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Open access

A. Kulawik and A. Bokota

Modelling of Heat Treatment of Steel Elements with the Movement of Coolant

A mathematical and numerical model of hardening process using the generalized finite difference method for the movement of fluid and heat transport have been proposed in this paper. To solve the Navier-Stokes equation the characteristic based split scheme (CBS) has been used. The solution of the heat transport equation with the convective term has been obtained by a stabilized meshless method. To determine of the phase transformation the macroscopic model built on the basis of CCT diagrams for continuous cooling of medium-carbon steel has been used. The temporary temperature fields, the phase transformation, thermal and structural strains for the heat treated element and the fields of temperature and velocity for the coolant have been determined. The comparative analysis of the results of calculations for the model without taking into account movement of coolant has been carried out. The effect of the notch in the shaft on the cooling rates and fields of the kinetics of the phase transformations has been presented.

Open access

L. Sowa and A. Bokota

Numerical Model of Thermal and Flow Phenomena the Process Growing of the CC Slab

The mathematical and numerical simulation model of the growth of the solid metal phase within a continuous cast slab is presented in this paper. The problem was treated as a complex one. The velocity fields are obtained by solving the momentum equations and the continuity equation, whereas the thermal fields are calculated by solving the conduction equation with the convection term. One takes into consideration in the mathematical model the changes of thermophysical parameters depending on the temperature and the solid phase volume fractions in the mushy zone. This formulation of the problem is called a complex model in contrast to the simplified model in which the conduction equation is solved only. The problem was solved by the finite element method. A numerical simulation of the cast slab solidification process was made for different cases of continuous casting mould pouring by molten metal. The influences of cases of the continuous casting mould pouring on the velocity fields in liquid phase and the solid phase growth kinetics of the cast slab were estimated, because these magnitudes have essential an influence on high-quality of a continuous steel cast slab.

Open access

L. Sowa and A. Bokota

The mathematical and numerical simulation model of the liquid steel flow in a tundish is presented in this paper. The problem was treated as a complex one. The velocity fields are obtained by solving the momentum equations and the continuity equation, whereas the thermal fields are calculated by solving the conduction equation with the convection term. One takes into consideration in the mathematical model the changes of thermophysical parameters depending on the temperature. The problem was solved by the finite element method. The one-strand slab tundish is used to casting slabs. The internal work space of the tundish was modified by flow control devices. The first device was a striker pad situated in the pouring tundish zone. The second device was a baffle with three holes. The main purpose of using these was to put barriers in the steel flow path as well as give directional metal flow upwards which facilitated inclusion floatation. The visualization of interaction of flow control devices on hydrodynamic conditions was received from numerical simulations. As a result of the computations carried out, the liquid steel flow and steel temperature fields were obtained. The influences of the tundish modifications on the velocity fields in liquid phase of the steel were estimated, because these have essential an influence on high-quality of a continuous steel cast slab.

Open access

T. Domański and A. Bokota

Numerical Models of Hardening Phenomena of Tools Steel Base on the TTT and CCT Diagrams

In work the presented numerical models of tool steel hardening processes take into account thermal phenomena, phase transformations and mechanical phenomena. Numerical algorithm of thermal phenomena was based on the Finite Elements Methods in Galerkin formula of the heat transfer equations. In the model of phase transformations, in simulations heating process, isothermal or continuous heating (CHT) was applied, whereas in cooling process isothermal or continuous cooling (TTT, CCT) of the steel at issue. The phase fraction transformed (austenite) during heating and fractions of ferrite, pearlite or bainite are determined by Johnson-Mehl-Avrami formulas. The nescent fraction of martensite is determined by Koistinen and Marburger formula or modified Koistinen and Marburger formula. In the model of mechanical phenomena, apart from thermal, plastic and structural strain, also transformations plasticity was taken into account. The stress and strain fields are obtained using the solution of the Finite Elements Method of the equilibrium equation in rate form. The thermophysical constants occurring in constitutive relation depend on temperature and phase composite. For determination of plastic strain the Huber-Misses condition with isotropic strengthening was applied whereas for determination of transformation plasticity a modified Leblond model was used. In order to evaluate the quality and usefulness of the presented models a numerical analysis of temperature field, phase fraction, stress and strain associated hardening process of a fang lathe of cone shaped made of tool steel was carried out.

Open access

W. Piekarska, M. Kubiak and A. Bokota

Numerical Simulation of Thermal Phenomena and Phase Transformations in Laser-Arc Hybrid Welded Joints

The paper concerns mathematical and numerical modelling of temperature field with convective motion of liquid metal in the melted zone taken into account and numerical estimation of structure composition of a plate made of S355 steel, butt-welded by laser-arc hybrid welding technique. Coupled transport phenomena, including heat transfer and fluid flow in the melted zone, were described respectively by transient heat transfer equation with convective term and Navier-Stokes equation. Latent heat associated with the material's state changes and latent heat of phase transformations in solid state were taken into consideration in the solution algorithm. The kinetics of phase transformations and volumetric fractions of arising phases were calculated on the basis of the Johnson-Mehl-Avrami (JMA) and Koistinen-Marburger (KM) classic mathematical models. In modelling of phase transformations during heating continuous heating transformation (CHT) diagram was used, whereas continuous cooling transformation (CCT) diagram was used in modelling of phase transformations during cooling of welded steel.

Transient heat transfer equation was solved using finite element method in Petrov-Galerkin formulation and Navier-Stokes equation was solved in Chorin's projection method. The solution algorithms were implemented in ObjectPascal programming language.

Open access

A. Bokota, A. Kulawik, R. Szymczyk and J. Wróbel

In the paper the complex model of hardening of the hot-work tool steel is presented. Model of estimation of phase fractions and their kinetics is based on the continuous heating diagram (CHT) and cooling diagram (CCT). Phase fractions which occur during the continuous heating and cooling (austenite, pearlite or bainite) are described by Johnson-Mehl (JM) formula. To determine of the formed martensite the modified Koistinen-Marburger (KM) equation is used. Model takes into account the thermal, structural, plastic strains and transformation plasticity. To calculate the plastic strains the Huber-Mises plasticity condition with isotopic hardening is used. Whereas to determine transformations induced plasticity the Leblond model is applied. The numerical analysis of phase compositions and residual stresses in the hot-work steel (W360) element is considered.

Open access

J. Wróbel, A. Kulawik and A. Bokota

Abstract

In the paper the use of the artificial neural network to the control of the work of heat treating equipment for the long axisymmetric steel elements with variable diameters is presented. It is assumed that the velocity of the heat source is modified in the process and is in real time updated according to the current diameter. The measurement of the diameter is performed at a constant distance from the heat source (Δz = 0). The main task of the model is control the assumed values of temperature at constant parameters of the heat source such as radius and power. Therefore the parameter of the process controlled by the artificial neural network is the velocity of the heat source. The input data of the network are the values of temperature and the radius of the heated element. The learning, testing and validation sets were determined by using the equation of steady heat transfer process with a convective term. To verify the possibilities of the presented algorithm, based on the solve of the unsteady heat conduction with finite element method, a numerical simulation is performed. The calculations confirm the effectiveness of use of the presented solution, in order to obtain for example the constant depth of the heat affected zone for the geometrically variable hardened axisymmetric objects