Machinability study of hybrid-polymer composite pipe using response surface methodology and genetic algorithm

Abstract

Polymer–matrix composites are very popular due to their low cost and simple fabrication methods. While techniques and methodologies for composites design are emerging, the knowledge and understanding of machining issues lag far behind. The objective of the work is to analyze the influence of machining parameters on the material characteristics of hybrid-composite pipes. Turning operation was carried out as per the design of experiments by central composite design in hybrid polymer composite pipe made of carbon fiber and Aramid fiber. Based on the experimental results, regression analysis was conducted to determine the input–output relationships of the process. A mathematical model is developed, and the responses are predicted. The effects of each process parameter on the response were analyzed using response surface methodology. The process parameters were then optimized using genetic algorithm to yield minimum cutting force and minimum surface roughness (R_a).

Keywords

Hybrid-polymer composite machining CFRP composites response surface methodology

Introduction

Polymeric composites are a class of novel materials with many desirable properties. Composite materials offer high strength and stiffness, resistance to fatigue and corrosion, low weight, and the ability to be formed into complex shapes. As such, they provide performance and energy-saving advantages that make them excellent substitutes for traditional materials in applications, ranging from aerospace and automotive components to sports equipment [1]. Composites as a group of materials are generally extremely abrasive and are difficult to machine due to its anisotropy nature [2]. A hybrid composite represents a combination of two or more fiber materials, consisting of a continuous matrix material reinforced by strands of another material. Both the matrix and the reinforcing elements are highly abrasive, limiting the tool life. Delamination is the major phenomenon of work piece failure since composites are laid as layers in polymeric matrix composites [3]. When machining a composite, chipped cutting edges will often cause additional damage to the material [4]. Palanikumar et al. [5] carried out machining of CFRP composites to evaluate the effect of fiber-orientation angle. They also reported that delamination is the major failure occurring in GFRP while machining. They observed that feed rate and cutting speed are the key parameters affecting the surface roughness. Ferreira et al. [6] found that only PCD tools are suitable for finish operations after studying the performance of different tool materials while turning CFRP composites. Rahman et al. [7] established that for a fixed material-removal rate, the tool wear was minimum when the CFRP composite materials are machined at lower cutting speeds. Lina et al. [8] studied the effect of machining forces and tool wear relationship of aluminum metal matrix composites using multiple regression analysis. Palanikumar et al. [9] assessed the influence of machining parameters on GFRP composites using design of experiments concept and developed a procedure to attain minimum surface roughness using ANOVA technique. Abrao et al. [10] investigated the effect of cutting-tool geometry when drilling glass fiber-reinforced plastic composites. Davim and Mata [11] investigated the machinability of GFRP composites produced by hand lay-up technique and proposed a new machinability index. Krishnamurthy et al. [12] studied the application of gray fuzzy logic for the optimization of drilling parameters for CFRP composites. Gunraj and Murugan [13] used response surface method (RSM) to develop a mathematical model. Jain et al. [14] optimized the process parameters of machining process using genetic algorithm (GA). Sait et al. [15] analyzed the quality of machined surfaces and found that optimized cutting parameters reduce tool wear and damage on machined surfaces. In turning filament-wound GFRP pipe, moderate feed rate and lower depth of cut are the ideal machining conditions for machining [16]. The experimental values and regression models are approximately identical in machining using cemented carbide-cutting tool [17, 18]. Lower cutting velocity, moderate feed rate, and moderate depth of cut were found to be the ideal machining conditions for machining hand lay-up GFRP pipes [19 –21]. Modeling of machining operations was carried out using RSM by various researchers [22 –25]. The major challenge in machining is the determination of the behavior of a particular material when it is cut since strength and fiber orientation are different for hybrid fibers. Since no valuable theory is available for machining bi-directional fiber composite materials based on cutting force and surface roughness, an attempt is made to study the machining characteristics using design of experiments and optimize the machining parameters for minimum cutting force and minimum surface roughness using GA. The paper focuses on the investigation of machinability and the evaluation of surface finish of hybrid-composite tube of carbon and aramid fiber-woven bi-directionally with bisphenol resin manufactured by hand lay-up process through turning operations by cemented carbide-cutting tools. CFRP pipes were selected since the applications of CFRP pipes would be more than the CFRP rod, especially in the transfer of alkalis at elevated temperature in the process industries. The cost of exclusive carbon bi-directional fiber is higher than the hybrid bi-directional fiber, and hybrid CFRP is taken for investigation to minimize the overall cost of producing pipes for specific application. RSM is used to predict the influence of machining parameters, and ANOVA was employed to investigate the cutting characteristics.

