Nomenclature

  • Pinion: The smaller of two gears. The larger is often called the gear.
  • Pitch circle: Theoretical circle for analysis. The pitch circles of a pair of mating gears are tangent to each other.
  • Pitch diameter (): Diameter of pitch circle
  • Circular pitch (): Distance between teeth. Measured from the from a point on one tooth to a corresponding point on an adjacent tooth. This can be thought of as the sum of the tooth thickness and the width of space.
    • Units of or
    • Note that (circumference divided by number of teeth)
  • Number of teeth ()
  • Module (): .
  • Diametrical pitch (): Number of teeth divided by diameter.
    • This includes a conversion from mm to in, since 1 in = 25.4 mm
    • Note that
  • Gear ratio:
  • Addendum (): Radial distance between the top land and the pitch circle.
  • Dedendum (): Radial distance from the bottom land to the pitch circle.
  • Whole depth (): Sum of the addendum and dedendum
  • Clearance circle: Circle that is tangent to the addendum circle of the mating gear.
  • Clearance (): Amount by which the dedendum in a given gear exceeds the addendum of its mating gear.
  • Backlash: Amount by which the width of a tooth space exceeds the thickness of the engaging tooth measured on the pitch circles.
  • Mating gears must have the same tooth size

  • Addendum , Dedendum
  • Pressure angle typically

Example: Basic Gear Parameters

Question

A gearset consists of a 16-tooth pinion driving 40-tooth gear. The diametral pitch is 2 and pressure angle .

  • (a) Compute circular pitch, center distance, radii of base circles
  • (b) Compute addendum and dedendum
  • (c) In mounting this gear set, the center distance was incorrectly made 1/4 inch larger. Compute the new values of the pressure angle and the pitch-circle diameters.

We have:

Since , we have .

(a) We can calculate circular pitch to be:

Center distance is:

Base circle radii:

(b) Addendum:

Dedendum:

(c) The center distance was made a 1/4 inch larger, so we have:

We still have the same gear ratio:

Solving this gives:

Since the base circle remains the same, we have