1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
47
APPLICATION OF TAGUCHI METHOD AND ANOVA IN
OPTIMIZATION OF CUTTING PARAMETERS FOR MATERIAL
REMOVAL RATE AND SURFACE ROUGHNESS IN TURNING
OPERATION
Vishal Francis*, Ravi.S.Singh, Nikita Singh, Ali.R.Rizvi, Santosh Kumar
Department of Mechanical Engineering, SSET, SHIATS, Allahabad – 211007, Uttar Pradesh,
INDIA
*Corresponding Author- Assistant Professor, Dept. of Mechanical Engineering, SSET,
SHIATS, Allahabad – 211007, Uttar Pradesh, INDIA
ABSTRACT
The intend of this research work is to employ Taguchi method and Analysis of
Variance to find out the influences of cutting parameters such as spindle speed, depth of cut
and feed on material removal rate and surface roughness for their optimization. The
experimental results obtained were analyzed to find out the most significant factor effecting
MRR and surface roughness. Spindle speed was found to be the most significant parameter
influencing material removal rate followed by feed and depth of cut in turning of mild steel
(0.18% C). Feed rate was found to be the most influencing parameter in case of surface
roughness.
Keywords: Taguchi Method, ANOVA, Mild Steel, Material Removal Rate, Surface
Roughness.
INTRODUCTION
Turning is one of the common metal cutting operations used for manufacturing of
finished parts. The surface texture of the produced parts must fulfill the specified limitations
so it is vitally important to produce parts with adequate surface finish in order to ensure
product performance and reliability. The present work investigates the effect of cutting
parameters on surface roughness and material removal rate, experiment was conducted with a
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ISSN 0976 – 6340 (Print)
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Volume 4, Issue 3, May - June (2013), pp. 47-53
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
48
HSS tool for turning of mild steel. Mild steel is a malleable and ductile material with a low
tensile strength. The surface hardness can be increased through carburizing.
The experiment was designed using Taguchi method, an L27 orthogonal array was
selected and the three process parameter, depth of cut, feed and spindle speeds were varied to
analyze the results obtained in order to find the optimal levels of the parameters for
maximum material removal rate and minimum surface roughness.
ANOVA was employed to find out significance of the different parameters on MRR
and surface roughness.
METHODOLOGY
Essentially, traditional experimental design procedures are too complicated and not
easy to use. A large number of experimental works have to be carried out when the number of
process parameters increases. To solve this problem, the Taguchi method uses a special
design of orthogonal arrays to study the entire parameter space with only a small number of
experiments. This method uses a special set of arrays called orthogonal array. This standard
array gives a way of conducting the minimum number of experiments which could give the
full information of all the factors that affect the response parameter instead of doing all
experiments.
Analysis of variance was invented by Sir Ronald Fisher, who was a Statistician and
Geneticist. He coined the phrase "analysis of variance," defined as "the separation of variance
ascribable to one group of causes from the variance ascribable to the other groups. It is a
statistical method of comparing means between groups; it computes the F-statistics, named
after the inventor Fisher. The computed F value is compared with the critical F value to
determine the significance of the parameters on the response. Variation observed (total) in an
experimental attributed to each significant factor or interaction is reflected in percent
contribution (P), which shows relative power of factor or interaction to reduce variation.
MATERIALS AND METHOD
A Mild steel rod of 150mm length and 32mm diameter was used for the experimental work.
The chemical composition consists of (0.18%) carbon and (0.68%) manganese. The
experiment was performed by high speed steel tool in dry cutting condition.
Turning operation was performed 27 times in Sparko Engineering Workshop,
Allahabad (U.P.) India. The total length of the work piece was divided into 4 equal parts and
the surface roughness was measured for each 37.5mm length across the lay. Correspondingly
MRR was calculated using standard relation:
MRR= VFD mm3
/min (1)
Where,
MRR= Material Removal Rate, V= cutting velocity in mm/min, F= feed rate in mm/rev, D=
depth of cut in mm.
The three process parameters, viz. depth of cut, feed and spindle speeds were varied
as shown in table 1.

