Chain Drives

Chain drives use positive engagement between a chain and sprockets. They maintain the mean ratio without frictional slip and can drive several shafts over substantial center distances.

Kinematics

The mean ratio is

$$i=\frac{n_1}{n_2}=\frac{z_2}{z_1}.$$

Because a chain wraps a sprocket as a polygon, instantaneous chain speed fluctuates. More teeth on the small sprocket reduce this polygonal effect.

Forces

Chain speed and tangential force are approximately

$$v=\frac{pz_1n_1}{60},\qquad F_t=\frac{1000P}{v},$$

for \(P\) in kW. Design load includes dynamic, service, and lubrication factors. Centrifugal force and sag-side tension are added where relevant.

Wear and lubrication

Wear at pin–bushing joints increases effective pitch rather than stretching the plates. Operating elongation is

$$\varepsilon_L=\frac{L-L_0}{L_0}100\%.$$

Lubricant must enter the pin–bushing interface. Check joint pressure, plate fatigue, roller and sprocket wear, alignment, controlled slack, vibration, noise, and replacement compatibility of chain and sprockets.

Chain construction

A roller chain consists of inner and outer plates, pins, bushes, and rollers. The pin rotates relative to the bush as each link enters and leaves the sprocket. Silent and toothed chains use different engagement geometry when lower noise or higher speed is required.

Sprocket selection

A small tooth count increases polygonal speed fluctuation, articulation angle, tooth impact, and wear. A very large sprocket increases size and makes a given pitch elongation more likely to cause poor seating. Tooth numbers should also avoid repeatedly pairing the same chain links and sprocket teeth where practical.

Chain length and center distance

In pitches, an approximate length for an open drive is

$$L_p=2a_p+\frac{z_1+z_2}{2}+\frac{(z_2-z_1)^2}{4\pi^2a_p},$$

where \(a_p=a/p\). The result is rounded to a feasible even number of pitches and the center distance is recalculated.

Dynamic actions

Entry impact, polygonal velocity variation, chordal vibration, speed fluctuation, and shaft misalignment add dynamic load. High-speed drives need smaller pitch, more teeth, accurate sprockets, good lubrication, and controlled guides. Resonance of the free spans should be avoided.

Joint pressure and wear

A preliminary bearing-pressure check at the pin–bush joint is

$$p_b=\frac{F_d}{A_b}le[p_b].$$

Wear enlarges pin–bush clearance and increases chain pitch. It does not represent uniform elastic elongation of the plates. Excess pitch causes the chain to ride higher on sprocket teeth and eventually skip or disengage.

Lubrication and layout

Oil must reach the clearance between pin and bush near the slack-span entry. Manual, drip, bath, disk, or forced lubrication is selected from speed and power. Shafts should be parallel and sprockets coplanar. A nearly horizontal drive is preferred; vertical layouts require special control of the slack span.

Design sequence

1. Calculate design power and select chain type, pitch, and number of strands.
2. Choose sprocket tooth counts and check ratio and speed.
3. Determine chain length, center distance, and slack arrangement.
4. Calculate tangential, centrifugal, dynamic, and sag forces.
5. Check joint pressure, fatigue, wear life, shafts, and bearings.
6. Specify lubrication, alignment, guarding, tension adjustment, and wear limits.