Ziggy

A simple calculation can be made as follows.

F = AxHxDxCf

F = force required to move gate in pounds

A = Area of gate opening in square feet

H = Height of material over gate in feet

D = Bulk density of material in PCF

Cf = Coefficient of static friction

To calculate the resistive torque to rotate the gate

RT = RxF

RT = Resitive Torque in in-lbs.

R = Radius from bottom of gate to pivot point in inches

F = Force required to move gate in pounds

Regards

Gary Blenkhorn ■

May I add a couple of small possible corrections. THe calculation can be extended from a belt feeder slot pressure computation. In so doing, the height of the pressure would more closely be associated with the free flowing material below the equilibrium stress along the arch forming stable geometry.

Mod 1:

A simplified assumption would be to take an included angle of about 80 degrees from each of the bottom gate side walls extended up till they meet at their apex. Calculate the mass below this region and apply the coeficient of breakway friction or about twice (2.5x) the free flowing friction.

Mod 2:

If the drop height is higher than the noted apex, then an initial compacted material may exceed a load of the above and may be taken as Mod 1 plus the extra pressure applied from the remaining free fall during the inital filling.

These factors assume free flowing and cohesion resistance is small over the range of temperatures (freezing?) and time (drying and agglomerating). ■

As always with bulk solids applications, there are various different operating circumstances to be taken into account when assessing a situation. In the case of gates under hopper outlets four situations may arise.

1Opening and closing the gates with no product present. This is trivial unless, as may be the position with some slide designs, the gate is clogged with product from previous use.

2.Opening the gate from first fill, the worst case being a full, mass flow hopper, left for a period of time consolidation.

3.Closing the gate during flow, again the maximum load being with a full hopper and a fully mobilised flow channel.

4.Opening the gate after some flow has taken place from the hopper, again the greatest load follows the maximum duration of being shut.

The forces acting on the gate in each case depends on whether the hopper is off mass flow, or non-mass flow design, but case 2 is the one offering the greatest resistance to movement. Mass flow offers the highest gate load for a given size of gate, as the overpressures relate to the degree by which the opening exceeds the critical arching span for the product being stored. It will be apparent that a thorough analysis of a given situation demands wall friction, density and shear testing in order to address the technical position.

For those that are unable or unwilling to undertake a proper study, a crude rule of thumb may be considered on the lines of the previous suggestions as it is not usually a life or death situation. These follow an assessment of the load acting on the gate based on the material weight not supported by the hopper walls. This takes the form of all that product laying under the static or dynamic dome where the material has collapsed onto the gate. The volume of the parabolic form may be roughly approximated by a considering a pyramid with a base as the area of the gate and a height chosen according by an inspired guess that is related to the state of the material. A figure of eight times the hydraulic radius of the outlet dimensions is usually a reasonably safe value. Taking this volume, times the material density in a condition of medium compaction, times the static frictional coefficient of the material on the slide surface, should give a reasonable approximation of the maximum resisting force to be overcome.

Lyn Bates ■