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Optimization of Cutting Parameters for ImprovingMachining Quality Andproduction Rate in Drilling ofCFRP CompositesQian Wang ( [email protected] )
Northwestern Polytechnical UniversityXiaoliang Jia
Northwestern Polytechnical University https://orcid.org/0000-0003-2108-1738
Research Article
Keywords: Multi-objective optimization, Hole quality, Production e�ciency, NSGA-, Decision schemes
Posted Date: May 24th, 2021
DOI: https://doi.org/10.21203/rs.3.rs-479219/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Optimization of cutting parameters for improving machining quality and
production rate in drilling of CFRP composites
Qian Wang, Xiaoliang Jia
School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
Abstract
Carbon fiber reinforced polymer (CFRP) composites need to be machined by operations like trimming,
reaming and drilling for the dimensional tolerance and final assembly. This paper presents a cutting
parameters optimization method for drilling of CFRP composites to improve hole quality and
production efficiency. Hole quality indicators including exit delamination and average surface
roughness are expressed as functions of cutting parameters based on the regression analysis of
experimental data. Multi-objective optimization of cutting parameters for decreasing exit delamination
and surface roughness, increasing material removal rate is accomplished with non-dominated sorting
genetic algorithm Ⅱ (NSGA-Ⅱ). Optimization results are large numbers of Pareto optimal solutions
widely distributed in the objective space, the reliability of Pareto optimal solutions is checked with the
global convergence and spacing distance. Moreover, posterior analysis is implemented to identify key
solutions of better performance from the Pareto optimal solutions to facilitate the decision-making.
Results show that the identified key solutions are capable of achieving satisfactory drilling
performances with different preferences for exit delamination, surface roughness and material removal
rate. This study provides a feasible way to determine the appropriate cutting parameters, with which
demands for multiple responses could be satisfied simultaneously in practical machining operations.
Keywords: Multi-objective optimization; Hole quality; Production efficiency; NSGA-Ⅱ; Decision
schemes.
1. Introduction
CFRP composites have extensive applications in aeronautical and aerospace industries owing to their
excellent properties such as high strength and stiffness-to-weight ratios, fatigue and corrosion
resistance [1-3]. CFRP composites are fabricated to near-net shape by processes such as hand lay-up,
pultrusion, compression moulding, filament winding etc., however, secondary machining processes like
trimming, reaming and drilling are still needed to be performed afterwards for the dimensional
Corresponding author
E-mail addresses: [email protected] (Xiaoliang Jia)
tolerance and final assembly [4, 5]. Drilling is one common post-machining operation for CFRP
composites to produce holes for the fastening of parts by riveting or bolting [6]. The peculiar
anisotropic and inhomogeneous characteristics of CFRP composites make them one of those
difficult-to-machine materials, the material removal mechanisms in machining of CFRP composites are
distinct from those in machining of homogeneous materials. Different modes of machining damage are
exhibited in drilling of CFRP composites, the most frequently induced defects include fiber-matrix
de-bonding, burr, delamination and matrix burning [7, 8].
Many attempts have been made to examine the behaviors of drilling responses under different
cutting conditions, the generally considered out-put responses are thrust force, torque, quality
characteristics, tool wear and efficiency. Eneyew and Ramulu [9] conducted an experimental
investigation on unidirectional CFRP laminates using polycrystalline diamond drill, with aims to
analyze the effects of cutting parameters on thrust force, torque, entry delamination, exit delamination
and surface roughness. It is found that the minimum thrust force, delamination and better surface
quality is obtained with a combination of higher cutting speed and lower feed rate. Tsao and Hocheng
[10] carried out a Taguchi orthogonal array for drilling of woven CFRP composites using candle stick
drill under dry cutting condition. Experimental results show that feed rate and drill diameter contribute
significantly to thrust force and surface roughness, while spindle speed only has strong impact on
surface roughness. Krishnamoorthy et al. [11] combined the grey relational analysis with fuzzy logic
approach to determine the optimum combination of spindle speed, point angle and feed rate for good
hole quality. Five out-put performance characteristics including thrust force, torque, entry delamination,
exit delamination and eccentricity of holes are integrated into one quality metric by weighting method.
Ameur et al. [12] experimentally examined the performances of thrust force, torque, exit delamination
and cylindricity error at different spindle speeds and feed rates using drills of different materials.
Response surface methodology (RSM) is used to correlate the cutting parameters and out-put responses
for different drills. The optimal values of cutting parameters, the desired tool material are found based
on the desirability function approach and Design-Expert software. Romoli and Lutey [13] investigated
the influences of cutting speed and feed rate on thrust force, tool flank wear and exit delamination in
drilling of CFRP composites using high-speed steel drill bits. A quality monitoring and control strategy
is proposed by predicting exit delamination in terms of thrust force and tool wear measurement using a
fuzzy logic algorithm, feed rate is controlled based on the predicted exit delamination to ensure
acceptable machining quality over the entire lifespan of tool.
Some researchers employed heuristic algorithms to find the optimal cutting conditions for drilling
performance improvement. Krishnaraj et al. [14] employed a full factorial experiment for high speed
drilling of woven CFRP laminates to investigate the effects of spindle speed and feed rate on hole
quality characteristics including hole diameter, circularity, entry delamination and exit delamination. A
multiple objective function is formulated by introducing weight coefficients to regression models of
quality characteristics, the optimal cutting parameters for defect free drilling are obtained based on
genetic algorithm (GA). Abhishek et al. [15] optimized the cutting speed, drill diameter and feed rate to
improve drilling performance of CFRP laminates. Multiple performance characteristics, namely thrust
force, torque, surface roughness and delamination factor (both at entry and exit) are aggregated into
one equivalent performance index using a fuzzy inference system. A non-linear regression model is
developed to correlate the performance index with cutting parameters, and harmony search (HS)
algorithm is employed to determine the optimal cutting condition for the performance index.
