Pulleys are used to change speed or torque when used with motors or other rotatory power sources.

The next formulas are used to calculate the theoretical mechanical advantage of pulley systems and the change of speed. See figure 1.


 

(a) Belt and pulley

(b) O-ring

(c) chain driver

 

Formulas

a) Change of speed:

tangential:

V1/V2 = d2/d1 (1)

 

angular:

ω1/ω2 = d2/d1 (2)

 

rpm

rpm1/rpm2 = d2/d1 (3)

 

Where: v1 and v2 are the tangential speed of the pulleys

ω1 and ω2 are the angular speed of the pulleys

rpm1 and rpm2 are the revolution per minute of the pulleys

d1 and d2 are the diameters of the pulleys

 

Obs: the speed of the belt is constant

 

b) Change of torque:

 

M1/M2 = d2/d1 (4)

 

Where: M1 and M2 are the torque

d1 and d2 are the diameters ot the pulleys

 

c) TMA:

 

TMA = M2/M1 = d1/d2 = ω1/ω2 = rpm2/rpm1 = v2 /v1 (5)

 

Where: TMA is the theoretical mechanical advantage

v1 and v2 are the tangential speed of the pulleys

ω1 and ω2 are the angular speed of the pulleys

rpm1 and rpm2 are the revolution per minute of the pulleys

d1 and d2 are the diameters of the pulleys

 

d ) Complex systems

Figure 2 shows a complex system using pulleys and belts. The next formulas are valid for calculus involving TMA, change of speed and torque.

 


 

 

 

Formulas:

a) Change of speed

Tangential/Angular

S2 = S1 x nD/nd (6)

 

Where: S1 is the speed of the first pulley in train

S2 is the speed of the last pulley in train

nD is the product of the diameters on all drivers

nd is the product of diameters on all driven gears

 

b) Change of torque

M2/M1 = S1/S2 (7)

 

Where: M1 and M2 are the torque of the pulleys

S1 is the speed of the first pulley in train (angular or tangential)

S2 is the speed of the last pulley in train (angular or tangential)

 

c) TMA

TMA = M2/M1 = S2/S1 (8)

 

 

Datasheets


N° of component