Design of optimisation of cutting parameters for turning metal matrix composites based on the orthogonal arrays

Journal of Materials Processing Technology 132 (2003) 340±344

Design of optimisation of cutting parameters for turning metal matrix composites based on the orthogonal arrays J. Paulo Davim Department of Mechanical Engineering, University of Aveiro, Campus Santiago, 3810-193 Aveiro, Portugal Received 29 January 2001; accepted 24 September 2002

Abstract This paper presents a study of the in¯uence of cutting conditions (cutting velocity and feed) and cutting time on turning metal matrix composites (MMCs). A plan of experiments, based on the techniques of Taguchi, was performed machining with cutting conditions pre®xed in workpieces. An orthogonal array and the analysis of variance (ANOVA) are employed to investigate the cutting characteristics of MMC (A356/20/SiCp-T6) using PCD cutting tools. The objective was to establish a correlation between cutting velocity, feed and the cutting time with the tool wear, the power required to perform the machining operation and the surface roughness in workpiece. These correlations were obtained by multiple linear regression. Finally, con®rmation tests were performed to make a comparison between the experimental results foreseen from the mentioned correlations. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Turning; Metal matrix composites; Taguchi's techniques; Orthogonal arrays; Analysis of variance

1. Introduction 1.1. Machining metal matrix composites Typical metal matrix composites (MMCs) are composed of a metal as the base and reinforcement as a minor component. Common matrix metals are the alloys with known characteristicsÐlight weight, or high temperature resistanceÐsuch as aluminium, magnesium or titanium. The typical reinforcing ceramics are Al2O3, SiC, B4C, as long ®bres, short whiskers or particles in either an irregular or spherical shape. The MMCs, therefore can also be classi®ed as continuous or discontinuous reinforced composites depending on the geometric con®guration of the reinforcement [1,2]. The properties of the resulting composite are generally controlled by three critical components: the matrix, the reinforcement and the interface. Many of the considerations arising due to fabrication, processing and service performance of composites are related to processes that take place in the interfacial region between matrix and reinforcement. Among modern composite materials, particle reinforced MMCs are ®nding increased application due to their very favourable properties, including high mechanical properties and good wear resistance. SiC reinforced aluminium is very E-mail address: [email protected] (J.P. Davim).

common and others compositions for the matrix are available commercially. A continuing problem with particulate MMCs is that they are dif®cult to machine, due to the hardness and abrasive nature of the SiC or other reinforcing particles. The particles used in MMCs are harder than tungsten carbide (WC), the main constituent of hard metal, and even than the majority of the cutting tool materials. Polycrystalline diamond (PCD) is an exception, as its hardness is approximately three to four times that of the silicon carbide (SiC). This is the reason why PCD is recommended by many researchers [3±9] who have studied the turning of these materials. 1.2. Taguchi's techniques Taguchi's techniques have been used widely in engineering analysis. The techniques of Taguchi consist of a plan of experiments with the objective of acquiring data in a controlled way, executing these experiments, in order to obtain information about the behaviour of a given process. After the completion of the experiment the data from all the experiments in the set are analysed to determine the effect of the various design parameters. Conducting Taguchi experiments in terms of orthogonal arrays allows the effects of several parameters to be determined ef®ciently and is an important technique in robust design. The treatment of the

0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 9 4 6 - 9

J.P. Davim / Journal of Materials Processing Technology 132 (2003) 340±344

experimental results is based on the analysis average and the analysis of variance (ANOVA) [10±14]. 2. Experimental procedure 2.1. Means and materials In order to achieve the objective of this experimental work, MMCs of type A356/20/SiCp-T6 (aluminium with 7.0% silicon, 0.4% magnesium, reinforced with 20% volume particles of silicon carbide (SiC)Ðheat treatment, solutionising and ageing T6 for 5 h at 154 8C) were tested. The average dimension of the SiC particle is about 20 mm. A lathe with 6 kW spindle power was used to perform the experiments. The TMCW 16T308F (according to ISO 1832) inserts with PCD were used to turn MMC billets of 95 mm diameter. The used tool geometry was as follows: rake angle 08, clearance angle 78, edge major tool cutting angle 608 and cutting edge inclination angle 08. A Kistler piezoelectric dynamometer with the appropriate load ampli®er was used to monitor the cutting forces. Several different programs for data acquisition have been developed and used based on the LabView1 software. They allow direct and continuous recording and simultaneous graphical visualisation of the evolution of cutting force, feed force and radial force. The cutting tool wear was measured (according to ISO 3685) with a Mitutoyo optical microscope with 30 magni®cation and 1 mm resolution. The surface roughness was evaluated (according to ISO 4287/1) with a Homeltester T500 pro®lometer. 2.2. Plan of experiments (Taguchi's techniques) For the elaboration of experiments plan we used the method of Taguchi for three factors at three levels. By levels we mean the values taken by the factors. Table 1 indicates the factors to be studied and the assignment of the corresponding levels. The array chosen was the L27 (313) which has 27 rows corresponding to the number of tests (26 degrees of freedom) with 13 columns at three levels, as shown in Table 2. The factors and the interactions are assigned to the columns. The plan of experiments is made of 27 tests (array rows) in which the ®rst column was assigned to the cutting velocity (V) and the second column to the feed (f) and the ®fth Table 1 Assignment of the levels to the factors

