Chaotic Phenomena Induced by the Fast Plastic Deformation of Metals During Cutting

2005 ◽  
Vol 73 (2) ◽  
pp. 240-245 ◽  
Author(s):  
Zoltan Palmai
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Shear Stress ◽  
General Structure ◽  
Equation System ◽  
Qualitative Description ◽  
Balance Equations ◽  
Different Types ◽  
Energy Equations ◽  
The Mathematical Model

In the present study the examination of chip formation is focused on the primary shear zone, which is divided into two layers, and the variation of shear stress and temperature in time are given by two mechanical balance equations and three energy equations. All the five evolution differential equations are autonomous and nonlinear. The material characteristics are determined by an exponential constitutive equation. The mathematical model is suitable for the qualitative description of different types of chips, such as continuous chips and periodic or aperiodic shear localized chips, which is demonstrated by the general structure and typical solutions of the equation system.

scholarly journals Mathematical modeling of plastic deformation of a tube from dispersion-hardened aluminum alloy

2018 ◽  
Vol 243 ◽  
pp. 00008 ◽  
Author(s):  
Oleg Matvienko ◽  
Olga Daneyko ◽  
Tatyana Kovalevskaya
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Plastic Deformation ◽  
External Pressure ◽  
Dislocation Loops ◽  
Balance Equations ◽  
Deformable Solid ◽  
Deformation Defects ◽  
Resistance Decrease ◽  
The Mathematical Model

The influence of the internal and external pressure subjected to the tube from dispersion-hardened aluminium alloy was investigated. The approach which combines methods of crystal plasticity and mechanics of deformable solid was used to explore the limits of elastic and plastic resistance. The mathematical model of plastic deformation includes balance equations for deformation defects with regard to the generation and annihilation of shear dislocations, vacancy and interstitial prismatic dislocation loops, and dislocations in dipole configurations of vacancy and interstitial types and also equilibrium equation, geometrical and physical relations between the deformations, displacements and stresses. It has been established that as the temperature increases, the limits of the elastic and plastic resistance decrease. Results of investigation demonstrate that the hardening the alloy by nanoparticles significantly improves the strength characteristics of the material.

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

scholarly journals Mathematical model for reliability indicators calculation of tethered UAV hybrid navigation system

2021 ◽  
Vol 2091 (1) ◽  
pp. 012033
Author(s):  
V M Vishnevsky ◽  
K A Vytovtov ◽  
E A Barabanova ◽  
V E Buzdin
Keyword(s):  
Mathematical Model ◽  
Navigation System ◽  
Analytical Method ◽  
Mathematical Expression ◽  
Equation System ◽  
Kolmogorov Equation ◽  
Reliability Indicators ◽  
Technical Vision ◽  
The Mathematical Model ◽  
First Time

Abstract The mathematical model for reliability indicators calculation of the hybrid navigation system containing microwave and technical vision subsystems is proposed in this paper for the first time. The proposed method is based on the translation matrix concept of solutions to the Kolmogorov equation system and it allows us to obtain the mathematical expression of availability factor, downtime ratio, and other reliability indicators. Also the presented approach allows finding the reliability indicators for the cases of jump change of transition intensities caused by external influences. Besides the analytical method can be used for investigation of hybrid navigation system transient mode functioning. The results of the numerical calculations clearly demonstrated correctness of the proposed approach.

An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

2021 ◽  
pp. 0734242X2110337
Author(s):  
Tea Sokač ◽  
Anita Šalić ◽  
Dajana Kučić Grgić ◽  
Monika Šabić Runjavec ◽  
Marijana Vidaković ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Simulation ◽  
Process Conditions ◽  
Air Flow Rate ◽  
Optimal Process ◽  
Composting Process ◽  
Different Types ◽  
Adiabatic Reactor ◽  
The Mathematical Model ◽  
Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

Experimental and Theoretical Investigation of Performance of a Solar Chimney Model Part II: Model Development and Validation

2021 ◽  
Vol 5 (2) ◽  
Author(s):  
Ibrahim A Abuashe ◽  
Bashir H Arebi ◽  
Essaied M Shuia
Keyword(s):  
Mathematical Model ◽  
Power Output ◽  
Model Development ◽  
Geometrical Parameters ◽  
Balance Equations ◽  
Solar Chimney ◽  
And Performance ◽  
Development And Validation ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model based on the momentum, continuity and energy balance equations was developed to simulate the behavior of the air flow inside the solar chimney system. The model can estimate the power output and performance of solar chimney systems. The developed mathematical model is validated by the experimental data that were collected from small pilot solar chimney; (experiment was presented in part I). Good agreement was obtained between the experimental results and that from the mathematical model. The model can be used to analyze the solar chimney systems and to determine the effect of geometrical parameters such as chimney height and collector diameter on the power output and the efficiency of the system

Asymptotic Model of Free Convection Flow on a Vertical Surface in Porous Media with Newtonian Heating

2015 ◽  
Vol 756 ◽  
pp. 469-475
Author(s):  
Anna A. Bocharova ◽  
Irina V. Plaksina ◽  
Andrey A. Obushnyy
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Free Convection ◽  
Vertical Surface ◽  
Momentum Equation ◽  
Convection Flow ◽  
Asymptotic Model ◽  
Free Convection Flow ◽  
Energy Equations ◽  
The Mathematical Model

The mathematical model based on system of momentum and energy equations for free convection flow along a vertical surface in porous media under boundary conditions of the third sort is solved analytically using the method of matched asymptotic expansions. The region of validity for boundary layer model and expansions for stream function and temperature with parameter of perturbations were defined. The dependence of characteristic flow from governing dimensionless parameters and was analyzed numerically. The influence of viscous and convective terms of momentum equation in the proposed mathematical model significantly increases the rate of heat transfer on plate in porous media in comparison with Darsy flow model.

