System analysis of vulcanization kinetics. The main regularities of the process of vulcanization of rubbers of various nature

Sergei G. Tikhomirov, Olga V. Karmanova, Yurii V. Pyatakov, Alexander A. Maslov Enter the title of the article here Sergei G. Tikhomirov, Olga V. Karmanova, Yurii V. Pyatakov, Aleksandr A. Maslov in English Bulletin of VSUET/Proceedings of VSUET, 3, 06 Review article/eview article UDC 6.53 DOI: http://doi.org/0.094/30-0-06-3-93-99 Software package for solving problems of mathematical modeling process of isothermal vulcanization Sergey G. Tikhomirov, Olga V. Karmanova, Yuri V. Pyatakov, Alexander A. Maslov [email protected] [email protected] [email protected] [email protected] Department of Information and Control Systems, Voronezh. state un-t. eng. techn., Revolutsii Ave., 9, Voronezh, Russia Department of Chemistry and Chemical Technology of Organic Compounds and Polymer Processing, Voronezh. state un-t. eng. tech., Leninsky Ave., 4, Voronezh, Russia Abstract. Based on the general regularities of sulfur vulcanization of diene rubbers, the principles of efficient process implementation using multicomponent structuring systems are considered. It is noted that the description of the mechanism of action of complex cross-linking systems is complicated by the variety of interactions of the components and the influence of each of them on the vulcanization kinetics, which leads to various recipe and technological complications of the real technology and affects the quality and technical and economic indicators of the production of rubber products. The system analysis of the process of isothermal vulcanization was carried out on the basis of well-known theoretical approaches and included the integration of various research methods and techniques into a single interconnected set of methods. In the course of the analysis of the kinetics of vulcanization, it was found that the parameters of the formation of a spatial network of vulcanizates depend on many factors, the evaluation of which requires special mathematical and algorithmic support. As a result of the stratification of the studied object, the main subsystems were identified. A software package has been developed for solving direct and inverse kinetic problems of the process of isothermal vulcanization. Information support "Isothermal vulcanization" was developed in the form of application programs for mathematical modeling of the process of isothermal vulcanization and is aimed at solving direct and inverse kinetic problems. When solving the problem of refining the general scheme of chemical transformations, a universal mechanism was used, including side chemical reactions. The software product includes numerical algorithms for solving a system of differential equations. To solve the inverse kinetic problem, algorithms for minimizing the functional are used, in the presence of restrictions on the desired parameters. To describe the operation of this product, a logical block diagram of the program is provided. An example of solving the inverse kinetic problem with the help of a program is given. The developed information support is implemented in the C++ programming language. To determine the initial concentration of the actual vulcanization agent, a universal dependence was used, which allows using a model with different properties of multicomponent structuring systems Keywords: isothermal vulcanization, mathematical modeling, vulcanization kinetics scheme, information support The software package for solving problems of mathematical modeling of isothermal curing process . Tikhomirov, Olga V. Karmanova, Yuri V. Pyatakov, Alexander A. Maslov [email protected] [email protected] [email protected] [email protected] information and control systems department, Voronezh state university of engineering technologies, evolution Av., 9 Voronezh, ussia chemistry and chemical technology of organic compounds and polymers processing department, Voronezh state university of engineering technologies, Leninsky Av., 4 Voronezh, ussia Summary. On the basis of the general laws of sulfur vulcanization diene rubbers the principles of the effective cross-linking using a multi-component agents was discussed. It is noted that the description of the mechanism of action of the complex cross-linking systems are complicated by the diversity of interactions of components and the influence of each of them on the curing kinetics, leading to a variety of technological complications of real technology and affects on the quality and technical and economic indicators of the production of rubber goods. ased on the known theoretical approaches the system analysis of isothermal curing process was performed. It included the integration of different techniques and methods into a single set of. During the analysis of the kinetics of vulcanization it was found that the formation of the spatial grid parameters vulcanizates depend on many factors, to assess which requires special mathematical and algorithmic support. As a result of the stratification of the object were identified the following major subsystems. A software package for solving direct and inverse kinetic problems isothermal curing process was developed. Information support Isothermal vulcanization is a set of applications of mathematical modeling of isothermal curing. It is intended for direct and inverse kinetic problems. When solving the problem of clarifying the general scheme of chemical transformations used universal mechanism including secondary chemical reactions. Functional minimization algorithm with constraints on the unknown parameters was used for solving the inverse kinetic problem. Shows a flowchart of the program. An example of solving the inverse kinetic problem with the program was introduced. Dataware was implemented in the programming language C++. Universal dependence to determine the initial concentration of the curing agent was applied. It allowing the use of a model with different properties of multicomponent curing systems. informed decisions. Keywords: isothermal curing, mathematical modeling, the scheme of the curing kinetics, informational software For citation Tikhomirov S.G., Karmanova O. V., Pyatakov Yu.V., Maslov A.A. Software complex for solving problems of mathematical modeling of the process of isothermal vulcanization. Vestnik VGUIT. 06. 3. С 93 99. doi:0.094/30-0-06-3-93-99 For citation Tihomirov S.G., Karmanova O.V., Pyatakov Yu.V., Maslov A.A The software package for solving problems of mathematical modeling of isothermal curing process. Vestnik VSUET. 06. no 3 pp. 93 99 (in uss.). doi:0.094/30-0-06-3-93-99 93

