30120140507009 2

International INTERNATIONAL Journal of Mechanical JOURNAL Engineering OF and MECHANICAL Technology (IJMET), ISSN ENGINEERING
0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 80-100 © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 7, July (2014), pp. 80-100
© IAEME: www.iaeme.com/IJMET.asp
Journal Impact Factor (2014): 7.5377 (Calculated by GISI)
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80

IJMET
© I A E M E
EFFECT OF VIBRATION ON MICRO-ELECTRO-DISCHARGE
MACHINING
Amol S. Todkar1, Dr. M.S. Sohani2, Prashant R. Patil3, P. N. Deshmukh4
1, 3, 4(Department of Mechanical Engineering, TKIET, Warananagar, Kolhapur, India)
2(Professor, Department of Mechanical Engineering, AITM, Belgaum, India)
ABSTRACT
The Principal objective of the research work is decided to carryout Response Surface
Methodology (RSM) based investigations into the effect of Voltage, Capacitance and work piece
vibration Frequency, amplitude on different materials. The RSM based mathematical models of
Material Removal Rate (MRR) and Tool Wear Rate (TWR) have been developed using the data
obtained through Central Composite Design (CCD). The Analysis of Variance (ANOVA) was
performed along with Fisher’s statistical test (F-test) to verify the lack-of-fit and adequacy of the
developed mathematical models for the desired confidence interval. The ANOVA table includes sum
of squares (SS), degrees of freedom (DF) and mean square (MS). In ANOVA, the contributions for
SS is from the first order terms (linear), the second order terms (square), the interaction terms, lack
of fit and the residual error. The lack of fit component is the deviation of the response from fitted
surface, whereas the residual error is obtained from the replicated points at the center. The MS are
obtained by dividing the SS of each of the sources of variation by the respective DF. The p-value is
the smallest level of significance at which the data are significant. The Fisher’s variation ratio (F-ratio)
is the ratio of the MS of the lack of fit to the MS of the pure experimental error. As per the
ANOVA technique, the model developed is adequate within the confidence interval if calculated
value of F-ratio of lack of fit to pure error does not exceed the standard tabulated value of F-ratio and
the F-values of model should be more than the F-critical for a confidence interval. Further,
conformation test was performed to ascertain the accuracy of the developed models.
The entire research work is experiment oriented and the conclusions are drawn based on
graphical analysis of experimental results. The research work carried out reveals that the findings are
encouraging in establishing the effect of Voltage, Capacitance and work piece vibration Frequency,
amplitude on different materials μEDM drilling process performance characteristics. The results of
this investigations can be adopted in deciding the optimal values of input process parameters μEDM
drilling process.

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
Keywords: Electrical Discharge Machining (EDM), Central Composite Design (CCD), Material
Removal Rate (MRR), Tool Wear Rate (TWR), Response Surface Methodology (RSM). Analysis of
Variance (ANOVA).
81
Abbreviations
I Discharge current
ton Pulse on time
toff Pulse of time
A Tool area
MRR Material removal rate
TWR Tool wear rate
WRW Workpiece removal weight
TWW Tool wear weight
Density
T Machining time
R.No Run number
F Fisher ratio
R2 Coefficient of determination
INTRODUCTION

The basis of controlling the micro electro-discharge machining (μEDM) process mostly relies
on empirical methods largely due to the stochastic nature of the sparking phenomenon involving both
electrical and nonelectrical processes parameters. Thus the performance of micro electro-discharge
machining (μEDM) process is commonly evaluated in the terms of Material Removal Rate (MRR)
and Tool Wear Rate (TWR); and to compute MRR and TWR mathematical models are developed.
Modeling and analysis of Material Removal Rate (MRR) and Tool Wear Rate(TWR) with the effect
of processes parameters like Voltage, Capacitance Amplitude, Frequency of Vibration on different
workpiece thickness is described in this investigation. Conventional Statistical Regression analyses
based mathematical models have been developed to establish the input out put relationships. Material
Removal Rate (MRR) and Tool Wear Rate(TWR) mathematical models have been developed using
the data obtained through Central Composite Design(CCD) The lack-of-fit and adequacy of the
developed mode was verified by applying Analysis of Variance (ANOVA).Further the conformation
tests were performed to ascertain the accuracy of the developed models.[1]
EXPERIMENTAL DETAILS
Experimental set-up
In the present investigation, the experiments were performed in ‘Electronica machine tool
EDM Drill (Rapid drill -II)’ machine. Fig. 2 shows a photograph of EDM machine. The
specifications of micro EDM machine are shown in the Table 1.1 The electrolytic copper is used as a
tool material because of its higher MRR and less TWR, it also yields a better surface finish. The
electrolytic copper tools with different size used to erode water quenched steel k 340 workpiece. The
impulse flushing of tap water (dielectric fluid) was employed throughout the experimental
investigations. The other quantitative and qualitative micro EDM processes parameters were kept
constant for given set of trials.

