Conveyor pulley shaft load and bearing life calculator
Resultant belt load on drive, snub, bend and tail pulley shafts, the radial load on each bearing and the ISO 281 basic rating life.
Result
How it works
Every conveyor pulley carries the vector sum of the belt pull on each side of it. On the drive pulley the two pulls differ (T1 and T2) and the load is largest; on a snub or bend pulley the tension is the same on both sides and the load depends on the wrap angle — a 30° snub carries only about half of the belt tension.
The calculator adds the pulley’s own weight, splits the total between the two bearings and, if you enter the bearing’s dynamic load rating from its catalogue, gives the ISO 281 basic rating life in hours at the pulley speed.
Formula
Belt resultant: FW = √(T1² + T2² − 2 · T1 · T2 · cos β) Special cases: β = 180° → T1 + T2; equal tensions T → 2 · T · sin(β/2) With pulley weight W = m · g at angle φ: F = √(FW² + W² + 2 · FW · W · cos φ) (φ unknown: F = FW + W) Per bearing (pulley centred): P = F / 2; pulley speed n = 60 · v / (π · D) Basic rating life (ISO 281): L10h = (C / P)^p · 10⁶ / (60 · n), p = 10/3 roller, 3 ball
| Symbol | Meaning | Unit |
|---|---|---|
| T1, T2 | Belt tensions either side of the pulley (equal on a non-drive pulley) | kN |
| β | Wrap angle | ° |
| m | Pulley mass (drum and shaft) | kg |
| φ | Angle between belt resultant and vertical-down | ° |
| C | Bearing basic dynamic load rating (catalogue) | kN |
| P | Radial load per bearing | kN |
| n | Pulley speed | rpm |
Worked example
Inputs: Pulley = drive ; Tight-side tension T1 (non-drive: tension at pulley) = 27 kN; Slack-side tension T2 (drive only) = 9 kN; Wrap angle β = 210 °; Pulley mass = 450 kg; Angle φ to vertical (blank = worst case) = °; Belt speed = 1.3 m/s; Pulley diameter over lagging = 524 mm; Bearing dynamic rating C (catalogue) = 300 kN; Bearing type = roller ; Required life = 50000 h.
- Drive pulley 500 mm + 12 mm lagging (D = 524 mm), T1 = 27 kN, T2 = 9 kN, wrap 210° with a snub, mass 450 kg; bearing C = 300 kN is an illustration — use your catalogue value
- FW = √(27² + 9² − 2 × 27 × 9 × cos 210°) = 35.08 kN
- Weight 4.41 kN; worst-case total 39.50 kN → 19.75 kN per bearing
- n = 47.4 rpm; L10h = (300 / 19.75)^(10/3) × 10⁶ / (60 × 47.4) = 3,053,539 h
- Same belt on a 30° snub (T = 9 kN): 2 × 9 × sin 15° = 4.66 kN
- Checks: β = 180° gives T1 + T2 and equal tensions give 2·T·sin(β/2), the special cases printed in Forbo Siegling 301 p.10.
Assumptions and limits
- T1, T2 and the local tension at each pulley must come from a tension calculation (effective tension calculator), including take-up tension, which acts even when the belt is stopped.
- Bearings are assumed equally loaded (pulley centred between them); an overhung drive or coupling load needs the shaft maker’s calculation.
- Forbo Siegling suggests about 1.5 × the belt resultant while tensioning synthetic-carcass belts; shown as a reference.
- Bearing life is the ISO 281 basic rating life with radial load only; lubrication, contamination (aISO) and axial load are not included.
- Screening only; shaft stress and deflection need the pulley maker’s design.
Screening estimate, not a design approval. Verify measured inputs, current standards, manufacturer limits and site procedures before purchasing, cutting or installation. Isolate and lock out equipment before any hands-on measurement.
Questions
Why is the snub pulley load so much smaller than the drive pulley load?
A snub pulley turns the belt through a small angle, so the two equal pulls almost cancel: at 30° wrap the load is only 2 × sin 15° = 0.52 times the belt tension.
Which tension should I use for a bend or take-up pulley?
The local belt tension at that pulley, from the tension calculation. For a gravity take-up pulley with 180° wrap it is twice the tension there, which equals the counterweight.
Source notes
- Forbo Siegling, “Calculation methods – conveyor belts”, ref. 301-2 (03/19), p.10 — drive drum (β ≠ 180°), end drum and snub roller shaft loads, ×1.5 at tensioning. The p.10 snub formula is printed with a root sign over 2·F2·sin(β/2); the vector sum (used here) has no root.
- ISO 281 — basic rating life L10 = (C/P)^p. Bearing C values from the bearing maker’s catalogue.
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