Practice of Taguchi design of experiments in the valuation of mechanical behavior of rigid polyurethane foam composites

Abstract

In the present study, Taguchi design of experiments (DOEs) L₁₈ orthogonal array has been used for the investigation of the mechanical behavior of rigid polyurethane foam (RPUF) composites. The outcome of the process parameters such as polyol, filler, surfactant, catalyst, blowing agent, and anti-flaming agent on the mechanical properties, such as tensile, flexural, and compressive strengths and hardness (Shore D) of RPUF composites, has been examined, and the resulted data were analyzed by means of Taguchi design of experiments. The raw data for the average values of the mechanical properties and the signal-to-noise (S/N) ratio for each parameter were evaluated at three levels, and the analysis of variance (ANOVA) and optimum process parameters are determined. The confirmation experiments were performed for the validation of the improved performance and to measure the contribution of individual parameter on the responses. The confirmation experiments revealed the average tensile strength, average compressive strength, average flexural strength, and average hardness (Shore D) as 5.24 MPa, 6.37 MPa, 12.28 MPa, and 72.43, respectively, which fall within the 95% confidence interval of the anticipated optimum process parameters.

Keywords

Rigid polyurethane foam composites response curve analysis of variance signal-to-noise ratio

Introduction

Polyurethane (PU) is one of the leading contenders of the highly diverse family of polymers. The unending adaptability of the polyurethane has led to its numerous applications, that is, from low density packaging products to high performance medical substances and, from thermally stable insulation for space exploration vehicles to extremely flame-retarded flexible cushioning. Rigid polyurethanes foams (RPUFs) are one of the important classes of cellular materials finding recognition in different industrial sectors due to their high-performance applications. Rigid polyurethanes foams can display a range of properties which enable them flaunting a variety of applications, depending upon the chemical reagent used in their synthesis.

Like other engineering products, in order to improve the price and reliability of RPUF composites, it is desirable to optimize their processing limits that govern the inclusive properties of the final products. The processing limits of any product can be optimized by using statistical tools that involve a strategic experimentation, followed by a derivation of the variables of interest over a definite range.¹ Taguchi Design of Experiment (DOE) is one of the easiest, reliable, and practical statistical methods and is efficient for designing processes that operate consistently and optimally over a variety of conditions. Taguchi’s signal-to-noise ratios (S/N), are the log functions, based on Orthogonal Array (OA), that provide a set of well balanced (minimum) experiments and desired output on the basis of independent evaluation of the factors.² The importance of these factorial designs is their foundation of industrial experimentation for product and process development and improvement. Being easy and reliable, this approach has been used by many researchers for the optimization of the process parameters in their respective studies.³ Barick et al. optimized the processing parameters for the fabrication of thermoplastic polyurethane/millable polyurethane blend systems, reinforced with organoclay.⁴ Melt mixing of polypropylene/ethylene propylene diene monomer rubber (EPDM)/organoclay nanocomposites was also optimized by employing the Taguchi methodology.⁵ Arunkumar et al. used the response surface methodology (RSM) for generating a mathematical model and to optimize the coating procedure of polyurethane on the acrylonitrile butadiene styrene. Paint flow rate, part–applicator distance, and paint viscosity were considered as input parameters to optimize the responses (dry film thickness, rating value, and distinctness of image).⁶ Bil et al. optimized the polyurethane structure for applications in bone tissue engineering. The results obtained by them indicate that, an optimal ratio of hard to soft segments may be obtained for the culture of human osteogenic cells.⁷ Bratov et al. optimized the composition of ammonium ion sensitive membrane based on a photo-curable aliphatic urethane diacrylate oligomer.⁸ Eslick et al. used a stochastic optimization method for predicting the polyurethane structures having a given set of physical and chemical properties.⁹ They described an extension of the use of connectivity indices, within a computational molecular design framework to design novel polyurethane structures. Im et al. used central composite design optimization method to examine the conditions for pyrolysis of polyurethane to attain a solid product with a high iodine number. Under the optimum conditions, the iodine number and the yield of solid product were estimated to be 582 mg/g and 15 g, respectively.¹⁰ El-Shekeil et al. employed Taguchi L₉ OA to optimize the processing parameters of thermoplastic polyurethane reinforced with cocoa pod husk fibers, and the ultimate tensile strength was considered as the response.¹¹ Zavala et al. performed the optimization of polyurethane production in a semi-batch reactor. The performance of the polyurethane reactor was reportedly enhanced by implementing the tools and approaches from the process system engineering discipline.¹²

