Enhancing Cutting Efficiency and Minimizing Forces for Nomex Honeycomb Core Using Grey Relational Analysis and Desirability Function Analysis

Nomex Honeycomb core is the foundational building block for manufacturing aerospace composite components. Its usage requires machining honeycomb in complex aerodynamic profiles where the quality of the core is governed by accuracy and precision of cut profiles. The assessment of accuracy and precision is directly related to forces induced in the cutting tool and cutting efficiency. These two parameters form the basis of a multi‐objective function that this paper aims to optimize for the milling operation. The parameter of depth of cut considered in this paper has not been analyzed in a multi‐objective optimization study of the Nomex Honeycomb core previously. A Taguchi‐based array of Design of Experiments followed by Analysis of Variance and correlation analysis is utilised. The results indicate that the most significant factor is the feed rate, with a percentage contribution of 72% for the cutting forces and depth of cut, with a percentage contribution of 85% in the case of cutting efficiency. The two parameters are optimized using Desirability Function Analysis and Grey Relational Analysis. The results are validated through experimental runs with an error within 5% of the statistical predictions, with the percentage improvement in cutting forces for optimum runs as compared to the worst experimental run at 47.8%. The percentage improvement in cutting efficiency likewise is 11%.


Introduction
The aerospace sector extensively relies on honeycomb core-based raw materials for aircraft manufacturing. [1]The aerostructures DOI: 10.1002/smtd.202300958 are heavily profiled to cater for the aerodynamic stability of the structures.With technological advancements, lightweight, energy-efficient, and robust materials are used for aircraft manufacturing.In this arena of new materials, honeycomb cores stand out because of their extraordinary out-of-plane compressive and shear strengths. [2,3]Some examples of aircraft components made from honeycomb cores are fairings, rudders, overhead stowage bins etc. Manufacturing of these aircraft structures requires the machining of a honeycomb.
It is viable to produce good quality sandwich structures only when the machining process induces the least defects in the cut honeycomb.There are very few shapes available that could be directly used to manufacture the end products, [4] and thus, it is inevitable that the honeycomb cores would be subject to machining processes.Apart from machining, ultrasonic assisted cutting with special cutter is also utilized to cut honeycomb cores. [5,6]However, in this case the equipment is costly and the depth of cutting is limited to thin sections.Some researchers have proposed special setups (low-temperature fixtures) for the machining process to reduce machining defects. [6]The process of low-temperature machining is prone to longer setup times, due to additional setup for cryocooling the honeycomb core.The process is also energy intensive, however, the research shows that it increases cut quality of the honeycomb core in terms of chipping and burr formation. [7]Others have proposed cutting honeycomb cores using special multi-helix cutting tools with chip breakers. [8]This is the most feasible method of cutting honeycomb cores as this requires no additional setups, it is a fast process, and can cut greater depths of the materials while maintaining good quality.However, machining with tool induces many defects including crushing, chipping, fraying, tearing, and surface deformation. [2,9]These defects were reported in the literature and the studies have tried to simulate the optimal conditions using numerical analysis and have shown that minimizing cutting forces result in the reduction of these defects.The literature also suggests that the meniscus (adhesive layer) between the composite lamination layer and   core material should not exceed 300 μm. [10]The machining defects greater than this could cause irregularities in the formation of sandwich panels resulting in the loss of desired mechanical properties.Yongqing et al. [11] have studied the surface roughness through a 3D surface roughness measurement system and have concluded that a roughness of 218 μm can be achieved through process optimization, [12] however, this study is specifically designed for aluminium honeycomb cores.Similar studies have been conducted for Fibre Reinforced Plastics (FRPs).Jenarthanan et al. [13] have optimized the machining process (cutting force and delamination factor) of Glass FRPs using composite desirability function while considering the helix angle of the tool, fibre orientation angle, spindle speed, and feed rate.This study does not consider the depth of cut as an influencing parameter.Similar studies were conducted by, Wang and Zhang, [14] Davim,15] and Haddad et al. [16] These authors have used ANOVA, correlation methods, and SEM (Scanning Electron Microscope) image-based methods to optimize the machining process of different FRPs; however, only [13] has considered a variable of delamination factor that is similar to the cutting efficiency considered in the present research.Aluminium honeycomb cores are also widely used in aerospace and automotive sectors, and [6] has researched the milling process efficiency of the aluminium honeycomb core.The damage mechanics-based models are utilized to predict the failure of honeycomb cores using simulations.These models rely on the different approaches adopted to model the core.Among these models, the most popular are the Hashin, [17] Tsai-Wu, [17] Tsai-Hill, [18] and Johnson Cook [19] criteria.While the Tsai-Wu criteria identify damage to each element, the Hashin criteria enable the identification of the different modes and directions of failure. [20]wing to these challenges, researchers have tried to optimize the machining process of honeycomb cores and composite materials. [12,13,21]Various parameters related to machining were analyzed in the literature.Jaafar [5] has experimented with the machining process and concluded that the feed rate is the most significant factor during machining. [22]Similarly, others have conducted only the simulated studies and have concluded that the simulation is consistent with the experimental results. [23]he considered factors by these authors were feed rate, spindle speed, and depth of cut, while the response variables were mainly forces.Experimental studies conducted in the above research do not consider the depth of cut in detail, and an important response variable of cutting efficiency is also not considered.No multi-objective optimization study is available in the literature that considers the depth of cut as a factor and cutting efficiency as a response variable.The study will help in identifying the optimal settings of machining honeycomb cores through multihelix cutting tool, thereby, improving the cutting efficiency of the process as well while decreasing the cutting defects.Better machined quality of honeycomb cores will enable production of good quality sandwiched structures and hence increasing the quality of making profiled composite parts for aerospace sector.
The present study considers the multi-objective optimization of the machining process of Nomex honeycomb cores through desirability function analysis (DFA) [24] and grey relational analysis (GRA). [25]The considered factors are spindle speed, feed rate, and depth of cut.The response factors considered are force and cutting efficiency.First, the Taguchi L9 array is used to construct experimental runs. [12]Second, Taguchi analysis and ANOVA [15] are performed to establish the most significant factors for the machining process.Third, optimization using DFA and GRA is performed.Last, validation runs are executed to verify the optimized model's research methodology Figure 2.This study could provide high fidelity input data for the computational analysis of the manufacturing of honeycomb core.Moreover, the methodology developed gives key insights on cutting efficiency based on the novel parameter of Depth of cut, the same method could be implemented for other combination of parameters to enhance the cutting efficiency.