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
49
Table 1: Process parameters and their levels
Process
Parameters
Level 1 Level 2 Level 3
Depth of cut (mm) 0.5 1.0 1.5
Feed (mm/rev) 0.08 0.20 0.32
Spindle speed
(rpm)
780 1560 2340
REULTS AND ANALYSIS OF EXPERIMENTS
Table 2 shows the values of the responses obtained from the experimental runs,
designed by Taguchi method, the corresponding value of S/N Ratio is mentioned for each
run.
Table 2: Results for Experimental Trial Runs
Exp.
No.
Depth
of cut
(mm)
Feed
(mm/rev)
spindle
speed
(rpm)
Surface
Roughness
(microns)
Material
Removal
Rate
(mm3
/min)
S/N Ratio for
Surface
Roughness
S/N Ratio for
Material
Removal
Rate
1 0.5 0.08 780 97.5 3134976 -39.7801 129.925
2 0.5 0.08 1560 22.5 6269952 -27.0437 135.945
3 0.5 0.08 2340 100.0 9404928 -40.0000 139.467
4 0.5 0.20 780 95.0 783744 -39.5545 117.883
5 0.5 0.20 1560 105.0 15674880 -40.4238 143.904
6 0.5 0.20 2340 137.5 23512320 -42.7661 147.426
7 0.5 0.32 780 150.0 12539904 -43.5218 141.966
8 0.5 0.32 1560 110.0 25079808 -40.8279 147.986
9 0.5 0.32 2340 55.0 37619712 -34.8073 151.508
10 1.0 0.08 780 87.0 6269952 -38.7904 135.945
11 1.0 0.08 1560 95.0 12539904 -39.5545 141.966
12 1.0 0.08 2340 96.0 15674880 -39.6454 143.904
13 1.0 0.20 780 90.0 31349760 -39.0849 149.925
14 1.0 0.20 1560 96.0 12539904 -39.6454 141.966
15 1.0 0.20 2340 86.0 47024640 -38.6900 153.447
16 1.0 0.32 780 98.0 25079808 -39.8245 147.986
17 1.0 0.32 1560 100.0 50159616 -40.0000 154.007
18 1.0 0.32 2340 98.0 75239424 -39.8245 157.529
19 1.5 0.08 780 85.0 9404928 -38.5884 139.467
20 1.5 0.08 1560 96.7 18809856 -39.7085 145.488
21 1.5 0.08 2340 97.0 28214784 -39.7354 149.010
22 1.5 0.20 780 85.0 2351232 -38.5884 127.426
23 1.5 0.20 1560 93.0 47024640 -39.3697 153.447
24 1.5 0.20 2340 89.0 70536960 -38.9878 156.968
25 1.5 0.32 780 95.0 37619712 -39.5545 151.508
26 1.5 0.32 1560 100.0 37619712 -40.0000 151.508
27 1.5 0.32 2340 89.0 112859136 -38.9878 161.051

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May
A. Analysis of the S/N Ratio
Taguchi method stresses the importance of
signal – to – noise (S/N) ratio, resulting in minimization of quality characteristic variation
due to uncontrollable parameter.
The S/N Ratio is calculated using larger the better characteristics
And the S/N Ratio for Surface roughness is calculated using smaller the better
characteristics.
Where n is the number of measurement in a trail/row and Yi is
run/row.
Table 3 and 4 shows the
smaller the better for each level of the parameters
Table 3: Response Table for Signal to Noise Ratios Larger is better
Level Depth of cut (mm)
1 139.6
2 147.4
3 148.4
Delta 8.9
Rank 3
Table 4: Response Table for Signal to Noise Ratios Smaller is better
Level Depth of cut (mm)
1 -38.75
2 -39.45
3 -39.28
Delta 0.70
Rank 3
A greater value of S/N ratio is always considered for better performance regardless of
the category of the performance characteristics.
The difference of S/N Ratio between level 1 and level 3 indicates the significance of the
process parameters, greater the difference, greater will be the significance.
Table 3 shows that the spindle speed contributes most significantly towards
the delta valve (difference between maximum and minimum values) is highest (13.1)
followed by feed (11.5) and depth of cut (8.9)
Table 4 indicates that for surface roughness the parameter that had the most influence
is feed with delta value of (1.61), followed by spindle speed (1.19) and depth of cut (0.70)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online) Volume 4, Issue 3, May - June (2013) © IAEM
50
Taguchi method stresses the importance of studying the response variation using the
noise (S/N) ratio, resulting in minimization of quality characteristic variation
S/N Ratio is calculated using larger the better characteristics for MRR.
the S/N Ratio for Surface roughness is calculated using smaller the better
Where n is the number of measurement in a trail/row and Yi is the measured value in the
Table 3 and 4 shows the Responses for Signal to Noise ratios of larger the better and
the better for each level of the parameters.
Response Table for Signal to Noise Ratios Larger is better
(mm) Feed (mm/rev) Spindle speed
140.1 138.0
143.6 146.2
151.7 151.1
11.5 13.1
2 1
Response Table for Signal to Noise Ratios Smaller is better
(mm) Feed (mm/rev) Spindle speed
-38.09 -39.70
-39.68 -38.51
-39.71 -39.27
1.61 1.19
1 2
A greater value of S/N ratio is always considered for better performance regardless of
the category of the performance characteristics.
S/N Ratio between level 1 and level 3 indicates the significance of the
process parameters, greater the difference, greater will be the significance.
Table 3 shows that the spindle speed contributes most significantly towards
the delta valve (difference between maximum and minimum values) is highest (13.1)
feed (11.5) and depth of cut (8.9).
Table 4 indicates that for surface roughness the parameter that had the most influence
is feed with delta value of (1.61), followed by spindle speed (1.19) and depth of cut (0.70)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
June (2013) © IAEME
studying the response variation using the
noise (S/N) ratio, resulting in minimization of quality characteristic variation
for MRR.
the S/N Ratio for Surface roughness is calculated using smaller the better
measured value in the
larger the better and
Response Table for Signal to Noise Ratios Larger is better
Spindle speed(rpm)
138.0
146.2
151.1
Response Table for Signal to Noise Ratios Smaller is better
Spindle speed(rpm)
39.70
38.51
39.27
A greater value of S/N ratio is always considered for better performance regardless of
S/N Ratio between level 1 and level 3 indicates the significance of the
Table 3 shows that the spindle speed contributes most significantly towards MRR as
the delta valve (difference between maximum and minimum values) is highest (13.1),
Table 4 indicates that for surface roughness the parameter that had the most influence
is feed with delta value of (1.61), followed by spindle speed (1.19) and depth of cut (0.70).

