The question if older straight bevel gears, manufactured with a two-tool generator, can be replaced by Coniflex parts, cut with a circular cutter, is “yes”. The flanks are the same, and the differences are only at the root. If the correct build procedure (for new and old single-member replacements) is followed, then the flanks and the tooth tips never get to see the clearance area below the flank root transition of their mating member. The tooth tips only roll down to the wear step. Any complications due to wear-step interference are resolved by the application of topland chamfering. Strength of Coniflex Parts Made with Circular Cutters Most applications where single gear members are replaced apply to straight bevel gears. For this reason, this section about strength comparison was added to this chapter. The question was raised whether the strength of a Coniflex pinion or gear may be lower than the strength of a gearset that was originally manufactured with a two-tool generator. Regarding the comparison of Coniflex straight bevel gears, which have a curved root line with straight bevel gears with a straight root line, the following facts can be presented: The curvature of the root line depends on the cutter radius, which results in a deeper tooth at the center of the face width. The calculation of the additional amount of root depth ΔR is explained in Figure 4.

Several industrial users of Coniflex straight bevel gears claim that they experienced a dam effect, which increases the moment of inertia in the tooth bending direction compared to a noncurved root line. A second positive effect is caused by the hourglass shape of the root slot width. Not only is the tooth depth larger at midface, but also the tooth thickness below the flank working area increases by: (1) In the root bending stress calculation, the increase of root tooth thickness reduces the bending stress quadratic while the moment arm from the force application point to the root (due to the depth increase) only increases linearly. This shows in the root bending stress calculation (e.g., in a deflection beam calculation) as follows: (2) (3) (4) (5) Whereas: a… Pressure Angle at Flank-Root Transition M… Bending Moment W… Section Modulus b… Face Width h… Tooth Root Thickness l… Force Application arm = Module F… Force σ… Root Bending Stress Calculated as Cantilever Deflection Beam For example, the formal relationship in equations 1 through 8 applied to a straight bevel gear with a straight root, which has a module of 5 mm, a face width of 30 mm, and a root tooth thickness at the center of 7.5 mm, shows that for a force of 12,500 N, the root bending stress is equal: (6) For a comparable Coniflex bevel gear with a root which is DR = 1 mm deeper at the center and 0 mm deeper at the ends, the following assumptions can be made: Average value of deeper root over entire face = 60 percent of value at center (1 mm• 0.6=0.6 mm). Pressure angle at the stress critical 30-degree tangent is 30 degrees. The resulting root bending stress is equal: (7) The comparison example in Equations 6 and 7 shows that the effect of taller tooth at midface and larger root tooth thickness at midface cancel each other out, such that the Coniflex straight bevel gear shows even some reduction of calculated root stress compared to the straight bevel gear with a straight root. The limits of this principle are given by the fact that in the case of a too large curvature of the root line, the hourglass-shaped root width will cause the cutter to mutilate the opposite flank. The output of the Gleason Straight Bevel Gear software gives a warning in cases where this is critical. The rule is that the relation between face width and cutter radius should be below 40 percent to achieve optimal root geometry. (8) 40 percent of the radius of a cutter with 9 in. diameter is (4.5 in. or 114.3 mm) • 0.4 = 45.7 mm, which leads, in the case of a recommended face width of 33 percent of the outer cone distance, to a maximal ring gear diameter of about 275 mm. This dimension is close to the limit of Phoenix 275 or Phoenix 280 machines, where the maximal Coniflex cutter diameter is equal to 9 in., “which closes the circle” (Ref. 2).