Indian Journal of Engineering & Materials Sciences
Vol. 17, December 2010, pp. 463-470
Influence of cutting parameters on thrust force and torque in drilling of
E-glass/polyester composites
S Jayabal* & U Natarajan
Department of Mechanical Engineering, A C College of Engineering and Technology, Karaikudi 630 004, India
Received 5 March 2010; accepted 1 October 2010
This paper discusses the influence of cutting parameters in drilling of glass fiber reinforced composites. The
experiments are conducted to study the effect of point angle, spindle speed and feed rate on thrust force and torque using
HSS twist drills. This paper presents a mathematical model for correlating the interactions of drilling parameters and their
effects on thrust force and torque. The optimum value of cutting parameters is also determined to get minimum value of
thrust force and torque.
Keywords: Response surface methodology, CNC milling machine, Drill tool dynamometer, Thrust force, Torque
A number of research endeavors have been made in
the recent past to fully characterize the drilling
process of fiber reinforced composite materials1. The
efforts have been made in the direction of
optimization of the operating variables and conditions
for minimizing the drilling induced damage2. Singh3
used finite element approach to study the effect of
drill point angle on drilling induced damage while
drilling unidirectional glass fiber reinforced
composite laminates. They observed that 90° drill
point angle gives better results as compared to 104°
and 118°. Ramulu4 observed that in case of drilling
with High Speed Steel (HSS) and HSS-Co drills, the
highest temperatures occurred at higher cutting speeds
and lower feeds. Increasing speed leads to increased
tool wear, larger entrance and exit burrs, larger
damage rings and decreased number of holes drilled.
Increasing feed leads to increased drill thrust and
torque, smaller entrance and exit burrs, reduced
damage width and increased number of holes drilled5.
Bhattarcharya and Horrigan6 studied hole drilling in
kevlar composites under ambient and cryogenic
conditions, the latter being obtained by the application
of liquid nitrogen at the drill site. The drill bits under
cryogenic conditions underwent a much lower wear
rate, resulting in much lower thrust forces and
material damage. Chen7 observed that the effect of the
cutting speed on the cutting forces is insignificant for
the same drill material. The cutting forces on the other
__________________
*Corresponding author (E-mail: jayabalsubbaian@rediffmail. com)
hand were found to be lower at lower feed rates. It
was further concluded that in order to improve the
hole quality at exit, the feed rate at exit needs to be
decreased during the drilling process. Caprino and
Tagliaferri8 stated that the type of damage induced in
a composite material during drilling is strongly
dependent on the feed rate. When the feed rates are
high, the failure modes show the features typical of
the impact damage, with step-like delamination, intralaminar cracks and the high-density micro failure
zones. If the feed rate is sufficiently low, the failure
consists essentially of delamination mainly
originating near the intersection between the conical
surface generated by the main cutting edges and the
cylindrical surface of the hole. Ilio9 reported
experimental studies on Aramid fiber reinforced
plastic (AFRP). It was stated that the large oscillations
of the thrust force while drilling AFRP might be
attributed to the inhomogeneity inside the single
lamina and to the presence of interfaces in between
the laminate. These oscillations can be interpreted as
non-uniform distribution of the thrust force along the
tool cutting edge and the poor inter-laminar strength
of the composites that can cause piercing effects at the
interfaces. The tool material and tool design have also
been found to influence the drilling process in the
context of fibrous composites.
The present research initiative is an attempt to
investigate the relative significance of the drilling
parameters such as point angle, spindle speed and
feed rate on the thrust force and torque using response
464
INDIAN J. ENG. MATER. SCI., DECEMBER 2010
surface methodology (RSM). A series of experiments
were conducted using computer numerical control
(CNC) milling machine to drill the glass fiber
reinforced composites. A drill tool dynamometer was
used to record the thrust force and torque. In this
work, thrust force and torque were taken as response
variables (output variables) and point angle, cutting
speed and feed rate were taken as input variables.
Mechanical Properties of E-glass-Polyester composites
The specimen used in this study was made of glass
fiber reinforced composite material. E glass/polyester
specimens of 3 mm thickness were prepared using the
hand lay-up process. The reinforcement was in the
form of E-glass fiber and the matrix was polyester. A
gel coat was applied on the mould prior to the lay-up
process to facilitate easy removal of the laminate.
