INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 6, pp. 995-1001 JUNE 2013 / 995

© KSPE and Springer 2013

Experimental Study of the Dry Facing of Magnesium

Pieces Based on the Surface Roughness

Eva Maria Rubio1, Jose Luis Valencia2, Adolfo Jose Saa1,#, and Diego Carou1

1 Dept. of Manufacturing Engineering, UNED, C/ Juan del Rosal, 12, E28040-Madrid, Spain2 Dept. of Statistics and Operation Research III, UCM, Av, Puerta de Hierro s/n, E28040-Madrid, Spain

# Corresponding Author / E-mail: adolfo.saa.sarria@gmail.es, TEL: +34-91-3988226, FAX: +34-91-3986046

KEYWORDS: Dry face turning, Magnesium UNS M11917, Surface roughness, Sustainable machining, Optimization, Taguchi design of experiments, ANOVA

This paper shows an experimental study of dry face turning carried out on UNS M11917 magnesium pieces. The work is

focused on repair and maintenance operations which are generally carried out under cutting conditions of low performance.

The main goal is to determine if such type of operations can be reached successfully by dry machining, the most drastic and

sustainable cooling technique that exists, and, if so, what factor or factors among the involved ones in the machining (spindle

speed, feed rate and tool coating) and their possible interactions are more influential in the quality of surface finish. To achieve

this objective, a sustainable methodology that combines Taguchi design of experiment (DOE) and the analysis of variance

(ANOVA) method are considered. The main result is the establishment of a model for estimating the expected surface roughness,

in terms of average roughness, Ra, that allows selecting the best combination of cutting conditions and type of tool to obtain

pieces within a certain range of surface roughness. The principal conclusion is that the dry machining technique can be used

in the face turning repair and maintenance operations of pieces of magnesium producing a very good quality of the surface

roughness and reducing costs and environmental impact.

Manuscript received: October 29, 2012 / Accepted: April 18, 2013

1. Introduction

Magnesium is widely used in industries such as aeronautics and

automotive due to the excellent strength to weight ratio that presents.1-4

Magnesium alloys may be combined with other materials to form

hybrid structures (magnesium-aluminium, magnesium-titanium and

magnesium-sintered steel) in order to reduce the weight and to improve

the strength and the wear and fatigue characteristics.5-9 The high cost of

these components makes necessary to carry out repair and maintenance

operations when they have suffered any damage.

Magnesium alloys usually have a good performance in machining.

However, this material presents problems with the heat generated

during the machining process, since it has a tendency to ignite.8-10 To

ensure adequate cooling for the machining of these alloys is not easy.

On the one hand, the use of refrigerants containing water is dangerous

in case of chip ignition; burning magnesium, in the presence of water,

decomposes to form hydrogen atmospheres which are highly explosive.

On the other hand, the use of lubricants or coolants during machining

is an undesirable factor due to economic and environmental factors.7-9

In general, in order to analyse and, if it is possible, to optimize the

machining processes, it is necessary to investigate, among other

aspects, the influence of the cutting conditions (cutting parameters,

types of tools and use, or not, of coolant/lubricant) in the response

variable or variables selected; usually, the surface roughness of the

mechanized pieces, in terms of average roughness, Ra.11-22

In the present work, in order to improve the knowledge about the

magnesium alloys machining, an experimental study is made. Namely,

the work is focused on the selection of the best cutting conditions to

NOMENCLATURE

d = depth of cut (mm)

D = measuring circle (mm)

f = feed rate (mm/rev)

N = spindle speed (rpm)

R = measuring radius (o)

Ra = average roughness (μm)

T = tool coating

DOI: 10.1007/s12541-013-0132-9

996 / JUNE 2013 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 6

reach a certain surface roughness in pieces of UNS M11917

magnesium alloys obtained by facing cutting under low performance

conditions, own of repair and maintenance operations.

The mechanized has been made without any coolant (dry

machining). This cooling technique is the most drastic but, as well, the

most sustainable and constitutes a good alternative in this occasion

because it has been probed in previous works7-11,23,24 that, under such

low performance conditions, the heat generated in the machining does

not reach values that compromise safety.

