Mathematical modeling of high-strength steel processing

Authors

DOI:

https://doi.org/10.20535/2521-1943.2019.85.160358

Keywords:

regression analysis, mathematical modeling, design experiments, fuzzy cluster analysis, processing of high-strength steels, factor space heterogeneity

Abstract

In the work, a study was conducted of the technological process of processing high-strength steels with a tool made of metal-ceramic, tungsten-free hard alloys. The study took into account both the process parameters (cutting speed, longitudinal feed, cutting depth, processing time) and the material being processed  and the material of the cutting tool. As indicators of the quality of the technological process, the wear of the tool on the back surface and the roughness of the machined surface are chosen. For the experiment, a robust plan was built based on multifactorial regular plans (34×42//64). Due to the fact that the factor space for surface roughness turned out to be inhomogeneous, it was divided into homogeneous subspaces using fuzzy cluster analysis, each of which had its own model. All regression models are constructed using the PRIAM software tool (design, regression, and model analysis), which provides automatic generation of the model structure. The constructed models satisfy the requirements of adequacy, information content, structural and computational stability. The use of these models allows both to design a technological process with specified properties, and to analyze the phenomena occurring during this

References

  2. Greene, W. H. (2016), Ecoonometric analysis. Fours Edition, Pearson Education Company, New Jersey, USA.
  3. Radchenko, S.G. (2011), Metodologiya regessionnogo analiza [Regression analysis methodology], Korniychuk, Kiev, Ukraine.
  4. Draper, N. R. and Smith, H. (1998), Applied Regression Analysis Third Edition, John Wiley & Sons, Inc, New York, USA.
  5. Lapach, S.N., Chubenko, A.V. and Babich, P.N. (2002), Statistika v nauke i biznese [Statistics in science and business], Morion, Kiev, Ukraine.
  6. Carlberg, C. (2016), Regression Analysis Microsoft Excel, Pearson Education, Inc, Indianapolis, USA.
  7. Ermakov, S.M. (ed.) (1983), Matematicheskaya teoriya planirovaniya eksperimenta [Mathematical theory of experiment planning], Nauka, Moscow, Russia.
  8. Katsev, P.G. (1974), Statisticheskie metody issledovaniya rezhushchego instrumenta [Statistical research methods of cutting tools], 2 nd. ed., Mashinostroenie,Moscow,Russia.
  9. Radchenko, S.G. (1998), Matematicheskoe molelirovanie tekhnologicheskikh protsessov v mashinostroenii [Mathematical modeling of technological processes in mechanical engineering], Ukrspetsmontazhproekt, Kiev, Ukraine.
  10. Solonin, I.S. (1972), Matematicheskaya statistika v technologii mashinostroeniya [Mathematical statistics in engineering technology], Mashinostroenie, Moscow, Russia.
  11. Ufimychev, Yu.I., Mikhailov, S.K., Svyatkin, B.K. and Prokhorov, I.I. (1976), Regressionnyi analiz kachestva stalei i splavov [Regression analysis of the quality of steels and alloys], Metallurgiya, Moscow, Russia.
  12. Shterenzon, V.,А. (2010), Моdelirovanie tekhnologicheskirh protsessov: konspekt lektsii [Modeling of technological processes: lecture notes], Izdatelstvo Rossiiskogo gosudarstvennogo professionalno-pedagogicheskogo universiteta, Ekaterinburg, Russia, http://www.rsvpu.ru/filedirectory/3468/shterenzon.pdf
  13. Barbot’ko, А.I, Kudinov, V.А., Ponkratov, P.А. and Barbot’ko A.A. (2013), Planirovanie, organizatsiya i provedenie nauchnykh issledovanii v mashinostroenii [Planning, organizing and conducting research in mechanical engineering], Tonkie naukoemkie tekhnologii, Staryi oskol, Russia.
  14. Morgunov, А.P. and Revina, I.V. (2005), Planirovanie i obrabotka rezul'tatov eksperimenta [Planning and processing the results of the experiment], Izdatelstvo Omskogo gosudarstvennogo tekhnicheskogo universiteta, Omsk, Russia.
  15. Моrozov, Е.А. (2015), “Investigation of the properties of carbide inner coating obtained by laser cladding”, Sovremennye problemy nauki i obrazovaniya, vol. 2, no.2, http://www.science-education.ru/ru/article/view?id=22828
  16. Lapach, S.М., Radchenko, S.G. and Babich, P.N. (1993), Planirovanie, regressiya i analiz modelei PRIAM, Programmnye produkty Ukrainy: katalog [Planning, regression and analysis of models PRIAM, Software products of Ukraine: catalog], Кiev, pp. 24–27.
  17. Lapach, S.М. (2014), “Problemy pobudovy regresiinykh modelei protsesiv rizannya metaliv” [Problems of building regression models of metal cutting processes], Journal of Mechanical Engineering NTUU “Kyiv Polytechnic Institute”, vol. 72, no. 3, pp. 40–47.
  18. Lapach, S.М. and Radchenko, S.G. (2012), “The main problems of building regression models”, Matematychni mashyny i systemy, no. 4, pp. 125–133.
  19. Shtovba, S.D. (2007), Proektirovanie nechetkikh sistem sredstvami MATLAB [Design of fuzzy systems using MATLAB], Goryachaya liniya–Telekom, Moscow, Russia.
  20. Lapach, S.М. and Radchenko, S.G. (2016). “Regression analysis in conditions of heterogeneity of factor space”, Matematychni mashyny i systemy, no. 3, pp. 55–63.
  21. Lapach, S.М. (2014). “Determination of the optimal number of clusters ”, ІХ international scientific-practical conference Mathematical and simulation modeling of systems MODS 2014, 23–27 June 2014, Kyiv – Zhukin, Ukraine, pp. 272–275.
  22. Lapach, S.М. (2014). “ Cluster analysis in determining homogeneous areas of factor space in regression analysis ”, Fifteenth international Name Conference academician Mikhail Kravchuk, 15–17 May 2014, Kyiv, Ukraine, vol. 3, pp. 82–84.

Downloads

Published

2019-04-14

How to Cite

[1]
S. Lapach and S. Radchenko, “Mathematical modeling of high-strength steel processing”, Mech. Adv. Technol., no. 1(85), pp. 101–110, Apr. 2019.

Issue

No. 1(85) (2019)

Section

Original study

License

Copyright (c) 2020 Mechanics and Advanced Technologies

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The ownership of copyright remains with the Authors.
 
Authors may use their own material in other publications provided that the Journal is acknowledged as the original place of publication and National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” as the Publisher.

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under CC BY 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work