Generalized mechanical-mathematical model for optimization of two-bearing shafts of minimal material consumption

2020 ◽  
pp. 8-12
Author(s):  
B.M. Abdeev ◽  
G.A. Guryanov ◽  
E.A. Klimenko
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Process Model ◽  
Geometric Parameters ◽  
Universal Theory ◽  
Minimum Volume ◽  
Applied Mechanics ◽  
Strength Condition ◽  
Material Consumption ◽  
Calculation Algorithm

A universal theory of solving the original problems of applied mechanics was developed to determine the rational geometric parameters of two-bearing three-stage shafts of the smallest volume with two nozzles, covering three modifications of the design under consideration. The optimization process model is brought to the calculation algorithm and is illustrated by a characteristic numerical example. Keywords: optimization, strength condition, minimum volume, extremum, objective function. [email protected]

scholarly journals Analysis of the stability of the computational algorithm to a change in the geometric parameters of cylindrical shell structures

2021 ◽  
pp. 12-21
Author(s):  
P. A Bakusov ◽  
A. A Semenov
Keyword(s):  
Mathematical Model ◽  
Cylindrical Shell ◽  
Computational Algorithm ◽  
Ritz Method ◽  
Complex Surface ◽  
Geometric Parameters ◽  
Shell Structures ◽  
Algebraic Equations ◽  
Calculation Algorithm ◽  
Symbolic Calculations

This study deals with testing sustainability of a computational algorithm to a change in geometric parameters of cylindrical shell structures. A change in geometry implies the replacement of one type of a cylindrical shell (elliptic, hyperbolic, parabolic) with another so that the quantitative change (the difference in elevations) in the area under consideration is minimal. On the one hand, this test allows to assessing the correctness of the algorithm itself and is relevant for algorithms that use both numerical methods and symbolic calculations. On the other hand, it allows to evaluating the possibility of simplifying calculations by approximating a complex surface with a simpler one both in understanding the surface definition itself and in expressing its basic characteristics such as Lame coefficients and main curvatures. A mathematical model of deformations of shell structures based on the hypotheses of Timoshenko (Mindlin - Reisner) are used in the work. The model takes into account transverse shifts, geometric nonlinearity and orthotropy of the material, and its written in the form of a functional of the total potential strain energy. The calculation algorithm is built on the basis of the Ritz method to reduce the variational problem of the minimum functional to the solution of a system of nonlinear algebraic equations, and on the method of continuing the solution with the best parameter for its solution. All calculations were carried out in dimensionless parameters. Three types of cylindrical panels are calculated, and critical loads of buckling and deflection fields at subcritical and supercritical moments are obtained. It is shown that for the considered class of problems the previously proposed mathematical model and computational algorithm are resistant to changes in the geometry of the structure.

The Optimization Design on Transmission Mechanism of Tightening Machine

2014 ◽  
Vol 621 ◽  
pp. 227-232
Author(s):  
Quan Ying Sun ◽  
Yi Li Wang ◽  
Xiu Li Meng ◽  
Xiao Dong Yu
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Design ◽  
Optimal Solution ◽  
Planetary Gear ◽  
Transmission Mechanism ◽  
Minimum Volume ◽  
Sqp Method ◽  
Design Variables

This article, to optimize the transmission mechanism of tightening machine, select the involute planetary gear with two teeth differences a research object, determine the design variables about modification coefficient, modulus and tooth thickness, based on the target of having the minimum volume, a mathematical model of optimization was established, the optimal solution of the objective function is obtained by using the SQP method on fmincon function of optimization toolbox of Matlab. The results showed, the volume of pinion decreased 15% after optimizated, the volume of the corresponding gear will also greatly reduced, achieved the optimization goal.

scholarly journals Passive Measurement of Three Optical Beacon Coordinates Using a Simultaneous Method

