Tooth correction of bevel gears

1. Straight bevel gears

Because the tooth profile of bevel gears is positioned in the complementary cone surface, this profile matches with that of a right pinion of which the radius has the length of the descriptive line of this cone distance.

The tooth profile of a bevel gear corresponds to this of a cylindrical gear with a number of teeth that is equal to those of the complementary cone surface. This number will be that of a bevel gear divided by the cosinus of the reference cone angle (half of the reference cone tip angle δ).

At bevel gears undercut will only occur when the teeth numbers are below (32 x cosδ) for a pressure angle of 14°30′ and below (17 x cosδ) for a pressure angle of 20°.
Displacement of the dedendum and addendum circle changes the value of dedendum and addendum angle; this change is the same for the pinion and the complementary wheel, but this happens in the opposite sense. The different pitch circle angles remain unchanged.
For the purpose of calculating the size of the correction one takes the formula for straight gears and of the virtual number of teeth.
(Zv = Z/cosδ )
In the formulas for the calculation of bevel gears the angle changes into θa and becomes θ’a and,

tgθ’a = (2*sinδ*(m+x*m))/(z*m)

with: x*m = addendum modification in mm
m = module
z = real number of teeth
The angle θf, becomes θ’f and

tg θ’f = (2,32*sinδ*(m-x*m))/(z*m)

For the complemental gear the values for the addendum and dedendum angle naturally change in opposite sense. In order to calculate the tooth correction (addendum modification) for straight bevel gears easier, we present below a table with the recommendations of Gleason, for defining the corrected addendum for the gears, in function of the ratios; the modification of the addendum of the wheels results also in the modification of the addendum of the pinions, of course in the opposite sense.

Addendum of straight bevel gears bobbed according to the hobbing method
RATIO
U
ADDENDUM
OF WHEEL
RATIO
U
ADDENDUM
OF WHEEL
RATIO
U
ADDENDUM
OF WHEEL
RATIO
U
ADDENDUM
OF WHEEL
FROM TO FROM TO FROM TO FROM TO
1,00 1,00 1,00xm 1,15 1,17 0,88xm 1,42 1,45 0,76xm 2,06 2,16 0,64xm
1,00 1,02 0,99xm 1,17 1,19 0,87xm 1,45 1,48 0,75xm 2,16 2,27 0,63xm
1,02 1,03 0,98xm 1,19 1,21 0,86xm 1,48 1,52 0,74xm 2,27 2,41 0,62xm
1,03 1,04 0,97xm 1,21 1,23 0,85xm 1,52 1,56 0,73xm 2,41 2,58 0,61xm
1,04 1,05 0,96xm 1,23 1,25 0,84xm 1,56 1,6 0,72xm 2,58 2,78 0,60xm
1,05 1,06 0,95xm 1,25 1,27 0,83xm 1,6 1,65 0,71xm 2,78 3,05 0,59xm
1,06 1,08 0,94xm 1,27 1,29 0,82xm 1,65 1,7 0,70xm 3,05 3,41 0,58xm
1,08 1,09 0,93xm 1,29 1,31 0,81xm 1,7 1,76 0,69xm 3,41 3,94 0,57xm
1,09 1,11 0,92xm 1,31 1,33 0,80xm 1,76 1,82 0,68xm 3,94 4,82 0,56xm
1,11 1,12 0,91xm 1,33 1,36 0,79xm 1,82 1,89 0,67xm 4,82 6,81 0,55xm
1,12 1,14 0,90xm 1,36 1,39 0,78xm 1,89 1,97 0,66xm 6,81 0,54xm
1,14 1,15 0,89xm 1,39 1,42 0,77xm 1,97 2 0,65xm

According to these recommendations (increased addendum for pinion and decreased addendum for wheel) addendum modification is applicable for all ratios different from 1. As for the straight gears such an addendum modification results also in strengthening of the thickness of the tooth foot of the pinion, avoids undercut and improves the meshing conditions.

2. Bevel gears with spiral teeth

Bevel gears with spiral teeth are always manufactured with corrected teeth. The calculation of the addendum modification, however, differs from that for spur teeth and is highly time and knowledge consuming; these must be therefore entrusted to specialists. For orders of spiral bevel gears, we make a drawing, after the complete calculation, in which the customer finds the final characteristics and dimensions.