Vestnik VGUIT/Proceedings of VSUET, 3, 06 94 Introduction To date, the general regularities of sulfur vulcanization of diene rubbers have been established, based on the existence of real elastomer vulcanization agents (DAV) in compositions. However, the principles of effective implementation of the process using multicomponent structuring systems have not been studied enough. The description of the mechanism of their action is complicated by the variety of interactions of the components and the influence of each of them on the vulcanization kinetics. This leads to various prescription and technological complications of the real technology and affects the quality and technical and economic indicators of the production of rubber products. An analysis of the kinetics of vulcanization has shown that the existing approaches to its description are based on the chemical reactions of macromolecules with vulcanizing agents, and the parameters for the formation of a spatial network of vulcanizers depend on many factors, the influence of which can only be assessed using special mathematical and algorithmic software. To improve the efficiency of the study, to identify the causes leading to the production of products that do not meet regulatory requirements, to predict the course of the process, it is necessary to create special software (SW). The purpose of this work is to develop a software package for solving direct and inverse kinetic problems of the process of isothermal vulcanization. System analysis of the vulcanization process An analysis of known theoretical approaches to the description of vulcanization, as well as other processes in the chemical industry [4] and aspects of their practical implementation, taking into account the characteristics of individual stages, made it possible to identify general system properties and basic patterns of processes and determine the direction of research to obtain new information on optimization of vulcanization modes and properties of finished products . System analysis includes the integration of various research methods and techniques (mathematical, heuristic) developed within the framework of various scientific fields into a single interconnected set of methods. Multivariate analysis of the process allowed the development of the overall structure of the study (figure). The object of study is weakly structured, since it contains both qualitative elements (elastomers, fillers, process conditions) and poorly studied ones (multicomponent structuring systems, uncontrolled perturbations), which tend to dominate. The composition of the general structure includes elements that need to be theoretically substantiated (kinetic model, heat and mass transfer processes, optimization of modes, processing processes). Thus, in order to evaluate the solutions, it is necessary to determine all existing relationships and establish their influence, taking into account interactions, on the behavior of the entire system as a whole. An analysis of the general structure showed that the mechanical properties of vulcanizates are determined by the chemical reactions of macromolecules with vulcanizing agents, and to evaluate the parameters of the spatial network of vulcanizates, it is necessary to develop special mathematical and algorithmic support. As a result of the stratification of the object under study, the following main subsystems were identified:) analysis and accounting for thermal fluctuation phenomena that accelerate the course of chemical reactions;) kinetic model of vulcanization; 3) optimization of vulcanization modes, providing the required mechanical properties. Mathematical modeling of the process of isothermal vulcanization Obtaining reliable information about the processes of crosslinking elastomers by complex structuring systems is closely related to the problems of design, optimization and control of vulcanization modes in industry. It is known that one of the traditional ways of describing the formal kinetics of vulcanization is the use of piecewise defined functions for individual stages of the process: induction period, structuring, and reversion. The description of the process as a whole and the calculation of the kinetic constants are currently performed only for certain types of rubbers and vulcanizing systems. The main conclusions about the kinetics of the process are based on model systems with low molecular weight analogs of elastomers. At the same time, it is not always possible to extend the obtained quantitative data to production processes.

Vestnik VSUET/Proceedings of VSUET, 3, 06 Figure. Scheme of the study of the process of vulcanization of elastomers Figure. Scheme of study process of vulcanization of elastomers Evaluation of the physical and mechanical properties of industrial rubbers, according to the data obtained at the enterprise, is, of course, a progressive method in solving the problem of modeling the vulcanization process, but requires a strict internal unity of the physical and chemical approach at each stage of the study and development of computational algorithms and programs. This question can only be answered by carefully executing experiments according to a plan corresponding to the proposed kinetic model and by calculating several alternative versions of the model. This requires an independent method to establish the number of formal reaction mechanisms responsible for structuring the elastomer composition. Traditional methods for analyzing processes in the time domain do not make it possible to clearly separate processes with synergistic interaction, which, in turn, does not allow them to be used for the analysis of industrial rubbers. When solving the problem of refining the general scheme of chemical transformations, it is expedient to proceed from a mechanism that is maximal in a certain sense. Therefore, the kinetic scheme includes additional reactions describing the formation and destruction of labile polysulfide bonds (Vu lab), intramolecular cyclization, and other reactions leading to the modification of macromolecules, the formation of a macroradical, and its reaction with DAW suspensions. The system of differential equations (DE) by stages of the process will have the following form: dca / dt k CA k4ca C *, dc / dt k CA kc k4ca C * k 8C *, dc * / dt k C k3 k5 k7 C * k C k C C, 6 VuLab 4 A * dcvust / dt k3 C *, dcvulab / dt k5c k6cvulab, dcc / dt k7 C *, dc * / dt k8c k 8C *, dc / dt k8 C. () 95

Vestnik VGUIT/Proceedings of VSUET, 3, 06 96 Initial conditions: 0 0 CA S8 AC Akt C ; C 0 0; C 0 0; * VuSt C 0 0; C 0 0; VuLab C C 0 C 0, * C 0 0; C0 4.95; where ς, θ, η, coefficients, initial concentration of sulfur, initial concentration of accelerator, θ initial concentration of activator (zinc oxide), [C (0)] η initial concentration of macroradicals. Here A is the actual vulcanizing agent; In the crosslinking precursor; B* its active form; C intramolecular bound sulfur; VuSt, VuLab stable and labile knots of the vulcanization mesh; rubber; * rubber macroradical as a result of thermal fluctuation decomposition; α, β, γ and δ stoichiometric coefficients, k, k, k 8, k 9 (k 8) reaction rate constants related to the respective stages of the process. The direct problem of kinetics (DKK) is the problem of finding the concentration of vulcanization nodes as a function of time. The solution of the PZK is reduced to the solution of the system DE () under given initial conditions. The kinetic curve of the vulcanization process is determined by the magnitude of the torque Mt. The inverse problem of kinetics (IKK) is the problem of identifying reaction rate constants, stoichiometric coefficients and variables in the system (). The solution of the OPC is carried out by minimizing the functional: where Ф k, k,..., k, k, 8 8 t k q k, k,..., k8, k 8, tdt 0 q k, k,..., k k, t 8 8 M t M M M С min / max min Vu (), (3) M max, M min respectively the maximum and minimum values of the coefficient. Mt, scale Description of the software The software "Isothermal vulcanization" was developed as a set of applied programs for solving problems related to mathematical modeling of the process of isothermal vulcanization. To solve the DE system, the package provides numerical methods, including: the Runge-Kutta method of the fourth order; Adams method. The solution of the inverse kinetic problem is reduced to estimating the reaction rate constants, stoichiometric coefficients, and variables in the DE () system. To minimize the functional () in the software package, at the discretion of the user, the following methods can be used: coordinate descent, Hook-Jeeves, Rosenbrock, Powell, Nelder-Mead, coordinate averaging (using random search elements). Gradient methods (first order): steepest descent, conjugate directions (Fletcher-Reeves), variable metrics (Davidon-Fletcher-Powell), parallel gradients (Zangwill). The figure shows a block diagram of the developed software. The process of identification of reaction rate constants, coefficients of equations and stoichiometric coefficients is carried out in several stages: digitization of rheograms; translation of torques into concentrations; determination of initial concentrations; determination of the values of the required parameters of the constants providing the minimum of the functional (). Rheograms can be digitized manually or automatically using the GrDigit program integrated into the package. Processing of experimental data can be carried out both for one measurement and for a set (up to 6 rheograms). The conversion of torques in the concentration of nodes of the vulcanization mesh is carried out as follows: the values of torques are converted into conventional units: arb / M M M M M (4) current min max min then the conventional units are converted into (mol / kg), by multiplying M arb by the scale factor. Determination of the initial concentration C 0 DAV is carried out according to the formula: A 0 0 CA S8 AC Akt C (5)

