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Optimizing a PU formulation by the Taguchi Method.

Optimizing a PU Formulation by the Taguchi Method

The powerful tools of statistical experimental design can greatly enhance the efficiency and reliability of chemical systems development. Its application to product design can reduce manufacturing variations and improve the field performance of chemical systems developed from components having the lowest possible cost. Moreover, statistical experimental design promotes a team approach to experimentation in which unfruitful paths are discovered and dropped quickly, and attention is directed exclusively to promising alternatives. This approach often results in rapid, efficient product development.

In Japan, the use of experimental design for product development is considered to be part of an upstream quality control effort. The Japanese refer to these techniques that improve quality upstream from the manufacturing line as "off-line quality control. "This article describes the application of the Taguchi Method, a methodology for direct product development developed by Dr. Genichi Taguchi, to the problem of finding commercial applications for an experimental polyol.

The Taguchi Method

The Taguchi Method is a strategy for off-line quality control, conducted at the product and process design stages of the manufacturing and reliability, and to manufacturing cycle to improve product manufacturability and reliability, and to reduce product development and lifetime costs. Dr. Taguchi developed his ideas approximately forty years ago as a communications engineer in Japan. Today, he and his systems are becoming well known in the United States, particularly by organizations supplying the automotive industry.

In the United States, Dr. Taguchi is often exclusively associated with statistical experimental design. But actually, Dr. Taguchi's method is a comprehensive, three-stage process for direct product development in which statistical experimentation is simply a tool. Taguichi's three stages are system design, System design is the process of applying scientific and engineering principles to develop a working prototype. Tolerance design is a method for determining final product specifications. Whereas these stages are essentially equivalent to the traditional activities of scientists and engineers, parameter design is the distinguishing characteristic of the Taguichi Method.

Parameter Design

Parameter Design is a process in which design parameters under the direct control of the product designer are varied in a scientific fashion to determine the best or optimum settings for these variables. For practically any product, there is a working range of possible settings of the variables. For example, in a polyurethane formulation, the product designer can select particular settings of water contents, chlorofluorocarbon-11 (CFC-11) concentrations, and catalyst types to produce usable foam. Different combinations of these design settings or levels, however, will also vary the quality of the product under development. Although an acceptable product may be produced, it is likely that a particular combination of levels will produce a superior product.

According to Taguchi, the product designer must not only produce a working prototype, but must also explore the parameter settings fully to develop the one that works best. Unfortunately, in the West, parameter design is often passed over or performed poorly simply because efficient methods to study the parameter design space are unknown. The tool Dr. Taguchi recommends for parameter design experiments is statistical experimental design, which greatly improves both the efficiency and reliability of experimental work. In particular, Dr. Taguchi recommends orthogonal array experiments as the basic tool for optimization.

Orthogonal Array


The function of an orthogonal array is to select a subset of the entire parameter design space, i.e., all combinations of possible parameter settings that will provide the essential information to determine optimal factor settings. Orthogonal arrays are standard plans for multifactor experiments that have a pairwise balancing property such that every setting of all other design parameters the same number of times. This pairwise balancing property, or orthogonality, gives excellent downstream reproducibility of laboratory results with greater precision than can be obtained from "one-factor-at-a-time" experiments because the conclusions about factor effects are all based over the entire range of test settings for the other design parameters.

Usually it is not efficient to conduct a thorough study of the parameter space unless there are only a few factors and levels of interest. Consider an experiment involving seven factors. Assuming that two or three levels are spaced "boldly," an excellent strategy of reducing the size of the investigation would be to limit the study to those levels. Yet, all possible combinations of two or three levels would still require 128 and 2187 trials, respectively. In these cases, the experimenter may drop some factors to further reduce the size of the study.

According to Dr. Taguchi, it is far better to include as many factors as possible in the initial screening and reduce the number of trials by using an orthogonal array because that experiment can often extract the essential information about the main effects, and sometimes two-factor interactions, with far fewer trials. In the example, a seven-factor main-effect study at two levels can be accomplished with an 8-trial orthogonal plan ([L.sub.8]) and at three levels with a 27-trial orthogonal plan ([L.sub.27]). This simply amounts to studying a fraction of all possible combinations described by the complete factorial experiment. Thus, orthogonal array experiments are often fractional-factorial experiments, which have been commonly used in the chemical industry for over forty years. Innovations provided by Dr. Taguchi that make the designs more applicable to polyurethane screening problems include:

* linear graphs to aid in the design of complicated screening experiments involving both main effects and interactions;

* provisions for including multilevel factors into two-and three-level orthogonal arrays:

* techniques that permit factors with various numbers of levels to coexist in a standard orthogonal array; and

* a complete system for statistical experimental design that can be learned quickly by technical people having a minimum of prior training in statistics.

