O+P Fluidtechnik 11-12/2024

DICHTUNGEN FORSCHUNG UND

DICHTUNGEN FORSCHUNG UND ENTWICKLUNG PEER REVIEWED F2 Results of immersion tests for SRE-NBR 28/SX 2-Chlorophenol 1,3-Dioxolan Cyclopentanon Acetophenone Brombenzene Cyclohexanon Butanol E-Caprolactone Diisopropylketone Benzylalkohol 2-Methyltetrahydrofuran Butyllevulinate Benzol Ethylacetat Diethylketon (DEK) Ethylbenzene Toluol Methylisobutylketon Isopropylmethylketon 2-Methylfuran Dimethoxymethan Aceton Methylketone EN 228 EBCC Butanal KEAA Pentanal 2-Methoxyethanol Propylencarbonat Cyclohexanol Diethoxymethan Cyclohexan Di-n-butyl ether 2-Methylpropan-2-ol Hexanal 1-Octanol Diesel 2-Propanol 1-Decanol Ethanol n-Heptan HyFit40 HyFit15 Dodecane Hexadecane Cyclopentan Methanol Change of hardness Change of volume -100% -50% 0% 50% 100% 150% 200% 250% T3 Composition of SRE-NBR 28/SX according to ISO 13226] Formulation of the rubber mixture NBRwith 28 %by mass of acrylonitrile (PerbunanNT 2845) AntidegradantTMQ(VulkanoxHS) Zinc oxide (Zinkoxydaktiv) Stearic acid Carbon black N 550 (CoraxN 550) Accelerator TBzTD Accelerator CBS(Vulkacit CZ) Sulphur Splitting the dataset into a training and a test subset ensures that the subsequent training of the model is not performed on the entire dataset. The withheld test dataset is later used to evaluate the performance of the model. This also allows to assess the model’s ability to generalize, which is defined as the ability to perform well on previously unseen data. Subsequently only the training subset is considered for the fitting of the model. Based on the training input and output values, underlying patterns in the relationship between input and output are learned by the model. During this process different parameters of the models, such as weights and biases, are adjusted iteratively. If the model describes the training data well enough or if a maximum number of iterations is reached, the training process is finished, and the model can be applied to the unseen testing subset to evaluate its performance. Based only on the testing input data, the trained model applies the learned patterns and predicts new output data. To evaluate the accuracy of this predictions, the actual testing output data are compared to the predicted values. A score is calculated using metrics, which allows the model’s performance to be compared. Two commonly used metrics are introduced in Equation (2) and (3). For calculating the mean squared error (MSE), first the difference between an actual output value Y and the predicted output value Y pred is computed. The difference is then squared and averaged over all n samples. A better performance is represented by a lower MSE. The coefficient of determination R² provides a measure of how well the regression model fits the actual data. It quantifies the proportion of the variance in the predicted values to a scale from 0 to 1, with larger values representing a better model fit. The main benefit of observing training and testing performance is the detection of overfitting and underfitting. The former is a common weakness of SL models, where parameters are customized too specifically to a particular problem rather than learning the underlying patterns. The latter occurs when a model is insufficiently trained, often due to a lack of quality or quantity of data. 3 STRUCTURE AND APPROACH In the following section, the underlying experimental investigation as well as the preselection process of suitable parameters and machine learning methods are presented. 3.1 IMMERSION TESTS The application of machine learning methods for predicting material compatibility in this study is founded upon experimental immersion tests conducted in accordance with ISO 1817 [15]. Standard reference elastomers (SRE) according to DIN ISO 13226 (SRE-NBR 28/SX and SRE-FKM/2X) were used as sealing materials and immersed into the fuels [16]. The size of the specimen is 25´25´2 mm 3 . It was ensured that the specimen was always covered with sufficient fuel in the vessels during investigation. The specimens are removed from the vessels filled with the investigated fuel after defined intervals to evaluate the change of seal properties. The time intervals for evaluation were chosen in accordance with standard DIN 53521 [17]. For this study, only the measurements of the specimen volume and hardness at the final time interval after 672 h in relation to Parts by mass its initial state are considered. In the work of Hofmeister et al. the measurement 100.0 techniques and devices are presented in 2.0 detail. It was especially paid attention to the fact, that most investigated liquids 5.0 have a high vapor pressure at standard conditions and therefore significant evaporation rates are present. [1] 1.0 65.0 In the following, the focus solely is on SRE-NBR 28/SX, since in comparison to 2.5 FKM a higher number of fluids are investigated. The composition of SRE-NBR 28/SX 1.5 is shown in Table 3. Figure 2 lists the 0.2 change of volume and hardness of SRE- NBR for all investigated fuels and fluids. 30 O+P Fluidtechnik 2024/11-12 www.oup-fluidtechnik.de

