scholarly journals Graph model development in the context of the grain cleaning machine

2018 ◽  
Vol 224 ◽  
pp. 05012 ◽  
Author(s):  
Andrey Butovchenko ◽  
Artem Dorochenko ◽  
Inna Kotelnikova
Keyword(s):  
Mathematical Model ◽  
Model Development ◽  
Graph Model ◽  
Oriented Graph ◽  
Control Factors ◽  
Schematic Layout ◽  
Cleaning Machine ◽  
General Mathematical Model ◽  
Output Characteristics ◽  
Working Bodies

Schematic layout and graph model of seed-cleaning unit are introduced in the article. Input vector, vector of control factors and vector of output characteristics are mentioned. The general mathematical model of purification section process is given. This model together with an oriented graph allows to conduct a program forecast and to find out the rational directions of increasing the efficiency of the work of individual working bodies and the system as a whole.

Mathematical Model of Flat Surface Machining Inaccuracies due to Elastic Strains of Technological System

2018 ◽  
pp. 1-14 ◽  
Author(s):  
I. I. Kravchenko
Keyword(s):  
Mathematical Model ◽  
Vector Field ◽  
Model Development ◽  
Technological System ◽  
Mutual Arrangement ◽  
Real Surface ◽  
Main Bearing ◽  
Flat Surfaces ◽  
Internal Surfaces ◽  
Elastic Strains

The paper considers the mathematical model development technique to build a vector field of the shape deviations when machining flat surfaces of shell parts on multi-operational machines under conditions of anisotropic rigidity in technological system (TS). The technological system has an anisotropic rigidity, as its elastic strains do not obey the accepted concepts, i.e. the rigidity towards the coordinate axes of the machine is the same, and they occur only towards the external force. The record shows that the diagrams of elastic strains of machine units are substantially different from the circumference. The issues to ensure the specified accuracy require that there should be mathematical models describing kinematic models and physical processes of mechanical machining under conditions of the specific TS. There are such models for external and internal surfaces of rotation [2,3], which are successfully implemented in practice. Flat surfaces (FS) of shell parts (SP) are both assembly and processing datum surfaces. Therefore, on them special stipulations are made regarding deviations of shape and mutual arrangement. The axes of the main bearing holes are coordinated with respect to them. The joints that ensure leak tightness and distributed load on the product part are closed on these surfaces. The paper deals with the analytical construction of the vector field F, which describes with appropriate approximation the real surface obtained as a result of modeling the process of machining flat surfaces (MFS) through face milling under conditions of anisotropic properties.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

Research on an axial-mounted dual magnetostrictive material rods-based electro-hydrostatic actuator

2021 ◽  
pp. 1045389X2110145
Author(s):  
Yuchuan Zhu ◽  
Chang Liu ◽  
Yunze Song ◽  
Long Chen ◽  
Yulei Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Flow Rate ◽  
Flow Distribution ◽  
Maximum Flow ◽  
Magnetostrictive Material ◽  
Simulation Techniques ◽  
Motion State ◽  
New Type ◽  
Output Characteristics ◽  
Active Rectification

In this paper, an electro-hydrostatic actuator driven by dual axial-mounted magnetostrictive material rods-based pumps (MMPs) with a new type of active rectification valve is designed in the current study. Based on flow distribution of the active rectification valve and driving energy provided by two MMPs, the actuator can output continuous and bidirectional displacement. By establishing a mathematical model of the actuating system, using simulation techniques, the change rule of hydraulic cylinder’s motion state caused by different driving signals are studied and analyzed. Test equipment platform is constructed in the laboratory to test the output characteristics and confirm the feasibility of the new concept. The experimental results indicate that the maximum flow rate can reach approximately 2.7 L·min−1, while the operating frequency is 180 Hz.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Matrix-graph model of the polymer materials destruction process

2018 ◽  
Vol 80 (3) ◽  
pp. 50-55
Author(s):  
A. A. Khvostov ◽  
S. G. Tikhomirov ◽  
I. A. Khaustov ◽  
A. A. Zhuravlev ◽  
A. V. Karmanov
Keyword(s):  
Mathematical Model ◽  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Graph Model ◽  
Polymer Materials ◽  
Simulation Environment ◽  
Destruction Process ◽  
Molecular Weights ◽  
The Mathematical Model

The paper deals with the problem of mathematical modeling of the process of thermochemical destruction using the theory of graphs. To synthesize a mathematical model, the Markov chain is used. For the formalization of the model a matrix-graph method of coding is used. It is proposed to consider the process of destruction as a random process, under which the state of the system changes, characterized by the proportion of macromolecules in each fraction of the molecular mass distribution. The intensities of transitions from state to state characterize the corresponding rates of destruction processes for each fraction of the molecular weight distribution (MWD). The processes of crosslinking and polymerization in this work have been neglected, and it is accepted that there is a probability of transition from any state with a lower order index (corresponding to fractions with higher molecular weights) to any state with a higher index (corresponding fractions with lower molecular weights). A computational formula is presented for estimating the number of arcs and model parameters from a given number of fractions of the molecular weight distribution of the polymer. An example of coding in a matrix form of a graph model of the process of degradation of polybutadiene in solution for the case of six fractions of the molecular weight distribution is shown. As the simulation environment, the interactive graphical simulation environment of MathWorks Simulink is used. To evaluate the parameters of the mathematical model, experimental studies of the degradation of polybutadiene in solution were carried out. The chromatography of the polybutadiene solution was used as the initial data for the estimation of the MWD polymer. The considered matrix-graph representation of the structure of the mathematical model of the polymer destruction process makes it possible to simplify the compilation of the model and its software implementation in the case of a large number of vertices of the graph describing the process of destruction

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