Shahrajabian and Farahnakian [16] presented a methodology to optimize the cutting parameters
(spindle speed, feed rate and point angle) during the drilling process of CFRP composites for
maximizing material removal rate, with the constraints of surface roughness, delamination and thrust
force. Response surface method (RSM) is applied to construct the models of objective and constraints
based on experimental data, and genetic algorithm (GA) is used to identify the optimum combination
of cutting parameters.
Delamination causes severe structural damage of materials and considerable performance
deteriorations of mechanical parts [6, 17], it results in rejections of parts during the final assembly of an
aircraft [18] and causes significant economic loss in the aircraft industry. Surface roughness is one
important indicator for machined surface quality [19], components with low surface roughness are
desired in real productions to meet with the requirements in dimensional and geometric tolerance [20].
Given the fact that cutting parameters can significantly affect delamination [14, 15, 21], surface
roughness [22, 23] and production efficiency in drilling of CFRP composites, this paper optimizes the
cutting parameters for decreasing exit delamination and surface roughness, increasing material removal
rate. Firstly, exit delamination and average surface roughness at different spindle speeds and feed rates
are examined with drilling tests. Experimental data are subjected to analysis of variance (ANOVA) to
determine the effects of cutting parameters on out-put responses. Secondly, regression analysis is
performed to express delamination factor and average surface roughness as functions of cutting
parameters. Multi-objective optimization is accomplished with NSGA-Ⅱ to find the Pareto optimal
solutions determined by exit delamination, surface roughness and material removal rate. The
performance of NSGA-Ⅱ is validated with global convergence and spacing distance to ensure the
quality of Pareto optimal solutions. Finally, posterior analysis is implemented to identify key solution
from the large numbers of Pareto optimal solutions taking into account decision makers’ preferences
for drilling responses. Results show that the identified key solutions can be applied in practical
machining operations to achieve the desired overall performance involving multiple responses.
Overview of the research procedure is shown in Fig. 1.
Fig. 1. Overview of research procedure in this study.
2. Experimental study
A full factorial experiment is carried out on multi-directional CFRP composite without coolant to
examine the influences of cutting parameters upon exit delamination and surface roughness, the ranges
of spindle speed n and feed rate f are represented in Table 1. Drilling tests are performed with
YG8 cemented carbide twist drills, the geometrical specifications of drills are listed in Table 2. Twist
drill is replaced with a new one after drilling five holes to avoid the tool wear. Three holes are drilled
under each cutting condition and the average of measured values is calculated as the final results to
ensure the consistency of data. The composite is made of T700 carbon fiber and epoxy resin, the fiber
volume fraction is 75% and the Poisson ratio is 0.34. The composite has a thickness of 5 mm and is
stacked in the sequence of [90°/-45°/0°/45°/90°]4s.
Table 1
Ranges of the cutting parameters for the full factorial experiment.
Spindle speed n (rpm) Feed rate f (mm/rev)
1500, 2000, 2500, 3000, 3500 0.03, 0.06, 0.09, 0.12, 0.15
Table 2
Geometrical specifications of twist drills.
Diameter
(mm)
Width of chisel
edge (mm)
Point angle
(°)
Helix angle
(°)
Shank length
(mm)
Working
length (mm)
Overall length
(mm)
6 0.2 118 30 32 30 62
2.1. Exit delamination
As drill approaches the exit of hole, the stiffness of remaining plies under the drill may be
insufficient to resist the applied thrust force. Once the thrust force exceeds the interface bonding
strength of composites, interfacial de-bonding occurs and delamination is generated in these
de-bonding areas [8, 24]. Exit delamination is examined using the microscope, and the size of
delamination is quantified by delamination factor d outF given as [25]:
2
max max1d out
nom nom
D DF
D D
(1)
max
4dam
nom
A
D D
(2)
The hole diameter nomD , maximum diameter of delamination area maxD and actual delamination
area damA are illustrated in Fig. 2, maxD and dam
A are measured by image analyses using the
ImageJ software.
Fig. 2. Schematic of delamination at hole exit.
2.2. Surface roughness
Average surface roughness aR of machined holes is measured using a portable surface roughness
tester MarSurf M300C produced by Mahr company. The measurements are carried out at three depths
along the feed direction, namely at the entry of hole, at the middle of hole and at the exit of hole. At the
same depth, aR is measured at four positions on the circumference of hole wall and three
measurements are done at each position to ensure reliable results. The value of aR at each depth is the
average value of measurements done at four positions. It is found that the worst surface damage is
produced at hole exit with the largest value of aR , thus a
R at hole exit is considered to represent the
surface quality of machined holes.
2.3. Analysis of experimental results
Experimental results of delamination factor d outF and average surface roughness a
R under
different cutting conditions are presented in Table 3.
Table 3
Experimental results of delamination factor d outF , average surface roughness aR in the full factorial experiment.
Test
No.
n
(rpm)
f
(mm/rev) d outF aR
(µm) Test
No.
n
(rpm)
f
(mm/rev) d outF aR
(µm)
1 1500 0.03 1.3440 1.707 14 2500 0.12 1.4533 3.355
2 1500 0.06 1.3958 2.181 15 2500 0.15 1.5125 3.724
3 1500 0.09 1.4211 2.524 16 3000 0.03 1.3354 2.384
4 1500 0.12 1.5092 2.880 17 3000 0.06 1.3676 2.837
5 1500 0.15 1.5414 3.382 18 3000 0.09 1.4264 3.276
6 2000 0.03 1.3276 1.985 19 3000 0.12 1.4574 3.486
7 2000 0.06 1.3998 2.250 20 3000 0.15 1.5194 3.659
8 2000 0.09 1.4202 2.604 21 3500 0.03 1.3060 2.615
9 2000 0.12 1.4819 3.096 22 3500 0.06 1.3472 3.276
10 2000 0.15 1.5496 3.510 23 3500 0.09 1.4056 3.550
11 2500 0.03 1.3191 2.240 24 3500 0.12 1.4602 3.692
12 2500 0.06 1.3950 2.508 25 3500 0.15 1.4980 4.000
13 2500 0.09 1.4268 3.038
Table 4 presents the results of analysis of variance (ANOVA) for delamination factor and average
surface roughness. It is found that feed rate has a predominant influence on delamination and accounts
for a large contribution of 93.74%, while the effect of spindle speed on delamination is insignificant.
