Simultaneous optimization of surface roughness and ... - Springer Link

Int J Adv Manuf Technol (2014) 74:879–891 DOI 10.1007/s00170-014-6043-9

ORIGINAL ARTICLE

Simultaneous optimization of surface roughness and material removal rate for turning of X20Cr13 stainless steel Lakhdar Bouzid & Smail Boutabba & Mohamed Athmane Yallese & Salim Belhadi & Francois Girardin

Received: 18 February 2014 / Accepted: 3 June 2014 / Published online: 14 June 2014 # Springer-Verlag London 2014

Abstract The objective of this article is to manufacture lowcost, high-quality products with maximum productivity in short time. In this work, four stages are considered: statistical investigation of the experimental results based on ANOVA, modelling based on regression analysis and mono- and multiobjective optimizations. In the first stage, turning experiments were carried out using an orthogonal array (L16) of Taguchi. Effects of cutting parameters on surface roughness and material removal rate were determined using ANOVA and interaction plots. In the second stage, regression analysis was utilized to formulate second-order models of all data gathered in the experimental works; these models could be used to predict responses in turning of X20Cr13 steel with a minor error. In the third stage, responses were used alone in an optimization study as an objective function. To minimize all responses, Taguchi’s signal-to-noise ratio was used. In the fourth stage, responses were optimized simultaneously using grey relational analysis. L. Bouzid (*) : M. A. Yallese : S. Belhadi Mechanics and Structures Research Laboratory (LMS), Mechanical Engineering Department, May 8th 1945 University, P.O. Box 401, Guelma 24000, Algeria e-mail: [email protected]

Keywords Surface roughness . Material removal rate . ANOVA . Taguchi method . Grey relational analysis Nomenclature Vc f ap MRR Ra GRA bii bj bij R2 ANOVA df SS MS Cont.% α χr γ λ

Cutting speed (m/min) Feed rate (mm/rev) Depth of cut (mm) Material removal rate Arithmetic mean roughness (μm) Grey relational analysis Quadratic terms Coefficients of linear terms Cross product terms Determination coefficient Analysis of variance Degrees of freedom Sequential sum of squares Adjusted mean squares Contribution ratio (%) Clearance angle (°) Major cutting edge angle (°) Rake angle (°) Cutting edge inclination angle (°)

M. A. Yallese e-mail: [email protected] S. Belhadi e-mail: [email protected] S. Boutabba Laboratoire de Mécanique Appliquée des Nouveaux Matériaux (LMANM), BP. 401 Université 8 Mai 1945, Guelma 24000, Algérie e-mail: [email protected] F. Girardin Laboratoire Vibrations Acoustique, INSA-Lyon, 25 bis avenue Jean Capelle, 69621 Villeurbanne Cedex, France e-mail: [email protected]

1 Introduction In modern industry, the goal is to manufacture low-cost, highquality products with maximum productivity in a short time. Turning is the most common method for cutting and especially for the finishing of machined parts. Furthermore, in order to produce with desired quality and maximum productivity of machining, cutting parameters should be selected properly. In turning process, parameters such as materials, tool’s geometry

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and cutting conditions (depth of cut, feed rate, cutting speed) have impact on the material removal rate and the machining qualities like the surface roughness [1]. Usually, roughness is taken as a good criterion for a mechanical component performance and also to appraise production cost [2], while material removal rate (MRR) can be defined as the volume of material removed divided by the machining time. Another way to define MRR is to imagine an "instantaneous" material removal rate as the rate at which the cross-section area of material being removed moves through the workpiece [3]. When considering product manufacturing process, both optimization and modelling are carefully taken into account as two important issues. Surface roughness and material removal rate are difficult to model because they are affected by various variables. Recently, several studies presented different models using surface roughness measurements, material removal rate and a specified machining process with the aim to simulate and subsequently optimize the cutting regime [4, 5]. The use of a new optimization method allows us to find the optimal cutting parameters for surface roughness and material removal rate in turning operations. The grey relational analysis and Taguchi orthogonal array have been used quite successfully in process optimization [6]. Yang and Tarng [7] employed Taguchi method to investigate the cutting characteristics of S45C steel bars using tungsten carbide cutting tools. The optimal cutting parameters of the cutting speed, the feed rate and the depth of cut for turning operations with regard to performance indexes such as tool life and surface roughness are considered. Fung et al. [8] studied the grey relational analysis to obtain the optimal parameters of the injection moulding process for mechanical properties of yield stress and elongation in polycarbonate/acrylonitrile-butadiene-styrene (PC/ABS) composites. Shen et al. [9] studied different polymers (such as PP, PC, PS and POM) with various process parameters of a microgear. The simulation used the Taguchi method, and the grey relational analyses were provided. Lin [10] employed the Taguchi method and the grey relational analysis to optimize the turning operations with multiple performance characteristics. Ahmet and Ulaş [11] investigated the effect and optimization of machining parameters on surface roughness and tool life in a turning operation using the Taguchi method. Conclusions revealed that the feed rate and cutting speed were the most influential factors on the surface roughness and tool life, respectively. Ihsan et al. [12] determined the optimum cutting speed when turning AISI 304 austenitic stainless steel using cemented carbide tools. The results showed that the surface finish decreased with increasing the cutting speed. Liew and Ding [13] found that the ductility of the workpiece and the tool wear appeared to have influences on the surface roughness during the milling of AISI 420. El-Tamimi and El-Hossainy [14] used the carbide cutting tools to study the highest stainless steel AISI 420 at different cutting conditions. Mean effect and interaction