The study is raised following a sustainable approach in which tests

are performed according to a design of experiments (DOE) of Taguchi

that allows maximum information with minimum possible number of

resources.23,25-29

To determine the influence of each factor and their interactions in

the surface roughness, the analysis of the variance (ANOVA) method

is used in the treatment of data.

Finally, a statistical model is also established with the aim of

determining the surface roughness expected for different combinations

of factors.

The main novelties that this work presents versus others ones

existing about magnesium machining can be summarized like this:

- The machining operation selected, the face turning, is an operation

much less studied that the horizontal turning.

- The cutting conditions of low performance (low depths of cut,

cutting speeds and feed rates), own of the repair and maintenance

operations, are used when the usual conditions analysed in the

magnesium machining are at high-speed.

- As in the face turning the cutting speed varies linearly with the

instantaneous radius of cut, the necessary factors and levels to

analyse the surface roughness evolution throughout the workpiece

radius are included in the DOE.

- A ranking for the best combinations of cutting parameters and tool

coatings based on the expected values of surface roughness given by

the statistical model is provided.

2. Experimental procedures

This experimental study is focused on the measurement of surface

roughness in dry facing operations of UNS M11917 magnesium

workpieces, with a chemical composition shown in Table 1. The

workpieces are cylindrical bars with a diameter of 110 mm and an

initial length of 100 mm (see Fig. 1).

As a previous consideration, three potential factors of design that

influence the process have been considered: the spindle speed, N, the

feed rate, f and the tool coating, T. It is suspected that these factors

interact with each other.

As repair and maintenance operations of magnesium alloys are

usually conducted at low values of spindle speed and feed rate, the

levels of the cutting parameters in the experimental tests were chosen

among these of low performance. Three levels were selected for feed

rate (0.04, 0.08, 0.12 mm/rev) and for spindle speed (280, 500, 800

rpm). The depth of cut, d, in these repair and maintenance operations,

needs to be small in order to keep the dimensional tolerances required.

To ensure this, the depth of cut was kept constant at 0.25 mm. These

cutting conditions are expressed in units commonly employed in

manufacturing workshops instead of International System of Units

(S.I.) in order to give a more intuitive description of the used values.

The cutting tools employed in the machining, from SECO

manufacturer, have identical geometry (Fig. 2) but different coatings

since it was taken into account that, in the main aeronautical and

automotive applications, magnesium is normally used as part of hybrid

materials such as magnesium-aluminium, magnesium-titanium and

magnesium-steel.29-34 Thus, three different types of coatings were

selected, one specifically for non-ferrous metals and two for other

materials with a coating of Ti(C,N) + Al2O3 + TiN. The manufacturer

references are: HX, TP200 and TP2500 respectively.

The cylindrical magnesium bars were dry faced on a Pinacho L-1/

200 lathe. The surface roughness of workpieces after each test was

measured with a Mitutoyo Surftest SJ-401 surface roughness tester. For

every test considered in the design of experiments, as the cutting speed

decreases as the machining progresses, surface roughness was

measured in three different zones of the face of the bars to depict the

surface roughness evolution throughout the radius.

Table 1 Chemical composition of the workpieces (mass %)

Al Cu Fe Mg Mn Ni Si Zn

8.3-9.7 ≤ 0.03 ≤ 0.005 90 0.15-0.5 ≤ 0.002 ≤ 0.1 0.35-1

Fig. 1 Workpiece in the machine

Fig. 2 Types of tools employed: (a) HX and (b) TP200 and (c) TP2500

Fig. 3 Measuring zones

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 6 JUNE 2013 / 997

The surface roughness was measured in terms of average roughness,

Ra:

(1)

Fig. 3 shows the measuring zones considered. Two factors were

used to locate each of these measuring zones: the measuring radius, R,

and the measuring circle, D. For the measuring radius, R, three radii

separated one from each other 120o and denoted by R1, R2 and R3 were

selected. And, for the measuring circle, D, three circles concentric with

the centre of the workpiece were established and denoted by D1, D2

and D3 respectively. These two factors -with three levels each- were

also considered as potentially influential, and therefore included in the

experimental design.