82

Fig. 1: Schematic diagram of the developed vibration unit
Vibration Unit
A simple vibration device has been designed and developed. In order to create a low
frequency oscillation on the work piece (Fig.4). An electromagnet is used as the actuator. The
electric power is supplied periodically to the electromagnet with the help of a power transistor
switch. The on-off sequence of the power transistor is controlled by a frequency controllable pulse
generator. When the switch is kept on, the electricity flowing through the circuit causes the
electromagnet to be energized, which triggers a pull action on the vibration pad. The flexure beams
are bent at that time. Again, the electromagnet is de-energized when the transistor switch is turned
off, causing the flexure beams to release and push the vibration pad in upward direction. In this way,
a low frequency vibration is induced on the work piece during micro-EDM.
Fig.2: Photograph of ‘electronica machine tool EDM drill (rapid drill -ii)’

83

Table 1.1: Electronica machine tool edm drill (rapid drill)
Technical Specifications
Machine Tool Rapid drill II
Work table 450 x 300 mm (Granite)
X Y axes travel 350, 250 mm
Z axis travel 350 + 300 mm
Max. Electrode length 400 mm
Size of electrode dia. Ø 0.3-3.0 mm
Max. drill depth 300 mm
Max. coolant pressure 6 MPA
Max. weight of the workpiece 350 kg
Connected load 3 kVA
Work tank 800 x 450 mm
Input power supply 3 phase, AC 415 V*, 50Hz
Net Weight 750 kg
Machine foot print 950 x 850 x 1980 mm
Max. machining current 30 A
TECHNOLOGY
Job material Steel/Brass/Aluminium/Carbide/other
conducting materials
Dielectric Tap water/ Coolant soap
Max. drilling speed 20-60mm/min (dia0.5 mm)
Materials used for the experiments
Work piece material
1) Work piece material used for the experiment was K340 steel with the density of 7.77g/cm³ and
After quenching of 1040 °C and 520 ~ 530 °C high temperature tempering, the hardness of HRC up
to 62 to 63. Table 4.2 depicts the chemical composition of K340 steel.
Table 1.2: Chemical Composition Of K340 Steel By Weight Percentage
C Si Mn Mo V Cr P
1.00 0.91 0.32 2.00 0.28 8.00 0.007
2) Iron sinter is the thermally agglomerated substance formed by heating a variable mixture of iron
ores, finely divided coke, limestone, blast furnace dust, steelmaking dust, mill scale and other
miscellaneous iron bearing materials in the temperature range 1315 to 1480°C. The product iron
sinter is used exclusively as a burden material in the production of iron in the blast furnace. The

identity of iron sinter is summarized in Table 1.The typical [sameness] specification for Iron Sinter is
given in Table 2.
84

Table 1.3: Identity Of Iron Sinter
Chemical name Iron, sinter
IUPAC name
Other names (usual name, trade name,
Iron sinter
abbreviation)
EINECS No. 265-9979
CAS name and CAS No. 65996-669
Other identity code: Related CAS No. Hematite (Fe2O3) 1317-608
Molecular formula Fe2O3
Structural information (Crystal lattice)
Minerals of identical or similar composition Hematite
MW (g/mole) MW (g/mole) 159.69
Table 1.4: Sameness Specification For Iron Sinter
Constituent Typical range, % m/m
Fe2O3 55
FeO 23
SiO2 3-11
Al2O3 3
CaO 4-20
MgO 4.5
Other elements [Zn, Ti, K, Cr, Mn, S] 5
Free moisture content 6
Grain size distribution
-8 mm 16%
-10 mm 26%
-20 mm 60%
-30 mm 75%
-50 mm 90%
-70 mm 99%
overall 85% in the range 570 mm
It is conventional to represent the bulk composition of complex oxide materials, such as iron
sinter, iron ore pellets, minerals, ores and refractory products, in terms of the simple oxides of the
constituent elements, as shown in the chemical analysis in Table 2. However, this does not imply that