Int J Adv Manuf Technol (2014) 74:879–891

plots were used to present the most influential factors. Bouchlaghem et al. [15] concluded that the feed rate remains the most affecting factor on the surface roughness values in turning of AISI D3. Mor et al. [16] used the statistical analysis ANOVA to determine the effect of cutting speed and feed rate on the tool wear and surface finish in turning of hardened AISI 4340 steel. Bouacha et al. [17] fond that the surface roughness is mainly influenced by feed rate and cutting speed using ANOVA. Aouici et al. [18] determined the optimum surface roughness (Ra=0.327–0.34 μm) using the response surface methodology RSM in turning of AISI H11 by CBN7020 tool. They also found that the best surface roughness was achieved at the lower feed and the highest cutting speed. Suresh et al. [19] established a correlation between cutting parameters with machining force, power and surface roughness, in the machining of hardened AISI 4340 steel, using cemented carbide tools. Results showed that the feed rate has the highest influence on surface roughness (83.79 %), followed by cutting speed which has a lower effect (10.08 %), and finally depth of cut (3.99 %) which has a negligible effect on roughness evolution. Eyup and Seref [20] employed orthogonal arrays of Taguchi, the signal-to-noise (S/N) ratio and ANOVA to find the optimal levels and to analyse the effect of the milling parameters on surface roughness. Yallese et al. [21] predicted the effect of feed rate on surface roughness by a power model deduced from experimental data and compared it with a theoretical model in turning of X200Cr12 steel. Fnides et al. [22] determined statistical models of surface roughness criteria in hard turning of X38CrMo V5-1. Results showed that the feed rate is the dominant factor influencing surface roughness followed by cutting speed. This study presents the optimisation of turning parameters for X20Cr13 stainless steel so as to minimize the surface roughness and maximize the material removal rate simultaneously, using Taguchi-based grey relational analysis (Fig. 1). Surface roughness and material removal rate have been studied intensively, mostly through experiments.

2 Experimental procedures 2.1 Material The material used in this study was a martensitic stainless steel designated as X20Cr13. The reference chemical composition is shown in Table 1. Because of its relatively important corrosion resistance and fair hardness (about 180 HB), it is widely employed for many applications such as tools for food processing, surgery, chemical containers and transportation equipment. The workpieces were used in the form of round bars having 75 mm in diameter and 300 mm length. The machining experiments were performed under dry conditions using a conventional lathe type SN 40C with 6.6 kW spindle power.


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Work-piece

Tool Typical record of roughness profile

Roughness meter

Ra, MRR

Mono-Objecve Opmizaon (Taguchi’s Method)

Mul-Objecve Opmizaon (Grey Method)

Ra A

4

B

C

Opmal Result

3 2 1 0 -1 -2 -3 -4 -5 A1

A2

A3

A4

B1

B2

B3

B4

C1

C2

C3

C4

GRG

MRR A

28

B

A

-3,0

C

B

C

-3,5

27 26

-4,0

25 24

-4,5

23

-5,0

22 21

-5,5

20

-6,0

19 A1

A2

A3

A4

B1

B2

B3

B4

C1

C2

C3

A1

C4

A2

A3

A4

B1

B2

B3

B4

C1

C2

C3

C4

Fig. 1 Optimization setups for Ra and MRR

Table 1 Chemical composition of X20Cr13 stainless steel (wt%)