Experimental details

Materials and processes

Bi-directional hybrid-composite pipe made up of carbon fiber and aramid fiber along with bishphenol as resin is used in this study. Bisphenol resin was chosen because of its higher molecular weight in the resin resulting in fewer ester linkages, thereby increasing the stability of the resin. Moreover, the resin offers a high degree of chemical resistance to a wide range of acids, alkalis, and salt solutions at elevated temperatures especially applicable for process and paper industries where resistance to corrosion at high temperatures is desired. The properties of the fibers are presented in Table 1. The pipe is manufactured using hand lay-up method with external diameter of 50 mm and thickness of 5 mm as shown in Figure 1. The direction of lay for fibers is on both directions in a bi-directional CFRP, and hand lay-up method is selected for the manufacture of pipe.

Figure 1.

Hybrid composite pipe with bisphenol resin.

Table 1.

Hybrid carbon–aramid fabric properties.

Style	Weight (g)	Weave	Material		Share		Linear density		Settings		Thickness (mm)
Style	Weight (g)	Weave	Warp	Weft	CF (%)	KF (%)	Warp	Weft	Warp	Weft	Thickness (mm)
646	215	Plain	Aramid	Carbon	61	39	127	200	6.5	6.5	0.25
761	170	Plain	Carbon	Glass	72	29	200	68	6.0	7.0	0.25

A CNC lathe (LEADWELL) with spindle speed in the range of 45–4500 rpm and maximum spindle motor power 7.5 kW shown in Figure 2 was used to perform the experiments. From the literature, it is observed that carbide tool is more suitable for machining polymer composites owing to its economy. Hence, carbide tool was selected even though other tools are available. Coated carbide-cutting tool inserts of Kennametal make (CNMG 120 408P KC 5010) were used for machining. In this work, the surface roughness was measured by Mitutoyo surf test SJ-201P.

Figure 2.

Cutting tool setup.

Plan of experiments

The design matrix chosen to conduct the experiment was a central composite design (CCD) having 20 experimental runs. From the knowledge of machining at various input parameters, the closest values are segregated and eliminated. Thus, the final values of machining parameters were fixed for experimentation by RSM. Thus, the 20 experimental runs allowed the estimation of linear, quadratic, and two-way interactive effects of the process parameters on cutting force and surface roughness. RSM was used to predict the influence of machining parameters and surface roughness of the machined hybrid-composite pipe. ANOVA is used to check the validity of the model. Multiple response optimizations were performed after analyzing each response. The factors considered were spindle speed, feed rate, and depth of cut, and their corresponding levels are shown in Table 2. The process parameters are also optimized using GA to yield minimum cutting force (resultant force) and minimum surface roughness (R_a). Due to the heterogeneous nature of the fiber and composite materials, removal rate is not considered in this investigation, and surface roughness is kept as a predominant factor.

Table 2.

Factors and their levels for machining.

Factor	Units	Notation	Levels
Factor	Units	Notation	1	2	3
Cutting speed	m/min	V	75	97.5	120
Feed rate	mm/rev	f	0.05	0.125	0.2
Depth of cut	mm	d	0.5	0.75	1

Results and discussion

In the present work, the concept of CCD with 20 experimental runs is carried out to determine the optimum process parameters. The process parameters considered are cutting speed, feed rate, and depth of cut. Each experimental run was conducted using different cutting tool inserts for a length of 10 mm. The responses considered after machining are cutting force and surface roughness, which are presented in Table 3. In the present study, the 20 experimental runs allowed the estimation of linear, quadratic, and two-way interactive effects of the process parameters on cutting force and surface roughness. After analyzing each response, multiple response optimizations were performed by the inspection of the interpretation plots with the provided graphical and numerical tools. RSM designs helped in quantifying the relationships between one or more measured responses and the vital input factors. The data collected was analyzed in a statistically sound manner using regression to determine the relationship between the factors and responses. A regression was performed in order to describe the data collected, whereby an observed empirical variable or response is approximated based on a functional relationship between the estimated variable, F(x), and one or more regressor or input variable x₁, x₂… x_i.

