scholarly journals MATHEMATICAL MODEL OF THE DYNAMICS DISPERSED MEDIA IN THE SHAPING PROCESSES BILLETS OF POWDER METALLURGY

2021 ◽  
pp. 70-75
Author(s):  
Yaroslav Ivanchuk ◽  
Rostislav Iskovych-Lototsky ◽  
Ivan Sevostianov ◽  
Natalia Veselovska ◽  
Olexander Manzhilevskyy
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Powder Metallurgy ◽  
Local Area ◽  
Dynamic Force ◽  
Powder Metal ◽  
Various Boundary Conditions ◽  
Dispersed Particles ◽  
Dispersed Medium ◽  
Vibration Compaction

A mathematical model has been developed for changing the dynamics of the movement of a dispersed medium in vibro-impact technological processes of shaping of powder metallurgy blanks. On the basis of the problem of two-dimensional dynamic interaction of dispersed particles of powder metal of a spacer dispersed medium, the obtained differential equation in partial derivatives under various boundary conditions. This equation describes the state of the local area of the dispersed medium. In it, the powder material of the workpiece passes from the concentrated dynamic force to the excitation phase. A partial differential equation is obtained. It describes the change in normal stress during vibrations of a dispersed medium during vibration compaction of a workpiece in powder metallurgy.

Simulation the sedimentation of a finely dispersed medium under the impact of pressure waves

2012 ◽  
Vol 9 (2) ◽  
pp. 80-85
Author(s):  
C.I. Mikhaylenko ◽  
Yu.R. Valeeva
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Disperse System ◽  
Dispersion Medium ◽  
Solid Particles ◽  
Pressure Waves ◽  
Dispersed Particles ◽  
Coagulation Of Particles ◽  
Dispersed Medium ◽  
The Impact

A mathematical model for a disperse system of gas-solid particles when passing pressure waves is decribed. The following assumptions are made: dispersed particles are capable of coagulation with increasing concentration; the dispersed particles are acted upon by the Stokes forces on the side of the dispersion medium and by gravity. The results of numerical simulation of the processes of sedimentation of a dispersed medium are presented. It is shown that one of the mechanisms of precipitation of fine disperced medium can be coagulation of particles during the passage of pressure waves.

Mathemathical Model of Powder Sintering with Nano- and Microadditives

2011 ◽  
Vol 312-315 ◽  
pp. 1204-1207 ◽  
Author(s):  
I.E. Ignatiev ◽  
V.I. Bulanov ◽  
A.N. Dmitriev
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Powder Metallurgy ◽  
Thin Layer ◽  
Powder Materials ◽  
Metal Powders ◽  
Powder Metal ◽  
Powder Sintering ◽  
Metal Sintering

One of the problems of powder metallurgy still remaining is the problem of billets shrinkage at sintering. Introduction of a small impurity coating consisting of a very thin layer of the particles on the basic powder is a known method of compacting at sintering of powder materials. The mathematical modeling of such a process encounters ambiguity some issues of the sintering theory of metal powders, therefore forcedly leans on experiments. A mathematical model of powder metal sintering with nano- and microadditives is presented.

DURATECH PYROVAN HC

Alloy Digest ◽  
2008 ◽  
Vol 57 (7) ◽  
Keyword(s):  
Fracture Toughness ◽  
Wear Resistance ◽  
Powder Metallurgy ◽  
Physical Properties ◽  
Heat Treating ◽  
Powder Metal ◽  
Steel Company ◽  
Specialty Steel

Abstract DuraTech Pyrovan HC is air hardened and has a combination of strength, wear resistance, and toughness for use in blanking and sizing dies. The alloy is made by powder metallurgy. This datasheet provides information on composition, physical properties, hardness, and elasticity as well as fracture toughness. It also includes information on heat treating, machining, and powder metal forms. Filing Code: TS-667. Producer or source: Latrobe Specialty Steel Company.

BÖHLER S692/S693 MICROCLEAN

Alloy Digest ◽  
2017 ◽  
Vol 66 (2) ◽  
Keyword(s):  
Powder Metallurgy ◽  
Physical Properties ◽  
Small Diameter ◽  
Heat Treating ◽  
Powder Metal ◽  
High Carbon ◽  
Low Sulfur ◽  
Machining Characteristics

Abstract Böhler (or Boehler) S692 Microclean is a high sulfur, high carbon PM M4, with higher manganese and 0.22 sulfur for improved machining characteristics, and is available in rounds greater than or equal to 64.16 mm (2.562 in.) diameter. S693 Microclean is the low sulfur version of high carbon PM M4, available in flats and small diameter rounds. PM refers to powder metallurgy. This datasheet provides information on composition, physical properties, hardness, and elasticity. It also includes information on surface qualities as well as heat treating and powder metal forms. Filing Code: TS-739. Producer or source: Böhler Edelstahl GmbH & Company KG.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

A MATHEMATICAL MODEL OF ANEURYSM OF CIRCLE OF WILLIS

1995 ◽  
Vol 03 (03) ◽  
pp. 653-659 ◽  
Author(s):  
J. J. NIETO ◽  
A. TORRES
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Nonlinear Analysis ◽  
Existence Of Solutions ◽  
Circle Of Willis ◽  
Second Order ◽  
Qualitative Properties

We introduce a new mathematical model of aneurysm of the circle of Willis. It is an ordinary differential equation of second order that regulates the velocity of blood flow inside the aneurysm. By using some recent methods of nonlinear analysis, we prove the existence of solutions with some qualitative properties that give information on the causes of rupture of the aneurysm.

scholarly journals Enhanced Central System of the Traversing Rod for High-Performance Rotor Spinning Machines

2017 ◽  
Vol 17 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Jan Valtera ◽  
Petr Žabka ◽  
Jaroslav Beran
Keyword(s):  
Mathematical Model ◽  
High Performance ◽  
Mechanical Energy ◽  
Optimal Number ◽  
Dynamic Force ◽  
Rectilinear Motion ◽  
Central System ◽  
Rotor Spinning ◽  
New System

Abstract The paper deals with the improvement of central traversing system on rotor spinning machines, where rectilinear motion with variable stroke is used. A new system of traversing rod with implemented set of magnetic-mechanical energy accumulators is described. Mathematical model of this system is analysed in the MSC. Software Adams/View and verified by an experimental measurement on a real-length testing rig. Analysis results prove the enhancement of devised traversing system, where the overall dynamic force is reduced considerably. At the same time, the precision of the traversing movement over the machine length is increased. This enables to increase machine operating speed while satisfying both the maximal tensile strength of the traversing rod and also output bobbin size standards. The usage of the developed mathematical model for determination of the optimal number and distribution of accumulators over the traversing rod of optional parameters is proved. The potential of the devised system for high-performance rotor spinning machines with longer traversing rod is also discussed.

Mathematical Modeling of the λ Switch

2010 ◽  
pp. 573-603
Author(s):  
Dmitriy Laschov ◽  
Michael Margaliot
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Gene Regulation ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Verbal Description ◽  
Quantitative Understanding ◽  
Living Organisms ◽  
Scientific Challenge

Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the Lambda switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch.

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