12.8 Profile shift coefficient

A profile shift or addendum mofification can be made to have an influence on tooth shape and tooth thickness. According AGMA 908 the factor is called addendum modification coefficient according AGMA 913 and newer ISO standards profile shift coefficient is used.

12.8.1 Gears with standard addenda

For gears with standard addenda, the profile shift coefficients or addendum modification coefficients are zero, i.e.:

x1 = x2 =  0

The standard outside diameters may be calculated from the following equations using the gear ratio mG = NG∕NP

Standard pitch radii:

 r  =  N  ∕ (2 ⋅ P  ⋅ cos ψ)
         P       nd
R   =  r ⋅ mG

Standard addenda:

ha1  =   1∕Pnd
ha2  =   1∕Pnd

Standard outside diameters:

 do =   2 ⋅ (r + ha1)

Do  =   2 ⋅ (R + ha2)

Standard inside diameter (internal gears):

Di =  2 ⋅ (R - ha2)

NOTE: The inside diameter of an internal gear is frequently made larger than that given by the above equation to avoid interference between the tips of the pinion and gear teeth.

12.8.2 Gears with addendum modification

Gear teeth may have modified addenda in order to avoid undercut, to balance the bending stresses in the pinion and gear, or to vary the relative amounts of approach and recess action. For external gears with increased addendum, there is a corresponding reduction in dedendum; i.e., the teeth are moved outward from the center of the gear. This profile shift, as it is called in newer standards, is expressed in terms of a profile shift coefficient or an addendum modification coefficient x where x is the proportionate distance (in terms of unity normal diametral pitch) by which the datum line of the generating rack (e.g., hob) and the generating pitch circle of the gear are separated.

The profile shift x is positive when the addendum is increased (the tooth thickness is also increased) by shifting the generating rack outward of the material of the generated gear. Existing conventions vary for internal gears; for AGMA2001 we define x2 as positive when the reference generating rack is shifted out of the material of the gear resulting in an increased tooth thickness of the gear teeth.

The sum of the addendum modification coefficients is given by:

Σx = x1 + x2

Gear pairs with modified addenda may operate on the same standard center distance as unmodified gears if the addendum modification coefficients are chosen as follows:

x2 =  - x1

Then Σx = 0 and the gear pair may operate on standard centers.

Alternatively, Σx may be a positive number with the gear pair operating at a center distance larger than standard, or Σx may be a negative number with the gear pair operating at a center diatance smaller than standard.

The sizing button PIC at the side of this field allows the program to calculate coefficients suitable for a range of operating criteria: