Introduction

The method used to determine the effect by systematically changing the values of the controllable variables (factors) that affect the related output (response) of a process is called DOE. DOE is used for purposes such as evaluating material alternatives, determining design parameters that affect performance and comparing designs, formulating new products, increasing process efficiency, quality and reliability [1].

RSM is one of the DOE techniques used in process optimization. Myers et al. [1] defined the RSM as a method in which statistical and mathematical techniques necessary for the development and optimization of processes are used together. It is known that there are generally multiple and conflicting responses in real problems. By choosing the appropriate experimental strategies such as Box-Behnken [2] or Central Composite Design-CCD [3], the levels of the factors are systematically changed in accordance with the goal to be achieved, and the response are optimized simultaneously with the help of mathematical and statistical analysis.

DOE and RSM have several advantages over classical trial and error methods:

  • Fewer trials DOE and RSM minimize the number of experiments, allowing statistically fewer trials to be conducted. This leads to more efficient use of resources and time [1].

  • Focus on relevant variables and statistical reliability DOE and RSM help determine which variables affect process outcomes. They enable focusing on the correct variables for process improvement. RSM utilizes statistical methods such as ANOVA and linear/nonlinear regression models to analyze the second and third-order interaction effects of factors affecting the response variable, as well as the second and higher-order effects of a factor [4, 5]. This allows determining the optimal levels of factors affecting the response variable. When factors are kept at optimal levels, the range of values the response variable can take for a certain confidence level is estimated. The reliability of the results is tested with validation experiments. This methodological approach helps prevent erroneous results and facilitates making more reliable decisions [6]

  • Ease of optimization Models obtained with RSM, whether linear or nonlinear, can be optimized independently of each other or simultaneously using optimization methods such as response surface methodology, loss functions, or multi-objective optimization techniques. This systematic approach facilitates determining and optimizing relationships between variables to achieve the desired output [4, 7].

When the literature reviewed on rubber blends and composite materials, researchers aim to improve the vulcanization characteristics and mechanical or swelling properties of rubber blends. They have examined the performance of rubber blends with respect to adding different fillers, chemical fillers, and various types and ratios of rubbers. Some representative studies using the traditional (trial and error) methods [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] are summarized in Table 1.

Table 1 Literature review
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In recent years, it becomes evident that systematic and statistical approaches such as DOE, RSM, and Taguchi methods have been widely used in various sectors for improving the production processes of rubber and composite materials and creating ideal rubber blend [26,27,28,29,30,31,32]. The types of blends and fillers, design type (such as Box-Behnken, CCD, full factorial), and response variables used in this studies are summarized in Table 1 under the heading “Statistical methods”.

In this study, the authors utilized RSM with CCD to achieve an optimal CR/NR rubber blend for SAMPA, a company producing spare parts for the automotive sector. To the best of our knowledge, this study is the first to simultaneously address the five objectives (response variables such as hardness, TS, CRI, torque difference and Tan δ) in optimizing the CR/NR blend. In this research, the optimal levels of NR percentage, accelerators like TMTM 80 and DPG 80, retarder CTPI 80, and curative S80 were determined. The effects of accelerators, retarder, curative, and NR masterbatch ratio in the final batch on curing characteristics and mechanical properties were investigated by ANOVA. Linear and nonlinear regression models for response variables were obtained using Design Expert 11. Based on the regression models, all response variables were simultaneously optimized using desirability functions.

In this research, two distinct (CR and NR) masterbatches are prepared. Due to the differences in polarity between NR and CR polymers, their compatibility is not ideal. The CR polymer demonstrates certain advantages over the NR polymer in properties such as higher service temperature and resistance to chemicals, ozone, and UV radiation. However, CR is also costly than NR. Consequently, these polymers are blended in various proportions to balance performance and cost. The CR masterbatch contains CR, MgO as an activator, N 550 as carbon black, and various other chemicals as antidegradants. On the other hand, the NR masterbatch comprises NR, ZnO, and Stearic acid as activators, N 375 as carbon black, and other chemicals serving as antidegradants. Different types of carbon blacks, N 550 and N 375, are used in the two polymers to achieve comparable shore hardness values, as their distinct surface area and structure influence their properties. After the preparation of the CR and NR masterbatches, accelerators, retarders, and sulfur as a crosslinker are added to each masterbatch. Vulcanization chemicals are added to create the final batch. In the second part of the study, detailed info is given about the methodology; preparation of the CR/NR batches; the fillers used as accelerator, retarder, or crosslinker; laboratory environment where the experiments were carried out, the test equipment used, and the experimental procedure.