C

Cr

Ni

Si

Al

S

Mo

Mn

Sn

Cu

P

Fe

0.36

13.87

0.19

0.28

0.005

0.018

0.04

0.52

0.005

0.04

0.019

Rest

882 Table 2 Factors and levels used in the experimental plan


Symbol

Factors

Unit

Levels Level 1

Level 2

Level 3

Level 4

A

Cutting speed (Vc)

m/min

120

170

200

280

B C

Feed rate (f) Depth of cut (ap)

mm/rev mm

0.08 0.15

0.12 0.3

0.16 0.45

0.2 0.6

2.2 Cutting tool and tool holder Coated carbide inserts of ISO geometry SNMG 120408 were used throughout the investigation. The CVD coating used was a multilayer of TiN/TiCN/Al2O3 formed on a cemented carbide substrate. It consists of a thick, moderate temperature chemical vapour deposition (MT CVD) of TiN for heat resistance and providing low friction coefficient. Despite the fact that TiCN offers a good resistance to wear and thermal stability, a layer of Al2O3 is required to bear effects like crater wear damage resulting from high-temperature conditions and hardness. By now, it is well confirmed that this combination of top coating and associated gradient substrate confers excellent behaviour during dry machining [19]. The tool holder ISO reference was PSBNR 2525K12 and the tool geometry was characterized by: χr =+75°, is λ=−6°, γ=−6° and α=+6°.

was directly measured on the workpiece without dismounting from the lathe. The measurements were repeated three times on the surface of the workpiece at three reference lines equally positioned at 120°. The final result is an average of these values. The MRR (mm3/min) was calculated using the following Eq. 1. MRR ¼ 1; 000 Vc f ap

ð1Þ

In Eq. 1, Vc (m/min) denotes the cutting speed, f (mm per revolution) describes the feed rate and ap (mm) presents the cutting depth of the turning operation.

3 Results and discussion 3.1 ANOVA analysis

2.3 Design with Taguchi method Taguchi method uses specially constructed tables named as “orthogonal array” to design the experiments and using these orthogonal arrays diminishes the number of experiments [23]. As a result, experimental cost and time will reduce. Taguchi’s L16 orthogonal array was used for the experimental design in order to achieve the aims of how the controlled factors affect the output factors and what the optimal turning controlled parameters to obtain lower surface roughness and higher material removal rate. Spindle speed, feed rate and depth of cut were considered as controlled factors, while surface roughness and material removal rate were selected as output factors. The control factors and their levels were given in Table 2. The experimental plan for three turning parameters (cutting speed, feed rate and depth of cut) with four levels (4^3) was organized by the Taguchi method (L16 orthogonal array in Table 3). 2.4 Measurement setup Instantaneous measurements of arithmetic mean roughness (Ra), for each cutting condition, were obtained by means of a Mitutoyo Surftest 201 roughness meter. The length examined was 4 mm with a cut-off of 0.8 mm, and the measured values of Ra were within the range of 0.05–40 μm. In order to reduce uncertainties due to resumption operations, roughness

ANOVA is useful to figure out the influence of given input parameters from a series of experimental results by the method of design of experiments for machining processes and it also allows to supply an interpretation output data [19]. It essentially consists of partitioning the total variation in an Table 3 Taguchi L16 (43) orthogonal array Experimental number

A (m/min)

B (mm/rev)

C (mm)

1

A1

B1

C1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A1 A1 A1 A2 A2 A2 A2 A3 A3 A3 A3 A4 A4 A4 A4

