Page 86 - Gear Technology Solutions

6.3 The Mechanisms of Undercutting

Provided the gear is manufactured with a hob cutter, which has straight cutting
edges and a rounding at the tip corners, then the hob cutter in Figure 3
represents the teeth of a trapezoidal generating profile and only the section of
the cutting edge which stays above or at the base circle can form an involute
profile [1].

Figure 3: Hob cutter representing the trapezoidal generating profile

The angle of the trapezoid side walls is equal to the pressure angle. This
means, if the pitch diameter is given by the product of the module and the
number of teeth, then the base circle is automatically defined by the rules of
the involute function:

Pitch Diameter cos(Pressure Angle) = Base Circle Diameter

In case of a depth factor larger than 1.00 and a large root clearance value, it is
possible that the tip of the cutting edge protrudes below the base circle and will
not generate any involute profile. On the contrary, the finish profile below the
base circle is formed by the tip edge of the blade profile. The mathematical
function it creates is a Trochoid.

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