From the literature studies, it is evident that only a few studies have reported the application of Taguchi method for the estimation and improvement of the mechanical and surface properties of RPUF composites. The present study has been conducted with an aim to develop RPUF composites and to optimize their formulation for desired mechanical properties by using Taguchi DOE, with a purpose to improve their reliability for the selective applications. The L₁₈ mixed OAs are used to increase the experimental efficiency. The effects of different process parameters such as polyol, filler, surfactant, catalyst, blowing agent, anti-flaming agent on tensile, flexural, and compressive strength, as well as hardness (Shore D) of RPUF have been extensively investigated.

Materials and methods

Materials

Castor oil (99%), 4, 4′-diphenylmethane diisocyanate, and dibutyltin dilaurate (DBTDL; catalyst) were brought from Shivathene Linopack Ltd, Parwanoo, Himachal Pradesh, India. Calcium carbonate (CaCO₃; filler), silicon oil (surfactant), and n-pentane (blowing agent) were purchased from CDH(P) Ltd., New Delhi, India. Triethylenediamine (TEDA) (99%; catalyst), melamine (2,4,6-triamino-1,3,5-triazine; anti-flaming agent), tris (2-chloroethyl)phosphate (TCP; anti-flaming agent), tris (1,3-dichloro-2-propylphosphate) (TDCPP; anti-flaming agent), cobalt octoate (catalyst), and fly ash (filler) were supplied by Standard Chemicals (ISO 9001:2008 certified), Tilak Bazar, New Delhi, India. Glycerol was obtained from Sisco Industries Pvt. Ltd. All the reagents were of analytical grade and were used as supplied.

Development of rigid polyurethane foam composites

Rigid polyurethane foam composites were prepared by employing a two-step method. First, the castor oil was modified to obtain polyol according to the procedure reported in prior studies.^13–15 Then all the components, as per the experimental design strategy, were added into a beaker and stirred at room temperature for the adequate mixing. The prepared mixture was spread into a pre-lubricated metal mould (200 × 200 × 100 mm) and left to stand for 96 h, for complete curing. After de-moulding, the prepared composite foam was cut into required dimensions and tested for its hardness, compressive, flexural, and tensile strengths. The samples of different formulations are given in Figure 1.

Figure 1.

Different formulations of rigid polyurethane foam.

Mechanical testing of rigid polyurethane foam composites

The mechanical properties of the prepared RPUF composites have been determined according to the standard procedures. Testing is conducted on three specimens of each concentration, and the average value of the three has been reported. Tensile, compressive, and flexural strengths of the resulted foam composites were measured at room temperature using Instron (Model No. 3369) universal testing machine (UTM) as per ASTM D-638, ASTM D 695, and ASTM D 790 methods, respectively. Shore D hardness of the RPUF composites was determined by Durometer Hardness Tester (Model: PosiTector^® SHD) as per the ASTM D2240 method.

