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

Weźmy pod uwagę płaski pasek owinięty wokół zestawu kół pasowych, w którym występują naprężenia paska na końcach koła pasowego napędowego.
W przypadku ruchu koła pasowego w kierunku przeciwnym do ruchu wskazówek zegara wielkość T2 jest większa niż T1 ze względu na tarcie między paskiem a powierzchnią koła pasowego.
Znajomość całkowitego kąta przylegania pasa do powierzchni i współczynnika tarcia umożliwia oszacowanie naprężeń.
Narysowany jest schemat swobodnego korpusu elementu różnicowego AB pasa.
Zakładając ruch zbliżający się, siła tarcia przeciwstawia się ruchowi ślizgowemu pasa, powodując wzrost wielkości naprężenia paska działającego w punkcie B o dT.
Stosując równowagę sił poziomych i pionowych oraz stosując przybliżenia cosinusa i sinusa, uzyskuje się dwa równania równowagi sił.
Iloczyn dwóch różniczek w porównaniu z różniczkami pierwszego rzędu jest pomijany w równaniach równowagi pionowej, podczas gdy równanie równowagi poziomej jest jeszcze bardziej uproszczone.
Połączenie równań równowagi i całkowanie między odpowiadającymi im granicami daje wyrażenie korelujące naprężenia pasa.
Równanie to ma zastosowanie do pasów płaskich przechodzących przez dowolną zakrzywioną powierzchnię styku.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. Strony 439 \u2012 440.</li>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley. Str. 373.</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. Strona 463</li>
</ol>

siły tarcia na płaskich pasach

Frictional Forces on Flat Belts

Płaskie pasy są szeroko stosowane w różnych aplikacjach przemysłowych do przenoszenia mocy pomiędzy kołnierzami. Gdy płaski pas jest owinięta wokół zestawu kołnierzy, doświadcza różnych naprężeń na końcach napędzającego kołnierza z powodu tarcia między pasem a powierzchnią kołnierza. Gdy płaski pas owinięty jest wokół zestawu kołnierzy, powstają naprężenia na końcach napędzającego kołnierza, wynikające z tarcia pomiędzy pasem a powierzchnią kołnierza.

Do oszacowania naprężeń w płaskim pasie niezbędne jest poznanie całkowitego kąta kontaktu pasa z powierzchnią oraz współczynnika tarcia między powierzchniami. Można narysować diagram swobodnego ciała elementu różnicowego AB pasa, zakładając ruch grożący.

<img alt="Figure 1" src="/files/ftp_upload/14322/14322_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Siła tarcia przeciwstawia się poślizgowi pasa, powodując zwiększenie wartości napięcia pasa działającego w punkcie B o dT. To różnicowe napięcie może być używane do związania napięć w różnych punktach na pasie.

Aby określić zależność między napięciami pasów, używane są równania równowagi siłowej w kierunkach poziomej i pionowej, wraz z przybliżeniami cosinusa i sinusa.

<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;" />

Te równania uwzględniają działające siły na element różnicowy AB w kierunkach poziomym i pionowym. W równaniach równowagi pionowej zaniedbuje się iloczyn dwóch różniczkowych w porównaniu do różniczki pierwszego rzędu, podczas gdy równanie równowagi poziomej jest jeszcze bardziej uproszczone. Równania równowagi są łączone i całkowane między odpowiednimi ograniczeniami.

<img alt="Equation 3" src="/files/ftp_upload/14322/14322_PT_Equation_3v2.svg" style="text-align: center; height: 45px;" />

Wynik daje wyrażenie zależności napięć na pasach.

<img alt="Equation 4" src="/files/ftp_upload/14322/14322_PT_Equation_4v2.svg" style="text-align: center; height: 15px;" />

To równanie dotyczy płaskich pasów przechodzących przez dowolną zakrzywioną powierzchnię kontaktową.

Siły tarcia na płaskich pasach są kluczowe dla określenia wydajności i efektywności układu napędzanego pasami. Nadmierne napinanie pasa może powodować przedwczesne zużycie i zmniejszenie efektywności, podczas gdy niedociągnięcie może powodować poślizg i zmniejszać przekazywaną moc. Odpowiednie napinanie osiąga się poprzez dostosowanie odległości między kołnierzami lub stosowanie urządzenia napinającego.

Siły tarcia na płaskich pasach

Pasy płaskie są powszechnie stosowane w różnych zastosowaniach przemysłowych do przenoszenia mocy z jednego koła pasowego na drugie. Gdy płaski pasek jest owinięty wokół ...

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Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Friction

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KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

dry friction

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static friction

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kinetic friction

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frictional forces on flat belts

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...

flat belts: problem solving

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Journal bearings support rotating shafts and axles while helping keep them stable. They are used in machines such as engines, turbines, and pumps. Their job is to reduce friction, wear, and vibration. A journal bearing works by keeping a thin film of lubricant between the bearing surface and the rotating shaft. This film limits direct contact and lowers frictional force. The video uses a rope winch with dry or only partly lubricated journal bearings to show the idea. As the spool turns...

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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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Flat Belt Tension and Friction

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