Factor analysis of physical properties of electrode graphite

FACTOR

ANALYSIS OF PHYSICAL PROPERTIES ELECTRODE GRAPHITE P.

Institute

of Geotechnics, (Received

Czechoslovak

20 April

OF

GL~GAR

Academy of Sciences,

1990; uccel~ted in revised @VI

Prague. 10 April

Czechoslovakia 1991)

Abstract-A factor analysis method was adopted for identification of background common factor5 responsible for the greater part of the total variance of the measured physical properties of samples taken from graphite electrodes from IO production sources. The factors were interpreted as a manifestation of: I) impregnation, 2) mixture formulation and, 3) filler coke quality. Contributions of particular factors to the properties of various types of electrodes were estimated. Key Words-Electrode

graphite.

physical

properties.

1. INTRODUCTION

The physical properties of polycrystalline graphite designated for the manufacture of graphite electrodes for electric steel furnaces are closely observed by their producers and users, because they exert an influence upon electrode consumption and thus upon the costs of the whole metallurgical process. The following properties are declared in catalogues: coefficient of thermal expansion, electrical resistivity, thermal conductivity, Young’s modulus, compressive strength, flexural strength, apparent density and impurity content. The actual values, however, are found to be within broad limits because they are in individual cases affected by various technological factors. The paper sets out to establish the dominant factors and to estimate quantitatively to what extent they manifest themselves in individual cases. For this purpose. a statistical analysis of the physical properties of a relatively large number of specimens originating in electrodes of various types and sources was performed, and an attempt was made to interpret the statistical results in terms of particular technological parameters. The paper does not, however, intend to compare the properties of electrodes from various sources (manufacturers), as we try to avoid commercial aspects of electrode production. Moreolier, we do not possess any systematic access to eiectrode performance data. 2. SPECIMENS

The study was performed on a set of specimens sampled for the purpose of a quality check on imported electrodes. The shaped specimens were manufactured from core samples drilled axially from the electrode socket base. The core size was limited to 36-mm diameter and 270-mm length, as the sampling had to be performed using a hand-held electric drill in steel plant shops. This limitation made it impossible to prepare specimens for measurement in the radial direction.

impregnation.

mix formulation.

coke quality.

The powdered fraction which had arisen during drilling was used for determination of the impurity content. The survey consisted of 303 specimens from 300 to 600-mm diameter, premium and regular grade electrodes from the following manufacturers (in alphabetical order): AGL, COVA, NCK, SDK. SEC. SIGRI. STEEG. TOKAI. TOYO, and UCAR

3. EXPERIMENTAL The specimens were tested for the following properties regarded as important quality parameters in graphite electrodes: a) the mean coefficient of thermal expansion a,,,,( 1@ hK ‘) was measured along the electrode axis direction using a quartz push-rod dilatometer by heating from room temperature to 200°C. The confidence interval (c.i.) of the resulting average value of at least three measurements was ~0.06 x IO “K ‘. Prism-shaped specimens 20 x 20 x 120 mm were heated twice up to 200°C and cooled slowly to room temperature prior to rneasurement, in order to remove stress-induced effects[ 1,2]. We have established experimentally that this procedure is sufficient for obtaining reproducible results[3]. Their validity was supported by comparative measurements on specimens that had been tested in the laboratory of the Anglo Great Lakes. Newcastle upon Tyne, UK. b) The electrical resistivity p(p n.m) was measured by a current voltage method along the electrode axis using the same specimen as above. The average value of 20 measurements made on 3 lateral sides was determined with the c.i. ~0.1 /L a.m. c) The dynamic Young’s modulus E, (GPa) was also measured using the same specimen as above by a resonant frequency method. The result of repeated measurements was determined with the c.i. 50.02 GPa. d) The above-mentioned test specimen was eventually destroyed during the flexural strength test using a center-loading 3-point arrangement, yielding the value u,, (MPa). (The specimen size might be regarded as too 12Y

