# Belt Transmissions - Length and Speed of Belt

## Length and speed of belt and belt gearing

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Belts are used to transfer power through rotational motion from one shaft to an other. Belt driven fans are common in heating, ventilation, air-conditioning and cooling (HVAC) systems.

**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 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

d_{f}n_{f}= d_{m}n_{m }(3)

### Horsepower

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

P_{hp}=Fv_{b}_{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

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