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5235
Author(s):  
Jiri Nemecek ◽  
Martin Polasek
Keyword(s):  
Mathematical Model ◽  
Relative Position ◽  
Experimental Tests ◽  
Image Sensor ◽  
Geometric Parameters ◽  
Light Sources ◽  
Feature Points ◽  
Passive Measurement ◽  
The Mathematical Model ◽  
Physical Principles

Among other things, passive methods based on the processing of images of feature points or beacons captured by an image sensor are used to measure the relative position of objects. At least two cameras usually have to be used to obtain the required information, or the cameras are combined with other sensors working on different physical principles. This paper describes the principle of passively measuring three position coordinates of an optical beacon using a simultaneous method and presents the results of corresponding experimental tests. The beacon is represented by an artificial geometric structure, consisting of several semiconductor light sources. The sources are suitably arranged to allow, all from one camera, passive measurement of the distance, two position angles, the azimuth, and the beacon elevation. The mathematical model of this method consists of working equations containing measured coordinates, geometric parameters of the beacon, and geometric parameters of the beacon image captured by the camera. All the results of these experimental tests are presented.

Optimization Research on Dynamic Balance of Spatial Engine under Limiting Shaking Moment

2009 ◽  
Vol 626-627 ◽  
pp. 693-698
Author(s):  
Yong Yong Zhu ◽  
S.Y. Gao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Kinetic Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Dynamic Balance ◽  
Optimized Design ◽  
Design Variables ◽  
The Mathematical Model ◽  
Shaking Moment

Dynamic balance of the spatial engine is researched. By considering the special wobble-plate engine as the model of spatial RRSSC linkages, design variables on the engine structure are confirmed based on the configuration characters and kinetic analysis of wobble-plate engine. In order to control the vibration of the engine frame and to decrease noise caused by the spatial engine, objective function is choosed as the dimensionless combinations of the various shaking forces and moments, the restriction condition of which presents limiting the percent of shaking moment. Then the optimization design is investigated by the mathematical model for dynamic balance. By use of the optimization design method to a type of wobble-plate engine, the optimization process as an example is demonstrated, it shows that the optimized design method benefits to control vibration and noise on the engines and improve the performance practically and theoretically.

Application of Honey-Bee Mating Optimization to Naphtha Reforming Reactor

2013 ◽  
Vol 11 (1) ◽  
pp. 293-308 ◽  
Author(s):  
Somayeh Karimi ◽  
Navid Mostoufi ◽  
Rahmat Sotudeh-Gharebagh
Keyword(s):  
Objective Function ◽  
Honey Bee ◽  
Process Model ◽  
Global Optimum ◽  
Inlet Temperature ◽  
Local Optimum ◽  
Naphtha Reforming ◽  
Decision Variables ◽  
Algorithm Comparison ◽  
Honey Bee Mating Optimization

Abstract Modeling and optimization of the process of continuous catalytic reforming (CCR) of naphtha was investigated. The process model is based on a network of four main reactions which was proved to be quite effective in terms of industrial application. Temperatures of the inlet of four reactors were selected as the decision variables. The honey-bee mating optimization (HBMO) and the genetic algorithm (GA) were applied to solve the optimization problem and the results of these two methods were compared. The profit was considered as the objective function which was subject to maximization. Optimization of the CCR moving bed reactors to reach maximum profit was carried out by the HBMO algorithm and the inlet temperature reactors were considered as decision variables. The optimization results showed that an increase of 3.01% in the profit can be reached based on the results of the HBMO algorithm. Comparison of the performance of optimization by the HBMO and the GA for the naphtha reforming model showed that the HBMO is an effective and rapid converging technique which can reach a better optimum results than the GA. The results showed that the HBMO has a better performance than the GA in finding the global optimum with fewer number of objective function evaluations. Also, it was shown that the HBMO is less likely to get stuck in a local optimum.

scholarly journals Art of Formulating LPs and IPs from Real Life Problems

2013 ◽  
Vol 61 (2) ◽  
pp. 185-191
Author(s):  
Md Hasib Uddin Molla ◽  
M Babul Hasan
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Real Life ◽  
Linear Constraints ◽  
Decision Problems ◽  
System Of Equations ◽  
Present Formulation ◽  
Real Life Problem ◽  
Life Problems ◽  
Life Decision

Formulation of LPs and IPs is a technique to convert real life decision problems into a mathematical model. This model consists of a linear objective function and a set of linear constraints expressed in the form of a system of equations or inequalities. In this paper, we present formulation from real life problem as an art. We discuss formulation through real life example and solve them using computer techniques AMPL and LINDO. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17068 Dhaka Univ. J. Sci. 61(2): 185-191, 2013 (July)

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 %.