130 I’. GLOGAR small in view of the grain size which can exceed 12 structure of the common factors. In so doing, the mm; however, the core size limitation allowed no factor analysis method tries to explain the observed larger test specimen. A good correlation established dependences in the simplest possible way and to minbetween flexural strength and Young’s modulus imize the number of extracted factors. gives some justification for the adopted procedure.) Nine variables were chosen for analysis of our e) The compressive strength a, (MPa) was estabexperimental results (Table 2). Seven of these corlished under a uniaxial compressive loading along respond to the measured properties of the graphithe electrode axis direction using cube-shaped spectized material, and the remaining two variables were imens 20 x 20 x 20 mm. An average of 4 deterchosen to characterize the electrode as a commodity: minations was taken. (A similar substantiation of the Xl corresponds to the electrode diameter, X2 enspecimen size as in the preceding case is necessary.) codes the declared electrode grade. Contingent missf) The impurity content Ad (%) was determined by ing values of certain variables (see Table 1) were in heating a 1 g powdered specimen (grain size less than individual cases replaced by estimates determined 0.2 mm) at 815°C in air until a constant weight was by a regression with all nonmissing variables within achieved. The c.i. of the mean value of 3 determithe case[7]. nations was ~0.05%. g) The apparent density d, A standard analysis procedure[7] has been (gem-‘) was calculated from the dimensions and adopted. The correlation matrix was used as input weights of the shaped specimens used in other ex- data. Its diagonal and subdiagonal elements periments. The mean value of at least 2 determinations was established with the c.i. ~0.02 g.cmex. (Yl, - LJ (Yk, - e)

c

,=I

4. RESULTS

Trk =

A pattern of mutual relations between individual properties is the subject of essential interest here. This pattern may reflect substantial causal relations of a “structure-property” type. In view of this, no numerical values of the determined properties are presented. Only basic univariate statistics of the data classified, by the electrode diameter and grade, into 3 groups are summarized in Table 1. The properties of specimens from any particular electrode graphite can exhibit a considerable scatter of values. The scatter is due partly to a substantially random-sampling procedure and partly to variations in processing from one source to another. As a rule, the property spread within a source is much less than its overall spread given for any of the three groups in Table 1. It means that the specimens from individual sources are well distinguished by their properties. The individual properties of graphite specimens are not independent because some observed trends in mutual changes can be approximated by linear regression relations with correlation coefficients (in absolute values) between 0.55 and 0.87 (e.g., E, vs. CT,,,d, vs. up, d, vs. p, or a,, vs. a,). This may testify to the existence of causal relations between the mentioned variables, which is understandable in view of the well-known influence of technological parameters (coke quality, mixture formulation, impregnation, graphitization, etc.) on the whole complex of physical properties of graphitized artifacts[4,5]. In other words, the observed relations between quantitative variables can be treated as manifestations of a minor amount of directly non-observable common background factors. The latter proposition is a working hypothesis of the statistical method of factor analysis[6]. 5. FACTOR

ANALYSIS

OF EXPERIMENTAL

RESULTS

An objective of the factor analysis of a given set of properties of numerous objects is to propose a

?,

n

(1)

(y,, denotes the value of the i-th variable in the j-th case, j = 1, 2, . . .n, 7, = l/n Z;=, y,,) are summarized in Table 3. An initial factor extraction was performed using a principal component method. This allowed an explanation of 81% of the total observed variance by means of three factors. Squared multiple correlations of the variables with all these factors (“communalities”) are listed in Table 4. These express that part of the variable’s variance which is due to the common factors. The main result of factor analysis is a determination of factor loadings (i.e., correlation coefficients of a variable with individual factors). The obtained pattern of the factor-loading scheme (see Table 5) enables one to identify any particular factor according to a set of variables strongly correlated with it. A well-known ambiguity of factor solutions allows one to perform a factor rotation (i.e., such a transformation of both factors and factor loadings to make sure that the final solution reaches the maximum factual interpretability). A scheme of factor loadings obtained using a varimax-type orthogonal rotation is given in Table 5 (factor loadings less than 0.25 in absolute value have been replaced by zero). A pattern of this scheme remained unaltered when other available rotation methods (including the oblique ones) were adopted. It is therefore sufficient to use Table 5 when attempting a factor interpretation.

