Chain drive calculation per ISO 606
Design B-series roller chain drives (06B … 24B, simplex/duplex/triplex): from power or torque, speed, target ratio, tooth count and desired centre distance you get z2, pitch diameters, chain speed, an even number of links with the exact centre distance, the polygon effect and a guideline design rating.
Chain drive calculator (B-series roller chain, ISO 606)
Design rating is an approximation: power guideline per ACA formula (A series, typically ±15 … 20 % deviation). Manufacturer rating charts or DIN ISO 10823 are binding.
Geometry and kinematics
- Tooth count z2 (large sprocket)
- 57
- Actual ratio i
- 3
- Speed n2
- 483.3 1/min
- Pitch diameter d1
- 77.16 mm
- Pitch diameter d2
- 230.54 mm
- Chain speed v
- 5.831 m/s
- Engagement frequency f
- 459.2 Hz
Chain length and centre distance
- Number of links X0 (calculated)
- 117.67
- Number of links X (even, selected)
- 118
- Chain length L
- 1,498.6 mm
- Centre distance a (exact)
- 502.13 mm
Make the centre distance adjustable (travel ≥ 1.5·p) or provide an idler sprocket in the slack span.
Power and forces
- Design power PB = P·KA
- 3 kW
- Guideline PR (ACA · strand factor)
- 6.43 kW
- Working tension Ft
- 514 N
- Centrifugal tension Fc
- 23.8 N
- Total tension Fges
- 538 N
- Minimum breaking load FB (ISO 606)
- 18 kN
- Chain mass q
- 0.7 kg/m
Notes
- Lubrication at v = 5.8 m/s: provide oil bath lubrication or a slinger disc.
- Slack span sag: guideline 1 … 2 % of the centre distance; with span inclination above about 60° or shock operation, plan a tensioner sprocket or rail.
Sketch: sprocket pitch circles with chain spans and centre distance (to scale)
Formulas and fundamentals
Ratio and tooth counts: The ratio of a chain drive is i = n1/n2 = z2/z1. The calculator determines z2 = i_target·z1, rounds to a whole tooth count and reports the actual ratio. For the small sprocket the hard limit is z1 ≥ 9; 17 to 25 teeth are recommended, with z1 = 19 as the standard choice. Odd tooth counts (ideally primes such as 17, 19, 23) combined with an even number of links make every chain link engage a different tooth in turn, distributing wear evenly. The large sprocket is limited to z2 ≤ 120, because beyond that the permissible wear elongation becomes too small.
Geometry and kinematics: The pitch diameter of a sprocket follows exactly from d = p/sin(180°/z), since the chain wraps the sprocket as a chordal polygon with pitch p. The mean chain speed is v = z1·p·n1/60000 in m/s (p in mm, n1 in rpm). Speeds up to 15 m/s are common; the practical limit is around 20 m/s.
Number of links and centre distance: From the desired centre distance a0 the calculated number of links is X0 = 2·a0/p + (z1 + z2)/2 + ((z2 − z1)/2π)²·p/a0; the last term corrects for the span inclination with unequal sprockets. X0 is rounded up to the next even number, because an odd link count requires a cranked (offset) link with significantly reduced fatigue strength. The chain length is L = X·p. Solving the link formula for a gives the exact centre distance a = p/4·(A + √(A² − 2·((z2 − z1)/π)²)) with A = X − (z1 + z2)/2.
Polygon effect: Because the chain lies on the sprocket as a polygon, the effective radius and hence the chain speed pulsate periodically. The speed variation is δ = 1 − cos(180°/z1), and the tooth engagement frequency is f = z1·n1/60. From about z1 = 19 onwards δ stays below 1.4 % and is practically uncritical; below 15 teeth the effect becomes clearly noticeable (traffic light in the calculator: green ≥ 19, amber 15 … 18, red < 15).