Both feed rate and spindle speed have strong impacts on average surface roughness, contributing by
70.39% and 26.27% respectively.
Table 4
Analysis of variance (ANOVA) for delamination factor and average surface roughness.
Delamination factor d outF
Source DF SS MS F-Value P-Value Percentage contribution (%) n 4 0.0046 0.0011 6.8320 0.0021 3.09
f 4 0.1188 0.0297 178.2774 0 93.74
Error 16 0.0026 0.0002 3.17
Total 24 0.1260 100
Average surface roughness aR
Source DF SS MS F-Value P-Value Percentage contribution (%) n 4 2.4984 0.6246 48.1774 0 26.27
f 4 6.6064 1.6516 127.3948 0 70.39
Error 16 0.2074 0.0130 3.34
Total 24 9.3122 100
DF: Degree of freedom, SS: Sum of squares, MS: Mean square, F-Value: a ratio of two variances,
P-Value: Probability.
The variations of delamination factor and average surface roughness at different combinations of
spindle speed and feed rate are shown in Fig. 3. Fig. 3(a) indicates that more severe delamination is
observed at exit of holes drilled at larger feed rate. More material is removed in per revolution of drill
as feed rate elevates, this would lead to increased thrust force and deteriorated delamination. A minor
reduction of delamination is observed in some tests of higher spindle speed. More cutting heat and
friction heat are generated in the machining area and causes the softening of matrix, this makes the
removal of material easier and thus delamination is reduced.
Fig. 3. Experimental results of drilling responses under different cutting conditions
(a) delamination factor; (b) average surface roughness.
Fig. 3(b) shows that good surface quality is produced at the combinations of low feed rate and
spindle speed. The change of removal mechanism accounts for the different surface quality at different
feed rates. A complete shearing of fibers from the matrix at low feed rate leads to better surface finish
(low surface roughness), the removal of fibers from matrix is partially sheared at high feed rate and
results in worse surface finish (high surface roughness) [26]. The interfacial adhesion between fibers
and matrix weakens due to the softening of matrix caused by temperature elevation at higher spindle
speed, fiber pull-out is more likely to occur and worse surface finish is produced.
3. Multi-objective optimization via Pareto optimality
3.1. Formulation of optimization model
The multi-objective optimization model for improving hole quality and production efficiency in
drilling of CFRP composites is presented with Eq. (3). d outF , a
R are the hole quality indicators
representing exit delamination and average surface roughness, MRR is the material removal rate and
is used as the index for production efficiency.
1500 3500
0 03 0 15
min F , , , , , ,
. .
. .
d out an f F n f R n f MRR n f
s t
n
f
(3)
The upper and lower bounds of spindle speed n and feed rate f are identical with their
maximum and minimum values in the full factorial experiment. The expressions of d outF and a
R
are presented with Eqs. (4) and (5), which are determined using the linear least squares fitting method
based on experimental data in Table 3. The established regression models are capable of producing
accurate predictions since they both give statistically significant values of R2. MRR in drilling
operation can be calculated with Eq. (6).
2
2 2
1.301 1.125 6 1.665 2.378 9 6.066 5
0.6088 (R =0.9755)
d outF e n f e n e nf
f
(4)
2
2 2
0.5353 3.623 4 19.37 4.554 8 1.615 3
17.98 (R =0.9812)
aR e n f e n e nf
f
(5)
2
MRR R nf (6)
Fig. 4. Comparisons of experimental results and predicted values of regression models.
Fig. 4 shows that the predicted values of delamination factor and average surface roughness are both
in reasonable agreements with experimental data under cutting conditions in the full factorial
experiment. To testify the robustness of regression models, drilling tests are conducted with cutting
parameters different from those in the full factorial experiment. The results of verification tests are
given in Table 5. The predicted values are very close to the experimental results, the average relative
error is 1.76% for d outF and 4.26% for a
R . This proves that the regression models of d outF and
aR are able to give satisfactory predictions for cutting conditions not given by the full factorial
experiment.
Table 5
Results of the validation tests for the regression models.
Test
No.
n
(rpm)
f
(mm/rev)
Experimental Predicted Relative error (%)
d outF aR (μm) d outF aR (μm) d outF aR (μm)
1 1800 0.04 1.3677 1.857 1.3545 1.965 0.97 5.82
2 2100 0.07 1.3708 2.599 1.3988 2.527 2.04 2.77
3 2400 0.14 1.4944 3.643 1.5093 3.484 1.00 4.36
4 2800 0.11 1.4285 3.194 1.4510 3.322 1.58 4.01
5 3100 0.08 1.4298 2.984 1.3967 3.130 2.32 4.89
6 3400 0.13 1.4313 3.939 1.4696 3.794 2.68 3.68
3.2. Pareto optimality
Most practical situations require the possible optima of multiple objectives depending on the same
influential factors. But rarely the same factors can achieve the best possible values for all the objectives
being optimized [27], the improvement of one objective may lead to the performance worsening of
other objectives. As for drilling of CFRP composites, exit delamination and surface roughness are two
important quality indicators, and material removal rate needs to be improved for cost-saving. Exit
delamination, surface roughness and material removal rate can’t reach their optimum values under the
same cutting condition, for instance, high spindle speed would leads to worse surface finish, while it
would be beneficial for reducing the exit delamination and improving the material removal rate
according to 2MRR R nf .