the product is composed of a mixture of such simple compounds. It is simply a convenient means of
representing the overall elemental composition of the material with each element concentration
expressed in the form of its stable oxide. Therefore, although the typical analysis shown for iron
sinter indicates that it contains silica [SiO2] and lime [CaO], this does not mean that silica is actually
present in free crystalline form, such as quartz or cristobalite, nor does the calcium oxide exist as free
lime. In addition, the reference to ‘FeO’ in Table 2 should not be taken as the concentration of the
wüstite phase [FeO] in iron sinter since the analysis given for ‘FeO’ is a measure of the amount of
iron (II) present in sinter, most of which is present in the form of iron (II,III) oxide or magnetite,
Fe3O4. Similarly, ‘Fe2O3’ represents the total iron content expressed as Fe2O3, not the actual
Fe2O3 concentration.

85
a) Tool Electrode Material

The tool electrode material used for the experiments is a pure electrolytic copper (99.9% Cu).
The physical and mechanical properties of electrolytic copper are melting point of 1,082 0C, density
of 8.97g/cm³, electrical resistivity of 16.7nm and thermal conductivity of 393 W/m K.

INPUT PARAMETERS PROCESS OUTPUTS
Fig. 3: General scheme of the micro-edm processes for different parameters
EXPERIMENTAL PROCEDURE
The top and bottom faces of k340 steel workpiece were ground to a good surface finish using
a surface grinding machine before experimentation. The initial weights of the workpiece and tool
were weighted using a 1 mg accuracy digital weighing machine. The workpiece was held on the
machine table using a specially designed fixture. The workpiece and tool were connected to positive
and negative terminals of power supply, respectively. The dielectric fluid used was tap water with
impulse flushing. The experiments were conducted in a random order to remove the effects of any
unaccounted factors. At the end of each experiment, the workpiece and tool were removed, washed,
dried, and weighted on digital weighing machine. A stopwatch was used to record the machining
time.
Machining Performance Evaluation
Material Removal Rate (MRR) and Tool Wear Rate (TWR) are used to evaluate machining
performance, expressed as the Workpiece Removal Weight (WRW) and Tool Wear Weight (TWW)
per density () over a period of machining time (T) in minutes, that is
MRR (mm³/min) = WRW/T (1.1)

86

TWR (mm³/min) = TWW /T (1.2)
Relative Tool Wear (RTW), defined as the ratio of material Removal Rate (MRR) to Tool
Wear Rate (TWR) and expressed as a percentage, that is
RTW(%) = TWR/MRR X 100 (1.3)
Higher the MRR is the better, where as smaller the TWR and RTW is the better machining
performance in EDM process. Therefore, MRR is higher the- better, where as TWR is lower-the-better
the better performance characteristics in EDM process. The experimental results are given in
table 4.5.
Development of Rsm Based Mathematical Models
The following steps were used for developing RSM based mathematical models
1. Identifying the important process parameters.
2. Developing the design matrix and finding upper and lower limits of process parameters.
3. Conducting the experiments as per the design matrix and recording the responses.
4. Evaluating the regression coefficients and developing the mathematical models for MRR and
TWR.
5. Checking the adequacy of the mathematical models.
Identification of Process Parameters
The independently controllable μEDM parameters affecting the MRR and TWR were
identified as voltage (V), Capacitance (C), Amplitude(A) and Frequency of vibration(f) shown in
Table 4.4 The other quantitative and qualitative EDM parameters were kept constant for given set of
trials.
Developing The Design Matrix And Finding Upper And Lower Limits Of Process Parameters
RSM is used in the design matrix formation which is an empirical modeling approach using
polynomial as local approximations to obtain the true input/output relationships. The most popular of
the many classes of RSM design is the CCD, which can be naturally partitioned into two subsets of
points; the first subset estimates linear and two parameter interaction effects while second subset
estimates curvature effects. CCD is a very efficient method for providing much information on
parameter effects and overall experimental error in a minimum number of required runs [3, 4].
Thirty–one sets of coded and natural conditions are used to form the design matrix of full factorial
central composite design shown in Table 4.5 The design compromises a 24 full factorial Central
Composite Design for four independent parameters each at five levels with sixteen cube point plus
eight star points and seven replicates at center points [3]. All parameters at the intermediate (0) level
constitute the centre points and the combinations of each of the process parameters at either its
lowest (-2) or highest (+2) with the other three parameters of the intermediate levels constitute the
star points. Run indicates the sequence of trials under the consideration Table 4.5 X1, X2, X3 and X4
represents the notation used for the controllable parameters as shown in Table 4.4. Intermediate
levels of coded values were calculated from from the following relationship.
Xi = 2[2X – ( Xmax + Xmin )]/ Xmax - Xmin
Where
Xi: required coded values of parameter X