The Basic Approach

Dr. Taguchi's approach to industrial experimentation is outlined below:

* Define the problem and the experimental objectives.

* Assemble a group knowledgeable with the problem area, and brainstorm factors and levels to be included in the design.

* Design the experiment by selecting and/or modifying an appropriate orthogonal array.

* Conduct the experiment, analyze the data, and interpret the results.

* Run confirmatory trials to determine whether the optimal settings derived from the parameter design experiment actually result in visible improvements.

The team approach and brainstorming are encouraged to prevent preconceived notions from unduly biasing the scope of the experiment. Further, the stress on confirmatory trials follows from the fact that all fractional-factorial designs achieve their economies through confounding main effects with interactions among factors. If Dr. Taguchi's recommendations are followed, the resulting parameter design experiments will often confound the main effects of interest with two-factor and higher-order interactions.

Usually, two-factor interactions are assumed to be not present in an orthogonal array screening experiment or they will at least be dominated by the main effects of interest. In chemical systems, this is often a highly questionable assumption. Its lack of validity, if present, will be shown by the confirmatory trials. Additional trials will then be required to understand exactly what effects and interactions are important.

Experts in the field of study often can assess from first principles or experience whether interactions should be accounted for in the initial screening experiments. According to Dr. Taguchi, this further demonstrates the need for engineers and scientists to design their own statistically guided experiments.

Formulation Development


This study was conducted shortly after one of the authors attended a two-week training session in the Taguchi Method. Its objective was to find a commercially feasible application for an experimental polyol product. A brainstorming session was conducted to select factors and levels for investigation. The initial objective of this project was to screen a number of possible formulation combinations to determine exactly what parameter settings, if any, produced a reasonable foam product.

The factors and levels listed in Table 1 for investigation in this initial screening study were assigned to Taguchi's [L.sub.16] orthogonal array using some advanced techniques of design construction that are beyond the scope of this article. Taguchi's method for assigning orthogonal array experiments may be found in his System of Experimental Design (ASI Press, 1987). The resulting experiment is presented in Table 2.

Table : TABLE 1. Factors and Levels.
 Number of
Factor levels Description
Polyol type 4 A, B, C, D
Catalyst 5 1, 2, 3
 package 4, 5
Surfactant 3 S1, S2, S3

Water, wt% 2 0.5, 1.5
CFC-11, wt% 2 25, 35
Isocyanate 2 11, 12


Constraints: Isocyanate index = 105; hydroxyl number = 410 [+ or -] 20; all surfactant conc. @ 1%.

Table : TABLE 2. Taguchi [L.sub.16] Screening Experiment.
 Polyol/ Surfac-
Trial water Catalyst tant CFC-11 Isocyanate
1 A 3 S2 25 11
2 B 1 S2 35 12
3 C 3 S1 35 12
4 D 1 S1 25 11
5 B 3 S1 25 12
6 A 2 S1 35 11
7 D 3 S2 35 11
8 C 2 S2 25 12
9 B 3 S3 25 11
10 A 4 S3 35 12
11 D 3 S2 35 12
12 C 4 S2 25 11
13 A 3 S2 25 12
14 B 5 S2 35 11
15 C 3 S3 35 11
16 D 5 S3 25 12

The construction of this design required repetition of certain factor levels of the catalyst variable more than others as a consequence of the balancing property of the orthogonal array. While a four-level column for the polyol/water factor could be included using Taguchi's recommendations without losing the balancing property of the array, a five-level column cannot be constructed directly. Instead, a seven-level column was created for the catalyst variable and the two extra levels were replaced with an existing level considered to be of great importance. Taguchi calls this procedure "dummy treatment" and has a detailed discussion of it in his book.

In order to use the [L.sub.16] orthogonal array, it was necessary to combine the water and polyol levels using a technique called combination design. Thus, the main effects of both polyol and water were estimated under the assumption that no interaction existed between the two factors.

Experimental Procedure

Reactivity profile and friability (subjective rating) were determined from hand-mix foams prepared in 1-gal paper cans. Free rise densities were measured on core samples of open blow foams. Height of rise at gel, final rise height, and flow ratio were determined in a flow tube.