Table 3.

Cutting force and surface roughness.

Ex no	X₁	X₂	X₃	Cutting speed (V) m/min	Feed rate (f) in mm/rev	Depth of cut (d) in mm	Hybrid-composite material
Ex no	X₁	X₂	X₃	Cutting speed (V) m/min	Feed rate (f) in mm/rev	Depth of cut (d) in mm	Cutting force (N)	R_a (µm)
1	1	1	1	75	0.05	0.5	600.2591	2.05
2	2	2	2	97.5	0.125	0.75	604.7162	3.95
3	1	3	1	75	0.2	0.5	564.6724	3.55
4	2	2	3	97.5	0.125	1	691.3599	4.30
5	3	3	3	120	0.2	1	634.6845	2.00
6	3	2	2	120	0.125	0.75	588.8443	5.60
7	3	3	1	120	0.2	0.5	589.9250	3.50
8	2	1	2	97.5	0.05	0.75	539.4078	4.25
9	2	3	2	97.5	0.2	0.75	564.4304	3.50
10	2	2	2	97.5	0.125	0.75	578.8686	3.90
11	3	1	1	120	0.05	0.5	573.0188	2.35
12	2	2	2	97.5	0.125	0.75	617.4876	4.20
13	2	2	2	97.5	0.125	0.75	602.6831	5.30
14	3	2	1	97.5	0.125	0.5	601.8046	5.20
15	3	1	3	120	0.05	1	597.4997	4.00
16	1	3	3	75	0.2	1	553.1718	2.85
17	1	1	3	75	0.05	1	629.1070	3.40
18	2	2	2	97.5	0.125	0.75	602.5225	3.95
19	1	2	2	75	0.125	0.75	580.9079	5.00
20	2	2	2	97.5	0.125	0.75	593.7380	5.50

The least-square technique was used to ﬁt a model equation containing the said repressors or input variables by minimizing the residual error measured by the sum of square deviations between the actual and the estimated responses that estimate the regression coefficients, i.e. the coefficients of the model variables including the intercept or constant term. The calculated coefficients or the model equation was tested for statistical signiﬁcance by performing test for significance of the regression model with ANOVA by calculating the F-ratio, which is the ratio between the regression mean square and the mean square error. Test for significance on individual model coefficients was conducted. As replicate measurements are available, test indicating the significance of the replicate error in comparison to the model dependent error was performed.

The mathematical model to establish the relationships between input and output parameters was developed using Minitab-16 software at a confidence level of 95%, based on the experimental data collected as per the CCD based on RSM. Cutting force and surface roughness were expressed in the form as a non-linear function of process parameters. Additionally, checks were made in order to determine whether the model actually describes the experimental data. The checks performed here include determining the various coefficient of determination, R². These R² coefficients have values between 0 and 1. In addition to the above, the adequacy of the model is also investigated by the examination of residuals using ANOVA technique. The relationship may be considered to be adequate, if it satisfies the following: (a) the calculated F value of the model developed should not exceed the standard tabulated F value and (b) the calculated R value of the developed relationship should exceed the standard tabulated R value for a desired level of confidence.

Mathematical model for hybrid-composite material

The response function representing any of the force acting in cutting-tool dimensions can be expressed as Y = f(V, f, d), where V is cutting speed in rate per m, f is the feed rate in millimeter/rev, and d is the depth of cut in millimeters. The relationship selected being a second-degree response is expressed as follows in equation (1).

