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'''Belt friction''' is a term describing the friction forces between a [[Belt (mechanical)|belt]] and a surface, such as a belt wrapped around a [[bollard]]. When one end of the belt is being pulled only part of this force is transmitted to the other end wrapped about a surface. The friction force increases with the amount of wrap about a surface and makes it so the [[tension (physics)|tension]] in the belt can be different at both ends of the belt. Belt friction can be modeled by the [[Capstan equation|Belt friction equation]].<ref name=Attaway>{{cite conference | last = Attaway | first = Stephen W. | title = The Mechanics of Friction in Rope Rescue | url = http://www.jrre.org/att_frict.pdf | format = PDF | accessdate = February 1, 2010 | conference = International Technical Rescue Symposium | year = 1999}}</ref>
 
In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.
 
== Equation ==
{{main|Capstan equation}}
The equation used to model belt friction is, assuming the belt has no [[mass]] and its material is a fixed composition:<ref>{{cite web
| last = Mann
| first = Herman
| title = Belt Friction
| date = May 5, 2005
| url = http://www.esr.ruhr-uni-bochum.de/rt1/currentcourse/node57.html
| publisher = Ruhr-Universität
| accessdate = 2010-02-01}}</ref>
 
: <math>T_2=T_1e^{\mu_s\beta} \, </math>
 
where <math>T_2</math> is the tension of the pulling side, <math>T_1</math> is the tension of the resisting side, <math>\mu_s</math> is the [[static friction]] coefficient, which has no units, and <math>\beta</math> is the angle, in [[radian]]s, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.<ref>{{cite web
| last = Chandoo
| title = Couloumb Belt Friction
| url = http://web.mst.edu/~bestmech/preview/chandoo/8_2_2_1/8_2_2_1.htm
| publisher = Missouri University of Science and Technology
| accessdate = 2010-02-01}}</ref>
 
The tension on the pulling side of the belt and pulley has the ability to increase [[exponential growth|exponentially]]<ref name=Attaway/> if the magnitude of the belt angle increases (e.g. it is wrapped around the pulley segment numerous times).
 
== Friction coefficient ==
 
There are certain factors that help determine the value of the [[friction coefficient]]. These determining factors are:<ref>{{cite web
| title = Belt Tension Theory
| url = http://www.ckit.co.za/secure/conveyor/troughed/belt_tension/belt_tension_factors.htm
| publisher = CKIT – The Bulk Materials Handling Knowledge Base
| accessdate = 2010-02-01}}</ref>
 
* Belting material used – The age of the material also plays a part, where worn out and older material may become more rough or smoother, changing the sliding friction.
* Construction of the drive-pulley system – This involves strength and stability of the material used, like the pulley, and how greatly it will oppose the motion of the belt or rope.
* Conditions under which the belt and pulleys are operating – The friction between the belt and pulley may decrease substantially if the belt happens to be muddy or wet, as it may act as a lubricant between the surfaces. This also applies to extremely dry or warm conditions which will evaporate any water naturally found in the belt, nominally making friction greater.
* Overall design of the setup – The setup involves the initial conditions of the construction, such as the angle which the belt is wrapped around and geometry of the belt and pulley system.
 
== Applications ==
 
An understanding of belt friction is essential for sailing crews and mountain climbers.<ref name=Attaway/> Their professions require being able to understand the amount of weight a rope with a certain tension capacity can hold versus the amount of wraps around a pulley. Too many revolutions around a pulley make it inefficient to retract or release rope, and too few may cause the rope to slip. Misjudging the ability of a rope and capstan system to maintain the proper frictional forces may lead to failure and injury.
 
==See also==
*[[Capstan equation]]
*[[Frictional contact mechanics]]
 
==References==
{{reflist}}
 
[[Category:Mechanics]]

Revision as of 04:06, 12 February 2013

Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard. When one end of the belt is being pulled only part of this force is transmitted to the other end wrapped about a surface. The friction force increases with the amount of wrap about a surface and makes it so the tension in the belt can be different at both ends of the belt. Belt friction can be modeled by the Belt friction equation.[1]

In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.

Equation

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The equation used to model belt friction is, assuming the belt has no mass and its material is a fixed composition:[2]

T2=T1eμsβ

where T2 is the tension of the pulling side, T1 is the tension of the resisting side, μs is the static friction coefficient, which has no units, and β is the angle, in radians, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.[3]

The tension on the pulling side of the belt and pulley has the ability to increase exponentially[1] if the magnitude of the belt angle increases (e.g. it is wrapped around the pulley segment numerous times).

Friction coefficient

There are certain factors that help determine the value of the friction coefficient. These determining factors are:[4]

  • Belting material used – The age of the material also plays a part, where worn out and older material may become more rough or smoother, changing the sliding friction.
  • Construction of the drive-pulley system – This involves strength and stability of the material used, like the pulley, and how greatly it will oppose the motion of the belt or rope.
  • Conditions under which the belt and pulleys are operating – The friction between the belt and pulley may decrease substantially if the belt happens to be muddy or wet, as it may act as a lubricant between the surfaces. This also applies to extremely dry or warm conditions which will evaporate any water naturally found in the belt, nominally making friction greater.
  • Overall design of the setup – The setup involves the initial conditions of the construction, such as the angle which the belt is wrapped around and geometry of the belt and pulley system.

Applications

An understanding of belt friction is essential for sailing crews and mountain climbers.[1] Their professions require being able to understand the amount of weight a rope with a certain tension capacity can hold versus the amount of wraps around a pulley. Too many revolutions around a pulley make it inefficient to retract or release rope, and too few may cause the rope to slip. Misjudging the ability of a rope and capstan system to maintain the proper frictional forces may lead to failure and injury.

See also

References

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  1. ↑ 1.0 1.1 1.2 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

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  2. ↑ Template:Cite web
  3. ↑ Template:Cite web
  4. ↑ Template:Cite web
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