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Power Calculation for Rotating Vessel
I need help, please.
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.
I need help, please.
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.