Chains and Sprockets
Roller chain, pitch and speed, the polygon effect, power rating, lubrication, tension and a worked drive selection.
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What roller chain is
Roller chain is a series of steel link plates, pins, bushings and rollers. It engages the teeth of a sprocket positively (no slip, like a timing belt) but is far stronger and tolerates dirt, heat and shock; it needs lubrication and makes more noise. It is used in conveyors, agricultural and construction machinery, motorcycles and bicycles and in industrial drives. Each link has two parts: an inner link (bushings pressed into plates, with rollers) and an outer link (pins pressed into plates). A master (connecting) link with a clip joins the ends. An offset link (for an odd number of pitches) is weaker and is best avoided: use an even number of pitches.
Chain sizes and strength
| ANSI chain (ISO) | Pitch p (mm) | Average tensile strength (kN, single strand) | Roller or pin diameter (mm) |
|---|---|---|---|
| #40 (ISO 08B) | 12.7 | 16.5 | 3.96 |
| #50 (10B) | 15.875 | 27.1 | 5.08 |
| #60 (12B) | 19.05 | 37.8 | 5.94 |
| #80 (16B) | 25.4 | 64.5 | 7.92 |
| #100 (20B) | 31.75 | 107 | 9.53 |
The ANSI number is the pitch in eighths of an inch (a #40 chain has 4/8 in = 12.7 mm pitch; #80 has 8/8 = 1 in). The tensile strength is the load at which a new chain breaks. The working load is far less: a common rule is about one eighth to one tenth of the tensile strength for normal conditions, less at high speed or with shock, because the real limit is the fatigue of the plates and the wear of the pins and bushings, not the break. Multi-strand chain (duplex, triplex) carries about 1.7, 2.5 times the load of a single strand (not the full 2 or 3, because the load shares unevenly). The values above are typical; use the chain maker’s catalog.
Sprockets: diameter, ratio and the polygon effect
D = p ÷ sin(180° ÷ N) i = N2 ÷ N1 v = N p n ÷ 60 000 (m/s, p in mm, n in rpm)
The pitch diameter D of a sprocket with N teeth is the circle through the chain pin centers; the chain wraps it as a polygon of N sides. The speed ratio is the ratio of the tooth counts. Because the chain moves round a polygon, its speed varies slightly with each link: the polygon (chordal) effect, a variation of (1 − cos(180° ÷ N)) × 100 percent, falls sharply with more teeth. It causes vibration and noise at the tooth-passing frequency and limits the high-speed use of small sprockets.
- Minimum teeth: 17 on the small sprocket for general drives, 21 or more for high speed or heavy duty (a variation of 1.4 percent at 19 teeth against 7.6 percent at 8).
- Maximum teeth: about 120 (wear makes the chain climb the teeth: only a few percent elongation is tolerable on a big sprocket).
- Ratio: up to about 7:1 per stage; above that use two stages.
- Wrap angle: at least 120° on the small sprocket (three teeth engaged at least).
- Odd teeth on the small sprocket and an even number of chain pitches (a hunting-tooth effect that spreads the wear), as in the example below.
Chain length and center distance
Lp = 2C ÷ p + (N1 + N2) ÷ 2 + ((N2 − N1) ÷ 2π)² × p ÷ C C = (p ÷ 4) [ K + √(K² − 8 ((N2 − N1) ÷ 2π)²) ], K = Lp − (N1 + N2) ÷ 2
Lp is the length in pitches; round it up to an even whole number, then recompute the center distance C from the rounded length (the second formula). A center distance of 30 to 50 pitches is the usual range; shorter increases the wear, longer needs a support or a tensioner.
Worked example: selecting a chain drive
- Duty: 3.0 kW at 1 450 rpm to a conveyor at about 574 rpm, a ratio of 2.5 with a service factor 1.5 (moderate shock). Try a #40 chain (p = 12.7 mm), sprockets N1 = 19 and N2 = 48 (2.53:1, output 574 rpm).
- Chain speed: v = 19 × 12.7 × 1 450 ÷ 60 000 = 5.83 m/s, moderate (the limit for a #40 chain is about 12 to 15 m/s with good lubrication).
- Chain pull: F = P ÷ v = 3 000 ÷ 5.83 = 514 N; with the service factor 772 N. A #40 chain has a tensile strength of about 16.5 kN: the factor is 21 and the load is 42 percent of one ninth of the strength: acceptable. Always confirm with the manufacturer’s power rating table, which takes the fatigue and wear limits into account.
- Sprocket diameters: D1 = 12.7 ÷ sin(180° ÷ 19) = 77.2 mm; D2 = 194.2 mm.
- Length: for C ≈ 600 mm, Lp = 2 × 600 ÷ 12.7 + (19 + 48) ÷ 2 + (4.6)² × 12.7 ÷ 600 = 128.4, so use 130 pitches (even). The true center distance for 130 pitches is C = 610.0 mm.
- Wrap: 169° on the small sprocket: fine. Polygon effect: 1.4 percent: acceptable at this speed.
- Initial slack: about 2 percent of the center distance, 12 mm of free movement mid-span on the slack side (see below).
- Wear limit: a chain is worn out at about 2 to 3 percent elongation: for 130 pitches of 12.7 mm (1 651 mm) that is about 33 mm of stretch. Past it the chain rides high on the teeth and skips.
