Maximum power density gearing

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification,
• the tooth pair stiffness curve of said pair being elastically self-complementary over most, and preferably all, of the operating load range of said pair.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification,
• the larger of the directional contact ratios of said pair being within 0.08, and preferably 0.04, of an integer.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification,
• the larger of the directional contact ratios of said pair being between 0.05 and 0.15 smaller than an integer.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification,
• the mesh stiffness of said pair when its contact lines are in the centroid-straddled position being substantially the same as when they are in the centroid-contained position.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification,
• the shape of said liminal cross modification being substantially a triangle, one side of which coincides with a straight line generator lying in (a) the working surface of one of said pair and (b) the field of contact of said pair at a particular roll angle of said one of said pair,
• said straight line generator when lying in said field being further from the centroid of said field than the lines of contact that are symmetrically disposed with respect to said centroid and furthest therefrom.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification that has no boundary parallel to the straight line generators of any working surface of said teeth.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification applied to narrow spiked-shaped regions along at least one edge of the tooth working surface.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification that varies in amount non-linearly with distance from the end face of the tooth at which it has its maximum value.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification that produces precision stiffness values at the quarter point and the midpoint of the tooth pair stiffness curve ramp.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal spike-shaped cross modification that is formed to give to the ordinates of the outer halves of the tooth pair stiffness curve ramps the particular value at each roll angle that when added to the ordinates of the inner halves of the complementary ramp give to the half-lengths of the tooth pair stiffness curve polar symmetry with respect to their midpoints.

A pair of mating gears having teeth slantingly disposed with respect to the common pitch element,

• said teeth on at least one, and preferably both, of said pair having liminal cross modification,
• the profile and face contact ratios of said pair differing by an amount that is within 0.05, and preferably 0.02, of an integer.