{Y = b}_{0} {+ b}_{1} {V + b}_{2} {F + b}_{3} {D + b}_{11} V^{2} {+ b}_{22} F^{2} {+ b}_{33} D^{2} {+ b}_{12} {VF + b}_{13} {VD + b}_{23} VD

(1)

The values of the coefficients were calculated by regression analysis with the help of Minitab 16 software. The calculated values of regression coefficients for cutting force are being presented in Table 4.

Table 4.

Regression coefficients for cutting force.

Term	Coefficient	SE coefficient	T	P
b0	329.36	329.51	1	0.341
b1	0.6	7.05	0.085	0.934
b2	455.62	1086.36	0.419	0.684
b3	907.52	470.79	1.928	0.083
b11	0.01	0.04	0.347	0.735
b22	−5661.17	3165.77	−1.788	0.104
b33	−562.43	284.92	−1.974	0.077
b12	−17.12	6.19	−2.767	0.02
b23	−0.16	1.86	−0.088	0.932
b13	174.48	556.83	0.313	0.76

S = 29.5303; Press = 38676.4.

R-Sq = 97.75%; R-Sq (pred) = 90.03%; R-Sq (adj) = 95.73%.

The coefficient of correlation was found to be equal to 0.9801. The normal probability plot for the above model Figure 3 shows that the parameters are uniformly distributed throughout the model. Thus, the model was seen to be statistically adequate to make further predictions. The lack of fit was found to be insignificant. The calculated values of regression coefficients for surface roughness (R_a) are being presented in Table 5.

Figure 3.

Normal probability plot of cutting force.

Table 5.

Regression coefficients for surface roughness.

Term	Coefficient	SE coefficient	T	P
b0	5.93	3.1316	1.894	0.088
b1	−0.087	0.067	−1.298	0.223
b2	64.947	10.3246	6.291	0
b3	−0.776	4.4743	−0.174	0.866
b11	0	0.0003	1.141	0.28
b22	−196.768	30.087	−6.54	0
b33	−0.109	2.7078	−0.04	0.969
b12	−0.107	0.0588	−1.827	0.098
b23	0.017	0.0176	0.945	0.367
b13	−13	5.292	−2.457	0.034

S = 0.280652; Press = 4.55695.

R-Sq = 91.50%; R-Sq (pred) = 50.83%; R-Sq (adj) = 83.85%.

The coefficient of correlation was found to be equal to 0.9150. Thus, the model was seen to be statistically adequate to make further predictions. The lack of fit was found to be insignificant. The normal probability plot for the model Figure 4 shows that the parameters are uniformly distributed throughout the model, which is a clear indication of the fitness of the model.

Figure 4.

Normal probability plot of surface roughness.

Development of the final models

The insignificant terms are eliminated in the model presented above after maintaining hierarchy rules. Thus, the terms b11, b22, b33, b23, and b13 are eliminated for cutting force, and the terms b11, b33, b12, and b23 are eliminated for surface roughness since their p values are found to be higher than the standard values (95% confidence limit). The final mathematical models as determined by the above analysis are presented in Tables 6 and 7. The normal probability plot, for the final models, is shown in Figures 5 and 6.

Figure 5.

Normal probability plot of cutting force after eliminating insignificant terms.

Figure 6.

Normal probability plot of surface roughness after eliminating insignificant terms.

Table 6.

Regression coefficients for cutting force after eliminating insignificant terms.

Term	Coefficient	SE coefficient	T	P
b0	583.152	125.341	4.653	0
b1	2.861	1.201	2.383	0.031
b2	−828.809	842.662	−0.984	0.341
b3	69.805	51.102	1.366	0.192
b12	−17.117	8.464	−2.022	0.061

S = 40.3997; Press = 47509.0.

R-Sq = 93.69%; R-Sq (pred) = 87.75%; R-Sq (adj) = 92.00%.

Table 7.

Regression coefficients for surface roughness after eliminating insignificant terms.