6.FACTOR

INTERPRETATION

a) Factor 1 is strongly and positively correlated to the variables X2 (grade), X8 (apparent density), and Xl (diameter), negatively to X4 (electrical resistivity), and positively but less strongly to X6 (com-

131

Physical properties of electrode graphite Table 2. Variables of the factor analysis

-

Variable

Meaning

Xl x2 x3 x4 X5 X6 Xl XX x9

electrode diameter (mm) electrode grade (regular-l, premium-2) coeff. of thermal expansion electrical resistivity flexural strength compressive strength Young’s modulus apparent density impurity content

pressive interpret

strength). It occurs therefore readily to Factor 1 as an influence of electrode im-

-

-

pregnation. The latter is widely used for the purpose of lowering porosity (i.e., raising the apparent density), lowering electrical resistivity, and improving the mechanical strength, particularly of premium grade electrodes, which-within our sample setpossess the largest diameter of 600 mm. Obviously, these very tendencies are expressed by the Factor 1 loading pattern. The axial coefficient of thermal expansion X3 does not seem to be affected significantly by the impregnation. The latter will probably raise the radial thermal expansion which, unfortunately, because of sampling technique could not be measured. (One should also expect an impregnation-induced increment of Young’s modulus, but X7 does not enter Factor 1 loading significantly at the present level of analysis; see paragraph 8.) b) There exists no correlation between Factor 3 and the declared electrode grade X2, its diameter Xl, apparent density X8, or flexural strength X5 of the graphitized material. This factor obviously expresses an influence of the filler coke quality, because it significantly correlates with the coefficient of thermal expansion X3, and less significantly with the electrical resistivity X4 and the compressive strength X6. Positive factor loadings of these variables in Factor 3 correspond to the fact that the material with a low thermal expansion reveals also a low electrical resistivity and a low mechanical strength, which are all typical of premium petroleum needle cokes. A similar coherence of expansion and resistivity values was pointed out in[8]. The impurity content X9 enters Factor 3 rather unexpectedly as the residual ash in the graphite may originate in iron oxide or other additions to the original mixture, and may not be solely a function of the used coke. Similarly, the weak negative correlation of Factor 3 with Young’s modulus X7 can hardly be explained in terms of the coke quality. c) Factor 2 very markedly and positively correlates with Young’s modulus X7 and flexural strength X5, less markedly positively with compressive strength X6 and apparent density X8, and negatively with diameter Xl and electrical resistivity X4. The prop-

132

R GLOGAR

Table 3. Correlation matrix of variables from Table 2 Xl X1 x2 x3 X4 x5 X6 X7 X8 x9

x2

x3

X4

X5

X6

X7

X8

x9

1.000 0.415 - 0.025 0.284 - 0.353 0.046 0.453

1.000 -0.312 - 0.260 - 0.366 - 0.565 0.471

1.000 0.592 0.817 0.339 0.046

1.000 0.402 0.609 0.173

0.224 - 0.087

1.000 - 0.048

1.000

1.000

0.646 0.047 -0.380 - 0.173 0.115 - 0.348 0.471 -0.125

1.000

-0.051 - 0.609 0.137 0.323 0.033 0.687 -0.192

Table 4. Communalities (i.e., squared multiple correlations of a variable with all the factors) Variable

Communality

Xl x2 x3 x4 x5 X6 x7 X8 x9

0.6018 0.6544 0.6067 0.7048 0.7851 0.6228 0.8271 0.6767 0.3447

account for the actual Factor 2 loading pattern. The small diameter electrodes would almost certainly be made from a finer coke sizing which would yield higher mechanical and lower resistivity values. On the other hand, the graphitization temperature variation or graphitization process alteration would primarily influence thermal expansion X3 which, however, is in our data set strictly bound up with Factor 3. The author therefore prefers an interpretation of Factor 2 as an influence of the mixture formulation. 7.FACTOR

