Belt Transmissions - Speed and Length of Belts
Calculate length and speed of belt and belt gearing.
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
lb = (dm π / 2) + (df π / 2) + (2 lfm) + ((df - dm)2 / (4 lfm)) (1)
where
lb = length of belt (mm, inches)
df = pulley (sheave) diameter fan (mm, inches)
dm = pulley (sheave) diameter motor (mm, inches)
π = 3.14..
lfm = 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 dm nm / 12 (2)
where
v = velocity of belt (ft/min)
nm = revolutions motor (rpm)
- or alternatively in metric units:
vb = π dm nm / 60 (2b)
where
vb = velocity of belt (m/s)
dmb = diameter motor pulley (m)
| Belt Velocity (ft/min) | |||||||
|---|---|---|---|---|---|---|---|
| Pitch Diameter of Pulley (in) | |||||||
| Revolutions Pulley - n - (rpm) | |||||||
| 850 | 1050 | 1075 | 1140 | 1550 | 1725 | 3450 | |
| 1 | 223 | 275 | 281 | 298 | 406 | 452 | 903 |
| 2 | 445 | 550 | 563 | 597 | 812 | 903 | 1806 |
| 3 | 668 | 825 | 844 | 895 | 1217 | 1355 | 2710 |
| 4 | 890 | 1100 | 1126 | 1194 | 1623 | 1806 | 3613 |
| 5 | 1113 | 1374 | 1407 | 1492 | 2029 | 2258 | 4516 |
| 6 | 1335 | 1649 | 1689 | 1791 | 2435 | 2710 | 5419 |
| 7 | 1558 | 1924 | 1970 | 2089 | 2841 | 3161 | 6322 |
| 8 | 1780 | 2199 | 2251 | 2388 | 3246 | 3613 | 7226 |
| 9 | 2003 | 2474 | 2533 | 2686 | 3652 | 4064 | 8129 |
| 10 | 2225 | 2749 | 2814 | 2985 | 4058 | 4516 | 9032 |
Belt Gearing
The relationship between the rotational speed of the motor and the fan and the disc diameter can be expressed as
df nf = dm nm (3)
or
nf = nm dm / df
Belt Gearing Calculator
nm - speed driver (rpm)
dm - diameter driver (mm, in)
df - diameter follower (mm, in)
Horsepower
If belt tension and belt velocity are known - horsepower transferred can be calculated as
Php = Fb vb / 33000 (4)
where
Php = power (hp)
Fb = belt tension (lbf)
vb = velocity of belt (ft/min)
If torque and revolution per minute are known - horsepower transferred can be calculated as
Php = T n / 5252 (4)
where
Php = power (hp)
T = torque (ft lbf)
n = revolutions per minute (rpm)
Speed Ratio
Speed ratio can be calculated as
SR = nf / ns (5)
where
SR = speed ratio
nf = revolutions per minute - fastest machine
ns = revolutions per minute - slowest machine
