scholarly journals Deformation of cylindrical shells of steel 45 under complex loading

2019 ◽  
Vol 97 ◽  
pp. 04025
Author(s):  
Stepan Cheremnykh ◽  
Vladimir Zubchaninov ◽  
Vadim Gultyaev
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Circular Cylindrical Shell ◽  
Compressive Force ◽  
Complex Loading ◽  
Theory Of Elasticity ◽  
Complex Nature ◽  
State Technical ◽  
Axial Compressive Force ◽  
The Mathematical Model

Reviewing the numerical simulation of the process of non-proportional elastic-plastic deformation of steel 45 by a knot of constant curvature, taking into account the complex nature of deformation under complex subcritical loading by axial compressive force and torque for a thin-walled circular cylindrical shell. The theory of Quas and simple processes of A. A. Ilyushin and the mathematical model of V. Zubchaninov were applied taking into consider the parameters of the complex loading for plane trajectories To assess the accuracy of accepted theories, the simulation results are compared with experimental results, received on the automated complex СNcomputer in the laboratory of the faculty of «Strength of materials and theory of elasticity and plasticity» of the Tver state technical University. Was introduced the scheme of calculations disproportionate plastic deformation of steel 45 using the proposed mathematical model showed a satisfactory result and recommended for further use. Remarks, that in the described processes the lack of some parameters complex loading in approximations reduces the accuracy of the final calculated values, differences significantly compared to the experimental data.

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.

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.

Vibration Analysis of a Vertical Roller Mill: Modeling and Validation

2014 ◽  
Author(s):  
Engin H. Çopur ◽  
Metin U. Salamci ◽  
Selahattin Gülbeyaz
Keyword(s):  
Mathematical Model ◽  
Vibration Analysis ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Physical Parameters ◽  
Roller Mill ◽  
Vibration Tests ◽  
Working Parameters ◽  
The Mathematical Model ◽  
Vertical Roller

In this paper, vibration characteristics of a Vertical Roller Mill (VRM) are studied by using physical parameters of an operating VRM. The mathematical model is derived and simulated for a set of working parameters. Mechanical properties of the grinding material and the physical properties of the mechanical construction are used in the vibration model in order to obtain more realistic results. Simulation results are presented which give critical frequencies of the VRM. The effects of the hydraulic compressive force to the vibration characteristics are investigated. The effects of the material feeding rate (which affects the mineral thickness to be grinded) to the vibration characteristics are also simulated. In order to validate the mathematical model, a set of experimental vibration tests are performed on the VRM. Vibrations are measured during the run-down procedure of the VRM in order to determine natural frequencies of the mill as well as excitation frequencies of the system. The measurements showed the validity of the proposed mathematical model for the vibration analysis of the VRM.

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.

scholarly journals RESULTS OF RESEARCH OF PROCESSES OF EXTRACTION OF CUT WITH IMPLEMENTATION OF ULTRASOUND OSCILLATIONS ON THE INSTRUMENT

2020 ◽  
pp. 32-43
Author(s):  
Volodymyr Rutkevych
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Contact Pressure ◽  
Physical And Mechanical Properties ◽  
Torsional Vibrations ◽  
Ultrasonic Vibrations ◽  
Thread Rolling ◽  
Deformation Processes ◽  
The Mathematical Model

The possibility of improving the quality of rubber due to the directional action of various types of ultrasonic vibrations, with the aim of forming the maximum compressive residual stresses, will ultimately improve the performance of the rize joint under variable loads. The process of rizenization using forced ultrasonic vibrations has been investigated. When compiling a mathematical model of the process of extrusion of rubber with the imposition of ultrasonic vibrations on the tool, it was assumed that the phenomenon of surface hardening has little effect on the magnitude of the contact pressure and the friction force during plastic deformation. This assumption allows us to simplify the mathematical model by not taking into account this factor. New methods of calculating the contact pressure and specific frictional force during rubber extrusion with the imposition of axial, radial and torsional vibrations are proposed. The description of the deformation processes with the superposition of ultrasonic vibrations was carried out on the basis of the rheological model of deformation of an ideal elastic-plastic body. The work developed nonlinear mathematical models for the study of plastic deformation processes, consisting of equations of tool displacement and equations taking into account the elastic-plate properties of the processed material. This structure of the mathematical model most fully reflects the processes occurring during thread rolling with the imposition of ultrasonic vibrations. As a result of the research, it has been established that the use of forced ultrasonic vibrations during machining with a tool will significantly increase the productivity, tool durability and quality of the processed surface, especially when processing with special physical and mechanical properties. In the study of the contact interaction of the tool with the part with the imposition of ultrasonic vibrations in the axial and radial directions, as well as in the imposition of torsional vibrations, it was found that the use of axial vibrations is on average 50 % more effective.

