Justification of the mathematical model of grain raw materials and  screw feeder  interaction in disperser

The authors of the article produce the algorithm to evaluate the stability of the steady states for microbiological synthesis using mathematical models for kinetics based on the unstructured approach. The object under study is a continuous biotechnological process aiming to obtain a target product, in addition to biomass. The estimation of stability is performed using Hurwitz matrix. In this process the use of raw materials containing components for additional producing of the primary substrate are possible. The algorithm includes five steps: formulation of the mathematical model that takes into account biological and technological limits; definition of steady states (one or several) for which it is necessary to evaluate conditions of stability and to calculate process parameters for the adopted steady states resulted from solving a system of nonlinear algebraic equations of the mathematical model; formulation of the equations of the first approximation (the system of first-order linear differential equations with constant coefficients) and evaluation of the coefficients corresponding to the adopted steady states; formation of Hurwitz matrix and calculation of its items; calculation of necessary and sufficient conditions for stability using Hurwitz matrix. Two methods of calculating Hurwitz matrix have been shown. The first method is implemented by transforming the system of four differential equations of the first approximation into one fourth-order ordinary differential equation. In the course of transformation there were determined calculated ratios for coefficients of the matrix. In the second method the coefficients are calculated by solving vector equation for the system of first approximation with the introduction of eigen values. The algorithm has been used for evaluating steady states of microbiological synthesis for lactic acid production from raw materials containing the component reproducing the main substrate. The estimation has been carried out for two steady states, one of which is optimal. For numerical values of the constants (from the literature) both steady states were stable.

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Obtaining highly active magnesia: modeling and experiment

NOVYE OGNEUPORY (NEW REFRACTORIES) ◽

10.17073/1683-4518-2019-5-92-95 ◽

2019 ◽

Vol 1 (5) ◽

pp. 92-95

Author(s):

M. Yu. Turchin ◽

A. V. Masalimov ◽

A. N. Smirnov ◽

I. A. Grishin

Keyword(s):

Carbon Dioxide ◽

Mathematical Model ◽

Raw Materials ◽

Laboratory Studies ◽

Equilibrium Conditions ◽

Highly Active ◽

Complete Extraction ◽

Simulation Results ◽

Chelyabinsk Region ◽

The Mathematical Model

The results of the analysis of the thermodynamic equilibrium conditions of the carbon dioxide leaching process are presented. The mathematical model for determining the properties for the most complete extraction of magnesium oxide present in raw materials was developed on their basis. Data from laboratory studies of magnesite samples from the Satkinskoe deposit of the Chelyabinsk region confirmed the adequacy of the simulation results.

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Development of the mathematical model for the process of oil raw materials pressing

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i2.13.11629 ◽

2018 ◽

Vol 7 (2.13) ◽

pp. 145

Author(s):

Ainura Kairbayeva ◽

Vitalii Vasilenko ◽

Seit Dzhinguilbayev ◽

Lyazzat Baibolova ◽

Larisa Frolova

Keyword(s):

Mathematical Model ◽

Chemical Interaction ◽

Raw Materials ◽

Screw Press ◽

Design Stage ◽

Design Parameters ◽

Single Screw ◽

Porous Skeleton ◽

The Mathematical Model ◽

Oil Filtration

The mathematical model for the process of oily raw materials pressing with single-screw oil press has been developed, which makes it possible to calculate the main design parameters of an oil press for extracting oil from oil crop seeds.This model of pressing describes the process of moving meal in the pressure zone and expression of oil in the pressing cage of the screw press, taking into account the following assumptions: porous skeleton and oil have the same density, they have no chemical interaction, the process of oil filtration occurs under isothermal conditions with laminar conditions of motion.The developed mathematical model corresponds to physical meaning of the occurring phenomena and can be used to analyze the work of active presses, and at the design stage.

