The authors have declared that no competing interests exist.

In this work, Taguchi design (orthogonal array, OA_{9}) was used for the adhesion investigation of an epoxy insulator to a double base (DB) propellant grain. In this manner three epoxy resins based on diglycidylether bisphenol A (DGEBA) and three polyamine curing agents with an active diluent based on DGEBA were used. Therefore, the effects of resin type, curing agent type with its amount and diluent quantity as main factors were investigated on the single lap shear strength (adhesion strength) and then the results were quantitatively evaluated by the analysis of variance (ANOVA). The data given of ANOVA predicted that the best adhesion strength of 15.584 ± 1.606 MPa was obtained for the optimum conditions of MANA POX-102 as epoxy resin, H-37 as curing agent with 57 phr, ERYSYS GE-30 as diluent with 5 phr. In comparison, practical result of adhesion strength obtained for the optimum conditions was 15.4 ± 0.2 MPa. Also the Pull-off test results on the surface of the DB propellant showed that the maximum adhesion strength (related to the optimal conditions) is 2.64 ± 0.2 MPa.

Insulation and insulators for rocket motors containing double base (DB) propellants were developed in recent decades

The matrix of DB propellant insulators usually consists of organic materials such as epoxy resins, plastics and phenolic compounds. Epoxy resins provide excellent strength and adhesion to a wide range of materials such as solid propellants. This advantage makes them indispensable in adhesive applications where high strength is prerequisite

Epoxy resins belong to a family of molecules or oligomers having epoxide groups (oxiranes). The greatest commercial epoxy resin is formed by the reaction of bisphenol A and epichlorohydrin. Therefore, this resin is well known as the diglycidyl ether bisphenol A or DGEBA

A group of chemical compounds with active hydrogen that reacts with these epoxides is aliphatic polyamines which are known as the curing agent (or hardener). Hardeners modify the properties of epoxy polymers and provide appropriate flexibility, tensile strength, toughness for them. Traditional aliphatic polyamines such as diethylenetriamine (DETA), triethylenetetramine (TETA) and also aliphatic amines have been extensively used as hardeners for the curing of epoxy resins in ambient temperatures

DGEBA epoxy resins have high viscosities lead to numerous difficulties on their processes and the applications. Therefore, it is necessary to use a diluent. There are many various diluents, depending on their reactive or non-reactive nature. When these epoxy resins mix with a reactive diluent, due to the diluent epoxy groups, some important properties of the original system (such as tensile strength, glass transition temperature, and lifetime) are changed. The extent to which properties are altered is a function of both diluent type and its concentration

One of the most widespread approaches for optimizing the design factors is the (Genichi) Taguchi method

Taguchi method classifies the factors as controllable factors and noise factors. Noise factors are variables that influence on the response of a process but can not be controlled economically. They are not maintained at particular levels during the process period for the expected performance in optimum conditions with the least variations

In this research, after preparation of an epoxy insulator at ambient temperature the adhesion of it on a DB propellant surface was investigated by the Taguchi method. It is used for design of the main effects (average effects of factors and interactions) of four control factors of the forecasting model. These four factors were epoxy resin type, curing agent type, curing agent amount and diluent quantity. To match the objectives of this study, a design affected minimally by noise is considered.

Epoxy resins based on bisphenol A: Epon 828 (Epoxy Equivalent Weight, EEW: 185-192 g.eq-1, viscosity: 11000-15000 cP), MANA POX 95 (EEW: 190 g.eq-1, viscosity: 10000-14000 cP) and MANA POX 102 modified with a reactive diluent based on bisphenol A (EEW: 205 g.eq-1, viscosity: 500-900 cP). Polyamine curing agents H-30 (Active Hydrogen Equivalent Weight, AHEW: 106 g.eq-1, viscosity: 2000-4000 cP), H-35 (AHEW: 110 g.eq-1, viscosity: 2000-4000 cP) and H-37 (AHEW: 110 g.eq-1, viscosity: 1500-3000 cP) were obtained from Mana polymer Co. (Iran). Reactive diluent by name ERYSYS GE-30, based on bisphenol A with three functional groups (EEW: 135-150 g.eq-1, viscosity: 100-200 cP) was prepared from C.V.C Co. (USA).

