Belt Feeder Design Calculation: Capacity, Resistances and Drive Power

This belt feeder design calculation follows the order of the calculation itself: the material a belt feeder suits, capacity with skirt width and belt speed, the resistances F1–F5, pulley tensions, and motor power.

For the other feeder types used in crushing and screening plants, see the feeder design and selection guide.

Which Material Suits a Belt Feeder

Belt feeders are generally used to feed materials of limited size stored in hoppers. Large and abrasive materials are not suitable for belt feeders, because these materials can easily damage the top cover of the feeder belt. The maximum material size for belt feeders is around 100 mm. The damage that abrasive, sharp-edged materials cause to the belt top cover can be offset to a certain extent by making the cover thicker.

Figure 1 shows typical MEKA belt feeder views.

Belt feeder under a hopper — Figure 1. Typical belt feeder views

Belt feeder with hopper — Figure 1. Typical belt feeder views

Belt Feeder Capacity Calculation: Skirt Width and Belt Speed

Taking into account the parameters shown in Figure 2, the capacity is:

Q = 3600 · w · d · v · δ

Q: capacity, t/h
w: width between the hopper skirts, m
v: belt speed, m/s
δ: bulk density of the material, t/m³
d: bed depth on the belt at the hopper outlet, m

Depending on the maximum lump size of the material being fed, the width w between the hopper skirts should not be less than the following values:

w = 3.40 · b_max for low-abrasive material and limited hopper heights
w = 4.25 · b_max for low-abrasive material and large hopper heights
w = 4.50 · b_max for highly abrasive material and limited hopper heights
w = 5.0 · b_max for highly abrasive and large hopper heights

b_max: maximum lump size

With h as the gate height at the hopper outlet:

d ≅ 0.75h ≅ 0.58w ∼ 0.75w

Belt feeder speed selection depends on the size distribution and abrasiveness of the material being fed and on the structure of the hopper feed zone. Depending on these properties, it can be selected between 0.08 m/s and 0.5 m/s. The 0.25–0.35 m/s range is the belt feeder speed range most commonly used in crushing and screening plants.

Belt Feeder Resistances F1–F5

In belt feeders, the pulling force transmitted by the motor to the feeder belt through the drive pulley has to overcome the following resistances.

F1: Frictional resistance to conveying the material

F₁ = CfL (Q / (3.6 v))

F₁: frictional resistance arising from material movement, daN
Q: capacity, t/h
v: belt feeder speed, m/s
C: belt feeder length coefficient (taken from Chart 1)
f: roller friction coefficient, taken between 0.020 and 0.022
L: belt feeder length (between pulley centres), m

Chart 1. Length coefficient C by belt feeder length

F2: Shear force from the active weight in the hopper

The shear force that the active weight in the hopper exerts against belt movement:

F₂ = 2000 μ₀L_sw²δ

F₂: shear force required to overcome the frictional resistance of the material in the hopper, daN
L_s: length of the belt feeder under the hopper, m
w: width of the hopper outlet, m
δ: bulk density of the material, t/m³
μ₀: hopper friction factor, which varies with the way the belt is carried
μ₀ = 0.4: carrying rollers in the section of the belt feeder loaded from the hopper
μ₀ = 0.6: slide plates in the section of the belt feeder loaded from the hopper
μ₀ = 0.8 ~ 1: feeding under heavy conditions

F3: Skirt resistance

Resistance arising from the skirts acting on belt movement and from friction of the material against the skirts (parameters shown in Figure 2):

F₃ = h · δ · ((1 − sin ∅) / (1 + sin ∅)) · μ_s · ((2.4w − h) · L_e + h · L_s) + 9L

F₃: resistance from the skirts on the feeder belt and from friction of the material against the skirts, daN
h: gate height, m
δ: bulk density of the material, t/m³
μ_s: friction coefficient between the material and the skirts (Table 1)
w: width between the skirts, m
L_e: length of the belt feeder beyond the hopper, m
L_s: length of the belt feeder under the hopper, m
L: total belt feeder length, m
∅: angle of repose of the material, ° (Table 1)

