DOI https://doi.org/10.15407/pmach2017.02.054
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20 no. 2, 2017 (June)
Pages 54-60
Cited by J. of Mech. Eng., 2017, vol. 20, no. 2, pp. 54-60



T. I. Sheyko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: sheyko@ipmach.kharkov.ua, ORCID: 0000-0003-3295-5998

K. V. Maksymenko-Sheiko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail:  m-sh@ipmach.kharkov.ua, ORCID: 0000-0002-7064-2442

Yu. S. Litvinova, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: litjuli56@gmail.com

D. A. Lisin, V. N. Karazin Kharkiv National University (4, Svobody Sq., Kharkiv, 61022, Ukraine), ORCID: 0000-0002-6718-7389



In this paper, based on the R-functions theory, we developed techniques and constructed equations for various heat transfer finning surfaces, including chevron ones. Finning not only increases the heat exchange surface, but also greatly influences the flow hydrodynamics, thereby influencing the heat transfer coefficient. The resulting surface equations were implemented on a 3D printer. Chevron wheels solve the problem of axial force, however, due to the complexity and high cost of manufacturing, chevron gears are used less frequently. 3D printing technology allows reducing the cost and complexity of manufacturing products, including chevron wheels. An analytical recording of the objects under design makes it possible to use alphabetic geometric parameters, complex superposition of functions, which, in turn, allows you to quickly change their structural elements. The property of positivity of the constructed functions in the internal points of the object is very convenient for the implementation of 3D printing.


Keywords: R-functions, mathematical model, finning of heat transfer surfaces, chevron



  1. Petukhov, B. S., Genin, L. G., & Kovalev, S. A. (1974). Teploobmen v yadernykh energeticheskikh ustanovkakh [Heat transfer in nuclear power plants]. Moscow: Atomizdat, 367 p. (in Russian).
  2. Andreyev, P. A. (1969). Teploobmennyye apparaty yadernykh energeticheskikh ustanovok [Heat exchangers for nuclear power plants]. Leningrad: Sudostroyeniye, 255 p. (in Russian).
  3. Antufyev, V. M. (1966). Effektivnost razlichnykh form konvektivnykh poverkhnostey nagreva [Efficiency of various forms of convective heating surfaces]. Moscow: Energiya, 310 p. (in Russian).
  4. Requicha, A. A. G. (1980). Representations for rigid solids: theory, methods, and systems. ACM Computing Surveys, vol. 12, iss. 4, pp. 437–464. https://doi.org/10.1145/356827.356833
  5. Requicha, A. A. G. & Voelcker, H. B. (1982). Solid modeling: a historical summary and contemporary assessment. IEEE Computer Graphics and Applications, vol. 2, iss. 2, pp. 9–24. https://doi.org/10.1109/MCG.1982.1674149
  6. Requicha, A. A. G. & Voelcker, H. B. (1983). Solid modeling: current status and research directions. IEEE Computer Graphics and Applications, vol. 3, iss. 7, pp. 25–37. https://doi.org/10.1109/MCG.1983.263271
  7. Rvachev, V. L. (1982). Teoriya R-funktsiy i nekotoryye yeye prilozheniya [The R-functions theory and some of its applications]. Kiyev: Naukova Dumka, 552 p. (in Russian).
  8. Maksimenko-Sheyko, K. V. (2009). R-funktsii v matematicheskom modelirovanii geometricheskikh obektov i fizicheskikh poley [R-functions in mathematical modeling of geometric objects and physical fields]. Kharkov: A. Podgorny Institute of Mechanical Engineering Problems of NASU, 306 p. (in Russian).
  9. Lisin, D. O. (2012). Kompiuterna prohrama «Systema vizualizatsii ta pobudovy sitky na poverkhni heometrychnykh obiektiv, yaki opysani za dopomohoiu matematychnykh zasobiv teorii R-funktsii «RFPreview» [Computer program “The system of visualization and grid construction on the surface of geometric objects, which are described using mathematical means of the theory of R-functions “RFPreview”]. Certificate of registration of copyright in the work, no. 45951. (in Ukrainian).
  10. Lisin, D. A., Maksimenko-Sheyko, K. V., Tolok, A. V., & Sheyko, T. I. (2011). R-funktsii v kompyuternom modelirovanii dizayna 3D-poverkhnosti avtomobilya [R-functions in computer simulation of the design of a 3D car surface]. Prikladnaya informatikaApplied Informatics, no. 6 (36), pp. 78–85 (in Russian).


Received 28 March 2017

Published 30 June 2017