In the “Findings and discussion” section, the analysis results were interpreted, optimum levels for the factors were determined, and the results obtained through simultaneous optimization were shared. Validation experiments were also included in this section. When fillers such as TMTM80, DP80, S80, and CTPI80 are at their optimum levels, and the percentage of NR in the CR/NR blend is around 27%, Tan δ, hardness, and TS reach their optimal values. These values are estimated to be 0.144, 55.183 Shore A, and 21.085 MPa, respectively. The results obtained from the validation experiments are consistent with the estimated ones and fall within the 95% prediction interval. Similarly, the torque difference and CRI values measured from the validation experiments fall within the range associated with processing ease and operational efficiency in the rubber industry.

In the last section of the study, conclusion and recommendations for further research were provided.

Materials and methods

This section provides an overview of the methodology employed, including the sequential steps followed throughout the study. It discusses the materials utilized in the research, outlines the experimental conditions under which tests and experiments were conducted, and describes the instruments utilized for data collection and analysis. Additionally, it highlights the factors and response variables that were considered within the study’s framework.

Methodology

The methodological approach of RSM depicted in Fig. 1 and consisting of subsequent stages was employed in this study: (1) selecting the critical factors and their levels in the system through preliminary trials and literature research, (2) determining the experimental strategy of RSM and performing the experiments in accordance with the chosen experimental plan, (3) fitting the collected experimental data to a polynomial function and providing mathematical and statistical analyzes, (4) evaluating the fitness of the model, (5) verifying the possibility and necessity of performing a displacement toward the best region direction, and (6) obtaining the best values for each variable [6].

Fig. 1
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The methodological approach of RSM

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CCD was selected as one of the most frequently experimental strategy in RSM. This design model (with k factor number) consists of 2k factorial trials coded as − 1 and + 1, n number of center points, and 2*k axial points at α distance from the center point. The total number of experiments to be performed is calculated as N = 2k + 2*k + n. The main effects of the factors and the first-order interactions of these factors are determined with data from 2k experiments. The curvature of the model is tested with the help of center points. The quadratic terms of the model are found with the help of 2*k axial points in the second-order model given in Eq. 1 [4, 5].

$$ y = \beta_{o} + \beta_{1} \,x_{1} + \beta_{2} \,x_{2} + \beta_{11} \,x_{1}^{2} + \beta_{22} \,x_{2}^{2} + \beta_{12} \,x_{1} \,x_{2} + \varepsilon $$
(1)

Responses in RSM can be optimized with the help of desirability functions. In cases where there is no single response variable, all responses are tried to be optimized at the same time with a holistic approach [32]. Individual desirability values (di) are between 0 and calculated via different methods in line with the purpose (maximization, minimization, target is best). When the value of the response is optimized, the value of di increases [7]. di values can be combined using the geometric mean and this value is represented by D as seen in Eq. 2:

$$ D = \left[ {\mathop \prod \limits_{i = 1}^{r} d_{i} } \right]^{1/r} $$
(2)

Materials

CR, also known as Neoprene in the industry, was the first commercially developed synthetic rubber in America in 1930. CR can be made more resistant to tear and abrasion with the addition of carbon black and other fillers. It has high resistance to air and ozone. Although it is weaker than NR in some properties, its resistance to oil is superior [33]. NR consists of the latex of the rubber tree (Hevea brasiliensis). It is used alone or widely as an additive in the production of many types of blends. It tends to crystallize at low temperatures; therefore, it shows very good TS, tear resistance, and low permanent deformation (compression set) properties [34, 35].

In this study, two different masterbatches are prepared. The first one is CR masterbatch, and the second one is NR masterbatch. These two masterbatches are prepared by using an intermeshing type internal mixer, separately. CR masterbatch includes CR, MgO as activator and N 550 as carbon black and other chemicals as antidegradants. NR masterbatch includes NR, ZnO and Stearic acid as activators and N 375 as carbon black and other chemicals as antidegradants. After the CR and NR masterbatches are prepared, accelerators, retarder, and sulfur as crosslinker are added to the masterbatches separately and mixed in double roller mills. The final batch is prepared by adding vulcanization chemicals at the end. Tables 2, 3 include the ingredients of CR and NR masterbatches.

