The accompanying chart has been drawn for the convenience of engineers as a means of quickly determining the correct number of plies of conveyor belts operating under specific conditions.
The calculations are based on the average safe strength (factor of safety, 15) of the various standard rubber conveyor belts.
The calculations assume maximum loading conditions; that is, the belt is considered as carrying the greatest load that it will handle without spillage at ordinary belt speeds. This not only produces the most economical operating conditions, but also the maximum tension in the belt.
The chart is a graphical representation of the formula :
Where, p = kgW(L + 10H)
p = the correct number of plies
k = a constant, depending on the type of drive
g = the weight in pounds per cubic foot of material handled
W = the width of the belt in inches
L = the length of the belt in feet (approximately twice the center distance).
H = the difference in elevation between the head and tail pulleys, in feet.
For a simple drive, with a bare pulley, k = 1/250,000
For a simple drive, with a rubber-lagged pulley, k = 1/300,000
For a tandem drive, with bare pulleys, k = 1/375,000
For a tandem drive, with rubber-lagged pulleys, k = 1/455,000
The chart is drawn for a simple drive, with a bare pulley (k = 1/250,000);
therefore, the number of plies obtained from the chart should be multiplied by the factor 0.83 or 5/6 for simple, lagged drive; the factor 0.67 or 2/3 for tandem, bare; and the factor 0.55 or 11/20 for tandem, lagged.
The formula p = kgW(L + 10H) has been developed mathematically
from the following formulas, which have been found to work very satisfactorily in average good practice:
U = 0.08W²Sg/5000
HP = (0.02l/100 + 0.01H/10)U
T = C x HP x 100/S
p = T/24W
Where, U = Capacity in tons per hour
W = Width of belt in inches
S = Belt speed in feet per minute
g = Weight per cubic foot of material handled
HP = Horsepower developed in driving conveyor belt
l = Length of the conveyor, in feet (approximately ½L)
H = The difference in elevation between the head and tail pulleys, in feet
T = The total tension in the belt, in pounds
p = Correct number of plies
C = The constant of the drive.
For a simple drive, bare pulley, C = 600
For a simple drive, rubber-lagged pulley, C = 500
For a tandem drive, bare pulleys, C = 400
For a tandem drive, rubber-lagged pulleys, C = 330
The length factor, f = (L + 10H), represented on the chart by the lines 500, 600, 700, etc., is a developed factor equal to the sum of the length of the belt and ten times the difference in elevation between the head and tail pulleys.
To find the correct number of plies for a conveyor belt, knowing the width, the length, the difference in elevation between the head and tail ends, and the kind of material to be handled:
Start from the width given at the top of the chart and move down until this line intersects the line corresponding to the proper length factor; then move either right or left until the line corresponding to the given material is met; then move down again to the scale of plies, where the next largest figure will give the correct number of plies.
For example: To find the correct number of plies for a conveyor belt 36 in. wide and 300 ft. long, with 20 ft. difference in elevation; handling sand and gravel.
Follow the line from the 36-in. width downward until it intersects the 500 length factor line; then follow to the right until the sand and gravel line is intersected; then down to the ply scale, where the ply will be found to be 7.