341

Table 2 Orthogonal array L27 (313) of Taguchi [10] L27 (313) test

1

2

3

4

5

6

7

8

9

10 11 12 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2

1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2

1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1

1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2

1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1

1 2 3 2 3 1 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 3 1 2 1 2 3

1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1

1 2 3 3 1 2 2 3 1 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3

1 2 3 3 1 2 2 3 1 3 1 2 2 3 1 1 2 3 2 3 1 1 2 3 3 1 2

column to the cutting time (T) and the remaining were assigned to the interactions (Fig. 1). The responses to be studied are the tool wear (VB), the power required to perform the machining operation (Pm) and the surface roughness (Ra) in workpiece. The tests were replicated, resulting in a total of 54 tests, to allow the analysis of the variance of the results. 3. Data analysis results and discussion The plan of tests was developed with the aim of relating the in¯uence of the cutting velocity (V), feed (f) and cutting time (T), with the tool wear (VB), the power required to perform the machining operation (Pm) and the surface roughness (Ra) in workpiece. The statistical treatment of the data was made in two phases. The ®rst phase was concerned with the ANOVA and the effect of the factors and of the interactions. The second phase allowed us to obtain the correlations between the parameters. Afterwards, the results were through con®rmation tests.

Level

Cutting velocity, V (m/min)

Feed, f (mm/rev)

Cutting time, T (min)

3.1. ANOVA and effects of factors

1 2 3

500 350 250

0.05 0.1 0.2

1 5 10

An ANOVA of the data with the tool wear (VB), the power required to perform the machining operation (Pm) and the surface roughness (Ra) in workpiece, with the objective of

342

J.P. Davim / Journal of Materials Processing Technology 132 (2003) 340±344 Table 4 ANOVA table for the tool wear (VB)a

Fig. 1. Linear graph L27 (313) [10].

analysing the in¯uence of the cutting velocity (V), of feed (f) and cutting time (T) on the total variance of the results. The orthogonal arrays to obtain VB, Pm and Ra may be observed in Table 3. Tables 4±6 show the results of the ANOVA with the tool wear (VB), the power required to perform the machining operation (Pm) and the surface roughness (Ra) in workpiece, respectively. This analysis was carried out for a level of signi®cance of 5%, i.e. for a level of con®dence of 95%. The last column of the tables previously shown shows the percentage of contribution (P) of each factor on the total variation indicating then, the degree of in¯uence on the result. From the analysis of Table 4, we can observe that the cutting velocity factors …P ˆ 42:5%†, the cutting time …P ˆ 29:6%† and feed …P ˆ 10:2%† have statistical and Table 3 Orthogonal array of Taguchi for VB, Pm and Raa Test

V (m/min)

f (mm/rev)

T (min)

VB (mm)

Pm (kW)

Ra (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

500 500 500 500 500 500 500 500 500 350 350 350 350 350 350 350 350 350 250 250 250 250 250 250 250 250 250

0.05 0.05 0.05 0.1 0.1 0.1 0.2 0.2 0.2 0.05 0.05 0.05 0.1 0.1 0.1 0.2 0.2 0.2 0.05 0.05 0.05 0.1 0.1 0.1 0.2 0.2 0.2

1 5 10 1 5 10 1 5 10 1 5 10 1 5 10 1 5 10 1 5 10 1 5 10 1 5 10

0.18 0.45 0.55 0.11 0.32 0.43 0.11 0.24 0.30 0.09 0.23 0.28 0.06 0.13 0.22 0.05 0.15 0.18 0.05 0.13 0.15 0.04 0.08 0.10 0.03 0.06 0.09

1.15 1.83 1.85 1.41 1.85 1.85 2.12 2.78 2.80 1.08 1.34 1.35 1.10 1.35 1.35 1.65 2.03 2.05 0.69 1.00 1.01 0.85 1.01 1.02 0.97 1.50 1.51

0.33 0.46 0.59 0.56 0.45 1.00 1.50 1.60 3.63 0.70 0.97 1.56 0.50 0.35 0.90 1.34 1.24 3.24 0.95 1.32 2.20 1.64 2.28 3.80 2.83 3.02 3.53

0.18

1.50

1.57

Means a

Average of two replications.

