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## Homework Statement

a) Determine the input power required at shaft 1.

b) Specify the efficiency of the gear train as a percentage.

c) Determine an equation for the efficiency of the gear train in terms of the load (torque) on shaft 2 (all other factors remaining constant).

Knows:

4 gear train lie on a line.

N

_{A}=80, r

_{A}=80mm, ω

_{A}=10π/3 rads

^{-1}(input shaft)

N

_{B}=50, r

_{B}=50mm, ω

_{B}=-16π/3 rads

^{-1}

N

_{C}=50, r

_{C}=50mm, ω

_{C}=16π/3 rads

^{-1}

N

_{D}=20, r

_{D}=20mm, ωD=-40π/3 rads

^{-1}(output shaft)

All shafts have a friction resistance of T

_{fr}=5Nm

Load on shaft 2 T

_{L}=200Nm

## Homework Equations

## The Attempt at a Solution

a)

Total torque T

_{T}=T

_{L}+2*T

_{fr}=200+10=210Nm

P=T

_{T}*ω

_{D}=210*(-40π/3)=-2800π=-8.7965kW

Required input power at shaft 1 due to load and friction is 8.7965kW.

b)

gear train efficiency η=(-power at output/power at input)*100%

T

_{A}={[ω

_{D}*(T

_{L}+T

_{fr})]/ω

_{A}}-T

_{fr}=815Nm

input power=T

_{A}*ω

_{A}=815*10π/3=2716.6667π=8534.6600W=8.5347kW

Something not right here as input should be greater then output?

C)

Will need some help with it, not sure where to start.