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# Belt Transmissions - Length and Speed of Belt

## 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)

df  - pulley (sheave) diameter fan (mm, inches)

dm - pulley (sheave) diameter motor (mm, inches)

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)
850105010751140155017253450
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 dmdf

#### 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

PhpFb 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

## Related Topics

• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
• Ventilation - Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more

## Tag Search

• en: belt fans motors pulley
• es: cinturĂ³n de motores ventiladores polea
• de: Riemenscheibe Fans Motoren

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## Citation

• Engineering ToolBox, (2005). Belt Transmissions - Length and Speed of Belt. [online] Available at: https://www.engineeringtoolbox.com/length-belt-fans-motors-d_872.html [Accessed Day Mo. Year].

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