Name: flat belt forces and pulley moment
Uploaded: 2023-09-22T11:49:30.000Z
Duration: 1 min 28 s
Channel: JoVE

Une courroie plate s’enroule autour de deux poulies, A et B, avec des rayons de 30 cm et 10 cm, respectivement.
L’angle entre la courroie et l’horizontale est de 20 degrés au niveau des poulies.
La poulie B tourne dans le sens des aiguilles d’une montre et entraîne la poulie A, provoquant la tension T2 à une extrémité de la courroie et la tension T1 à l’autre.
Étant donné que la tension maximale admissible T2 est de 1000 N et que le coefficient de frottement statique entre la courroie et les poulies est de 0,4, quel est le moment maximal sur la poulie A ?
L'angle de contact entre la ceinture et la surface, calculé à partir de la géométrie du système, est de 140 degrés.
L’angle de contact ceinture-surface en radians et le coefficient de frottement statique sont substitués dans l’expression des tensions de courroie pour obtenir T1.
Lorsque la poulie B tourne dans le sens des aiguilles d’une montre, une différence de tension créée à la poulie B génère un moment à la poulie A.
Un schéma de corps libre pour la poulie A est dessiné et la condition d’équilibre du moment est appliquée.
Les valeurs de rayon et de tension sont substituées pour obtenir le moment maximum.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. Pages 439 à 441.</li>
	<li>Meriam, J.L. ; Kraige, L.G. et Bolton, J.N. (2020). Génie mécanique \u2012 Statique. Hoboken, New Jersey : John Wiley. Pages 372.</li>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. Pages 469 et 470.</li>
</ol>

courroies plates : résolution de problèmes

Flat Belts: Problem Solving

Les courroies plates sont essentielles dans de nombreuses applications industrielles car elles aident à transmettre la puissance d'une poulie à une autre. Le concept de forces et de moments est utilisé pour déterminer le moment maximal sur une poulie. Par exemple, prenons une courroie plate qui enveloppe deux poulies, A et B, ayant respectivement des rayons de 30 cm et 10 cm. L'angle entre la courroie et l'horizontale est de 20 degrés au niveau des poulies. Lorsque la poulie B tourne dans le sens des aiguilles d'une montre et entraîne la poulie A, une tension T2 est créée à une extrémité de la courroie, tandis qu'une tension T1 est créée à l'autre extrémité. <img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;"> L'angle de contact de la courroie avec la surface, β, doit être calculé pour déterminer le moment maximal. Cet angle est obtenu à partir de la géométrie du système et on trouve qu'il est de 140 degrés. Par conséquent, l'angle de contact de la courroie avec la surface en radians, ainsi que le coefficient de frottement statique, 0,4, sont substitués dans l'expression des tensions de la courroie. <img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;"> En considérant que la tension maximale autorisée T2 est de 1000 N, la valeur calculée de T1 est de 376,93 N. Lorsque la poulie B tourne dans le sens des aiguilles d'une montre, une différence de tension est créée au niveau de la poulie B, générant un moment au niveau de la poulie A. En considérant un diagramme du corps libre pour la poulie A, la condition d'équilibre des moments peut être appliquée. <img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> Les valeurs du rayon et des tensions sont ensuite substituées pour obtenir le moment maximal de 186,921 N.m.

Courroies plates : Résolution de problèmes

Les courroies plates sont cruciales dans de nombreuses applications industrielles car elles aident à transmettre la puissance d’une poulie à une autre. Le concept de forces et de moments est utilisé ...

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flat belt forces and pulley moment

Flat belts transmit power from one pulley to another, and the forces on the belt help determine the moment on a pulley. In this example, a belt wraps around pulleys A and B, with radii of 30 cm and 10 cm. The belt meets the pulleys at a 20 degree angle from the horizontal, which sets up the force balance in the system.

As pulley B rotates clockwise, it drives pulley A. That motion creates tension T2 on one side of the belt and tension T1 on the other side. The belt-to-surface contact angle, β, is needed to find the maximum moment, so it is first found from the geometry of the setup. The angle is 140 degrees.

Next, the contact angle in radians and the coefficient of static friction, 0.4, are used in the belt tension equation. With the maximum allowable tension T2 set to 1000 N, the value of T1 is calculated as 376.93 N. A free-body diagram for pulley A then helps apply moment equilibrium. Using the pulley radius and the belt tensions, the maximum moment is found to be 186.921 N.m.

Flat Belt Forces and Pulley Moment

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key terms and concepts

Learn how belt tension, friction, and pulley radius are used to calculate the maximum moment in a flat belt drive system with two pulleys.

Flat Belt Forces and Pulley Moment | JoVE K12

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Flat Belt Forces and Pulley Moment

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