Determine the overall efficiency of a 4 into one gearbox configuration

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The discussion focuses on calculating the overall efficiency of a four-into-one gearbox configuration, where each gearbox operates at 90% efficiency. With four gearboxes, each receiving one horsepower, the total output power is calculated to be 3.6 kW after accounting for efficiency losses. The importance of creating a Free Body Diagram (FBD) for each gearbox is emphasized to better understand torque and power flow. The initial assumption of achieving 9 horsepower through multiplication of efficiencies is corrected, highlighting the need for accurate calculations. Understanding these principles is crucial for determining the system's efficiency accurately.
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Trying to determine the overall efficiency of a 4 into one gearbox configuration
So I'm trying to figure out the overall efficiency of this particular gear system. I have four gearboxes, each stationary in and of themselves, all driving a central ring gear which is permanently attached to a rotating shaft. Please see the attached sketch. If each one of the perimeter gearboxes is 90% efficient and they're directly feeding a ring gear that is attached permanently to a drive shaft, what would the overall power transfer efficiency be? One more piece of information, each gearbox has an input power of one horsepower. My first guesstimation would be that one horsepower reduced by 90% efficiency would be 9 horsepower.. but then when you multiply 9 x .9 x .9 v .9?
IMG_20230625_211620287.jpg
 
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Pinon1977 said:
TL;DR Summary: Trying to determine the overall efficiency of a 4 into one gearbox configuration

My first guesstimation would be that one horsepower reduced by 90% efficiency would be 9 horsepower.
If only we could be so lucky, but we do not allow the discussion of free energy machines on PF.

At 90% efficiency, for each 1 kW that flows from an input shaft, through one gearbox, to a common output shaft, 900 watt will appear at the output. With four input shafts, the output power will be 4 * 1 kW * 0.9 = 3.6 kW.
 
Always the same advice:
jack action said:
Do a Free Body Diagram (FBD) on each gearbox to get the answer.
It would be really beneficial for you to do so. It would help you understand how the torque and power flow through your system.
 
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