QC of the discontinuous compounding process in a rubber internal mixer by regression and neural networks process models.

The world economy is confronted with a strong international competition. Only the manufacturer of high quality products can establish his position in the market. For this reason, the commitment to quality management holds a position of prime importance. The classical quality assurance, i.e., an inspection of the end product, can no longer exist in this new understanding. On the contrary, actions of quality management have to be integrated in an earlier step of production and development. Accordingly, small and medium size rubber processors find themselves confronted with new tasks in the field of quality management.

The growing quality requirements and increasing cost pressure being imposed on industrial items made of rubber are making it necessary for the rubber-processing industry to assure and document the product quality that is required. Elastomer articles usually consist of an application-specific compound, which is generally produced by the rubber processor himself. The first step is the production of the rubber compound in the internal mixer. For this process, deviations are unavoidable here within certain limits, which means that the compound and component properties are subject to fluctuation (refs. 1 and 2). An additional problem is the large number of formulations, compounding regulations and different quality assurance methods that are available. Industry has not been able to solve this problem fully up to now. A registration and interpretation of all relevant process parameters at the internal mixer is not realized today in the rubber industry, The reasons are missing knowledge about the evidence of the data and the lack of concepts for data processing. Present-day control concepts for compound production are seldom based on the actual parameters of the process and are frequently unable to detect disturbances such as time deviations or changes in the thermal conditions which have an influence on the compound properties. Therefore, this article presents the development and testing of a new system that allows the on-line characterization of rubber compound viscosity and viscoelastic properties, process data recording and reporting errors based on measured process parameters with the support of mathematical process models (ref. 2).

Process modeling with statistical methods - theory and definitions

As an approach to the problem of process modeling for the prediction of the rubber mix properties, mathematical modeling methods as multiple linear regression and artificial neural networks are used. The general purpose of modeling is to learn more about the relationship between several independent or predictor; variables and a dependent or criterion variable. In this case, measured process values are independent and the rubber properties are dependent variables. In the engineering sciences, mathematical prediction procedures are very widely used in research. They allow the researcher to ask (and hopefully answer) the general question, "What is the best predictor of ...?"

Linear regression

Most empirical research belongs to one of the following two general categories: In correlational research of the production data we do not (or at least try not to) influence any but only measure them and look for correlations between some set of variables (e.g., rubber compound temperature and compound viscosity). In experimental research, we manipulate some variables and then measure the effects of this manipulation on other variables. For example, a researcher might artificially increase rotor speed and then measure the viscosity. Production data analysis in experimental research also comes down to calculating "correlations" between variables, specifically those manipulated and those affected by the manipulation. However, experimental data may provide qualitatively better information: Only experimental data can conclusively demonstrate causal relations between variables. For example, if we found that whenever we change variable A, then variable B changes, we can conclude that "A influences B." Data from correlational research can only be "interpreted" in causal terms based on some theories that we have, but correlational data cannot conclusively prove causality.

The general computational problem that needs to be solved in multiple regression analysis is to fit a straight line to a number of points (in the simplest case for one dependent y and one independent x variable). The goal of linear regression procedures is to fit a line through the points. In general, multiple regression procedures will estimate a linear equation (equation 1) of the form:

(1) y = [b.sub.0] + [b.sub.1][x.sub.1] + [b.sub.2][x.sub.2] + [b.sub.3][x.sub.3] + ... + [b.sub.k][x.sub.k]

Independent variables [x.sub.k] are those that are manipulated (process duration, number of revolutions, ram pressure, characteristic process values), whereas dependent variable y is only measured (Mooney viscosity, shear modulus) or registered. This distinction appears terminologically confusing because, as some scientists say, "all variables depend on something." However, once you get used to this distinction, it becomes indispensable. The terms dependent and independent variable apply mostly to experimental research where some variables are manipulated, and in this sense they are independent from the initial reaction patterns, features, intentions, etc., of the subjects. Some other variables are expected to be dependent on the manipulation or experimental conditions. That means they depend on what the subject will do in response. Somewhat contrary to the nature of this distinction, these terms are also used in studies where we do not literally manipulate independent variables, but only assign subjects to experimental groups based on some pre-existing properties of the subjects.

The smaller the variability of the deviations around the regression line relative to the overall variability of measured properties, the better is the prediction. The r-square ([r.sup.2]) value is an indicator of how well the model fits the data (ref. 3).

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The description of equation 2 and regression calculation is shown in figure 1. An r-square close to 1.0 indicates that we have accounted for almost all of the variability with the variables specified in the model.

[Figure 1 ILLUSTRATION OMITTED]

Artificial neural networks

Artificial neural networks were motivated by research on biological nervous systems which consist of densely connected networks of neurons. In the human nervous system, there are more than 100 types of neurons. A simplified diagram of one type of neuron is shown in figure 2.

