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10 Independent Profile Shift for Bevel Gears

10.1 The Effect of Profile Shift

Bevel and hypoid gears as well as straight bevel gears require, similar to
cylindrical gears, a positive profile shift for the pinion in case of low number of
teeth. If the number of pinion teeth is below 18, or even below 10, the pinion
develops a severe undercut which eliminates a large portion of the tooth profile in
particular at the toe area (small diameter area). This effect leads to a weakening of
the tooth root and also a reduction of the flank contact area. As result, the root
bending stress and the surface stress are high, and the bevel gear pair has only a
fraction of the load carrying capacity compared to a bevel gearset without
undercut [1].

Profile shift has, according to international standards [2], the symbol “X”. In order
to determine the amount of profile shift, X is multiplied with the normal module mn
of the gear, resulting in the amount of shift.

Figure 1: The effect of profile shift

The effect of profile shift is shown in Figure 1. The left profile in Figure 1 has no
profile shift. The profile in the center of Figure 1 has a positive profile shift
coefficient of X = 0.3. In practice this means the tooth is shifted towards the
manufacturing tool by 0.3 * mn and the manufacturing tool is shifted away from the
work axis by the same amount. That way the tooth depth stays the same, but the
tooth is now at a larger diameter. As a result, the tooth becomes thicker in the root
and thinner at the tip. The right-side graphic in Figure 1 shows a negative profile
shift coefficient of X = -0.3. The tooth is shifted away from the manufacturing tool

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