Table 2 CR masterbatch
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Table 3 NR masterbatch
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Due to the differences in polarities between the two polymers, NR and CR, their compatibility is not optimal. CR polymer exhibits superiority over NR polymer in certain properties, such as higher service temperature and resistance to chemicals, ozone, and UV radiation. However, CR is also more expensive than NR. Therefore, in applications like windshield wiper blades, these two polymers are blended in various ratios to overcome cost issues. Additionally, different types of carbon blacks are used in different polymers to reach similar shore hardness values, owing to the distinct surface area and structure of N 550 and N 375 carbon blacks.

Determination of factors

The effects of the amounts of five different chemical fillers on the mechanical properties and curing characteristics were investigated. These factors were chosen by considering the literature given in Table 1 as well as the experience of the personnel working in the production processes of SAMPA Automotive where the experiments were carried out.

Accelerators reduce the time spent during curing while improving mechanical and physical properties as well as aging properties. The aforementioned effects will be greater with the employment of multiple accelerators. Hence, the amount of Tetramethyl thiuram monosulfide (TMTM 80) and N, N’-diphenyl guanidine (DPG 80) were determined as critical factors.

Retarders are added to the blend to prevent premature curing during processing and storage. The amount of N-(cyclohexylthio)-phthalimide (CTPI 80) was determined as the third critical factor. Curatives form cross-links in rubber during the curing process so sulfur (S 80) was determined as the fourth factor.

The origins and trade names of these materials are listed in Table 4.

Table 4 The origins and trade names of materials
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To obtain better mechanical properties, CR masterbatch is mixed with relatively inexpensive NR masterbatch. Therefore, NR ratio in the finalbatch was determined as the fifth critical factor to balance cost and product performance.

The levels of the factors were determined by taking into account the experience on the process and sectoral needs. Center, axial and factorial points of each factor and the corresponding coded values are shown in Table 5.

Table 5 Factors and coded levels
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Response variables

Vulcanization is the process of curing the rubber with sulfur or similar chemicals under a certain temperature and pressure, resulting in a more durable structure. High plastic properties before vulcanization are replaced by high elastic properties after vulcanization. After vulcanization, the material hardens and gains strength. The vulcanization should not start while the rubber is moving through the injection machine. Otherwise, rubber cannot be injected, and this affects product quality and process efficiency [35].

The start of curing is expressed as ts2 (scorch time). ts2 is an important parameter of the process and it is aimed to be in a certain value range. If ts2 gets small values, it indicates early curing. In this case, there may be problems such as deterioration of shape stability and surface roughness. Its high value causes insufficient curing and negatively affects the physical properties of the rubber. Having a high value of ts2 can be ignored when t90 is short. Its unit is minutes: seconds. t90 indicates the time needed for the 90% of curing is completed. It is the optimum curing time. Shorter or longer curing time than t90 affects the physical properties negatively. The remaining 10% is spread over the curing time so that the product preserves its physical properties. Since the evaluation of ts2 and t90 is made through the CRI, it is selected as the first response and calculated as CRI = 100/(t90 − ts2).

In the automotive sector, many spare parts require high TS, so the second response variable has been determined accordingly. Hardness indicates the material’s resistance to abrasion and is selected as the third response since hardness is of critical importance for the rubber compound used in metal-rubber products operating in dynamic environments. Some parts of vehicles dampen unwanted vibrations. Tan δ is the ratio of loss modulus to the storage modulus, is a measure of energy dissipation and is proportional to the damping ability of the material, and was determined as the fourth response.

ML is the minimum and MH is the maximum value of the torque in the rheometer curve that is generated upon curing. The unit of the torque is Nm. MH − ML, torque difference, is generally used as the response variable [36]. In this study, it is used as the fifth response.

Experiments, tests, and instruments

To examine the correlation between factors and response variables, the rubber underwent tests including TS, stiffness, and dynamic/mechanical analysis. The testing conditions and instruments utilized in the study are outlined in Table 6.

Table 6 Tests and instruments used
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Findings and discussion

50 experiments were performed in accordance with the CCD strategy. The first 32 experiments represent 25 factorial points, experiments between 33 and 42 represent axial points and the remaining are center points.

Analysis of hardness

The analysis confirms that the linear model is appropriate, and the results are presented in Table 7. Following the determination of the model type, the variables to be included in the equation were selected using the backward elimination method.