Specimens were cured at room temperature for 24 h in
ambient conditions. After fabrication the test
specimens were subjected to mechanical tests as per
ASTM standards. The standards followed were
ASTM D638 & ASTM D790 for tensile tests and
flexural tests respectively. To obtain a statistically
significant result for each condition, five specimens
were tested to evaluate the mechanical properties. The
average tensile strength is 306.68 MPa and flexural
strength is 194.75 MPa.
Experimental Procedure
The standard high-speed steel twist drill of 6 mm
diameter with different point angles was used in the
present investigation. Drilling operations were carried
out on a MTAB make MAXMILL CNC machining
center using HSS twist drill bit. Sensing signaled
[thrust force (0-5000 N) and torque (500 Nm)] were
measured using drill tool dynamometer (Make: IEIOS
Model: 651).The photograph of experimental set-up is
shown in Fig. 1.
Response surface methodology
RSM is the procedure for determining the
relationship between various parameters and with the
various machining criteria and exploring the effect of
these process parameters on the coupled responses.
The steps involved in this research work for the
experimental investigation include the following :
(i) identifying the important process control variables,
(ii) finding the upper and lower limits of the control
variables, viz., point angle (p), spindle speed (s), and
feed rate (f), (iii) developing of the design matrix
using box-behnken design and conducting the
experiments as per the design matrix, (iv) recording
the responses, viz., thrust force (th) and torque (tq),
(v) the development of mathematical models,
(vi) calculating the coefficients of the second order
polynomials, (vii) checking the adequacy of the
models developed, (viii) testing the significance of the
regression coefficients, (ix) presenting the main
effects and the significant interaction effects of the
process parameters on the responses in two and three
dimensional (3D surface, 3Dcube, interaction and
contour plots) graphical form and (x) optimization of
parameters for minimum value of responses.
Design of experiments
Design of experiments, or experimental design, is
the design of all information-gathering exercises
where variation is present, whether under the full
control of the experimenter or not. The response
variables, thrust force and torque were recorded for
each run using drill tool dynamometer. The effect of
the machining parameters is another important aspect
to be considered. The detail of control variables and
their levels (low, medium and high) used in the
experiment are shown in Table 1. For getting quality
holes and delamination free holes the levels were
selected based on the literatures. For planning of
experiments Box-Behnken design was preferred
because it was mostly used for 3 level factorial
designs. According to one block of Box-Behnken
Table 1Assignment of the levels to the factors
Level Point angle (°) Spindle speed (rpm) Feed rate (mm/rev)
Fig. 1Photographic view of experimental set-up
-1
0
+1
90
104
118
600
1200
1800
0.1
0.2
0.3
JAYABAL & NATARAJAN: DRILLING OF GLASS FIBER REINFORCED COMPOSITES
design 12 runs were carried out. The schematic of Box
Behnken design is shown in Fig. 2. The thrust force
and torque values of responses measured using drill
tool dynamometer for each run are given in Table.2.
Nonlinear regression analysis
In statistics, nonlinear regression is a form of
regression analysis in which observational data are
modeled by a function which is a nonlinear combination
of the model parameters and depends on one or more
independent variables. The data are fitted by a method of
successive approximations. The statistical tool,
regression analysis helps to estimate the value of one
variable from the given value of another. The process
variables in this response surface modeling are:
x1u = p = point angle in degrees
x2u = s =spindle speed in rpm
x3u = f = feed rate in mm/rev
The response variables in this response surface
modelingare: yu =th or tq where th = thrust force and tq
= torque.
Results and Discussion
Coefficient of determination
In statistics, the coefficient of determination, R2 is
used in the context of statistical models whose main
purpose is the prediction of future outcomes on the
basis of other related information. It is the proportion
of variability in a data set that is accounted for by the
statistical model. It provided a measure of how well
future outcomes are likely to be predicted by the
model. There are several different definitions of R2
which are only sometimes equivalent. One class of
such cases includes that of linear regression. In this
case, R2 is simply the square of the sample correlation
coefficient between the outcomes and their predicted
values, or in the case simple linear regression,
between the outcome and the values being used for
Fig. 2Basic Box-Behnken design of 3 factors
465
prediction. In such cases, the values varied from
0 to 1. An R2 of 1.0 indicated that the regression line
perfectly fits the data. It is important to note that
values of R2 outside the range 0 to 1 occurred where it
was used to measure the agreement between observed
and modeled values and where the "modeled" values
are not obtained by linear regression and depending
on which formulation of R2 is used. R-squared
adjusted for the number of parameters in the model
relative to the number of points in the design.
