Statistically designed experiments: applications in compound mixing studies.

Statistically designed experiments: Applications in compound mixing studies

Production scale mixing problems often challenge the rubber compounder. Solutions are difficult to find without generating excessive scrap. Thus, methods to evaluate mixing on a small scale can be helpful and effective [1, 2]. The frugal investigator minimizes effort and maximizes information through statistical experimental methods. Statistical experimentation will improve efficiency and reliability of the study[3,4].

This article demonstrates the effectiveness of combining small scale mixing studies with statistically designed experiments to overcome in-plant mixing deficiencies.

Experimental

Planning

This investigation grew out of a customer inquiry to improve production scale mix quality of a high performance ethylene-propylene-diene rubber (EPDM) compound. The customer provided compound details and established mix conditions. This information and the results of an earlier laboratory mixing evaluation prompted the selection of the following factors for study:

* Fill factor;

* Mix speed;

* Mix procedure.

The earlier lab scale screening experiment suggested the use of response surface methodology. Central composite designs are a good choice for this method and have many advantages over [3.sup.k] factorials[5]. An attractive feature of the central composite experiment is its sequential nature when run in blocks[6]. However, all factors in a central composite must be continuous; mix procedure is not.

To accommodate this limitation, the rotatable central composite design detailed in table 1 was selected to study fill factor and mix speed. To evaluate two mix procedures, the design was used twice, creating one experiment per mix procedure. Table 1 depicts the blocking scheme for both experiments. Through inter-randomizing Block 1 of both experiments, and running them concurrently, the extraction of a third statistical analysis was possible. The extractable matrix compound in table 2, is a [2.sup.3] full factorial. Its analysis provides a direct evaluation of all three factors and their interactions.

Established mix conditions and findings of the earlier study determined experimental levels for fill factor and mix speed. When calculated according to the central composite design, the experiment depicted in table 3 resulted. This experiment was utilized twice, once for each mix procedure under investigation. Table 4 describes the orders of addition for raw materials for the two mix procedures. Ingredient addition orders led to the mix procedure nomenclature used in this article, "sandwich" and "right-side up."

Table 5 is an unrandomized compilation of Block 1 of both experiments. These runs were conducted first to best utilize the sequential nature of the central composite designs. Analysis of Block 1 results determined how much of Block 2 to run. Prior to experimentation, runs were randomized within blocks.

Table 1 - selected design

Run number     Fill     Mix
  Block 1     factor   speed
     1          -1       -1
     2          -1       +1
     3          +1       -1
     4          +1       +1
     5          0        0
     6          0        0
     7          0        0

Block 2

     8       -1.414      0
     9       +1.414      0
    10          0      -1.414
    11          0      +1.414
    12          0        0
    13          0        0
    14          0        0

Table 2 - extractable design

 Run     Fill     Mix       Mix
number  factor   speed   procedure[*]
  1       -1       -1        -1
  2       -1       +1        -1
  2       +1       -1        -1
  4       +1       +1        -1
  5       -1       -1        +1
  6       -1       +1        +1
  7       +1       -1        +1
  8       +1       +1        +1

(*)-1 = Sandwich mix procedure

+1 = Right-side up procedure

Table 3 - calculated experiment

Run number     Fill    Mix
  Block 1     factor  speed
     1        0.725     28
     2        0.725     42
     3        0.825     28
     4        0.825     42
     5        0.775     35
     6        0.775     35
     7        0.775     35

Block 2

     8        0.704     35
     9        0.846     35
    10        0.775     25
    11        0.775     45
    12        0.775     35
    13        0.775     35
    14        0.775     35

Table 4 - mix procedures

Procedure          Mix addition order
Sandwich              Polymer A
                   Fillers and cures
                          Oil
                      Polymer B

Right-side up

                   Polymers A and B
                          Oil
                   Fillers and cures

Table 5 - Block 1 combined experiment

Run number    Fill     Mix        Mix
             factor   speed    procedure
     1       0.725      28     Sandwich
     2       0.725      42     Sandwich
     3       0.825      28     Sandwich
     4       0.825      42     Sandwich
     5       0.775      35     Sandwich
     6       0.775      35     Sandwich
     7       0.775      35     Sandwich
     8       0.725      28   Right-side up
     9       0.725      42   Right-side up
    10       0.825      28   Right-side up
    11       0.825      42   Right-side up
    12       0.775      35   Right-side up
    13       0.775      35   Right-side up
    14       0.775      35   Right-side up

Mixing

Compounds were mixed in the Haake Rheomix 600 torque rheometer. The System 40 drive unit monitored mix speed, melt temperature and torque responses. The 60 cc capacity chamber was held at 121 [degrees] C and ram pressure at 87 kPa throughout the experiment. Batch ingredients were added as specified by mix procedure at 28 rpm mix speed. The ram was lowered, mix speed adjusted and mix time initiated. At 110 seconds mix time, a five-second sweep was performed and the ram lowered once more. All batches were dropped after 150 seconds total mix time. One pass through a two-roll mill with a 2.3 mm nip setting followed to cool the batch.