Term	Coefficient	SE coefficient	T	P
b0	5.24	1.7216	3.044	0.009
b1	−0.026	0.0168	−1.547	0.144
b2	39.756	6.9589	5.713	0
b3	−2.565	2.1431	−1.197	0.251
b22	−176.889	27.2295	−6.496	0
b13	0.017	0.0215	0.774	0.452

S = 0.342490; Press = 4.93597.

R-Sq = 82.28%; R-Sq (pred) = 46.74%; R-Sq (adj) = 75.95%.

The validity of the above model can be justified from their high coefficients of correlation, which are presented in Figures 7 and 8, and show the relationship between the measured and computed model values of cutting force and surface roughness. These scatter diagrams indicate that the above equations show a good relationship between the measured and the computed values of cutting force and surface roughness.

Figure 7.

Scatter diagram for cutting force.

Figure 8.

Scatter diagram for surface roughness.

Figure 9.

Cutting speed versus cutting force.

Individual effects of process parameters on responses

Based on the regression equations, the variation of the responses with respect to each of the three process parameters, cutting speed, feed rate, and depth of cut was plotted by keeping two parameters constant at their lower limit and varying the third within the upper and lower bounds.

Cutting force increases with the increase in cutting speed, and surface roughness decreases with the increase in cutting speed as shown in Figures 9 and 10, respectively.

Figure 10.

Cutting speed versus surface roughness.

Cutting force decreases with the increase in feed rate as shown in Figure 11, whereas surface roughness increases with the increase in feed rate up to 0.12 mm/rev and then found to be decreasing as shown in Figure 12.

Figure 11.

Feed rate versus cutting force.

Figure 12.

Feed rate versus surface roughness.

Cutting force increases with the increase in depth of cut as shown in Figure 13, and surface roughness decreases with the increase in depth of cut as presented in Figure 14.

Figure 13.

Depth of cut versus cutting force.

Figure 14.

Depth of cut versus surface roughness.

Interaction effects of process parameters on responses

Interactive effects of process parameters on each of the responses have been presented in Figures 15 and 16 using contour plots. Contour plots are generated using Minitab 16 software for all pairs of factors. From the contour plots, it is clear that feed-rate cutting speed has the maximum influence on the cutting force and surface roughness.

Figure 15.

Contour plots for cutting force.

Figure 16.

Contour plots for surface roughness.

Optimization of machining parameters using GA

GAs are adaptive heuristic search algorithm that uses the idea of survival of the fittest amongst an interbreeding population to create a search strategy. The GA creates a population of solutions and applies genetic operators such as mutation and crossover to evolve the solutions in order to find the best one(s). A MATLAB function was written using the developed RSM model. The objective of the optimization was to (a) minimize force and (b) minimize surface roughness. Developed mathematical models are given below in equations (2) and (3).

Objective functions:

F 1 (x) = 583.152 + 2 . 861^{*} V - 828 . 809^{* F} + 69 . 805^{*} D - 17 . 117^{*} V^{*} F

(2)

F 2 (x) = 5.24 - 0 . 026^{*} V + 39 . 756^{* F} - 2 . 565^{*} D - 176 . 889^{*} F 2 + 0 . 017^{*} V^{*} D

(3)

Minimize F1(x); Minimize F2(x); where F1(x), F2(x) = f (S, F, D), F1(x) the cutting force, F2(x) the surface roughness, V the cutting speed, F the feed rate, and D the depth of cut, such that the process parameters lie within the limits: {75 ≤ S ≤ 120; 0.05 ≤ F ≤ 0.2; .05 ≤ D ≤ 1;}

The weighted average change in the fitness function value over 200 generations was used as the criteria for stopping the algorithm. The optimized Pareto front achieved after 126 iterations is shown in Figure 17. The input decision variables corresponding to each of the Pareto optimal solutions are tabulated in Table 8.

Figure 17.

Pareto front plot.

Table 8.

GA solution points for hybrid-composite material.