[Figure 2 ILLUSTRATION OMITTED]

The neuron is essentially a chemical processing plant. Packets of chemicals are transported through the dendritic tree to the synaptic bulb. Depending on the nature of the synaptic gap, the activity in the neuron is either increased or decreased. The size of the synaptic gap determines the magnitude of the influence. Artificial neural nets exploit the concept of densely connected networks made of simple processing units for practical computational use. Neural networks as used by engineers and data analysts are compact ways of discovering complex formulas and have little to do with simulating intelligence. An artificial neural net is a network of artificial neurons which have several input paths and one output path. A typical artificial neuron is shown in figure 2.

Comparing this with figure 2, pulses have been converted to pulse rates or frequencies. The effects of the synaptic gap on the internal activation of the neuron are modeled by weights (Ws) which are multiplied by the frequencies (Xs). These individual contributions are summed to form the internal activity (S) in the neuron. A constant input called bias is used to simulate thresholding effects in the neuron and simplify the mathematics. The internal activation usually is the sum of the input multiplied by its associated weight (refs. 4 and 5). The internal activity of the neuron is transformed through a non-linear transfer function. The sigmoid is one common transfer function. Other common transfer functions are linear, hyperbolic tangent and sine.

When the transfer function is linear, a single neuron represents a linear equation. The weights associated with the neuron are equivalent to the parameters in the linear equation and standard linear regression techniques can be used to solve for the weights (ref. 5).

The learning with neural networks involves two phases. During the first one, the inputs, in this case the characteristic values of the mixing process, are presented and propagated through the network structure with hidden layers to compute the output values. This output is compared with its desired value. The second phase involves a backward pass through the network during which the error signal is passed to each unit in the network and appropriate weight changes are calculated.

Description of equipment and processes

The presented results were achieved at IKV Aachen for both a laboratory and a production rubber internal mixer. The following investigations were done on 1.51 (GK 1.5 E), 5.41 (GK 5 E) and 320 1 (GK 320 E) intermeshing internal mixers. The working part of an internal mixer consists of a cylindrical chamber holding two horizontally arranged rotors. The rotors are driven by a motor and gears. The chamber is fed through the filling chute which is closed by a lid. The discharge opening of the internal mixer is closed by a rectangular hinged door which is operated hydraulically. For the presented investigations, process parameters like electrical engine power, ram position, several temperatures, ram pressure and rotor revolutions per minute were measured (figure 3).

[Figure 3 ILLUSTRATION OMITTED]

To determine the rubber properties, a Mooney viscometer and a RPA 2000 (rubber process analyzer) were used. Both allow a simple but also very accurate and repeatable measurement of the rubber properties. As quality characteristics, the Mooney viscosity and the elastic and loss modulus were measured.

The main criteria for selecting a method for elastomer testing are the costs of testing, as well as the validity of the testing methods, as far as the relevant differences in mixtures are concerned. The experiments of this research project prove that the main parameters which influence the rubber mixture are the formulation itself, as well as the parameters in the following manufacturing steps. However, in the current manufacturing process, all testing of characteristics and parameters are off-line methods. A further disadvantage is the fact that a small quantity of material is taken to characterize a whole batch (ref. 2).

Modeling of the rubber compounding process

As already mentioned, the model developed for the mixing process was carded out with two different methods:

* multiple linear regression;

* artificial neural networks.

The first phase of the mixing process analysis was the building of the predictive models with the ordinary machine set parameters as cooling water temperature, ram pressure, rotor speed or with mixing phase duration as independent values. This part of the investigations was carded out on two laboratory rubber mixers with chamber volumes of 1.51 and 5.41.

In the second part of the analysis, the characteristic discrete values taken from the actual process parameter curves are used as source for the process description and the modeling. The analyzed curves, frequently referred to as fingerprints, reflect the course of the mixing process much more effectively than fixed process settings. They contain information on any disturbances and unexpected changes in the specific process sequence that arise. However, the process curves are difficult to handle in mathematical theorems. An attempt is being made to reduce the quantity of information by forming characteristic mathematical values, such as mean values, integrals, maxima, gradients values and the like. This method allows one to establish empirical correlation models between the process conditions and the resulting compound properties (figure 4).

[Figure 4 ILLUSTRATION OMITTED]

To avoid extraordinary costs, the first investigations carried out were focused on modeling carbon black compound under laboratory conditions (laboratory rubber mixers GK 1.5 E and GK 5 E). A typical tire tread compound and styrene-butadiene rubber (SBR) were mixed (refs. 2, 6 and 9). The investigated tire mixture is shown in table 1. SBR compound ingredients are shown in table 2.

