Gear ratios are one of the most useful tools in mechanical design because they allow a system to trade rotational speed for torque. The calculation is simple; choosing the ratio correctly requires understanding the real load and efficiency.
Basic Gear Ratio
For a simple pair of gears, the speed ratio can be written as i = Ninput/Noutput = Zoutput/Zinput, where N is rotational speed and Z is tooth count.
Worked Example
Suppose a 20-tooth input gear drives a 60-tooth output gear at 1800 rpm. The ratio is 60/20 = 3:1. The output speed is therefore approximately 600 rpm.
For an ideal system, torque rises by the same ratio. In a real gearbox, losses reduce the output torque. If the input torque is 10 N·m and the gearbox efficiency is 90%, the approximate output torque is 10 × 3 × 0.90 = 27 N·m.
Speed and Torque Trade-Off
| Ratio | Speed effect | Torque effect |
|---|---|---|
| 1:1 | Approximately unchanged | Approximately unchanged before losses |
| 2:1 reduction | Output speed halves | Output torque approximately doubles before losses |
| 4:1 reduction | Output speed becomes one quarter | Output torque approximately quadruples before losses |
What a Real Gearbox Requires
Do not stop at the ratio. Check gear tooth strength, shaft torque, bearing loads, lubrication, efficiency, backlash, thermal behavior, service factor, and gear geometry. For multiple stages, multiply the individual ratios to obtain the overall ratio.
Mechanism Example
If a motor runs too fast for a conveyor but has sufficient power, a reduction gearbox can lower speed and increase available shaft torque. The final ratio should come from the required conveyor speed and load torque, not from a convenient round number alone.
Common Mistakes
- Ignoring gearbox efficiency.
- Calculating ratio from diameter without considering tooth geometry where appropriate.
- Ignoring starting torque and transient loads.
- Using the motor’s rated torque as the only design load.
- Forgetting that gear ratio does not create power.
Conclusion
A gear train redistributes speed and torque while real losses reduce output power. Calculate the required output speed first, determine the ratio, then verify torque, efficiency, tooth loads, shafts, bearings, and thermal limits.