Belt Transmissions - Speed and Length of Belts

Belts (or chains) are used to transfer power (or convert torque) through rotational motion from one shaft to an other. Belt driven fans are common in heating, ventilation, air-conditioning and cooling (HVAC) systems. Chain are common in many transmission systems like bicycles and other.

• friction belts - transfer the power through friction between the pulley and the belt
• synchronous belts - transfer the power through a mechanical linkage between the teeth in the belt and the grooves in the pulley

Belt Length

The length of the belt can be calculated as

l_b = (d_m π / 2) + (d_f π / 2) + (2 l_fm) + ((d_f - d_m)² / (4 l_fm))                                (1)

where

l_b = length of belt (mm, inches)

d_f = pulley (sheave) diameter fan (mm, inches)

d_m = pulley (sheave) diameter motor (mm, inches)

π = 3.14..

l_fm = center to center distance of fan and motor pulleys (mm, inches)

Belt Velocity

The velocity at which a belt travels may be expressed as

v = π d_m n_m / 12                                    (2)

where

v = velocity of belt (ft/min)

n_m = revolutions motor (rpm)

- or alternatively in metric units:

v_b = π d_m n_m / 60                         (2b)

where

v_b = velocity of belt (m/s)

d_mb = diameter motor pulley  (m)

Belt Gearing

The relationship between the rotational speed of the motor and the fan and the disc diameter can be expressed as

d_f n_f = d_m n_m                               (3)

or

n_f = n_m d_m / d_f 

Belt Gearing Calculator

n_m - speed driver (rpm)

d_m - diameter driver (mm, in)

d_f - diameter follower (mm, in)

Horsepower

If belt tension and belt velocity are known - horsepower transferred can be calculated as

P_hp = F_b v_b / 33000                                (4)

where

P_hp = power (hp)

F_b = belt tension (lb_f)

v_b = velocity of belt (ft/min)

If torque and revolution per minute are known - horsepower transferred can be calculated as

P_hp = T n / 5252                                  (4)

where

P_hp = power (hp)

T = torque (ft lb_f)

n = revolutions per minute (rpm)

Speed Ratio

Speed ratio can be calculated as

SR = n_f / n_s                            (5)

where

SR = speed ratio

n_f = revolutions per minute - fastest machine

n_s = revolutions per minute - slowest machine

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm