Construction of a flat workpiece for manufacturing a turn of the right helicoid

Authors

DOI:

https://doi.org/10.15587/1729-4061.2023.275508

Keywords:

right closed helicoid, flat workpiece, continuous bending, parametric equations

Abstract

In technology, a common helical surface is a right closed helicoid (auger). It is formed by a helical movement of a horizontal segment, provided that the axis of the auger crosses at one of its ends. The formation of the surface of an open helicoid is similar but the segment must intersect the axis and be located at a constant distance from it. It is known from differential geometry that the helical surface can be transformed by bending to the surface of rotation. This fact is taken as the basis for calculating the geometric shape of a flat workpiece. The surface of the open helicoid is non-disjointed, so the shape of the workpiece must be found in such a way as to minimize plastic deformations during surface formation.

Parametric equations of continuous flexion of the turn of an open helicoid into the section of a single-cavity hyperboloid of rotation have been derived. Continuous bending can be represented as a gradual deformation of the turn while reducing its step. The meridian of hyperboloid rotation is the corresponding area of hyperbola. The hyperboloid section is proposed to be approximated by the surface of the truncated cone. This approximation will be more accurate in the area of the hyperbole where it asymptotically approaches the segment of the right line. After selecting a cone, it becomes possible to determine its size and build its exact sweep since the cone is a unfolding surface. The sweep is constructed in the form of a flat ring with a cut sector and will be the desired flat workpiece to form a turn of the auger from it.

Most accurately, the surface of the turn of the open helicoid can be made by stamping the workpiece of the resulting form. For small-scale production of the helical surface of an open helicoid, it is advisable to weld flat rings together and, during installation, stretch along the shaft while twisting around its axis. The accuracy of the obtained surface will depend on the accuracy of the approximation of the hyperboloid section of rotation with a truncated cone, which is the topic of this work.

Author Biographies

Tatiana Volina, National University of Life and Environmental Sciences of Ukraine

PhD, Associate Professor

Department of Descriptive Geometry, Computer Graphics and Design

Serhii Pylypaka , National University of Life and Environmental Sciences of Ukraine

Doctor of Technical Sciences, Professor, Head of Department

Department of Descriptive Geometry, Computer Graphics and Design

Vyacheslav Hropost, National University of Life and Environmental Sciences of Ukraine

Postgraduate Student

Tetiana Kresan, Separate Subdivision of National University of Life and Environmental Sciences of Ukraine "Nizhyn Agrotechnical Institute"

PhD, Associate Professor, Head of Department

Department of Natural, Mathematical and General Engineering Disciplines

Oleksandr Zabolotnii, Separate Subdivision of National University of Life and Environmental Sciences of Ukraine "Nizhyn Agrotechnical Institute"

PhD, Associate Professor

Department of Natural, Mathematical and General Engineering Disciplines

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Construction of a flat workpiece for manufacturing a turn of the right helicoid

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Published

2023-04-28

How to Cite

Volina, T., Pylypaka , S., Hropost, V., Kresan, T., & Zabolotnii, O. (2023). Construction of a flat workpiece for manufacturing a turn of the right helicoid . Eastern-European Journal of Enterprise Technologies, 2(1 (122), 6–11. https://doi.org/10.15587/1729-4061.2023.275508

Issue

Vol. 2 No. 1 (122) (2023): Engineering technological systems

Section

Engineering technological systems

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Copyright (c) 2023 Tatiana Volina, Serhii Pylypaka , Vyacheslav Hropost, Tetiana Kresan, Oleksandr Zabolotnii

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