Table 2 shows the factors, codes and levels of the experimental

design. In order to analyse the influence of the six factors considered

–five with three levels each, and one with only one level- an L27

orthogonal Taguchi12-14 design with three replications nested was

selected for this study.

To avoid the influence of uncontrollable factors, the experimental

runs were conducted in randomized order. Table 3 shows the

orthogonal array of the design and the order of the randomized

experiments.

3. Data analysis and discussion of results

The results of the surface roughness values measured in each

experimental run are given in Table 4.

The analysis of variance was applied to identify the influential

factors. An ANOVA fixed-effect analysis was performed by removing

one factor each time (with p-value greater than 0.05) considering

Snedecor’s F as the statistical test. The final results of the analysis of

variance are shown in Table 5. In this table, DF represents the degrees

of freedom of each factor or interaction. The information given in the

last column represents the probability that Snedecor´s F distribution

had a value greater than the computed F value. When this probability

is greater than 0.05 (p-value > 0.05), it is considered in this analysis

that the effect corresponding to this factor is not statistically significant.

The statistical analysis was performance with SAS® software.35

Throughout the ANOVA it was found that factors D and R are not

statistically influential. The interactions of D and R with T, N and f,

Ra1

L--- Y x( )

0

L

∫ dx=

Table 2 Factors, codes and levels for the experimental design

Factor Code Level 1 Level 2 Level 3

Feed rate (mm/rev) f 0,04 0,08 0,12

Spindle speed (rpm) N 280 500 800

Depth of cut (mm) d 0,25

Tool coating T HX TP200 TP2500

Measuring radius (o) R 0 120 240

Measuring circle (mm) D 18,33 55 91,67

Table 3 Randomized experiment orthogonal array L27 with three

replications nested

Test f T N Ra1 Ra2 Ra3

1 1 1 3 D3 R2 D2 R1 D1 R3

2 3 2 2 D1 R2 D3 R1 D2 R3

3 3 1 2 D1 R2 D2 R3 D3 R1

4 3 1 1 D2 R2 D1 R1 D3 R3

5 3 1 3 D1 R3 D3 R2 D2 R1

6 1 2 3 D2 R2 D1 R3 D2 R1

7 2 1 2 D2 R3 D1 R2 D3 R1

8 3 3 3 D3 R2 D2 R1 D1 R3

9 1 1 2 D2 R3 D1 R2 D3 R1

10 2 3 2 D1 R2 D2 R3 D3 R1

11 1 3 2 D2 R3 D1 R2 D3 R1

12 3 2 3 D3 R2 D1 R3 D2 R1

13 1 3 3 D1 R3 D3 R2 D2 R1

14 2 1 1 D3 R3 D2 R2 D1 R1

15 1 2 1 D3 R3 D2 R2 D1 R1

16 3 3 1 D1 R1 D2 R2 D3 R3

17 1 2 2 D1 R2 D3 R1 D2 R3

18 2 2 1 D1 R1 D2 R2 D3 R3

19 2 3 3 D2 R1 D1 R3 D3 R2

20 1 1 1 D1 R1 D2 R2 D3 R3

21 3 2 1 D1 R1 D2 R2 D3 R3

22 1 3 1 D1 R1 D3 R3 D2 R2

23 2 2 3 D1 R3 D3 R2 D2 R1

24 2 2 2 D1 R2 D3 R1 D2 R3

25 3 3 2 D1 R2 D3 R1 D2 R3

26 2 1 3 D1 R3 D2 R1 D3 R2

27 2 3 1 D1 R1 D2 R2 D3 R3

Table 4 Experimental results of surface roughness, Ra

TestFactor

Surface roughness, Ra

(µm)

