Page 141 - Gear Technology Solutions

by 0.3 * mn and the manufacturing tool is shifted towards the work axis by the
same amount. That way the tooth depth stays the same, but the tooth is now at a
smaller diameter. This makes the tooth thinner in the root and thicker at the tip.
The tooth thickness at the reference circle is kept constant in all profile shifted
cases, which happens automatically in cylindrical gear hobbing when the same
hob is used to cut gears with different profile shifts. The negative profile shift
weakens the root of the tooth and also causes undercut, while the positive profile
shift reduces or eliminates undercut [3].

In bevel and hypoid gears, as well as straight bevel gears, a so called V0 profile
shift is always applied. V0 profile shift means that the pinion profile shift coefficient
X1 and the gear profile shift coefficient X2 have the same absolute amount but
opposite signs (X1 = -X2 or X1 + X2 = 0). In cylindrical gears the V0 profile shift
prevents a change of the center distance between pinion and gear. In bevel gears
this is analogous to preventing a shaft angle change. This means that a positive
profile shift in both members of a bevel gearset would change the shaft angle S
by:

DS= (X1 + X2) * mn / Mean Cone Distance

If a bevel gearset is designed with a shaft angle of 90°, any profile shift which is
not a V0 shift would result in a shaft angle being not equal to 90°, which is not
permissible. This is the reason why all state-of-the-art gear design calculation and
manufacturing systems strictly apply the V0 profile shift.

The side effect of the V0 profile shift is the fact that although a “healthier” pinion
profile can be achieved (if X1 is positive), the profile of the mating gear teeth takes
an adverse effect. Even a gear with three times the number of pinion teeth will
develop undercut from a certain amount of negative profile shift. This means, in
turn, the amount of V0 profile shift is limited to the point where the lost root area on
the gear teeth above the root fillet (or above the undercut) increases visibly and
diminishes the improvement in the pinion teeth profiles.

Figure 2: Ratio = 2.9, Ease-Off (left) and Tooth contact (right) for
X1 = 0 and X2 = 0

126