You need to look at all three conditions and compare results as the belt tensions will vary greatly with all three. A partially loaded belt can increase the tension in the area of the concave curve as the load moves closer to the curve.

Our Belt Analyst software will show you this in detail. ■

Any elementary text on conveyor design has the procedure. You need to do a little reading.

Based on the cloths line or high voltage power line shows the maximum radius equation is a hyperbolic function, degenerated to a quadratic equation for conveyor designer ease of use. The curvature is highly dependent on tension and gravity force along the member's curvature. Higher gravity (ie. material load plus belt mass) means smaller radius as given by the equation Radius ~ Tension/mass => higher tension = larger radius; higher mass (belt ; material load) = smaller radius.

The maximum concave curve radius has limitations to check:

1. Belt edge buckling - different criteria between fabric and steel cord construction - must keep the steel cord wire strands from fretting failure, but, tension of the outer few cords can be forced into compression.

2. Belt center tension - in part is dependent on the minimum belt safety factor - see point 3.

3. Belt tension is normally calculated for the maximum condition along the curve where the location of interest has an empty belt - uphill curves have the highest tension on the highest elevation along the curve, while downhill have the highest tension at the beginning of the horizontal. ■

I assume that you are asking about uplift. As mentioned in Larry's post there is the up-lift issue and there are the radius of curvature constraints that limit the edge compressive stresses and the middle tensile stresses due to curvature. In the case of uplift, at any given point of the profile I determine the maximum belt tension, loaded or empty or with discontinuities in the material flow, and I determine uplift for the locally unloaded belt. As Larry articulated the belt sag is a catenary because the lineal weight, which is constant along the length is not constant along the horizontal projection. If we approximate it as the the latter then the sag is parabolic. This is actually simplified even further, locally treating the sag as the arc of a circle. Thus maximum local up lift radius is Tmax/Wb (max tension / weight of the belt).

Joe Dos Santos ■