Gear Ratio and Output Torque
Gear Ratio and Output Torque
A gear pair trades speed for torque. The gear ratio sets both the speed reduction and the torque multiplication.
The gear ratio is GR = N_out/N_in and the output torque is T_out = T_in·GR (ignoring losses). where N_out and N_in are the output and input tooth counts and T_in the input torque.
Inputs
N_in := 18=18
N_out := 54=54
T_in := 12 N·m=12 Nm
The ratio is the driven-to-driver tooth count.
GR := N_out/N_in=3
Output torque is multiplied by the gear ratio.
T_out := T_in·GR=36 Nm
Results
A ratio above 1 reduces speed and multiplies torque by the same factor; the output shaft turns GR times slower than the input. Real gears lose a few percent to friction.
Assumptions & limitations
- Ideal (loss-free) gear mesh.
- Rigid teeth, no backlash effects.
- Constant input torque.