The impact of 200 series CB on C&C resistance of solid tire tread compound--part 2.

Part 1 appeared in the April 2005 issue

Statistical analysis

Many statistical methods are used to study the relation between independent and dependent variables (ref. 33). Factor analysis is different; it is used to study the patterns of relationship among many dependent variables, with the goal of discovering something about the nature of the independent variables that affect them, even though those independent variables were not measured directly (ref. 34).

Factor analysis generates a table in which the rows are the observed raw indicator variables and the columns are the factors or latent variables that explain as much of the variance in these variables as possible. The cells in this table are factor loadings, and the meaning of the factors must be induced from seeing which variables are most heavily loaded on which factors.

There are several different types of factor analysis, with the most common being principal components analysis (PCA), R-mode factor analysis. R-mode is by far the most common. In R-mode, rows are cases, columns are variables, and cell entries are scores of the cases on the variables. In R-mode, the factors are clusters of variables on a set of other entities, at a given point of time. The eigen value for a given factor measures the variance in all the variables, which is accounted for by that factor. The ratio of eigen values is the ratio of explanatory importance of the factors with respect to the variables. If a factor has a low eigen value, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant with more important factors. Thus, eigen values measure the amount of variation in the total sample accounted for by each factor. Note that the eigen value is not the percent of variance explained, but rather a measure of "amount"; used for comparison with other eigen values. A factor's eigen value may be computed as the sum of its squared factor loadings for all the variables. Rotation serves to make the output more understandable, and is usually necessary to facilitate the interpretation of factors. Factors are rotated according to various possible criteria, with the object of making the factors each relatively independent of the independent variables, consistent with the other objectives. The different methods (Varimax, Equimax and Orthomax) are different compromises (ref. 35). The sum of eigen values is not affected by rotation, but rotation will alter the eigen values of particular factors and will change the factor loadings. Varimax rotation is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor (column) on all the variables (rows) in a factor matrix, which has the effect of differentiating the original variables by extracted factor. That is, it minimizes the number of variables that have high loadings on any one given factor. Each factor will tend to have either large or small loadings of particular variables on it. A Varimax solution yields results that make it as easy as possible to identify each variable with a single factor. Multivariate statistical analyses have been done using Minitab software (ref. 36).

The data taken for the present analysis were discussed in our previous manuscript (ref. 37), (part 1, tables 2 and 3A-3C). The results of factor analysis are shown in table 4. It has been observed that the four factors calculated in the present study are responsible for 80% of the total variations. The four factors f1 to f4 seem to have almost equal importance, with eigen value varying from 20.7 to 18.8, and with cumulative variations of 80%. For interpretation of factors, here is a rule of thumb: Factor loading >[+ or -]0.30 = important; >[+ or -]0.40 = more important; and >[+ or -]0.50 = very significant. The factor loadings below 0.40 were not considered in the present study because of their lower significance. The plus and minus symbols of the factor loading indicate their intercorrelation as positive or negative with respect to each other within the factor.

Factor 1

Factor 1 consists of heat build-up and tan [delta] values and found to have negative correlation with rebound resilience indicating that with increase of rebound resilience value, heat build-up and tan [delta] values observed at different temperatures decrease. It also contains three primary properties, including nitrogen surface area ([N.sub.2]SA), compressed oil absorption number (COAN) and tint with lower factor loading levels. Rebound resilience had a positive correlation with primary properties like surface area and tint strength, whereas all three primary properties are negatively correlated with heat build-up and tan [delta] at the different testing temperatures. Within this narrow range of 200 series carbon blacks, it is peculiar to observe that both structure and particle size ([N.sub.2]SA) played an equal role in the heat build-up properties; otherwise they would be mostly related to only particle size (refs. 38 and 39). The negative correlation of rebound resilience with tan [delta] is clearly understood, that with the increase of resilience values tan [delta] values will decrease (ref. 40). From the above, it can be said that the factor 1 is considered to be mainly an application factor constituting of heat build-up and tan & with a contribution of 20.7% of total variance.

Factor 2

Factor 2 consists of theological properties, tear strength, heat build-up and abrasion loss. Interestingly, abrasion loss is found to have negative correlation with all other properties mentioned. The factor loading between [t.sub.90] and tear strength (both are having negative values) indicates that with the increase of [t.sub.90], tear strength increases (ref. 41), and its reverse correlation with abrasion loss shows that with the increase of tear strength, abrasion loss decreases. Abrasion loss and heat build-up are negatively correlated to each other, showing that higher scorch and cure time favor improvement in tear strength, the lowering of heat build-up values, along with low abrasion loss (ref. 42). This factor can be termed as an abrasion loss factor, which also has equal importance like factor 1 with the variance of 20.6%.