f T N Ra1 Ra2 Ra3

1 0.04 HX 800 0.34 0.22 0.28

2 0.12 TP200 500 0.64 0.71 0.68

3 0.12 HX 500 0.78 0.76 0.73

4 0.12 HX 280 0.82 0.76 0.75

5 0.12 HX 800 0.74 0.78 0.76

6 0.04 TP200 800 0.22 0.22 0.24

7 0.08 HX 500 0.45 0.49 0.44

8 0.12 TP2500 800 0.68 0.71 0.68

9 0.04 HX 500 0.23 0.28 0.24

10 0.08 TP2500 500 0.74 0.73 0.71

11 0.04 TP2500 500 0.29 0.31 0.24

12 0.12 TP200 800 0.71 0.69 0.73

13 0.04 TP2500 800 0.24 0.24 0.24

14 0.08 HX 280 0.44 0.41 0.40

15 0.04 TP200 280 0.22 0.21 0.22

16 0.12 TP2500 280 0.67 0.62 0.70

17 0.04 TP200 500 0.32 0.31 0.34

18 0.08 TP200 280 0.41 0.33 0.41

19 0.08 TP2500 800 0.36 0.41 0.42

20 0.04 HX 280 0.28 0.27 0.29

21 0.12 TP200 280 0.63 0.61 0.59

22 0.04 TP2500 280 0.24 0.19 0.20

23 0.08 TP200 800 0.32 0.37 0.36

24 0.08 TP200 500 0.38 0.32 0.36

25 0.12 TP2500 500 0.68 0.66 0.68

26 0.08 HX 800 0.32 0.38 0.40

27 0.08 TP2500 280 0.37 0.34 0.37

998 / JUNE 2013 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 6

neither appear in the final ANOVA results because were also not

significant. The feed rate, f, is the factor that most influences by far, and

on a much lesser degree have also statistical influence, by this order,

interaction tool coating-feed rate, T*f, spindle speed, N, interaction

spindle speed-feed rate, N*f, interaction tool coating-spindle speed,

T*N, and the tool coating, T.

Table 6 includes the percent contribution of the factors and

interactions that were found to statistically influence the variability of

Ra. Nearly 85% of the variability of Ra is caused by the feed rate

(89,4% of the controlled variability).

Equation (2) models the variability of surface roughness from

ANOVA. In this equation, µ is the intercept, fi, tj and nk, represent the

effect of the levels of feed rate, tool coating and spindle speed; (ft)ij,

(fn)ik and (tn)jk represent the interactions feed rate-tool coating, feed

rate-spindle speed and tool coating-spindle speed respectively; and, åijk,

represents the error of the model. Table 7 shows the estimates of the

model parameters given by Equation (2).

(2)

The hypotheses of the model were checked, and there was no

evidence or lack of normality (Table 8). Neither has been found

evidence of existence of any pattern nor heteroscedasticity (Fig. 4).

The graphs of box-and-whiskers serve to see the dispersion of the

response variable values versus each factor when they are considered

in isolation. Fig. 5 collects the graphs of box-and-whiskers of the

surface roughness, in terms of Ra, versus the factors: (a) feed rate, (b)

spindle speed and (c) tool coating. Fig. 5(a) shows that the best surface

finishes are obtained machining with a low feed rate value (0.04 mm/

rev) and that Ra increases when feed rate increases. In Fig. 5(b) the

intermediate spindle speed (500 rpm) presents the highest Ra average

value but the lesser dispersion. And, finally, regarding the type of tool

coating, Fig. 5(c) shows as the TP200 tool provides slightly better

values of the Ra than the other two coatings (lesser Ra average values

and dispersion).

yijk μ ft tj nk ft( )ij fn( )ik tn( )jk εijk+ + + + + + +=

Table 5 Final results of analysis of variance

Source DF Sum of squares Mean square F Pr > F

T 2 0.04557284 0.02278642 8.63 0.0005

N 2 0.06459506 0.03229753 12.23 <.0001

f 2 2.73520247 1.36760123 517.69 <.0001

T*f 4 0.09080494 0.02270123 8.59 <.0001

T*N 4 0.05941235 0.01485309 5.62 0.0006

N*f 4 0.06249383 0.01562346 5.91 0.0004

Error 62 0.16378765 0.00264174

Total 80 3.22186914

Table 6 Percent contribution factors to Ra variability

Source Model (%) Variability (%)

f 89.4% 84.9%

T*f 3.0% 2.8%

N 2.1% 2.0%

N*f 2.0% 1.9%

T*N 1.9% 1.8%

T 1.5% 1.4%

Total 100% 94.9%

Table 7 Estimation of parameters in the model of equation (2)

Parameter EstimateStandard

errort Value Pr> |t|

Intercept µ 0.6788 0.0249 27.27 <.0001

f = 0.04 f1 -0.4578 0.0313 -14.63 <.0001

f = 0.08 f2 -0.2519 0.0313 -8.05 <.0001

f = 0.12 f3 0 . . .