Design of experiments

Taguchi method is a standardized approach for determining the best combination of inputs to produce a product or service. This is accomplished through DOEs.^16,17 Process parameters for the present study, such as polyol, fillers, surfactant, catalyst, blowing agent, anti-flaming agent, and their chosen levels, for conducting Taguchi experiment are reported in Table 1. Each experiment was repeated thrice in every trial condition and their tensile strength, flexural strength, compressive strength, and hardness (Shore D) were measured. Since the error observed in the experimental values is within the limit of ± 0.01 only, the average values of the tensile strength, flexural strength, compressive strength, and hardness (Shore D) have been reported. For every replication, experimental trial conditions are shown in Table 2. Analysis of variance (ANOVA) is conducted to determine the important process variables. The optimum combinations of the process parameters are selected using S/N and ANOVA analysis.

Table 1.

Selected process parameters and their levels.

Notation	Process parameter	Level 1	Level 2	Level 3
A	Filler	Fly ash	CaCO₃	-
B	Polyol	2:1	3:1	4:1
C	Surfactant	1%	3%	5%
D	Catalyst	Cobalt octoate	TEDA	DBTDL
E	Blowing agent	5%	10%	15%
F	Anti-flaming agent	Melamine	TDCPP	TCP

CaCO₃: calcium carbonate; TEDA: triethylenediamine; DBTDL: dibutyltin dilaurate; TDCPP: tris (1,3-dichloro-2-propylphosphate); TCP: tris (2-chloroethyl)phosphate.

Table 2.

Experimental trial conditions.

Exp. No.	Input process parameters
	A	B	C	D	E	F
	Filler	Polyol	Surfactant	Catalyst	Blowing agent	Anti-flaming agent
1	1	1	1	1	1	1
2	1	1	2	2	2	2
3	1	1	3	3	3	3
4	1	2	1	1	2	2
5	1	2	2	2	3	3
6	1	2	3	3	1	1
7	1	3	1	2	1	3
8	1	3	2	3	2	1
9	1	3	3	1	3	2
10	2	1	1	3	3	2
11	2	1	2	1	1	3
12	2	1	3	2	2	1
13	2	2	1	2	3	1
14	2	2	2	3	1	2
15	2	2	3	1	2	3
16	2	3	1	3	2	3
17	2	3	2	1	3	1
18	2	3	3	2	1	2

Result and discussion

The experiments are designed by using the parametric approach of the Taguchi’s L₁₈ OA. Analysis of data is conducted by employing the standard strategy suggested by Taguchi. The most favorable (optimal) conditions of the process parameters are determined by analyzing the response curves and the ANOVA tables. Further, the effects of process parameters, that is, filler, polyol, surfactant, catalyst, blowing agent, and anti-flaming agent on the selected response characteristics, that is, tensile strength, flexural strength, compressive strength, and hardness have been determined.

Tensile strength, flexural strength, compressive strength, and hardness

The experiments are performed against each of the trial condition. Each experiment is repeated at a trial condition, and the data (raw data) have been recorded for the each. Table 3 shows the tensile strength, compressive strength, flexural strength, and hardness results of the samples at different levels. The collected data were analyzed by using Taguchi method, and the mean S/N ratios at each level of factors are given in Table 4.

Table 3.

Tensile strength, compressive strength, flexural strength, and hardness of different formulations of rigid polyurethanes foams.

	Level	Filler	Polyol	Surfactant	Catalyst	Blowing agent	Anti-flaming agent
Tensile strength (MPa)	L1	3.37	3.14	2.67	2.33	1.98	2.33
	L2	2.31	3.05	3.81	3.65	3.16	3.47
	L3	*	2.33	2.04	2.53	3.37	2.72
Compressive strength (MPa)	L1	3.48	3.16	2.54	2.04	1.73	1.89
	L2	1.89	2.93	3.54	3.67	3.16	3.46
	L3	*	1.98	1.98	2.35	3.18	2.71
Flexural strength (MPa)	L1	13.33	12.88	11.17	11.44	9.31	9.53
	L2	9.85	12.02	13.79	12.69	12.23	12.82
	L3	*	9.86	9.80	10.63	13.22	12.41
Hardness	L1	56.00	54.06	48.00	44.28	43.67	46.00
	L2	39.44	47	52.50	53.17	49.67	51.83
	L3	*	42.11	42.67	45.72	49.83	45.33

Table 4.