Vacuum oven (J.P. Selecta, model: TV-4001490). Universal testing machine (UTM) or tensile- compressive apparatus (Hiva, model: HIWA-2126, under the standard ASTM-D1002) with the accuracy of measurement 0.1 MPa (25˚C) was used for measurements of single lap shear strength of epoxy insulators. Pull-off device (Defelsko, model: Posi-ATA, under the standard ASTM-D4541) was used to evaluate the adhesion strength of epoxy insulator to the surface of a double base propellant. All data handling of Taguchi method was performed by using Qualitech-4 software.

10 g of the epoxy resin weighed and after adding of a certain amount of diluent, the resulted mixture was stirred for 5 minutes. Then, the mixture was placed for 25 minutes in a vacuum oven. Afterward certain amount of the curing agent was added to the above mixture and was stirred for 5 minutes again. The prepared blend put between two pieces of sandblasted steel (10 × 2.5 cm2) for complete curing at ambient temperature (25˚C). After 7 days the cured samples (insulators) were subjected to single lap shear testing by using a constant crosshead speed of 2 mm/min and the gauge length of 45 mm. Also, tensile strength of adhesive (adhesion strength) of the optimum insulator (a blend prepared under the optimal conditions) was determined by Pull-off test after complete adhesion of it (7 days) to the surface of a double base propellant.

One of the most important tests for determination of the mechanical properties and joint behavior of the polymeric adhesives is single-lap-shear test. Single lap shear testing is a method for evaluation of adhesion by pulling bonded layers along the plane of adhesion. In this test, the apparent shear strengths of adhesives or the ability of an adhesive to tolerate shear forces in the joint surfaces under specific conditions of preparation and test characterized

Optimization is a necessary step for stabilizing a multistage process and in this manner common procedures of optimization are sequential and simultaneous methods

In simultaneous optimization methods such as mixture designs

In designing experiments, Taguchi applied OAD, which represent the least fractional factorials and are used for the most experiment designs. The number of possible designs, N, in a full factorial design is as followed:

N = L^m(1)

Where L is number of levels for each factor and m = number of factors.

Thus, if the qualities of a given product depend on four factors (A, B, C, and D) and each factor are to be tested at three levels, a full factorial experiment would require 34 or 81 runs but may not provide appreciably more useful information. This array identified by the symbol L9 (OA9 or L-9) and is used to design experiments involving up to four three-level factors

In this research, four factors (epoxy resin type, curing agent type, curing agent amount and diluent quantity) at three levels were considered and Taguchi method was applied for the study adhesion of an epoxy insulator to the DB propellant surface. The design of 9 experiments based on OA9 (34) and also practical results of single lap shear strength were summarized in

As shown in

Trial No. | Resin Type | Curing Agent type | Curing Agent Amount (phr |
Diluent Quantity (phr) | Adhesion strength |

1 | Epon 828 | H-30 | 52 | - | 8.1 ± 0.5 |

2 | Epon 828 | H-35 | 57 | 5 | 12.3 ± 0.7 |

3 | Epon 828 | H-37 | 62 | 10 | 13.3 ± 0.2 |

4 | MANA POX 95 | H-35 | 62 | - | 7.5 ± 1.0 |

5 | MANA POX 95 | H-37 | 52 | 5 | 12.1 ± 0.0 |

6 | MANA POX 95 | H-30 | 57 | 10 | 9.7 ± 0.4 |

7 | MANA POX 102 | H-37 | 57 | - | 12.9 ± 0.7 |

8 | MANA POX 102 | H-30 | 62 | 5 | 8.8 ± 0.2 |

9 | MANA POX 102 | H-35 | 52 | 10 | 13.4 ± 0.1 |

Per hundred resin.

Average of two replicates run (n=2).

The effect of resin types (Epon 828, MANA POX 95 and MANA POX 102) on single lap shear strength of the epoxy insulator at three different levels was investigated. The analysis of Taguchi software on the preliminary data is shown in

All three curing agents (H-30, H-35 and H-37) were based on polyamine compounds with differences in their AHEWs or viscosities.

