scholarly journals Coupling Model of Energy Flow and Material Flow in SKS Lead Smelting

2014 ◽  
Vol 8 (1) ◽  
pp. 131-135
Author(s):  
Hongcai Wang ◽  
Zhangming Shi ◽  
Liufang Lin ◽  
Bo Chen
Keyword(s):  
Mathematical Model ◽  
Material Flow ◽  
Energy Flow ◽  
Optimization Problems ◽  
Coupling Model ◽  
Flow Angle ◽  
Energy Saving Potential ◽  
Lead Smelting ◽  
Flow Changes ◽  
The Mathematical Model

This paper studied the coupling model of material flow and energy flow in the production process of lead smelting enterprises, and established the mathematical model for material flow and energy flow to resolve optimization problems. From the point of energy flow, the paper analyzed three kinds of energy flow changes which have an effect on the enterprise products. Through calculation and analysis, it has been found that there is 38.42% energy-saving potential in this enterprise. Separately from the material flow and energy flow angle, the paper put forward five aspects suggestions to reduce the energy consumption of the enterprise products.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

Shock Waves in Mathematical Models of the Aorta

1970 ◽  
Vol 37 (1) ◽  
pp. 34-37 ◽  
Author(s):  
George Rudinger
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Shock Waves ◽  
Method Of Characteristics ◽  
Wave Form ◽  
Shock Formation ◽  
Rapid Flow ◽  
Latex Tube ◽  
Flow Changes ◽  
The Mathematical Model

If the nonlinear equations for nonsteady blood flow are solved by the method of characteristics, shock discontinuities may develop as a result of omitting from the mathematical model some aspect of the system that becomes significant at rapid flow changes. As an illustration, the flow from the heart into the aorta at the beginning of systole is analyzed. An equation is derived which yields shock formation distances between a few centimeters and several meters depending on the elastic properties of the aorta. Since knowledge of the actual wave form would be useful for computer programming, a few exploratory experiments were performed with an unrestrained latex tube. They indicated wave transitions extending over several tube diameters, but maximum steepening of the wave has not yet been achieved.

scholarly journals OPTIMIZATION PROBLEMS OF MATHEMATICAL MODELLING OF A BUILDING AS A UNIFIED HEAT AND POWER SYSTEM

2020 ◽  
Vol 16 (1) ◽  
pp. 156-161
Author(s):  
Yuri Tabunshchikov ◽  
Marianna Brodach
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Energy System ◽  
Heat Energy ◽  
Objective Functions ◽  
Outdoor Climate ◽  
Energy Flows ◽  
The Mathematical Model ◽  
The Pontryagin Maximum Principle

The mathematical model of a building as a single heat energy system by the decomposition method is represented by three interconnected mathematical models: the first is a mathematical model of the energy interaction of a building’s shell with an outdoor climate; the second is a mathematical model of energy flows through the shell of a building; the third is a mathematical model of optimal control of energy consumption to ensure the required microclimate. Optimization problems for three mathematical models with objective functions are formulated. Methods for solving these problems are determined on the basis of the calculus of variations and the Pontryagin maximum principle. A method for assessing the skill of an architect and engineer in the design of a building as a single heat energy system is proposed.

scholarly journals Mathematical model of centrifugal compressor vaneless diffuser based on CFD calculations

2020 ◽  
Vol 178 ◽  
pp. 01014
Author(s):  
Olga Solovyeva ◽  
Aleksandr Drozdov
Keyword(s):  
Mathematical Model ◽  
Centrifugal Compressor ◽  
Similarity Criteria ◽  
Relative Width ◽  
Inlet Flow ◽  
Flow Angle ◽  
Gas Dynamic ◽  
Modelling Method ◽  
Vaneless Diffusers ◽  
The Mathematical Model

The approximate engineering techniques based on mathematical modelling are used in centrifugal compressor design. One of such methods is the well-proven Universal Modelling Method, developed in the scientific and research laboratory “Gas dynamics of turbo machines”, SPbPU. In the modern version of the compressor model, vaneless diffusers mathematical model was applied based on a generalization of the CFD calculations. The mathematical model can be used for vaneless diffusers with a relative width in the range of 1.4 – 10.0%, with a radial length up to 2.0, in the range of inlet flow angles 10 to 90 degrees, the inlet velocity coefficient in the range of 0.39 – 0.82, Reynolds number varying from 87 500 to 1 030 000. The model was also used for calculating low-flow-rate model stages with narrow diffusers with diffusers’ relative width in the range of 0.5 – 2.0%. The mathematical model showed lesser accuracy. To widen the model applicability, new series of CFD-calculations were executed. A series of vaneless diffusers was designed with relative width in the range of 0.6 – 1.2%, The gas-dynamic characteristics of loss coefficients and outlet flow angle versus inlet flow angle of diffuser were calculated. Regression analysis was used to process the calculated data. System of algebraic equations linking geometric, gas-dynamic parameters and similarity criteria was developed. The obtained equations are included in a new mathematical model of the Universal Modelling Method.

Mathematical Modelling of Material Flow during Friction Stir Welding of Aluminium Alloys

2018 ◽  
Vol 1146 ◽  
pp. 115-120
Author(s):  
Cosmin Ighisan ◽  
Bogdan Radu ◽  
Cristian Ciucă
Keyword(s):  
Mathematical Model ◽  
Friction Stir Welding ◽  
Aluminium Alloys ◽  
Material Flow ◽  
Good Precision ◽  
Two Dimensional ◽  
Element Analysis ◽  
Friction Stir ◽  
The Mathematical Model ◽  
Distribution Field

The paper presents the results of a mathematical model of the material flow during Friction Stir Welding (FSW) of aluminium alloys using a Finite Element Analysis. The authors presented their work on a two-dimensional visco-plastic model, using User Define Functions (UDF) in a commercial CFD code (FLUENT). The model developed was validated by microstructural investigations on experimental FSW joints and by a comparative analysis of temperature distribution field of the experimental FSW joint and numerical simulated model. The results confirmed that the mathematical model describes with a good precision the material flow and temperature field during FSW process.