Source of variance

SDQ

gl

Variance

Test F

Faˆ5% P (%)

A (V, m/min) B (f, mm/rev) C (T, min) AB AC BC

0.23233 0.05645 0.16219 0.01748 0.04474 0.01150

2 2 2 4 4 4

0.11617 0.02823 0.08110 0.00437 0.01119 0.00288

207.95 50.53 145.17 7.82 20.02 5.15

3.27 3.27 3.27 2.64 2.64 2.64

Error Total

0.01955 0.54424

35 53

0.00056

42.48 10.17 29.60 2.80 6.11 1.70 7.14 100

a

SDQ: sum of squares; gl: degrees of freedom; P: percentage of contribution.

Table 5 ANOVA table for the power required to perform the machining operation (Pm)a Source of variance A (V, m/min) B (f, mm/rev) C (T, min) AB AC BC Error Total

SDQ

gl

Variance

Test F

Faˆ5%

3202.50 2240.00 888.13 118.13 48.13 26.25

3.27 3.27 3.27 2.64 2.64 2.64

7.320 5.120 2.030 0.540 0.220 0.120

2 2 2 4 4 4

3.6600 2.5600 1.0150 0.1350 0.0550 0.0300

0.040 15.390

35 53

0.0011

P (%) 47.55 33.25 13.18 3.48 0.65 0.75 1.14 100.00

a SDQ: sum of squares; gl: degrees of freedom; P: percentage of contribution.

Table 6 ANOVA table for the surface roughness (Ra)a Source of variance

SDQ

gl

Variance

Test F

Faˆ5%

A (V, m/min) B (f, mm/rev) C (T, min) AB AC BC

18.340 20.750 13.370 4.630 1.810 1.690

2 2 2 4 4 4

9.1700 10.3750 6.6850 1.1575 0.4525 0.4225

80.44 91.01 58.64 10.15 3.97 3.71

3.27 3.27 3.27 2.64 2.64 2.64

Error Total

3.990 63.170

35 53

0.1140

P (%) 28.67 32.49 20.80 6.61 0.19 1.95 9.29 100

a

SDQ: sum of squares; gl: degrees of freedom; P: percentage of contribution.

Table 7 Cutting conditions and cutting time used in turning confirmation tests Test

V (m/min)

f (mm/rev)

T (min)

1c 2c 3c

300 400 450

0.16 0.12 0.08

9 6 3

J.P. Davim / Journal of Materials Processing Technology 132 (2003) 340±344

343

Table 8 Experimental plan confirmation turning tests and their comparison with the results Test

Tool wear, VB (mm)

1c 2c 3c

Power, Pm (kW)

Experiment

Model (Eq. (1))

Error (%)

Experiment

Model (Eq. (2))

Error (%)

Experiment

Model (Eq. (3))

Error (%)

