Belts - Pulley Diameters vs. Speed

The pulley laws - driver and driven - diameter and rpm

Pulley belt transmission - diameters and speed

For a system with two shafts and two pulleys - as indicated with pulley 1 and 2 in the figure above:

d₁ n₁= d₂ n₂ (1)

where

d₁ = driving pulley diameter (inch, mm)

n₁ = revolutions of driving pulley (rpm - rounds per minute)

d₂ = driven pulley diameter (inch, mm)

n₂ = revolutions of driven pulley (rpm - rounds per minute)

Equation (1) can be transformed to express the

n₂ = d₁ n₁ / d₂ (2)

n₁ = d₂ n₂ / d₁ (3)

d₂ = d₁ n₁ / n₂ (4)

d₁ = d₂ n₂ / n₁ (5)

For a system a with three shafts and four pulleys - as indicated in the figure above:

n₂ = n₃ (6)

n₄ = n₁ (d₁ d₃) / (d₂ d₄) (7)

The revolutions of shaft 4 in a multiple belt transmission like indicated in the figure above where

n₁ = 1000 rpm

d₁ = 100 mm

d₂ = 50 mm

d₃ = 110 mm

d₄ = 60 mm

can be calculated as

n₄ =(1000 rpm) (100 mm) (110 mm) / ((50 mm) (60 mm))

= 3667 rpm