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

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.

Simplified Adaptive Nonlinear Robust Controller for Linearized Pantagraph-Type Manipulator

1995 ◽  
Vol 7 (3) ◽  
pp. 242-249 ◽  
Author(s):  
Kiyotaka Izumi ◽  
◽  
Keigo Watanabe ◽  
Masatoshi Nakamura ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Physical Parameters ◽  
Additional Mass ◽  
Robust Controller ◽  
End Effector ◽  
Linear Controller ◽  
The Mathematical Model ◽  
Nonlinear Robust

If physical parameters are adjusted suitably in the pantagraph-type manipulator, the mathematical model becomes linear so that we can apply a linear controller. However, when the manipulator has an additional mass as an end-effector, the linear controller does not work well because the resultant model becomes nonlinear. In this paper, we propose a simplified adaptive nonlinear robust controller which we can apply to the manipulator, irrespective of the system linearity or nonlinearity. The effectiveness of the controller is illustrated by some simulations.

Analysis of Vibrating Natural Frequency of Pressure Pipeline

2011 ◽  
Vol 421 ◽  
pp. 98-101
Author(s):  
Ting Yue Hao
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Flow ◽  
Physical Parameters ◽  
Beam Model ◽  
Instability Condition ◽  
Coupling Vibration ◽  
Critical Flow Velocity ◽  
Pressure Pipeline ◽  
The Mathematical Model

The pressure pipeline is simplified as the beam model with two simple supported ends. The mathematical model is established, considering influence of the fluid-solid coupling vibration. Then the critical flow velocity is obtained by calculation and solving. By analyzing the practical numerical example，the influence of physical parameters on the first three-order natural frequency is discussed. Using Matlab software for programming, the instability condition of pressure pipeline is obtained, which is consistent with the result of numerical calculation.

Vibration Analysis of a Vertical Roller Mill: Modeling and Validation

2014 ◽  
Author(s):  
Engin H. Çopur ◽  
Metin U. Salamci ◽  
Selahattin Gülbeyaz
Keyword(s):  
Mathematical Model ◽  
Vibration Analysis ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Physical Parameters ◽  
Roller Mill ◽  
Vibration Tests ◽  
Working Parameters ◽  
The Mathematical Model ◽  
Vertical Roller

In this paper, vibration characteristics of a Vertical Roller Mill (VRM) are studied by using physical parameters of an operating VRM. The mathematical model is derived and simulated for a set of working parameters. Mechanical properties of the grinding material and the physical properties of the mechanical construction are used in the vibration model in order to obtain more realistic results. Simulation results are presented which give critical frequencies of the VRM. The effects of the hydraulic compressive force to the vibration characteristics are investigated. The effects of the material feeding rate (which affects the mineral thickness to be grinded) to the vibration characteristics are also simulated. In order to validate the mathematical model, a set of experimental vibration tests are performed on the VRM. Vibrations are measured during the run-down procedure of the VRM in order to determine natural frequencies of the mill as well as excitation frequencies of the system. The measurements showed the validity of the proposed mathematical model for the vibration analysis of the VRM.

ALGORITHM OF USING HURWITZ CONDITIONS TO STUDY STABILITY OF STEADY STATES OF CONTINUOUS FERMENTATION PROCESSES WITH NONLINEAR KINETICS

2017 ◽  
pp. 125-135
Author(s):  
Aleksey Georgievich Borodkin ◽  
Elena Lvovna Gordeeva ◽  
Yuliya Lvovna Gordeeva ◽  
Yuriy Alekseevich Komissarov
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Continuous Fermentation ◽  
Raw Materials ◽  
Sufficient Conditions ◽  
Steady States ◽  
Microbiological Synthesis ◽  
Hurwitz Matrix ◽  
First Approximation ◽  
The Mathematical Model

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.

scholarly journals Automatic Construction of Digital Woven Fabric by Using Sequential Yarn Images

2019 ◽  
Vol 19 (2) ◽  
pp. 147-156
Author(s):  
Zhongjian Li ◽  
Fei Yu ◽  
Ning Zhang ◽  
Yichen Lu ◽  
Ruru Pan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Image Processing ◽  
Cross Sections ◽  
Woven Fabric ◽  
Intensity Curve ◽  
Automatic Construction ◽  
Weave Structure ◽  
Fabric Structure ◽  
Curve Model ◽  
The Mathematical Model

Abstract In this article, a computerized method is proposed for simulating digital woven fabric (DWF) based on sequential yarn images captured from a moving yarn. A mathematical model of woven fabric structure is established by assuming that the crimped shape of yarns in weave structure is elastica, and the cross-sections of yarn in sequence image and fabric are circular and ellipse, respectively. The sequential yarn images, which are preprocessed and stitched first by image processing methods, are resized based on the mathematical model. Then a light intensity curve, which consists of radial curve model and axial curve model, is used to simulate the gray texture distribution of interlacing points in radial and axial directions. Finally, a Boole Matrix model is used to control the woven pattern. In the experiment, a slub yarn and a normal yarn samples with same count are applied to simulate gray texture fabrics. Then the gray fabrics are transformed to color fabrics based on three color maps. The fabric simulations are confined to single fabrics of plain, 2/2 matt, and 1/3 twill weaves.

scholarly journals Obtaining highly active magnesia: modeling and experiment

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.

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

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. 

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

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.

Multi-objective storage location allocation optimization and simulation analysis of automated warehouse based on multi-population genetic algorithm

2018 ◽  
Vol 26 (4) ◽  
pp. 367-377 ◽  
Author(s):  
Yu-ling Jiao ◽  
Xiao-cui Xing ◽  
Peng Zhang ◽  
Liang-cheng Xu ◽  
Xin-Ran Liu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Dynamic Simulation ◽  
Population Genetic ◽  
Physical Parameters ◽  
Location Allocation ◽  
Multi Objective ◽  
Storage Location ◽  
Population Genetic Algorithm ◽  
The Mathematical Model

Aiming at the requirement of working efficiency and security of automated warehouse and taking the operation time of outbound–inbound, the equivalent center of gravity of overall shelf and the degree of relative accumulation of related products as the multi-objective functions, the mathematical model is constructed for multi-objective storage location allocation optimization. According to the simple weighted genetic algorithm, it is easily prone to the problem of immature convergence when solving multi-objective programming problems. So, the multi-population genetic algorithm is proposed to solve the mathematical model of storage location allocation optimization. Combining with the experiment data of toy car assembly and automated warehouse, the results of the automated warehouse storage location allocation are obtained. FlexSim dynamic simulation model is established based on the storage location allocation solution, the physical parameters of automated warehouse and the experimental requirements plan of vehicle model assembly. The operation effect of the model and the utilization rate of the equipment are analyzed. The result of multi-population genetic algorithm is more reasonable and effective. It is proved that the result of multi-population genetic algorithm is superior to the result of simple weighted genetic algorithm, which provides an effective method for storage location allocation optimization and outbound–inbound dynamic simulation.

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

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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