A measure of the amount of variation is the mean
explained by the model. Both the R-squared and
related adjusted R-squared statistics should be close to
one. A value of 1.0 represents the ideal case at which
100 percent of the variation in the observed values
can be explained by the chosen model. The predicted
R-squared estimates the amount of variation in new
data explained by the model. It can be negative, but
this is very bad and suggests that the model consisting
of only the intercept is a better predictor of the
response than this model. The closer to 1.0, the better
the predicted R-squared. Predicted residual error sum
of squares (PRESS), indicates how well the model fits
the data. The PRESS for the chosen model should be
small relative to the other models under consideration.
Predicted R-squared is a measure of how good the
model predicts a response value. It is computed as
… (1)
1 - (PRESS/(SSmodel + SSresidual))
The adjusted R-squared and predicted R-squared
should be within approximately 0.20 of each other to
be in "reasonable agreement. The multiple correlation
coefficients computed as
Table 2 12 runs of box-Behnken design
Run
Point
Spindle
angle (°) speed (rpm)
Feed rate
Thrust
(mm/rev) force (N)
Torque
(N-Cm)
1
2
90
90
1200
600
0.1
0.2
61.5
107
34
46.8
3
90
1800
4
90
1200
0.2
107
46.8
0.3
152.1
73.6
5
104
6
104
600
0.1
81.6
27.8
1800
0.1
81.6
27.8
7
104
1800
0.3
152.1
73.6
8
104
600
0.3
172.2
66.9
9
118
1200
0.1
101.7
21.5
10
118
600
0.2
147.2
33.8
11
118
1800
0.2
147.2
33.8
12
118
1200
0.3
192.3
60.1
466
1-SSresidual/(SSmodel + SSresidual)]
INDIAN J. ENG. MATER. SCI., DECEMBER 2010
… (2)
Adequate precision is a measure of the range in
predicted response relative to its associated error, in
other words a signal-to-noise ratio. Its desired value is
4 or more.
Mathematical models
The best model for the given set of data was
suggested on the basis of fit summary (F-probability).
The F-value was used to test the significance of adding
new model terms to those terms already in the model A
small p-value (probability >F) indicated that adding
terms had improved the model. The mathematical
relationship for correlating the responses thrust force
(th) and torque (tq) and the considered process variables
were obtained from the coeffients resulting from
MINITAB 15 software. R-Squared value for thrust
force is 99.1% and for torque is 99.4%
th = 161 - 4.11 p + 0.0112 s + 528 f - 0.0838 sf +
0.0267 p2 + 0.000001 s2 … (3)
tq = - 445 + 8.83 p + 0.0425 s + 189 f + 0.0279 sf –
0.179 fp - 0.0445 p2 - 0.000019 s2
… (4)
Figure 3 shows the comparison graph from which
the closeness of experimental values are observed.
Analysis of variance (ANOVA)
The initial techniques of the analysis of variance
were developed by the statistician and geneticist R A
Fisher in the 1920s and 1930s, and is sometimes
known as Fisher's ANOVA or Fisher's analysis of
variance, due to the use of Fisher's F-distribution as
part of the test of statistical . Analysis of variance
(ANOVA) is a collection of statistical models, and
their associated procedures, in which the observed
variance is partitioned into components due to different
explanatory variables. Degrees of freedom are used to
describe the number of values in the final calculation of
a statistic that are free to vary. Estimates of statistical
parameters were based on different amounts of
information or data. The number of independent pieces
of information that go into the estimate of a parameter
is called the degrees of freedom. In general, the degrees
of freedom of an estimate is equal to the number of
independent scores that go into the estimate minus the
number of parameters estimated as intermediate steps
in the estimation of the parameter itself. The mean
squared error (MSE) of an estimator is one of many
ways to quantify the amount by which an estimator
differs from the true value of the quantity being
estimated. As a loss function, MSE is called squared
error loss. MSE measures the average of the square of
the "error." The error is the amount by which the
estimator differs from the quantity to be estimated. The
difference occurs because of randomness or because
the estimator doesn't account for information that could
produce a more accurate estimate. Mathematically,
degrees of freedom are the dimension of the domain of
a random vector, or essentially the number of 'free'
components: how many components need to be known
before the vector is fully determined.This design
consisted of three factors, each at three levels.