The traditional method reduces the dimension of objectives by converting the multiple objectives
into one equivalent objective, it searches for a single optimal solution for the equivalent objective.
Although this method is simple to implement but it fails to take into account the multiple criteria of
objectives, and the final optimal solution is very sensitive to the adopted dimensionality reduction
techniques.
The ideal method to handle a multi-objective optimization would be to generate many Pareto optimal
solutions, constructing a point-wise approximation to the Pareto front [28]. Pareto optimal solutions are
non-dominated solutions that are characterized by the fact that no objective can be improved without
compromising other objectives. Let 1 2( , ,..., )
i l ix x xx be a vector that contains l influential factors,
1 2( , ,..., )i i M i
y y y y F x is the objective values corresponding to ix . Suppose that all objectives
( 2)M M need to be minimized, it is said that ix dominates jx when
ix performs not worse
than jx in all objectives and outperform
jx in at least one objective. If there is no solution
dominating ix , i
x is a non-dominated solution and the corresponding i
y is a Pareto optimal solution.
Pareto optimal solution represents the global optimal performance with tradeoffs among objectives, the
set of Pareto optimal solutions forms the Pareto front in the objective space. Since Pareto front contains
all possible tradeoffs considering the different performances of objectives, it is more suitable to be the
results of optimization involving multiple objectives.
3.3. Optimization algorithm (NSGA-Ⅱ)
Many multi-objective evolutionary algorithms have been proposed to find the Pareto front,
non-dominated sorting genetic algorithm (NSGA) is one of the first proposed algorithms and is able to
to find multiple Pareto optimal solutions [29]. However, NSGA has shortcoming of high computational
complexity, lack of elitism and the need for specifying the sharing parameter [30]. To handle these
issues, NSGA-Ⅱ is proposed later as an improved version of NSGA, it introduces elite-preserving
mechanism and has been proved to be capable of finding diverse solutions well converged towards the
true Pareto front. To this end, NSGA-Ⅱ is applied to solve the optimization model for minimizing exit
delamination and surface roughness, maximizing material removal rate.
The initial population (including s individuals) is generated based on real coding given the lower
and upper bounds of spindle speed n and feed rate f . The randomly generated values are modified
to discrete values available for CNC machine, the interval is 50 rpm for n , 0.01 mm/rev for f .
All individuals in the initial population are sorted on the basis of elite-preserving mechanism, and
top 80% individuals are selected as the superior ones to form the parent population. Then the offspring
population is created by executing crossover and mutation operations to the parent population. The
parent and offspring populations are combined into the new population, from which superior
individuals are again selected to generate the parent population. The algorithm stops when it reaches
the maximum number of iterations. The cutting parameters optimization procedure based on NSGA-Ⅱ
is illustrated in Fig. 5.
Fig. 5. Cutting parameters optimization procedure based on NSGA-Ⅱ.
3.3.1. Elite-preserving mechanism
Elite-preserving mechanism is adopted in NSGA-Ⅱ to ensure the diversity of individuals and to
enhance the convergence of algorithm. In NSGA-Ⅱ, the individuals in the population are first sorted
by the non-domination rank based on the concept of dominance and then compared by the crowding
distance. Non-dominated solutions in the population are grouped into the first non-dominated front and
given the lowest non-domination rank. Solutions in the first front are discarded temporarily from the
population, and non-dominated solutions in the reduced population are grouped into the second
non-dominated front and given the second lowest non-domination rank. This sorting procedure is
repeated until all solutions are given a non-domination rank. Solutions of lower rank are prior to those
of higher rank. The crowding distance is introduced to compare the solutions in each non-domination
rank, it measures the density of solutions surrounding each solution. A solution with larger crowding
distance normally lies in a more sparse area and is given priority to ensure the diversity of population.
3.4. Optimization results
3.4.1. Evaluation of algorithm performance
The size of initial population (s), iteration times (τ), cross probability (pc) and mutation probability
(pm) would affect the convergence of algorithm and the quality of solutions. Several trials are made
with different algorithm parameters aiming at obtaining desired optimization results, two evaluation
metrics are applied to evaluate the performance of algorithm. The reliable and satisfactory Pareto
optimal solutions are found with parameters setting: s=250, τ=100, pc=0.9, pm=0.5.
(1) Global convergence
As the iteration times increases, the average values of objectives would converge to their fixed
values, this demonstrates that the identified solutions are stable and can be considered as the final
optimization results [31]. As shown in Fig. 6, the average values of material removal rate, delamination
factor and surface roughness fluctuate significantly with few iteration times and stabilize at
approximately 50th generation. Since all objectives reach the stable values before the maximum
iteration times, the obtained Pareto optimal solutions are considered to be reliable and desirable.
Fig. 6. Average values of objectives in each generation (s=250, τ=100, pc=0.9, pm=0.5).
(2) Spacing metric
Spacing metric is used to evaluate the uniformity of solutions in the objective space, smaller value of
spacing metric signifies a better uniformly distribution of solutions [32]. Spacing metric measures the
standard deviation of distances between adjacent solutions. Eq. (7) offers the formula for calculating
the spacing metric, jd is the distance between the j th and ( 1)j th solution, _
d is average
distance, s is the number of solutions in the population.
1 _
1
1
2
s
j
j
SM d ds
(7)
Fig. 7 shows that the value of spacing metric remains unchanged at a smaller value after approximate
40 generations, this implies that the uniformity of solutions achieves its optima without any
improvement space before the algorithm stops.
Fig. 7. Spacing metric in each generation (s=250, τ=100, pc=0.9, pm=0.5).