Minimum-fill-density and packed panels were prepared in a 2-x3-x25-in mold press at 120 [degrees] F. Core densities and k-factors were determined from core samples of packed panels. The "freeze stable density" of a foam is defined as the lowest panel density above the minimum-fill-panel density that exhibits no significant changes in dimensions after being held at -20 [degrees] C for at least 2 hrs. The bottom sections of the packed panels were tested for compressive strength.

Isocyanate and masterbatch temperatures were maintained at 20 [degrees] C. Masterbatches were cooled down to 12 [degrees] C before panels were prepared in the mold press.

The 16 trials were performed in a completely random fashion to avoid experimental bias from unknown sources of variation. The randomized sequence is shown in Table 3 along with values of some of the nine response variables studied. Other variables included flow and demold properties. [Tabular Data Omitted]

Most of the foams produced were of poor quality, as expected, since the purpose of the study was to deliberately induce variation into the results to determine important factor effects. The notable exception was trial #14, a low-density foam system with good freeze stability and thermal conductivity.

Data Analysis

The analysis was done in two parts. First, the statistical significance for each response was assessed using the Analysis of Variance or ANOVA. This procedure essentially determines whether the total variation observed in a set of trials is due to chance and simultaneously determines the contribution of each factor to the total variation.

Second, for those factors that were determined to be statistically significant, the levels responsible for the best performance were identified. The underlying model of this screening experiment was far too complex to be analyzed by the simple analysis tools of the Taguchi Method. Instead, the results were analyzed using the General Linear Models procedure contained in the SAS statistical analysis program. These analyses revealed a significant "lack of fit" for many of the responses, i.e., the assumption concerning the absence of interactions among the factors was unjustified. Nevertheless, several main effects of importance were identified for each response.

The results are summarized in Table 4, in which the relative importance of factors and their optimal setting is presented in descending order of significance. The various responses differ with respect to their optimal factor and treatment combinations. For example, density and flow are most strongly influenced by the CFC-11 and polyol factors, while the catalyst is the single most significant factor affecting cream time.

Table : TABLE 4. Optimum Factor Combinations in Order of Significance for the Responses.

A. Cream time, sec

Target: 5-6
 Catalyst: 3, 4, or 5
 Polyol: B or C
 Water: 1.5

B. Gel time, sec

Target: 26-30
 Polyol: B, C, or D
 Water: 1.5
 Catalyst: 3, 4, or 5
 CFC-11: 25

C. Core density, pcf

Target: 1.50-1.60
 CFC-11: 35
 Water: 1.5
 Polyol: B or C

D. Flow, cm

Target: 125-140
 CFC-11: 35
 Water: 1.5
 Polyol: B or C
 Isocyanate: 11

E. Free rise density, pcf

Target: 1.20
 CFC-11: 35
 Water: 1.5
 Polyol: B

F. k-Factor, Btu in/h [degrees] F [ft.sup.2]

Target: smallest best
 Polyol: A
 Catalyst: 3
 Water: 0.5
 CFC-11: 25

A desirability scale was assigned to each response to establish those factors that produced the best overall performance. These factors and their levels are shown in Table 5. The analyses indicated no significant difference among any of the surfactants and only a slight preference for one of the isocyanates, so these two factors were set at their most economical levels.

Table : TABLE 5. Factor Settings in Order of Decreasing Performance for Optimal Foam Performance.
Factor Level
Polyol B or C
CFC-11 35
Water 1.5
Catalyst 3, 4, or 5
Isocyanate 11

Confirmatory Trials

Using the information in Table 5, the six additional experiments described in Table 6 were performed to determine the best combination of polyol and catalyst. Note that only one of the confirmatory trials, #5, was observed as part of the original experiment (trial #14). A characteristic of statistical experimental design is that a sequential approach to experimentation is promoted, in which information from an initial experiment is used as a guide for further experimentation.

The confirmatory trials represent a full-factorial experiment for two levels of polyol and three levels of catalyst. According to the results of the initial experiments, most of the properties of these foams should all be essentially equivalent. However, the additional trials are absolutely required for verification purposes because the analysis of the first 16 trials indicated that the assumption of no interaction among the factors was not strictly valid.

At this stage, foam performance was judged more critically, and the foams were graded on a "pass/fail" basis to simplify interpretation. The results listed in Table 6 clearly indicate that polyols B and C are not equivalent, as suggested by the initial design. Instead, all foams produced with polyol C were too fast for existing commercial processing.

