Determine the overall efficiency of a 4 into one gearbox configuration

[Pinon1977]

TL;DR

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?

 

[Baluncore]

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.

 

[jack action]

Always the same advice:

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.