Amount of curing agent is also another important factor for the single lap shear strength of the cured polymers. This test according to

This factor was considered at three levels of 0, 5 and 10 phr of the diluent (ERYSYS GE-30). According to

Analysis of variance (ANOVA) was applied to a survey statistical or quantitative evaluation of effects of each factor on single lap shear strength for the insulator- steel system and the results are presented in

Factor | Code | DOF | S | Variance | F- |
S¢ | P (%) |

Resin type | R | 2 | 12.826 | 6.413 | 8.344 | 11.289 | 11.604 |

curing agent type | H | 2 | 46.352 | 23.176 | 30.157 | 44.815 | 46.065 |

Curing agent amount | C | 2 | 10.044 | 5.022 | 6.534 | 8.507 | 8.744 |

Diluent quantity | D | 2 | 21.147 | 10.573 | 13.758 | 19.61 | 20.157 |

Error | 9 | 6.915 | 0.768 | - | - | 13.43 |

As a general rule, the optimum performance (here, for preparation of the epoxy insulator with highest adhesion strength) could be calculated by Eq. (2):

Yopt = T/N + (R3 - T/N) + (H3- T/N) + (C2 - T/N) + (D3 - T/N)(2)

Where Yopt (single lap shear strength at the optimum conditions) is equal to the T/N (ratio of the grand total of all results to the total number of all experiments) plus the contributions of R3 (resin type at level 3 (MANA POX 102)), H3 (curing agent type at level 3 (H-37)), C2 (curing agent amount at level 2 (57 phr)) and D3 (diluent quantity at level 3 (10 phr)). The procedure for computation the confidence interval (CI) of the optimum performance is explained following by Eq. (3).

CI= ±√((F_α (f_1,f_2 ) V_e)/n_e )(3)

Where, Fα (f1, f2) is the critical value for F at degrees of freedom (DOF) f1 and f2 at the significance confidence level (In this work α= 90%). f1 is DOF of the mean (which always equals to 1), f2= DOF of the error term, Ve is the variance of error term (from ANOVA), ne is defined as effective number of replications, and expressed by ne = number of trials/(f1 + DOF of all factors applied in the estimation of optimum results)

Due to validation of the optimal conditions obtained by Taguchi method, a single lap shear testing was applied for an insulator mixture of the resulted ingredients. According to

Finally, in order to examine the applicability of the proposed method, adhesion strength of the blends of trials no. 3, 7 and 9 (due to their highest strength of adhesive) along with a blend prepared under the optimal conditions were determined. This work was performed by using pull-off test with a 500 µm thickness of the cured blends on the surface of the DB propellant (with three replicate runs) and the results are given in

Blend- Trial number | Adhesion strength |

3 | 1.82 ± 0.4 |

7 | 1.91 ± 0.3 |

9 | 2.07 ± 0.3 |

Optimum conditions | 2.64 ± 0.2 |

Average of three replicates run (n=3).

The data given in

In this study, an epoxy insulator with the best adhesion strength was prepared for a DB propellant grain at ambient temperature. Taguchi robust design method using Qualitech-4 software was applied to optimize experimental conditions of the preparation process. In this manner the resin type, curing agent type with its amount and diluent quantity were chosen as the main parameters. Under the optimum conditions, the participation of each parameter on the yield of the process are: curing agent type (H-37, 46.065%), diluent quantity (ERYSYS GE-30, 20.157%), resin type (MANA POX 102, 11.604 %) and curing agent amount (8.744 %). All of the mentioned parameters were important and any of them were not pooled. According to Taguchi method and mechanical test results, the optimal composition of epoxy insulator was obtained as MANA POX 102, 57 phr H-37 and 5 phr ERYSYS GE-30. The results obtained from predicted data were analyzed by the Taguchi design (adhesion strength = 15.584 ± 1.606 MPa) and those of practical samples (average adhesion strength = 15.4 ± 0.2 MPa) were in satisfactory agreement. Finally, the results of pull-off tests revealed that Taguchi method could be successfully applied to predict the optimal insulator with the highest adhesion to the DB propellant.