Table : TABLE 6. Confirmatory Trials Suggested by Table 5.(a)
Trial Polyol Catalyst Result
1 B 3 Pass
2 C 3 Fail
3 B 4 Pass
4 C 4 Fail
5 B 5 Pass
6 C 5 Fail

(a) Levels: CFC-11 = 35; Water = 1.5; Isocyanate = 11. Surfactant level S1 used for all trials.

The properties of the acceptable foams given in Table 7 demonstrate remarkable similarities, especially in their kinetic properties. Obvious differences exist, however, in their thermodynamic properties, especially thermal conductivity. Presumably, these differences are due to the catalyst. The data in Table 7, however, are not sufficient to reliably estimate the effect of catalyst. These data do suggest that the experimental polyol will indeed produce a commercial product.

Table : TABLE 7. Properties of Foams That Passed Confirmatory Trials.
Property 1/3 3/4 5/5
Cream time, sec 4 6 4
Gel time, sec 27 28 30
Tack free, sec 42 45 40
Height of rise, 147 144 144


Free rise 1.12 1.10 1.10

density, pcf

Core density, 1.34 1.35 1.35


Molded overall 1.45 1.55 1.52

density, pcf k-Factor, 0.125 0.124 0.120

Btu in/h[degrees] F ft(2)

Final Product Optimization

Polyol B (Multranol E-9280) was further studied by means of Response Surface Methodology. The objectives of this final study were to remove remaining ambiguities about the effects of catalyst, water content, and CFC-11 content; to develop an advanced computational model for all important parameters of the urethane product; and to determine the optimum settings for all parameters. The result of these final studies was a commercial product (Tables 8 and 9), now under patent protection, with good thermal conductivity (k-factor) and, as illustrated in Figs. 1 and 2, exceptional demold characteristics. The demold properties of this product result in increased productivity for the customer without capital investment, in accordance with the Taguchi philosophy.

Table : TABLE 8. Commercial Formulation.
Component Weight %
Polyol B (E-9280) 69.45
Surfactant, catalyst 2.35
Water 1.20
CFC-11 27.00
Total 100.00
Polymeric MDI 97.2

Table : TABLE 9. Properties of Commercial Formulation.(a)

Processing data: isocyanate/resin
 Temperature, [degrees] F 100/70
 Pour pressure, psi 1500/1500

Reactivity data, sec:
 Cream time 2-3
 Gel time 33
 Tack free 56

Density, pcf:
 Free rise 1.12
 Minimum fill 1.65
 Freeze stable 1.85
 Molded core 1.70
k-Factor, initial 0.117

Btu in/h [degrees] F ft(2) Compressive strength, psi
 Parallel at yield 19.1
 Perpendicular at yield 18.3

Dimensional stability

% vol. change @
 -30[degrees] C, 1 day 0.6
 +70[degrees] C, 1 day 0.0

(a)HK-100 machine, MQ 12-2 mixing head.

PHOTO : FIGURE 1. Demold properties by Brett opening method.

PHOTO : FIGURE 2. Demold properties, % thickness change method. Conclusions

1. Taguchi's group approach to problem solving resulted in highly efficient use of both personnel and material resources. Although more time was required to plan experiments, the overall time required to complete this project was far less than required for conventional experiments. Further, the wealth of information obtained during the brainstorming sessions did serve to prevent experimental bias and ensure a broad search for applications.

2. The 16-trial screening experiment, although somewhat complicated, made very efficient use of technical resources and indentified critical factors and levels for further study.

3. The six additional confirmatory trials removed some ambiguities concerning blend composition and verified that commercially feasible foams could be produced from the experimental polyol.

4. The authors found Taguchi's orthogonal arrays to be too restrictive and inefficient for final product optimization, so nonlinear methods were used for this purpose. Thus, in the authors' laboratory, the Taguchi Method has become a screening tool in formulations development.

5. A commercial product, Multranol E-9280, with exceptional demold properties was perfected as an end result of this study.

Although some of Dr. Taguchi's techniques are controversial and are a matter of dispute among statisticians, the Taguchi concept of direct product design has been accepted and promoted by Mobay management and is currently being directed toward the CFC issue in rigid foam formulations.
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Title Annotation:polyurethane quality control
Author:Lunnery, Sohelia R.; Sutej, Joseph M.
Publication:Plastics Engineering
Date:Feb 1, 1990
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