Vestnik VSUET/Proceedings of VSUET, 3, 06 Figure. Block diagram of the software Figure. Structural software scheme Approbation of the developed software Rheometric curves obtained under the following initial conditions were used as initial data: Sulfur concentration value in the mixture: = 0.0078 mol/kg. Accelerator concentration: = 0.009 mol/kg. 3. Activator concentration: θ = 0.00 mol/kg. Figure 3 shows the experimental and calculated values of the concentration of vulcanization knots, obtained as a result of solving the BCC. The table shows the calculated values of the reaction rate constants, the table shows the estimated values of the stoichiometric coefficients and model parameters. Table The value of the reaction rate constants k5,89 0-0 Figure 3. Changes in the concentrations of the vulcanization grid points in time. approximation and search range of constants, after which the optimization method is selected. 97-4, 97

Bulletin of VSUET/Proceedings of VSUET, 3, 06 Conclusion On the basis of a systematic analysis of theoretical approaches to the description of vulcanization, the general block diagram of the study of this process has been improved. The mathematical model of the vulcanization process is supplemented with initial conditions, which are defined as functions of the initial concentrations of the components of the vulcanizing group. To solve the inverse kinetic problem, additional criteria for the quality of the model are proposed. A software product has been developed for conducting scientific research in the study of the processes of vulcanization of rubber compounds using multicomponent structuring systems. The checkpoint has a block-modular structure, which allows its expansion without loss of functionality. The directions of its modernization are the inclusion in the composition of the mathematical description of the non-isothermal vulcanization mode with further integration into the APCS circuit as an expert information and control system for issuing recommendations for managing the vulcanization process and making decisions. The work was financially supported by the state task 04/ (number NIR 304) on the topic "Synthesis of multifunctional quality control systems for the food and chemical industry" LITERATURE Tikhomirov S.G., Bityukov V.K., Podkopaeva S.V., Khromykh E. BUT. and other Mathematical modeling of control objects in the chemical industry. Voronezh: VSUIT, 0. 96 p. Khaustov I.A. Control of the synthesis of polymers in a batch method based on the fractional supply of reaction components // Bulletin of the TSTU. 04. 4 (0) S. 787 79. 3 Khaustov I.A. Control of the process of polymer degradation in solution based on fractional loading of the initiator. Vestnik VGUIT. 04. 4. P. 86 9. 4 V. K. Bityukov, I. A. Khaustov, and A. A. Khvostov, Russ. et al. System analysis of the process of thermal-oxidative degradation of polymers in solution as a control object. Vestnik VGUIT. 04.3(6). P. 6 66. 5 Karmanova O.V. Physical and chemical bases and activating components of polydienes vulcanization: diss. Dr. tech. Sciences. Voronezh, 0. 6 Molchanov V.I., Karmanova O.V., Tikhomirov S.G. Modeling the kinetics of polydienes vulcanization. Vestnik VGUIT. 03. P. 4 45. 7 Hardis., Jessop J.L.P., Peters F.E., Kessler M.. Cure kinetics characterization and monitoring of an epoxy resin using DSC, aman spectroscopy, and DEA // Composite. 03. Part A. V. 49. P. 00 08. 8 Javadi M., Moghiman M., eza Erfanian M., Hosseini N. Numerical Investigation of Curing Process in eaction Injection Molding of ubber for Quality Improvements // Key Engineering Materials. 0. V. 46 463. P. 06. EFEENCES Tikhomirov S.G., ityukov V.K. Podkopaeva S.V., Khromykh E.A. et al. Mathematicheskoe modelirovanie ob ektov upravleniya v khimicheskoi promyshlennosti Voronezh, VSUET, 0. 96 p. (in Russian). Khaustov I.A. Management polymer synthesis batch process based on the fractional flow of the reaction components. Vestnik TGTU 04, no. 4(0), pp. 787 79. (in ussian). 3 Khaustov I.A. Process control degradation of polymers in the solution based on the fractional loading of the initiator. Vestnik VGUIT 04, no. 4, pp. 86 9 (in ussian). 4 ityukov V.K., Khaustov I.A., Khvostov A.A. System analysis of the thermooxidative degradation of polymers in solution as a control object. Vestnik VGUIT 04, no. 3 (6), pp. 6 66. (in ussian). 5 Karmanova O.V. Fiziko-khimicheskie osnovy i aktiviruyushchie komponenty vulknizatsii polidienov Voronezh, 0. (in ussian). 6 Molchanov V.I., Karmanova O.V., Tikhomirov S.G. Modeling the kinetics of vulcanization polydienes. Vestnik VGUIT 03, no., pp. 4 45. (in ussian). 7 Hardis., Jessop J.L.P., Peters F.E., Kessler M.. Cure kinetics characterization and monitoring of an epoxy resin using DSC, aman spectroscopy, and DEA. Composite, 03, part A, vol. 49, pp. 00 08. 8 Javadi M., Moghiman M., eza Erfanian M., Hosseini N. Numerical Investigation of Curing Process in eaction Injection Molding of ubber for Quality Improvements. key engineering materials. 0, vol. 46463, pp. 06.98

Bulletin of VSUET/Proceedings of VSUET, 3, 06 INFORMATION ABOUT THE AUTHORS Sergey T. Tikhomirov Professor, Department of Information and Control Systems, Voronezh State University of Engineering Technologies, Revolution Ave., 9, Voronezh, 394036, Russia, [email protected] Olga V. Karmanova Head of Department, Professor, Department of Chemistry and Chemical Technology of Organic Compounds and Polymer Processing, Voronezh State University of Engineering Technologies, Leninsky Prospect, 4, Voronezh, 394000, Russia, [email protected] Yury V. Pyatakov Associate Professor, Department of Information and Control Systems, Voronezh State University of Engineering Technologies, Revolution Ave., 9, Voronezh, 394036, Russia, [email protected] Alexander A. Maslov Postgraduate Student, Department of Information and Control Systems, Voronezh State University of Engineering Technologies, 9 Revolution Avenue, Voronezh, 394036, Russia, [email protected] ail.ru INFOMATION AOUT AUTHOS Sergei G. Tikhomirov professor, department of information and control systems, Voronezh state university of engineering technologies, evolution Av., 9 Voronezh, ussia, [email protected] Olga V. Karmanova professor, head of department, department of chemistry and chemical technology of organic compounds and polymers processing, Voronezh state university of engineering technologies, Leninsky Av., 4 Voronezh, ussia, [email protected] Yurii V. Pyatakov associate professor, department of information and control systems, Voronezh state university of engineering technologies, evolution Av., 9 Voronezh, ussia, [email protected] Aleksandr A. Maslov graduate student, department of information and control systems, Voronezh state university of engineering technologies, evolution Av., 9 Voronezh, ussia, [email protected] CRITERION OF AUTHORSHIP Sergei T. Tikhomirov proposed the methodology for conducting the experiment and organized production tests Alexander A. Maslov reviewed the literature on the problem under study, conducted the experiment, performed the calculations Olga V. Karmanova consultation during the study Yuri V. Pyatakov wrote the manuscript, corrected it before submitting it to the editors and is responsible for plagiarism CONFLICTS OF INTEREST The authors declare no conflicts of interest. CONTIUTION Sergei G. Tikhomirov proposed a scheme of the experiment and organized production trials Aleksandr A. Maslov review of the literature on an investigation of an problem, conducted an experiment, performed computations Olga V. Karmanova consultation during the study Yurii V. Pyatakov wrote the manuscript, correct it before filing in editing and is responsible for plagiarism CONFLICT OF INTEEST The authors declare no conflict of interest. ACCEPTED 7.07.06 ECEIVED 7.7.06 ACCEPTED 08.06.06 ACCEPTED 8..06 99