B2 B3 B4 B1 B2 B3 B4 B1 B2 B3 B4 B1 B2 B3 B4

C2 C3 C4 C2 C1 C4 C3 C3 C4 C1 C2 C4 C3 C2 C1

Int J Adv Manuf Technol (2014) 74:879–891 Table 4 Analysis of variance for Ra

883

Source

df

SS

MS

F value

P value

Cont.%

Remarks

Model Vc f ap Vc×f

9 1 1 1 1

2.865 0.003 2.452 0.025 0.014

0.318 0.059 0.025 0.044 0.008

26.746 4.954 2.102 3.734 0.676

0.0004 0.7422 0.0002 0.2095 0.4424

97.57 0.10 83.50 0.84 0.47

Significant Insignificant Significant Insignificant Insignificant

Vc×ap f×ap Vc2 f2 ap2 Residual Cor total

1 1 1 1 1 6 15

0.002 0.046 0.152 0.153 0.018 0.071 2.937

0.002 0.017 0.152 0.153 0.018 0.012

0.195 1.427 12.805 12.887 1.491

0.6739 0.2773 0.0117 0.0115 0.2675

0.08 1.55 5.19 5.22 0.60

Insignificant Insignificant Significant Significant Insignificant

experiment into components ascribable to the control factors and generated errors. The statistical significance of the fitted quadratic models is evaluated by the P values and F values of ANOVA. The last but one column of ANOVA tables shows the factor contribution (percentage, Cont. %) on the total variation, indicating the degree of influence on the result. The obtained results were analysed using two statistical software Design-Expert 8 and Minitab 16. Tables 4 and 5 illustrate ANOVA results for Ra and MRR, respectively, for the 99 % confidence level (the level significance is 1 %). Table 4 summarizes the interaction results for Ra. The most important factor affecting the quality of surface finish is the feed rate (f) as confirmed in another study. Its contribution is (83.5 %) in this type of models, and it is known that augmentation of (f) generates furrows in the form of helicoids imparted by tool shape and the system tool-workpiece movements. The furrows are deeper and broader as the feed rate increases [18]. The effects of products (Vc2, f2) are significant with contribution values (5.19 and 5.22 %), respectively.

Table 5 Analysis of variance for MRR

The amount of heat generation increases with increasing feed rate, as the cutting tool has to remove more volume of material from the workpiece. The workpiece plastic deformation is usually proportional to the amount of generated heat and promotes roughness on the surface finish [24, 25]. Because of the increased length of contact between the tool and the workpiece, depth of cut has a much smaller effect compared to that of the feed rate. Based on these results, feed rate was found to be the most significant factor on surface roughness evolution for this kind of steel. This is in good agreement with previously published research work [15, 19, 26, 27]. Table 5 presents ANOVA results for the material removal rate. It can be stated that the depth of cut has the highest statistical significance (58.74 %) followed by feed rate (19.67 %) and cutting speed (14.45 %). The interactions (Vc×f, Vc×ap and f×ap) and the products (Vc2, f2 and ap2) were found to be less significant.

Source

df

SS

MS

F value

P value

Cont.%

Remarks

Model Vc f ap Vc×f Vc×ap f×ap Vc2 f2 ap2 Residual Cor total

9 1 1 1 1 1 1 1 1 1 6 15

387,836,938 56,035,184 76,284,180 227,812,500 1,339,950 10,445,370 12,982,920 1,093,634 921,600 921,600 4,562 387,841,500

43,092,993 56,035,184 76,284,180 227,812,500 1,339,950 10,445,370 12,982,920 1,093,634 921,600 921,600 760

56,676.4 73,698.2 100,329.9 299,621.9 1,762.3 13,737.9 17,075.3 1,438.4 1,212.1 1,212.1

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

100 14.45 19.67 58.74 0.35 2.69 3.35 0.28 0.24 0.24

Significant Significant Significant Significant Significant Significant Significant Significant Significant Significant

884


Fig. 2 Comparison between predicted and measured values for Ra

3.2 Regression analysis

The material removal rate model (MRR) is given by Eq. 4.

The relationship between input parameters and performance measurements (outputs) are modelled by quadratic regressions. The general form of the second-order model is given in Eq. 2. Y ¼ bo þ

k X

bi X i þ

i¼1

k X ij

bij X i X j þ

k X

bii X i 2

Ra ¼ −0:5866 þ 0:0118869Vc−8:94362f þ 2:88804ap −3:35055E −5 Vc2 þ 0:0145713Vc f −0:00208921Vc ap þ 61:1979f f −6:90999f ap−1:48148ap ap

Fig. 3 Comparison between predicted and measured values for MRR

−150; 000f f þ 198; 262f ap−10; 666:7ap ap ð4Þ

ð2Þ

i¼1

where b0 is the free term of the regression equation, the coefficients b1, b2 … bk and b11, b22, bkk are the linear and the quadratic terms, respectively, while b12, b13, bk−1 are the interacting terms. Xi represents the input parameters (Vc, f, ap), and Y represents the outputs [surface roughness and material removal rate]. The arithmetic mean roughness (Ra) model is given below in Eq. 3.