Material	Angle of repose (°)	Friction coefficient between material and skirt, μ_s
Fly ash	41	0.60
Cement clinker	44	0.55
Portland cement, non-aerated	37	0.45
Bituminous coal	36	0.49
Bituminous coal, fines	41	0.50
Coke	35	0.55
Granite, black, −75 mm	38	0.57
River gravel	37	0.48
Iron ore, pellets	36	0.55
Lignite, dry	37	0.55
Limestone, crushed	37	0.50
Limestone, fines	38	0.50
Sand, dry	37	0.48
Wheat	30	0.38

Table 1. Angle of repose and friction coefficients between material and skirt

The 9L term at the end of the formula indicates that a friction force of 4.5 daN/m is added per metre of rubber-lined skirt.

F4: Lift resistance on an inclined belt feeder

If the belt feeder is installed on an incline, the resistance arising from lifting the material:

F₄ = w · h · δ · H

H: lift height of the material, m

F5: Belt cleaner and scraper resistance

Resistance arising from belt cleaners and scrapers:

F₅ = (n_c·μ_c + n_s·μ_s) · B

n_c: number of belt cleaners used
μ_c: belt cleaner friction resistance, 112 daN/m
n_s: number of scrapers used
μ_s: scraper friction resistance, 41 daN/m
B: belt width, m

Total peripheral force

Thus the peripheral force that the drive system has to transmit to the drive pulley is:

F = F₁ + F₂ + F₃ + F₄ + F₅

Pulley Tensions and the Euler-Eytelwein Equation

This force equals the difference between the tension T₁ on the tight, carrying side of the belt wrapped around the drive pulley and the tension T₂ on the non-carrying side.

F = T₁ − T₂

According to the Euler-Eytelwein formula (Figure 3), T₁ and T₂ are related by:

T₁ / T₂ = e^μα

Here α is the wrap angle in radians and μ is the friction coefficient between the belt and the pulley. This coefficient is generally taken as 0.25 for bare pulleys and 0.35 for rubber-lagged pulleys. However, it is more appropriate to use Table 2 to determine this coefficient, because it varies widely, particularly with the operating conditions of the pulley.

K = 1 / (e^μα − 1)

K is known as the friction factor. Hence:

T₂ = KF

T₁ = (K + 1)F

Operating conditions	Pulley surface
Operating conditions	Bare steel	Grooved polyurethane lagging	Grooved rubber lagging	Ceramic lagging
Dry	0.35–0.40	0.35–0.40	0.40–0.45	0.40–0.45
Wet but clean	0.10	0.35	0.35	0.35–0.40
Wet and dirty	0.05–0.10	0.10	0.25–0.30	0.35

Table 2. Friction coefficients μ between belt and pulley

Belt Feeder Power Calculation: Motor Power and Efficiency

The motor power is:

P = Fv / (102 η)

P: motor power, kW
v: belt feeder speed, m/s
F: total peripheral force, daN
η: mechanical efficiency

For normal helical gear reducer drives, the mechanical efficiency is selected in the range 0.90–0.95. For worm gear units, selecting a mechanical efficiency in the range 0.60–0.70 will be more appropriate.

Frequently Asked Questions

What is the maximum material size for a belt feeder?

The maximum material size for belt feeders is around 100 mm. Belt feeders are generally used to feed materials of limited size stored in hoppers. Large and abrasive materials are not suitable for them, because these materials can easily damage the top cover of the feeder belt.

Which materials are not suitable for a belt feeder?

Large and abrasive materials are not suitable for belt feeders, because these materials can easily damage the top cover of the feeder belt. The damage that abrasive, sharp-edged materials cause to the belt top cover can be offset to a certain extent by making the cover thicker.

How is the skirt width of a belt feeder selected?

Depending on the maximum lump size b_max of the material being fed, the width w between the hopper skirts should not be less than 3.40 · b_max for low-abrasive material and limited hopper heights, 4.25 · b_max for low-abrasive material and large hopper heights, 4.50 · b_max for highly abrasive material and limited hopper heights, and 5.0 · b_max for highly abrasive and large hopper heights.

What is a typical belt feeder speed?