Building a drilling model using the concept of fuzzy systems

The problems of constructing mathematical models of metal cutting processes in the optimization of processing modes are considered. The well-known task of constructing a model of drill resistance is formulated depending on the feed rate per revolution and rotational speed. The construction of a persistent model allows its further use to determine the optimal cutting conditions. To build the models, we used the data of a specially conducted persistence experiment with a volume of 50 observations, including repeated ones. A new class of resistance models related to the class of fuzzy regression models is proposed. To build them, the domain of definition of each input factor is divided into two intersecting subdomains, called fuzzy partitions. On fuzzy partitions, a membership function belonging to the trapezoidal class is set. Fuzzy regression models allow us to describe local features of response behavior, while remaining in the class of linear or quadratic models. The persistent fuzzy drilling models constructed from experimental data are compared with the previously proposed logarithmic quadratic model. Logarithmic response was carried out in order to reduce the range of variation of its values. Relevant illustrations are provided. It is noted that the proposed models are tested for adequacy.

1. Karmanov V.S.Issledovaniematematicheskikhmodeleistoikostirezhushchegoinstrumenta. [The study of mathematical models of resistance of the cutting tool] Nauchnyi vestnik Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta – Science bulletin of the Novosibirsk state technical university. 2006;2:55-64

2. Smagin G.I. Karmanov V.S. Primenenie metoda kharakteristicheskikh linii I kharakteristicheskikh poverkhnostei pri normirovanii rezhimov rezaniya. Obrabotka metallov (Metal working and material science).2009;1:16-19.

3. Smagin G.I., Karmanov V.S., Fedin I.V. Use of basic model of process of drilling for rationing of the modes of cutting of the hardly processed materials. Obrabotka metallov (Metal working and material science).2015;4(69):6-17. 4. Karmаnov V.S., Smagin G.I. Korrektsiya ehkstrapolyatsionnoi oblasti kharakteristicheskoi stoikostnoi modeli pri normirovanii rezhimov rezaniya trudnoobrabatyvaemykh materialov (na primere sverleniya). Obrabotka metallov (Metal working and material science).2006;2(31):34-35.

4. Karmаnov V.S., Smagin G.I. Korrektsiya ehkstrapolyatsionnoi oblasti kharakteristicheskoi stoikostnoi modeli pri normirovanii rezhimov rezaniya trudnoobrabatyvaemykh materialov (na primere sverleniya). Obrabotka metallov (Metal working and material science).2006;2(31):34-35.

5. BabuskaR. Fuzzy Modelling for Control. London. Boston: Kluwer Academic Publishers. 1998.

6. Piegat A. Fuzzy Modeling and Control. BINOMIAL. Knowledge lab, 2013.

7. Popov A. A. Regressionnoe modelirovanie na osnove nechetkih pravil. Sbornik nauchnyh trudov NGTU, Novosibirsk: Izd-vo NGTU, 2000;2(19):49-57.

8. Popov A.A. Postroenie derev'ev reshenii dlya prognozirovaniya kolichestvennogo priznaka na klasse logicheskikh funktsii ot lingvisticheskikh peremennykh. Science bulletin of the Novosibirsk state technical university, 2009;3(36):77–86.

9. Popov A.A. Optimal desing of the experiment with the active identification of fuzzy linear regression models. Modeling, optimization and information technology. 2019;7(1):99–114. Available at: https://moit.vivt.ru/wpcontent/uploads/2019/04/Issue_1(24)_2019.pdf (accessed01.02.2020)

10. AivazyanS.A. Enyukov I.S. Meshalkin L.D. Prikladnaya statistika. Issledovanie zavisimostei.M: Finance and Statistics.1985.

11. Dreiper N., Smit G. Prikladnoi regressionnyi analiz. M .: Statistics.1973:392.

12. . Popov A.A. Optimal'noe planirovanie ehksperimenta v zadachah strukturnoj i parametricheskoj identifikacii modelej mnogofaktornyh sistem: monografiya A.A. Popov. Novosibirsk: Izd-vo NGTU, 2013.