Table 7 ANOVA results of hardness
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There was no need for Box-Cox transformation. The linear model fitted in Eq. 3 is significant (p value < 0.05) where lack of fit is found to be insignificant (p > 0.05). The insignificance of lack of fit indicates that the fitted values obtained from the model are in accordance with the actual ones. Since the p values for factors A, C, and E are less than 0.05, these factors have been included in the linear model, while factors B and D have been excluded. The R2 values (determination coefficient) that express the power of the model in explaining the response are given in Table 7. Based on the R2 value, the model can explain 70% of the variation in hardness. Adjusted and predicted R2 values appear to be consistent with each other. The linear model used in the prediction of the hardness (H) is given in Eq. 3.

$$ \hat{H} = 51.72 - 0.60A + 1.95C + 0.18E $$
(3)

The graphs showing the main effects of the factors on the hardness are presented in Fig. 2a–c. The quantity of S80 and NR percentage affect the hardness of the blend positively, while the quantity of TMTM80 has a negative effect on it. When the TMTM80 quantity is kept at the lowest level and the S80 quantity along with the NR percentage are maintained at the highest level, the hardness reaches its optimum value. Figure 2d demonstrates that the residuals are normally distributed and the regression assumptions are met.

Fig. 2
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Main effect plots of hardness

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Analysis of TS

A third-order regression model seems to be appropriate for estimating TS. According to Table 8, the model is significant and the lack of fit is insignificant. BC and BD second-order interaction terms; quadratic terms of A, B, C, D, E, and third-order interaction terms (ADE, CDE, A2E) are included in the model (p < 0.05), while those with p values greater than 0.05 are excluded.

Table 8 ANOVA results of TS
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Approximately 62% of the variability in TS can be explained with the established model given in Eq. 4. The BD and A2E interactions have a positive effect on TS, while BC, A2, B2, C2, D2, E2, and ADE interactions have a negative effect on it.

$$ \begin{aligned} \widehat{{{\text{TS}}}} = & 21.937 - 0.5469*B*C + 0.309*B*D - 0.433*A^{2} \\ & - \,0.596*B^{2} - 0.721*C^{2} - 0.346*D^{2} - 0.421*E^{2} \\ & - \,0.309*A*D*E - 0.359*C*D*E + 0.484*A^{2} E \\ \end{aligned} $$
(4)

The graphs showing the main effects and interaction effects on the TS and the normal probability plot of the data are shown in Fig. 3.

Fig. 3
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Main and interaction effect plots of TS

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According to Fig. 3b, when A, D, and E factors are constant (TMTM80 = 1.2 PHR, CTPI80 = 1.2 PHR, NR percentage = 20.00), B is at its lowest level (DP80 = 1.25), and C is at its highest level (S80 = 3.5), the TS reaches its highest value.

Analysis of tan δ

The result of ANOVA in Table 9 shows that the best model to be used in estimating the Tan δ is the cubic model. The variables in the equation are selected by the backward elimination method. The variables are not subjected to any transformation. The third-order nonlinear model is significant and the lack of fit is insignificant. The p value of factors A, C, and D, as well as AB, AC, AD, BD, CD, CE second-order interactions; B2, C2, E2 quadratic effects; ACE, ADE, BDE, CDE third-order interactions; A2C, A2E, AB2 effects, is less than 0.05.

Table 9 ANOVA results of Tan δ
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A high R2 value indicates that the factors and interactions can explain the variability in Tan δ very well (approximately 96%).

$$ \begin{aligned} \widehat{{{\text{Tan}} \, \delta }} = & 0.16 + 0.0058*A - 0.0123*C + 0.0029*D + 0.0018*A*B + 0.0018*A*C \\ & + \,0.0014*A*D + 0.0015*B*D - 0.0016*B*E + 0.0014*C*D - 0.0031*C*E \\ & + \,0.0021*B^{2} + 0.003*C^{2} + 0.0044*E^{2} + 0.0026*A*C*E + 0.0015*A*D*E \\ & + \,0.0013*B*D*E + 0.0012*C*D*E + 0.0046*A^{2} C + 0.0066*A^{2} E - 0.0027*AB^{2} \\ \end{aligned} $$
(5)

When examining Fig. 4a–c, it is observed a negative correlation between Tan δ and factor C, and a positive correlation between Tan δ and factor A or factor D. It means that, an increase in the quantity of S80 and a decrease in the quantity of TMTM80 and CTPI80 decreases the Tan δ value. According to Fig. 4d, when examining the CE interaction effect, the Tan delta reaches its minimum when the quantity of S80 and the NR percentage are maximized.