Metodika postanovki i resheniya zadachi optimizacii raskroya pilovochnika krupnih razmerov s vipilivaniem dvuh brusev i chetireh par bokovih obreznih dosok s uchetom shirini propila

2016 ◽  
Author(s):  
А.И. Агапов
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Classical Method ◽  
Optimal Size ◽  
Cross Sectional ◽  
Reduced Dimensions ◽  
Method Of Lagrange Multipliers ◽  
The Mathematical Model

Предложена математическая модель задачи оптимизации для такой схемы раскроя пиловочника, включая целевую функцию и уравнения связи. В статье рассматривается пифагорическая зона пиловочника. Поэтому целевая функция представлена в виде суммы площадей поперечных сечений обрезных досок. Уравнения связи представлены в виде уравнений, в которых установлена взаимосвязь диаметра пиловочника в вершинном торце с размерами получаемых обрезных досок. Эта взаимосвязь описывается на основе использования теоремы Пифагора. Такое представление математической модели задачи оптимизации вполне логично. Однако решение такой математической модели классическим методом оказалось проблематичным. Для решения математической модели использовался метод множителей Лагранжа. Предложен алгоритм решения задачи для определения оптимальных размеров брусьев и боковых обрезных досок с учетом ширины пропила. Используя численный метод, определены оптимальные размеры брусьев и досок, при которых целевая функция принимает максимальное значение. Оказалось, что с увеличением ширины пропила толщина брусьев возрастает, а размеры боковых обрезных досок уменьшаются. Размеры крайних боковых досок с увеличением ширины пропила уменьшаются в большей степени, чем боковые доски, которые расположены ближе к центру бревна. Алгоритм решения задачи оптимизации рекомендуется использовать для расчета и составления поставов при проектировании и эксплуатации лесопильных линий по производству пиломатериалов. При использовании предлагаемого алгоритма решения задачи оптимизации выход пиломатериалов повышается на 3-5%. For the first time made up a mathematical model of optimization problems for this scheme cutting logs, including the objective function and constraint equations. The article discusses pifagoricheskaya zone logs. Therefore, the objective function is represented as the sum of the cross sectional area of ​​edging boards Equations communication presented in the form of equations, in which the interrelation diameter logs in the vertex end with the size of the edging boards. This relationship is described based on the use of the Pythagorean theorem. This representation of a mathematical model of the optimization problem is quite logical. However, the solution to this mathematical model of the classical method proved problematic. In order to solve the mathematical model of the method of Lagrange multipliers. An algorithm for solving the problem to determine the optimal size of the boards and the side edging boards considering cutting width. Using a numerical method for the optimum size of beams and boards, in which the objective function takes the maximum value. It was found that with an increase in the thickness of the boards of the kerf increases and the size of the lateral edging boards are reduced. Dimensions outer sideboards with increasing kerf reduced to a greater extent than the side boards, which are located closer to the center of the log. An algorithm for solving the optimization problem it is recommended to use for calculation and put in the design and operation of the saw lines for the production of lumber. When using the proposed algorithm for solving the optimization problem lumber output increases by 3-5 percent.

scholarly journals An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

2018 ◽  
Vol 22 ◽  
pp. 01009 ◽  
Author(s):  
Fırat Evirgen ◽  
Mehmet Yavuz
Keyword(s):  
Mathematical Model ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Variational Iteration Method ◽  
Test Problems ◽  
Optimal Solutions ◽  
Constrained Optimization Problems ◽  
Alternative Approach ◽  
Equality Constrained Optimization ◽  
The Mathematical Model

In this study, a fractional mathematical model with steepest descent direction is proposed to find optimal solutions for a class of nonlinear programming problem. In this sense, Caputo-Fabrizio derivative is adapted to the mathematical model. To demonstrate the solution trajectory of the mathematical model, we use the multistage variational iteration method (MVIM). Numerical simulations and comparisons on some test problems show that the mathematical model generated using Caputo-Fabrizio fractional derivative is both feasible and efficient to find optimal solutions for a certain class of equality constrained optimization problems.

A Coupling Model for Production and Energy Consumption Used in Continuous Production Industry

2011 ◽  
Vol 347-353 ◽  
pp. 3131-3134
Author(s):  
Rong Yong Zhao ◽  
Jian Wang ◽  
Wei Qing Ling
Keyword(s):  
Energy Consumption ◽  
Information Flow ◽  
Coming Out ◽  
Material Flow ◽  
Energy Flow ◽  
Continuous Production ◽  
Coupled Model ◽  
Energy Coupling ◽  
Coupling Model ◽  
Production Industry

In continuous production industry, to develop energy-saving technology, an essential modeling method should be selected to reflect both production process and the energy consumption simultaneously. In this work, we propose a novel coupling model for production and energy consumption. In this production-energy-coupled model (PECM), four flows are included, the material flow, the energy flow, the information flow and the emission flow. The material flow is abstracted from traditional technological documents about process description; the energy flow represents the any kind of energy transformation and consumption of all possible energy sources used in current factories, the electrical power, coal, diesel, steam, water etc.; the information flow is the running status, pre-alarm, alarm information from the production devices, and the control information from the controller in a distributed computer system(DCS) in the production field or a remote control signal from a central dispatch & control center in a big enterprise; and the emission flow is defined as any kind of emission coming out from the production at both middle production units or the final units of a whole continuous production line. Finally some specific conclusions of the production-energy-coupling model (PECM) are drawn respectively.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

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