PAEA Webinar September 2023

Purpose of Webinar:
This video was recorded during the September 2023 meeting of the Polish-American Engineers Association meeting in Chicago, IL. It presents how to design a bulk conveyor belt drive system using CEMA "Historical Methodology" and the Rulmeca Corporation Conveyor Drive Power Calculation Program, version 7.30. Additionally, it presents and explains the equations required to minimize power consumption in a typical hopper feeder drive system.
How to Calculate Required Conveyor Belt Pull:
Te = LKt (Kx + KyWb + 0.015Wb) + Tp + Tac + Wm(LKy + H) + Tam
This is the equation developed in the 1950s by CEMA. It enables us to calculate the amount of belt pull required to overcome friction, gravity, and momentum in the bulk handling conveyor belt. Once we know the required belt pull, we can convert that into horsepower by multiplying belt pull (in lbs) by belt speed (in fpm).
Rulmeca Software Demonstration:
Now we will demonstrate the Rulmeca software to show how the program calculates required belt pull and power for "standard loading condition". I've loaded the parameters in to save time.
For the operating requirements (e.g. 500 tph on a 100' long conveyor moving at 300 fpm) and ambient conditions we have shown, the program shows that required belt pull is 1,976 lbs. Since we've specified a 300 foot per minute belt speed, the program shows we need to install a 20 HP drive system.
How to Plot Material Trajectory:
This trajectory plotter shows the center of mass of the flowing material at the design speed and an alternate speed. We know from experience that if the center of mass of the material impacts the vertical chute wall above the horizontal centerline, the material would be prone to plugging. Our design belt speed falls below the horizontal centerline. So, material should flow freely through.
How to Plot Material Cross Section:
This cross section plotter shows how full the material will be on the selected belt width at the selected belt speed. Notice that the black line depicts the CEMA recommendation for a maximum fill of the belt.
The program also enables the user to check the "slack side tension", which is the tension on the bottom strand of the conveyor belt required to resist:
- slippage between the pulley and the belt
- sag between the conveyor support rollers.
Efficiency Comparison:
Now, let's compare three types of conveyor drives:
- motor and helical gearbox (e.g. Rulmeca Motorized Pulley)
- motor and helical gearbox and 2nd transmission (e.g. chain/sprocket)
- motor and worm gearbox
Mechanical efficiency for each of there drives are:
- 95%
- 87%
- 70%
Assume a plant has 20 conveyors at 20 HP/each working 24 hrs/day, 7 days/week, 50 weeks/yr (8,400 operating hrs/yr) and the utility charges $0.10/kW-hr. Convert mechanical power into electrical as follows:
Since 1 HP = 0.746 kW, 20 HP = 14.9 kW.
Direct Drive savings compared to helical reducer/chain & sprocket = 250,000 kW-hrs/yr. This converts to $25,000/yr savings.
Direct Drive savings compared to worm gear reducer = 950,000 kW-hrs/yr.
This converts to $95,000/yr savings.
How to Calculate Required Hopper Feeder Conveyor Drive Power:
The total amount of material in a hopper is irrelevant, assuming "hopper arching theory" is correct. The size and shape of the "active volume" of material can be assumed to take a parabolic shape. That defines the amount of material which is pushing down on the conveyor belt.
The parabolic shape can be conservatively estimated by using the shape of a prism having a certain width, length, and height. The prism volume equals the hopper opening width x hopper opening length x the prism height. Height is set three times the width or three times the length, whichever is smaller.
Once we know the active volume in cubic feet, we multiply the volume by the bulk density to determine the active weight. Drag load on the belt equals 50% of the active weight.
Now let's learn how the program can help designers reduce hopper feeder electrical consumption by installing hopper pressure relief.
How to Install Hopper Pressure Relief:
Let's compare a hopper with one opening (36 " wide by 66 " long) with a hopper with four openings (each at 18 " wide by 33 " long).
The feeder drive beneath a hopper with one opening requires 23.2 HP because hopper drag = 6,7679 lbs and belt speed = 100 fpm.
The feeder drive beneath a hopper with four openings requires 12.2 HP because hopper drag = 3,384 lbs and belt speed = 100 fpm.
How to Calculate Electrical Power Savings from Hopper Pressure Relief:
The electrical power to be saved by installing the pressure relief system is calculated as follows:
Assume plant is working 24 hrs/day, 7 days/week, 50 weeks/yr (8,400 operating hrs/yr).
If mechanical power savings = 11 HP
Electrical power savings = 11 HP x 0.746 kW/HP x 8,400 hrs/yr = 69,300 kW-hrs/yr
Cost savings = $6,930/yr, based on $0.10/kW-hr.
Thanks for your attention.