Dear Mr. Brown:

There are a number of references that you can use for trajectory calculation. One of the most useful is the CEMA (Conveyor Equipment Manufacturers Associatyion) publication BELT CONVEYORS FOR BULK MATERIALS.

This book indicates that the calculations offered are in close agreement with actual observed trajectories.

Good luck with your calculations. ■

Dear Mr. Brown,

The best approach to predicting conveyor belt material discharge trajectories depends on what you want to use the information for. The CEMA approach offers a very simple method of calculation which gives you a reasonable approximation quickly. If, however, you require a more precise approximation to the trajectory, you would be better off to use another method, such as the Dunlop conveyor design method, the Stephens-Adamson method or the Probelt method. All three calculation methods effectively provide the same results.

The main difference between the CEMA method and the others occurs when the belt speed is not high enough to cause the material to leave the belt at the point of tangency of the belt and the pulley. CEMA assumes, in this case, that the material will accelerate to match the tangential velocity of the discharge pulley. In fact, this only occurs on very slow conveyors. This is an extremely simplified method of approximating the frictional forces between the material and the belt.

None of these methods take other factors into account, such as wind currents, adhesive properties of the material and the cohesiveness of the material. However, these methods are generally accurate enough to provide sufficiently accurate predictions.

According to Hill and Arnold (BSH Vol. 10 No. 4 10-1990), the Dunlop method is more accurate than the CEMA method, as proven by testing.

L.P. Huitema

EMS-Tech Inc.

www.ems-tech.net ■

Peter

I have a very simple excel program that I use for calculating trajectories from belts. It gives me the X & Y coordinates to plot from 0,0 in auto cad or on a graph. I use Pline in autocad and then transfer the pline to the appropriate point on the pulley.

The program is based on formulas from CEMA and I have found it to be quite accurate for my chute designs working with road salt.

Send me your e-mail and I will forward it to you if you like.

Regards, Gary Blenkhorn

blenkhor@compassminerals.com ■

Dear Mr Brown,

CEMA or MHEA graphical methods are sufficient for most situations with the hope that most of the elaborate attention devoted to slow conveyors is no longer of much importance. Admittedly some material characteristics do require slower belts but they should never be so slow that material slides off the end of the belt and so increase top cover wear at the region of maximum tension. Surely that defeats the object of slowing the belt down in the first place.

During transition a lot of material accelerates sideways in a very short time. That is why we have to have liners on the sides of chutes. Present 2 dimensional analyses of conveyor discharge do not consider this lateral disturbance of the cross section except to describe the material cross section at discharge in terms of an arc sector.

By confining the examination to a 2D situation the present methods seem to contradict the Conservation of Energy. Since many particles are given a lateral velocity during transition then they probably cannot be moving ahead at exactly the same speed as the belt.

In 2002 we ought to be examining conveyor discharge trajectories using the particle dynamics add ins of CFD packages. This would be the most reliable and practical approach. With reference to photographic data; I can only imagine conventional photography providing 2D data with the complication of providing a backlight source when taking head on shots. ■

I had occasion to test the accuracy of the trajectory calculations, according to Newtons Laws without regard to air friction, adhesion or other complications (this is the CEMA method). In a coal unloading upgrade project our conveyor to the plant had the options of transfer to the the plant bunker feeding conveyor, or to stackout. to complicate matters the plant system was not upgraded and could not handle the new 1000 stph rate, it is limited to 800 stph design rate. When feeding to the plant we were required to deflect the trajectory to skim the excess 200 stph from the trajectory's underside, to stackout. The existing chute design and the new deflector required accurate prediction of the trajectory in order to accomplish the material deflection (only above the 800 stph rate) and the precise split in very limited space (with limited adjustment because of space). Our calculations (an excel program that produces x/y coordinate points and a trajectory plot) proved very accutate with little adjustment required and mission accomplished.

Joe Dos Santos ■