Effect of cutting width on the optimum size of bars and boards when cutting sawlogs with sawing three bars of equal thickness and four pairs of side boards

10.12737/4517 ◽  
2014 ◽  
Vol 4 (2) ◽  
pp. 128-135 ◽  
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimality Criterion ◽  
Constraint Equations ◽  
First Pass ◽  
Method Of Lagrange Multipliers ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Equal Thickness

There is a task of cutting optimization of sawlogs considering the width of cut. Output of sawn timber produced after the first pass of cutting sawlogs is chosen as optimality criterion. The objective function is represented as the sum of the cross-section of bars and planks. Such a mathematical model of the objective function establishes a relationship between size of bars and planks. Constraint equations represent the relationship of sawlogs diameter with the size of bars and boards, as well as the width of the cut. To solve the mathematical model the method of Lagrange multipliers is used.

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 %.

Study on High Frequency Hydraulic Exciter Based on Rotary Valve Control

2012 ◽  
Vol 490-495 ◽  
pp. 1441-1445 ◽  
Author(s):  
Jian Zhuo Zhang ◽  
Li Zhe Guan ◽  
Kang Kang Li
Keyword(s):  
Mathematical Model ◽  
High Frequency ◽  
Rotary Valve ◽  
Exciting Frequency ◽  
Working Principle ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Valve Control

A kind of hydraulic exciter based on rotary valve control was studied in this paper, the composition of the exciter and its working principle were introduced, and the mathematical model of the system was established. The characters of the system were simulated using MATLAB. From the results of the simulation, we get the relationship of the amplitude of Vibration oil cylinder between the system’s pressure and the exciting frequency. The results can provide theoretical bases to design the hydraulic exciter.

Shaping Law and Motion Design in NC-ECM under Effect of Twiste Angle

2011 ◽  
Vol 128-129 ◽  
pp. 1010-1014
Author(s):  
Rui Wu ◽  
Dan Wen Zhang ◽  
Juan Sun
Keyword(s):  
Mathematical Model ◽  
Electrochemical Machining ◽  
Experimental Results ◽  
Working Face ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Motion Design

The twiste angle has a great effect on shaping law and stability of Numerical Controlled Electrochemical Machining (NC-ECM) process. In order to avoid the disadvantages caused by twiste angle, a methode of study shaping law by dispersing cathode working face in NC-ECM was proposed, and a mathematical model of the shaping law with the effects of twiste angle has been established in this paper. The mathematical model disclosed the relationship of twiste angle β, feeding velocity vf and thickness of removal material h in NC-ECM. Theoretical and experimental results show the the mathematical model of shaping law described in this paper can be considered as a useful reference and is helpful for the analysis of the NC-ECM and general ECM process.

Investigation on Silicon-Glass Electrostatic Bonding Time Experiment

2011 ◽  
Vol 483 ◽  
pp. 78-82
Author(s):  
Xiao Wei Liu ◽  
Jia Lu Tang ◽  
Rong Yan Chuai ◽  
Hai Feng Zhang ◽  
Xi Lian Wang
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Bonding Process ◽  
Bonding Time ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Electrostatic Bonding

In this paper, we make a detail analysis of some factors, which affects the electrostatic bonding process. According to the electrical properties of glass, combined with the principle of electrostatic bonding, we analysed the relationship of critical bonding time, voltage and temperature as well as the factors which affect electrostatic bonding. Then we come up with the mathematical model of the intensity and temperature of electrostatic bonding. In accordance with the above-mentioned formula and the experimental data, we can get the following conclusions: the intensity of electrostatic bonding is much greater between 280°C to 370°C; the best temperature for this bonding is about 350°C; however, when the temperature is below 280°C,the intensity of electrostatic bonding is lower due to the great impact of particles under low temperature; but when the temperature is higher than 370°C,the mismatch of coefficient of thermal expansion of silicon and glass gets larger, then as a result, the intensity of this bonding has a significant decrease with the increasing of temperature.

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.

Temperature Influence on Performance of Oxidation Ponds

1991 ◽  
Vol 24 (5) ◽  
pp. 85-96 ◽  
Author(s):  
Qingliang Zhao ◽  
Zijie Zhang
Keyword(s):  
Mathematical Model ◽  
Temperature Influence ◽  
Field Scale ◽  
Experiment Data ◽  
Computer Technique ◽  
Oxidation Pond ◽  
Optimum Model ◽  
Oxidation Ponds ◽  
The Mathematical Model ◽  
The Relationship

By means of simulated tests of a laboratory–scale oxidation pond model, the relationship between BOD5 and temperature fluctuation was researched. Mathematical modelling for the pond's performance and K1determination were systematically described. The calculation of T–K1–CeCe/Ci) was complex but the problem was solved by utilizing computer technique in the paper, and the mathematical model which could best simulate experiment data was developed. On the basis of experiment results,the concept of plug–ratio–coefficient is also presented. Finally the optimum model recommended here was verified with the field–scale pond data.

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.

Design of the Conjugate Cam Induction Hardening Mechanism and Establishment of the Motion Controlling Mathematical Model

2012 ◽  
Vol 155-156 ◽  
pp. 726-730
Author(s):  
Zhong Hua Li ◽  
Qian Tang ◽  
Di Yan ◽  
Jie Wu
Keyword(s):  
Mathematical Model ◽  
Induction Hardening ◽  
Uniform Motion ◽  
Hardening Mechanism ◽  
Kinematic Relationship ◽  
Nc Machine ◽  
The Common ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Basic Motion

The common methods of cam induction hardening are discussed at present. By analyzing the basic motion law of conjugate cam, a new induction hardening mechanism is designed. The motion controlling mathematical model is built on the basis of the kinematic relationship of the transmission of the induction hardening mechanism. Through the mathematical model calculation, we can get angular velocity of the workbench, then realize that single axis on NC machine controls the inductor to make isometric uniform motion relative to the cam surface, so that the cam hardening depth distribution is uniform.

scholarly journals Relation between swine weight and morphometric measurements

2020 ◽  
Vol 9 (9) ◽  
pp. e891998013
Author(s):  
Mônica Calixto Ribeiro de Holanda ◽  
Marco Aurélio Carneiro de Holanda ◽  
Leandro Ricardo Rodrigues de Lucena
Keyword(s):  
Mathematical Model ◽  
Body Weight ◽  
Regression Models ◽  
Hip Circumference ◽  
Morphometric Measurements ◽  
Large White ◽  
Male And Female ◽  
Lactation Phase ◽  
Relationship Of ◽  
The Relationship

Objective was to define a mathematical model that better explain the relationship of the animals weight depending not only on the animals age but also on the animals morphometric measurements. 40 piglets, half Duroc-Large White blood, were used, 20 males and 20 females, from 3 to 35 days of age (lactation phase) initially weighing 1.518 ± 0.121 kg and from 36 to 66 days of age (calving phase) with a body weight of 7.010 ± 0.704 kg. The animals were weighed weekly on a digital balance. The relationship of animal weight, age and morphometric measurements of male and female piglets were performed using regression models: existing, linear and power. The models were evaluated according to nine criterialinear model was the most adequate to explain the weight of male pigs, while for female pigs was the power. The age of the pig, the shank and palette length, as well as the circumference of the shank jointly explain the weight of the male piglets. The weight of females is explained jointly by age, body length, thorax and hip circumference.

Sign in / Sign up

Export Citation Format

Share Document