Optimization of Cutting Parameters for Improving Machining Quality Andproduction Rate in Drilling of CFRP Composites

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


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][2][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 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.

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.

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 out F  given as [25]: The hole diameter nom D , maximum diameter of delamination area max D and actual delamination area dam A are illustrated in Fig. 2, max D and dam A are measured by image analyses using the ImageJ software.

Surface roughness
Average surface roughness a R 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, a R 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 a R 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 a R , thus a R at hole exit is considered to represent the surface quality of machined holes.

Analysis of experimental results
Experimental results of delamination factor d out F  and average surface roughness a R under different cutting conditions are presented in Table 3.

Table 3
Experimental results of delamination factor d out F  , average surface roughness a R in the full factorial experiment.

Test
No.  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.  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.

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 out F  , 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.
d out a 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 out F  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 5. The predicted values are very close to the experimental results, the average relative error is 1.76% for d out F  and 4.26% for a R . This proves that the regression models of d out F  and a R 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 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 12 ( , ,..., ) be a vector that contains l influential factors, x performs not worse than j x in all objectives and outperform j x in at least one objective. If there is no solution 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.

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 .

Elite-preserving mechanism
Elite-preserving mechanism is adopted in NSGA-Ⅱ to ensure the diversity of individuals and to distance normally lies in a more sparse area and is given priority to ensure the diversity of population.

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) 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).

Pareto front of drilling responses
The optimal set of cutting parameters is identified, the values of spindle speed and feed rate are  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.

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.

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 Step , M is the number of Pareto optimal solutions. () j X has a characteristic of the "higher-the-better" can be normalized with Eq. (8), while () j X has a characteristic of the "lower-the-better" can be normalized with Eq. (9) [34,35]: is the new sequence after data normalization, N is the number of objectives, , min ( j) X are respectively the largest and smallest value of () j X . Step , solution k S will always has better performance than the reference solution with   1 P  * k SS while k S will always has worse performance than the reference solution with Step   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， 12    holds if 12   .

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].

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 a R and material removal rate MRR in this study. Fig. 9 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 a R ), 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.  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.

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. 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.  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. Cutting parameters optimization procedure based on NSGA-.

Figure 8
The obtained Pareto optimal solutions for drilling responses. See the Manuscript Files section for the complete gure caption.

Figure 10
See the Manuscript Files section for the complete gure caption. Figure 11