Mathematical Model and Program Development for the Efficient Process Conditions Determination during FeC0.15Cr12Ni2 Steel Diamond Smoothing

2016 ◽  
Vol 684 ◽  
pp. 477-482 ◽  
Author(s):  
Aleksei Nicolaevich Shvetcov ◽  
Dmitrii Leonidovich Skuratov
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Surface Layer ◽  
Program Development ◽  
Synthetic Diamond ◽  
Process Conditions ◽  
Deformation Degree ◽  
Efficient Process ◽  
The Mathematical Model

In this paper the mathematical model and the program based on this model for efficient process conditions during a diamond smoothing is introduced. The mathematical model has been tested with heatproof martensite category steel FeC0.15Cr12Ni2 by the synthetic diamond DSB-1 using as a smoothing tool. The mathematical model takes into account plastic deformation degree which could have both smoothing and reinforcing nature. Through the smoothing conditions the surface has a microroughnesses crumpling but reinforcing conditions involve also surface layer microhardness increasing.

Experimental Study and Mathematical Modeling of Development of Crystallographic Slip in Heterophase FCC Alloys

2014 ◽  
Vol 1013 ◽  
pp. 300-306
Author(s):  
Nina Grigorjeva ◽  
Olga Daneyko ◽  
Tatiana Kovalevskaya
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Experimental Study ◽  
Plastic Deformation ◽  
Experimental Results ◽  
Plastic Behavior ◽  
Crystallographic Slip ◽  
Fcc Alloys ◽  
Fcc Materials ◽  
The Mathematical Model

The experimental results of plastic behavior investigation of Al-6%Zn-3%Mg alloy are compared with the mathematical model of plastic deformation of dispersion hardened FCC materials with undeformed particles. Were determined the factors, when model properly describes the regularities of slip development in this alloy.

The Mathematical Model of the Relation among the Resistance, the Distortion Temperature and the Rate of the Steel in the Plastic Deformation

2012 ◽  
Vol 502 ◽  
pp. 184-188
Author(s):  
Hong Li ◽  
Xiao Lin You
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Tensile Strength ◽  
Basic Theory ◽  
Deformation Resistance ◽  
Deformation Degree ◽  
Plastic Processing ◽  
Hardening Curve ◽  
Fundamental Equations ◽  
The Mathematical Model

the hardening curve of the steel in the plastic deformation only considers the influence of the deformation degree on the resistance. This paper, according to the basic theory of plastic processing, proposes out the respective relation between the deformation resistance and the deformation degree, the temperature, as well as the rate. This paper gets the curves of these relations by experiments, summarizes the fundamental equations by simulation and finally deduces the plastic conditional equations relating to the material performance----the tensile strength.

scholarly journals A software package for modeling the propagation of dynamic wave disturbances in heterogeneous multi-scale media

2021 ◽  
Vol 2056 (1) ◽  
pp. 012012
Author(s):  
N. Khokhlov
Keyword(s):  
Mathematical Model ◽  
Software Package ◽  
Heterogeneous Media ◽  
Numerical Algorithms ◽  
Theory Of Elasticity ◽  
Multi Scale ◽  
Wave Disturbances ◽  
The Mathematical Model ◽  
Selection Of ◽  
Dynamic Wave

Abstract The paper considers a software package designed to simulate the propagation of dynamic wave disturbances in heterogeneous media. One of the main features of the considered software package is numerical algorithms with an explicit selection of inhomogeneities. Within the framework of the work, such inhomogeneities as pores, fractures and interfaces between media (contact boundaries) are considered. The considered algorithms make it possible to perform calculations in different scale settings in micro and macro sizes. The mathematical model is based on the equations of the linear theory of elasticity. For the calculation, block structural meshes are used. The software package is parallelized using MPI and OpenMP technologies. Separate parts of the algorithm are parallelized using graphics accelerators such as GPGPU. The paper describes the features of the algorithms under consideration and provides examples of calculations that demonstrate the capabilities of the algorithm.

Study on the Mathematical Model of the Milling Force and Residual Stress

2013 ◽  
Vol 568 ◽  
pp. 103-107
Author(s):  
W.W. Song ◽  
H.F. Wang ◽  
J.L. Wang ◽  
X.L. Duan
Keyword(s):  
Mathematical Model ◽  
Residual Stress ◽  
Plastic Deformation ◽  
Deformation Theory ◽  
Milling Process ◽  
Milling Force ◽  
Elastic Plastic ◽  
Machining Deformation ◽  
Nc Milling ◽  
The Mathematical Model

Metal milling processing principle and the elastic-plastic deformation theory were combined in this paper. The mathematical model of milling force and residual stress in the NC milling process was deduced by the theory. By the obtained mathematical model, could further analyze the effect of milling force on the residual stress and then obtain the law of milling force to milling deformation. This proved the strong a theoretic guarantee for controlling the machining deformation.

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