Modified Volterra operator as a temperature modelling technique while metalworking


Аuthors

Lapshin V. P.

Don State Technical University, DSTU, 1, Gagarin square, Rostov-on-Don, 344003, Russia

Abstract

The presented work is an attempt to combine the approach, adopted by technologists on processing

with metal cutting machines, to the description of temperature regimes of cutting, with

the approach based on solving differential equation of thermal conductivity. Here, all specifics

of converting the power, released in the contact zone of the tool and machined workpiece, into

the heat, as well as evolutionary (growing) nature of the thermal field in the same zone are accounted

for. By evolutionary nature, we understand the heredity of the current temperature field

in relation to all previous facts of heat release and dissipation resulting from the workpiece

transformation. The article proposes the Volterra operator for solving such problem, previously

modified to account for time-space dissipation of thermal potentials, which allows obtaining

general solution differential equation of thermal conductivity. The article considers options of

stationary change of temperature in the cutting zone, and a case of the operator transforming for

the discrete version of temperature evaluation. Both options were simulated, in the stationary

case the simulation results revealed aperiodic character of the temperature field behavior in the

contact zone of the tool and workpiece, which agreed well with the observed temperature effects

in metals. Discrete modeling was performed based on the previously obtained experimental

data. The experiment was conducted on a lathe. The force, decomposed along the axes

of the tool deformation, vibrations of the tool itself, and temperature in the contact zone of the

tool and processed workpiece were measured herewith. As a result of experimental data processing

and numerical modeling, the curves depicting the experimentally measured temperature

in the contact zone of the tool and the workpiece, as well as the temperature, modeled as the result

of the proposed technique in the same zone were plotted. As is clear from the obtained results,

simulation results almost completely coincide with the results, obtained in the field experiment,

which allowed us to conclude that the proposed mathematical model is highly adequate.

We see further development of the proposed modelling technique of the thermal field, occurring

in the cutting zone, as application of the obtained models while new mathematical apparatus

formation, describing complex dynamics of metal cutting machining with metal cutting machine

tools. It is utterly important here to account not only for complex evolutionary nature of

the temperature field formation, but also for the new complex nonlinear relationships, formed

by this field in the forces hindering the shaping movements of the tool.

Keywords:

temperature, power of irreversible transformations, Volterra operator, machining by cutting.

References

  1. Ryzhkin A.A. Teplofizicheskie protsessy pri iznashivanii instrumental’nykh rezhushhikh materialov [Thermophysical processes during wear of tool cutting materials]. Rostov on Don: Publishing center of DGTU, 2005. 311 p. In Russ.

  2. Reznikov A.N., Reznikov L.A. Teplovye protsessy v tekhnologicheskikh sistemakh [Thermal processes in technological systems]. Moscow: Mashinostroenie, 1990. 288 p. In Russ.

  3. Makarov A.D. Iznos i stojkost’ rezhushhikh instrumentov [Wear and tear of cutting tools]. Moscow: Mashinostroenie, 1966. 264 p. In Russ.

  4. Vistoropskaya F.A., Ryzhkin A.A., Moiseenko S.A. K voprosu o koehffitsiente raspredeleniya teplovogo potoka v zone deformatsii pri rezanii [On heat-sharing ratio in deformation zone under cutting]. Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta — Bulletin of the Don State Technical University, 2012. no. 6 (67). pp. 41–46. In Russ.

  5. Zakovorotny L.V., Vinokurova I.A. Vliyanie proizvodstva tepla na dinamiku processa rezaniya [The influence of heat production on the dynamics of the cutting process]. ]. Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta — Bulletin of the Don State Technical University, 2017, vol. 17, no. 3 (90), pp.14—26. In Russ.

  6. Reznikov A.N. Teplofizika rezaniya [Thermophysics of cutting]. Moscow: Mashinostroenie, 1968. 288 p. In Russ.

  7. Lapshin V.P., Bordachev E.V. Matematicheskoe modelirovanie temperatury v zone kontakta instrumenta i izdeliya pri tokarnoj obrabotke metallov [Mathematical modeling of temperature in the contact zone of a tool and product during metal turning]. Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta — Bulletin of the Don State Technical University. 2019, vol. 19, no. 2, pp. 130–137. In Russ.

  8. Belyaev N.M., Ryadno A.A. Metody teorii teploprovodnosti. T. 1 [Methods of the theory of thermal conductivity. Vol. 1]. Moscow: Vysshaya shkola, 1982. 327 p. In Russ.