Tool, Workpiece, and Machine
The workpiece material used in the study was the Nomex Honeycomb core, produced using aramid fibers.The selected honeycomb core has thin fibers manufactured by soaking the aramid fibers in phenolic resin.The cores thus produced have continuous features of expanded aramid sheets glued together to form the hexagonal structure.This resulted in a lightweight and rigid structure that has high compression strength.The geometrical properties of the honeycomb core selected are given in Table 1.The Honeycomb core sheet is shown in Figure 1 and the methodology for the study is outlined in Figure 2.
There are many cutting tools available in the market to cut honeycomb cores depending on the type of material they are produced, [4] the machining operation that needs to be carried out, and the final finish required.For this research, the cutting tool chosen was manufactured by Core Hog, America. [26]The cutting tools are called medium-sized finishing tools and consist of two parts: the main shredder/hogger body made from solid Carbide, and the other is a medium core slicer coated with TiCN.The tool was recommended to be used for milling operations.The tool specifications are mentioned in Table 2.The geometry of the tool is shown in Figure 3.
The machine utilized for the cutting operation was a three-axis vertical CNC machine manufactured by YDPM.It has a bed size of 1180 × 560 mm, and the controller is Fanuc.The maximum spindle speed of the machine was 8000 rpm and could be enhanced using specialized spindles.

Machining Fixture
For the measurement of force Bran Sensor Tri-axial force transducer based on a strain gauge sensor was used.The fixture plate was designed to fasten the honeycomb core during machining, which was then mounted on the transducer plate of the sensor.The design of the plate is depicted in Figure 4(a-c).