3.4.2. Pareto front of drilling responses
The optimal set of cutting parameters is identified, the values of spindle speed and feed rate are
within the ranges of [1500-3500] rpm and [0.03-0.15] mm/rev. The obtained Pareto front and its
projections on different planes are showed in Fig. 8, the front consists of 195 Pareto optimal solutions
and has a large coverage in the objective space. The values of objectives are within wide ranges, with
[1.3121-1.5148] for delamination factor, [1.673-4.014] µm for surface roughness and [21.21-247.40]
mm3/s for material removal rate.
Fig. 8. The obtained Pareto optimal solutions for drilling responses.
The Pareto front is divided into 13 regions (one local region is circled in red in Fig. 8), in which the
distribution of solutions can be represented approximately by one space curve. In each region, spindle
speed varies with feed rate maintained at a certain value, for instance, in the circled region, spindle
speed increases from 2900 to 3500 rpm with feed rate of 0.15 mm/rev. The number of divided regions
is 13 since the optimal set of cutting parameters gives 13 different feed rates varying from 0.03 to 0.15
mm/rev.
The overall trend in Fig. 8 shows that the decrease of material removal rate leads to reduced
delamination factor and surface roughness, this indicate that the improvement of production efficiency
would compromise the machining quality. But different interactions of drilling responses occur in the
divided local regions, material removal rate and exit delamination are improved simultaneously at the
cost of increased surface roughness. This is due to the fact that spindle speed is the only influential
factor in the local regions since feed rate is kept constant. The increase of spindle speed gives rise to a
significant increase in the material removal rate and a slight reduction in delamination, but it would
result in worse surface finish (higher surface roughness). High spindle speed and feed rate both could
improve the production efficiency, however, high spindle speed would be a better choice since it is able
to achieve substantial gains in efficiency without severely deteriorating hole quality compared to feed
rate.
Each Pareto optimal solution weighs three drilling responses differently and represents the best
possible tradeoff among exit delamination, surface roughness and material removal rate. The optimal
value of one response is under the influences of the other two responses, for instance, when
delamination factor d outF is 1.4263 and surface roughness
aR is 2.916 µm, the maximum material
removal rate MRR is 101.79 mm3/s. It should be pointed out that different pairs of ( d outF ,
aR ) may
result in the same MRR , for example, MRR is the same value of 35.34 mm3/s in the two situations
when ( d outF ,
aR ) are respectively (1.3293, 2.169 µm) and (1.3742, 1.984 µm). Different combinations
of n and f would give different performance in exit delamination and surface roughness, however,
they may generate the same MRR according to the expression: 2MRR R nf .
4. Post-Pareto optimality analysis
Another obstacle encountered in the implementation of optimization results is how to select the
appropriate solutions from the large numbers of Pareto optimal solutions, which are widely distributed
in the objective space. Since all the solutions achieve tradeoffs among drilling responses, decision
makers can select their preferred solutions directly from the set of Pareto optimal solutions. However,
studies in cognitive science highlights the pitfalls of imprecise decision-making in presence of a large
number of alternatives [33], thus it is very challenging for decision makers to manually select the most
promising alternatives. To facilitate the final decision-making, a filter procedure based on the
possibility degree and performance tradeoff is presented to reduce the Pareto optimal solutions to a few
number of key solutions. Possibility degree is introduced to select the solutions of interest (SOI) to
meet the decision maker’s demands for objectives, the selected SOI are further ranked in terms of
performance trade-off. In this way, key solutions of higher tradeoffs can be identified and can be
presented to decision makers as final alternatives.
4.1. Solutions of interest (SOI)
Possibility degree is a measurement of likelihood that a solution can satisfy the decision maker’s
preferences, its value is within the range of [0, 1] and can be adjusted to identify different sets of
solutions according to actual requirements. Each solution is attached to an interval of potential scores,
which depend on the priorities among objectives. Possibility degree of all solutions are determined by
intervals comparisons, and the solution of higher possibility degree are more likely to meet the
preferences of decision maker. The calculation of possibility degree mainly includes 4 steps:
Step 1: Normalize the original data of objectives
Objective values are normalized first to ensure that all objectives are commensurable. Let ( )jX be
the original data sequence of j th objective, '
( ) , , ...,1 j 2 j Mj
j f f f X , M is the number of Pareto
optimal solutions. ( )jX has a characteristic of the “higher-the-better” can be normalized with Eq. (8),
while ( )jX has a characteristic of the “lower-the-better” can be normalized with Eq. (9) [34, 35]:
* ( j) min ( j)( j) (1 j N)
max ( j) min ( j)
X X
XX X
(8)
* max ( ) ( )( ) (1 )
max ( ) min ( )
j jj j N
j j
X XX
X X
(9)
where *( )jX is the new sequence after data normalization, N is the number of objectives,
max ( )jX , min ( j)X are respectively the largest and smallest value of ( )jX .
Step 2: Calculate the intervals of solutions
Each solution is attached to an interval ,I L U to quantify the potential scores it can get after an
aggregation process. Decision makers’ preferences for objectives are given by a weight relationship
1 2 ...n
w w w given the fact that specific weights of objectives are normally not available in
practice, 0,1i
w and 1i
w . Three sets of weights following the predefined relationship
1 2 ...N
w w w , namely 1 2 31, ... 0N
w w w w , 1 2 1... 1 1 , 0N N
w w w N w and
1 2 ... 1N
w w w N are used to determine the intervals of solutions. The considered sets of
weights are the extreme situations and can efficiently reduce the computational complex [36].
The interval ,k k k
I L U gives the range of scores of solution kS , kL and k
U are respectively
the minimum and maximum values obtained by multiplying the objective values and the three special
sets of weights.