0.18 0.20 0.22

0.17 0.22 0.23

5.5 10.0 4.5

1.58 1.63 1.55

1.63 1.66 1.52

3.2 1.8 1.9

2.64 1.59 0.58

2.78 1.53 0.52

5.3 3.8 10.3

physical signi®cance on the tool wear obtained, especially the cutting velocity factor. The interactions cutting velocity/feed …P ˆ 2:8%†, cutting velocity/cutting time …P ˆ 6:1%† and feed/cutting time …P ˆ 1:7%† do not present percentages of physical signi®cance of contribution on the tool wear. From the analysis of Table 5, we can observe that the cutting velocity factors …P ˆ 47:6%†, the feed …P ˆ 33:3%† and the cutting time …P ˆ 13:2%† have statistical and physical signi®cances on the power required to perform the machining operation, especially the cutting velocity factor. The interactions cutting velocity/cutting time …P ˆ 0:7%† and feed/cutting time …P ˆ 0:8%† do not present percentages of physical signi®cance of contribution on the power required to perform the machining operation. The interaction cutting velocity/feed …P ˆ 3:5%† present percentage of marginal physical signi®cance. Equally, from the analysis of Table 6 we can observe that the feed factors …P ˆ 32%†, the cutting velocity …P ˆ 29%† and the cutting time …P ˆ 21%† have statistical and physical signi®cance on the surface roughness in workpiece. The interactions cutting velocity/feed …P ˆ 6:6%†, cutting velocity/cutting time …P ˆ 0:2%† and feed/cutting time …P ˆ 2:0%† do not present percentages of signi®cance of contribution on the surface roughness obtained. In this study, the factors and the interactions present a statistical signi®cance Test F > Faˆ5% . Notice that the error associated to the table ANOVA for the VB was approximately 7.1%, for the Pm was approximately 1.1% and for Ra was 9.3%. The interactions do not present a physical signi®cance P …percentage of contribution† < error associated. 3.2. Correlations The correlations between the factors (cutting velocity, feed and cutting time) and the measured tool wear, power required to perform the machining operation and surface roughness in workpiece were obtained by multiple linear regression. The equations obtained were as follows: VB ˆ

0:179

0:674f ‡ 0:899  10 3 V

‡ 20:574  10 3 T; Pm ˆ

Roughness, Ra (mm)

R ˆ 0:78

(1)

0:604 ‡ 4:771f ‡ 3:573  10 3 V ‡ 44:344  10 3 T;

R ˆ 0:88

(2)

Ra ˆ 1:481 ‡ 9:817f R ˆ 0:71

4:727 10 3 V ‡ 127:559  10 3 T; (3)

being, VB the tool wear in mm, Pm the power required to perform the machining operation in kW, Ra the arithmetic average roughness in mm, f the feed in mm/rev, V the cutting of velocity in m/min and T the cutting time in min. 3.3. Confirmation tests In Table 7, the cutting conditions and cutting time used in the turning con®rmation tests are shown. In Table 8 it shows the results obtained where a comparison was done between the foreseen values from the model developed in the present work (Eqs. (1)±(3)), with the values obtained experimentally. From the analysis of Table 8 we can observe that the calculator error is greater especially for the tool wear VB (maximum value 10.0% and minimum 4.5%) and surface roughness Ra (maximum value 10.3% and minimum 3.8%) than for the power Pm (maximum value 3.2% and minimum 1.8%). Therefore, we can consider that Eqs. (1)±(3) correlate the evolution of the tool wear, power required to perform the machining operation and surface roughness in workpiece with the cutting conditions (cutting velocity and feed) and cutting time with a reasonable degree of approximation. 4. Conclusions At the end of this work we thought of establishing a few valid conclusions for turning MMCs considering the methodology used:  The cutting velocity is the cutting condition that has the highest physical as well statistical influence on the tool wear (42.3%) right after the cutting time (29.6%) and the feed (10.2%).  The cutting velocity is the cutting condition that has the highest physical as well statistical influence on the power required to perform the machining operation (47.6%) right after the feed (33.3%) and the cutting time (13.2%).  The feed is the cutting condition that has highest physical as well as statistical influence on the surface roughness in workpiece (32.5%) right after the cutting velocity (28.7%) and the cutting time (20.8%).

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J.P. Davim / Journal of Materials Processing Technology 132 (2003) 340±344

 The interaction cutting velocity/feed (3.5%) is the physical significance to the interactions analysed in the power required to perform the machining operation. The error associated to the table ANOVA for this interaction was approximately 1.1%. The rest of interactions cutting velocity/cutting time and feed/cutting time has no physical significance on influence of tool wear, power required to perform the machining operation and surface roughness.  The error associated to the table ANOVA (maximum value 9.3% and minimum 1.1%) for the factors and the coefficients of regression obtained with the multiple regression (maximum value 0.88% and minimum 0.71%) shows that the satisfactory correlation was obtained.  The confirmation tests showed that the error associated to tool wear (maximum value 10.0% and minimum 4.5%) and surface roughness (maximum value 10.3% and minimum 3.8%) is higher than the error associated with the power required to perform the machining operation (maximum value 3.2% and minimum 1.8%). References [1] M. Taya, R. Arsenault, Metal Matrix Composites, Pergamon Press, Oxford, 1989, pp. 1±9. [2] T. Clyne, P. Withers, An Introduction to Metal Matrix Composites, Cambridge Solid State Science Series, 1995, pp. 1±10.

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