Page 144 - Gear Technology Solutions

Enlarged detail A is shown in Figure 4. The original crossing point moved to the
location of the new crossing point. The offset coordinates between the original and
the new crossing point are d in vertical direction and c in horizontal direction.
Because the crossing points are the origin of pinion and gear and determine their
location and the location of their teeth, the offset coordinates have to be calculated
in order to position pinion and gear correctly relative to each other in order to mesh
and roll both members after the profile shift:

(1)

(2)

where:
c …horizontal offset
a … vertical shift of pinion member axis
b … vertical shift of gear member axis

rearranging (1): (3)

plug (3) into (2): (4)

(4) rearranged: (5)

(5) solving for a: (6)

from (2):

(7)
where:
g 1… pinion pitch angle
g 2… gear pitch angle
mn… normal module
d … vertical offset

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