X any value of the parameter from Xmin to Xmax
Xmin and Xmax: lower and upper levels of the parameter X

87

Table 4.4: Parameter and Range and Levels
Parameters
Notation
Units
Range and levels
Natural coded -2 -1 0 1 2
Voltage V X1 V 80 100 120 140 160
Capacitance C X2 PF 1000 1200 4700 10000 15000
frequency f X4 f 500 650 675 700 750
Amplitude A X3 A 0.8 1.2 1.5 1.8 2.5
Conducting The Experiments As Per The Design Matrix And Recording The Responses
Thirty-one experimental runs were conducted as per the design matrix at the random to avoid
any systematic error creeping into the system. The observed and calculated values of MRR and TWR
for different materials and tools are as indicated in design matrix Table 4.5
Evaluating the Regression Coefficients and Developing the Mathematical Models for MRR and
TWR
The values of the regression coefficients of the linear, Quadratic and interaction terms of the
models were determined by the following formula:
b= (XT X)-1XTY (1.5)
Where,
B: matrix of Parameter estimates
X: calculation matrix
XT: transpose of X
Y:matrix of measured response
Response surface modeling was used to establish the mathematical relationship between the
response (Yn) and the various machining parameters [159,164]. The general second order polynomial
response surface mathematical model, which analysis the parametric influences on the various
response criteria, could be described as follows:

Where
Yn: responses under study e.g. MRR and TWR
Xi: coded values for i= V, C, A and f
bo, bi, bii, bij : second order regression coefficients
The second term under the summation sign of this polynomial equation is attributable to
linear effect, whereas the third term corresponds to the higher-order effect. The fourth term of the
equation includes the interactive effects of the process parameters.
Design of Experiments (DOE) features of MINITAB statistical software [7] were utilized to
obtain the central composite second order rotatable design and also to determine the coefficients of
the mathematical modeling best on the response surface regression model. MINITAB software can
also produce ANOVA tables to test the lack-fit of the RSM based models, and offers the “graphic
option” to obtain a response surface plot for the selected parametric ranges of the developed response

surfaces. Furthermore, MINITAB, software also has features enabling data and file management,
basic statistics and optimization analysis.
88