Testing

Before mill cooling, samples for capillary rheometry via the Monsanto processability tester (MPT) were cut. Processability tests were conducted at 125 [degrees] C with a 1.5 mm orifice diameter. Viscosity, stress-relaxation and die swell responses were monitored over the following shear rate profile:

100 [sec.sup.-1], 200 [sec.sup.-1], 317 [sec.sup.-1], 400 [sec.sup.-1]

The MPT samples also served for visual observation of mix quality. Two individuals rated the samples for mix quality on a 1 to 10 scale. A rating of 1 represented a non-mixed state; a rating of 10 signified a glossy, continuous mixed compound.

Rheometer samples were die cut from the mill-cooled material. Samples were prepared and cure was monitored at 177 [degrees] C according to ASTM D-2084. The remaining mill-cooled material was compression molded for further testing according to ASTM D-3182. ASTM D-412 served as the protocol for tensile tests of the molded specimens.

Data analysis

Statgraphics from STSC, Inc. served as the main statistical analysis tool. Lotus 1-2-3 also aided in data management. Procedures conducted include[5-8]:

* Variance calculations;

* Factor effects calculations;

* Analysis of variance (Anova);

* Pearson correlations;

* Multiple linear regression;

* Response surface generation. Guidelines for evaluation of statistical significance, such as the determination of critical F-ratios and p-values, were followed[4,6,8].

Due to the sequential nature of central composite designs, data analysis was conducted in segments. The first analysis was performed on the [2.sup.2] full factorials from Block 1 of each mix procedure experiment. To complete the analysis of Block 1 experimentation, the extracted [2.sup.3] full factorial was examined. At this point, analysis results determined the extent of Block 2 experimentation needed. The investigation was completed with Block 2 experimentation for only one mix procedure. Resulting central composite analysis procedures included multiple linear regression, Anova and response surface generation.

Results and discussion

Block 1 experiments

Block 1 of each experiment was analyzed independently for factor effects. In order to evaluate statistical significance of the effects, variances were calculated for the three center-points of each mix procedure. F-ratios for each response effect were then calculated as[6]:

F-ratio = Factor [effect.sup.2]/Variance For both studies, the critical F-ratio for a 95% confidence interval was 18.51.

Factor effects for the sandwich mix procedure appear in table 6. The list includes only statistically significant effects. The sandwich mix results suggest a strong dependence on fill factor. Mix speed appears three times, and the two-factor interaction only once. The high levels of both factors are suggested as preferred.

Table 7 reveals fewer and weaker significant effects in the right-side up mix procedure experiment. Even so, the high levels of both factors are suggested as preferred.

Centerpoint analysis results for both Block 1 experiments appear in table 8. Overall, the right-side up mix procedure is more consistent than its counterpart, evidenced by reduced variances. In light of this realization and the fewer, weaker effects observed, there is much less differentiation between right-side up mixes contained in the factor space we studied than there is between the sandwich mixes. Centerpoint data suggest a better overall mix with the right-side up mix procedure.

Extracted experiment

The extracted [2.sup.3] full factorial was also evaluated prior to a decision on the need for Block 2 experimentation. Factor effects were determined, and Anova procedures were used to evaluate statistical significance. Critical F-ratios and p-values served as judgement baselines.

Mixing responses with significant factor effects appear in table 9 and property responses are available. Fill factor, mix procedure and their interaction dominate the effects. Mix speed emerges occasionally. In those cases, measured responses, such as maximum torque and tensile strength, indicate a preference for the high level of mix speed.

Figure 1 graphically illustrates factor effects on torque at 72 seconds mix time. The high levels of fill factor and mix procedure result in higher torque responses. Evaluation of the interaction plot suggests that torque dependence on fill factor is greatly determined by mix procedure. Torque responses for the sandwich mix procedure are highly dependent on fill factor, where they are not in the right-side up procedure. These same trends occur in tensile strength responses. Figure 2, the ODR rheometer minimum viscosity effects plot, indicates that higher levels of fill factor and mix procedure produce lower viscosities, suggesting better mix quality. Again, the interaction suggests much stronger dependence on fill factor in the sandwich mix procedure than in its counterpart.

Torque rheographs in figure 3 and 4 further support mixing response factor effects. Figure 3 illustrates the high fill factor dependence of torque development in the sandwich mix procedure. Figure 4 suggests that torque development dependence is more evenly distributed over fill factor and mix speed for the right-side up procedure.

Pearson Correlation analysis revealed some interesting relationships between responses. Several strong correlations between mixing responses and property responses were seen (data available). These relationships suggest that higher torque development produces property responses indicative of improved mix quality[1,9], such as: increased tensile strength and elongation; reduced minimum viscosity, scorch time and relaxation time; and increased die swell.