The main methods of vulcanization of rubbers. To carry out the main chemical process of rubber technology - vulcanization - vulcanizing agents are used. The chemistry of the vulcanization process consists in the formation of a spatial network, including linear or branched rubber macromolecules and cross-links. Technologically, vulcanization consists in processing the rubber compound at temperatures from normal to 220 ° C under pressure and less often without it.

In most cases, industrial vulcanization is carried out with vulcanizing systems that include a vulcanizing agent, accelerators and vulcanization activators and contribute to a more efficient flow of spatial network formation processes.

The chemical interaction between the rubber and the vulcanizing agent is determined by the chemical activity of the rubber, i.e. the degree of unsaturation of its chains, the presence of functional groups.

The chemical activity of unsaturated rubbers is due to the presence of double bonds in the main chain and the increased mobility of hydrogen atoms in -methylene groups adjacent to the double bond. Therefore, unsaturated rubbers can be vulcanized with all compounds that interact with the double bond and its neighboring groups.

The main vulcanizing agent for unsaturated rubbers is sulfur, which is usually used as a vulcanizing system in conjunction with accelerators and their activators. In addition to sulfur, organic and inorganic peroxides, alkylphenol-formaldehyde resins (AFFS), diazo compounds, and polyhaloid compounds can be used.

The chemical activity of saturated rubbers is significantly lower than the activity of unsaturated ones, therefore, highly reactive substances, such as various peroxides, must be used for vulcanization.

Vulcanization of unsaturated and saturated rubbers can be carried out not only in the presence of chemical vulcanizing agents, but also under the influence of physical influences that initiate chemical transformations. These are high-energy radiation (radiation vulcanization), ultraviolet radiation (photovulcanization), prolonged exposure to high temperatures (thermal vulcanization), shock waves and some other sources.

Rubbers having functional groups can be vulcanized at those groups with cross-linking agents that interact with the functional groups.

The main regularities of the vulcanization process. Regardless of the type of rubber and the vulcanizing system used, some characteristic changes in material properties occur during the vulcanization process:

The plasticity of the rubber compound sharply decreases, the strength and elasticity of the vulcanizates appear. Thus, the strength of a raw rubber compound based on NC does not exceed 1.5 MPa, and the strength of a vulcanized material is not less than 25 MPa.

The chemical activity of rubber is significantly reduced: in unsaturated rubbers, the number of double bonds decreases, in saturated rubbers and rubbers with functional groups, the number of active centers. This increases the resistance of the vulcanizate to oxidative and other aggressive influences.

Increases the resistance of the vulcanized material to the action of low and high temperatures. Thus, NC hardens at 0ºС and becomes sticky at +100ºС, while the vulcanizate retains strength and elasticity in the temperature range from -20 to +100ºС.

This character of the change in the properties of the material during vulcanization unambiguously indicates the occurrence of structuring processes, ending with the formation of a three-dimensional spatial grid. In order for the vulcanizate to retain elasticity, cross-links must be sufficiently rare. For example, in the case of NC, the thermodynamic flexibility of the chain is retained if one cross bond occurs per 600 carbon atoms of the main chain.

The vulcanization process is also characterized by some general patterns of changes in properties depending on the vulcanization time at a constant temperature.

Since the viscosity properties of mixtures change most significantly, shear rotational viscometers, in particular Monsanto rheometers, are used to study the vulcanization kinetics. These devices make it possible to study the vulcanization process at temperatures from 100 to 200ºС for 12 - 360 minutes with various shear forces. The recorder of the device writes out the dependence of the torque on the vulcanization time at a constant temperature, i.e. the vulcanization kinetic curve, which has an S-shape and several sections corresponding to the stages of the process (Fig. 3).

The first stage of vulcanization is called an induction period, a scorch stage, or a pre-vulcanization stage. At this stage, the rubber mixture must remain fluid and fill the entire mold well, therefore its properties are characterized by a minimum shear moment M min (minimum viscosity) and a time t s during which the shear moment increases by 2 units compared to the minimum.

The duration of the induction period depends on the activity of the vulcanization system. The choice of a vulcanizing system with one or another value of t s is determined by the mass of the product. During vulcanization, the material is first heated to the vulcanization temperature, and due to the low thermal conductivity of rubber, the heating time is proportional to the mass of the product. For this reason, vulcanizing systems that provide a sufficiently long induction period should be selected for vulcanizing products of large mass, and vice versa for products with low mass.

The second stage is called the main vulcanization period. At the end of the induction period, active particles accumulate in the mass of the rubber compound, causing rapid structuring and, accordingly, an increase in torque up to a certain maximum value M max. However, the completion of the second stage is not the time to reach M max, but the time t 90 corresponding to M 90 . This moment is determined by the formula

M 90 \u003d 0.9 M + M min,

where M – torque difference (M=M max – M min).

Time t 90 is the optimum vulcanization, the value of which depends on the activity of the vulcanizing system. The slope of the curve in the main period characterizes the rate of vulcanization.

The third stage of the process is called the overvulcanization stage, which in most cases corresponds to a horizontal section with constant properties on the kinetic curve. This zone is called the vulcanization plateau. The wider the plateau, the more resistant the mixture to overvulcanization.

The width of the plateau and the further course of the curve mainly depend on the chemical nature of the rubber. In the case of unsaturated linear rubbers, such as NK and SKI-3, the plateau is not wide and then deterioration occurs, i.e. slope of the curve (Fig. 3, curve a). The process of deterioration of properties at the stage of overvulcanization is called reversion. The reason for the reversion is the destruction of not only the main chains, but also the formed cross-links under the action of high temperature.

In the case of saturated rubbers and unsaturated rubbers with a branched structure (a significant amount of double bonds in the side 1,2-units), the properties change insignificantly in the overvulcanization zone, and in some cases even improve (Fig. 3, curves b and in), since the thermal oxidation of the double bonds of the side links is accompanied by additional structuring.