Based on Eq. 1.6, the effects of the above mentioned process parameters on the magnitude of
the MRR and TWR has been evaluated by computing the values of various constants using
MINITAB statistical software and the relevant experimental data from the Table 1.5.
Regression coefficients for the Material Removal Rate (MRR) and Tool Wear Rate (TWR)
mathematical models were calculated using the coded units. Regression analysis (refer to Table 4.6)
indicates the individual and higher order effects of parameters such as Voltage (V), Capacitance (C),
Amplitude (A) and frequency(f) with the interaction terms. Predictors with significant contributions
in mathematical models are indentified with their p-values less than 0.05. In significant Predictors
were eliminated to adjust the fitted mathematical models. R² is another important coefficient called
the determination coefficient in the resulting ANOVA test, defined as the ratio of the explained
variation to the total variation and as measure of goodness of fit. Hewidey, et. al.,[8]. The R² value is
always between 0 and 1. Values of R², R² (pred) and R² (adj) were also calculated (refer to Table 1.7
for the MRR and TWR mathematical models, as R² value approaches unity, the better the response
model fit the actual data. Lee and Li [9]. It also indicates the difference between the predicated and
actual values.
Table 1.5: Experimental Layout Plan As Per Ccd And Responses
Sr.
No.
Run
No.
Coded values Natural values Responses for different materials
X1
X2
X3
X4
V
C f A
MRR-mm3/mm TWR-%
Y1 Y2 Y3 Y4
1 6 1 -1 1 -1 160 1000 750 0.8 0.000584 0.003084 19 30.19
2 14 1 -1 1 1 160 1000 750 2.5 0.000212 0.002212 19 33.03
3 17 -2 0 0 0 40 8000 625 1.65 0.000348 0.002348 22 32.44
4 12 1 1 -1 1 160 15000 500 2.5 0.000204 0.002204 27 33.05
5 18 2 0 0 0 200 8000 625 1.65 0.000432 0.002432 23 32.54
6 4 1 1 -1 -1 160 15000 500 0.8 0.000576 0.002576 28 31.53
7 28 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24
8 13 -1 -1 1 1 80 1000 750 2.5 0.00019 0.00217 18 32.98
9 10 1 -1 -1 1 160 1000 500 2.5 0.00039 0.002204 28 33.05
10 27 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24
11 1 -1 -1 -1 -1 80 1000 500 0.8 0.000534 0.002534 28 31.47
12 7 -1 1 1 -1 80 15000 750 0.8 0.000542 0.002542 18 31.46
13 23 0 0 0 -2 120 8000 625 -0.05 0.000728 0.002694 26 30.04
14 30 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24
15 22 0 0 2 0 120 8000 875 1.65 0.00098 0.002398 14 32.46
16 15 1 1 1 1 80 15000 750 2.5 0.00017 0.00217 17 32.98
17 29 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24
18 21 0 0 -2 0 120 8000 375 1.65 0.000382 0.002382 30 32.51
19 5 -1 -1 1 -1 80 1000 750 0.8 0.000542 0.00258 18 31.46
20 24 0 0 0 2 120 8000 625 3.35 -0.00016 0.00195 23 33.08
21 8 1 1 1 -1 160 15000 750 0.8 0.000584 0.002584 19 31.51
22 20 0 2 0 0 120 22000 625 1.65 0.00039 0.00239 23 32.49
23 16 1 1 1 1 160 15000 750 2.5 0.000212 0.002212 18 33.03
24 9 -1 -1 -1 1 80 1000 500 2.5 0.000162 0.002162 27 33
25 31 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24
26 2 1 -1 -1 -1 160 1000 500 0.8 0.00039 0.002576 28 31.53
27 19 0 -2 0 0 120 -6000 625 1.65 0.00039 0.00239 24 32.49
28 3 -1 1 -1 -1 80 15000 500 0.8 0.000534 0.002534 28 31.48
29 11 -1 1 -1 1 80 15000 500 2.5 0.000162 0.002162 27 33.03
30 26 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24
31 25 0 0 0 0 120 8000 625 1.65 0.0036 0.0056 24 24

2+ 0.000037 X1 X3 + 0.00184 X1 X4- 0.000032 X2 X4+ 0.00059 X3 X4
2- 0.000006 X1X3+ 0.000846 X1 X4- 0.000005 X2X4+ 0.000271 X3 X4
89

