Bevel gear depthwise tapers

The tooth taper influences the final tooth proportions and the size and shape of the blank:

• User specified: Input of the addendum angle θ_a and the dedendum angle θ_f at the wheel. From this, the tip and root angles for the wheel and the pinion are calculated internally.
• Uniform depth: The tooth depth does not change over the tooth width, consequently the tip and root angles are the same. The following applies: Addendum angle θ_a = 0 and dedendum angle θ_f = 0. Bevel or hypoid gears with constant tooth depth can be manufactured using both continuous gear cutting processes and single-part processes.
• Standard depth: The tooth depth changes over the tooth width. The pitch taper line and the root taper line intersect the wheel axis at the pitch cone apex. The tip angle is determined from the root angle of the mating gear and the clearance. The addendum angle θ_a and the dedendum angle θ_f are calculated internally according to ISO 23509. Gears with standard depth are manufactured using the single-part process. Straight bevel gears are mostly designed with standard depth taper.
• Constant slot width: The tooth depth changes over the tooth width. The root line of the pinion and wheel is adjusted so that there is a constant gap width in the tooth root in the normal section. The cutter head radius r_C0 is included in the calculation of the addendum angle θ_a and the dedendum angle θ_f according to ISO 23509. In order to obtain reasonable tooth depths at the toe and heel, the following conditions should be met for the cutter head radius r_C0 and the mean reference cone distance R_m2:
  (1.1 · R_m2 · sin β_m2) ≤ r_C0 ≤ R_m2 (A warning is issued if this condition is violated.)
  Gearings with constant slot width can be manufactured in the completing process.
  
• Modified slot width: The tooth depth changes over the tooth width. The root line of the wheel is rotated around the center with respect to the tooth width so that the slot width in the tooth root is constant. However, only the wheel has a constant slot width in the tooth root (see: constant slot width). At the pinion, the tooth depth is adjusted accordingly and thus a taper can occur in the pinion tooth root. The addendum angle θ_a and the dedendum angle θ_f are calculated internally according to ISO 23509. Only the wheel can be manufactured in the completing process.