Mean signal-to-noise ratios for each level of process parameters.

	Level	Filler	Polyol	Surfactant	Catalyst	Blowing agent	Anti-flaming agent
Tensile strength	L1	9.45	8.95	8.16	6.87	5.68	6.93
	L2	6.92	8.46	10.66	10.04	8.79	10.03
	L3	*	7.14	5.74	7.64	10.09	7.60
Compressive strength	L1	9.41	8.24	7.48	5.39	4.44	5.13
	L2	5.09	7.93	9.08	9.65	8.03	9.52
	L3	*	5.59	5.20	6.72	9.28	7.10
Flexural strength	L1	22.07	21.74	20.83	21.08	19.19	19.44
	L2	19.66	21.19	22.29	21.17	21.22	21.59
	L3	*	19.66	19.47	20.34	22.18	21.56
Hardness	L1	34.78	34.33	33.47	32.67	32.65	33.10
	L2	31.77	33.14	33.95	34.06	33.41	33.92
	L3	*	32.36	32.40	33.10	33.76	32.80

The signal-to-noise (S/N) ratio associates the two different types of the parameters (mean value of the quality trait and variance about this mean) into a single one. The average values and the S/N ratios of the response traits for each parameter, at different level, are measured from the experimental data. The response curves (main effects) of each process parameter are used to study their effects on the response traits. The analysis of variance (ANOVA) for the raw data and the S/N ratio is performed to identify the most influential parameters and to determine their effects on the response characteristics. The effect curves of process parameters, both for S/N ratio and raw data, are drafted as Figure 2(a)–(d). The Table 5 shows the results of ANOVA for different response traits, that is, for (a) tensile strength, (b) compressive strength, (c) flexural strength, and (d) hardness. The optimal combination of process parameters is confirmed by analyzing these response curves and the ANOVA tables and the most influential parameters have been identified.

Figure 2.

Signal-to-Noise ratio and raw data curves versus process parameters on (a) tensile strength, (b) compressive strength, (c) flexural strength, and (d) hardness.

Table 5.

Results of ANOVA for (a) tensile strength, (b) compressive strength, (c) flexural strength, and (d) hardness.

Tensile Strength
Source	SS	DOF	V	F-ratio	P %	SS′
Filler	15.29	1	15.29	45.16	14.52	14.94
Polyol	7.22	2	3.61	10.67	6.86	6.54
Surfactant	28.81	2	14.40	45.16	27.36	28.13
Catalyst	18.21	2	9.11	26.91	17.30	17.54
Blowing agent	9.63	2	4.82	14.23	9.14	8.95
Anti-flaming agent	11.92	2	5.96	17.62	11.32	11.25
Error	14.21	42	0.34		13.50	17.94
Total	105.29	53			100	105.29
Compressive strength
Source	SS	DOF	V	F-ratio	P %	SS′
Filler	33.97	1	33.97	244.89	22.15	33.84
Polyol	14.12	2	7.06	50.90	9.21	13.84
Surfactant	22.63	2	11.31	244.89	14.75	22.35
Catalyst	26.76	2	13.38	96.46	17.45	26.46
Blowing agent	27.74	2	13.87	99.99	18.09	27.46
Anti-flaming agent	22.33	2	11.16	80.47	14.56	22.05
Error	5.83	42	0.14		3.80	7.35
Total	153.38	53			100	153.35
Flexural strength
Source	SS	DOF	V	F-ratio	P %	SS′
Filler	163.53	1	163.53	58.11	21.77	160.71
Polyol	86.95	2	43.47	15.45	11.57	81.32
Surfactant	148.53	2	74.26	58.11	19.77	142.90
Catalyst	39.10	2	19.55	6.95	5.20	33.47
Blowing agent	79.61	2	39.81	14.15	10.60	73.99
Anti-flaming agent	115.42	2	57.71	20.51	15.36	109.80
Error	118.18	42	2.81		15.73	149.14
Total	751.32	53			100	751.33
Hardness
Source	SS	DOF	V	F-ratio	P %	SS′
Filler	3700.17	1	3700.17	207.57	43.83	3682.34
Polyol	1298.11	2	649.06	36.41	15.38	1262.46
Surfactant	872.33	2	436.17	207.56	10.33	836.68
Catalyst	819.11	2	409.55	22.97	9.70	783.46
Blowing agent	544.06	2	272.02	15.26	6.44	508.40
Anti-flaming agent	460.33	2	230.16	12.91	5.45	424.68
Error	748.72	42	17.83		8.87	944.82
Total	8442.83	53			100	8442.84