Table 1.6: Regression Coefficients For Mrr And Twr Mathematical Models
1.6.1: Estimated Regression Coefficients For First Tool
Predictor Y1-MRR model Y2-MRR model Y3-TWR model Y4-MRR model
Coefficient p-value Coefficient p-value Coefficient p-value Coefficient p-value
Constant
X1
X2
X3
X4
X1 x X1
X2 x X2
X3 x X3
X4 x X4
X1 x X2
X1 x X3
X1 x X4
X2 x X3
X2 x X4
X3 x X4
0.003386
0.000113
-0.000001
0.000053
-0.000182
-0.000813
-0.000813
-0.000740
-0.000839
0.000001
-0.000001
0.000022
-0.000001
-0.000025
-0.000022
0.000 *
0.373
0.970
0.028*
0.000*
0.000*
0.000*
0.000*
0.000*
0.964
0.964
0.426
0.964
0.377
0.426
0.005600
0.000119
-0.000022
0.000026
-0.000208
-0.000797
-0.000797
-0.000797
-0.000814
-0.000029
-0.000029
-0.000029
-0.000034
0.000034
-0.000034
0.000 *
0.024
0.184
0.121
0.000*
0.000*
0.000*
0.000*
0.000*
0.163
0.163
0.163
0.108
0.108
0.108
24.000
-0.31598
-0.20
-4.458
-0.458
-0.4063
-0.1563
-0.5313
0.0937
-0.062
0.187
0.063
-0.062
-0.188
0.063
0.000*
0.012*
0.060
0.000*
0.000*
0.001*
0.118
0.000*
0.336
0.627
0.157
0.627
0.627
0.157
0.627
24.0000
0.0435
0.183
-0.0283
0.7783
2.1183
2.1183
2.1171
1.8858
0.0225
-0.0237
0.0225
0.0225
-0.0238
0.0225
0.000*
0.595
0.203
0.057*
0.000*
0. 000*
0.000*
0.000*
0.000*
0.202
0.180
0.202
0.202
0.180
0.202
*Indicates the significant term
Hence, the mathematical models in coded form for correlating the Material Removal Rate
(MRR) and Tool Wear Rate (TWR) with the considered μ-EDM processes parameters for different
materials are given below.
Material Removal Rate (MRR)
2 + 0.000001 X1X4
Y1 = 0.003386 + 0.000113 X1 + 0.000056 X3 + 0.003460 X4- 0.001088 X4
(1.7)
2- 0.000001 X1X4
Y2 = 0.005600 + 0.000119 X1 + 0.000064 X3 + 0.003727 X4 - 0.001126 X4
(1.8)
Tool Wear Rate (TWR)
Y3 = 24 + 0.0435 X1+ 0.000145 X2 + 0.00193 X3 - 1.304 X4 - 0.000254 X1
2- 0.000034 X3
2
+ 0.130 X4
(1.9)
Y4= 24 - 0.31598 X1 - 0.000713 X2 - 0.16953 X3- 7.918 X4 + 0.001323 X1
2 + 0.000135 X3
2
+ 2.6087 X4
(1.10)
These developed mathematical models are used to analyze the effect of materials along with
considered μ-EDM process parameters on the Material Removal Rate (MRR) and Tool Wear Rate
(TWR) values

Checking the Adequacy of the Mathematical Models for MRR and TWR
90

The Analysis of Variance (ANOVA) [159,160] was performed along with Fisher’s statistical
test (F-test) to verify the lack-of-fit and adequacy of the developed mathematical models for the
desired confidence interval. The ANOVA table includes sum of squares (SS), degrees of freedom
(DF) and mean square (MS). In ANOVA, the contributions for SS is from the first order terms
(linear), the second order terms (square), the interaction terms, lack of fit and the residual error. The
lack of fit component is the deviation of the response from the fitted surface, whereas the residual
error is obtained from the replicated points at the centre. The MS are obtained by dividing the SS of
each of the sources of variation by the respective DF. The p-value is the smallest level of
significance at which the data are significant. The Fisher’s variance ratio (F-ratio) is the ratio of the
MS of the lack of fit to the MS of the pure experimental error. As per the ANOVA technique, the
model developed is adequate within the confidence interval if the calculated value of F-ratio of lack
of fit to pure error does not exceed the standard tabulated value of F-ratio and the F-values of model
should be more than the F-critical for a confidence interval.
Table 1.7 presents the ANOVA for Material Removal Rate (MRR) and Tool Wear Rate
(TWR) Mathematical models. It is found that the F-values for MRR and TWR models are greater
than the F-critical for a significance level of = 0.05 and their calculated p-values lack-of-fit are
found to be insignificant, as it is desired. Hence, this indicates that the developed second order
regression models that link the various machining parameters with MRR and TWR for different
materials are adequate at 95% confidence level.
Table 1.7: Anova for mrr and twr mathematical models
Response surface regression: mrra versus A, B, C, D
Analysis of Variance Y1
Source DF Adj SS Adj MS F-Value P-Value
Model 14 0.000050 0.000004 92.17 0.000
Linear 4 0.000001 0.000000 5.67 0.005
Square 4 0.000049 0.000012 316.78 0.000
Interaction 6 0.000000 0.000000 0.11 0.005
Error 16 0.000001 0.000000
Lack-of-Fit 10 0.000000 0.000000 0.26 0.970
Pure Error 6 0.000000 0.000000
Total 30 0.000050
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.0001959 98.78% 97.70% 96.70%
Model 14 0.000057 0.000004 649.76 0.000
Linear 4 0.000001 0.000000 44.40 0.000
Square 4 0.000056 0.000014 2226.00 0.000
Interaction 6 0.000000 0.000000 2.51 0.046
Error 16 0.000000 0.000000
Lack-of-Fit 10 0.000000 0.000000 1.7 0.98
Pure Error 6 0.000000 0.000000
Total 30 0.000057