Rim Sealing of Rotor-Stator Wheelspaces in the Absence of External Flow

1991 ◽  
Author(s):  
J. W. Chew ◽  
S. Dadkhah ◽  
A. B. Turner
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Reynolds Numbers ◽  
External Flow ◽  
Rotating Disc ◽  
Different Types ◽  
The Mathematical Model

Sealing of the cavity formed between a rotating disc and a stator in the absence of a forced external flow is considered. In these circumstances the pumping action of the rotating disc may draw fluid into the cavity through the rim seal. Minimum cavity throughflow rates required to prevent such ingress are estimated experimentally and from a mathematical model. The results are compared with other workers’ measurements. Measurements for three different types of rim seal are reported for a range of seal clearances and for rotational Reynolds numbers up to 3 × 106. The mathematical model is found to correlate the experimental data reasonably well.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

2011 ◽  
Vol 04 (02) ◽  
pp. 207-225 ◽  
Author(s):  
J. C. MISRA ◽  
A. SINHA ◽  
G. C. SHIT
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
External Magnetic Field ◽  
Volumetric Flow Rate ◽  
Hematocrit Level ◽  
Flow Through ◽  
The Mathematical Model

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.

An Application for Analysis of Temperature during Cold Rolling

2013 ◽  
Vol 199 ◽  
pp. 131-136
Author(s):  
Olena Yevtushenko
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Temperature Field ◽  
Numerical Analysis ◽  
Cold Rolling ◽  
Partition Ratio ◽  
Transient Temperature ◽  
Heat Partition ◽  
Transient Temperature Field ◽  
The Mathematical Model

The problem of software creation for the analysis of transient temperature field in cold rolling of metals is under consideration. Firstly, the mathematical model of the process of heating the strip and rolls at cold rolling it is proposed. This model assumes that the generation of heat during the rolling takes place due to friction on the contact surface of the rolls and the strip as well as plastic deformation of the strip material. Next, some fragments of created application for the purpose of an overall numerical analysis of heat partition ratio between the rolls and a strip as well as the temperature in any point of these elements are presented.

scholarly journals DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE RESEARCH OF THE DYNAMICS OF VIBRATION MILL WITH TWO DRIVES FOR BULK MATERIALS FINE GRINDING

2021 ◽  
pp. 89-99
Author(s):  
Volodymyr Topilnytskyy ◽  
Dariya Rebot
Keyword(s):  
Mathematical Model ◽  
Optimal Designs ◽  
High Tech ◽  
Bulk Materials ◽  
Fine Grinding ◽  
Different Types ◽  
Parameterized Model ◽  
The Mathematical Model ◽  
Universal Equipment ◽  
Vibration Mill

Reducing by grinding the size of various materials as raw materials for its further use is an urgent applied task. The requirements for the final product obtained by fine grinding are its homogeneity in shape and size of individual parts. It is necessary to reduce the time of the grinding operation, reduce energy consumption to obtain a unit of product of the required quality. One way to solve the problem is to use high-tech universal equipment, namely mills for fine grinding of materials. One way to solve the given problem is to use high-tech universal equipment, namely mills for fine grinding of materials. Their optimal design, construction, manufacture and operation are ensured by studying their dynamics at the stage of their development. In particular, such a study of the dynamics can be carried out on the basis of previously created mathematical models of these mills. The use of computer technology and appropriate mathematical CAD systems will speed up and optimize the process of studying the dynamics of the corresponding mill of fine grinding of materials. The purpose of the research is to build a mathematical nonlinear parameterized model of vibrating mill with two drives for bulk materials fine grinding for further study on its basis the dynamics of the mill with the development of optimal designs for mills with similar structure and the principle of operation and selection of optimal modes of operation. The mathematical model is presented as a system of expressions describing the of the mill points motion, which will include in the form of symbolic symbols all its parameters (kinematic, geometric, dynamic, force). This model is constructed using the Lagrange equation of the second kind and asymptotic methods of nonlinear mechanics. The mathematical model for studying of the dynamics of vibration mill with two drives for bulk materials fine grinding is nonlinear and universal. The non linearity of the model makes it possible to adequately determine of the above parameters influence on the amplitude of oscillations of the mill working chamber as the main factor in the intensity in the technological process of the fine grinding bulk materials fine grinding. The possibility of a wide range of changes in the parameters of the mill in the obtained models makes it universal based on the possibility of application for the study of dynamic processes in vibrating mills of different types with two or one drive which are different by shape, size, location of the suspension and more. This model can also be used to develop optimal designs for vibrating mills for different industries, which will be used to grind different types of materials in different volumes and productivity.

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