Fig. 3Comparison of actual and predicted responses
JAYABAL & NATARAJAN: DRILLING OF GLASS FIBER REINFORCED COMPOSITES
The analysis of variance (ANOVA) of the
experimental data was done to statistically analyze
the relative significance of the parameters, point
angle (p), speed (s) and feed rate (f), under
investigation on the response variables, the thrust
force and the torque. The detailed analysis of
variance (ANOVA) of the experimental data gave
the valuable information regarding the significance
of the factors under study on the thrust force and the
torque. The point angle and the speed are the two
significant factors that influence the thrust force in
the experimental domain. The torque is affected by
the point angle, feed rate and the interaction of the
two. The significant factors and their interactions
were then used to develop predictive equations for
the thrust force and the torque using the regression
analysis. It was evident that the thrust and torque
models fit the experimental data reasonably well and
can be used to predict the drilling forces while
467
drilling glass fiber reinforced (GFR) composite
laminates. It has hereby been proven statistically that
it is the speed and the drill point angle that
significantly affect the drilling forces while drilling
fiber reinforced polyester composite materials.
ANOVA for thrust force model
The Model F-value of 67.18 implies the model is
significant. There is only a 0.27% chance that a
"Model F-Value" this large could occur due to noise.
If there are many insignificant model terms model
reduction may improve the model. The ANOVA table
for thrust force model is shown in Table 3.
ANOVA for torque model
The Model F-value of 126.13 implies the model
was significant. There is only a 0.11% chance that a
"Model F-Value" this large could occur due to noise.
The ANOVA table for thrust force model is shown in
Table 4.
Table 3–ANOVA for thrust force model
Source
Sum of squares
Degrees of freedom
Mean square
F value
p-value probability > F
Model
18112.79
8
2264.099
67.18193
0.0027
p
3235.297
1
3235.297
96
0.0023
s
50.55151
1
50.55151
1.5
0.3081
f
14655.58
1
14655.58
434.8705
0.0002
p-s
0
1
0
0
1.0000
p-f
0
1
0
0
1.0000
s-f
101.103
1
101.103
3
0.1817
2
54.75811
1
54.75811
1.624821
0.2922
2
s
0.08405
1
0.08405
0.002494
0.9633
f2
0
0
p
Table 4 ANOVA for torque model
Source
Sum of squares
Degrees of freedom
Mean square
F-value
p-value probability > F
Model
3854.207
8
481.7759
126.1339362
0.0011
p
338.2601
1
338.2601
88.55999057
0.0025
s
5.661613
1
5.661613
1.482268892
0.3104
f
3328.056
1
3328.056
871.3196192
< 0.0001
p-s
0
1
0
0
1.0000
p-f
0.3136
1
0.3136
0.082103734
0.7931
s-f
11.32323
1
11.32323
2.964537785
0.1836
2
151.9896
1
151.9896
39.79245746
0.0081
s2
98
1
98
25.65741676
0.0149
f2
0
0
p
INDIAN J. ENG. MATER. SCI., DECEMBER 2010
468
Variance of design
The standard error plot also called variance of
design plot is shown in Fig. 4. These evaluation
graphs were used to understand the prediction error of
the design. Since these plots are generated before any
data is collected, a standard deviation of 1 is used to
calculate relative prediction error. In statistics, the
variance inflation factor (VIF) is a method of
detecting the severity of multicollinearity. More
precisely, the VIF is an index which measures how
much the variance of a coefficient (square of the
standard deviation) is increased because of colinearity. Ideal VIF is 1.0. VIF's above 10 are cause
for alarm, indicating coefficients are poorly estimated
due to multicollinearity. Ideal Ri-squared is 0.0. High
Ri-squared means terms are correlated with each
other, possibly leading to poor models. If the design
has multilinear constraints multicollinearity will exist
to a greater degree. The presence of multicollinearity
increases the VIF’s and the Ri-squareds. Due to
imposed constraints, the design was only valid for a
limited set of combinations. High VIF’s and high Risquareds were less of a concern. Power is an
inappropriate tool to evaluate response surface
designs. The variance of design for thrust force and
torque models are given in Tables 5 and 6.