Model Summary
0.0000791 99.82% 99.67% 98.99%
Model 14 499.336 35.667 139.76 0.000
Linear 4 485.167 121.292 475.27 0.000
Square 4 12.794 3.199 12.53 0.000
Interaction 6 1.375 0.229 0.90 0.020
Error 16 4.083 0.255
Lack-of-Fit 10 4.083 0.408 1.79 1.2
Pure Error 6 0.000 0.000
Total 30 503.419
Model Summary
0.505181 99.19% 98.48% 95.33%
Model 14 383.660 27.404 3899.52 0.000
Linear 4 14.733 3.683 524.12 0.000
Square 4 368.845 92.211 13121.28 0.000
Interaction 6 0.082 0.014 1.94 0.000
Error 16 0.112 0.007
Lack-of-Fit 10 0.112 0.011 1.77 0.92
Pure Error 6 0.000 0.000
Total 30 383.772
Model Summary
0.0838308 99.97% 99.95% 99.83%
CONFORMITY EXPERIMENTS OF MATHEMATICAL MODELS
91

In order to determine the accuracy of developed mathematical models, the conformity
experiments were conducted using the same experimental set up. The process parameters were
assigned the intermediate values other than that used in design matrix and the validation test runs
where carried out. The responses were computed and compared with the predicted values and are
given in Table 1.8 and Table 1.9 for MRR and TWR mathematical models respectively. The
percentage error of the developed RSM based mathematical models is found to be within ±5%,
which clearly indicates the accuracy of developed mathematical models. The experimental and the
predicated values of MRR and TWR for Validation data set are illustrated in Fig.3 and 4
respectively.

92

Table 1.8: Conformity Experiments for MRR Mathematical Models
Run Natural values Experimental Values -MRR
V C f A MRRA MRRB
1 60 800 400 0.6 0.003001 0.009050
2 120 900 450 0.7 0.002731 0.01870
3 75 1200 470 0.5 0.004820 0.01515
4 110 1300 450 0.9 0.004216 0.01770
5 90 1100 420 0.8 0.003400 0.01650
Predicted Values % Error
MRR – mm3/min Experimental – predicted/Experimental x 100
0.002923 0.008832 2.60 2.41
0.002651 0.01935 2.93 -3.48
0.005005 0.01485 -3.84 1.98
0.004125 0.01853 2.16 -4.48
0.003504 0.01599 -3.06 3.00
1 2 3 4 5
0.020
0.018
0.016
0.014
0.012
0.010
Run no
Material Removal Rate (mm3/mm)
Variable
Experimental Values
Predicted Values
Experimental Values, Predicted values
Fig. 3: Comparison of the experimental and predicted values for MRR