Step 3: Calculate the possibility degree of solutions
The possibility degree of solutions are the results of intervals comparisons, it refers to the probability
that a solution has higher scores than the other one. The possibility degree of solutions is calculated by
comparing their intervals with that of a predetermined reference solution *S , whose interval has the
largest lower bound among all solutions. The possibility degree *
kS SP
of solution kS with
respect to *S is determined following the rules:
1. if * ,k
I I I *
*
0
1
k
k
U LP
L U
*
kS S
2. if * ,k
I I I
*
*
*
k
k
k
U
L
U U
L L
g x dxP
g x dx g x dx
*
kS S ,
where g x is a function reflecting the attitude of decision maker to the solutions. g x c ,
g x x and 1g x x respectively describe neutral, optimistic and pessimistic attitudes.
0,1P *
kS S , solution kS will always has better performance than the reference solution
with 1P *
kS S while kS will always has worse performance than the reference solution with
0P *
kS S .
Step 4: Select the set of solutions of interest (SOI)
Performances of solutions compared to the reference solution can be evaluated with their
corresponding values of possibility degree. The set of solutions of interest (SOI) can be defined as:
*
k kS P I I (10)
0,1 gives the minimal value of P , only solutions with the value of P larger than
would be considered as an individual of the set of SOI. Therefore, different sets of SOI can be
identified by assigning a proper value to given the actual needs of decision makers， 1 2
holds if 1 2 .
4.2. Performance tradeoff
Solutions in the set of SOI are incomparable to each other since they are all Pareto optimal solutions,
but they present different trade off magnitudes among objectives [37]. The identified solutions are
evaluated by their performance tradeoff to determine the final key solutions, which exhibit the
characteristic that significant gains in some objectives can be obtained at the cost of slight
deteriorations in other objectives [33, 38].
Performance tradeoff of solution kS is defined as the least amount of gain per unit
deterioration obtained by replacing other solutions with solution kS , Eq. (11) gives the mathematic
expression of performance tradeoff .
( , ) min ,j
k k jS
S S ST
(11)
,T k jS S measures the tradeoff level between two solutions kS and jS , it corresponds to the
net gain of improvement in some objectives offset by the accompanying deterioration in other
objectives when solution jS is substituted with solution kS . ,i jy yT can be calculated by [37]:
max min1
max min1
max 0,
max 0,
Mmm
m m m
Mm m
m m m
S ST
S S
j k
k j
k j
S S
S , SS S
(12)
mkS refers to the m th objective value of solution kS , max
mS and min
mS are the maximum and
minimum values of m th objective. The numerator evaluates the aggregated improvement made with
substituting jS with kS , the denominator evaluates the deterioration caused by this substitution.
4.3. Final key solutions for decision makers
The filter procedure is applied to identify satisfactory key solutions taking into account decision
makers’ preferences for objectives, which are delamination factor d out
F , surface roughness aR and
material removal rate MRR in this study. Fig. 9 presents the evaluation results of Pareto optimal
solutions under the assumption of d out aMRR F R
w w w
, as can be seen, solution kS
has zero
probability to score higher than the reference solution *S
when its lower bound kL is smaller than
that of reference solution *L . This means there is no set of weights capable of making solutions with
zero possibility degree P *
kS S perform better than *S . The number of SOI decreases with the
increasing value of . Fig. 10 presents the identified SOI with different values of . Larger value of
represents a stronger preference of decision makers for MRR , hence fewer solutions of better
performance in the MRR would be found with larger value of .
Fig. 9. Evaluation of Pareto optimal solutions under the assumption of
d out aMRR F Rw w w
(a) Probability degree
P(Sk≥S*) of Pareto optimal solutions；(b) The number of SOI with different values of .
Fig. 10. Identified solutions with different values of (a) 0 ; (b) 0 3 . ; (c) 0 5 .
under the assumption of d out aMRR F R
w w w
Fig. 11 and Table 6 present the identified SOI and key solutions considering all possible priorities to
drilling responses. The SOI and key solutions showed in Fig. 11 (a)-(f) are the combined results of the
weight relationships and the minimum value of possibility degree , they present different
performance in drilling responses and could be used as guidance to assist decision-making. Fig. 11
(a)-(d) give top priority to machining quality index (d out
F or aR ), the identified solutions are
desirable to be chosen to obtain holes of high quality. Fig. 11 (e)-(f) put the emphasis on MRR , the
identified solutions can be used to produce rough holes at a high production efficiency when machining
quality is not an important goal.
Fig. 11. Identified solutions with different values of considering different priorities to objectives.
Table 6
Identified SOI and key solutions with different values of considering different priorities to drilling responses.
Priorities to
drilling responses
Key solution Reference solution S* Number
of SOI d outF aR
(μm)
MRR (mm3/min)
d outF aR
(μm)
MRR (mm3/min)
d out aF R MRRw w w
1.3579 1.830 28.27 1.3417 1.674 21.21 0.40-0.51 28
d out aF MRR Rw w w
1.3365 2.584 56.55 1.3140 2.694 48.07 0.40-0.51 18
a d outR F MRRw w w
1.3742 1.984 35.34 1.3417 1.674 21.21 0.35-0.49 17
a d outR MRR Fw w w
1.3742 1.984 35.34 1.3417 1.674 21.21 0.35-0.49 20
d out aMRR F Rw w w
1.5124 3.806 212.06 1.3880 3.344 131.95 0.60-0.73 20
a d outMRR R Fw w w
1.5124 3.806 212.06 1.4351 3.653 181.43 0.51-0.62 17
It needs to be pointed out the key solution is normally not the solution that has the largest value of
P *
kS S , solution with the largest value of P *
kS S gives the highest priority to weight
relationship while the key solution emphasizes more on the performance trade off among all responses.
In some cases, the same key solution may be found from different SOI, such as in Fig. 10 (c) and (d), in
Fig. 10 (e) and (f). This implies that the key solution may still present the best performance trade off
among the solutions, which cover a larger objective space than the SOI.