Lubrication and life
A chain wears at the pin and bushing: they slide on each other every time the chain engages and leaves a sprocket. Lubrication is the main factor in life. Manufacturers (ANSI B29.1, ISO 10823) define three methods by speed and power:
| Type | Method | Used for |
|---|---|---|
| Type I | Manual or brush oiling, drip feed at a low rate | Low speed (up to about 3 m/s) and light duty |
| Type II | Drip lubrication or an oil bath (the chain dips into oil) | Moderate speed |
| Type III | Oil stream or forced circulation with a pump and a cooler | High speed and high power (a chain case) |
- Oil: a clean mineral oil of viscosity about ISO VG 100 to 150 at normal temperatures (VG 68 in cold conditions, VG 220 hot); the oil must reach the pin-bushing gap, so apply it to the inside of the lower span, where the chain is slack and the plates open.
- Grease and sealed chain: O-ring or X-ring sealed chains keep the grease in for life and suit lightly loaded, hard-to-reach drives; they are not as good at high speed (they run hotter).
- Dry or dusty places: use a dry lubricant (PTFE-based) or a non-lubricated chain type, and keep the chain clean.
- Life: with good lubrication and alignment a chain lasts 15 000 hours or more; without it, it can be worn out in days.
Installation and tension
- Align the sprockets in one plane and with parallel shafts: misalignment makes the chain run to one side and wear the plates and teeth.
- Set the tension: a chain should be slack (a sag of about 2 percent of the center distance on the slack side, or 1 to 3 mm per 100 mm of span for horizontal drives), not tight like a belt. Too tight overloads the bearings; too slack makes it whip.
- Use a tensioner or an idler for long drives, vertical drives and reversing loads; a spring or an adjustable sprocket on the slack side (never on the tight side).
- Guard the drive and fit a chain case or housing for oil.
- Use a master link with the closed end of the clip facing the direction of travel.
- Replace the chain and both sprockets together as a set when the chain is worn: a new chain on worn sprockets wears out quickly.
Other chain types
| Type | Features | Use |
|---|---|---|
| Silent (inverted-tooth) chain | Link plates with teeth mesh with the sprocket; quiet, with a smooth action | High-speed, quiet drives; engine timing |
| Leaf chain | Plates and pins only (no rollers), no sprocket | Lifting, forklift masts, counterweights |
| Conveyor and attachment chains | Extended pins and plates carry a load | Conveyors, elevators |
| Double-pitch chain | Twice the pitch with the same strength | Light, slow conveyors |
| Engineering (steel, bushing) chain | Heavy, sturdy | Mining, dredging |
| Stainless and nickel-plated chain | Corrosion resistant, lower rating | Food, outdoor, marine |
Chain or something else?
| If you need… | Chain | Alternative |
|---|---|---|
| Positive drive, high shock, dirty environment | Roller chain | Gears if the center distance is short |
| Quiet, clean, light, no lubrication | Silent chain or | Timing belt (see Belts and Pulleys) |
| Very high precision | — | Gears or a precision timing belt |
| Long center distance, moderate power | Roller chain | V-belt (but it can slip) |
Troubleshooting chain drives
| Symptom | Likely cause | Check |
|---|---|---|
| Chain whips or slaps | Too slack, resonance, a worn chain | Tension; add a guide or tensioner |
| Noisy, rattling | Poor lubrication, polygon effect with small sprockets, wear | Lubricate; more teeth; replace worn parts |
| Chain climbs the sprocket teeth, skips | Elongated (worn) chain, worn sprocket teeth | Measure the stretch (above 2 to 3 percent); replace chain and sprockets |
| Wear on the plate edges | Misalignment of sprockets | Align with a straight edge |
| Stiff links, rust | No lubrication, water, corrosion | Clean and lubricate; use plated or stainless chain |
| Chain breaks | Overload, fatigue, a worn chain, a poor joint | Load and shock, master-link clip direction, replace on time |
| Hot chain or oil | Too fast for the lubrication, too tight | Lubrication type, tension |
Related
- Gears and Power Transmission: the overview of this guide.
- Belts and Pulleys and Gear Trains, Ratios and Efficiency: the alternatives.
- Lubrication, Wear and Gear Failures: lubricants and film thickness.
- Shafts, Keys and Couplings and Bearings and Bearing Selection: the shaft loads from the chain pull.
FAQ
How do I know when to replace a roller chain?
When it has stretched about 2 to 3 percent in length (measure the length over a number of pitches against a new chain of the same pitch) or when you see a worn step on the pins or tight links. Replace the sprockets with the chain.
Why should the number of chain pitches be even?
Chain is made of alternating inner and outer links, so an even number closes into a loop with a normal master link. An odd number needs an offset link, which is weaker and wears faster.
Why are sprockets with few teeth bad?
The chain wraps the sprocket as a polygon, so its speed fluctuates and each link hits the tooth hard; the smaller the sprocket the worse the effect (see the polygon figure). Use at least 17 teeth, more for fast drives.
Can a chain run without lubrication?
For a short time, but the life falls dramatically. If lubrication is impossible, use sealed, self-lubricating or stainless chain and reduce the load and speed to the manufacturer’s rating.
References
- Shigley, J. E. and Mischke, C. R., Mechanical Engineering Design, McGraw-Hill: roller chain drives.
- ANSI/ASME B29.1 and ISO 606 (roller chain dimensions and strength), ISO 10823 (guidance on the selection of roller chain drives).
- Renold, Tsubaki, Rexnord and Diamond chain catalogs and engineering guides (power ratings, lubrication, installation).
Last reviewed: October 2026. Strengths and speeds are typical; use the chain manufacturer’s power rating tables for selection.