[R2 =97.57 %]

MRR ¼ 2; 973:58−16:7099Vc−32; 348:3f −19; 756:7ap −0:0897506Vc2 þ 375Vc f þ 140Vc ap

ð3Þ

[R2 =100 %] To justify the validity of developed second-order model, R2 (R squared, correlation coefficient) value is used. R2 can be defined as follows: R2 ¼ 1−

SSR SST

ð5Þ

where SSR is the sum squared of residual, and SST the sum squared total. R2 is a coefficient of multiple determinations, which measures variation proportion in the set of data points [28]. In the present study, R2 values for Ra (97.57 %) and MRR (100 %) are very close to 1, suggesting a reasonable goodness of the model which can be used for prediction within the limits of the


885

factors investigated. The adequacies of the developed equations were also checked by ANOVA technique. SSE and SST values were used. SSE values for Ra and MRR were found to be 2.865 and 387836938, respectively. SST values for Ra and MRR were obtained as 2,937 and 387,841,500, respectively. The models are adequate as F calculated values (26.746 and 56,678.9, respectively, to Ra

and MRR) are greater than F table value at 99 % confidence level. The predicted values obtained from second-order models were compared with experimental results, and the relationship between these values was plotted as shown in Figs. 2 and 3. It was found from these figures that the variations between experimental and predicted values were minimal.

2

25000

1.8 20000

MRR, mm3/min

1.6 1.4 1.2 1 0.8 0.6 0.4

0.20

280 0.17

15000 10000 5000 0

0.20

240 0.14

200 0.11

f, mm/rev

280 0.17

160

0.14

Vc, m/min

0.08 120

240

2

200 0.11

f, mm/rev

160

Vc, m/min

0.08 120

25000

1.8 20000

MRR, mm3/min

1.6 1.4 1.2 1 0.8 0.6 0.4

0.60

280 0.49

15000 10000 5000 0

0.60

240 0.38

200 0.26

ap, mm

280 0.49

160

0.38

Vc, m/min

0.15 120

240

ap, mm

2

200 0.26

160

Vc, m/min

0.15 120

25000

1.8

20000

MRR, mm3/min

1.6 1.4 1.2 1 0.8 0.6 0.4

0.60

0.20 0.49

0.17 0.38

ap, mm

15000 10000 5000 0

0.60

0.20 0.49

0.14 0.26

0.11 0.15 0.08

0.17 0.38

f, mm/rev

Fig. 4 3D plots for surface roughness (Ra) and material removal rate (MRR)

ap, mm

0.14 0.26

0.11 0.15 0.08

f, mm/rev

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Table 6 Experimental and S/N results Experimental

Ra

Number

Result (μm)

S/N (dB)

Result (mm3/min)

S/N (dB)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.51 0.72 1.21 1.61 0.65 0.85 1.22 1.83 1.04 1.14 1.18 1.92 0.58 0.80

5.91 2.85 −1.63 −4.14 3.70 1.41 −1.70 −5.23 −0.34 −1.11 −1.46 −5.65 4.68 1.90

1,440 4,320 8,640 14,400 4,080 3,060 16,320 15,300 7,200 14,400 4,800 12,000 13,440 15,120

10.01 22.08 25.45 27.30 21.74 19.75 27.70 27.49 24.68 27.30 22.69 26.68 27.07 27.45

15 16

1.14 1.69

−1.14 −4.54

13,440 8,400

27.07 25.34

From the interaction plot of Fig. 4b, it can be observed that the MRR sharply increases with cutting speed, feed rate and depth of cut. It should be noted that the maximal material removal rate occurred for the combination of the three highest values of the parameters (Vc, f and ap).

MRR

3.4 Mono-objective optimization using S/N analysis The term signal represents the desirable effect for the output characteristic, and the term noise stands for the undesirable effect for the output characteristic [23]. S/N ratio measures the quality characteristics deviating from the desired values. The highest S/N ratio means the optimal level of the process parameters. Since low surface roughness and high material removal rate were desirable in this study, the smaller-thebetter S/N quality characteristic was used for the surface roughness and the larger-the-better S/N for the material removal rate. Quality characteristics of the smaller-the-better and the larger-the-better S/N are calculated with the following equations: –

3.3 Effect of cutting parameters on responses

" . 1 S N ¼ −10log10 n

To evaluate the effects of turning parameters on surface roughness and material removal rate, 3D surface plots were drawn changing two parameters while the other parameter was kept constant. 3D surface plots of responses vs. different combinations of cutting parameters are shown in Fig. 4. As deduced from the interaction plot of Fig. 4a, it can be observed that the surface roughness (Ra) rapidly increases with increasing feed rate. However, cutting speed and depth of cut have weak influence on surface roughness. It should be noted that the minimal surface roughness occurred for the combination of three low values of the parameters (f, ap and Vc). Fig. 5 Main effects plot of S/N ratios for Ra