T = HX t1 0.1037 0.0313 3.32 0.0015

T = TP200 t2 0.02 0.0313 0.64 0.5249

T = TP2500 t3 0 . . .

N = 280 n1 -0.05630 0.0313 -1.80 0.0768

N = 500 n2 0.0467 0.0313 1.49 0.1408

N = 800 n3 0 . . .

T = HX*f = 0.04 (ft)1,1 -0.0622 0.0343 -1.82 0.0742

T = TP200*f = 0.04 (ft)1,2 0.0222 0.0343 0.65 0.5190

T = TP2500*f = 0.04 (ft)1,3 0 . . .

T = HX*f = 0.08 (ft)2,1 -0.1689 0.0343 -4.93 <.0001

T = TP200*f = 0.08 (ft)2,2 -0.1222 0.0343 -3.57 0.0007

T = TP2500*f = 0.08 (ft)2,3 0 . . .

T = HX* f = 0.12 (ft)3,1 0 . . .

T = TP200*f = 0.12 (ft)3,2 0 . . .

T = TP2500*f = 0.12 (ft)3,3 0 . . .

N = 280*f = 0.04 (fn)1,1 0.0233 0.0343 0.68 0.4984

N = 500*f = 0.04 (fn)1,2 0.0533 0.0343 1.56 0.1247

N = 800*f = 0.04 (fn)1,3 0 . . .

N = 280*f = 0.08 (fn)2,1 0.0522 0.0343 1.52 0.1326

N = 500*f = 0.08 (fn)2,2 0.1600 0.0343 4.67 <.0001

N = 800*f = 0.08 (fn)2,3

N = 280*f = 0.12 (fn)3,1 0 . . .

N = 500*f = 0.12 (fn)3,2 0 . . .

N = 800*f = 0.12 (fn)3,3 0 . . .

T = HX*N = 280 (tn)1,1 0.0533 0.0343 1.56 0.1247

T = HX*N = 500 (tn)1,2 -0.09778 0.0343 -2.85 0.0059

T = HX*N = 800 (tn)1,3 0 . . .

T = TP200*N = 280 (tn)2,1 0.0056 0.0343 0.16 0.8717

T = TP200*N = 500 (tn)2,2 -0.0956 0.0343 -2.79 0.0070

T = TP200*N = 800 (tn)2,3 0 . . .

T = TP2500*N = 280 (tn)3,1 0 . . .

T = TP2500*N = 500 (tn)3,2 0 . . .

T = TP2500*N = 800 (tn)3,3 0 . . .

Table 8 Tests for normality

Test Statistic p Value

Shapiro-Wilk W 0.991488 Pr < W 0.8761

Kolmogorov-Smirnov D 0.062836 Pr > D > 0.1500

Cramer-von Mises W-Sq 0.03453 Pr > W-Sq > 0.2500

Anderson-Darling A-Sq 0.232754 Pr > A-Sq > 0.2500

Fig. 4 Residuals versus predicted Ra values

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 6 JUNE 2013 / 999

Fig. 6 shows the dependence of surface roughness versus the feed

rate for: (a) each tool coating and (b) each spindle speed. Fig. 6(a)

shows that, for the three types of tool coatings (HX, TP200 and

TP2500), the two first (HX and TP200) have a very similar

behaviour; being slightly better the Ra values obtained with the

TP200 coating. Besides, for the lowest feed rate (0.04 mm/rev) the

three coatings provide low and very similar Ra values (almost

coincident). It can be seen as well, that the highest values of Ra are

reached at the highest feed rate (0.12 mm/rev), obtaining the worst

values of Ra with the HX coating. Fig. 6(b) shows that, for the three

spindle speeds probed: 280 rpm, 500 rpm and 800 rpm, the surface

roughness versus the feed rate has a very similar behaviour at

280 rpm and at 800 rpm and, in general, presents a worse behaviour

for the intermediate value of 500 rpm (that only presents better Ra

values for high values of the feed rate than the obtained ones using

the highest spindle speed, 800 rpm).

