Total Efficiency in Parallel Transmissions

[sdvermillion]

I'm trying to figure out an expression for the total power efficiency from engine to wheel of a parallel transmission in terms of the efficiency of all the components in between (i.e. spur gears, motors, pumps, etc.) such that

$$P_{engine}$$ = $$\eta$$($$\eta_{i}$$)*2$$P_{wheel}$$

See attached image.

 

[sdvermillion]

The problem occurs when the power paths are reunited before going into a differential and out to the wheel. At this point, the torques are being added together (or subtracted etc.). So for one path, the efficiency may be n1*n2*n3 and the other path may be n4*n5*n6 such that, from the diagram attached, T3 = n1*n2*n3*(1/m1)*T1 + n4*n5*n6*(1/m2)*T2, where m1 and m2 are gear ratios. I want to be able to say T3 = n*((1/m1)*T1 + (1/m2)*T2). I can't simply pull out the efficiencies because they may not be the same number.

 

[DickL]

As the efficiencies of the transmissions are probably variable with torque transmitted (and system speed), I think this becomes an indeterminate problem for the general case. The torque flow or split can, and will, vary greatly due to small secondary influences. For a specific torque split it can be computed by looking up the efficiency for the specific speed and torque for each transmission.

On a couple of somewhat similar systems I was acquainted with, they used an active control to manage the torque split between dual engines. On 1 of these the active control system was the pilot reading a torque meter.