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DEVELOPMENT OF A CONCEPTUAL MODEL OF A ROBOTIC COMPLEX FOR THE PRODUCTION OF RAVIOLI OF SPECIAL FORMS

EUREKA Life Sciences ◽

10.21303/2504-5695.2020.001532 ◽

2020 ◽

pp. 32-41

Author(s):

Oleg Burdo ◽

Igor Bezbakh ◽

Pavel Golubkov ◽

Serhii Shyshov ◽

Aleksander Gavrilov ◽

...

Keyword(s):

Mathematical Model ◽

Production Process ◽

Conceptual Model ◽

Raw Materials ◽

Control Object ◽

Automatic Process ◽

Effective System ◽

Objective Basis ◽

The Mathematical Model ◽

Functional Purpose

The article provides a substantiation of the conceptual model of the production process of special forms of dumplings. It is the first stage in the development of a model of this process as a control object. The purpose of which is to form an objective basis for the development of an effective system for automatic process control. The development of the conceptual model presupposes the specification and description of the properties of control channels and acting disturbances to the level of their mathematical model, which can be implemented in a simulation environment. Problems of identification of the mathematical model of the process of the production of dumplings, i. e. obtaining a mathematical description of processes based on the results of its purposeful experimental research, due to its complexity as a control object.The experimental approach, in this case, gives much more reliable results on the properties of the process. An attempt to obtain such general properties on the basis of experimental data would inevitably lead to the need for very complex and lengthy multifactorial experiments and nontrivial procedures for their processing. But this will leave open the question of the adequacy of the model for those conditions of the process and types of raw materials that were not covered by the experiments. Fundamentally important is the fact that the mathematical model of the process is developed as a model of the control object.Model can be used in two ways. This is due to the fact that in the closed circuits of the SAC, the discrepancy between the models can be considered as a manifestation of uncontrolled coordinate and parametric disturbances. It is in conditions of this kind of disturbances that the SAC must fulfill its functional purpose. The developed mathematical model of the production process of special forms of dumplings will be used by us only in the direction, when it is of great importance not so much quantitative as its qualitative correspondence to the original object.

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Mathematical model used for predicting arc-flash protective performance of fabrics based on physical parameters

Textile Research Journal ◽

10.1177/00405175211022633 ◽

2021 ◽

pp. 004051752110226

Author(s):

Wen Zhu ◽

Hong Tang ◽

Qilong Sun ◽

Zhen Huang ◽

Chengjiao Zhang

Keyword(s):

Mathematical Model ◽

Raw Materials ◽

Principal Component ◽

Thermomechanical Properties ◽

Physical Parameters ◽

Weave Structure ◽

Arc Flash ◽

Protective Fabrics ◽

Protective Performance ◽

The Mathematical Model

In this study, parameters that may affect the performance of arc-flash protective fabrics were systematically analyzed. Sixteen different commonly used fabrics with different configurations and grammage were produced and investigated, namely four raw materials with different configurations (93:0:5:2, 70:23:5:2, 46:47:5:2, and 23:70:5:2) and four with different grammage (180, 210, 240, and 270 g/m2). It was found that factors had different effects on the arc protective performance. Principal component analysis showed that the four plain weave fabrics of 180 g/m2 behaved differently compared with other samples, which was ascribed to the related differences in weave structure. In addition, a predicting mathematical model was developed based on the parameters that have the greatest influence on arc protective performance. The prediction parameters were not added to the structure, but replaced with physical parameters such as air permeability and thermomechanical properties. The adjusted R2 was 0.867, which demonstrated the rationality of using multiple linear regression to accurately predict arc protective performance. It was hypothesized that the construction of the mathematical model could contribute to the arc protective fabric evaluation and future researches in this field.

