Ratios, tooth geometry, loads, efficiency and gear-train design.
MODULE OVERVIEW
Gears in practical engineering work.
Gears exchange speed and torque through controlled tooth contact. Ratio is only the first design step; tooth loading, contact ratio, lubrication, alignment and manufacture control durability.
CORE PRINCIPLES
What to establish first
The tooth-count ratio governs ideal speed ratio.
External gears reverse rotation direction; idlers alter direction but not the overall ratio.
Pitch-line velocity and mesh load affect tooth and lubrication selection.
DESIGN CONCEPTS
Terms worth checking
Pitch circle
Gear ratio
Backlash and contact ratio
Common applications: Speed reducers · Indexing mechanisms · Motor-to-machine transmissions
KEY RELATIONSHIP
Simple gear-pair speed ratio
i = Z₂/Z₁; N₂ = N₁/i
Z — number of teeth
N — rotational speed, rpm
i — speed ratio
The result assumes rigid, ideal gears with no slip; it does not rate tooth strength.
Use the relationship with compatible units, then review the result against the stated design conditions.
WORKED EXAMPLE
Known values → substitution → interpretation
Known values
Driver Z₁ = 20; driven Z₂ = 60; N₁ = 1440 rpm
Method
i = 60/20; N₂ = 1440/3
Interpretation
The ideal ratio is 3:1 and the driven gear turns at 480 rpm.
KEY DESIGN CHECKS
Confirm the conditions behind the number
Define the governing load case, duty cycle and required design life before using a simplified relation.
Use compatible units and material data for the actual condition, temperature and manufacturing state.
Compare the result with strength, stiffness, fatigue, safety, serviceability and applicable-code requirements.
COMMON ENGINEERING MISTAKES
Keep the model within its scope
Applying simple gear-pair speed ratio outside the assumptions shown on this page.
Using a nominal condition while a peak, alternating, transient or environmental case governs the design.
Treating a calculated value as a final component selection without checking interfaces, tolerances and the current governing standard.
ReferenceISO 21771 terminology and geometry references; AGMA or ISO gear-rating documents must control a production gear design.ScopeRelationships are presented for the assumptions stated on this page and linked tool.Design reviewCheck material condition, loads, environment and the applicable current code.SafetyResults are educational/preliminary and do not certify safety or compliance.
