Mathematical modeling of technological parameters of laser powder surfacing based on approximation of the deposition track profile

Objectives. Laser powder surfacing is a promising mechanical engineering technology used to effectively restore worn surfaces of parts and create special coatings with valuable properties. In the research and development of laser cladding technology, mathematical modeling methods are of crucial importance. The process of applying powder coating involves moving the spray head relative to the surface of the part to form a roller or spray path, whose sequential application results in the formation of coatings. The study sets out to evaluate methods of profile approximation and optimization of technological parameters in laser powder cladding processes.Methods. In order to describe the dependencies of the profile parameters of the deposition paths during laser surfacing on the technological parameters of the process, mathematical modeling methods were used. The contours of the profiles of the surfacing section were obtained by analyzing images of microphotographs of thin sections of the cross sections of parts with applied surfacing. To approximate the curves of the section contours, methods of linear and nonlinear regression analysis were used. The dependence of the parameters of the profile contours of the surfacing section on the technological parameters of the spraying was represented by a two-factor parabolic regression equation. The search for optimal values of spraying technological parameters was carried out using the method of conditional optimization with linear approximation of the confidence region.Results. A nonlinear two-parameter function was selected from three options for approximating functions of the section profile of a surfacing track. Technological surfacing parameters were mapped onto a set of parameters of the approximating contour line. Optimal values of the technological parameters of surfacing were obtained using regression models of these mappings to provide the maximum value of the area of the surfacing contour under restrictions on the proportion of the sub-melting area to the total cross-sectional area. The approximating function of the cross-sectional profile of the surfacing track was used to calculate the optimal pitch of the tracks that provides the most even surface.Conclusions. The results of the study represent a technique for optimizing the technological parameters of laser surfacing with powder metals to ensure specified characteristics of the deposition track profile and select the track deposition step at which the most even deposition surface is achieved.