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Gear Reducing Formulas

Output torque, speed and horsepower when using gears

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Gear - transmission ratio

Gear Output Torque

Mo = Mi r μ                               (1)


Mo = output torque (Nm, lbfft)

Mi = input torque (Nm, lbfft)

r = gear transmission ratio

μ = gear efficiency (%)

Example - Geear Output Torque

The output torque from a transmission with input torque 500 Nm, gear transmission ratio 3.8 and gear efficiency 0.9 - can be calculated as

Mo = (500 Nm) (3.8) (0.9)

    = 1710 Nm   

Gear Output Speed

So = Si / r                             (2)


So = output speed (rad/s, rpm)

Si = input speed (rad/s, rpm)

Example - Gear Output Speed

The output speed of a transmission with input speed 2000 rpm and transmission ratio 3.8 can be calculated as

So = (2000 rpm) / (3.8)

    = 526 rpm 

Gear Output Horsepower

Po = Pi  μ                              (3)


Po = output horsepower (W, hp)

Pi = input horsepower (W, hp)

Example - Gear Output Power

The output power from a transmission with input power 300 kW and efficiency 0.9 can be calculated as

Po = (300 kW) (0.9)

    = 270 kW 

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