# Науковий вісник НГУ

## Effect of centrifugal forces of a flexible body on traction friction implementation

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Authors:

N.A. Lubenets, Cand. Sci. (Tech.), Associate Professor, State Higher Educational Institution “National Mining University”, Senior Lecturer of the Department of Transport Systems and Technology, Dnipropetrovsk, Ukraine

T.N. Lubenets, State Higher Educational Institution “National Mining University”, Student, Dnipropetrovsk, Ukraine

Abstract:

Purpose. To establish the influence of centrifugal forces of the flexible body sliding over a fixed block on the friction force between them.
The influence of centrifugal forces of the flexible body is usually described by the Euler's law of flexible bodies friction (Euler's formula), which is widely used in international and domestic practice, research, engineering, technology and education. However, it was obtained in times when old notions of Amontons friction predominated and its imperfection results in the disagreement between practice and theory. Euler is the founder of analytical methods used now for study of the influences of centrifugal forces of the flexible body, but they need to be developed and improved by modern knowledge about friction and energy.

Findings. The article describes an alternative formula for solution of the problem of flexible body sliding over a fixed unit, taking into account the centrifugal forces. The conclusion is based on the Coulomb's concept of friction and modern methods of mechanics, the principles of conservation of energy.

Originality. The accurate data about the influence of the drum angle of contact, friction coefficient, tension in different segments of the flexible body, its linear mass and movement speed on realization of traction friction.

Practical value. An alternative solution overcomes the disagreement between the accumulated empirical data and solution of Euler's formula of flexible bodies. It was found that the effect of centrifugal forces of the flexible body moving on the block is very important for the implementation of the friction force. For example, for the conveyor belt at speeds of 2 and 4 meters per second the traction under the alternative solution of the Euler problem is reduced to 15 and 75% respectively compared to the maximum.
The knowledge gained develops analytical methods in mechanics, scientific concepts of friction, flexible bodies, contributing to the overall progress.

References:

1. Тарг С.М. Краткий курс теоретической механики: Учеб. для вузов / Тарг С.М. – [12-е изд.] – М.: Высш. шк., 1998. – 416 с.

Targ, S.M. (1998), Kratkiy kurs teoreticheskoy mekhaniki [Short Course of Theoretical Mechanics], Manual, Issue 12, Vysshaya shkola, Moscow, Russia.

2. Лубенец Н.А. Альтернативный формуле Эйлера закон реализации тягового усилия трением / Н.А. Лубенец // Науковий вісник НГУ. – Днепропетровск, 2008. – № 11.– С. 67 – 70.

Lubenets N.A. (2008), “The law of traction friction implementation alternative to the Euler formula”, Naukovyi visnyk Natsionalnoho hirnychoho universytetu, no.11, pp. 67–70.

3. Лубенец Н.А. Зависимость натяжения идеальной нити вдоль линии контакта с неподвижным блоком при скольжении / Н.А. Лубенец // Науковий вісник НГУ. – Днепропетровск, 2010. – № 9–10. – С. 27–32.

Lubenets N.A. (2010), “Dependence of pull of ideal filament along the line of contact with immobile block when sliding”, Naukovyi visnyk Natsionalnoho hirnychoho universytetu, no.9–10, pp. 27–32.

Files:
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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.

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