Analytical Modeling of a Heat Source under Welding of a Steel Sleeve by the Centrifugal Method Using an Axisymmetric Electric Arc

Introduction. The technology of centrifugal bimetallization using an independent axisymmetric electric arc is becoming increasingly important due to the high need to improve the quality of bimetallic compositions used in the manufacture of plain bearings, cylinder barrels for hydraulic units, and friction pair elements in internal combustion engines. The existing research in this area emphasizes the need for a more in-depth study of the features of thermal processes associated with this technology. In modern scientific literature, issues related to temperature control at the interface of materials are not fully disclosed, and the existing gap in the concept of the behavior of bimetallic compounds under heating conditions hinders the implementation of this technology in industrial production. The objective of this study is to conduct analytical modeling of a heat source in the form of an axisymmetric electric arc to determine the heat concentration coefficient and reduce the proportion of experimental data in the thermal process model, which will increase its versatility. The tasks arising from the stated goal are comparison of the results of calculating the effective heat flux density from two different expressions (using trigonometric and exponential functions), as well as evaluation of the distribution of the heat flux of an axisymmetric arc along the inner surface of the sleeves (this is required to establish the relationship between the temperature of the outer surface of the welded sleeve and the temperature at the interface between the materials).

Materials and Methods. Direct control of the temperature at the interface between the base material and the deposited layer is difficult, but it is possible to carry out indirect control using the temperature of the outer surface. To determine the relationship between the temperature of the outer surface of the deposited sleeve (billet) and the temperature on its inner surface, i.e., at the interface between the base material and the deposited layer, a heat source was modeled, the heat flux distribution of an axisymmetric electric arc along the inner surface of the sleeve was estimated, and an analytical expression was obtained to determine the heat concentration coefficient.

Results. In the course of the work, an analytical expression was obtained for determining the coefficient of heat concentration, k = 0.945 / R₁². It was required for calculating the electric arc parameters considering the distribution of the effective thermal power in the hot spot according to an exponential dependence. To simulate the heat source of the facing process (bimetallization) of the inner surface of steel sleeves with heating by an independent axisymmetric electric arc, the results of calculating the effective heat flux density were compared using two expressions: q = q₀ ∙ cos³φ and q = q₀ ∙ e^{–k· r²п}. This comparison showed that for calculating temperature fields during facing of the inner surface of steel sleeves (billets) with metal alloys under heating by an independent axisymmetric arc, it was possible to use the analytical exponential form of representation of the heat source.

Discussion and Conclusion. Modeling thermal processes of the centrifugal bimetallization using simplified schemes of uniform distribution of heat flow q = const on the entire free surface of the deposited layer, which simulates the spread of heat of an electric arc, requires the introduction of correction factors and a series of experiments to determine them. In this case, the description of the thermal process in the thermal process model contains a high proportion of experimental data and correction factors. Therefore, in order to exclude most of the experimental components when modeling the heat source and heat flow distribution of the facing process (bimetallization) of the inner surface of steel sleeves under heating by an independent axisymmetric electric arc, the author in this paper proposes an analytical solution for calculating the effective heat flow density in the form of an exponential function. This function allows determining the heat concentration coefficient of an independent axisymmetric electric arc during the facing process, which is required to increase the accuracy of calculating the temperature field of the bimetallized sleeve and improve the temperature control of the thermal parameters of the technological process.

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