Belt Transmissions - Speed and Length of Belts

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

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)

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

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

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 Transmissions - Belt Speed

Pitch Diameter of Pulley (in)	Velocity (ft/min)
	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)

or

n_f = n_m d_m / d_f 

Belt Gearing Calculator

n_m - speed driver (rpm)

d_m - diameter driver (mm, in)

d_f - diameter follower (mm, in)

Horsepower

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

P_hp = F_b v_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