Factor 3

In factor 3, two primary properties of carbon black, i.e., primary structure and particle or aggregate size ([N.sub.2]SA), gave a positive correlation with hardness, modulus and viscosity, and negatively correlated with elongation at break. This is a common phenomenon with polymers, that with increase of primary structure and aggregate size of the filler, viscosity of the compound increases, which hinders the elongation of the compound due to higher filler-filler and filler-robber interaction (refs. 43-45). Factor 3 can be termed a mechanical factor.

Factor 4

Here, the importance of the same two primary properties, structure and aggregate size ([N.sub.2]SA) of carbon black, has been observed, but found to have negative correlation with cut and chip properties. This indicates that C&C resistance of the compound will improve with primary structure and [N.sub.2]SA values of carbon black (ref. 46). With the increase of aggregate size and primary structure, C&C properties were improved through viscosity and tear strength improvements. As C&C properties play a major role in this factor, factor 4 can be termed as the cut and chip factor. Factors 3 and 4 both carry identical percentage of variance (19%).

All these four factors (f1 to f4) were found to have equal importance. From the factor analysis, it has been found that among three primary properties of carbon black considered in the present study, aggregate size ([N.sub.2]SA) and primary structure (COAN) carried the most importance for all application properties. Tint strength of carbon black was found to have importance limited to heat build-up and tan delta values; whereas for mechanical and cut and chip properties, the control of [N.sub.2]SA and COAN has been noticed. R-mode factor analysis with varimax rotation very clearly segregated and exhibited the correlation co-efficient values (factor loadings) of all the variables, classified depending upon the similarity and importance.

As the present study aims at the C&C behavior of solid tire tread compounds with different types of tillers and polymers, it could be easily visualized that for the improvement of C&C properties, the primary properties of carbon black that carry the importance are [N.sub.2]SA and COAN.

Cluster analysis

The underlying and basic difficulty, of course, is that factor analysis has no way of distinguishing between "true correlation" and "error correlation." Gray and Revelle (ref. 47) have reported the empirically greater usefulness of cluster analysis rather than factor analysis.

Cluster analysis identifies and classifies object individuals or variables on the basis of the similarity of the characteristics they possess. It seeks to minimize within-group variance and maximize between-group variance (ref. 48). The result of cluster analysis is a number of heterogeneous groups with homogeneous contents. There are substantial differences between the groups, but the individuals within a single group are similar. Each cluster thus describes, in terms of the data collected, the class to which its members belong; and this description may be abstracted through use from the particular to the general class or type.

The term cluster analysis actually encompasses a number of different classification algorithms, which organize observed data into meaningful structure. In general, whenever one needs to classify a "mountain" of information into manageable and meaningful piles, cluster analysis is of great utility (refs. 49 and 50).

The results of cluster analysis are shown in figure 6. It can be seen that the variables are divided into five (A1-A5) clusters, depending on their similarity percentage. Two clusters belong to primary properties (P1, P2 and P3) within cluster A3 and other clusters belong to application properties of the compounds (A1 to A5).

[FIGURE 6 OMITTED]

Cluster A1 consists of heat build-up and tan [delta] values. From their importance, it can be seen that heat build-up at 25[degrees]C and 70[degrees]C had more importance.

Cluster A2 consists of scorch properties, [t.sub.90] and tear strength. It seems that tear strength of presently investigated samples was more influenced by cure time.

From the cluster A3, it has been observed that there is an interlink between MH and 300% modulus, which has a bearing on hardness. This factor also constitutes all three primary properties, i.e. tint, COAN and [N.sub.2]SA. Both COAN and [N.sub.2]SA show a strong relation with MH, hardness and 300% modulus, whereas tint shows the importance for viscosity. Therefore, viscosity of the compound is more influenced by [N.sub.2]SA and COAN (P1, P2).

Cluster A4 consists of cut and chip properties along with abrasion loss. Abrasion loss seems to have a direct linkage with C&C weight loss and diameter reduction. Interestingly, the ten-minute test for both weight loss and diameter reduction showed more importance, which had a direct relation with abrasion loss of the compounds.

Cluster A5 constitutes tensile, elongation at break and rebound resilience, which are mechanical properties. Overall, it shows a lower similarity level.

The observations made from the factor analysis are very clearly reflected in the cluster analysis also. The two primary properties of carbon black, i.e., [N.sub.2]SA and COAN, have a direct bearing on the cut and chip performance of the solid tire tread compounds considered in the present study.

Summary

An attempt has been made to understand the impact of the control variables like the curing system, partial replacement of silica and the change of base polymer from NR to SBR, with the application properties of the compound having three carbon blacks belonging to the 200 series, i.e., N220, N231 and N234, in solid tire tread formulations.

From the statistical analysis, it was found that the viscosity, tear strength and abrasion loss of the compound had a linear correlation with cut and chip properties that are being controlled by the COAN and the [N.sub.2]SA of the carbon black in the defined formulation. Since N234 is a high structure and high surface area black, the advantages could be visualized in the performance properties of the rubber vulcanizates belonging to solid tire formulations.

