Analytical method of calculation of thermal fields of foundry cores

Abstract

The aim of the work is to create on the basis of the analysis of thermophysical parameters and regularities of mathematical methods, which allows to calculate the distribution of thermal fields in molds and rods using a system of analytical formulas. The method of calculating thermal fields in foundry molds and rods developed and presented in this publication is based on the finite difference method. Much attention is paid to the calculations of the dynamics of changes in the surface temperatures of the casting rod and its center. The article shows that the basis for the correct calculation of the thermal field of the rod is to establish the change in surface temperature in the first few seconds after the start of contact with the melt. All currently available methods do not take into account this change in temperature. A new concept is introduced - the period of thermal inertia of the rod. This is the period of time during which its surface temperature rises from the initial value (ambient temperature) to a value corresponding to the surface temperature of the casting. The period of thermal inertia depends exclusively on the thermophysical properties of the rod. To calculate the temperature change in the center of the casting rod, a modified method of S. Schwartz was used: instead of the constant contact temperature of the "casting-rod" in the formula takes into account the previously estab- ?ished dynamics of changes in this temperature. The thermal fields of cylindrical foundry rods with diameters of 50 mm and 16 mm were calculated according to the created mathematical method. A comparison of the results of calculations according to the developed method and with the use of existing software is presented. The difference in design temperatures is 100 oC and more. The difference in determining the thermal fields of a smaller diameter rod is particularly noticeable, which is due to the rapid dynamics of changes in the surface temperature of the casting, which is currently not taken into account by current methods. The developed mathematical technique can be offered as a theoretical basis for refining applied computer programs for foundry production.