The behavior of rubber compounds at the overvulcanization stage is important in the production of massive products, especially automobile tires, since due to reversion, overvulcanization of the outer layers can occur while undervulcanization of the inner ones. In this case, vulcanizing systems are required that would provide a long induction period for uniform heating of the tire, a high speed in the main period, and a wide plateau of vulcanization during the revulcanization stage.

3.2. Sulfur Vulcanizing Systems for Unsaturated Rubbers

Properties of sulfur as a vulcanizing agent. The process of vulcanization of natural rubber with sulfur was discovered in 1839 by C. Goodyear and independently in 1843 by G. Gencock.

For vulcanization, natural ground sulfur is used. Elemental sulfur has several crystalline modifications, of which only the α-modification is partially soluble in rubber. It is this modification, which has a melting point of 112.7 ºС, and is used in vulcanization. The -form molecules are an eight-membered cycle S 8 with an average activation energy of ring rupture E act = 247 kJ/mol.

This is a rather high energy, and the splitting of the sulfur ring occurs only at a temperature of 143ºС and above. At temperatures below 150ºС, heterolytic or ionic decomposition of the sulfur ring occurs with the formation of the corresponding sulfur biion, and at 150ºС and above, homolytic (radical) decomposition of the S ring with the formation of sulfur diradicals:

t150ºС S 8 →S + - S 6 - S - → S 8 + -

t150ºС S 8 →Sֹ–S 6 –Sֹ→S 8 ֹֹ.

Biradicals S 8 ·· easily break up into smaller fragments: S 8 ֹֹ→S х ֹֹ + S 8-х ֹֹ.

The resulting biions and biradicals of sulfur then interact with rubber macromolecules either at the double bond or at the site of the α-methylene carbon atom.

The sulfur ring can also decompose at temperatures below 143ºС if there are any active particles (cations, anions, free radicals) in the system. Activation occurs according to the scheme:

S 8 + A + →A - S - S 6 - S +

S 8 + B – → B – S – S 6 –

S 8 + Rֹ → R - S - S 6 - Sֹ.

Such active particles are present in the rubber compound when vulcanizing systems with vulcanization accelerators and their activators are used.

To convert soft plastic rubber into hard elastic rubber, a small amount of sulfur is sufficient - 0.10.15% wt. However, the actual dosages of sulfur range from 12.5 to 35 wt.h. per 100 wt.h. rubber.

Sulfur has a limited solubility in rubber, so the dosage of sulfur depends on the form in which it is distributed in the rubber compound. At real dosages, sulfur is in the form of molten droplets, from the surface of which sulfur molecules diffuse into the rubber mass.

The preparation of the rubber mixture is carried out at an elevated temperature (100-140ºС), which increases the solubility of sulfur in rubber. Therefore, when the mixture is cooled, especially in cases of its high dosages, free sulfur begins to diffuse onto the surface of the rubber mixture with the formation of a thin film or sulfur coating. This process in technology is called fading or sweating. Efflorescence rarely reduces the tackiness of the preforms, so preforms are treated with gasoline to freshen up the surface before assembly. This worsens the working conditions of assemblers and increases the fire and explosion hazard of production.

The problem of fading is especially acute in the production of steel cord tires. In this case, to increase the strength of the bond between metal and rubber, the dosage of S is increased to 5 wt.h. To avoid fading in such formulations, a special modification should be used - the so-called polymeric sulfur. This is the -form, which is formed by heating the -form to 170ºС. At this temperature, a sharp jump in the viscosity of the melt occurs and polymeric sulfur S n is formed, where n is over 1000. In world practice, various modifications of polymeric sulfur, known under the brand name "cristex", are used.

Theories of sulfur vulcanization. Chemical and physical theories have been put forward to explain the process of sulfur vulcanization. In 1902, Weber put forward the first chemical theory of vulcanization, elements of which have survived to this day. Extracting the product of the interaction of NK with sulfur, Weber found that part of the introduced sulfur is not extracted. This part was called by him bound, and the separated one - free sulfur. The sum of the amount of bound and free sulfur was equal to the total amount of sulfur introduced into the rubber: S total =S free +S bond. Weber also introduced the concept of vulcanization coefficient as the ratio of bound sulfur to the amount of rubber in the composition of the rubber compound (A): K vulk \u003d S bond / A.

Weber succeeded in isolating polysulfide (C 5 H 8 S) n as a product of the intramolecular addition of sulfur to the double bonds of isoprene units. Therefore, Weber's theory could not explain the increase in strength as a result of vulcanization.

In 1910, Oswald put forward a physical theory of vulcanization, which explained the effect of vulcanization by the physical adsorption interaction between rubber and sulfur. According to this theory, rubber-sulfur complexes are formed in the rubber mixture, which interact with each other also due to adsorption forces, which leads to an increase in the strength of the material. However, adsorption bound sulfur should be completely extracted from the vulcanizate, which was not observed in real conditions, and the chemical theory of vulcanization began to prevail in all further studies.

The main proofs of the chemical theory (bridge theory) are the following provisions:

Only unsaturated rubbers are vulcanized with sulfur;

Sulfur interacts with unsaturated rubber molecules to form covalent cross-links (bridges) of various types, i.e. with the formation of bound sulfur, the amount of which is proportional to the unsaturation of the rubber;

The vulcanization process is accompanied by a thermal effect proportional to the amount of added sulfur;

Vulcanization has a temperature coefficient of about 2, i.e. close to the temperature coefficient of a chemical reaction in general.

The increase in strength as a result of sulfur vulcanization occurs due to the structuring of the system, as a result of which a three-dimensional spatial grid is formed. Existing sulfur vulcanization systems make it possible to directionally synthesize practically any type of cross-link, change the vulcanization rate, and the final structure of the vulcanizate. Therefore, sulfur is still the most popular cross-linking agent for unsaturated rubbers.

The chemical activity of unsaturated rubbers is due to the presence of double bonds in the main chain and the increased mobility of hydrogen atoms in the a-methylene groups adjacent to the double bond. Therefore, unsaturated rubbers can be vulcanized with all compounds that interact with the double bond and its neighboring groups.

Rubbers having functional groups can be vulcanized at those groups with cross-linking agents that interact with the functional groups.

· Dramatically decreases the plasticity of the rubber mixture, there is strength and elasticity of vulcanizates. Thus, the strength of a raw rubber compound based on NC does not exceed 1.5 MPa, and the strength of a vulcanized material is not less than 25 MPa.

· The chemical activity of rubber is significantly reduced: in unsaturated rubbers, the number of double bonds decreases, in saturated rubbers and rubbers with functional groups, the number of active centers. This increases the resistance of the vulcanizate to oxidative and other aggressive influences.

· The resistance of the vulcanized material to the action of low and high temperatures increases. Thus, NC hardens at 0ºС and becomes sticky at +100ºС, while the vulcanizate retains strength and elasticity in the temperature range from -20 to +100ºС.

