Mathematical modeling and numerical calculation of the thermal conductivity process of a sample during electrolytic-plasma hardening

This paper presents a numerical simulation of temperature processes during electrolytic-plasma hardening of 45 and 65G steel components to optimize process parameters and reduce the scope of experimental studies. Heating with a concentrated plasma flow, reaching a power density of up to 3×10³ W/cm², results in a rapid increase in surface temperature and the formation of intense heat gradients throughout the component. Two approaches are used to describe heat transfer: an analytical solution to the heat conduction equation for a semi-infinite medium and a numerical finite-difference method that accounts for the finite thickness of the sample and realistic boundary conditions. Temperature and heating rate fields are constructed, and features of the material's thermal response at the initial and late stages of exposure are identified. The numerical simulation results are compared with experimental data obtained from heating 45 steel plates at 50 kW. It was established that the calculated values agree well with the experimental data at the early stages, and the observed discrepancies in the range of 10–20 s are due to model simplifications and the thermocouple's peculiarities in temperature recording. It is shown that the high heating rate (150–200 °C/s), characteristic of electrolytic plasma treatment, promotes the formation of martensitic structures with increased tetragonality, as confirmed by both model calculations and literature data. The presented results demonstrate the effectiveness of numerical modeling as a tool for engineering prediction of temperature fields during EPU and can be used to select rational hardening modes for large-sized parts of agricultural machinery.