# Power Required for Rotating Vessel

1. Aug 22, 2006

### edisonf

Power Calculation for Rotating Vessel

I have an application with a rotating cylinder in which material is tumbled for processing purposes. The following quantities are known although I have need of generic formulas in the future as these are variables between system applications.

Known Quantities:
Vessel mass (empty): 120,000 lbs.
Inside diameter: 11’-9”
Outside diameter: 11’-10”
Weight of material: 70,000 tons based on 13 lbs/ft3 bulk material density
Drive arrangement: 1800 rpm electric motor coupled to gear reducer driving steel wheel, 24” in diameter.
Number of drives: (4) each. The (4) steel wheels drive and cradle the vessel through (2) circumferentially mounted, 14’-1” diameter driven rings. Please refer to sketch.
Time to accelerate: approx. 5 seconds
Full speed rpm: 6 rpm

My Methodology:

1. Calculate moment of inertia I of vessel using:

m•(di2 + do2)/8

2. Calculate average angular α acceleration using:

6 rpm • 2•π/(60 sec/min•5 sec) = 0.126 rad/sec2

3. Calculate total torque required to accelerate from:

T=I•α

4. Calculate torque required from gear reducer output
5. Determine torque input to the gear reducer
6. Determine motor HP rating from the relationship:

T•rpm/5252

Conclusion:

Based on my calculations, each motor will need to develop approx. 399 lb-ft of torque to accelerate the vessel. I realize that the motor could be sized based on breakdown torque, not using the above simple HP=T•rpm/5252 relationship which yields approx. 137 HP to be developed by each motor. If breakdown torque is approximately 230% of full speed torque, (4) 60 HP motors would suffice. I just need verification that my methodology is valid and that my figures are reasonable. Also, I realize the above does account for the material to be processed in the vessel. Any help you can provide is greatly appreciated.

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2. Oct 11, 2007

### karandeepg

slip consideration

in your calculation, you are not taking into account the friction between the contact surfaces of rollers and vessel. Slip may cccur on contact surface. So, you must look into that part also because that will ultimately affect your power requirement.