DICHTUNGEN 3.2 CHOOSING RELEVANT PARAMETERS F3 3-fold cross validation and hyperparameter tuning. Redrawn from [26] The tendency of a fluid to cause polymer swelling depends largely on two factors: the polarity of the fluid and the elastomer as well as the size of the fluid molecules. According to the chemical principle “like dissolves like”, polar fluid molecules prefer to penetrate polar elastomers while nonpolar fluid molecules lead to an increased swelling of nonpolar elastomers. In terms of the steric requirement of the fluid molecules, larger molecules are more hindered to penetrate the elastomer crosslinked network. Besides fluid properties, properties of the elastomer such as the degree of crosslinking, the bulk modulus or the type and amount of additives play an important role when investigation property changes of the elastomer. Since standard reference elastomers are considered (a) Fold 1 Fold 2 Fold 3 (b) F4 Scaled Dataset Training set Training set i For each Fold Testing set Score 1 Score 2 Score 3 Hyperparam eter tuning Correlation matrix of input parameters (c) Testing set i Average Score Best Model i Best Model i Prediction Actual values Score i ACCESSABILITY OF PARAMETERS IS AN IMPORTANT FACTOR in this work, the influence of these parameters is not considered. Elastomer properties might be included as parameters in further investigations regarding technical seals. The quantification of the polarity of molecules is the subject of numerous research projects. Kier suggests the use of a structure-based numerical index to quantify polarity [18]. Palomar et al. introduce a quantum chemical parameter for this application [19]. Furthermore, the polarity of molecules is considered in the Hansen solubility parameters to predict compatibility between different compounds [20]. Having said that, those theoretical descriptors are not commonly available and can be complex to determine especially for compound mixtures. Additionally, the weaknesses of such parameters have already been demonstrated in various studies. For example, the work of Heitzig et al. concludes that the Hansen parameters are not suitable to predict polymer swelling. One reason for this is the copolymer structure of widely used sealing materials like NBR, whose solubility would presumably have to be quantified using more than one Hansen sphere. Additionally chemical reactions, that might occur during immersion, are not considered in the theory of Hansen. [12] For this reason, the approach presented here uses familiar physical and chemical parameters that can be found in common databases and handbooks for a wide variety of compounds. The aim was to find parameters that are both easily accessible as well as a good representation of the polarity and/or the steric requirement of the fluid-molecule. Eventually, a set of nine parameters was defined, which are presented in Table 1. The values of these parameters were taken from several open access databases and the own database of the FSC. For reasons of complexity, the focus is initially placed on the properties of the fluids while the polarity and properties of the elastomer is not taken into consideration. The molar volume of a compound, being the ratio of the molar mass and the density, is an indicator of the steric requirement of the fluid molecule. The reason for that becomes apparent when comparing molar volumes of different C6 organic compounds. Comparing the molar volumes of cyclohexane to hexane demonstrates the lower steric requirement of cyclic compounds compared to linear and branched molecules. Likewise, the comparison of cyclohexane to benzene shows the lower steric requirements of aromatic compounds due to their inherent planarity. This is important since compounds with a lower steric requirement show lower activation energies for diffusion and thus show a higher tendency to penetrate the elastomer network [21]. The boiling point, the molar enthalpy of vaporization, and the vapor pressure represent the magnitude of the occurring intermolecular interactions [22]. This is closely related to the polarity of the molecule due to the ability of polar substances to form stronger intermolecular interactions such as hydrogen bonds and π-π interactions in comparison to nonpolar substances. Oxygen content can be easily determined using molecular formula and can be an indicator for bond polarization due to the strong electronegativity of oxygen. Whether the compound is cyclic derives from the molecular structure and indicates a lower steric hindrance compared to the acyclic analogue. The decadic logarithm of the partition coefficient in octanol/water logP OW is a measure of the hydrophobicity of a substance. Since hydrophilicity correlates to a certain extent with the polarity of a substance, this parameter also provides an indication of polarity. www.oup-fluidtechnik.de O+P Fluidtechnik 2024/11-12 31