Gear-pair kinematics
The tooth-count relationship that determines speed ratio in an ideal simple external gear pair.
ENGINEERING PRINCIPLE
The pitch-line velocity is equal at a meshing pair, so speed is inversely proportional to tooth count.
N₁Z₁ = N₂Z₂Variables and units
- N = rotational speed (rpm)
- Z = tooth count
- i = Z₂/Z₁
Worked example
A 20-tooth driver at 1,440 rpm driving a 60-tooth gear has i = 3:1 and an ideal driven speed of 480 rpm.
Calculation method
- Identify driver and driven gears.
- Divide driven tooth count by driver tooth count for the reduction ratio.
- Divide driver speed by the ratio to obtain driven speed.
Practical applications
- Speed reducers
- Indexing drives
- Simple gear-train concept studies
Review boundary and reference
- A speed ratio does not check torque capacity, tooth strength, lubrication or backlash.
- Real trains include efficiency and may contain compound or planetary stages.
Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.
Source: ISO 21771 terminology context and standard gear-kinematic relations.