ANOVA: analysis of variance; DOF: degree of freedom; SS: sum of squares; V: variance; F-ratio tabulated: 3.223; P%: percentage contribution.

The optimum values of process parameters for the anticipated range of tensile strength, flexural strength, compressive strength, and hardness are reported in Table 6.

Table 6.

The optimum value of process parameters for the anticipated range of tensile strength, flexural strength, compressive strength, and hardness.

Notation	Process parameter	Level 1	Level 2	Level 3
A	Filler	Fly ash	CaCO₃	—
B	Polyol	2:1	3:1	4:1
C	Surfactant	1%	3%	5%
D	Catalyst	Cobalt octoate	TEDA	DBTDL
E	Blowing agent	5%	10%	15%
F	Anti-flaming agent	Melamine	TDCPP	TCP

CaCO₃: calcium carbonate; TEDA: triethylenediamine; DBTDL: dibutyltin dilaurate; TDCPP: tris (1,3-dichloro-2-propylphosphate); TCP: tris (2-chloroethyl)phosphate.

Filler (A, first level) = Fly ash has been observed as the best filler among the all chosen. Achievement of the optimal properties may be attributed to the proper dispersion of fly ash into the rigid polyurethane foam (RPUF). The properties of RPUF composites depend on the particle size, concentration, shape, and the interaction of the filler with the polymer matrix.¹⁸

Polyol (B, first level) = The polyol to isocyanate ratio of 2:1 represents the optimal value. More number of hydroxyl groups cause more crosslinking. The network properties of the RPUF composites are decided by the crosslinking density, which in turn is regulated by the functionality and hydroxyl value of the polyol. Thus, most of the foam properties are expected to depend on the type of vegetable oil used and the hydroxyl group content of the polyols, which directly influence the crosslinking density of the RPUF composites.¹⁹

Surfactant (C, second level) = The optimum requirement of the surfactant is established as 3%. The addition of surfactant diminishes the pressure differences between bubbles of different sizes by reducing the surface tension of the polyol, consequently leading to better stability of bubbles, and thus results in the achieving of small average pore size. In addition, the surfactant can stabilize the initial liquid-air dispersion by controlling the number of the cells. The excessive amount of the surfactant may result in the collapse of the foam, as the walls and struts of the rigid foam cells could not support the gas pressure.¹⁴

Catalyst (D, second level) = The most suitable catalyst found in this study is triethylenediamine (TEDA). The relative rates of the blowing and gelling reaction are controlled by the amine catalyst, which is governed by the structure of the catalyst, along with its electronic and steric effects. The amine catalysts work by using their free electronic pair available on the nitrogen atom, which activates the C=N moiety of the isocyanate group.²⁰

Blowing Agent (E, third level) = The optimal requirement of the blowing agent is 15%. The blowing agent used in this study is n-pentane, a physical blowing agent. Physical blowing agents are the volatile liquids that evaporate on getting heat from the reaction and give cellular structure to the foam. The increase in concentration of blowing agent results in the rise in number of cells per unit volume and smaller average cell size. A low concentration of blowing agent is not sufficient to produce foam due to the lack in the compatibility of the rates of foaming and gelling reactions, which is the prime requisite for the formation of cellular foams.

