OpenSpecEngineering

Lays out a two-shaft belt or roller chain drive. From the pulley diameters or sprocket tooth counts, the center distance and the driver speed, it gives the speed ratio, the driven shaft speed, the belt or chain speed and the length to order. Pick a V-belt section to check the smaller sheave against its minimum diameter, or an ASME B29.1 chain size to work in sprocket teeth. Machine designers and maintenance staff use it to set up or change a drive.

Equations

For a belt on pulleys of pitch diameter d₁ (driver) and d₂ (driven), C apart, with the driver turning at ω₁ [1]:

i = d₂/d₁     ω₂ = ω₁/i
v = π·d₁·ω₁
L ≈ 2C + π(d₁ + d₂)/2 + (d₂ − d₁)²/(4C)

i is the speed ratio, ω₂ the driven speed, v the belt speed and L the belt’s pitch length. For a chain of pitch p on sprockets of z₁ and z₂ teeth [1], [3]:

D = p/sin(180°/z)     v = z₁·p·ω₁
L/p = 2C/p + (z₁ + z₂)/2 + (z₂ − z₁)²/(4π²·C/p)

D is a sprocket’s pitch diameter and L/p the chain length in pitches. The page rounds it up to an even number of links, so the chain closes without an offset link. A larger driver than driven pulley is allowed: the drive then speeds up and i is below 1.

Limits and common mistakes

• Enter pitch diameters, not the outside diameters of the sheaves.
• The belt results assume no slip. A real belt creeps a little, so the driven shaft turns slightly slower.
• The length is a calculated value. Order the nearest standard belt and set the center distance to suit, with take-up room for tensioning.
• The minimum sheave diameter for each V-belt section is from Table 17-9 of [1]. A smaller sheave overstresses the belt in bending.
• The page doesn’t check power. Size the number of belts or the chain size from the maker’s ratings [2].

Worked example

A 1750 rpm motor drives a fan through a B-section V-belt. The sheaves are 140 mm and 355 mm pitch diameter, on shafts 600 mm apart. Find the fan speed and the belt length.

1. Choose Drive B section — sheaves 5.4 in and up.
2. Enter Driver Diameter 140 mm and Driven Diameter 355 mm.
3. Enter Center Distance 600 mm and Driver Speed 1750 rpm.
4. Press Solve. The Solution shows: Speed Ratio (d₂/d₁): 2.53571
   Driven Speed (ω₂): 690.141 rpm
   Belt/Chain Speed (v): 12.8282 m/s
   Belt/Chain Length (approx.): 1,996.8 mm
   Minimum Sheave Diameter, B Section: 137.16 mm

Check by hand. 355/140 = 2.536, and 1750/2.536 = 690 rpm. The length is 1,200 + π × 495/2 + 215²/2,400 = 1,200 + 777.5 + 19.3 = 1,996.8 mm. The 140 mm driver is just above the 5.4 in (137.16 mm) minimum, so no warning appears.