The CEMA Horsepower Equation
The CEMA Horsepower Equation
Large Sample Integration Example
For this example, we will predict the indentation losses of a carry side idler set in a straight, horizontal, section of a conveyor with the following parameters:
 B_{w} = belt width = 1600 mm = 1.6 m
 γ = bulk density = 800 kg/m^{3} = 7840 N/m^{3}
 v = belt speed, = 7.5 m/s
 Q = tonnage= 4860 t/h = 13,230 N/s
 Ø_{s} = surcharge angle, = 15 degs
 β = trough angle = 45° (carry), 30° (return)
 S_{i} = carry idler spacing = 2 m (carry), 8 m (return)
 D_{0} = idler diameter = 194 mm (carry), 178 mm (return)
 W_{b} = belt weight = 39.5 kg/m = 387.1 N/m
 R_{LC} = center roll length = 593.6 mm
 T = temperature = 20°C
 h_{0} = bottom cover thickness = 6 mm
 Bottom cover rubber type: LRR Rubber
Mathematical formula for the pressure distribution on an idler roll can be quite complicated [19] and are beyond the scope of this paper.
To simplify our example, we shall adopt the distribution used by Tapp [20]. For a 45° trough, Tapp evenly distributes 7% of the load in the center roll, and allocates the remaining 25% of the load to the wing rollers using a triangular distribution.
Accordingly, we compute q(z) for the carry:
The pressure of the belt against the wing roll is:
Note: Tapp’s distribution assumes a hydrostatic pressure and thus, includes no cos() term. In reality, Tapp overestimates the material pressure on the wing roll which is clear if we sum the loads measured by Grabner.
To calculate the pressure distribution on the wing roll we first compute the distance from the junction to the edge of the material. The Belt Book includes a complicated, accurate formula to compute the distance from the edge of the belt to the edge of material. Using this formula we compute this edge distance, B_{we} = 193 mm. From edge distance we compute the distance from the junction to the edge of material: L_{wm} = 0.5 · (B_{w}  R_{LC})  B_{we} = 310. From this we compute the wing roll pressure distribution:
Combining q_{c}(z), q_{w1}(z), and q_{w2}(z) we get the pressure distribution shown in Fig. 6.
Fig. 6: Simplified roll pressure for 45 degree trough.
The pressure levels in this figure are fairly typical of the pressures found in conveyor belts. A good range for large sample test data is between 0.5 N/mm and 9 N/mm. Some laboratories [17] are currently testing large samples at pressure several times higher than this. The LSIT data in CEMA7 combines results from several sources and thus includes a much wider range than the engineer is likely to find on trough belts operating in the field.
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