 Gear reference circle

A gear reference circle is the imaginary circle used to specify an individual gear's tooth geometry. For a spur gear, its diameter $d$ is defined by gear module $m$ and tooth count $N$ through $d=mN$. It supplies a common datum for tooth spacing and other dimensions, whether or not that gear is currently meshing with another one. The operating pitch circle, in contrast, describes the mounted pair's motion.^[ref]

For a 30-tooth spur gear with gear module $2\mathrm{mm}$, the reference diameter is $60\mathrm{mm}$. Thus successive teeth repeat at an angular interval of $2\pi /30$ and a gear circular pitch of $2\pi \mathrm{mm}$ on that circle. In the standard full-depth, unshifted geometry specified by KHK, the tooth-tip diameter is $d_a=d+2m$, giving $64\mathrm{mm}$ in this example. Measuring the outside diameter and calling it the reference diameter would therefore produce the wrong gear module.^[ref]

The gear base circle is another distinct geometric datum. For a tooth profile constructed as the involute of a circle, the gear base circle generates the curved tooth flank, whereas the gear reference circle fixes its nominal sizing. Their diameters obey $d_b=d\cos \alpha$, with reference gear pressure angle $\alpha$. With $d=60\mathrm{mm}$ and $\alpha =20{}^{\circ }$, the base diameter is approximately $56.382\mathrm{mm}$. These three diameters—base, reference and tip—answer different questions about the same physical gear.^[ref]