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

Abstract

MODELLING OF HEAT TREATMENT OF STEEL ELEMENTS WITH THE MOVEMENT OF COOLANT MODELOWANIE OBRÓBKI CIEPLNEJ ELEMENTÓW STALOWYCH Z UWZGLĘDNIENIEM RUCHÓW CHŁODZIWA 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.

Optimal Production of Electrolytic Copper Determined by the Concentration and Distribution of Copper Concentrates to Smelters on the Example of KGHM

“…-the suitable concentrates distribution system between the smelters, according to the formula (3) and also with the production of concentrate mixtures. -updating coefficients in formulas (13) and (14) because of the ore variability.…”

“…Various alporhitus can be used in order to solve optimisation models [12,13]. Calculations were proceeded by means of GAMS software.…”

The Numerical Analysis of the Phenomena of Superficial Hardening of the Hot-Work Tool Steel Elements / Analiza Numeryczna Zjawisk Przypowierzchniowego Hartowania Elementów Ze Stali Narzędziowej Do Pracy Na Gorąco

“…Tph ε caused by changes of the temperature and phase transformation in the heating and cooling processes are calculated using the following relations for heating and cooling respectively [3,10]: (8) where…”

“…The phenomena occurring during the heat treatment are very complex and still incompletely described. The model of the hardening process should contain at least with three coupling elements: thermal, structural and mechanical [3,4,[7][8][9][10][11]. Determination of the composition of each phases, their kinetics and obtained structures during the cooling process of iron alloys is necessary to calculate the stresses for the hardening process.…”

“…Therefore, in the paper paid attention to this problem by comparing the results from numerical simulation for the two rate of cooling, although both are relatively small. To implement this type of algorithms one usually applies the FEM, which makes it possible to take into account both nonlinearities and inhomogeneity of thermally processed material [1,3,10,13,19,20]. …”