The CEMA Horsepower Equation
The CEMA Horsepower Equation
DIN 22123 specifies that LSIT reports shall include a list of “Width Related Load [N/mm]” (W_{RL}) which is the applied load divided by test belt width, and a resulting “Width Related Indentation Rolling Resistance [N/mm]” (W_{RIRR}) which is the indentation resistance divided by test belt width. Sample data from a typical LSIT appear in Fig. 4.
Fig. 4: LIST data from an LRR belt.
The appendix of DIN 22123 recommends fitting each temperature line on this plot with the function:
W_{RIRR} = a · (W_{RL})^{b}.
Another function could be used, but DIN’s function is simple and passes through (0,0) which is critical. To compute the power loss over the crosssection of a real conveyor with the same idler diameter, temperature, and belt construction of the test, the engineer:
Step 1: Determines the distribution of load on the idlers at the interface between the belt and the idlers:
W_{RL}(z) = q(z).
Step 2: Fits the W_{RL} and W_{RIRR} data from the LSIT report with a function that relates load to resistance, such as:
Step 3: Computes:
The pressure distribution on an idler roll, q(z), is not trivial. Fig. 5 shows the pressure distribution Grabner [16] measured on typical carry side troughed belt idler rolls in a straight section of belt. Since the belt below the junction regions ‘A’ and ‘B’ does not touch the rolls, the load in these regions is supported by the belt at the edges of the junction.
Fig. 5: Idler roll pressure distribution measured by Grabner on a 30 degree trough.
While the integral of the force in the vertical direction must equal the weight of the belt plus material, the pressure distribution is different from a hydrostatic distribution because bulk materials, unlike fluids, support shear. This means that centrally located particles can transfer some of their weight to the wing rolls through friction forces. The effect is particularly pronounced when the belt is moving, because the sides of the trough compress into the material when the belt enters the idler trough and relax when the belt leaves the idler trough.
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