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

Una cinghia piatta avvolge due pulegge, A e B, con raggi rispettivamente di 30 cm e 10 cm.
L'angolo tra la cinghia e l'orizzontale è di 20 gradi in corrispondenza delle pulegge.
La puleggia B ruota in senso orario e aziona la puleggia A, provocando la tensione T2 a un'estremità della cinghia e la tensione T1 all'altra.
Dato che la tensione massima ammissibile T2 è 1000 N e il coefficiente di attrito statico tra la cinghia e le pulegge è 0,4, qual è il momento massimo sulla puleggia A?
L'angolo di contatto nastro-superficie, calcolato in base alla geometria del sistema, è di 140 gradi.
L'angolo di contatto cinghia-superficie in radianti e i valori del coefficiente di attrito statico sono sostituiti nell'espressione per le tensioni della cinghia per ottenere T1.
Quando la puleggia B ruota in senso orario, una differenza di tensione creata in corrispondenza della puleggia B genera un momento in corrispondenza della puleggia A.
Viene disegnato un diagramma di corpo libero per la puleggia A e viene applicata la condizione di equilibrio del momento.
I valori di raggio e tensione vengono sostituiti per ottenere il momento massimo.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. Pagine 439 - 441.</li>
	<li>Meriam, J.L.; Kraige, LG e Bolton, JN (2020). Ingegneria Meccanica \u2012 Statica. Hoboken, New Jersey: John Wiley. Pagine 372.</li>
	<li>Birra, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. e Self, B.P. (2019). Meccanica vettoriale per ingegneri \u2012 Statica e dinamica. New York: McGraw-Hill. Pagine 469-470.</li>
</ol>

nastri piatti: risoluzione dei problemi

Flat Belts: Problem Solving

I nastri piatti sono fondamentali in molte applicazioni industriali perché aiutano a trasmettere potenza da una puleggia all'altra. Il concetto di forze e momenti viene utilizzato per determinare il momento massimo su una puleggia. Ad esempio, consideriamo un nastro piatto che avvolge due pulegge, A e B, con raggi rispettivamente di 30 cm e 10 cm. L'angolo tra il nastro e l'orizzontale è di 20 gradi sulle pulegge. Quando la puleggia B ruota in senso orario e muove la puleggia A, si crea tensione T2 su un'estremità del nastro, e tensione T1 sull'altra.

<img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;" />

L'angolo di contatto tra il nastro e la superficie, β, deve essere calcolato per determinare il momento massimo. Questo angolo è ottenuto dalla geometria del sistema ed è risultato essere di 140 gradi. Di conseguenza, l'angolo di contatto tra il nastro e la superficie in radianti, insieme al coefficiente di attrito statico, 0,4, viene sostituito nell'espressione per le tensioni del nastro.

<img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;" />

Considerando che la tensione massima consentita T2 è di 1000 N, il valore calcolato di T1 è di 376,93 N. Quando la puleggia B ruota in senso orario, si crea una differenza di tensione sulla puleggia B, generando un momento sulla puleggia A. Considerando un diagramma del corpo libero per la puleggia A, si può applicare la condizione di equilibrio dei momenti.

<img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

I valori del raggio e delle tensioni vengono quindi sostituiti per ottenere il momento massimo, pari a 186,921 N.m.

Nastri piatti: risoluzione dei problemi

Le cinghie piatte sono fondamentali in molte applicazioni industriali in quanto aiutano a trasmettere la potenza da una puleggia all'altra. Il concetto di forze e momenti è usato ...

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Ingegneria Meccanica

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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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mechanical engineering

Flat Belt Forces and Pulley Moment

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