Simulation of the Electrical Parameters of Microarc Oxide Coatings Using the Matrix-Operator Method

The work addresses the issues of controllability of the microarc-oxidation process. This problem is mostly due to the difficulty of analytically characterizing the heterogeneous physical–chemical processes, which are nonlinear and nonstationary, that take place during microarc oxidation. To tackle this issue, a digital twin of the process is being developed, within which an analytical model is proposed to describe the behavior of the equivalent electrical circuit of the galvanic cell during coating deposition. The proposed analytical model of the process is nonlinear and nonstationary, which is attributed to the abrupt decrease in the active resistance of the coating during dielectric breakdowns. Based on experimentally obtained current and voltage oscillograms and the proposed analytical model, parametric identification of the electrical parameters of oxide coatings is performed using the matrix-operator method on the orthonormal Walsh basis. The matrix-operator method is selected because of its applicability to solving problems with both linear and nonlinear equations, as well as stationary and nonstationary parameters and variables, along with the relative simplicity of the mathematical and algorithmic implementation of computations. The calculations result in weight functions of the electrical model of the microarc-oxidation process, reflecting the relationship between the voltage and current in the galvanic cell (coating conductivity). The mean values of the weight functions (average conductivity) decrease during coating deposition, which confirms the adequacy of the proposed model and enables its use for implementing real-time procedures for monitoring coating properties. The scientific novelty of the work lies in the possibility of the real-time control of microarc oxidation through parametric identification of the electrical parameters of coatings using the matrix-operator method.