Fig. 4
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Main and interaction effect plots of Tan δ

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Similar analyses were conducted for CRI and torque difference. However, the lack of fit values for these two responses were found to be significant. Therefore, the regression models obtained for these responses were not utilized for simultaneous optimization. Nevertheless, while optimizing the other responses, it was ensured that these two responses were within a reasonable range.

Simultaneous optimization of responses

After the ANOVA and regression models, the optimization phase was started for each response with the help of Design Expert 11. Equal importance to the responses was assigned following a discussion with company authorities. After defining the optimization criteria (maximization/minimization) and calculating di values for each response, the overall desirability value was achieved as a result of the geometric means of di values (please see Eq. 2 in the methodology subsection). It is in the yellow region with the value of 0.782. Although all objectives are optimized simultaneously, it is seen that this value is as close to 1 as possible (the desirability value increases progressively from the blue region to the red region, from 0 to 1).

The desirability value and the contour plots corresponding to each response are given in Fig. 5. Figure 6 shows the values of the factors and the responses at this optimum, as well as where each are relative to the range that was chosen for the factors or measured for the responses.

Fig. 5
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Contour plots for desirability and responses

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Fig. 6
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Values of factor levels and responses for the proposed solution

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Validation experiments

For validation, three of the local best solutions with the same overall desirability value (0.782) were selected as seen in Table 10.

Table 10 Factor values in validation experiments
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Experiments corresponding to the specified factor levels were conducted, and their results were assessed to determine if they fell within the prediction interval. The prediction interval represents the range within which the predicted response for a new observation is expected to lie. It is delineated by lower and upper limits, calculated based on the confidence level and the standard error of the prediction. This interval is wider than the confidence interval due to the additional uncertainty associated with predicting a single response rather than the mean response. The prediction intervals for the 95% confidence level and the validated outcomes are provided in Table 11, along with the formula for computing the prediction interval.

Table 11 The prediction intervals and the results of validation experiments
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All results fell within the prediction interval. Although the Tan delta value is very close to the upper limit of the prediction interval, it has not been considered a significant issue by production authorities. The torque difference and CRI values fall within the range associated with processing ease and operational efficiency in the rubber industry. The results of the validation experiments about torque difference and CRI responses are given in Table 12.

Table 12 Torque difference and CRI values of validation experiments
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Conclusion and recommendations

This study aims to improve the curing characteristics and mechanical properties of the CR/NR blend used in the automotive industry. To determine the quantity of fillers (TMTM, DPG80, S80, CTPI80) and NR percentage in the blend thought to affect the curing process of rubber; TS, hardness and Tan δ, were optimized simultaneously by the help of desirability functions. Afterward, validation experiments were carried out to validate the three local best solutions. NR ratios of 0, 10, 20, 30, 40, etc., were tested, and it was found that the NR percentage optimizing the response variables was approximately 27%. When the TMTM80, DPG80, and CTPI80 additive amounts were around 1.08, 1.78, and 0.96 PHR, respectively, and S80 was at its highest level, i.e., 3.5 PHR, the estimated values for Tan δ, hardness, and TS were approximately 0.144, 55.183 Shore A, and 21.085 MPa, respectively.

The response values of TS, hardness and Tan δ, obtained from three different validation experiments, were observed to fall within the prediction interval for the 95% confidence level, confirming the results of the statistical analysis. It was observed that the torque difference and CRI values also fell within the desired limits in the industry for the mentioned values of additives and NR ratio.

In future work, by using different chemical fillers from the ones used in the study their effects on the curing process can be examined and different models/solution suggestions can be put forward. In future studies, different CR/NR ratios can be examined, as well as the effect of different types of rubber blends on the vulcanization process. Also it is possible to study the effect of mixing parameters like mixing time, drop temperature or feeding order of the material on mechanical properties of the mixtures.

As an optimization method, different experimental design techniques and multi-objective optimization methods can be preferred and the results can be compared with the results of desirability functions. This study examines the situation in which all responses have equal importance. Future studies can experiment with situations where the responses have different weights. It should be aimed to ensure that the most important response gets the best value, while the other responses are within the reasonable range in which the industry will determine.

This study both offers a more scientific approach to the industry and provides savings and profit in terms of experiment cost and time.