Smaller-the-better S/N:

–

!# ð6Þ

y2i

i¼1

Larger-the-better S/N:

" . 1 S N ¼ −10log10 n

n X 1 2 y i¼1 i

!# ð7Þ

where yi is the ith measured experimental results in a run/row, and n explains the number of measurements in each test trial/ row. A

4

n X

B

C

Mean of S/N ratios

3 2 1 0 -1 -2 -3 -4 -5 A1

A2

A3

A4

B1

B2

B3

B4

C1

C2

C3

C4


887

Fig. 6 Main effects plot of S/N ratios for MRR

A

28

B

C

Mean of S/N ratios

27 26 25 24 23 22 21 20 19 A1

A2

The experimental results and the S/N ratio values calculated by taking Eqs. 6 and 7 into consideration were given in Table 6. The level of a parameter with the highest S/N ratio gives the optimal level. All the optimal machining parameters were highlighted in circles in Figs. 5 and 6. So the optimal process parameter setting for Ra was A1, B1 and C1, namely cutting speed of 120 m/min, feed of 0.08 mm/rev and depth of cut of 0.15 mm (Fig. 5). A4, B4 and C4 were the optimum combination of process parameters for the highest MRR (Fig. 6). For MRR, the optimum parameters were as follows: cutting speed of 280 m/min, feed of 0.2 mm/rev and depth of cut of 0.6 mm. From the main effects plots, it can be concluded that the depth of cut was the most significant factor for MRR. For Ra, the most influential factor was feed rate. The percentage error between experimental values and predicted values for Ra and MRR using S/N ratio are 2.27 and 3.55 %, respectively. Table 7 gives the predicted and experimental results for Ra and MRR using mono-objective optimization.

A3

A4

B1

B2

B3

B4

C1

C2

C3

C4

Step 1 Grey relational generation The first step of grey relational analysis is to normalize (in the range between 0 and 1) the experimental data according to the type of performance response [29]. In the present study, as surface roughness had to be minimized (“the-smaller-the-better” is a characteristic of the original sequence) and material removal rate had to be maximized (“the-larger-the-better” is a characteristic of the original sequence), the original sequences should be normalized as follows: –

–

The-smaller-the-better: max x0i ðk Þ −x0i ðk Þ xi ð k Þ ¼ maxðx0i ðk ÞÞ−minðx0i ðk ÞÞ

ð8Þ

The-larger-the-better: xi ðk Þ

xki ðk Þ−min x0i ðk Þ ¼ maxðx0i ðk ÞÞ−minðx0i ðk ÞÞ

ð9Þ

3.5 Multi-objective optimization using grey relational analysis Grey relational grade is used to convert optimization problem from a multi-objective to a single-objective [23]. The aim of this study was to determine the optimal combination of turning parameters that simultaneously minimize surface roughness and maximize the material removal rate. To do so, grey relational analysis (GRA) was used in this study. Steps of GRA are as follows:

where x*i (k) is the value after grey relational generation (normalized value), and max(x0i (k)) and min(x0i (k)) are the largest and smallest values of x0i (k) for the kth response, respectively, k being 1 for surface roughness and 2 for material removal rate. Table 8 gives the processed data after grey relational generation. The normalized values were ranged between 0 and 1. Larger normalized results mean to better performance and the best normalized result should be equal to 1.

Table 7 Predicted and experimental values of individual machining characteristics Machining characteristic

Optimal parameters combination

Predicted optimal value

Experimental value

% error value

Ra MRR

120, 0.08, 0.15 280, 0.2, 0.6

0.45 32,406.109

0.44 33,600

2.27 3.55

888


Table 8 Normalized experimental results (x*i (k))

Exp. number (i)

Ra

MRR

Ideal value 1 2 3 4

1.00 1.00 0.85 0.50 0.22

5 6 7 8 9 10 11 12 13 14 15 16

0.90 0.76 0.50 0.06 0.62 0.55 0.52 0.00 0.95 0.79 0.55 0.16

Exp. number (i)

