Cement plant
Belt-driven crusher and mill shafts: how to work out the bearing loads
Belt pull, weights and coupling force on a shaft with the pulley between two bearings, and the shock factor that crushers need.
The arrangement
A pulley sits between two bearings and a coupling to the motor sits beyond one of them. The belt pull is the biggest load, the weights come next and the coupling adds a small force in an unknown direction.
The method
| Step | Formula | Note |
|---|---|---|
| Torque | T = 9,550 × P ÷ n (N·m) | P in kW |
| Belt tangential force | Ft = 60,000,000 × P ÷ (π × D × n) (N) | D = pulley pitch diameter in mm |
| Radial belt load | Fb = k × Ft | k is about 1.1 for synchronous belts, 1.5 to 2.0 for V-belts, 2.5 to 3.0 for flat belts |
| Coupling force | F = 5,600 × √(P/n) (N) | Rule of thumb for a semi-flexible coupling. Use the coupling maker's figure if you have it |
| Reactions | Moments about each bearing | Try the belt both ways and the coupling in every direction |
| Minimum shaft | d = 118 × (HP/n)^0.25 mm | Use twice the power for the starting torque |
Shock factor for the equivalent load
| Duty | fw |
|---|---|
| Smooth running | 1.0 to 1.2 |
| Light shock | 1.2 to 1.5 |
| Heavy shock, such as crushers | 1.5 to 3.0 |
Checks
- The bearing load, the life and the shock factor must all be written out, not only the total force at the pulley.
- A straight belt drive gives almost no axial load, so the located bearing is simply the one that fixes the shaft.
- Check the minimum load: a roller bearing needs about 1% of C as a radial load to avoid skidding.
- Keep the conservative one-line sum when the belt direction is not known.
Takeaway. Write out the load on each bearing and apply a shock factor. The pulley force alone does not give a life.
Put it to work in the tool