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Belt Transmissions - Speed and Length of Belts

Calculate length and speed of belt and belt gearing.

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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

Belt transmission - 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 Transmissions - Belt Speed
Pitch Diameter of Pulley
(in)
Velocity (ft/min)
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 transmission - pulley and belt velocity

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

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

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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.

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