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. 22, no. 1, 2019 (March)
Pages 60-66
Cited by J. of Mech. Eng., 2019, vol. 22, no. 1, pp. 60-66



Tatyana I. Sheyko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi Str., Kharkiv, 61046, Ukraine), e-mail:, ORCID: 0000-0003-3295-5998

Kyrylo V. Maksymenko-Sheiko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi Str., Kharkiv, 61046, Ukraine), V. N. Karazin Kharkiv National University (4, Svobody Sq., Kharkiv, 61022, Ukraine), e-mail:, ORCID: 0000-0002-7064-2442

Anna I. Morozova, Kharkiv National University of Radio Electronics (14, Nauky Ave., Kharkiv, 61166, Ukraine), ORCID: 0000-0002-7082-4115



The creation of mathematical models for the implementation of 3D printing is of considerable interest, which is associated with the active introduction of 3D printing in various industries. The advantages of using 3D printing are the following: the possibility of making non-standard models, reducing the time to create new prototypes, making simple and low cost products, and using modern super-strength materials. The manufacture of machine components with a screw-type symmetry occurs in various, often very complicated ways to include casting with the subsequent rotary machining, methods of hot deformation, electrophysical and electrochemical methods, etc. Their manufacture on a 3D printer can be very promising. In this paper, the R-functions theory is used for the mathematical and computer modeling of geometric objects with a screw-type symmetry for the case when 3D printing technology is to be implemented. An analytical recording of the objects being designed makes it possible to use alphabetic geometric parameters, complex superposition of functions, which, in turn, allows us to quickly change their structural elements. The working part of many mechanisms for moving a material along a helical rotating surface is a screw. Screws are used instead of wheels in some types of cross-country vehicles or combines. They are an indispensable part in extruders and boring stations. At large enterprises, they are used as a means of transporting bulk materials. Screws are indispensable in the food industry. Among other things, they are used in small arms, where they play the role magazines for cartridges. In this work, we build mathematical and computer models of the variable and constant pitch screws to be implemented on a 3D printer. In order to organize and intensify various processes in power plants and other technical devices, swirling is widely used. Swirling is an effective means of stabilizing the flame in the combustion chambers of gas turbine engines. It is also used to intensify heat and mass transfer in channels; in chemical, petroleum, gas and other industries. This paper considers mathematical and computer models of a screw swirler, locally twisted tube, and complex cross-section twisted tube intended for the implementation on a 3D printer. The process of building a desk lamp with a design in the form of elliptic twisted tori is shown as well.


Keywords: R-functions theory, 3D printing, screw-type symmetry, screw.


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Received 31 January 2019

Published 30 March 2019