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11 Zerol Slot Depth, Tooth Thickness and Spiral Angle

11.1 Zerol Bevel Gear Design

Zerol bevel gears are the special case of spiral bevel gears with a spiral angle
of 0°. They are manufactured in a single indexing face milling process with
large cutter diameters and tapered depth teeth. Zerol bevel gears can be un-
derstood as a kind of straight bevel gears which can be manufactured with
standard spiral bevel gear tools. The axis of Zerol bevel gears in most cases
intersect under an angle of 90°. Many applications require that the shaft angle
is larger than 90°, however, the axes always intersect which means they have,
at their crossing point, no offset between them. The pitch surfaces are cones
which are calculated with the following formula:

z1/z2 = sing 1/sing 2

S = g 1 + g 2

in case of S = 90° → g 1 = arctan(z1/z2) → g 2 = 90° - g 1

whereas:
z1... Number of pinion teeth
z2... Number of gear teeth
g 1... Pinion pitch angle
S... Shaft angle
g 2 ... Gear pitch angle

Advantages of Zerol bevel gears are their low axial forces like straight bevel
gears and their certain centering abilities during operation. Their manufacturing
process with completing face mill cutters is significantly faster than that of
straight bevel gears and grinding as hard finishing process with dressable
grinding wheels leads to highly precise gearsets which are often used in air-
craft applications.

Zerol bevel gear teeth follow in face width direction a curve on the conical gear
and pinion body which lies tangential to a cone element (zero spiral angle).
The tooth lead function in face width direction if unrolled into a plane, is a cir-
cle. The tooth profile is an octoide. The tooth form with an octoide function will
be associated to an initial “natural” profile crowning and depending on the ma-
chining setup some flank twist. Both effects are utilized together with certain
corrective machine settings in order to generate the desired crowning [1].

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