The vulcanization process is also characterized by some general patterns of changes in properties depending on the vulcanization time at a constant temperature.

M 90 \u003d 0.9 DM + M min,

where DM is the torque difference (DM=M max - M min).

Time t 90 is the optimum vulcanization, the value of which depends on the activity of the vulcanizing system. The slope of the curve in the main period characterizes the rate of vulcanization.

Natural rubber is not always suitable for making parts. This is because its natural elasticity is very low, and is highly dependent on the outside temperature. At temperatures close to 0, the rubber becomes hard, or as it is lowered further, it becomes brittle. At a temperature of about + 30 degrees, the rubber begins to soften and, with further heating, passes into a state of melt. When recooled, it does not restore its original properties.

To ensure the necessary operational and technical properties of rubber, various substances and materials are added to rubber - soot, chalk, softeners, etc.

In practice, several vulcanization methods are used, but they are united by one thing - the processing of raw materials with vulcanization sulfur. Some textbooks and regulations say that sulfur compounds can be used as vulcanizing agents, but in fact they can be considered as such only because they contain sulfur. Otherwise, they can affect vulcanization exactly like other substances that do not contain sulfur compounds.

Some time ago, research was carried out regarding the processing of rubber with organic compounds and certain substances, for example:

phosphorus;
selenium;
trinitrobenzene and a number of others.

But studies have shown that these substances have no practical value in terms of vulcanization.

Vulcanization process

The rubber vulcanization process can be divided into cold and hot. The first one can be divided into two types. The first involves the use of semichloride sulfur. The mechanism of vulcanization using this substance looks like this. A workpiece made of natural rubber is placed in the vapors of this substance (S2Cl2) or in its solution, made on the basis of some solvent. The solvent must meet two requirements:

It must not react with sulfur semichloride.
It should dissolve the rubber.

As a rule, carbon disulfide, gasoline and a number of others can be used as a solvent. The presence of sulfur hemichloride in the liquid prevents the rubber from dissolving. The essence of this process is to saturate the rubber with this chemical.

The duration of the vulcanization process with the participation of S2Cl2 as a result determines the technical characteristics of the finished product, including elasticity and strength.

The vulcanization time in a 2% solution can be several seconds or minutes. If the process is delayed in time, then the so-called overvulcanization can occur, that is, the workpieces lose their plasticity and become very brittle. Experience shows that with a product thickness of the order of one millimeter, the vulcanization operation can be carried out for several seconds.

This vulcanization technology is the optimal solution for processing parts with a thin wall - pipes, gloves, etc. But, in this case, it is necessary to strictly observe the processing modes, otherwise the upper layer of the parts can be vulcanized more than the inner layers.

At the end of the vulcanization operation, the resulting parts must be washed with either water or an alkaline solution.

There is a second method of cold vulcanization. Rubber blanks with a thin wall are placed in an atmosphere saturated with SO2. After a certain time, the blanks are transferred to the chamber, where H2S (hydrogen sulfide) is pumped. The exposure time of blanks in such chambers is 15 - 25 minutes. This time is enough to complete the vulcanization. This technology is successfully used for the processing of glued joints, which gives them high strength.

Special rubbers are processed using synthetic resins, vulcanization using them does not differ from that described above.

Hot vulcanization

The technology of such vulcanization is as follows. A certain amount of sulfur and special additives are added to molded raw rubber. As a rule, the volume of sulfur should lie in the range of 5 - 10%; the final figure is determined based on the purpose and hardness of the future part. In addition to sulfur, the so-called horn rubber (ebonite) containing 20 - 50% sulfur is added. At the next stage, blanks are formed from the obtained material and heated, i.e. curing.

Heating is carried out by various methods. The blanks are placed in metal molds or rolled into fabric. The resulting structures are placed in an oven heated to 130 - 140 degrees Celsius. In order to increase the efficiency of vulcanization, the oven can be pressurized.

Formed preforms can be placed in an autoclave containing superheated water vapor. Or they are placed in a heated press. In fact, this method is the most common in practice.

The properties of vulcanized rubber depend on many conditions. That is why vulcanization is one of the most complex operations used in the production of rubber. In addition, the quality of raw materials and the method of its pre-treatment also play an important role. We must not forget about the amount of added sulfur, temperature, duration and method of vulcanization. In the end, the properties of the finished product are also affected by the presence of impurities of various origins. Indeed, the presence of many impurities allows for proper vulcanization.

In recent years, accelerators have been used in the rubber industry. These substances added to the rubber compound accelerate the ongoing processes, reduce energy consumption, in other words, these additives optimize the processing of the workpiece.

When implementing hot vulcanization in air, the presence of lead oxide is necessary, in addition, the presence of lead salts in combination with organic acids or with compounds that contain acidic hydroxides may be required.

The following substances are used as accelerators:

thiuramide sulfide;
xanthates;
mercaptobenzothiazole.

Vulcanization under the influence of water vapor can be significantly reduced if chemicals such as alkalis are used: Ca (OH) 2, MgO, NaOH, KOH, or salts Na2CO3, Na2CS3. In addition, potassium salts will help speed up the processes.

There are also organic accelerators, these are amines, and a whole group of compounds that are not included in any group. For example, these are derivatives of substances such as amines, ammonia and a number of others.

In production, diphenylguanidine, hexamethylenetetramine and many others are most often used. Cases are not uncommon when zinc oxide is used to enhance the activity of accelerators.

In addition to additives and accelerators, the environment also plays an important role. For example, the presence of atmospheric air creates unfavorable conditions for vulcanization at standard pressure. In addition to air, carbonic anhydride and nitrogen have a negative effect. Meanwhile, ammonia or hydrogen sulfide have a positive effect on the vulcanization process.

The vulcanization procedure gives rubber new properties and modifies existing ones. In particular, its elasticity is improved, etc. The vulcanization process can be controlled by constantly measuring the changing properties. As a rule, for this purpose, the definition of force at break and tension at break is used. But these control methods are not accurate and are not used.

Rubber as a product of rubber vulcanization

Technical rubber is a composite material containing up to 20 components that provide various properties of this material. Rubber is obtained by vulcanizing rubber. As noted above, in the process of vulcanization, the formation of macromolecules occurs, which provide the operational properties of rubber, thus ensuring high rubber strength.

The main difference between rubber and many other materials is that it has the ability to elastic deformation, which can occur at different temperatures, ranging from room temperature to much lower. Rubber significantly exceeds rubber in a number of characteristics, for example, it is distinguished by elasticity and strength, resistance to temperature extremes, exposure to aggressive environments, and much more.

Cement for vulcanization

Cement for vulcanization is used for self-vulcanization operation, it can start from 18 degrees and for hot vulcanization up to 150 degrees. This cement does not include hydrocarbons. There is also an OTP type cement used for applying to rough surfaces inside tires, as well as OTR Type Top RAD and PN patches with extended drying times. The use of such cement makes it possible to achieve long service life of retreaded tires used on special construction equipment with high mileage.