  9. Makhnenko V.I., Kravtsov T.G. Teplovye processy pri mekhanizirovannoj naplavke detalej tipa krugovyh cilindrov [Thermal processes during mechanized surfacing of parts such as circular cylinders]. Kiev: Naukova dumka, 1976. 159 p. In Russ.

  10. Rykalin N.N. Raschety teplovyh processov pri svarke [Calculation of thermal processes during welding]. Moscow: Mashgiz, 1951. 296 p. In Russ.

  11. Mashrabov N., Gerenstein A.V., Gerenstein E.A. Obosnovanie metoda opredeleniya temperaturnogo polya pri naplavke, termicheskoj i mekhanicheskoj obrabotke [Justification of the method for detecting the temperature field when thermal and mechanical processing and surfacing]. АPK Rossii — Agro-Industrial Complex of Russia, 2015, vol. 73, pp. 69–75. In Russ.

  12. Zakovorotny L.V., Lapshin V.P., Babenko T.S. Modelirovanie iznosa po rabote i moshchnosti neobratimyh preobrazovanij energii [Modeling of wear by work and power of irreversible energy conversions]. STanki INstrument ,2018, no. 3, pp. 9–10. In Russ.

  13. Zakovorotny V.L., Tung F.D. Perestrojka dinamicheskoj sistemy, vzaimodejstvuyushchej s processom rezaniya, v hode eyo evolyucii [The reorganization of the dynamic system interacting with the cutting process, during its evolution]. Izvestiya Yuzhnogo federal’nogo universiteta. Tekhnicheskie nauki — Izvestiya SFeDU. Engineering Sciences, 2011, no. 6 (119), pp. 49–61. In Russ.

  14. Zakovorotny V.L. Modelirovanie evolyucionnyh preobrazovanij pri obrabotke na metallorezhushchih stankah s pomoshch’yu integral’nyh operatorov [Modeling evolutionary transformations during processing on metal cutting machines using integral operators]. Izvestiya vuzov. Severo-Kavkazskij region. Estestvennye nauki — University news. North-Caucasian region. Natural sciences series, 2004, no. S, pp. 26–40. In Russ.

  15. Zakovorotny L.V., Lapshin V.P., Babenko T.S. Assessing the regenerative effect impact on the dynamics of deformation movements of the tool during turning. Procedia Engineering, 2017, vol. 206, pp. 68–73. https://doi.org/10.1016/j.proeng.2017.10.439

  16. 16. Voronov S.A., Nepochatov A.V., Kiselev I.A. Kriterii ocenki ustojchivosti processa frezerovaniya nezhestkih detalej [Criteria for assessing the stability of the milling process of non-rigid parts ]. Izvestiya vysshikh uchebnykh zavedenij. Mashinostroenie — Proceedings of Higher Educational Institutions. Маchine Building, 2011, no. 1, pp. 50–61. In Russ.

  18. Voronov S.A., Veydun M. Mathematical modeling of the cylindrical grinding process. Journal of Machinery Manufacture and Reliability, 2017, vol. 46, no. 4, pp. 394–403. DOI: 10.3103/S1052618817030177

  19. Belyaev N.M., Ryadno A.A. Metody teorii teploprovodnosti. T. 2 [Methods of the theory of thermal conductivity. Vol. 2]. Moscow: Vysshaya shkola, 1982. 304 p. In Russ.

  20. Polozhij G.N. Uravneniya matematicheskoj fiziki [Equations of mathematical physics]. Moscow: Vysshaya shkola, 1964. 559 p. In Russ.

  21. Lapshin V.P., Babenko T.S., Minakov V.S., Kambulov S.I. Experimental evaluation of the influence of tool wear on the temperature in the cutting zone during the turning of metals. MATEC Web of Conferences, 2018, vol. 226. p. 02011. https://doi.org/10.1051/matecconf/201822602011

  22. Lapshin V.P., Babenko T.S., Moiseev D.V. Experimental evaluation of influence of tool wear on quality of turning. Proceedings of the 4th International Conference on Industrial Engineering. ICIE, 2018. pp. 853–859. https://doi.org/10.1007/978-3-319-95630-5_89

  23. Lapshin V.P., Babenko T.S., Radionova S.I. Аnaliz protsessov iznosa instrumenta pri tochenii metallov na metallorezhushhikh stankakh [Wear process analysis of the tool when turning metals in metal-cutting machine]. Molodoj issledovatel’ Dona — Don Young Researcher, 2018, no. 5 (14), pp. 73–77. In Russ.

mai.ru — informational site of MAI

Copyright © 2009-2024 by MAI