Ra

MRR

1.00 0.00 0.19 0.48 0.87

1 2 3 4 5

1.00 0.77 0.50 0.39 0.83

0.33 0.38 0.49 0.79 0.38

0.18 0.11 1.00 0.93 0.39 0.87 0.23 0.71 0.81 0.92 0.81 0.47

6 7 8 9 10 11 12 13 14 15 16

0.67 0.50 0.35 0.57 0.53 0.51 0.33 0.90 0.70 0.53 0.37

0.36 1.00 0.88 0.45 0.79 0.39 0.63 0.72 0.86 0.72 0.48

Step 3 Grey relational grade

Step 2 Grey relational coefficient Grey relational coefficients denote the relationship between the ideal and the actual experimental results. Grey relational coefficient (ξi(k)) can be calculated as the following: ξ i ðk Þ ¼

Δmin þ ψΔmax Δ0i ðk Þ þ ψΔmax

ð10Þ

0 < ξi ðk Þ≤ 1 where Δ0i(k) is the deviation sequence of reference sequence x*0(k) and comparability sequence x*i (k).

Δ0i ðk Þ ¼ x0 ðk Þ−xi ðk Þ ð11Þ

Δ0i ðk Þ ¼ min min x0 ðk Þ−xi ðk Þ

ð12Þ

Δmin ¼ min min x0 ðk Þ−xi ðk Þ

ð13Þ

Δmax ¼ max max x0 ðk Þ−xi ðk Þ

ð14Þ

∀ j∈i ∀k

∀ j∈i ∀k

∀ j∈i

∀k

Table 9 Grey relational coefficients (ξi(k))

ψ is the distinguishing coefficient (ψ∈ [0, 1]) and is used to adjust the difference of the relational coefficient. In this study, ψ was taken as 0.5, and the grey relational coefficients calculated using Eq. 10 are given in Table 9.

Grey relational grade shows the relationship among the series and is calculated as follows: 1X ξ ðk Þ n k¼1 i n

αi ¼

ð15Þ

where n is the number of performance characteristics (in this study, n is 2). The highest grey relational grade corresponds to the experimental value closest to the ideal normalized value. Table 10 Grey relational grade (αi) and its order Exp. number (i)

GRG (αi)

S/N (αi)

Order

1

0.667

−3.522

4

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.575 0.497 0.592 0.603 0.516 0.749 0.614 0.509 0.661 0.451 0.483 0.811 0.782 0.624 0.429

−4.804 −6.074 −4.548 −4.395 −5.748 −2.509 −4.240 −5.861 −3.590 −6.910 −6.321 −1.815 −2.131 −4.098 −7.347

10 13 9 8 11 3 7 12 5 15 14 1 2 6 16


889

Fig. 7 Grey relational grade (GRG)

The level of a parameter with the highest S/N ratio gives the optimal level, and optimal level was highlighted in circles in Fig. 8. So the optimal process parameter setting for the multiple performance characteristic was A4, B1 and C4 (Fig. 8). Thus, the best combination values for maximizing the multiple performance characteristic were cutting speed of 280 m/min, feed rate of 0.08 mm/rev and depth of cut of 0.6 mm. ANOVA results for the multiple performance characteristics are given in Table 11. The analyses were made for the level of confidence 95 % (the level significance is 5 %). Depth of cut, interactions (f×ap, Vc×ap), feed rate and cutting speed influenced the multiple performance characteristics by 35.02, 18.15, 15.55, 16.54 and 4.7 %, respectively, Table 11. From the analysis of this table, it could be concluded that depth of cut and feed rate were two dominant parameters that affect grey relational grade.

Thus, high grey relational grade corresponds to a parameter combination close to the optimal. Step 4 Grey relational ordering The highest grey relational grade is assigned an order of 1. Grey relational grade computed using Eq. 15 and grey relational order is given in Table 10. According to Table 10 and Fig. 7, the control parameters’ setting of experiment 13 had the highest grey relational grade and this meant that experiment 13 was the optimal turning factors’ setting for minimum surface roughness and maximum material removal rate simultaneously among the other experiments. Since higher multiple performance characteristics were desirable, the larger-the-better S/N quality characteristic was adopted for grey relational grade. Quality characteristic of the larger-the-better is calculated using Eq. 7.