SI no	Cutting force (N)	Surface roughness (R_a)	Cutting speed (m/min)	Feed rate (mm/rev)	Depth of cut (mm)
2	420.2494	2.48371	118.9268	0.199945	0.996861
3	420.2494	2.48371	118.9268	0.199945	0.996861
4	394.6737	2.696623	118.246	0.199937	0.624668
5	397.3677	2.663781	118.8242	0.199944	0.668205
6	392.048	2.71212	118.5137	0.199935	0.589129
7	395.5548	2.676481	118.9195	0.199937	0.642692
8	386.1097	2.76949	118.0343	0.199934	0.500167
9	403.7407	2.620264	118.4915	0.199936	0.756511
10	417.4182	2.50999	118.6518	0.199938	0.953819
11	390.4577	2.736493	118.1126	0.19987	0.560481
12	403.6215	2.642596	118.1398	0.199653	0.740418
13	414.4725	2.530469	118.8127	0.199943	0.913104
14	387.6406	2.749546	118.3876	0.199936	0.524998
15	418.0151	2.502923	118.798	0.199945	0.9638
16	410.3498	2.561704	118.8735	0.199943	0.854532

GA: genetic algorithm.

A set of solution points were predicted for simultaneously optimizing both responses. A change in the value of any one of the considered control parameters further improves any one of the responses at the cost of degrading the other responses. This result is helpful as it provides a wide range of optimal setting of control parameters for simultaneously optimizing both the responses. The optimized results obtained through GA are presented in Table 9.

Table 9.

Results of GA optimization.

Type		Cutting force (N)	Surface roughness (R_a)	Cutting speed (m/min)	Feed rate (mm/rev)	Depth of cut (mm)
Multi objective		386.1097	2.76949	118.0343	0.199934	0.5001
Single objective	Cutting force (N)	384.822		119.977	0.2	0.5000
Single objective	Surface roughness (R_a)		2.48475	118.5734	0.1999	0.9998

GA: genetic algorithm.

Confirmation tests

In order to verify the validity of the results obtained from GA, a confirmation test was performed. The conﬁrmation test results were compared with the predicted values. In total, three confirmation tests were performed, two for single objective and one for multi objective. The results obtained are given in Table 10. As surface roughness is a predominant factor for any application of a machined component, the readings obtained from the confirmation tests show that the variations of the predicted responses and the obtained values are negligible. The cutting force also increases with the increase in depth of cut. For a hybrid-composite material consisting of aramid, carbon fiber, and bishphenol resin, the optimized values obtained through GA are cutting speed = 118.0343 m/min, feed rate = 0.199934 mm/rev, depth of cut = 0.5001 mm, cutting force = 391.159 N, and surface roughness (R_a) = 2.76949 µm. Since the material selected for the investigation is a bi-directional fabric with two different fibers with different properties, the fracture mechanism of fibers is different from that of a unidirectional fiber due to shearing and bending that is dependent on the direction of lay of fibers.

Table 10.

Results of confirmation test to validate the GA values.

Type		Cutting force (N)	Surface roughness (R_a)	Cutting speed (m/min)	Feed rate (mm/rev)	Depth of cut (mm)
Multi objective		391.159	2.76949	118.0343	0.199934	0.5001
Single objective	Cutting force (N)	378.662		119.977	0.2	0.5000
Single objective	Surface roughness (R_a)		2.61	118.5734	0.1999	0.9998

GA: genetic algorithm.

Conclusion

From this study, it was found that when machining a hybrid carbon and aramid fiber pipes manufactured by hand lay-up process using carbide tool inserts, the cutting force increases with the increase in cutting speed while surface roughness decreases with the increase in cutting speed. With increase in feed rate, cutting force decreases and surface roughness increases intially and starts decreasing when feed rate exists, i.e. 0.12 mm/rev. The cutting force also increases with the increase in depth of cut. For a hybrid-composite material, the optimized values through GA are cutting speed = 118.0343 m/min, feed rate = 0.199934 mm/rev, depth of cut = 0.5001 mm, cutting force = 391.159 N, and surface roughness (R_a) = 2.76949 µm.

In this study, the objectives considered are significantly improved by using the GA and RSM. The experimental values and the regression model values follow an identical trend that shows that the models developed are best suited for this particular machining operation.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Conflict of interest

None declared.

Appendix

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