erties strongly correlated to Factor 1 and Factor 3 do not enter Factor 2 significantly. Its interpretation is not so straightforward as is the case with the other factors. It would be possible to interpret it as an influence of mechanical properties of graphitized filler coke particles. It is a well-known fact that more favorable strength properties can be reached with needle cokes at the cost of thermal expansion. Significant factor loadings of mechanical properties (X5, X6, and X7) should consequently appear in Factor 3, which, however, is not the case. As Factor 2 explains a significant part (23.4%) of the total observed variance, it should correspond to some important, hitherto unused technological agent (e.g., the mixture formulation, graphitization temperature, or the graphitization process employed (Acheson or lengthwise)). From these, the mixture formulation (particle sizes and fraction ratios) can

In addition to the factor extraction, factor analysis provides a method for a factor score estimation to appraise values assumed by the extracted factors at individual objects (cases) of the analyzed data set. The factor score expresses the contribution of a common factor to the resulting properties of each individual object. (A positive factor score is equivalent to an occurrence in that object of above-average values of variables positively correlated to the factor, and vice versa.) A survey of factor score patterns in the studied set of specimens grouped into 3 groups, similarly as in Table 1, is presented in histograms (Fig. 1, 2, and 3). The most pronounced difference between premium and regular grade electrodes can be seen at the Factor 1 score distribution (Fig. 1). Although this difference is somewhat exaggerated due to a strong correlation of the grouping variables (grade and diameter) with Factor 1, the same stratification of the data set occurs also with the electrical resistivity, apparent density, and compressive strength.

Table 5. Factor loadings Variable X2-grade Xl-diameter X8-apparent density X4-elec. resistivity X5-flexural strength X7-Young’s modulus X6-compressive strength X3-thermal expansion X9-impurity content Explained variance (%) Plausible interpretation

Factor 1 0.886 0.827 0.820 -0.616 0.000 0.000 0.451 0.000 0.000 36.5 impregnation

SCORES

Factor 2 0.000 -0.341 0.370 -0.318 0.926 0.909 0.675 0.000 0.000 23.4 mixture formulation

Factor 3 0.000 0.000 0.000

0.605 0.000 -0.287 0.376 0.877 0.778 20.9 c:oke quality

Physical Premium (550 -600)

I

_. I-‘::

1 Histogram

Fig.

of electrode

(Rgegg!ulaQoo,

I

I

2 -I 1

Regular (300 -400)

properties

of the Factor 1 scores grouped trode diameter and grade.

by elec-

Regular (550-600)

133

graphite

The Factor 2 score distribution (Fig. 2) is mostly influenced by relatively high values of Young’s modulus and flexural strength of small-diameter regular grade electrodes (mainly of SEC, TOKAI, and TOY0 products) when compared to those of largediameter electrodes. This corresponds to the fact that the smaller diameter electrodes are often made of mechanically stronger cokes of possibly lesser quality. The disadvantage of their higher thermal expansion is not as detrimental in this case as it would be in large-diameter electrodes. The Factor 3 score distribution is very broad. There is no essential difference among the three mvestigated electrode groups. Negative factor scores of small-diameter regular grade electrodes are noteworthy: they correspond to extremely low thermal expansion values of the SEC, TOKAI, and TOY0 electrodes. The cokes used for their manufacture cannot therefore be regarded as low quality. in spite of their remarkable strength (see above).

3 1.5 P ;

8. FACTOR

0

N

Fig. 2. Histogram

of the Factor 2 scores grouped trode diameter and grade.

Premium (550-600)

Fig. 3. Histogram

by elec-

Regular (300-400)

of the Factor 3 scores grouped trode diameter and grade.

by elec-

ANALYSIS

Grouping of the data set according to X2 (grade) and Xl (diameter) has proved justified at least from the viewpoint of the Factor 1 score distribution (Fig. 1). It is therefore reasonable to analyze the three data subsets separately and to exclude the two mentioned grouping variables from consideration, in order not to mix them with purely material properties. An interesting rearrangement of the factor loadings results from such an analysis: a) for each subset of regular grade electrodes only two factors emerge (instead of three for the complete data set). Their factor loadings are given in Tables 6 and 7. In spite of the slightly different numerical values in Tables 6 and 7 which influence the sequence of variables, the factor loading pattern is essentially the same for both data subsets, and the factor analysis results are valid equally for both. After spending the major part of the apparent density variation by splitting the data set to three subsets, the leftover variation of this variable, X8, enters Factor 1 (note the changing meaning of particular Factors for various analyzed data sets). Its loading pattern enables one to interpret Factor 1 (for the same reasons as

