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.

1. Toyserkani E., Khajepour A. Corbin S. Laser Cladding. Boca Raton: CRC Press; 2005. 263 p.

2. Ghasempour-Mouziraji M., LagarinhosJ., Afonso D., de Sousa R.A. A review study on metal powder materials and processing parameters in Laser Metal Deposition. Opt. Laser Technol. 2024;170:110226. https://doi.org/10.1016/j.optlastec.2023.110226

3. Cheng J., Xing Y., Dong E., Zhao L., Liu H., Chang T., Chen M., Wang J., Lu J., Wan J. An Overview of Laser Metal Deposition for Cladding: Defect Formation Mechanisms, Defect Suppression Methods and Performance Improvements of Laser-Cladded Layers. Materials. 2022;15(16):5522. https://doi.org/10.3390/ma15165522

4. Davis J.R. Handbook of Thermal Spray Technology. ASM International; 2004. 338 p.

5. Baldaev L.H. (Ed.). Gazotermicheskoe napylenie (Gas Thermal Spraying); Moscow: Market DS; 2007. 344 p. (in Russ.).

6. Il’yushchenko A.F., Shevtsov A.I., Okovityi V.A., Gromyko V.F. Protsessy formirovaniya gazotermicheskikh pokrytii i ikh modelirovanie (Processes of Formation of Gas-Thermal Coatings and Their Modeling). Minsk: Belarus. nauka; 2011. 357 p. (in Russ.).

7. Bian L., Shamsaei N., Usher J. (Eds.). Laser-Based Additive Manufacturing of Metal Parts: Modeling, Optimization, and Control of Mechanical Properties. Boca Raton: CRC Press; 2018. 328 p.

8. Steen W.M., Mazumder J. Laser Material Processing. London: Springer; 2010. 558 p.

9. Dowden J.M. The Mathematics of Thermal Modeling an Introduction to the Theory of Laser Material Processing. Boca Raton: CRC Press; 2001. 292 p.

10. Pinkerton A.J. Advances in the modeling of laser direct metal deposition. J. Laser Appl. 2015;27:S15001. https://doi.org/10.2351/1.4815992

11. Kovalev O.B., Bedenko D.V., Zaitsev A.V. Development and application of laser cladding modeling technique: From coaxial powder feeding up to the surface deposition and bead formation. Appl. Math. Modell. 2018;57:339–359. https://doi.org/10.1016/j.apm.2017.09.043

12. Khamidullin B.A., Tsivilskiy I.V., Gorunov A.I., Gilmutdinov A.Kh. Modeling of the effect of powder parameters on laser cladding using coaxial nozzle. Surf. Coat. Technol. 2019;364:430–443. https://doi.org/10.1016/j.surfcoat.2018.12.002

13. De Oliveira U., Ocelík V., De Hosson J.Th.M. Analysis of coaxial laser cladding processing conditions. Surf. Coat. Technol. 2005;197(2–3):127–136. https://doi.org/10.1016/j.surfcoat.2004.06.029

14. Ocelík V., De Oliveira U., De Hosson J.Th.M. Thick tool steel coatings with laser cladding. WIT Trans. Eng. Sci. 2007;55. https://doi.org/10.2495/SECM070021

15. Ocelik V., Nenadl O., Palavra A., De Hosson J.Th.M. On the geometry of coating layers formed by overlap. Surf. Coat. Technol. 2014;242:54–61. https://doi.org/10.1016/j.surfcoat.2014.01.018

16. Jhavar S., Jain N.K., Paul C.P. Development of micro-plasma transferred arc (µ-PTA) wire deposition process for additive layer manufacturing applications. J. Mater. Process. Technol. 2014;214(5):1102–1110. https://doi.org/10.1016/j.jmatprotec.2013.12.016

17. Jhavar S., Jain N.K., Paul C.P. Enhancement of Deposition Quality in Micro-plasma Transferred Arc Deposition Process. Mater. Manuf. Process. 2014;29(8):1017–1023. https://doi.org/10.1080/10426914.2014.892984

18. Jain N.K., Sawant M.S., Nikam S.H., Jhavar S. Metal Deposition: Plasma-Based Processes. In: Encyclopedia of Plasma Technology. 1st ed. V. II. New York: Taylor and Francis; 2016. 19 p. http://doi.org/10.1081/E-EPLT-120053919

19. Yu T., Yang L., Zhao Yu., Sun J., Li B. Experimental research and multi-response multi-parameter optimization of laser cladding Fe313. Opt. Laser Technol. 2018;108:321–332. https://doi.org/10.1016/j.optlastec.2018.06.030

20. Suzuki S., KeiichiA be. Topological structural analysis of digitized binary images by border following. Computer Vision, Graphics, and Image Processing. 1985;30(1):32–46. https://doi.org/10.1016/0734-189X(85)90016-7

21. Draper N.R., Smith H. Applied Regression Analysis: 3rd ed. New York: Wiley-Interscience; 1998. 736 p.

22. Bates D.M., Watts D.G. Nonlinear Regression Analysis and its Applications. New York: Wiley & Sons; 1988. 365 p.

23. Vugrin K.W., Swiler L.P., Roberts R.M., Stucky-Mack N.J., Sullivan S.P. Confidence region estimation techniques for nonlinear regression in groundwater flow: Three case studies. Water Resour. Res. 2007;43(3):W03423. https://doi.org/10.1029/2005WR004804

24. Powell M.J.D. Direct search algorithms for optimization calculations. Acta Numerica. 1998;7:287–336. https://doi.org/10.1017/S0962492900002841

25. Soloviev M.E., Kokarev S.S., Baldaev S.L., Baldaev L.Kh., Mishchenko V.I., Fedorova M.O. Approximation of the profile of the section of the spray spot during gas thermal deposition of powder coating. Informatsionno-tekhnologicheskii vestnik = Information Technology Bulletin. 2022;3(33):138–163 (in Russ.).

26. Niz’ev V.G., Khomenko M.D., Mirzade F.Kh. Process planning and optimisation of laser cladding considering hydrodynamics and heat dissipation geometry of parts. Quantum Electron. 2018;48(8):743–748. https://doi.org/10.1070/QEL16708

27. Cao Y., Zhu S., Liang X., Wang W. Overlapping model of beads and curve fitting of bead section for rapid manufacturing by robotic MAG welding process. Robotics and Computer-Integrated Manufacturing (RCIM). 2011;27(3):641–645. https://doi.org/10.1016/j.rcim.2010.11.002

28. Baldaev S.L., Soloviev M.E., Raukhvarger A.B., Baldaev L.Kh., Mishchenko V.I. The Influence of Aluminum Oxide Powder Plasma Spraying Parameters on the Adhesive Strength of Ceramic Coatings Applied to the Gas Turbine Engine Thermally Stressed Components. Vestnik MEI = Bulletin of MPEI. 2024;1:93–102 (in Russ.). https://doi.org/10.24160/1993-6982-2024-1-93-102