Name: flat belt tension and friction
Uploaded: 2023-09-22T11:49:29.000Z
Duration: 1 min 28 s
Channel: JoVE

Si consideri una cinghia piatta avvolta attorno a una serie di pulegge, che subisce tensioni della cinghia alle estremità della puleggia motrice.
Per un movimento della puleggia in senso antiorario, l'entità di T2 è maggiore di T1 a causa dell'attrito tra la cinghia e la superficie della puleggia.
Conoscere l'angolo totale di contatto cinghia-superficie e il coefficiente di attrito consente di stimare le tensioni.
Viene disegnato uno schema a corpo libero di un elemento differenziale AB della cinghia.
Assumendo un movimento imminente, la forza di attrito si oppone al movimento di scorrimento della cinghia, provocando un aumento di dT dell'entità della tensione della cinghia che agisce nel punto B.
Applicando l'equilibrio delle forze orizzontale e verticale e utilizzando le approssimazioni coseno e seno, si ottengono due equazioni di equilibrio delle forze.
Il prodotto di due differenziali rispetto ai differenziali del primo ordine è trascurato nelle equazioni di equilibrio verticale, mentre l'equazione di equilibrio orizzontale è ulteriormente semplificata.
Combinando le equazioni di equilibrio e integrando tra i limiti corrispondenti si ottiene un'espressione correlata alle tensioni della cinghia.
Questa equazione si applica alle cinghie piatte che passano su qualsiasi superficie di contatto curva.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 439 \u2012 440.</li>
	<li>Meriam, J.L.; Kraige, LG e Bolton, JN (2020). Ingegneria Meccanica \u2012 Statica. Hoboken, New Jersey: John Wiley. Pagine 373.</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 463</li>
</ol>

forze di attrito su cinghie piatte

Frictional Forces on Flat Belts

Le cinghie piatte vengono comunemente utilizzate in vari settori industriali per trasmettere potenza da una puleggia all'altra. Quando una cinghia piatta viene avvolta attorno a un gruppo di pulegge, essa sperimenta diverse tensioni alle estremità delle pulegge motrici a causa dell'attrito tra la cinghia e la superficie delle pulegge. Quando la puleggia si muove in direzione antioraria, la tensione T2 sul lato opposto della puleggia, dove la cinghia si allontana, è maggiore della tensione T1 sul lato in cui la cinghia si avvicina.

Per stimare le tensioni in una cinghia piatta, è necessario conoscere l'angolo totale di contatto tra la cinghia e la superficie e il coefficiente di attrito tra le superfici. È possibile disegnare un diagramma di corpo libero di un elemento differenziale AB della cinghia assumendo un moto imminente.

<img alt="Figure 1" src="/files/ftp_upload/14322/14322_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

La forza di attrito contrasta il moto di scorrimento della cinghia, facendo aumentare la magnitudine della tensione della cinghia agente nel punto B di dT. Questa tensione differenziale può essere utilizzata per correlare le tensioni in diversi punti lungo la cinghia.

Per determinare la relazione tra le tensioni della cinghia, vengono utilizzate le equazioni di equilibrio delle forze orizzontali e verticali, insieme ad approssimazioni di coseno e seno.

<img alt="Equation 1" src="/files/ftp_upload/14322/14322_PT_Equation_1v2.svg" style="text-align: center; height: 30px;" />

<img alt="Equation 2" src="/files/ftp_upload/14322/14322_PT_Equation_2v2.svg" style="text-align: center; height: 30px;" />

Queste equazioni considerano le forze che agiscono sull'elemento differenziale AB nelle direzioni orizzontale e verticale. Il prodotto di due differenziali diversi rispetto ai differenziali di primo ordine viene trascurato nelle equazioni di equilibrio verticale, mentre l'equazione di equilibrio orizzontale viene ulteriormente semplificata. Le equazioni di equilibrio vengono combinate ed integrate tra i limiti corrispondenti.

<img alt="Equation 3" src="/files/ftp_upload/14322/14322_PT_Equation_3v2.svg" style="text-align: center; height: 45px;" />

Il risultato fornisce un'espressione che correla le tensioni della cinghia.

<img alt="Equation 4" src="/files/ftp_upload/14322/14322_PT_Equation_4v2.svg" style="text-align: center; height: 15px;" />

Questa equazione si applica a cinghie piatte che passano su qualsiasi superficie di contatto curva.

Le forze di attrito su cinghie piatte sono cruciali per determinare le prestazioni e l'efficienza del sistema azionato dalla cinghia. Sovratensionare la cinghia può causare un'usura prematura e ridurre l'efficienza, mentre sottotensionarla può causare slittamento e ridurre la trasmissione di potenza. Una tensionatura corretta viene raggiunta regolando la distanza tra le pulegge o utilizzando un dispositivo tensionatore.

Forze di attrito su cinghie piatte

Le cinghie piatte sono comunemente utilizzate in varie applicazioni industriali per la trasmissione di potenza da una puleggia all'altra. Quando una cinghia piatta è avvolta attorno a un ...

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Ingegneria Meccanica

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Friction

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flat belt tension and friction

Flat belt tension and friction control how power moves from one pulley to another. Flat belts are used in many industrial systems to transmit power between pulleys. As the belt wraps around the pulleys, the tension changes because of friction between the belt and the pulley surface.

When a pulley turns counterclockwise, the belt side moving away from the pulley has the higher tension, called T2. The side moving toward the pulley has the lower tension, called T1. To estimate these tensions, the total angle of contact and the coefficient of friction between the surfaces must be known.

The belt can be analyzed with a free-body diagram of a small belt element, AB. This analysis assumes impending motion, which means the belt is close to slipping. Friction acts against the sliding motion, so the tension at point B increases by a small amount, dT.

The tension relationship is found using horizontal and vertical force equilibrium. Cosine and sine approximations help simplify the force equations for the small belt element. In the vertical equation, the product of two differentials is neglected, and the horizontal equation is simplified further. The equations are then combined and integrated between the proper limits to obtain the belt-tension expression.

This result applies to flat belts that pass over curved contacting surfaces. Frictional forces are important because they affect the performance and efficiency of the belt-driven system. If the belt is too tight, it can wear out early and reduce efficiency. If it is too loose, it can slip and reduce power transmission. Proper tension is usually set by changing the distance between the pulleys or by using a tensioning device.

Flat Belt Tension and Friction

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key terms and concepts

Learn how friction changes tension in a flat belt, why angle of contact matters, and how proper belt tension helps prevent wear and slippage.

Flat Belt Tension and Friction | JoVE K12

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mechanical engineering

Flat Belt Tension and Friction

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