1,721,206 research outputs found
GURU v2.0: An interactive Graphical User interface to fit rheometer curves in Han's model for rubber vulcanization
Full text linkA GUI software (GURU) for experimental data fitting of rheometer curves in Natural Rubber (NR) vulcanized with sulphur at different curing temperatures is presented. Experimental data are automatically loaded in GURU from an Excel spreadsheet coming from the output of the experimental machine (moving die rheometer). To fit the experimental data, the general reaction scheme proposed by Han and co-workers for NR vulcanized with sulphur is considered. From the simplified kinetic scheme adopted, a closed form solution can be found for the crosslink density, with the only limitation that the induction period is excluded from computations. Three kinetic constants must be determined in such a way to minimize the absolute error between normalized experimental data and numerical prediction. Usually, this result is achieved by means of standard least-squares data fitting. On the contrary, GURU works interactively by means of a Graphical User Interface (GUI) to minimize the error and allows an interactive calibration of the kinetic constants by means of sliders. A simple mouse click on the sliders allows the assignment of a value for each kinetic constant and a visual comparison between numerical and experimental curves. Users will thus find optimal values of the constants by means of a classic trial and error strategy. An experimental case of technical relevance is shown as benchmark
Iterative robust numerical procedure for the determination of kinetic constants in Han’s model for NR cured with sulphur
Full text linkA closed form procedure to determine kinetic constants for NR vulcanized with sulphur is presented. The kinetic scheme originally proposed by Han et al. (Polymer (Korea) 22:223–230, 1998) and further modified by Milani et al. (Polym Test 32:1052–1063, 2013) is adopted as starting point to deduce a closed form expression for rubber curing degree. Rheometer experimental data collected at different temperatures are used to tune model parameters. After the normalization of the rheometer curves and the exclusion of induction period from calculations, the model requires the estimation of three kinetic constants, two of them describing incipient curing and stable crosslinks formations, the last reproducing reversion phenomenon. Whilst such constants are almost always determined by least-squares best fitting, here a numerical iterative procedure—much more stable and efficient from a computational standpoint—is proposed. The approach requires as input parameters only the degree of vulcanization at infinite (i.e. at the end of vulcanization), the instant where the maximum torque is reached and initial rate of vulcanization. The condition that the numerical curve reaches a maximum at a given time translates mathematically into a non-linear equation in two of the kinetic constants, which are determined iteratively in the paper. The numerical initial vulcanization rate is tuned in such a way to globally minimize the absolute error between numerical and experimental curves. The main capability of the procedure proposed stands in the very straightforward determination of reaction kinetic constants, avoiding demanding least-squares fittings on rheometer experimental data. A set of experimental data available, relying into rheometer curves of the same rubber blend conducted at five different temperatures are used to estimate the fitting capabilities of the mathematical model proposed. Very good agreement with experimental data is observed
COMBINED NUMERICAL FINITE ELEMENT AND EXPERIMENTAL OPTIMIZATION APPROACH IN THE PRODUCTION PROCESS OF MEDIUM-VOLTAGE, RUBBER-INSULATED ELECTRIC CABLES VULCANIZED WITH STEAM WATER. PART 2: NUMERICAL SIMULATIONS AND INVERSE ANALYSES
Full text linkA comprehensive, combined, numerical model is presented, based on genetic algorithm (GA) optimization and heat-transfer finite-element computations. The numerical analyses were carried out to evaluate the final cross-linking degree of a medium-voltage electric cable subjected to industrial peroxide reticulation. The difference between numerically predicted and experimentally determined cross-linking degree along the thickness of the insulator is then minimized, when a variable steam-temperature profile along the pipe length is assumed to explain the unexpected undervulcanization of the cable in the internal layers. To minimize the gap between the experimentally determined degree of curing and numerical predictions, a GA optimization is used for best fit, instead of the steepest-descendent, standard least-squares, which is not applicable in this case because the objective function is not analytically known. The cable was supposedly vulcanized under four different