Table 1 - tire compound formulation

Ingredients                      Phr

Natural rubber (NR)               65
Styrene-butadiene rubber (SBR)    25
Butadiene rubber (BR)             10
Carbon black N375                 65
Plasticizer                       20
Zinc oxide                        <5
Stearic acid                      <5
Antioxidant                       <5
Antiozonant                       <5
Table 2 - SBR-compound formulation

Ingredients                      Phr

Styrene-butadiene rubber (SBR)   100
Zinc oxide                         5
Stearic acid                       1
Plasticizer                       10
Carbon black N-550                50
Curing agent sulfur              0.5
Curing agent Vulkacit CZ/C       1.3
Curing agent thiuram               1
Antioxidant Vulkapox 4010NA        1
Antioxidant Vulkanox 4020          1

Models were built on the basis of experimental plans, involving the variations of critical influencing parameters that are prone to fluctuations. The experimental designs for both compounds are shown in tables 3 and. 4. The elastic loss modulus and loss modulus, as well as the Mooney viscosity, were recorded as quality characteristics. For the determination of the models, the multiple linear regression was used.

Table 3 - experimental design for the laboratory (1.5 L mixer) mixing experiments with the tire tread compound

Description   Machine settings                           Units

              Variable

Independent   (1) Duration of the mastication                s
Variables         of the raw rubber
              (2) Duration of the filler                     s
                  dispersion phase
              (3) Moment of the oil addition                 s
              (4) Rotor speed after filler          [s.sup.-1]
                  addition                      ([min.sup.-1])

              Constant

              (1) Rotor speed                       [s.sup.-1]
                                                ([min.sup.-1])
              (2) Ram pressure                             Mpa
              (3) Filling factor                             %
Dependant     Mooney viscosity                          Mooney
variable      (ML 1.5 + 4, 100 [degrees] C)              units

Description   Machine settings                      -       +

              Variable

Independent   (1) Duration of the mastication      15      30
Variables         of the raw rubber
              (2) Duration of the filler          120     145
                  dispersion phase
              (3) Moment of the oil addition       15      30
              (4) Rotor speed after filler      0, 66   0, 83
                  addition                       (40)    (50)

              Constant

              (1) Rotor speed                   0, 66

              (2) Ram pressure                   (40)
              (3) Filling factor                    7
Dependant     Mooney viscosity                     65
variable      (ML 1.5 + 4, 100 [degrees] C)

Table 4 - experimental design for the laboratory (5.4 L mixer) mixing experiments (SBR compound)

Description   Machine settings                               Units

              Variable

Independent   (1) Chamber filling factor                         s
variables     (2) Mixer and rotor temperature                    s
              (3) Percentage of the filler and                 [%]
                  oil addition (1. filling phase)
              (4) Duration of the filler                         s
                  dispersion mixing phase

              (5) Rotor speed                           [s.sup.-1]
                                                    ([min.sup.-1])

              Constant

              Ram pressure                                     bar
Dependant     Shear modulus                                   Pa s
variable      Mooney viscosity                              Mooney
              [ML 1+4, 100 [degrees] C]                      units

Description   Machine settings                          +     -

              Variable

Independent   (1) Chamber filling factor               65    75
variables     (2) Mixer and rotor temperature          50    70
              (3) Percentage of the filler and         90   100
                  oil addition (1. filling phase)       0   100
              (4) Duration of the filler              120   150
                  dispersion mixing phase

              (5) Rotor speed                       0, 66
                                                     (40)

              Constant

              Ram pressure                             15
Dependant     Shear modulus
variable      Mooney viscosity
              [ML 1+4, 100 [degrees] C]

The usefulness of these models for the prediction of compound properties is achieved by applying them to an industrial mixing process of a tire compound. In order to keep the test outlay to a minimum and prevent the production flow from being impaired, the necessary information - the data sets - were taken on a batch by batch basis from running production. The investigated rubber mixture is shown in table 1. The data sets were recorded on two successive days. The models are developed by using regression analysis and neural networks.

Results - prognosis models

The regression formula was solved with statistical software package Statistica (ref. 3). For the best results, a stepwise linear regression was chosen. The modeling results with mixing process settings show that these values were not suitable for rubber mix property prediction. The process model only describes the properties' variations based on the varied machine settings (figure 5). These models were not able to reach the sufficient prediction certainty.

[Figure 5 ILLUSTRATION OMITTED]

For the SBR compound, it was possible to determine the prediction models based on the characteristic process values with a very high degree of certainty. The data sets were split into a learn data set and a test data set. The test set was not presented to the solving algorithms during the model development.