5. Conclusions
This paper proposes a cutting parameters optimization method for improving hole quality and
production efficiency in drilling of CFRP composites. Drilling tests are conducted without coolant to
examine the effects of spindle speed and feed rate upon hole quality indicators, namely exit
delamination and surface roughness. Multi-objective optimization for decreasing exit delamination and
surface roughness, increasing material removal rate is accomplished with NSGA-II, the set of optimal
cutting parameters and Pareto optimal solutions are determined. Moreover, post-Pareto optimality
analysis is implemented to identify the key solutions considering decision makers’ preferences for
objectives. The following conclusions can be drawn:
1. A full factorial experiment is carried out under dry cutting condition using twist drills,
experimental data are subjected to analysis of variance (ANOVA) to examine the effects of cutting
parameters on exit delamination and surface roughness. It is found that low feed rate produce better
hole quality with less delamination and lower surface roughness, high spindle speed would lead to a
great increase in surface roughness and a slight reduction in delamination. As a result, a combination of
low feed rate and spindle speed should be adopted for good hole quality.
2. Regression models are developed to express exit delamination and surface roughness as functions
of cutting parameters. Multi-objective optimization for decreasing exit delamination and surface
roughness, increasing material removal rate is accomplished with NSGA-II. In total, 195 Pareto
optimal solutions are found and each solution represents the optimal global performance with
improvements made in all drilling responses. Pareto optimal solutions give all possible tradeoffs among
drilling responses, thus it provides useful information for overall performance improvement taking into
account multiple criteria of responses.
3. It is very challenging for decision makers to determine the most promising solutions in presence
of many alternatives. To account for decision makers’ preferences for drilling responses, SOI are found
from the initial Pareto optimal solutions in terms of possibility degree, which reflects the probability a
solution perform better than a given reference solution. Then the SOI are further ranked based on the
performance trade off to identify the key solution exhibiting the characteristics that significant gains in
some objectives can be obtained at the cost of slight deteriorations in other objectives. The identified
SOI and key solutions under different situations are analyzed, and results show that the proposed filter
procedure is capable of identifying satisfactory solutions considering the priorities to objectives given
by decision makers. The key solutions could be used as guidance for drilling strategies adjustment to
meet the requirements of machining quality and production efficiency in practical machining
operations. In the filter procedure, the selection of reference solution plays a critical role in the
identified SOI and key solution. Given the specific requirements for machining quality and production
efficiency, an appropriate reference solution could be given.
Funding: This work was supported by the National Natural Science Foundation of China under Grant
52075452.
Competing Interests: The authors have no conflicts of interest to declare that are relevant to the
content of this article.
Availability of data and materials：The raw/processed data required to reproduce these findings can
not be shared at this time as the data also forms part of an ongoing study.
Authors Contributions：
Qian Wang: Methodology; Software; Validation; Investigation; Data Curation; Visualization;
Writing-original draft, Writing-review & editing.
Xiaoliang Jia: Supervision; Resources.
Consent to Publish：The authors warrant that the article is the authors’ original work, hasn’t received
prior publication and isn’t under consideration for publication elsewhere.
Ethical Approval and Consent to Participate: This work does not involve human participants or
animals.
References:
1. Singh AP, Sharma M, Singh I (2013) A review of modeling and control during drilling of fiber
reinforced plastic composites. Compos B Eng 47:118-125
2. Gaugel S, Sripathy P, Haeger A, Meinhard D, Bernthaler T, Lissek F, Kaufeld M, Knoblauch V,
Schneider G (2016) A comparative study on tool wear and laminate damage in drilling of
carbon-fiber reinforced polymers (CFRP). Compos Struct 155:173-183
3. Xu JY, Mansori ME (2016) Experimental study on drilling mechanisms and strategies of hybrid
CFRP/Ti stacks. Compos Struct 157:461-482
4. Isbilir O, Ghassemieh E (2013) Numerical investigation of the effects of drill geometry on drilling
induced delamination of carbon fiber reinforced composites. Compos Struct 105:126-133
5. Karpat Y, Değer B, Bahtiyar O (2012) Drilling thick fabric woven CFRP laminates with double point
angle drills. J Mater Process Technol 212:2117-2127
6. Qi ZC, Zhang KF, Li Y, Liu SN, Cheng H (2014) Critical thrust force predicting modeling for
delamination-free drilling of metal-FRP stacks. Compos Struct 107:604-609
7. Hou GY, Zhang KF, Fan XT, Luo B, Cheng H, Yan XY, Li Y (2020) Analysis of exit-ply temperature
characteristics and their effects on occurrence of exit-ply damages during UD CFRP drilling.
Compos Struct 231:111456
8. Girot F, Dau F, Gutiérrez-Orrantia ME (2017) New analytical model for delamination of CFRP
during drilling. J Mater Process Technol 240:332-343
9. Eneyew ED, Ramulu M (2014) Experimental study of surface quality and damage when drilling
unidirectional CFRP composites. J Mater Res Technol 3(4):354-362
10. Tsao CC, Hocheng H (2008) Evaluation of thrust force and surface roughness in drilling composite
material using Taguchi analysis and neural network. J Mater Process Technol 203:342-348
11. Krishnamoorthy A, Boopathy SR, Palanikumar K, Davim JP (2012) Application of grey fuzzy logic
for the optimization of drilling parameters for CFRP composites with multiple performance
characteristics. Measurement 45(5):1286-1296
12. Ameur MF, Habak M, Kenane M, Aouici H, Cheikh M (2016) Machinability analysis of dry
drilling of carbon/epoxy composites: cases of exit delamination and cylindricity error. Int J Adv
Manuf Technol 88(9-12):1-15
13. Romoli L, Lutey AHA (2019) Quality monitoring and control for drilling of CFRP laminates. J
Manuf Process 40:16-26
14. Krishnaraj V, Prabukarthi A, Ramanathan A, Elanghovan N, Kumar MS, Zitoune R, Davim JP
(2012) Optimization of machining parameters at high speed drilling of carbon fiber reinforced
plastic (CFRP) laminates. Compos B Eng 43:1791-1799
15. Abhishek K, Datta S, Mahapatra SS (2016) Multi-objective optimization in drilling of CFRP
(polyester) composites: Application of a fuzzy embedded harmony search (HS) algorithm.
