Issues $\rightarrow$ Volume 27, Issue 3 (2026)

Improving the Quality Parameters of Steel Surfaces by Combined Electrospark Carburizing Technologies. Pt. 2. Mathematical Models for Controlling the Properties of Metal Surfaces

TARELNYK V.B.$^{1}$, HAPONOVA O.P.$^{2,3}$, KONOPLIANCHENKO Ie.V.$^{1}$, TARELNYK N.V.$^{1}$, S.G. BONDAREV$^{1}$, and MIKULINA M.O.$^{1}$

$^1$Sumy National Agrarian University, 160 Herasyma Kondratieva St., 40021 Sumy, Ukraine
$^2$Sumy State University, 116 Kharkivska St., 40007 Sumy, Ukraine
$^3$Institute of Fundamental Technological Research, Polish Academy of Sciences, 5В Pawińskiego, 02-016 Warsaw, Poland

Received / final version: 02.04.2026 / 02.08.2026 Download PDF logo PDF

Abstract
Modern mechanical engineering is grounded in the latest advances in science and technology, necessitating the implementation of reliable and fail-safe engineering solutions, which ensure the reliability and durability of machine components operating under severe conditions, including intensive loading, extreme temperatures, and corrosive environments. Addressing these challenges requires the development of technological foundations for surface modification of machine parts, using environmentally benign methods, which remains a pressing and relevant task. The present study demonstrates that, among contemporary technologies, electrospark alloying (ESA) is of particular interest, as it enables the formation of surface-layer structures with unique physicomechanical and tribological properties. The objective of this work is to develop an adequate, physically substantiated mathematical model for predicting the quality parameters of surface layers of steel components during electrospark carburizing (ESC) and electrospark nitrocarburizing (ESNC) as functions of the energy and technological parameters of ESA equipment, employing a specialised saturating technological medium (SSTM). The paper presents the results of investigations of the influence of preliminary aluminium treatment on the quality parameters of modified steel surfaces, using an SSTM composed of nitrogen–carbon constituents. Phase-composition analysis reveals that the presence of an aluminium interlayer leads to the formation of aluminium-containing phases, resulting in a significant increase in both hardness and thickness of the surface layers. Experimental dependences of surface quality parameters on the energy and technological parameters of ESA during ESNC and ESC processes are established. Based on the conducted research, mathematical models describing the dependence of surface quality on ESNC and ESC are developed, including equations for the increment of the hardened-layer thickness and the increment of surface microhardness as functions of ESA-equipment parameters. These models enable the determination of key technological characteristics of the formed layer, namely, the thickness of the hardened layer and its microhardness. A methodology for determining the constants of the increment equations for ESNC and ESC processes is developed. This includes the evaluation of both hardened-layer thickness (considering the maximum increment as a function of discharge energy, process-intensiveness, and activation energy) and microhardness (considering the maximum increment as a function of discharge energy, process-intensiveness, and activation energy). The proposed mathematical models can be applied for strengthening the surface layers of components in compressor and pumping equipment, including protective sleeves, end faces of rings, mating surfaces of casings and covers, and bearing journals of centrifugal machinery shafts, etc.

Keywords: electrospark alloying, carburizing, nitrocarburizing, hardened layer, mathematical modelling.

DOI: https://doi.org/10.15407/ufm.27.03.***

Citation: V.B. Tarelnyk, O.P. Haponova, Ie.V. Konoplianchenko, N.V. Tarelnyk, S.G. Bondarev, and M.O. Mikulina, Improving the Quality Parameters of Steel Surfaces by Combined Electrospark Carburizing Technologies. Pt. 2. Mathematical Models for Controlling the Properties of Metal Surfaces, Progress in Physics of Metals, 27, No. 3: ***–*** (2026)

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