conditions. The degree of cross-linking is experimentally obtained by determining the differential scanning calorimetry (DSC) of the nondecomposed peroxide from the external layer to the core of the cable. The proposed GA approach exploits a specifically crafted, zooming strategy, consisting of the subdivision of the population at each iteration into two subgroups, depending on the individual's grade of fitness (elitist strategy). The integrated, numerical, experimental approach allows optimization of the amount of peroxide in the compound and comparison of the performances of different peroxide mixtures. The degree of cross-linking compliance can be obtained as a function of the temperature gradient measured in the steam pipe. Production conditions can be automatically calculated according to the cable parameters, by increasing the quality reliability and reducing the scraps
Optimal production of tires through an integrated experimental, kinetic and finite element Fe modelling approach
No full textAn integrated three-step approach for the optimization of tires mechanical properties based on experimental characterization, kinetic steady-state model and Finite Element FE heat transmission modelling is presented. The first experimental characterization is needed to calibrate a kinetic numerical model (second step), directly nested in the last step into a FE software for the simulation of 3D heat transmission problems. The kinetic model is a phenomenological approach based on 3 kinetic constants, which allows predicting the initial curing rate, maximum crosslinking and reversion. Kinetic constants are deduced fitting normalized experimental rheometer curves. FE transient curing computations are carried out on a real car tire, discretizing the geometry through a refined mesh. All element of the tire (e.g. belts, carcass, core etc.) can be separately meshed, so the exact vulcanization process in different phases can be eventually accounted for
Numerical kinetic model with regularization for NR–PB natural and poly-butadiene rubber blends: implementation and validation against experimental data
No full textA simple and versatile numerical approach of experimental data regularization plus a kinetic model to predict the vulcanization behavior in a rheometer for natural rubber (NR) and poly-butadiene (PB) blends is presented. The numerical model proposed uses generic rheometer experimental curves to estimate kinetic constants of the cure reactions, preliminarily regularizing input data through C n continuous polynomial splines of degree n, with spline knots equally spaced or placed at user’s discretion. Splines coefficients are efficiently evaluated through a standard non-linear least squares optimization procedure. In this way a set of meta-data fitting optimally experimental values is obtained, with a smooth prediction of the local curing rate. The kinetic approach adopted is classic but adaptable to a wide class of cases and characterized by only three kinetic constants, describing two reactions occurring in parallel and two in series (reversion phenomenon). The determination of the three kinetic constants characterizing the model is performed graphically in quasi analytical form. The model is benchmarked by means of an ad-hoc conducted experimental campaign carried out with different typologies of rubber blends constituted by NR and PB at 70–30% and 50–50% concentrations, with sulfur at 1 phr and two accelerants (TBSS and DPG) at 1 and 3 phr, under standard vulcanization conditions (rheometer) at 150 °C, 170 °C and 180 °C
Curing degree prediction for S-TBBS-DPG natural rubber by means of a simple numerical model accounting for reversion and linear interaction
No full textThe paper presents a simple numerical model able to provide directly kinetic constants and reliable numerical rheometer curves for S-TBBS-DPG natural rubber. The approach is suitable to calculate the kinetic constants and maximum torque (MH) at any S-TBBS-DPG concentration, following a 3D mathematical interpolation/extrapolation procedure, when kinetic constants on few grid points of S-TBBS-DPG concentrations are available. In particular, the possibility to estimate with sufficient accuracy the behavior of natural rubber at any intermediate concentration of S-TBBS-DPG having engineering relevance has been proved, calibrating the model by means of simple closed form standard best fitting on few experimental data. The model used is a three kinetic parameters one, derived from the well known Han's and co-workers approach, where constants have been evaluated normalizing experimental rheometers curves following the commonly accepted Sun and Isayev method. The procedure has been validated against experimentally obtained rheometer curves by means of inverse analysis, exhibiting excellent prediction capabilities. The approach may be used for practical purposes in order to avoid expensive and cumbersome experimental investigations
