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Material Effect on Power Requirements for Screw Feeders

February 7, 2013
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A screw feeder is commonly used to meter flow in powder processing applications because of ease of use, low maintenance, and material integrity without degradation. The relatively simplistic equipment design of the screw feeder can be misleading when selecting and specifying motor and auger sizes.
    Sizing feeders with the proper motor and auger for optimal processing is not as straight forward as matching the capacity of the auger/feeder to the material. Horsepower requirements can vary significantly with different materials. As the auger diameters increase, the differences in powder can result in a pronounced increase in horsepower requirements. This is because the surface area of auger and material contact increase dramatically. Powders that have a high coefficient of friction can result in big changes in horsepower requirements.
    The length of the feeder nozzle and auger is another significant factor in the horsepower requirements. When a feeder is elevating material, two additional factors must be considered: 1) the angle of the incline feeder and; 2) the overall height. The angle will determine the overall length of the feeder.
    An illustration of this concept requires a specified material example. The example materials selected in this study are used to demonstrate the differences in power requirements based on the extremes of material properties of seemingly similar elements. The mentioned example materials are not intended to be a comprehensive list.
    The basis for analysis will be a series of assumed low, medium, and high-volume feeder sizes. The low volume is 60 cu in/hr to 5 cu ft/hr, with a 600 cu in hopper. The medium volume is assumed 1 to 50 cu ft/hr, with a 1-cu-ft hopper. And the high volume is 5 to 1000 cu ft/hr, with a 3-cu-ft hopper.
    To calculate the horsepower required for a specific auger size, the following equations should be used:

HPf = LN FdFb =  (horsepower to run an empty feeder)
         1,000,000

HPm = CLp Ff FmFp =  (Horsepower to run a full feeder*)
                1,000,000

Total HP = (HPf + HPm)Fo
                             e
C = Capacity in cu ft/hr
e = efficiency (assumed to be 85% for chain driven augers)
Fb = Hanger bearing friction (use 2.0 for nylon bearing)
Fd = Auger diameter factor
Ff = Flight factor (assumed 1.0 for standard augers)
Fm = Material characteristics factor (friction factor)
Fo =  Overload factor (Use the equation Fo = -0.567(HPf+HPm) + 3.113) Use 1.0 for HPf+HPm > 5.2
L =   Total Length of auger, feet
N =  Operating speed, RPM (use 100 rpm)
p =   Density of material lb/cu ft
HPf = Friction Horsepower
HPm = Horsepower required to move material
HP = Total horsepower

* All assumptions and calculations in this study are assumed using a 100% full auger.

    Figure 1 shows the overall capacity of all three feeder sizes with various size augers. The 8-, 10-, and 12-in. are not part of the standard auger for these types of feeders, but are shown for completeness of data. Notice how capacity dramatically increases from 3 to 12 in.

Power Required for Different Materials
The graph in Figure 2 shows the calculated horsepower draw for three different size feeders using five different powders. The horsepower is graphed versus the size auger. The auger is sized based on the rate required. The power draw is a result of the size of the auger and the friction factor for the material. The graph in Figure 2 shows the power draw increase to 2.13 hp for sand with a 6½-in. auger. For augers larger than 6½ in., the horsepower increases dramatically and could be in excess of 4 hp for sand with a 12-in. auger.
    The lengths of the augers are based on industry standard feeder sizes and range from 22 to 30 in., and to 42 in. The standard auger length and diameter depends on the size feeder and delivery rate. However, when the length of the nozzle increases, the amount of horsepower required increases roughly proportionally (see Figure 3).
    Even when two separate materials appear to be the same, small variations in properties can produce very different result in the auger sizing and the horsepower requirements. When analyzing feeder sizing, it is critical to know the exact type of powder and not just the name of the material. As seen in Figure 4, non-hydrated lime and hydrated lime have very different horsepower requirements. This is the result of a much larger coefficient of friction (Fm = 2.0) for non-Hydrated Lime versus Hydrated Lime (Fm = 0.8). Clearly for hydrated lime, as the auger size increases, the horsepower size should also increase.

Special Vertical Feeder Case
To this point, the study has only evaluated a horizontal feeder. In many cases material must be fed vertically into a silo, mix tank, reactor, dry mixer, or some other storage or process equipment. Vertical feeding requires additional power. The total horsepower calculation can now be expanded by adding a third horsepower HPl (lift). So the completed equation would be:
   
Total HP = (HPf + HPm)Fo  + HPl
                             e
       The horsepower to raise a given amount of material is calculated as the work done lifting the material divided by the time, (power = work done/time). This can be expressed in the case of lifting 100 lb of material in 10 seconds up 10 ft. The work done is equal to 100 lb X 10 ft or 1000 lb-ft. Since it was done in 10 seconds, the power is equal to P = 1000 lb-ft/10 seconds, or 100 lb-ft/second. One hp is equal to 550 lb-ft/second. Therefore, the horsepower required is equal to 100/550 or 0.182 hp.
       Continuing with this logic, a comparison can be made between flour and non-hydrated lime. The 2- and 4-in. augers shown in Figure 5 illustrate how the horsepower requirement increases with both the length of the auger and the height the material lifted. When a feeder is set at a 20-degree angle, the length of the auger increases and larger horsepower requirements result.
       For the same type of powder, the 60-degree angle is best; however no slippage was calculated. In general, a shorter length of auger to reach the elevation is optimal. In practice, the amount of slippage will increase with increased angle, and operation is generally less efficient above 60 degrees.

Conclusion
This study evaluated the impact that auger diameter, material moved, length, and lifting height have on the power required for a screw feeder. The many different types of screw feeders were not considered in this study, but the foundation of principles will apply to most variations. The feeder auger must be completely full of material to allow for accurate and consistent delivery. For this reason, the study did not discuss less than 100% full auger. If the auger is less than 100% full, some modifications to the above equations are necessary, but the basic principles apply.
    When designing equipment for metered feeding with an auger-type feeder, it’s easy to be misled by overly complicated devices – thus, adding expense and unnecessary intricacy to the overall design of a powder handling system. This study validated the need for accurate identification of material, lift, and processing time related to auger sizing and horsepower requirements. Taking the time to understand the correct calculations and data required will result in an optimal equipment selection and expected performance.

       Dan Haugh is product manager, feeders, Hapman (Kalamazoo, MI). Haugh earned his Bachelor of Chemical Engineering degree from Georgia Institute of Technology, with a concentration in polymer science, and graduate work in biochemical engineering. He also studied electrical engineering at the University of Houston, and worked in the pharmaceutical, chemical, food, packaging, energy, and manufacturing industries.
 

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