Do-it-yourself tire hot vulcanization technology

To perform hot vulcanization of a tire or tube, you will need a press. The welding reaction of the rubber and the part takes place over a certain period of time. This time depends on the size of the repaired area. Experience has shown that it takes 4 minutes to repair a 1 mm deep damage at a given temperature. That is, to repair a defect with a depth of 3 mm, you will have to spend 12 minutes of pure time. Preparation time is not taken into account. And meanwhile, putting the vulcanizing device into operation, depending on the model, can take about 1 hour.

The temperature required for hot curing is between 140 and 150 degrees Celsius. To achieve this temperature, there is no need to use industrial equipment. For self-repair of tires, it is quite acceptable to use household electrical appliances, for example, an iron.

Repairing defects in a car tire or tube using a vulcanizing device is a rather laborious operation. It has many subtleties and details, and therefore we will consider the main stages of repair.

To provide access to the damaged area, the tire must be removed from the wheel.
Clean the rubber near the damaged area. Its surface should become rough.
Blow the treated area with compressed air. The cord that has appeared outside must be removed, it can be bitten off with wire cutters. Rubber must be treated with a special degreasing compound. Processing must be carried out on both sides, outside and inside.
On the inside, a patch prepared in advance in size should be laid on the site of damage. Laying starts from the bead side of the tire towards the center.
On the outside, at the place of damage, it is necessary to put pieces of raw rubber, cut into pieces of 10 - 15 mm, they must first be heated on the stove.
The laid rubber must be pressed and leveled over the surface of the tire. In this case, it is necessary to ensure that the layer of raw rubber is 3-5 mm higher than the working surface of the chamber.
After a few minutes, using an angle grinder (angle grinder), it is necessary to remove the layer of applied raw rubber. In the event that the bare surface is loose, that is, air is present in it, all the applied rubber must be removed and the rubber application operation repeated. If there is no air in the repair layer, that is, the surface is flat and does not contain pores, the repaired part can be sent under heated to the temperature indicated above.
To accurately position the tire on the press, it makes sense to mark the center of the defective area with chalk. To prevent the heated plates from sticking to the rubber, thick paper must be laid between them.

Do-it-yourself vulcanizer

Any hot curing device must contain two components:

a heating element;
press.

For self-production of a vulcanizer, you may need:

iron;
electric stove;
piston from the engine.

A do-it-yourself vulcanizer must be equipped with a regulator that can turn it off when the operating temperature is reached (140-150 degrees Celsius). For effective clamping, you can use an ordinary clamp.

The control method relates to the production of rubber products, namely, to methods for controlling the vulcanization process. The method is carried out by adjusting the vulcanization time depending on the time to obtain the maximum shear modulus of the rubber mixture during vulcanization of the samples on the rheometer and the deviation of the tensile modulus of rubber in finished products from the specified value. This allows you to work out the disturbing effects on the vulcanization process according to the characteristics of the initial components and the regime parameters of the processes of obtaining a rubber mixture and vulcanization. The technical result consists in increasing the stability of the mechanical characteristics of rubber products. 5 ill.

The present invention relates to the production of rubber products, namely, to methods for controlling the vulcanization process.

The process of production of rubber products includes the stages of obtaining rubber compounds and their vulcanization. Vulcanization is one of the most important processes in rubber technology. Vulcanization is carried out by keeping the rubber mixture in presses, special boilers or vulcanizers at a temperature of 130-160°C for a specified time. In this case, the rubber macromolecules are connected by transverse chemical bonds into a spatial vulcanization network, as a result of which the plastic rubber mixture turns into highly elastic rubber. A spatial network is formed as a result of heat-activated chemical reactions between rubber molecules and vulcanizing components (vulcanizers, accelerators, activators).

The main factors affecting the vulcanization process and the quality of finished products are the nature of the vulcanization environment, the vulcanization temperature, the duration of the vulcanization, the pressure on the surface of the vulcanized product, and the heating conditions.

With the existing technology, the vulcanization regime is usually developed in advance by calculation and experimental methods, and a program is set for the vulcanization process in the production of products. For the punctual implementation of the prescribed regime, the process is equipped with control and automation tools that most accurately implement the prescribed rigid program for the vulcanization regime. The disadvantages of this method are the instability of the characteristics of the manufactured products due to the impossibility of ensuring full reproducibility of the process, due to the limitation of the accuracy of automation systems and the possibility of shifting modes, as well as changes in the characteristics of the rubber mixture over time.

A known method of vulcanization with temperature control in steam boilers, plates or mold jackets by changing the flow rate of heat transfer fluids. The disadvantages of this method are the large variation in the characteristics of the resulting products due to the shift in operating modes, as well as changes in the reactivity of the rubber mixture.

There is a known method for controlling the vulcanization process by continuously monitoring the process parameters that determine its course: the temperature of the heat carriers, the temperature of the surfaces of the vulcanized product. The disadvantage of this method is the instability of the characteristics of the resulting products due to the instability of the reactivity supplied to the molding of the rubber mixture, and obtaining different characteristics of the product during vulcanization under the same temperature conditions.

There is a known method for adjusting the vulcanization mode, including determining the temperature field in the vulcanized product from controlled external temperature conditions on the vulcanizing surfaces of products by calculation methods, determining the kinetics of non-isothermal vulcanization of thin laboratory plates by the dynamic modulus of harmonic shift in the found non-isothermal conditions, determining the duration of the vulcanization process, at which optimal set of the most important properties of rubber, determination of the temperature field for multilayer standard samples simulating a tire element in terms of composition and geometry, obtaining the kinetics of non-isothermal vulcanization of multilayer plates and determining the equivalent vulcanization time according to the previously selected optimal level of properties, vulcanization of multilayer samples on a laboratory press at a constant temperature in during the equivalent vulcanization time and analysis of the obtained characteristics. This method is much more accurate than the methods used in industry for calculating the effects and equivalent vulcanization times, but it is more cumbersome and does not take into account the change in the instability of the reactivity of the rubber mixture supplied for vulcanization.

There is a known method for regulating the vulcanization process, in which the temperature is measured at the vulcanization process-limiting sections of the product, the degree of vulcanization is calculated from these data, when the specified and calculated degree of vulcanization is equal, the vulcanization cycle stops. The advantage of the system is the adjustment of the vulcanization time when the temperature fluctuations of the vulcanization process change. The disadvantage of this method is a large spread in the characteristics of the resulting products due to the heterogeneity of the rubber mixture in terms of reactivity to vulcanization and the deviation of the vulcanization kinetics constants used in the calculation from the real kinetic constants of the processed rubber mixture.