Diversity of some gene frequencies in European and Asian populations. Effects of longitude
No full textIn a study of the space distribution of eight red blood cells markers in European and Asian populations, evidence for a longitudinal cline of GLO, ESD, PGP, AK, and 6-PGD allele frequencies was found. The respective Fst values appeared significantly greater than those computed at loci whose allele frequencies are not associated with longitude, namely ADA, GPT, and SOD. A systematic pressure appears to have acted upon the former systems, even though the effects of selection can partially overlap with the effects of migratory movements, which have already been demonstrated in the studied area. Conversely, random genetic drift, or random fluctuation of selection coefficients, cannot account for the observed gene frequency diversity. © 1986 Academic Press Inc. (London) Limited
Closed form numerical approach for a kinetic interpretation of high-cis polybutadiene rubber vulcanization with sulphur
No full textA novel mathematical approach to predict the vulcanization degree of high-cis polybutadiene rubber vulcanized with sulphur is presented. The model has kinetic base, it is constituted by four reactions occurring in series and parallel and takes contemporarily into consideration, within a simplified but reliable scheme, the actual reactions occurring during polybutadiene sulphur curing, namely primary crosslinking and possible de-vulcanization. The first order differential equation system obtained is suitably rearranged and a closed form expression for the vulcanization degree is derived, depending the four kinetic constants characterizing the chemistry describing reactions. Instead of using classic least-squares optimization routines to characterize kinetic constants on experimental data, a simplified but reliable approach is proposed, where a system of four non-linear equations is solved with a recursive strategy, allowing estimating kinetic constants that proved to fit well normalized experimental data. The procedure is fast and its reliability is tested on a number of experimental data available, relying into a high-cis polybutadiene rubber cured under different temperatures and accelerators concentrations. Very good approximations of experimental data are obtained, also in comparison with a heuristic numerical approach where optimization is obtained interactively
Optimal vulcanization of tires: Experimentation on idealized NR-PB natural and poly-butadiene rubber blends, phenomenological smoothed numerical kinetic model and FE implementation
No full textAn integrated simulation tool for the optimal vulcanization of tires is presented. Three are the main issues discussed on the optimal vulcanization of 3D items with complex geometry, namely: (i) the results of a preliminary realistic experimental campaign on rubber blends constituted by NR and PB in two different proportions and cured with different accelerators; (ii) a phenomenological numerical smoothing and kinetic model of interpretation of the rheometer curves experimentally obtained; (iii) the implementation of the numerical model into a commercial FE software to simulate the optimal vulcanization of car tires industrially produced. The experimental campaign is carried out on different typologies of rubber blends constituted by NR and PB at 70-30% and 50-50% concentrations, with sulfur at 1 phr and two accelerants (TBSS and DPG) at 1 and 3 phr, under standard vulcanization conditions (rheometer) at 150°, 170° and 180 °C. The numerical kinetic model uses such rheometer experimental curves to estimate kinetic constants of the cure reactions, preliminarily smoothing input data through four C1 cubic splines, with spline knots interactively selected by the user with a mouse click. Position of knots and vulcanization rates in correspondence of knots are then adjusted automatically by means of a non-linear least squares optimization procedure. In this way a set of meta-data (fitting optimally experimental values) is obtained, with a smooth prediction of the local curing rate. The kinetic approach used is characterized by three kinetic constants, describing two reactions occurring in parallel and in series and suitably accounting for possible reversion. The determination of the three kinetic constants characterizing the model is performed graphically in a quasi-analytical form. The numerical model is then nested into a Finite Element FE commercial code, to predict the crosslinking degree in real curing conditions, i.e. where the temperature is not constant. A real tire is finally analyzed during the curing process and useful indications are provided on the optimal curing temperature and time to adopt
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