value and subsequently it

increases leading to a resultant increase of S/N ratio and decrease in Ra value. With the increase in

feed, S/N ratio decreases implying an increase in roughness value. With the increase in depth of cut,

there is a resultant decrease in S/N ratio and increase in Ra value. With the increase in nose radius,

there is a resultant increase in S/N ratio and a reduction in surface roughness. Greater the value of

S/N ratio for each parameter minimizes Ra. So the optimum conditions for achieving minimum

surface roughness is cutting speed 35m/min(A3),feed 0.08mm/rev (B1), DOC 0.15mm(C1) and nose

radius 1.2mm(D3). This implies that maximum cutting speed of 35m/min, minimum feed rate of

0.08mm/rev, minimum depth of cut of 0.15mm and maximum nose radius of 1.2mm optimizes the

response.

The response table for the average value of S/N ratios for each level of parameters is

displayed in table 4 and this is utilized to find out their relative importance and to rank them based

on the differences in the average values. It is found that feed is the most important parameter that

influences Ra followed by NR and interaction between feed and nose radius. DOC plays the next

important role where as speed is having least effect on Ra value.

Analysis of Variance (ANOVA) has been performed to investigate the statistical significance

of parameters at 95% confidence level and to determine the percentage of contribution of parameters

to the process response The significance of each parameter was tested using probability values (p-

value).When the p-value in the ANOVA table for S/N ratios is less than 0.05for a confidence level of

95%, it is considered as statistically significant. In addition, the percentage of contribution expresses

the importance of the parameters for the response.

From the result of ANOVA shown in table 5, it is found that the most significant parameter is

feed and its contribution is (57.98%) followed by NR with a contribution of (36.05%). Interaction

between Feed and Nose radius is depicted in fig 5 and is having a small contribution of



136

(2.32%).Other factors are not having significant effects since ‘p’ values are more than 0.05 for a

confidence level of 95%.

To establish a mathematical relationship between parameters and responses, the linear

regression analyses were performed and the following equations were developed.

Ra = 0.0194 - 0.00058 SPEED + 8.62 FEED + 0.0753 DOC - 0.344 NR+ 0.0104 SPEED*FEED -

0.000508 SPEED*NR - 0.141 FEED*NR

The significance of each coefficient in the equation and the regression model were analyzed

by ANOVA and tested by the probability (p value). Both the regression statistics and ANOVA

results for regression models are reported in table 6. Regression statistics indicate that coefficients

for feed and nose radius are statistically significant. ANOVA results of the regression shows that

regression model for Ra is statistically significant at 95% confidence level (p < 0.05) and at least one

of the regressor variables (control factors) is significantly related to response Ra. The predicted

values of the responses were compared with the measured values and the result is depicted as a graph

in fig.6.The graph shows that the predicted values are in reasonable agreement with measured values.

The value of R2

(97.54%) implies that 97.54% of variation in response values can be explained by

the variations in the control factors considered. A high value of determination coefficient ensures

model adequacy, goodness of fit and high significance of model. This indicates that the regression

model for the response can be used for determining and estimating Ra surface roughness value.

8. CONCLUSIONS

An investigation has been carried out to assess the effect of control parameters on the surface

roughness value in the turning process of INCONEL718 using uncoated carbide inserts. The

experiments were performed based on L27 Orthogonal array applying Taguchi’s technique. The input

parameters were cutting speed, feed, depth of cut and tool nose radius and the performance

characteristic investigated is Surface Roughness. The ANOVA was performed to evaluate the

statistical significance of each parameter on the performance characteristic. The relation between

input and output parameter is modeled using Multiple Regression Analysis for the estimation of Ra.

Mathematical model obtained by regression analysis and the equation (6) is reported in the main text.

Summary of the experimental results are tabulated and shown in table7 and results of confirmation

experiment are shown in table8.

Based on the results of theoretical analysis following conclusion are drawn

1) It is observed that the most significant parameter which affects surface roughness is feed and its

contribution is (57.98%) followed by NR with a contribution of (36.05%).Interaction between

feed and nose radius is having a contribution of 2.32% and other factors are not having

significant effects at a confidence level of 95%.

2) Linear regression model constructed using MINITAB software is used to predict the Surface

roughness Ra.

3) A comparison has been made between measured values and predicted values and it is shown in

fig.6.

4) Confirmation experiment using optimized parameter settings reported a surface roughness value

of 0.286 µm which is in accordance with the roughness value predicted by the mathematical

model of MRA within the acceptable range of errors; hence it validates the mathematical model.

5) Eventually it is concluded that Taguchi method is suitable for parametric optimization of turning

and MRA can predict responses reliably.



137

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