Guideline power rating and safety: The design power PB = P·KA (service factor 1.0 … 1.7 depending on the shock characteristics of driver and driven machine) is compared with a power guideline PR. PR comes from the published ACA approximation (American Chain Association): the minimum of a link-plate fatigue branch and a roller impact branch, multiplied by the multi-strand factor 1.0/1.7/2.5 for simplex/duplex/triplex. The formula was established for the dimensionally related A series; deviations of ±15 … 20 % from B-series manufacturer charts are typical – the result is a guideline for preliminary sizing, and the final selection belongs to the binding manufacturer rating charts or DIN ISO 10823. In addition the calculator checks the static safety factor S = FB/(Ft + Fc) from the working tension Ft = 1000·PB/v, the centrifugal tension Fc = q·v² and the minimum breaking load FB per ISO 606; S ≥ 7 is required.
Worked example
Reference example: A drive with chain 08B-1 (p = 12.7 mm), z1 = 19, target ratio i = 3 (z2 = 57), desired centre distance a0 = 500 mm and n1 = 1450 rpm. The pitch diameters are d1 = p/sin(180°/19) = 77.16 mm and d2 = 230.54 mm, the chain speed is v = 19·12.7·1450/60000 = 5.83 m/s. The link formula gives X0 = 78.74 + 38 + 0.93 = 117.67, rounded up to the even number X = 118; the chain length is therefore L = 1498.6 mm and the exact centre distance a = 502.13 mm.
With z1 = 19 the polygon effect is only δ = 1 − cos(180°/19) = 1.36 % (green). At P = 3 kW and smooth operation (KA = 1.0), PB = 3 kW; the ACA guideline for 08B simplex at 1450 rpm is about 6.4 kW – roughly 47 % utilisation. The chain tensions are Ft = 3000/5.83 = 515 N and Fc = 0.7·5.83² = 24 N; with FB = 18 kN the static safety factor is S = 18000/539 ≈ 33, well above the required minimum of 7.
Frequently asked questions
Why should the number of links be even?
An odd number of links requires a cranked (offset) connecting link whose plate is additionally loaded in bending, significantly reducing the chain's fatigue strength. The calculator therefore always rounds the number of links up to the next even value and outputs the matching exact centre distance.
Why are odd tooth counts recommended?
When an even number of links meets an odd tooth count (ideally a prime such as 17, 19 or 23), every chain link engages a different tooth gap in turn, so wear spreads evenly over chain and sprocket. With an even z1 and an even link count the same pairings always meet – the calculator warns in that case.
What is the polygon effect?
The chain does not lie on a circle but wraps the sprocket as a polygon. The effective lever arm therefore fluctuates periodically between d/2·cos(180°/z1) and d/2, and the chain speed pulsates with the variation δ = 1 − cos(180°/z1). From about 19 teeth δ stays below 1.4 % and is damped by chain elasticity; small tooth counts produce noticeable vibration and noise.
How reliable is the calculator's power rating?
It is a clearly marked guideline: the built-in ACA approximation reproduces the rating charts via a fatigue branch and an impact branch and was established for the American A series. For the B series, deviations of ±15 to 20 % from manufacturer charts are typical. The manufacturer rating charts (e.g. iwis, Wippermann, Renold) or DIN ISO 10823 govern the final selection.
What lubrication does a chain drive need?
Guidelines by chain speed: up to about 4 m/s regular manual, drip or grease lubrication is sufficient; between 4 and 7 m/s use oil bath or slinger disc lubrication; above that, forced circulation or spray lubrication. Poor lubrication drastically reduces the transmittable power and is one of the most common causes of failure. The exact range limits per chain size are given in the manufacturer chart.
Why is a static safety factor of at least 7 required?
The minimum breaking load FB per ISO 606 is a static value. Operation adds shocks, starting torques, centrifugal force and fatigue that the simple tension calculation does not capture. The guideline S = FB/(Ft + Fc) ≥ 7 covers these effects globally; for passenger transport at least 10 is used.