The model from Equation(2) and the estimates of parameters

illustrated in Table 7 were used to identify the optimal combination of

tool coatings and cutting parameters levels based on the Ra expected

(Table 9). The combination of tool coatings and cutting parameters that

minimized the surface roughness expected is a feed rate of 0.04 mm/

rev, a spindle speed of 280 rpm, and a TP2500 tool coating.

Nevertheless, as the differences between these machining conditions

and the other conditions just following them in the ranking seem small,

attending to economic issues, might be worth considering following

combinations with higher spindle speed.

Fig. 5 Box-and-whiskers plots of surface roughness, in terms of Ra

versus the factors: (a) feed rate, (b) spindle speed and (c) tool coating

Fig. 6 Dependence of surface roughness with the feed rate for: (a) each

tool coating and (b) each spindle speed

Table 9 Ranking of parameter combinations based on the Ra expected

FactorRa expected (µm)

f (mm/rev) T N (rpm)

0.04 TP2500 280 0.188

0.04 TP2500 800 0.221

0.04 TP200 280 0.236

0.04 HX 800 0.263

0.04 TP200 800 0.263

0.04 HX 500 0.265

0.04 TP200 500 0.268

0.04 HX 280 0.283

0.04 TP2500 500 0.321

0.08 TP200 800 0.325

0.08 TP200 280 0.326

0.08 HX 800 0.362

0.08 HX 280 0.411

0.08 TP2500 280 0.423

0.08 TP2500 800 0.427

0.08 TP200 500 0.436

0.08 HX 500 0.477

0.12 TP2500 280 0.623

0.08 TP2500 500 0.634

0.12 TP200 280 0.648

0.12 TP200 500 0.650

0.12 TP2500 800 0.679

0.12 TP200 800 0.699

0.12 TP2500 500 0.726

0.12 HX 500 0.731

0.12 HX 280 0.780

0.12 HX 800 0.783

1000 / JUNE 2013 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 6

4. Conclusions

This work presents an experimental study to determine if it is

possible to carry out repair and maintenance operations by dry facing,

on pieces of UNS M11917 magnesium alloy, own of the aeronautical

and automotive industries, achieving very exigent requirements of

surface roughness as the normally required in such sectors.

Then, in order to reach this objective, an L27 orthogonal Taguchi

design of experiments with three replications nested is selected for the

study along with the ANOVA method. The surface roughness is taken

as response variable for the reasons given above and, as possible

sources of its variability, the next factors: depth of cut, feed rate,

spindle speed, tool coating and measuring zones (defined by the circle

and the radius where the measurements are taken).

From the obtained results, a statistical model for calculating the

values of the expected surface roughness is developed. The model is

defined as a function of the feed rate, the tool coating, the spindle

speed, and the interactions feed rate-tool coating, feed rate-spindle

speed and tool coating-spindle speed; being the feed rate the first

responsible of the variability of surface roughness.

The higher the value of feed the greater roughness and vice versa (at

least in the value range studied). The interaction between spindle speed

and feed rate causes a slight increase in Ra values for intermediate

values of spindle speed when the feed rate also takes an intermediate

value.

This model allows establishing a ranking, based on the surface

roughness expected, and to select the best cutting conditions and tool

coatings for a certain range of surface roughness. The optimal

combination that provides the least surface roughness is the next one:

feed rate, 0.04 mm/rev, spindle speed, 280 rpm and coating TP2500.

Taking into account that all the surface roughness values reached

are very good, even better than those usually needed in the analysed

industries, in future works, it would be possible to increase the values

of the cutting conditions, feed rate and spindle speed, in order to

optimize or, at least, try to reduce the time of repair and maintenance

of magnesium pieces.

ACKNOWLEDGEMENT

The authors thank to the Research Group of the UNED “Industrial

Production and Manufacturing Engineering (IPME)” the given support

during the development of this work, and funding of the Spanish

Ministry of Science and Innovation (Projects DPI2011-27135 and

AGL2010-21501/AGR) and of the Industrial Engineering School-

UNED (Project REF2012-ICF01) to carry it out. Besides, the authors

thank to Grupo Antolín Magnesio S.L. the transfer of part of the

material used in this work.

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