DoE Parameters for Machining
During the literature review, various research papers were studied and analyzed for the process parameters that greatly influenced the machining of honeycomb core structures.It was revealed that most authors including, Jaafar et.Al and Tarik et.al, have used feed rate and spindle speed to measure their effect on the machining forces.However, the literature review revealed that the Depth of Cut had not been considered in detail as an influencing factor of machining forces during experimental analysis.Therefore, this parameter and other standard parameters (feed rate and spindle speed) were considered in this research to cover a wider array of influencing parameters.
To determine levels against each parameter/factor, literature was studied, and it was observed through trial and error that greater spindle speed yields better cutting width and lesser forces.The comparison of different speeds against the forces in the x-direction is shown in Figure 5.The sharp rise in forces for 2000 rpm was due to the accumulation of chips during machining.The relatively slow rpms did not allow rapid removal of chips and these chips restrict the further cutting thereby, increasing the cutting forces.Furthermore, utilizing statistical optimization to enhance processes was an important quality engineering function.Taguchi wields an important cornerstone in this area because of its ability to design experiments with minimum iterations while yielding statistically significant results.This resulted in efficient resource-saving and time-saving.Owing to these characteristics, Taguchi's Design of Experiments was utilized in the www.small-methods.comcurrent research.Specifically, L9 orthogonal array was used to design the iterations of the experiments.The Taguchi L9 array, along with the levels, are depicted in Tables 3 and 4.

Response Variables and Measurements
The literature review suggests that force is the most important factor during machining. [5]Tearing, fraying, and delamination were some of the phenomena that occur during the machining of the honeycomb core.To ascertain their influence cutting efficiency (CE) was also considered a response variable for this optimization study.
The force was measured using Bran Sensor Tri-axial force transducer.The dynamometer was mounted on a fixture plate and placed on the machine bed, and force was measured on each axis.Before the actual measurements voltage factor was calculated for 1 N of force by applying a known load of 1 N in each  direction.The voltages measured afterward were divided by this factor to obtain the force in newtons.For each experiment, the three force components were measured.The value in newtons was found by the difference between the minimum and maximum values (in millivolts) (Equation 1).Each configuration of the experiment was run two times, and the average of each run was also taken.Afterward, the resultant force was calculated using (Equation 2).Force calculation in each axis: Resultant Force Calculation: For the measurement of cutting efficiency, the image dimension measurement system of Keyence (Figures 6 and 7) was utilized and measurements of cutting widths were taken.Afterward, the measured cutting width was divided by the shredder diameter to obtain the cutting efficiency.The (Equation 3) depicts the calculation formula.The cutting width was measured by fitting a line on the cut honeycomb for each experiment slot and mea-

Data Analytics and Optimization
The experiments were conducted as per the runs mentioned in Table 4, and the response variables were measured using the force transducer and Keyence machine.The compiled results are elaborated in Table 5.The resultant force was calculated according to Equation 2, and CE is calculated as per Equation 3.

Data Analysis
The descriptive analysis of the results was carried out, and the means of cutting parameters were compared.The comparison of the means graph is depicted in Figures 8 and 9.The graph in Figure 8 compares the means of FR and SS.The trend is visible in the positive relation of feed rate vis-à-vis the resultant force.Whereas there is a negative relation between SS and resultant forces.It is because of better chip and burr removal for higher spindle speeds as compared to lower spindle speeds.This trend is also simulated by M. Jaafar et al. [5] and similar results were concluded.Similarly, Figure 9 indicates a positive linear trend of the DoC vis-a-vis the CE, whereas the SS and FR are not positively correlated.The increase in cutting efficiency in relation to Depth of Cut can be explained because the contact area of tool with the work piece increases and this engagement of tool with the workpiece enhances the cutting efficiency.Afterward, Taguchi's Analysis of the variables was carried out, and the results are tabulated in Tables 6 and 7.The response tables from Taguchi Analysis indicate that the most significant factor affecting the forces on the tool is FR, followed by SS and DoC, whereas, in the case of CE, DoC is the most significant factor, followed by FR and SS.
The ANOVA Analysis of the factors was carried out, and the results are tabulated in Tables 8 and 9.The results reveal that for forces, the p-value is most significant for FR (0.01), followed by SS (0.029), and DoC (0.247).Whereas, in the case of Cutting Efficiency, the p-value is most significant in the case of DoC (0.023), followed by FR (0.217), and SS (0.285).The main effects plot of S/N ratios are depicted in Figure 10(a,b).The plots endorse the results of the response tables and significant values indicating similar trends vis-à-vis cutting forces and cutting efficiency.Based on the ANOVA tables, the percentage contribution of each factor was also calculated, as depicted in Table 10.
Cutting Nomex Honeycomb core results in various defects, as highlighted in the studies of Liu et al. [2] These defects are responsible for higher cutting forces if the feed rate increases.The Nomex HC core is made up of aramid fibres, and these fibres have high hardness values.When the feed rate increases, the tool's contact area with the fibres increases, resulting in increased shearing forces.Jaafar et al. [22] and Tarik [27] have concluded similar results through simulation of the machining process and have shown that at higher feed rates, the cutting force increase while the chip size tends to be smaller.Similarly, in the case when DoC is increased, the accumulation of material results in increased shearing forces.The accumulation of the material is due to the elastoplastic behavior of the HC core.However, this accumulation is reduced when spindle speeds are high, tending to reduce the cutting forces. [28]NOVA shows that DoC is the most important factor in the case of CE.It is because the DoC allows uniform material  10 indicate this correlation, as DoC is the prime significant factor in the calculation of CE.Similar results were reported through simulations by Tarik et al. [29]

