Belts - Length and Speed of Belt

Length and speed of belt, belt gearing

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

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

Belt Length

belt length fan motor

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 = velocity motor (rpm)

Pitch Diameter of Pulley (in)Belt Speed (ft/min)
Revolutions Pulley (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 speed of the motor, the fan and their disc diameters can be expressed as

df nf = dm nm                 (3)

Horsepower

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

Php = T v / 33000               (4)

where

Php = power (hp)

T = belt tension (lbf)

v = velocity of belt (ft/min)

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

Php = M R / 63000               (4)

where

Php = power (hp)

M = torque (lbf)

R = revolutions per minute (rpm)

Speed Ratio

Speed ratio can be calculated as

SR = Rf / Rs            (5)

where

SR = speed ratio

Rf = revolutions per minute - fastest machine

Rs = revolutions per minute - slowest machine

Related Topics

  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
  • Ventilation - Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more

Related Documents

Search the Engineering ToolBox

- "the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Edition - Online 3D modeling!

3D Engineering ToolBox - draw and model technical applications

Engineering ToolBox - SketchUp Edition - add standard and customized parametric components - like flange beams, lumbers, piping and more - to your SketchUp model - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!