Figure 6 shows the comparison of measured and calculated elastic modulus for the SBR laboratory compound. On the left side of the graph, the training data are shown. A very high accuracy (r-square = 94%) is reached. The results of the test sets are exposed on the right side on figure 6. In this case, an r-square of 87% was reached. The calculated modulus corresponds very well with the measured qualities. The prediction model is presented in equation 3. (Nomenclature are given in table 5). The prediction model results for the Mooney viscosity (figure 7) show the same dependencies as in figure 6.

(3) elastic shear modulus G' = 115
                   -0.0451 x LE6IN
                   -0.3417 x TD5EN
                   -7.9117 x LE6MI
                   +4.0382 x LE1MI
                   +0.3354 x TD6EN

[Figures 6-7 ILLUSTRATION OMITTED]

Table 5 - nomenclature

i, j, k   index
LE6IN     integral of el. power in the 6th mixing phase
LE6MI     mean value of el. power in the 6th mixing phase
LE1MI     mean value of el. power in the 1st mixing phase
n         number of replications of measurements
N         number of machine settings
TD5EN     final value of temperature difference between compound
          and mixer walls in the 5th phase
TD6EN     final value of temperature difference between compound
          and mixer walls in the 6th phase
x         independent variable
y         dependant variable
y         calculated values of regression equation

y         mean value of all measurements

Using the production rubber mixture, large fluctuations during the two day test were observed (ref. 1). In order to study the process behavior, which is a pronounced function of time, an attempt was made to describe the production process with artificial neural networks. This application was specially useful for highly complex non-linear associations, like so-called start-up effects. The structures of the presented artificial neural networks were calculated with software package Predict (ref. 7). Figure 8 shows the comparison between calculated and measured Mooney viscosity for the tire compound. These results show that the predicted properties correspond very well with the measured changes in the Mooney viscosity. The predicting quality reaches a certainty of r-square = 87%.

[Figure 8 ILLUSTRATION OMITTED]

Working on the basis of the comprehensive process model developed for a laboratory and a production compound in the first phase of the project, the last phase of presented investigations has focused on the integration of this model into the measuring unit - DiaDem (ref. 8) in order to give comprehensive online quality control. Figure 9 shows the user interface of the rubber internal mixer, which presents the process parameters and information about the rubber mix properties, as well as error messages.

[Figure 9 ILLUSTRATION OMITTED]

Conclusions

These results present several possibilities of modeling the compounding process. Summarizing, it can be said that if linear relationships can be assumed in the relevant test range, corresponding regression models provide sufficiently good descriptions for predicting the compound properties. The presented results show that this method is capable of learning and reacting to changing requirements for three different rubber mixer sizes. This means that allowance can be made for dynamics and non-steady-state behavior of the mixing process as it was modeled. After verifying the suitability of the proposed approach for production mixers and other mixtures, it will be possible to take this as basis for the on-line prediction of compound properties, and thus cut back on the elaborate compound testing required.

The rubber compounding is the first and very important production step in the process chain of elastomer production. Thus, in addition to advancements in the design of the internal mixer process other following processing steps (figure 10) should be included in future research studies.

[Figure 10 ILLUSTRATION OMITTED]

References

(1.) Haberstroh, E., Meiertoberens, U., Ryzko, P., Kiel, A. and Schwarz, P. "Aufbereitung von Kautschukmischungen," Block 14, 19. Kunststofftechnisches Kolloquium, IKV, Aachen, (March 11-13, 1998).

(2.) Meiertoberens, U., "Charakterisierung von Kautschukmischungen im Innenmischer mit statistischen Prozessmodellen," Ph.D. thesis, RWTH Aachen, 1997.

(3.) Statistica for Windows. General Conventions & Statistics I, StatSoft, Inc., Tulsa, 1994.

(4.) Fausett, L., "Fundamentals of neural networks: Architectures, algorithms and applications," Englewood Cliffs, NJ, 1994.

(5.) S.Y. Kung, "Digital neural networks," Engelwood Cliffs, Prentice Hall. NJ. 1993.

(6.) Lettowsky, Ch., "Entwicklung von Regressionsmodellen fur eine SBR-Mischung, Unpublished student thesis at IKV, Aachen, 1998.

(7.) "Predict - Handbook" NeuralWare, Inc., Pittsburgh, PA 1996.

(8.) "DiaDem3-Handbuch" 1997, GFS Aachen

(9.) Ryzko, P., "Analyse von Reifenlaufstreifenmischungen bei der Aufbereitung in Innenmischern unterschiedlicher GroBe" unpublished diploma thesis at IKV, Aachen, 1996.

P. Ryzko and E. Haberstroh, Institut fur Kunststoffverarbeitung, Aachen, Germany