Multi-Objective Optimization
The optimization of machining parameters is essential for several reasons.First, the Nomex honeycomb core exhibits unique mechanical properties that are influenced by machining parameters undertaken by the current research.The appropriate selection of these parameters can significantly impact the structural behavior of the core material when sandwiched structures are produced through it. [30]Optimization techniques allow for identifying the optimal combination of machining parameters that minimize forces, enhance material properties, and cutting efficiency, and improve overall structural integrity. [31]or this purpose, desirability function analysis (DFA) was used to optimize the response variables about the influencing factors.This technique aims to calculate the desirability function that optimizes multiple responses.This desirability value represents how well the combination of factor settings achieves the desired response for each variable.The desirability function considers target values and acceptable ranges for each response variable.The first step in optimization through DFA is to define response variables, their target values, and their acceptability limits.Then desirability functions are assigned to each response.Then these functions are combined to calculate the composite desirability function. [24]Based on the steps highlighted above, the desirability function was calculated, and the response was optimized using Minitab Response Optimizer.The optimized results with composite desirability of 86% are tabulated below in Table 11.
Grey Relational Analysis (GRA) is a useful tool extensively used in multi-criteria decision-making and multi-objective optimization.It is a part of Grey System Theory that is an effective tool for prediction and forecasting in scenarios with little information available. [32]The GRG function was calculated based on the steps elaborated in Figure 11.The calculations based on the steps highlighted in Figure 11 are compiled in the following tables.First, the data was normalized based on the Equations (4) and (5).Normalization is done to compare the dataset points on a common scale. [25]e used max-min criteria to normalize the data, which involves maximization of the data points or minimization.In the case of force, we want to minimize the normalized data; therefore, Equation 4 was used.In the case of cutting efficiency, maximization was needed; therefore, Equation 5 was used to perform data normalization.
Smaller the better criteria: Larger, the better criteria: Afterward, the deviation sequence was calculated based on Equation 6.The deviation sequence is the deviation of the normalized values of the data points from the ideal values or ideal series of values.For the force and cutting efficiency, the ideal value is 1.Therefore, the difference of each data point is calculated from 1. Later, the GRA coefficient was calculated by using Equation 7. The GRA coefficient outlines the similarity between each input factor and the ideal values.Deviation Sequence: Grey Relational Coefficient Equation: After calculating the GRA Coefficient, the Grey Relational Grade (GRG) is calculated to determine the data points' greyness.Equation 8 is used to find the GRG.The results of each step are compiled in Figure 12.After calculating the GRG, the ranking was performed based on the maximum GRG value.The ranking is also shown in Figure 12.Finally, response tables were calculated based on GRG value to find the optimum parameters from the GRG function.both techniques are 6000 rpm for SS, 300 mm min −1 for FR and 15 mm for DoC.Equation for Grey Relational Grade: The visual results of the worst and best experimental runs are shown in Figure 13.It can be observed from the results that the best results (Experiment # 7) are without burrs or protrusions, the cut fibre is smooth, and the cut width is accurately achieved.For the worst experimental run (Experiment # 6), it can be seen there are fraying, burrs, and uncut fibers visible, whereas the cutting efficiency is badly affected.The results strongly correlate with quantitative analysis.As indicated earlier, as the feed rate increases, the contact time between the cutter and workpiece decreases, restricting the smooth execution of the cut.Whereas the opposite is true in the case of run 7, as the feed rate decreases, it allows maximum material removal time, decreasing burrs, and fraying.
After optimum parameters were calculated based on the optimization techniques, the forces, and cutting efficiency results were predicted, and the predicted results are tabulated below in Table 14.The prediction was calculated using Minitab's prediction function for ANOVA.For predictions using ANOVA in Minitab, the software calculates the means or fitted values for different factor levels or combinations based on the estimated coefficients and the observed data.These predictions represent the expected or average response for the specific factor settings.
After determining the optimal process parameter settings, the final step involves predicting and verifying the enhancements in performance characteristics using these optimal settings.A validation experiment uses the identified best parameter values to assess the combined objective.The results of the validation experiment are depicted in Table 15.The results are within a 5% error from the predicted results and show the accuracy of the optimized parameters through both optimization techniques.The comparison of worst predicted and validated results are depicted in Figure 14.

