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

Stellen Sie sich einen Flachriemen vor, der um einen Satz Riemenscheiben gewickelt ist und bei dem Riemenspannungen an den Enden der Antriebsriemenscheibe auftreten.
Bei einer Bewegung der Riemenscheibe gegen den Uhrzeigersinn ist die Größe von T2 aufgrund der Reibung zwischen der Oberfläche des Riemens und der Riemenscheibe größer als die von T1.
Die Kenntnis des Gesamtkontaktwinkels zwischen Riemen und Oberfläche und des Reibungskoeffizienten ermöglicht die Abschätzung der Spannungen.
Es wird ein Freikörperdiagramm eines Differentialelements AB des Gurtes gezeichnet.
Bei der Annahme einer bevorstehenden Bewegung wirkt die Reibungskraft der Gleitbewegung des Riemens entgegen, wodurch die Größe der an Punkt B wirkenden Riemenspannung um dT zunimmt.
Unter Anwendung des horizontalen und vertikalen Kraftgleichgewichts und unter Verwendung der Kosinus- und Sinusnäherungen erhält man zwei Gleichgewichtsgleichungen.
Das Produkt zweier Differentiale im Vergleich zu den Differentialen erster Ordnung wird in den vertikalen Gleichgewichtsgleichungen vernachlässigt, während die horizontale Gleichgewichtsgleichung weiter vereinfacht wird.
Die Kombination der Gleichgewichtsgleichungen und die Integration zwischen den entsprechenden Grenzwerten ergibt einen Ausdruck, der die Riemenspannungen korreliert.
Diese Gleichung gilt für Flachriemen, die über eine gekrümmte Kontaktfläche verlaufen.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. S. 439 \u2012 440.</li>
	<li>Meriam, J.L.; Kraige, L.G. und Bolton, J.N. (2020). Technische Mechanik \u2012 Statik. Hoboken, New Jersey: John Wiley. Seite 373.</li>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P. (2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. Seite 463</li>
</ol>

reibungskräfte auf flachriemen

Frictional Forces on Flat Belts

Flachriemen werden in verschiedenen industriellen Anwendungen häufig zur Übertragung von Leistung von einer Riemenscheibe auf eine andere verwendet. Wenn ein Flachriemen um eine Gruppe von Riemenscheiben gewickelt ist, erfährt er aufgrund der Reibung zwischen dem Riemen und der Riemenscheibenoberfläche unterschiedliche Spannungen an den Antriebsscheibenenden. Wenn sich die Riemenscheibe in counterclockwise-Richtung bewegt, ist die Spannung T2 auf der gegenüberliegenden Seite der Riemenscheibe, in welche sich der Riemen bewegt, höher als die Spannung T1 auf der Seite, in welche sich der Riemen bewegt. Um die Spannungen in einem Flachriemen abzuschätzen, muss der gesamte Winkel des Riemen-zu-Oberflächen-Kontakts und der Reibungskoeffizient zwischen den Oberflächen bekannt sein. Ein Freikörperdiagramm eines Differentialelements AB des Riemens kann gezeichnet werden, unter der Annahme einer drohenden Bewegung. <img alt="Figure 1" src="/files/ftp_upload/14322/14322_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> Die Reibungskraft wirkt der Gleitbewegung des Riemens entgegen und bewirkt, dass die Größe der am Punkt B wirkenden Riemenzugspannung um dT zunimmt. Diese differentielle Spannung kann verwendet werden, um die Spannungen an verschiedenen Punkten entlang des Riemens in Beziehung zu setzen. Um die Beziehung zwischen den Riemenzugspannungen zu bestimmen, werden die Gleichgewichtsgleichungen für horizontale und vertikale Kräfte, zusammen mit Kosinus- und Sinus-Näherungen, verwendet. <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;"> Diese Gleichungen berücksichtigen die auf das Differentialelement AB in horizontaler und vertikaler Richtung wirkenden Kräfte. Das Produkt zweier Differenziale im Vergleich zu den Differentiale erster Ordnung wird in den Vertikalequilibriumsgleichungen vernachlässigt, während die Horizontalgleichgewichtsgleichung weiter vereinfacht wird. Die Gleichgewichtsgleichungen werden kombiniert und zwischen entsprechenden Grenzen integriert. <img alt="Equation 3" src="/files/ftp_upload/14322/14322_PT_Equation_3v2.svg" style="text-align: center; height: 45px;"> Das Ergebnis ergibt einen Ausdruck, der die Riemenzugspannungen in Beziehung setzt. <img alt="Equation 4" src="/files/ftp_upload/14322/14322_PT_Equation_4v2.svg" style="text-align: center; height: 15px;"> Diese Gleichung gilt für Flachriemen, die über eine beliebig gekrümmte Kontaktfläche verlaufen. Die Reibungskräfte auf Flachriemen sind entscheidend für die Leistung und Effizienz des riemengetriebenen Systems. Eine Überbeanspruchung des Riemens kann zu vorzeitigem Verschleiß und verringerter Effizienz führen, während eine Unterbeanspruchung zu Schlupf und verminderte Leistungsübertragung führen kann. Eine ordnungsgemäße Spannung wird durch Einstellen des Abstands zwischen den Riemenscheiben oder durch Verwendung einer Spannvorrichtung erreicht.

Reibungskräfte auf Flachriemen

Flachriemen werden häufig in verschiedenen industriellen Anwendungen zur Kraftübertragung von einer Riemenscheibe zur anderen eingesetzt. Wenn ein Flachriemen um einen ...

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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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Flat Belt Tension and Friction

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