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
51
Figure 1 and 2 shows the main effect plot for S/N ratio for MRR and surface
roughness. It is clear from figure 1 that MRR increases on increasing the values of spindle
speed, feed and depth of cut. The greatest variation found was due to spindle speed, MRR
increases on increasing the spindle speed. In case of surface roughness, feed has the greatest
variation; as there is a considerable increase of surface roughness on increasing the feed.
1 . 51 . 00 . 5
1 5 2
1 4 8
1 4 4
1 4 0
0 . 3 20 . 2 00 . 0 8
2 3 4 01 5 6 07 8 0
1 5 2
1 4 8
1 4 4
1 4 0
D E P TH O F C U T (mm)
MeanofSNratios
F E E D R A TE (mm/re v )
S P IN D LE S P E E D (rp m)
M a in E f f e c ts P lo t f o r S N r a tio s
Da ta M e a n s
S ig n a l-to -n o is e : La r g e r is b e tte r
Figure 1 Effect of depth of cut, feed and spindle speed on MRR
1 . 51 . 00 . 5
-3 8 . 0
-3 8 . 4
-3 8 . 8
-3 9 . 2
-3 9 . 6
0 . 3 20 . 2 00 . 0 8
2 3 4 01 5 6 07 8 0
-3 8 . 0
-3 8 . 4
-3 8 . 8
-3 9 . 2
-3 9 . 6
D E P T H O F C U T (mm)
MeanofSNratios
F E E D R A TE (mm/re v )
S P IN D LE S P E E D (rp m)
M a i n E f f e c ts P lo t f o r S N r a tio s
D a ta M e a n s
S ig n a l- to -n o is e : S m a lle r is b e tte r
Figure 2 Effect of depth of cut, feed and spindle speed on MRR
B. Analysis of Variance (ANOVA)
The response data obtained via experimental runs for MRR and surface roughness
were subjected to ANOVA for finding out the significant parameters, at above 95%
confidence level and the results of ANOVA thus obtained for the response parameters are
illustrated in table 5 and 6.

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
52
Table 5: ANOVA table for S/N Ratios for MRR
Source DF SS MS F P
Depth of
cut(mm)
2 424.29 212.14 6.54 0.007
Feed
(mm/rev)
2 631.84 315.92 9.73 0.001
Spindle speed
(rpm)
2 793.97 396.98 12.23 0.000
Error 20 649.09 32.45
Total 26 2499.19
Table 6: ANOVA table for S/N Ratios for Surface Roughness
Source DF SS MS F P
Depth of
cut(mm)
2 2.426 1.213 0.13 0.877
Feed
(mm/rev)
2 15.327 7.663 0.83 0.449
Spindle speed
(rpm)
2 6.547 3.273 0.36 0.705
Error 20 183.935 9.197
Total 26 208.235
From Table 5, one can observe that the spindle speed (p=0.000) is the most significant
parameter having 31.77% effect on MRR followed by feed (p= 0.001) having 25.28%
influence on the response whereas depth of cut (p=0.007) influences the response only by
16.98%.
On comparing the percentage contribution of the process parameters on response from
table 6 it was found that feed have 7.36% influence on surface roughness whereas spindle
speed and depth of cut contributes less towards surface roughness.
CONCLUSION
The study discusses about the application of Taguchi method and ANOVA to
investigate the effect of process parameters on MRR and surface roughness. From the
analysis of the results obtained following conclusion can be drawn: -
• Statistically designed experiments based on Taguchi method are performed using L27
orthogonal array to analyze MRR and surface roughness. The results obtained from
analysis of S/N Ratio and ANOVA were in close agreement.
• Optimal parameters for MRR are spindle speed 2340rpm; feed 0.32mm/rev and
depth of cut 1.5mm. Whereas for surface roughness the optimal parameters found
were spindle speed 1560rpm; feed 0.08mm/rev and depth of cut 0.5mm.
• Spindle peed was found to be most significant parameter for MRR.

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