Conclusion
In conclusion, this study focused on optimizing the milling operation for machining Nomex Honeycomb core used in aerospace composite components.Through Taguchi-based Design of Experiments (DOE), ANOVA analysis, and correlation analysis, the influence of spindle speed, feed rate, and depth of cut on cutting forces and cutting efficiency was investigated.The results indicated that: i. ANOVA analysis indicates that the feed rate was the most significant factor with percentage contribution of 72% effecting cutting forces, whereas depth of cut was significant in case of cutting efficiency with percentage contribution of 85%.ii.The significance of feed rate for cutting forces had a p-value of 0.01, followed by Spindle Speed 0.029 and Depth of Cut 0.247.iii.The Depth of Cut had a notable impact on cutting efficiency with a p-value of 0.023 followed by Feed Rate 0.217 and Spindle Speed 0.285.iv.The results of Grey Relational Analysis (GRA) correlated with Desirability Function Analysis (DFA) results and both techniques demonstrate similar optimal settings of response parameters.The optimal settings were found to be 6000 rpm of spindle speed, 100 mm / min feed rate and 15 mm depth of cut.v. ANOVA based prediction of parameters was found to be correct in comparison to the experimental validation results for the optimal settings and the error was within 5% vi.The percentage improvement in cutting forces was found to be 47.8% as compared to the worst experimental run and cutting efficiency was improved by 11%.
This study provides valuable insights into improving the accuracy and precision of cut profiles in Honeycomb Core (HC Core) machining, ultimately contributing to enhancing aerospace composite component manufacturing processes.There are however, many vistas still unexplored in this area including the results of simulated / experimental studies on other machining / milling parameters of honeycomb core with different cutting tool geometries and different cut profiles.

Figure 4 .
Figure 4. a) Isometric view of Fixture Plate; b) Front view of fixture plate; c) Actual Experimental Setup.

Figure 6 .
Figure 6.Measurements from the Keyence system.

Figure 10 .
Figure 10.Main Effecrs Plot for S/N ratios a) Force & b) CE

Figure 13 .
Figure 13.Top cut represents run 7.The bottom cut represents run 6.

Table 1 .
Geometrical properties of Nomex honeycomb core.

Table 2 .
Specifications of cutting tool.
Figure 5. Trial Run Results for Forces in X-Axis.

Table 3 .
Taguchi design of experiments.

Table 4 .
Parameters for DoE.

Table 5 .
Results of forces and cutting efficiency.

Table 6 .
Response table for SN ratios (Force).

Table 8 .
ANOVA table of S/N ratios for F.

Table 9 .
ANOVA table for S/N ratios for CE.

Table 10 .
Percentage contribution based on ANOVA.

Table 11 .
Response optimization through composite desirability function.Results of Grey Relational Analysis.

Table 12 .
Response table from GRG function.

Table 13 .
Optimum levels based on GRG and DFA.

Table 12
outlines the response table, and Table13outlines the optimum parameters.The optimum levels from

Table 14 .
Predicted results from ANOVA.
Figure 14.Comparison of predicted, validated, and worst runs.