93

Table1.9: Conformity experiments for twr mathematical models
Run Natural values Experimental Values -TWR
V C f A EWRA EWRB
1 60 800 400 0.6 29.10 38.16
2 120 900 450 0.7 28.70 30.85
3 75 1200 470 0.5 28.12 33.10
4 110 1300 450 0.9 26.36 15.30
5 90 1100 420 0.8 27.60 34.83
Predicted Values % Error
TWR in % Experimental – predicted/Experimental x 100
30.03 39.75 -3.19 -4.17
29.69 31.70 -3.45 -2.76
28.82 34.20 -2.48 -3.32
25.27 14.81 4.13 3.20
28.59 33.95 -3.58 2.52
1 2 3 4 5
30
29
28
27
26
25
Run no
Tool Wear Rate in %
Variable
Experimental Values
Predicted Values
Experimental Values,Predicted Values
Fig. 4: Comparison of the experimental and predicted values for TWR
EXPERIMENTAL RESULTS AND DISCUSSION
The graphical analysis is the most useful approach to predict the response for different values
of the test parameters and to identify the type of interaction between test variables [160]. Hence,
analysis of the parametric influences along with effect of different material as well as amplitude and
frequency of vibration was done based on Response Surface Methodology (RSM) and presented in a
graphical form. The consolidated graphs are drawn based on the computed response value for the
analysis of parametric influences.
Direct Effect of process parameters on MRR and TWR
Effect of voltage on MRR and TWR
Experimentally it is found that increasing voltage increases the Material Removal rate (MRR)
and Tool Wear Rate (TWR) (Table 1.10 and 1.11) (Fig.5 and 6). It can be seen (Fig.5) that the
Material Removal Rate (MRR) increases almost linearly with increasing voltage. Whereas the Tool

Wear Rate (TWR) (Fig. 6) increases rapidly at the beginning and then slow down with increase in
voltage. The increase in voltage increases discharge current that means pulse energy, which leads to
an increase in the rate of heat energy, which is subjected to both of the electrodes, and in the rate of
melting and evaporation hence the Material Removal rate (MRR) and Tool Wear Rate (TWR)
increases with voltage, but after certain limit Tool Wear Rate(TWR) decreases because discharge
current and hence melting and evaporation. [10, 11].
94

Table 1.10: Effect of Voltage (V) On Mrr
Voltage Y1 Y2
40 0.000348 0.002348
80 0.000534 0.002534
120 0.0036 0.0056
160 0.000584 0.003084
200 0.00393 0.002432
50 75 100 125 150 175 200
0.006
0.005
0.004
0.003
0.002
0.001
0.000
Voltage (V)
Material Removal Rate (MRR) -mm3/mm
Variable
MRR Y1
MRR Y2
Materia Removal Rate MRR (MRR) mm3/mm for Y1and Y2
Fig 5: Effect of voltage (v) on mrr
Table 1.11: Effect of voltage (v) on twr
Voltage Y3 Y4
40 22 32.44
80 28 31.47
120 24 24
160 19 30.19
200 23 32.54

95

50 75 100 125 150 175 200
34
32
30
28
26
24
22
20
Voltage (V))
Tool Wear Rate (TWR) in %
Variable
TWR Y3
TWR Y4
Tool Wear Rate in % for Y3 Y4 Vs Voltage
Fig.6: Effect of voltage on TWR
Effect of capacitance on MRR and TWR
In the μEDM drilling process, for Electronica Rapid Drill Machine Tool for micro Drilling
between 0.3mm to 0.5mm drilling process. Best possible capacitance rang for micro drilling is 8000
C to 20000 C (Table 1.12) (Fig.7) below this capacitance there is not sufficient energy between
electrodes between anode and cathode and less melting and evaporation of the material. Hence Less
Material Removal Rate (MRR) above 20000 also as there is high energy between anode and cathode
and flow of melted materials solidifies their only and less evaporation.
Same case is there with Tool Wear Rate (TWR) best possible capacitance for tool wear rate
is 8000 C to 20000 C (Table 1.13) (Fig. 8) Minimum Tool Wear Rate is in between 8000 C to 20000
C because of optimum rate of tool material melting and evaporation in that zone . Above and below
of that zone there is no optimum melting and evaporation of tool material so in that zone there is
high Tool Wear Rate (TWR).
Table 1.12: Effect of Capacitance (C) on MRR
Capacitance Y1 Y2
1000 0.000212 0.002212
8000 0.000348 0.002348
15000 0.0036 0.0056
22000 0.00039 0.00239
-6000 0.00039 0.00239

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