Fig. 8 Main effects plot of S/N ratios for grey relational grade (multiple performance characteristics)

A

-3,0

B

C

Mean of S/N ratios

-3,5 -4,0 -4,5 -5,0 -5,5 -6,0 A1

A2

A3

A4

B1

B2

B3

B4

C1

C2

C3

C4

890


Table 11 ANOVA for grey relational grade

Source

df

SS

Ms

F value

P value

Cont.%

Remarks

Vc f ap Vc×f Vc×ap

1 1 1 1 1

0.009 0.033 0.070 0.000 0.031

0.010 0.028 0.046 0.007 0.031

4.505 12.879 20.760 3.009 14.107

0.0628 0.0059 0.0014 0.1169 0.0045

4.70 16.54 35.02 0.11 15.55

Insignificant Significant Significant Insignificant Significant

f×ap Residual Cor total

1 9 15

0.036 0.020 0.201

0.036 0.002

16.463

0.0029

18.15

Significant

The error between experimental values and predicted values for Ra and MRR using GRA are 3.27 and 0.01 %, respectively. Therefore, GRA process parameters can be successfully optimized for multiple machining characteristics during turning of X20Cr13 stainless steel. Table 12 shows the predicted and experimental results for Ra and MRR at a single optimal setting of process parameters using GRA.

4 Summary of results Using Taguchi method, process parameters were optimized individually for Ra and MRR. The percentage error between experimental values and predicted results are less than 4 % for both machining characteristics. Therefore, process parameters are successfully optimized for individual characteristics using Taguchi method. The optimal setting of process parameters for multiple machining characteristics, using GRA is A4, B1 and C4. Using ANOVA, two process parameters namely depth of cut (C) and feed rate (B) were found to affect the grey relational grade, significantly. The error between experimental values and predicted values for Ra and MRR using GRA are 3.27 and 0.01 %, respectively. Therefore, using GRA, process parameters can be successfully optimized for multiple machining characteristics during turning of X20Cr13 stainless steel. Table 13 summarizes the results for mono-objective and multi-objective optimization of machining characteristics.

Table 12 Predicted and experimental values of individual machining characteristics

5 Conclusions In this study, the effects of cutting speed, feed rate and depth of cut on surface roughness and material removal rate during turning of X20Cr13 were investigated using Taguchi experimental design method and ANOVA. Responses were also optimized through mono-objective and multi-objectives approach, considering grey relational analysis. All data gathered in the experimental studies were used to formulate second-order models. It was found that these models could be used to predict surface roughness and material removal rate with a minor error. The effect of factors on responses was determined by ANOVA. It was concluded that feed rate and depth of cut were the most significant factors for Ra and MRR respectively. Mono-objective optimization results are obtained considering Taguchi’s signal-to-noise ratio. It was concluded that the optimal values for minimizing surface roughness are cutting speed of 120 m/min, feed rate of 0.08 mm/rev and depth of cut of 0.15 mm. Cutting speed and depth of cut have less influence on Ra, whereas a rise in feed rate increases Ra. The optimal values for maximizing MRR were found to be cutting speed of 280 m/min, feed rate of 0.2 mm/rev and depth of cut of 0.6 mm. Multi-objective optimization results were obtained using grey relational analysis. It was found that the best combination values for minimizing the surface roughness and maximizing the material removal rate were cutting speed of 280 m/min, feed rate of 0.08 mm/rev and depth of cut of 0.6 mm. The percentage error between experimental values and predicted values for Ra and MRR using GRA are 3.27 and 0.01 %, respectively.

Machining Characteristic

Optimal parameters Combination

Predicted optimal Value

Experimental Value

% error Value

Ra MRR

280, 0.08, 0.6

0.63 13,453

0.61 13,440

3.27 0.01


891

Table 13 Summary and comparison of results Method

Optimization technique

Optimal parameters combination

Optimal value

Mono-objective optimization

Taguchi method

Multi-objective optimization

Grey relational analysis

120, 0.08, 0.15 280, 0.2, 0.6 280, 0.08, 0.6

Ra=0.51 μm MRR=33,600 mm3/min Ra=0.58 μm MRR=13,440 mm3/min

Therefore, the grey relational analysis based on an orthogonal array of the Taguchi method was shown to be a way of optimizing for multiple machining characteristics, the turning operations for X20Cr13 steel. The approach used in this study can be utilized for simultaneous optimization of the turning of other materials and responses. Acknowledgments This work was achieved in the laboratory LMS (Guelma University, Algeria) in collaboration with LaMCoS (INSALyon, France). The authors would like to thank the Algerian Ministry of Higher Education and Scientific Research (MESRS) and the Delegated Ministry for Scientific Research (MDRS) for granting financial support through CNEPRU Research Project, Code: 0301520080027.

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