Measurement 77:222-239
16. Shahrajabian H, Farahnakian M (2013) Modeling and multi-constrained optimization in drilling
process of carbon fiber reinforced epoxy composite. Int J Precis Eng Manuf 14(10):1829-1837
17. Su F, Zheng L, Sun FJ, Wang ZH, Deng ZH, Qiu XY (2018) Novel drill bit based on the
step-control scheme for reducing the CFRP delamination. J Mater Process Technol 262:157-167
18. Karnik SR, Gaitonde VN, Rubio JC, Correia AE, Abrão AM, Davim JP (2008) Delamination
analysis in high speed drilling of carbon fiber reinforced plastics (CFRP) using artificial neural
network model. Mater Des 29:1768–1776
19. Wang CY, Ming WW, An QL, Chen M (2017) Machinability characteristics evolution of CFRP in a
continuum of fiber orientation angles. Mater Manuf Process 32(9):1041-1050
20. Xu JY, An QL, Chen M (2014) A comparative evaluation of polycrystalline diamond drills in
drilling high-strength T800S/250F CFRP. Compos Struct 117:71-82
21. Sorrentino L, Turchetta S, Bellini C (2018) A new method to reduce delaminations during drilling
of FRP composites by feed rate control. Compos Struct 186:154-164
22. Raj DS, Karunamoorthy L (2016) Study of the effect of tool wear on hole quality in drilling CFRP
to select a suitable drill for multi-criteria hole quality. Mater Manuf Process 31(5):587-592
23. Zitoune R, Krishnaraj V, Almabouacif SB, Collombet F, Sima M, Jolin A (2012) Influence of
machining parameters and new nano-coated tool on drilling performance of CFRP/Aluminium
sandwich. Compos B Eng 43(3):1480-1488
24. Karimi NZ, Heidary H, Minak G (2016) Critical thrust and feed prediction models in drilling of
composite composites. Compos Struct 148:19-26
25. Joshi S, Rawat K, Balan ASS (2018) A novel approach to predict the delamination factor for dry
and cryogenic drilling of CFRP. J Mater Process Technol 262:521-531
26. Khashaba UA, EI-Sobaty IA, Selmy AI, Megahed AA (2010) Machinability analysis in drilling
woven GFR/epoxy composites: part I-effect of machining parameters. Compos A Appl Sci Manuf
41(3):391–400
27. Sánchez MS, Ortiz MC, Sarabia LA (2016) A useful tool for computation and interpretation of
trading-off solutions through pareto-optimal front in the field of experimental designs for mixtures.
Chemometr Intell Lab Syst 158:210-217
28. Das I (1999) On characterizing the knee of the Pareto curve based on normal-boundary intersection.
Struct Optim 18(2–3):107-115
29. Srinivas N, Deb K (1995) Multiobjective optimization using nondominated sorting in genetic
algorithms. Evol Comput 2:221-248
30. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic
algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182-197
31. Cao X, Wen ZG, Xu JJ, Clercq DD, Wang YH, Tao YJ (2020) Many-objective optimization of
technology implementation in the industrial symbiosis system based on a modified NSGA-III. J
Clean Prod 245:118810
32. Wang YH, Chen C, Tao Y, Wen ZG, Chen B, Zhang H (2019) A many-objective optimization of
industrial environmental management using NSGA-III: A case of China’s iron and steel industry.
Appl Energ 242:46-56
33. Bhattacharjee KS, Singh HK, Ryan M, Ray T (2017) Bridging the Gap: Many-Objective
Optimization and Informed Decision-Making. IEEE Trans Evol Comput 21(5):813-820
34. Rajmohana T, Palanikumar K, Prakash S (2013) Grey-fuzzy algorithm to optimise machining
parameters in drilling of hybrid metal matrix composites. Compos B Eng 50:297-308
35. Hong ZN, Liu CB, Li JL (2012) Parameter Optimization for Machined Round Parts by Using Grey
Relational Analysis. In: Luo J. (eds) Affective Computing and Intelligent Interaction. AISC.137:
441-448
36. Torres M, Pelta DA, Lamata MT, Yager RR (2020) An approach to identify solutions of interest
from multi and many-objective optimization problems. Neural Comput Appl https://doi.org/
10.1007/s00521-020-05140-x
37. Bechikh S, Said LB, Ghédira K (2011) Searching for knee regions of the Pareto front using mobile
reference points. Soft Comput 15:1807-1823.
38. Rachmawati L, Srinivasan D (2009) Multiobjective Evolutionary Algorithm with Controllable
Focus on the Knees of the Pareto Front. IEEE Trans Evol Comput 13(4):810-824.
Figures
Figure 1
Overview of research procedure in this study.
Figure 2
Schematic of delamination at hole exit.
Figure 3
Experimental results of drilling responses under different cutting conditions (a) delamination factor; (b)average surface roughness.
Figure 4
Comparisons of experimental results and predicted values of regression models.
Figure 5
Cutting parameters optimization procedure based on NSGA-.
Figure 6
Average values of objectives in each generation (s=250, τ=100, pc=0.9, pm=0.5).
Figure 7
Spacing metric in each generation (s=250, τ=100, pc=0.9, pm=0.5).
Figure 8
The obtained Pareto optimal solutions for drilling responses.
Figure 9
See the Manuscript Files section for the complete �gure caption.
Figure 10
See the Manuscript Files section for the complete �gure caption.
Figure 11
See the Manuscript Files section for the complete �gure caption.