Classification of mathematical models of technological design

2021 ◽  
pp. 68-71
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Technological Process ◽  
Process Design ◽  
Geometric Parameters ◽  
Technological Design ◽  
Technological Processes ◽  
Technological Preparation

The use of mathematical models is of great importance for the automation of the design of technological processes. Representation of the geometric parameters of the part in the form of mathematical models allows automating the development of the structure and calculation of the parameters of the technological process, which is important for the complete digitalization of the technological preparation of production. Keywords: technological process, design, mathematical model, digitalization. [email protected]

Methodology for calculating the parameters of adaptive decision support systems with service elements

2020 ◽  
pp. 63-70
Author(s):  
Э.Э. Акимкина
Keyword(s):  
Mathematical Model ◽  
Information Processing ◽  
Decision Support ◽  
Decision Support System ◽  
Objective Function ◽  
Decision Support Systems ◽  
Support System ◽  
Support Systems ◽  
Computer Tools ◽  
Internal Influences

Проанализированы компьютерные средства для реализации адаптивной системы поддержки принятия решений; показано, что в качестве основных элементов обслуживания используются контролируемые серверы, в качестве основных инструментов обработки информации - запросы. Сформулирована целевая функция адаптивной системы поддержки принятия решений, направленная на максимизацию количества обрабатываемых в единицу времени запросов при различных меняющихся внешних и внутренних воздействиях. Методика расчета параметров исследуемой системы строится на основе предложенной математической модели. Computer tools are analyzed for implementing an adaptive decision support system; It is shown that controlled servers are used as the main service elements, and requests are used as the main information processing tools. The objective function of the adaptive decision support system is formulated, aimed at maximizing the number of requests processed per unit time under various changing external and internal influences. The methodology for calculating the parameters of the studied system is based on the proposed mathematical model.

scholarly journals Optimal Operation Parameter Estimation of Energy Storage for Frequency Regulation

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1782 ◽  
Author(s):  
Sung-Min Cho ◽  
Jin-Su Kim ◽  
Jae-Chul Kim
Keyword(s):  
Energy Storage ◽  
Objective Function ◽  
Electricity Market ◽  
Optimal Parameter ◽  
Storage System ◽  
Optimal Operation ◽  
Electric Power System ◽  
Frequency Regulation ◽  
Optimal Parameters ◽  
Calculation Algorithm

This study proposes a method for optimally selecting the operating parameters of an energy storage system (ESS) for frequency regulation (FR) in an electric power system. First, the method allows the optimal objective function of the selected parameters to be set in a flexible manner according to the electric market environment. The objective functions are defined so that they could be used under a variety of electricity market conditions. Second, evaluation frequencies are created in order to simulate the overall lifespan of the FR-ESS. Third, calendar and cycle degradation models are applied to the battery degradation, and are incorporated into evaluations of the degradation progress during the entire FR-ESS lifespan to obtain more accurate results. A calendar life limit is set, and the limit is also considered in the objective function evaluations. Fourth, an optimal parameter calculation algorithm, which uses the branch-and-bound method, is proposed to calculate the optimal parameters. A case study analyzes the convergence of the proposed algorithm and the results of the algorithm under various conditions. The results confirmed that the proposed algorithm yields optimal parameters that are appropriate according to the objective function and lifespan conditions. We anticipate that the proposed FR-ESS algorithm will be beneficial in establishing optimal operating strategies.

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