There is a known method for controlling the vulcanization process, which consists in calculating the temperature in the controlled shoulder zone on the R-C grid using boundary conditions based on measurements of the surface temperature of the molds and the temperature diaphragm cavity, calculating the equivalent vulcanization times that determine the degree of vulcanization in the controlled area, when implementing the equivalent time vulcanization on the real process the process stops. The disadvantages of the method are its complexity and a wide spread of characteristics of the resulting products due to changes in the reactivity to vulcanization (activation energy, pre-exponential factor of the kinetic constants) of the rubber mixture.

Closest to the proposed one is a method for controlling the vulcanization process, in which, synchronously with the real vulcanization process, according to the boundary conditions, based on temperature measurements on the surface of a metal mold, the temperature is calculated in the vulcanized products on a grid electric model, the calculated temperature values are set on a volcameter, on which parallel to the main During the vulcanization process, the kinetics of non-isothermal vulcanization of a sample from a processed batch of rubber mixture is studied, when a given level of vulcanization is reached, control commands are generated on the vulcameter for the product vulcanization unit [AS USSR No. 467835]. The disadvantages of the method are the great complexity of implementation on the technological process and the limited scope.

The objective of the invention is to increase the stability of the characteristics of manufactured products.

This goal is achieved by the fact that the vulcanization time of rubber products on the production line is corrected depending on the time to obtain the maximum shear modulus of the rubber mixture during vulcanization of samples of the processed rubber mixture in laboratory conditions on the rheometer and the deviation of the rubber tensile modulus in the manufactured products from the specified value.

The proposed solution is illustrated in Fig.1-5.

Figure 1 shows a functional diagram of the control system that implements the proposed control method.

Figure 2 shows a block diagram of the control system that implements the proposed control method.

Figure 3 shows a time series of tensile strength of the Jubo coupling, produced at OJSC "Balakovorezinotekhnika".

Figure 4 shows the characteristic kinetic curves for the moment of shear images of the rubber mixture.

Figure 5 shows the time series of changes in the duration of the vulcanization of samples of the rubber mixture to 90 percent level of achievable shear modulus of the vulcanizate.

On the functional diagram of the system that implements the proposed control method (see figure 1), the stage of preparation of the rubber mixture 1, the stage of vulcanization 2, the rheometer 3 for studying the kinetics of vulcanization of samples of the rubber mixture, the mechanical dynamic analysis device 4 (or tensile machine) to determine rubber stretching module for finished products or samples of satellites, control device 5.

The control method is implemented as follows. Samples from batches of the rubber compound are analyzed on a rheometer and the values of the vulcanization time at which the rubber shear moment has a maximum value are sent to the control device 5. When the reactivity of the rubber mixture changes, the control device corrects the vulcanization time of the products. Thus, perturbations are worked out according to the characteristics of the initial components that affect the reactivity of the resulting rubber mixture. The tensile modulus of rubber in finished products is measured by dynamic mechanical analysis or on a tensile testing machine and is also fed to the control device. The inaccuracy of the correction obtained, as well as the presence of changes in the temperature of heat carriers, heat exchange conditions and other disturbing influences on the vulcanization process, are worked out by adjusting the vulcanization time depending on the deviation of the rubber tensile modulus in the manufactured products from the specified value.

The block diagram of the control system that implements this control method and is presented in Fig.2 includes a direct control channel control device 6, a feedback channel control device 7, a vulcanization process control object 8, a transport delay link 9 to take into account the length of time for determining the characteristics of rubber of finished products , a feedback channel comparator 10, an adder 11 for summing adjustments to the vulcanization time via the forward control channel and the feedback channel, an adder 12 for taking into account the effects of uncontrolled perturbations on the vulcanization process.

When changing the reactivity of the rubber mixture, the estimate τ max changes and the control device corrects the vulcanization time in the process by the value Δτ 1 via the direct control channel 1.

In a real process, the vulcanization conditions differ from the conditions on the rheometer, so the vulcanization time required to obtain the maximum torque value in the real process also differs from that obtained on the device, and this difference varies with time due to the instability of the vulcanization conditions. These disturbances f are processed through the feedback channel by introducing a correction Δτ 2 by the control device 7 of the feedback loop, depending on the deviation of the rubber module in the manufactured products from the set value E ass.

The transport delay link 9, when analyzing the dynamics of the system, takes into account the influence of the time required to analyze the characteristics of the rubber of the finished product.

Figure 3 shows the time series of the conditional breaking force of the Juba coupling, manufactured by Balakovorezinotekhnika OJSC. The data show the presence of a large scatter of products for this indicator. The time series can be represented as the sum of three components: low-frequency x 1 , mid-frequency x 2 , high-frequency x 3 . The presence of a low-frequency component indicates the insufficient efficiency of the existing process control system and the fundamental possibility of building an effective feedback control system to reduce the spread of finished product parameters in terms of their characteristics.

Figure 4 shows the characteristic experimental kinetic curves for the moment of shear during the vulcanization of samples of the rubber mixture, obtained on the rheometer MDR2000 "Alfa Technologies". The data show the heterogeneity of the rubber compound in terms of reactivity to the vulcanization process. The spread in time to reach the maximum torque ranges from 6.5 minutes (curves 1.2) to more than 12 minutes (curves 3.4). The spread in the completion of the vulcanization process ranges from not reaching the maximum value of the moment (curves 3.4) to the presence of the overvulcanization process (curves 1.5).

Figure 5 shows a time series of vulcanization times to the 90 percent maximum shear moment level obtained from a study of the vulcanization of rubber compound samples on an Alfa Technologies MDR2000 rheometer. The data shows the presence of a low frequency change in the cure time to obtain the maximum shear moment of the vulcanizate.

The presence of a large variation in the mechanical characteristics of the Juba coupling (figure 3) indicates the relevance of solving the problem of increasing the stability of the characteristics of rubber products to improve their operational reliability and competitiveness. The presence of instability of the reactivity of the rubber mixture to the vulcanization process (Fig.4,5) indicates the need to change the time in the process of vulcanization of products from this rubber mixture. The presence of low-frequency components in the time series of the conditional breaking force of finished products (figure 3) and in the vulcanization time to obtain the maximum shear moment of the vulcanizate (figure 5) indicates the fundamental possibility of improving the quality indicators of the finished product by adjusting the vulcanization time.

Considered confirms the presence in the proposed technical solution:

The technical result, i.e. the proposed solution is aimed at increasing the stability of the mechanical characteristics of rubber products, reducing the number of defective products and, accordingly, reducing the specific consumption rates of the initial components and energy;

Essential features, consisting in adjusting the duration of the vulcanization process, depending on the reactivity of the rubber mixture to the vulcanization process and depending on the deviation of the rubber tensile modulus in finished products from the specified value;