Factor analysis has identified the inter-correlation of the variables, bringing them into a closed group having correlatable numeric responses, and in a similar fashion, cluster analysis has established the linkage tree as per the similarity level of the responses. Both cluster and factor analysis, in combination, have very clearly pointed out the importance of independent variables, like COAN and [N.sub.2]SA, towards the application properties, like cut and chip, in solid tire compounds, irrespective of the curing system, partial replacement of silica and change of base polymer from NR to SBR.

Table 4--results of factor analysis

Variables                      Factor   Factor   Factor   Factor
                                    1        2        3        4

COAN No.                        -0.45              0.64     0.48
[N.sub.2]SA                     -0.44              0.64     0.48
Tint                            -0.41
Viscosity                                          0.62     0.47
t5                                       -0.89
t35                                      -0.91
tc90                                     -0.94
MH                                                 0.86
IRHD                                               0.86
300% modulus                                       0.91
Tensile strength
Tear strength                            -0.75              0.41
Elongation at break, %                            -0.81
Abrasion loss, mg                         0.83
Rebound                         -0.64
CWL 10 min.                                                -0.72
CWL 20 min.                                                -0.92
CWL 30 min.                                                -0.82
CRD 10 min.                                                -0.75
CRD 20 min.                                                -0.81
CRD 30 min.                                                -0.81
HBU at 25[degrees]C              0.66    -0.61
HBU at 70[degrees]C              0.66    -0.58
HBU at 100[degrees]C             0.60    -0.61
Tan [delta] at 25[degrees]C      0.95
Tan [delta] at 70[degrees]C      0.92
Tan [delta] at 100[degrees]C     0.88
% variance                       20.7     20.6     19.0     18.8
% cum. variance                  20.7     41.3     60.3     79.1

References

(33.) Donald F. Morrison, Multivariate Statistical Methods, McGraw-Hill, New York (1990).

(34.) Richard L. Gorsuch, Factor Analysis, Erlbaum, Hillsdale, NJ (1983).

(35.) J. Arbuckle and M. Friendly, "On rotating to smooth functions," Psychometrika, 42, 127-140 (1977).

(36.) Minitab Statistical Software, Release 13, Minitab Inc.

(37.) D. Mahapatra, B. Arun, M. Brindha and K. Ravichandran, "The impact of 200 series carbon black on C&C resistance of solid tire tread compound--Part 1," Rubber World, April 2005.

(38.) Gerard Kraus, "Reinforcement of elastomers by carbon black" Rubber Chemistry and Technology, 51 (2), p. 297 (1978).

(39.) A.I. Medalia, et al, "Effect of carbon black on hysteresis of rubber vulcanizates: Equivalence of surface area and loading," Rubber Chemistry and Technology, 49 (4), p. 1,076 (1976).

(40.) J.M. Buist and S. Mottram, Transactions', Institution of the Rubber Industry, 22, pp. 82-110 (1946).

(41.) David L Schwarz and Donald W. Askea, "A fundamental review of cut and chip testing for OTR tread compounds," Rubber World, August 2003.

(42.) Mitsuru Araki, "Heavy-load pneumatic tires with low heat build-up and excellent resistance to abrasion, tear-crack and wet skid," Jpn. Kokai Tokkyo Koho 1999, p. 8.

(43.) Avron I. Medalia, "Effect of carbon black on ultimate properties of rubber vulcanizates," Rubber Chemistry and Technology, 60 (1), p. 45 (1987).

(44.) W.M. Hess, et al, "The effects of carbon black and other compounding variables on tire rolling resistance and traction," Rubber Chemistry and Technology, 56 (2), p. 390 (1983).

(45.) S.K. De, et al, "The effects of carbon black--vulcanization system interactions on natural rubber network structure and properties," Rubber Chemistry and Technology, 55 (1), p. 23 (1982).

(46.) J.R. Beatty and B.J. Miksch, "A laboratory cutting and chipping tester for evaluating off-the-road and heavy-duty tire treads," Rubber Chemistry and Technology, 55 (5), pp.1,531-1,546, (1982).

(47.) D.B. Gray and W. Revelle, "A cluster analytic critique of the multifactor racial attitude inventory," Psych. Record, 22, 103-112, (1972).

(48.) B.F.J. Manly, Multivariate Statistical Methods, 3rd edition, Chapman and Hall/CRS, 2004.

(49.) Andre Hardy, "On the number of clusters," Computational Statistics and Data Analysis: volume 23, pp. 83-96 (1996).

(50.) D. Mahapatra, et al, "Performance evaluation of high structure carbon black in different polymer blends," Rubber World, 231 (2), pp. 33-42, November 2004.