Table 6. Factor loadings for the subset of small-diameter regular grade electrodes (electrode grade and diameter excluded from the analysis) Variable X3-thermal expansion X4-elec. resistivity XY-impurity content X5-flexural strength X&compressive strength X&apparent density X7-Young’s modulus Explained variance (%) Plausible interpretation

REFINEMENT

Factor

2

0.028 0.X60 0.854 0.000 0.396 0.000 - 0.022 36.3 coke quality

Factor

1

0.000 -0.335 0.000 0.806 0.790 0.770 0.700 30.7 mixture formulation

134

P. GLOGAR Table 7. Factor loadings for the subset of large-diameter regular grade electrodes (electrode grade and diameter excluded from the analysis) Variable X5-flexural strength X6-compressive strength X7-Young’s modulus X8-apparent density X3-thermal expansion X9-impurity content X4-elec. resistivity Explained variance (%) Plausible interpretation

Factor 1

Factor 2

0.902 0.863 0.836 0.710 0.000 0.000 -0.481 44.4 mixture formulation

0.000

0.364 0.000 0.000 0.835 0.688 0.611 24.4 coke quality

Table 8. Factor loadings for the subset of large-diameter premium grade electrodes (electrode grade and diameter excluded from the analysis) Variable X66compressive strength X5-flexural strength X8-apparent density Xsthermal expansion X7-Young’s modulus X9-impurity content X4-elec. resistivity Explained variance (%) Plausible interpretation

Factor 1 0.887 0.828 0.736 0.000 0.614 0.000 - 0.295 40.9 mixture formulation

in paragraph 6) as an influence of the mixture formulation. Factor 2 keeps its “coke-quality and impurity-content” interpretation. b) For the subset of premium-grade electrodes again three factors emerge, but their loading pattern (Table 8) and interpretation differs somewhat from the results for the complete data set. Factor 1 again corresponds to the mixture formulation, but the would-be coke quality factor (which is equivalent to Factor 3 in the complete set analysis and to Factor 2 in both regular grade subsets) breaks down to two new factors. From these, the Factor 2 loading pattern corresponds to the influence of graphitization temperature variations: a higher graphitization temperature leads to lower thermal expansion and electrical resistivity values. Surprisingly enough, the impurity content steadily accompanies the electrical resistivity in Factor 3. 9.CONCLUSIONS

Physical properties of regular and premium grade 300 to 600-mm diameter graphite electrode specimens from 10 manufacturers vary within broad lim-

Factor 2

Factor 3

0.000 - 0.347 0.000 0.886 - 0.700 0.000 0.495 24.8 graphitization temperature

0.000 0.000 0.000 0.000

0.000 0.928 0.676 14.3 -

its. By means of a factor analysis method a proposition was made to explain 81% of the total variance as being due to three common background factors. An interpretation of the factor loadings enabled one to identify these three factors as follows: Factor 1 = impregnation, Factor 2 = mixture formulation, Factor 3 = filler coke quality. Acknowledgment-The author is grateful to Mr. Arthur Ince of Anglo Great Lakes, Newcastle upon Tyne, UK, for his helpful discussion.

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43,350

(1988).

4. A. Ince, Ironmaking and Steelmaking, 3, 310 (1976). 5. F. Millhouse and I. W. Gazda, Iron and Steel ht., 56, 138 (1983). 6. K. Uberla, Faktorenanalyse. Springer, Berlin-Heidelberg (1971). 7. BMDP Stattitical Software Manual. BMDP Statistical Software, UCLA, Los Angeles (1985). 8. P. Glogar and V. Holubai: submitted for publication in Freiberger

Forschungshefte

(1990).