Apron Feeder Design Calculation: Chain, Pan Width, Capacity and Power

In crushing and screening plants, apron feeders, particularly those that feed primary crushers, are heavy-duty feeders.

The sections below follow the order of the calculation: chain, sizing inputs, pan and skirt width, capacity, and finally resistances and motor power. A general introduction to the machine, and its place among the other feeder types, are covered in separate guides.

Main Components of a Heavy-Duty Apron Feeder

The main components of these feeders are the same as the main components of the crawler undercarriages of the tracked dozers or excavators widely used in the industry. These components require no lubrication, do not need much maintenance, and their wear is at a minimum level. Figure 5 shows a cross-section of a heavy-duty apron feeder and the main components of the feeder. In summary, these main components are:

• Chain
• Carrier and return rollers
• Drive sprockets
• Tail wheels
• Apron pans
• Impact rails
• Main frame
• Side skirts

Optionally, a spillage conveyor can be placed under the feeder to collect and remove the material that sticks to the pans and spills on the return side. This conveyor can be a special belt conveyor or a flight conveyor.

Figure 6 shows the crawler undercarriage components of a dozer or excavator, and an apron feeder in which these components are used.

Apron Feeder Chain Selection and Safety Factor

The most important factor in selecting the chain of a heavy-duty apron feeder is the chain safety factor (chain breaking strength / calculated chain pull). This value should not be less than 5.

Table 7 shows the technical specifications of the dozer chains used in heavy-duty apron feeders.

Table 7. Technical specifications of the chains used in apron feeders

Apron Feeder Sizing Inputs

When determining the size of an apron feeder, the designer should take the following factors into account:

• Maximum lump size of the material to be fed
• Capacity to be fed, in t/h or m³/h
• Feeder speed permitted by the chain
• Size of the feed hopper and the hopper opening

Table 8 can be used as a reference for the average and maximum lump size values that can be fed according to the width between the apron feeder side skirts.

Table 8. Reference values of lump sizes that can be fed according to the width between the apron feeder side skirts

Apron Pan Width and Skirt Width

The empirical formula giving the apron pan width:

D = 0.0017 a_max + 0.2

• D: width of the apron pans, m
• a_max: maximum lump size, mm

The width between the skirts, B, will be 100 mm less than the width of the apron pans.

Apron Feeder Capacity Calculation

In apron feeders, capacity is calculated with the following formula:

Q = 3600 · B · d · v · δ · φ · c

• Q: capacity, t/h
• B: feeder side skirt width, m
• d: height of the conveyed material on the feeder, m. In closed hoppers, what determines this thickness is the height of the hopper discharge opening, that is, the gate height. If this height is H, d ≅ 0.75 H. In open hoppers, this height is determined by the width between the hopper skirts, according to the maximum lump size. For run-of-mine material feeds with a maximum lump size of 600–1000 mm, d ≅ (0.5–0.7)B can be used.
• v: feeder speed, m/s
• δ: bulk density of the material, t/m³
• φ: fill factor, 0.75–0.80
• c: coefficient depending on the feeder inclination
  c = (100 − β) / 100
• β: angle of the feeder to the horizontal

Approximate volumetric capacity values of apron feeders for a bed depth of 1000 mm and different chain speeds are given in Table 9.

Table 9. Approximate capacity values of apron feeders depending on the apron pan width and chain speed

Apron Feeder Power Calculation: Resistances and Motor Power

Resistances the feeder has to overcome, considering the general dimension parameters shown in Figure 7:

• R₁: frictional resistance of the carrier rollers, kN
• R₂: frictional resistance between material and hopper, kN
• R₃: frictional resistance between moving and stationary material, kN
• R₄: resistance due to lifting the material, kN
• R_T: total resistance, kN

R_T = R₁ + R₂ + R₃ + R₄

R₁ = 10 f (1.2 B²A₂ δ + B d A₃ δ + G)

R₂ = R_S A / 100

R₃ = 9 B²A₁ δ s_f

R₄ = 10 δ B d h

• f: friction coefficient of the rollers, 0.1–0.14
  f = 0.1 for manganese-alloy steel plate pans, f = 0.14 for cast pans
• G: weight of the moving parts, t
• R_S: frictional resistance of each metre of the hopper with the material, daN/m (Table 10)
• s_f: a correction factor depending on the type of material, its moisture content and maximum size. For safety, s_f = 1 is taken in the first calculation.

In open hoppers fed with coarse material, A₃ = 0 is taken, and A₁ = A₄ / 3 is taken (Figure 8).

• A₄: length of the material slope inside the hopper

Table 10. R_S values depending on the bulk density of the material and the bed depth at the feeder discharge

Note: For the chain to be selected for apron feeders, the safety factor must be at least 7.5.

The motor power required to overcome all these resistances:

P = R_T v / η

• P: required motor power, kW
• R_T: total resistance, kN
• v: feeder speed, m/s
• η: mechanical efficiency

Related Pages

How apron feeders compare with belt and vibrating feeders is covered in a separate guide. MEKA's apron feeders are presented on the product page.

Frequently Asked Questions

How is the skirt width chosen for a given lump size?

Table 8 can be used as a reference for the average and maximum lump sizes that can be fed according to the width between the side skirts, from 457 mm to 1829 mm. The empirical formula giving the apron pan width is D = 0.0017 a_max + 0.2, with D in m and a_max in mm. The width between the skirts will be 100 mm less than the width of the apron pans.

How is apron feeder capacity calculated?

In apron feeders, capacity is calculated with Q = 3600 · B · d · v · δ · φ · c, in t/h. B is the feeder side skirt width (m), d the height of the conveyed material on the feeder (m), v the feeder speed (m/s), δ the bulk density of the material (t/m³), φ the fill factor, 0.75–0.80, and c the coefficient depending on the feeder inclination, c = (100 − β) / 100, where β is the angle of the feeder to the horizontal.

How is the material height d taken in closed and open hoppers?

In closed hoppers, d is determined by the height of the hopper discharge opening, that is, the gate height; if this height is H, d ≅ 0.75 H. In open hoppers, it is determined by the width between the hopper skirts, according to the maximum lump size; for run-of-mine material feeds with a maximum lump size of 600–1000 mm, d ≅ (0.5–0.7)B can be used.

Which resistances does the apron feeder drive have to overcome?

The resistances the feeder has to overcome are R₁, the frictional resistance of the carrier rollers; R₂, the frictional resistance between material and hopper; R₃, the frictional resistance between moving and stationary material; and R₄, the resistance due to lifting the material. The motor power required to overcome all these resistances is P = R_T v / η, where R_T is the total resistance (kN), v the feeder speed (m/s) and η the mechanical efficiency.

Do apron feeder components need lubrication?

No. The main components of a heavy-duty apron feeder are the same as the main components of the crawler undercarriages of tracked dozers or excavators: chain, carrier and return rollers, drive sprockets and tail wheels. These components require no lubrication, do not need much maintenance, and their wear is at a minimum level.