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Model for Assessing the Effectiveness of the Formation of Sustainable Supply Chains of Raw Materials by Timber Industry Enterprises

Journal of Applied Economic Research ◽

10.15826/vestnik.2021.20.1.007 ◽

2021 ◽

Vol 20 (1) ◽

pp. 148-168

Author(s):

R. S. Rogulin ◽

Keyword(s):

Mathematical Model ◽

Supply Chains ◽

Heuristic Algorithm ◽

Raw Materials ◽

Golden Ratio ◽

Sustainable Supply Chains ◽

Average Value ◽

Evaluation Scheme ◽

Efficiency Assessment ◽

The Mathematical Model

The paper presents a model for evaluating the effectiveness of enterprise decisions on the formation of the vector of procurement of raw materials at the timber exchange based on the volume of costs incurred. Enterprises usually set themselves the goal of incurring costs no higher than the target costs, so it becomes very important to take this factor into account during the process of evaluating efficiency. The evaluator does not always know the level of target costs, in response to which such levels are generated in the work, and for each of them the effectiveness is evaluated and an average value is taken. To calculate the efficiency indicator, a non-linear economic and mathematical model was built, which differs in the calculation of the boundary costs (efficiency boundaries) that determine the categories of efficiency. The article applies the principle of the golden ratio to determine the boundaries and categories of effectiveness. The aim of the work is to draw up a mathematical model and a heuristic algorithm that allows for evaluating the effectiveness of a decision made at the enterprise for the formation of supply chains for raw materials, which is distinguished by the ability to take into account the generated different indicators of target costs and calculate the boundaries and categories of efficiency. The hypothesis of the study is the possibility of assessing the effectiveness of the decision made at the enterprise in the formation of sustainable supply chains of raw materials, provided that the evaluator is not aware of the level of targeted costs. The nonlinearity of the mathematical model predetermined the construction of a heuristic algorithm for finding the solution. With the estimate obtained, the problem of borders appears due to economic reasons. To solve this problem, the methods of fuzzy sets and fuzzy logic were used. The algorithm and model were tested on the data of one of the enterprises of the Primorsky Territory. In the course of pilot application, it was shown that the boundaries of efficiency change and, as a result, have different categories of efficiency at different values of the target costs due to the nature of the efficiency assessment function. The results of the model and algorithm test showed the effectiveness of the efficiency evaluation scheme.

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The mathematical model of producing winter diesel fuel (including logistic costs)

E3S Web of Conferences ◽

10.1051/e3sconf/202125811005 ◽

2021 ◽

Vol 258 ◽

pp. 11005

Author(s):

Valentin Nikonorov ◽

Andrei Kutuzov ◽

Viktor Nikonorov ◽

Irina Bagaeva ◽

Anna Letta

Keyword(s):

Mathematical Model ◽

Diesel Fuel ◽

Raw Materials ◽

Target Function ◽

Refining Process ◽

Oil Refining ◽

Transport Costs ◽

Main Research ◽

Oil Refineries ◽

The Mathematical Model

The authors reviewed the statistics of winter diesel fuel consumption in the Russian Federation for 2000–2017, revealed a positive growth rate. On this fact, the relevance of the study was substantiated. The complexity and importance of the refining process leads to the need for digitalization of oil refineries. The object of the study is obtaining winter diesel fuel, taking into account transport costs. The subject of the study is digitalization of the oil refining process on the base of constructing the mathematical model for obtaining winter diesel fuel, taking into account delivery costs. Main research methods: retrospective data analysis, synthesis, comparison, linear programming methods. The authors considered two stages of winter diesel fuel production: dewaxing a mixture of stages of hydrocarbon raw materials on zeolite and subsequent compounding. For each stage, the authors compiled a system of equations describing the process. The authors also compiled a target function for obtaining winter diesel fuel, taking into account the costs of receiving and delivering. The obtained mathematical model can be used to ensure the required quality of winter diesel fuel (in terms of sulfur content, density and flash point).

