Belt conveyor calculation
Design the drive power of a belt conveyor using the simplified main resistance method of DIN 22101: from mass flow, belt speed, conveying length and height, and belt/idler mass, the main resistance, gradient resistance, driving force at the drive pulley, and hence pulley and motor power follow.
Calculation
Design rating is an approximation: simplified main resistance method without start-up/braking cases, pulley friction and troughing resistance in detail.
Conveyed material and incline
- Conveyed material mass m_L'
- 27.78 kg/m
- Incline angle δ
- 5.71 °
- cos δ
- 0.995
Resistances and driving force
- Main resistance F_H
- 809.2 N
- Gradient resistance F_St
- 1,362.5 N
- Length surcharge factor C
- 2.2
- Driving force F_U
- 3,142.8 N
Drive power
- Pulley power P_T
- 6.286 kW
- Motor power P_M
- 6.984 kW
Sketch: inclined belt conveyor with pulleys, belt and conveyed material (not to scale)
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Formulas and fundamentals
Mass per Metre of Conveyed Material
The mass flow ṁ is spread over the belt length at belt speed v; the conveyed material mass per metre of belt length is:
With ṁ in t/h and v in m/s, m_L' follows directly in kg/m.
Main Resistance
The simplified main resistance method of DIN 22101 lumps idler rolling friction, indentation resistance and belt bending resistance over the idler spacing into a fictitious friction coefficient f (guideline 0.017 … 0.025, depending on idler design, temperature and contamination). The main resistance over the horizontally projected conveying length L is:
Here m_R' is the mass of the rotating idler parts per metre (carrying and return side combined), m_G' is the belt mass per metre (counted twice, since both the carrying and return side move the belt), and δ is the incline angle.
Incline Angle and Gradient Resistance
From the conveying height H and the horizontally projected length L, the incline angle follows:
Lifting the conveyed material requires the gradient resistance (for a decline, H negative, it acts as a relief and can reduce the driving force):
Driving Force and Length Surcharge
Secondary resistances (pulley friction, cleaning equipment, loading resistance, etc.) are approximated via the length surcharge factor C - short belts have a relatively high share of secondary resistances, long belts a low one:
The driving force at the drive pulley follows from the main and gradient resistance:
Drive and Motor Power
The drive power at the pulley follows from the driving force and belt speed; the motor power additionally accounts for the drive efficiency η (guideline 0.9 for a geared motor with coupling):
Typical belt speeds range from 0.5 to 5 m/s depending on the conveyed material; the guideline maximum incline is roughly 18 to 20° depending on the material, beyond which bulk material slides back on the belt.
Worked example
Reference example: a belt conveyor transports ṁ = 200 t/h at a belt speed v = 2 m/s over a horizontally projected length L = 50 m and a conveying height H = 5 m. The belt mass is m_G' = 15 kg/m, the mass of the rotating idler parts m_R' = 25 kg/m, and the main resistance coefficient f = 0.02. The conveyed material mass per metre is m_L' = 200/(3.6·2) = 27.78 kg/m.
The incline angle is δ = arctan(5/50) = 5.71° (cos δ = 0.995). The main resistance F_H = 0.02·50·9.81·[25 + (2·15 + 27.78)·0.995] = 809.2 N, the gradient resistance F_St = 9.81·5·27.78 = 1362.5 N. With the length surcharge factor C = 1 + 60/50 = 2.2 (approximation from L), the driving force is F_U = 2.2·809.2 + 1362.5 = 3142.8 N.
The drive power at the pulley is P_T = 3142.8·2 = 6286 W = 6.29 kW. With a drive efficiency η = 0.9, the motor power follows as P_M = 6.29/0.9 = 6.98 kW - for this conveyor a motor of at least about 7.5 kW (next standard size) should be selected. Belt speed, incline and friction coefficient are all within the usual guideline range.
Frequently asked questions
How do I calculate the drive power of a belt conveyor?
From mass flow, belt speed, conveying length, conveying height, and belt and idler mass, the main and gradient resistance follow first, then the driving force F_U at the drive pulley via the length surcharge factor C. The pulley power is P_T = F_U·v, the motor power P_M = P_T/η with the drive efficiency η. This calculator implements the simplified main resistance method per DIN 22101.
What is the main resistance coefficient f?
f is a fictitious, empirically determined friction coefficient that lumps together idler bearing rolling friction, belt indentation resistance on the idlers, and belt bending resistance between idlers. Common values range from 0.017 (free-running idlers, well maintained, warm environment) to 0.025 (contaminated, cold, stiff bearings); a default of f = 0.02 is frequently used.
How do I convert mass flow to mass per metre of belt length?
The conveyed material mass per metre of belt length is m_L' = ṁ/(3.6·v), with the mass flow ṁ in t/h and the belt speed v in m/s. The factor 3.6 converts t/h to kg/s (1 t/h = 1000 kg/3600 s); dividing by v spreads the mass conveyed per second over the belt length covered in that second.
What is the maximum incline for a belt conveyor?
The guideline maximum incline depends on the bulk material (friction, grain shape, moisture) and is typically around 18 to 20° for smooth standard belts; beyond that, bulk material starts to slide back on the belt. For steeper conveying, corrugated sidewall belts, ribbed belts, or steep conveyors with cleat profiles are required - these special designs are not part of this simplified calculation.
How do I choose the belt speed?
Typical belt speeds range from 0.5 to 5 m/s depending on the bulk material and plant size. Fine, dusty or abrasive materials as well as short conveyors with frequent starts tend to run slower; coarse, robust bulk materials on long conveying runs tend to run faster - a higher speed reduces the required belt cross-section for a given mass flow but increases wear and dust generation.
What does the length surcharge factor C mean?
C approximates the secondary resistances (pulley friction, loading resistance, cleaning equipment) that are large relative to the main resistance for short belts and small for long belts. The calculator uses the approximation C ≈ 1 + 60/L (L in m) with a minimum of 1.02; for a more precise design, a table or manufacturer data from the belt conveyor supplier should be consulted.
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