Friction (Belt Friction – exponential relation)

Key Concept: One model engineers use to represent sliding between a rope or belt and a cylinder or pulley is an exponential relation between the pulling tension and the restraining

tension in the rope or belt.

In a Nut Shell: Friction forces acting on a rope or belt wrapped around a fixed circular cylinder vary exponentially by the relation T₂/T₁ = e^μ_s^β where T₂ is the pulling tension on the rope, T₁ is the restraining tension of the rope, μ_s is the coefficient of static friction between the rope and the fixed cylinder, and β is the angle of “wrap” around the fixed cylinder.

T₂ = pulling tension of the rope in lb, Newtons, kips

T₁ = restraining tension of the rope in lb, Newtons, kips

μ_s = the coefficient of static friction between the rope and the fixed cylinder

β = the angle of “wrap” around the fixed cylinder measured in radians

See the figure below.

Note: T₁ > T₂ since T₁ must support both the restraining force, T₂,

and the frictional force between the rope and the fixed cylinder

Click here to return to discussion of friction.

Click here for an example.

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