Geometric modeling of pneumatic shaped surfaces of rotation, reinforced by winding thread

Kutsenko Leonid

National University of Civil Defenсe of Ukraine

https://orcid.org/0000-0003-1554-8848

Rudenko Svetlana

National University of Civil Defenсe of Ukraine

https://orcid.org/0000-0002-5688-0639

Kalynovskyi Andrii

National University of Civil Defenсe of Ukraine

http://orcid.org/0000-0002-1021-5799

Polivanov Oleksandr

National University of Civil Defenсe of Ukraine

https://orcid.org/0000-0002-6396-1680

Sukharkova Olena

National University of Civil Defenсe of Ukraine

https://orcid.org/0000-0003-1033-4728

DOI: https://doi.org/10.52363/2524-0226-2024-39-15

Keywords: meridian of the surface of revolution, average curvature of the surface, corrugated surface of revolution, reinforcement by thread winding

Аnnotation

A scheme is proposed for calculating the geometric forms of the family of meridians of a rubber pneumatic shaped surface of rotation depending on the function of changing the average curvature along the axis of this surface. It is proposed to strengthen the resulting shaped surface of rotation by winding the thread along the geodesic curves of the found surface. A method has been developed for determining the approximate shape of the elements of the family of meridians of the pneumatic surface of rotation. In addition, constructed surfaces of revolution, strengthened by winding threads along their geodesic lines, depending on the function of changing the curvature of the meridian. As a result, images of geodesic curves on shaped surfaces of revolution were obtained. The construction of a geodesic thread winding on a corrugated surface is generalized for the case of a sawtooth-shaped meridian. It is advisable to model a pneumatic surface based on calculating its average curvature. Since the value of the average curvature of the interface between two balanced physical media is proportional to the difference in pressure values in these media. By varying the average curvature of the surface, you can choose the amount of pressure that the pneumatic product will withstand. Approximate descriptions of the shape of the meridian of the shaped surface of revolution are obtained by solving the direct and inverse problems. The parameters of geodetic winding are calculated depending on the given meridian curvature function. The construction of geodesic winding of a thread on a corrugated surface is generalized for the case of a sawtooth-shaped meridian. For practice, the studies conducted are useful and important, since they provide calculations of rational pneumatic products intended for use during emergency rescue operations.

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