Thanks for your reply Gary. I have already developed an Excel spreadsheet based on the CEMA method. The problem is that the trajectory I see in the field does not match that predicted by the CEMA method. Through some reading and research by others it seems that the Dunlop/Booth method returns results that more closely match those found in actual practice. The Dunlop method is graphic based, the Booth method is based on formulas that can be entered into an Excel spreadsheet. The reading I have done indicates that the CEMA method will predict a trajectory that will overshoot the actual. My observations confirm this. I would like to see your calculator so that I can compare it to mine.

I have visited the E&MJ site but do not see anywhere in there that I can search on or download a past article on conveyor discharge trajectories. ■

I have checked with several sources now, some that have experience with a wide range of conveyor sizes, capacities and conveyed materials. Their conclusion is that every conveyor and material is a little different and that predicting the trajectory is very difficult. The material properties may change due to temperature, moisture content, particle size and gradation among others. They have found the Dunlop method to be the most reliable. This is in concurrence with the findings of Arnold and Hill.

The Dunlop method similar to the Link-Belt method uses a radius of either the outside of lagging on the pulley or the top surface of the conveyor belt to determine the velocity Vs. The difference between the two radii is small and either appears to provide reasonable results.

I have the good fortune of working at a sight where we have a number of conveyors that run at a wide range of speeds. The conveyor that spurred this thread is one that has a V^2/gr that is approximately 1.21. According to theory the material should leave the belt at the point of tangency with the head pulley. The material does not. It leaves at an angle approximately 20 deg. past the point of tangency.

The material is a copper ore after it leaves the primary crusher. The material size ranges from approximately 6" and smaller. Moisture has been added to the ore before and after it has been crushed. This leads me to believe that there is an adhesive effect, as Korzen has suggested, on this conveyor due to the nature of the ore and the addition of water. By taking the angle at the point of discharge I was able to calculate a value for the Korzen adhesive stress of 0.15 kPa.

I also took a look at the radius used to determine Vs. To do this I looked at the rigidity of the system. The conveyor pulley is usually fabricated from steel and is rigid. The pulley lagging is made from high durometer rubber, urethane, ceramic or a combination of these or similar materials. It is relatively rigid with only small deformations present. The belt is a flexible member. However, within the belt the fabric/steel chords are relatively rigid compared to the top and bottom covers. As the belt wraps around the drive and head pulleys, the steel chords/fabric retain their length and thus determine the speed of the belt. The top surface of the belt would travel faster as the belt travels around the pulley, but returns to the speed of the chords/fabric after the belt has traversed the pulley. The distance from the bottom of the belt to the structural component is approximately 1/3 the belt thickness. Therefore, the radius I used to determine Vs is r=pulley radius+lagging thickness+belt thickness/3. The adhesive stress value and this value of r was used in Korzen's equations to determine the point of departure from the belt and to determine the tangential velocity. The result is that the trajectory was very close to that which was observed for this conveyor.

This is by no means a scientific approach to the problem, however, it does explain what may be happening on this particular conveyor and did provide accurate results. The method was also used on a conveyor with Vs^2/gr=2.26 and a radius calculated by the method shown above. The trajectory on this conveyor was also observed to be very close to that predicted.

I invite any comments or criticism of this analysis. Please let me know if you find any flaws in my thinking on this.

AHStack

Senior Mechanical Engineer ■