 Gear pitch circle

A gear pitch circle is an imaginary circle used to represent the motion or reference geometry of a gear. A useful distinction is between the gear reference circle, specified for an individual gear, and the operating pitch circle, determined for a meshing pair. The terminology entry in KHK Gear Nomenclature calls the latter the intermeshing pitch circle and also uses the name working pitch circle.^[ref]

For an external pair with fixed axes and constant gear ratio, imagine two operating pitch circles in contact and rolling without slipping. If their radii are $r_1,r_2$ and their axis separation is $a$, their geometry and signed angular velocities obeyThe last equality follows by matching the gear ratio to tooth counts $N_1,N_2$. It is an ideal kinematic construction: the imaginary circles themselves are not physical rims carrying the contact force.

For standard unshifted straight-tooth gears at their standard axis separation, the gear reference circles coincide with the operating pitch circles. The gear module $m$ specifies reference diameter $d=mN$. With $m=2\mathrm{mm}$ and tooth counts 20 and 40, the reference diameters are $40\mathrm{mm}$ and $80\mathrm{mm}$, giving reference radii $20\mathrm{mm}$ and $40\mathrm{mm}$ and standard separation $60\mathrm{mm}$. The reference diameters differ from the larger tooth-tip diameters. If a compatible pair is operated at another axis separation, its gear reference circles remain properties of the individual gears, while its operating pitch circles must fit the new separation and the same tooth-count ratio. This is why an unspecified “pitch diameter” should not silently mix reference geometry with operating geometry.^[ref]