A Mathematical Model for Optimizing the Protective Coating Spraying Pitch Based on Minimizing the Second Central Moment
DOI:
https://doi.org/10.24160/1993-6982-2026-1-149-159Keywords:
plasma spraying, protective coatings, pitch parameter optimization, mathematical modeling, coating profile, objective function, second central moment, extrema, biquadratic approximation, spray track overlapsAbstract
One of the key parameters in the technology of powder plasma spraying and laser cladding of protective coatings is the spray tracks application pitch, which ensures the specified geometric characteristics of the coating and the quality of its surface. The aim of the study is to develop and analyze a mathematical model for optimizing the pitch parameter in the technology of plasma spraying and laser cladding of protective coatings to improve the quality and efficiency of the coating application process. The study is based on mathematical modeling of the plasma spraying process using analytical and numerical methods. An objective function characterizing the coating quality was developed based on the coating profile second central moment. A simple model with a parabolic spray track profile and a more complex model with biquadratic approximation of real profiles are analyzed. Differential and integral calculus methods were used to obtain analytical expressions, and numerical methods were employed to solve equations and plot the curves. A general analytical expression for determining the optimal pitch parameter value is obtained. Extrema of the objective function of various orders, corresponding to different spray track overlapping conditions are identified. It has been found that for the biquadratic track profile model, the optimal pitch value corresponds to weak third-order overlaps, rather than second-order ones as was assumed previously. The proposed optimization method is compared with the existing optimization method based on the area equality criterion. The obtained results can be used to optimize technological processes of plasma spraying and laser cladding of protective coatings in various industry branches, including aerospace, energy, and automotive industries. The proposed method for optimizing the pitch parameter based on minimizing the coating profile second central moment makes it possible to determine optimal spraying conditions more accurately in comparison with existing methods. The possibility to improve the coating quality through the use of third-order overlaps has been revealed. The developed mathematical model opens new prospects for improving the plasma spraying technology.
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Для цитирования: Соловьев М.Е., Кокарев С.С., Балдаев С.Л., Балдаев Л.Х., Малышев Д.В. Математическая модель оптимизации шага напыления защитных покрытий на основе минимизации второго центрального момента // Вестник МЭИ. 2026. № 1. С. 149—159. DOI: 10.24160/1993-6982-2026-1-149-159
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Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
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For citation: Soloviev M.E., Kokarev S.S., Baldaev S.L., Baldaev L.Kh., Malyshev D.V. A Mathematical Model for Optimizing the Protective Coating Spraying Pitch Based on Minimizing the Second Central Moment. Bulletin of MPEI. 2026;1:149—159. (in Russian). DOI: 10.24160/1993-6982-2026-1-149-159
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Conflict of interests: the authors declare no conflict of interest