Table 5
 Variance of design for thrust force model
Standard error
95% CI Low
Factor
Degrees of freedom
Intercept
1
5.0275
p
1
s
f
1
1
p-s
p-f
95% CI High
VIF
105.6627371
137.6623
2.052468
13.57812414
26.64188
1
2.052468
2.052468
-9.045625865
36.26937414
4.018126
49.33313
1
1
1
2.902628
-9.237467436
9.237467
1
1
2.902628
-9.237467436
9.237467
1
s-f
1
2.902628
-14.26496744
4.209967
1
2
1
4.104937
-7.83125173
18.29625
1.333333
2
1
0
4.104937
0
-12.85875173
13.26875
1.333333
p
s
f2
Table 6
 Variance of design for torque model
Factor
Degrees of freedom
Standard error
95% CI Low
95% CI High
VIF
Intercept
p
1
1
1.692533
0.690974
50.6410991
-8.701488958
61.4139
-4.30351
1
s
f
p-s
p-f
s-f
1
1
1
1
1
0.690974
0.690974
0.977185
0.977185
0.977185
-1.357738958
18.19726104
-3.109840008
-3.389840008
-1.427340008
3.040239
22.59524
3.10984
2.82984
4.79234
1
1
1
1
1
p2
1
1.381948
-13.11547792
-4.31952
1.333333
2
1
1.381948
-11.39797792
-2.60202
1.333333
s
Fig. 4Plot of Standard error design
JAYABAL & NATARAJAN: DRILLING OF GLASS FIBER REINFORCED COMPOSITES
Optimization of parameters
Indirect optimization based on self organization
(IOSO) is based on the response surface
methodology approach. At each IOSO iteration the
internally constructed response surface model for the
objective is being optimized within the current
search region. This step is followed by a direct call
to the actual mathematical model of the system for
the candidate optimal point obtained from
optimizing internal response surface model. During
IOSO operation, the information about the system
behavior is stored for the points in the neighborhood
of the extreme, so that the response surface model
becomes more accurate for this search area. The
following steps are internally taken while proceeding
from one IOSO iteration to another: (i) the
modification of the experiment plan, (ii) the adaptive
adjustment of the current search area, (iii) the
function type choice (global or middle-range) for the
response surface model, (iv) the adjustment of the
response surface model and (v) the modification of
parameters and structure of the optimization
469
algorithms; if necessary, the selection of the new
promising points within the search area.
Statistical package Design Expert 7.1.6 was used to
find the optimum parameters using IOSO. The
optimized parameters for minimum thrust force and
torque are shown in Table 7. The 3D response surface
plot for thrust force and torque model are shown in
Figs 5 and 6.
Quality of drilled holes
The quality of holes produced by drilling was
studied using the images taken by Rapid I Machine
vision system. Based on the images, the drilling
delamination factor is determined by the ratio of the
delaminated area (Ad) of the delamination zone to the
ideal hole area (A). The schematic diagram of
delamination analysis is shown in Fig. 7. The value of
delamination factor for optimum condition is 1.152
which is lower than the 12 set of experiments and the
image of drilled hole is shown in Fig. 8. The maximum
value of delamination factor is 2.30 and this was
obtained for maximum thrust force and torque values.
Table 7 Optimum parameters
Point angle (°)
Spindle speed (rpm)
Feed rate (mm/rev)
Thrust force (N)
Torque (N-Cm)
Desirability
90
615
0.10
61.75
27.33
0.94
Fig. 53D surface plot of thrust force
Fig. 63D surface plot of torque
470
INDIAN J. ENG. MATER. SCI., DECEMBER 2010
Fig. 7Schematic diagram of delamination analysis
Conclusions
Three main effects were p, s and f, second-order
effects were p2, s2 and f2 and interaction effects were
ps, sf and fp. All the terms were included in the
mathematical model of responses for getting
minimum standard error. Quadratic model was
suggested based on F test for thrustforce and torque
models. Response surface approach has been
proposed to study the drilling characteristics of Eglass/polyester composite laminates. The following
conclusions can be drawn from this study:
(i) The thrust force depends on the drill point
angle, speed and the feed rate and increases
with the increase of point angle and feed rate.
It was proven statistically using ANOVA that
speed and feed rate interactions significantly
influenced the drilling forces.
(ii) The torque also depends on the drill point
angle, speed and the feed rate and increases
with the increase of point angle and feed rate.
It was proven statistically using ANOVA that
the interactions between point angle and feed
rate and speed and feed rate were
significantly influenced the drilling forces.
Fig. 8Photograph of drilled hole for optimum conditions
(iii) Predictive models for thrust force and torque
were proposed (Eqs (3) and (4)) correlating
the significant factors. It was observed that
90° drill point angle gives better results as
compared to 104° and 118°.
Acknowledgement
Authors thank S Guru Sideswar, Indian Institute of
Technology, Chennai for helping in fabrication and
experimentation works.
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