Conveyor Belt Power Formulas
Belt conveyor power formulas: the material load per metre, the friction force, the power to lift the material and the motor power with the drive efficiency.
The formulas
| To find | Formula |
|---|---|
| Mass flow | ṁ = throughput (t/h) × 1000 / 3600 |
| Material per metre of belt | q = ṁ / v |
| Friction force | F = μ × g × L × (q + qb) |
| Power to lift the material | Pl = ṁ × g × h |
| Power to move against friction | Pf = F × v |
| Motor input power | Pm = (Pl + Pf) / η |
v is the belt speed in m/s, L the length in metres, h the lift in metres, qb the mass of the moving parts of the belt and rollers in kg per metre, μ an equivalent friction factor that covers the rollers, the belt flex and the seals, g = 9.81 m/s² and η the efficiency of the drive. The method is a first estimate for a straight belt. A full design follows a standard such as ISO 5048 or CEMA, and adds the acceleration, the skirts, the trippers and the belt tension. The values here are examples.
Worked example: 100 t/h at 2 m/s over 50 m with a lift of 5 m
- ṁ = 100 × 1000 / 3600 = 27.78 kg/s, and q = 27.78 / 2 = 13.89 kg/m
- Pl = 27.78 × 9.81 × 5 = 1,363 W
- F = 0.03 × 9.81 × 50 × (13.89 + 15) = 425.1 N, so Pf = 425.1 × 2 = 850.2 W
- At the drum, P = 1,363 + 850.2 = 2,213 W
- With a drive efficiency of 0.85, Pm = 2,213 / 0.85 = 2,603 W
Power by throughput for the same belt
| Throughput | Power at the drum | Motor input |
|---|---|---|
| 50 t/h | 1.327 kW | 1.561 kW |
| 100 t/h | 2.213 kW | 2.603 kW |
| 200 t/h | 3.984 kW | 4.687 kW |
| 400 t/h | 7.526 kW | 8.855 kW |
Frequently asked questions
Why is the empty belt included?
The belt and the rollers move even with no material, and they take power through the friction. For a long belt this is a large share of the total.
What does the lift add?
A rising belt lifts the material, which takes the power ṁ × g × h. A falling belt can give power back, and then it brakes the drive.
Is the motor chosen at the calculated power?
No. It is chosen with a margin for the starting, the wet or sticky material and the ageing. The standard gives the factors.
How does the speed affect the power?
The friction power rises with the speed, and the lift power rises with the mass flow. A faster belt with the same load per metre needs more power.
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