When the number of teeth of a hobbed gear according to the hobbing system gets below the limit number (32 for pressure angle 14°30′ and 17 for pressure angle 20°00′) one can see that the tooth foot displays a pocket; the smaller the tooth number, the greater the pocket.
In the common cases, it is only considered as a nuisance for tooth numbers < 17 for pressure angle 14°30 ‘ and < 12 for pressure angle 20°, because from this limit a noticeable weakening of the tooth foot occurs and an important part of the involute flank has been hobbed away below the pitch circle; this part of the flank has no longer contact during the meshing.
The result, especially for larger circumferential speeds, is a less good operation of the gear pair characterized by noise, vibration, a faster wear and of course a lesser resistance to tooth failure.
In order to avoid undercutting for small teeth numbers and to obtain better meshing conditions, without resorting to abnormal pressure angles, one applies tooth corrections.
The minimum number of teeth, where the undercut begins, one calculates with the following formula: zmin = 2*(k-x)/sin2α 2.
The coefficient of contact is the ratio of the length of the arc of action to the normal pitch. A smooth meshing requires the meshing of the 2 following teeth before releasing the previous one another.
This is the reason why the coefficient of contact is rated based on the number of teeth, the depth of the tooth and the pressure angle ε = engagement length/ Normal pitch > 1.
This ratio increased with the addendums and also with the pitch diameter of one of the gears, but decreased with the increase of the pressure angle.
The general formula: εα = [√(R a 2-Rb2)+√(r a 2-rb2)-a*sinα]/(π*m*cosα).
3 Approaching length
The meshing line includes an approaching and a take away part. The approaching length is the part between the first contact and the pole located at the intersection of the connecting line of both pitch centers and the meshing line. This part is the least favorable of the mesh as a result of the gliding of both profiles. The gliding reduces as the pole is being approached
4 Take away length
The opposite of the approaching length.
5 Specific gliding
The ratio of the gliding to the rolling; in the pole this ratio is zero.
6 Pressure angle
For cylindrical gears the pressure angle is constructed by the mesh line and the connecting line of the rotation points (the tangential between the 2 base circles).
7 Roll surfaces
These are the surfaces of 2 elements of a gear that rolls over each other without gliding. Their diameters are proportional to the number of teeth.
8 Centre distance – a
Distance between both centers of the pitch circles.
During the milling of a gear according to the hobbing method, the pitch circle rolls without gliding on the pitch line or face of the hob. The mesh line of the gear is tangential to the base circle of the gear and is perpendicular to the profile of the hob.
10 Normal teeth
Teeth obtained by milling the gear according to the pitch line of the gear. When neglecting the backlash, the tooth thickness at the pitch circle is equal to half of the pitch.
11 Corrected gears
Teeth obtained by milling the teeth of the gear deviating from pitch line of the gear. At the pitch line of the gear the tooth thickness will differ from the half of the pitch.