Experimental checkpoint

At this point in the investigation, a decision was needed on the extent of Block 2 experimentation to be performed. Data analysis indicated that the two mix procedures produced very different responses within the factor space studied. Data strongly suggested the right-side up procedure produced better, more consistent mix quality. Response differences in the right-side up experiment were fewer and less significant than in the sandwich experiment. In summary, the right-side up procedure exhibited less sensitivity to factor changes. Additional experimentation was not supported. Conversely, many highly significant effects were uncovered in the sandwich mix procedure. Differences observed across the factor space were vast. In addition, the customer normally used this mix procedure. Thus, Block 2 experimentation proceeded on the sandwich mix procedure to optimize responses.

Central composite experiment

Measured responses from Block 1 and Block 2 experimentation for the sandwich mix procedure were combined and analyzed as a central composite. Prior to analysis, blocking effects were determined insignificant[8]. In addition, no significant correlation coefficients between the blocks and responses were found. Experimental analysis proceeded with Pearson correlations and multiple linear regression. Anova procedures checked for regression significance. Given five degrees of freedom for the model and eight for error, the critical F-ratio for a 95% confidence level is 3.69. Since the computer software did not allow for lack of fit calculations, regression results were examined for lack of fit through the following estimation[6]: The regression equation does not exhibit lack of fit if:

Standard error < 1.5 (standard deviation of centerpoints).

Pearson correlations revealed relationships similar to those mentioned for the extracted experimental analysis. Thus, they are not discussed further. Multiple linear regression equations and Anova results on regressions are available. Response surfaces generated for each of the eight responses are also available. These surfaces suggest that a higher level of fill factor is most critical to achieving a good mix. They also support the higher mix speed, although it is not critical.

Conclusions

Experimental design

Statistical analysis results support the following set of conclusions:

* The right-side up mix procedure produces a higher quality, more consistent mix than the sandwich procedure. In addition, the right-side up procedure is more robust and less variable over the ranges studied for fill factor and mix speed.

* Regardless of mix procedure, a higher level of fill factor generates a better, more consistent mix. However, this effect is much more pronounced in the sandwich mix procedure. If a sandwich procedure is followed, a higher fill factor level will be crucial to insure a good mix.

* Mix speed has only weak effects on responses. Those responses it affects suggest a preference for the higher mix speed.

* Pearson correlations among responses suggest a strong relationship between torque development and compound property responses. This is good information for future small scale mixing studies.

Production scale confirmation run

The purpose of this study was to formulate suggestions for the customer to improve production scale mixing. Suggestions were tempered with the knowledge that levels preferred in the small scale study may not relate directly to production equipment. Recommendations included: switch to a right-side up mix procedure; raise fill factor to approach 85%; and maintain the current level of mix speed (which fell into the higher end of the range studied).

A plant trial was conducted to assess the validity of the small scale results in a production run. The customer mixed a control batch at the established mix conditions and two production batches incorporating the suggestions. Fill factors of 80% and 82% were evaluated. The batches were extruded and examined for dispersion differences. Significant improvements were noted in production mix quality when small scale experimental suggestions were incorporated.

Summary

This article illustrates the power of combining small scale mixing studies with statistical experimentation to attack production mixing problems. Small scale studies allow for broader, quicker and more economical investigations. Statistical experimental design and analysis techniques provide a systematic, comprehensive approach and strong statistical evidence for conclusions.

The concepts discussed broaden the existing basic concepts of rubber mixing evaluations. Combining small scale mixing studies with statistical techniques allows for a more complete understanding of the factors under investigation and their effects on mix quality. The successful transfer of results from the small scale experimental design to the production facility speaks well for this combination approach. [Table 6 to 9 Omitted] [Figures 1 to 4 Omitted]

References

[1]K.P. Beardsley and R.W. Tomlinson, "Processing of EPDM polymers as related to structure and rheology," presented at the ACS Rubber Division meeting, Detroit, October 1989. [2]J.W.M. Noordermeer and M.J.M. Wilms, "Processability of EPDM rubbers in internal mixers - dependence on molecular structure," Kautschuk + Gummi Kuntstoffe, Vol. 41 (1988), No. 6, pp. 558-563. [3]G.E.P. Box, W.G. Hunter and J.S. Hunter, "Statistics for experimenters," John Wiley & Sons, New York, 1978. [4]V.L. Anderson and R.A. McLean, "Design of experiments: A realistic approach," Statistics: Textbooks and Monographs, Volume 5, D.B. Owen, Ed., Marcel Dekker, Inc., New York, 1974. [5]R.H. Myers, "Response surface methodology," Allyn & Bacon, Inc., Boston, 1971. [6]G.C. Derringer, "A handbook for the design and analysis of experiments," Battelle Columbus Laboratories. [7]D.C. Montgomery, "Design and analysis of experiments," John Wiley & Sons, Inc., New York, 1984. [8]N.R. Draper and H. Smith, "Applied regression analysis," John Wiley & Sons, Inc., New York, 1966. [9]J.M. Funt, "Principles of mixing and measurement of dispersion," Rubber World, February 1986, pp. 21-32.