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The Mathematical Model of Naphtha Steam Cracking

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19922113 ◽

1992 ◽

Vol 57 (10) ◽

pp. 2113-2124

Author(s):

Zdeněk Bělohlav ◽

Josef Horák

Keyword(s):

Mathematical Model ◽

Large Scale ◽

Raw Materials ◽

Reaction Model ◽

Radical Reactions ◽

Inlet Temperature ◽

Outlet Temperature ◽

Outlet Pressure ◽

Steam Cracking ◽

The Mathematical Model

The mathematical model of naphtha steam cracking has been developed to predict products yields. The feedstock composition, feedstock rate, steam-oil ration, inlet temperature, outlet temperature and outlet pressure are introduced as inputs. The reaction model consists of two parts: the radical reactions of higher alkanes, higher alkenes, naphthenes and alkylaromatics and the formal molecular reactions of lower alkanes and lower alkenes. The model was identified using a series of large-scale experiments including four naphtha raw materials. Eight experiments were carried out for each naphtha kind at two levels of the temperature profile, feed rate and steam-oil ratio.

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Modeling of Bulk Material Loading Into Sieve of the Scissor-type Separator

National Interagency Scientific and Technical Collection of Works. Design, Production and Exploitation of Agricultural Machines ◽

10.32515/2414-3820.2020.50.59-68 ◽

2020 ◽

pp. 59-68

Author(s):

Іgor Dudarev ◽

◽

Vasyl Olkhovskyi ◽

Keyword(s):

Mathematical Model ◽

Raw Materials ◽

Bulk Material ◽

Physical And Mechanical Properties ◽

Raw Material ◽

Entire Surface ◽

Feed Production ◽

Favorable Conditions ◽

Oscillating Motion ◽

The Mathematical Model

In agriculture and feed production, seeds and grains of various crops that require cleaning and separation are used as sowing material and raw materials. For seed and grain cleaning and separation the separators of different type are used. During operation, these separators take into account the physical and mechanical properties of the raw material. The article proposes the design of bulk material separator of scissor type, which has small dimensions and is easy to maintain. The efficiency of separator depends on the uniformity of the bulk material loading on the sieve surface. Therefore, substantiation of rational parameters of separator is an extremely important task. So, the aim of the study is to model the loading process of bulk material from the unloading hole of the hopper on an inclined flat sieve of the scissor-type separator, which performs oscillating motion. The proposed mathematical model of the bulk material loading from the hopper to the separator sieve allows us to determine the trajectory of the particle falling and to describe the position of the sieve, which changes due to the rotation of the eccentric. Also, modeling allows us to justify the rational parameters of the separator, taking into account the kinematic mode of its operation. Under these parameters, a layer of material of the same height will be formed on the sieve, which will provide favorable conditions for the separation process. In addition, the mathematical model allows us to determine the rational parameters of the relative position of the hopper and the sieve. In this case the entire surface of the sieve is used effectively.

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MULTIPARAMETRIC OPTIMIZATION FOR THE SELECTION AND IMPLEMENTATION OF TECHNOLOGICAL SOLUTIONS FOR THE PRODUCTION OF BIODIESEL FROM WASTE OIL-CONTAINING MATERIALS

International Conference on Technics Technologies and Education ◽

10.15547/ictte.2019.02.078 ◽

2019 ◽

pp. 117-124

Author(s):

Evgeniy Ganev ◽

Yunzile Dzhelil ◽

Boyan Ivanov ◽

Dragomir Dobrudzhaliev

Keyword(s):

Mathematical Model ◽

Parameter Optimization ◽

Raw Materials ◽

Waste Oil ◽

Territorial Unit ◽

Multiparametric Optimization ◽

The Mathematical Model ◽

Selection Of

In this work, a multi-parameter, multi-criteria parameter optimization of the mathematical model we have developed is performed. The use of reasonable parameter limits, determined through extensive statistical observations and analyses, enables the generation of optimal technological and logistical solutions for the use of biodiesel. Based on the selection of suitable oil-containing raw materials and such wastes, it allows the construction of optimum technological-logistical chains, providing the necessary amount of biodiesel in a certain territorial unit.

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