Anti-flaming Agent (F, second level) = The presence of the anti-flaming agent influences the mechanical properties of the RPUF composites in addition to improving their flame-retardancy. Tris (1,3-dichloro-2-propylphosphate) (TDCPP) was recorded as the optimum flaming agent, which had significantly affected the mechanical behavior of the RPUF. The high value of tensile strength achieved with TDCPP indicates that the TDCPP was dispersed well in the PU matrix, with proper adhesion. On the other hand, the decrease in tensile strength, in case of melamine, is due to the involvement of its larger sized particles in the polyurethane matrix that results in the collapsing of cellular structure of the foam, and hence leading to its weakening.^21,22

Confirmation experiments

The confirmation experiments are the conclusive steps in validating the inferences from the former round of investigations. The selected numbers of experiments have been carried out by setting the significant parameters at the optimum conditions, while the insignificant parameters were kept at the economic levels. The average of the results of the confirmation experiments is compared with the predicted average, which depends on the tested parameters and their levels. The three confirmation experiments, each for the tensile strength, compressive strength, flexural strength, and the hardness, are performed at the optimum combination of the process parameters. Filler is set at first level, polyol at first level, surfactant at second level, catalyst at second level, blowing agent at third level, and anti-flaming agent at second level. From the confirmation experiments, the average values of the tensile strength, compressive strength, flexural strength, and the hardness (Shore D) are recorded as 5.24 MPa, 6.37 MPa, 12.28 MPa, and 72.43, respectively, which fall within the 95% confidence interval of the anticipated optimum process parameters.

Conclusions

The RPUFs are the most widely used materials in various industrial and engineering applications, including false roofing, sandwiched construction panels, railway assemblies, and in buildings for thermal insulation purposes. Rigid polyurethanes foams can be tailor-made to exhibit different properties, depending upon the applications to be employed. The present study has been conducted with an aim to develop RPUFs and optimize their formulation for desired mechanical properties, with a purpose to improve their reliability for the selective applications. For this, different fillers, catalysts, and anti-flaming agents are explored to find the best suitable formulation. Further, the concentrations of polyol, surfactant, and blowing agent are optimized for better mechanical properties. In order to achieve consistency in the final product, the effects of process parameters, that is, filler, polyol, surfactant, catalyst, blowing agent, and anti-flaming agent on the selected response characteristics, that is, tensile strength, compressive strength, flexural strength, and the hardness, have been studied by using Taguchi DOEs. The raw data for the mean values of the response characteristics and S/N ratio for each parameter have been analyzed at three levels (L₁, L₂, and L₃). The experiments are designed by applying the parametric approach proposed in the Taguchi’s L₁₈ OA. Each experiment is repeated thrice under trial condition and for every replication, tensile strength, compressive strength, flexural strength, and hardness (Shore D) are measured. The response curves of the process parameters are plotted for S/N ratio and the raw data, for analyzing the influence of the process parameters on the response traits. The ANOVA of raw data and the S/N ratio is performed to recognize the most influential parameters and their effects on the response characteristics. The optimal combination of process parameters is recorded as filler at first level, polyol at first level, surfactant at second level, catalyst at second level, blowing agent at third level, and anti-flaming agent at second level. The confirmation experiments for different response characteristics are performed at these optimum levels of the process parameters. It is concluded from the confirmation experiments that the average tensile strength is 5.24 MPa, the average compressive strength is 6.37 MPa, the average flexural strength is 12.28 MPa, and the average hardness (Shore D) is 72.43, which fall within the 95% confidence interval of the predicted optimum parameters.

Footnotes

Acknowledgments

We are thankful to Delhi Technological University for providing us necessary facilities to conduct these studies.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Raminder Kaur

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