Page 150 - Gear Technology Solutions

line moves to the new pinion pitch line location. The desired gear profile shift is
also used at the outer cone distance ROUT to calculate an angle xj 2:

xg 2 = atan(X2*mn/ROUT) (12)

The gear axis is then rotated around the crossing point about angle xj 2 to the pre-
corrected pinion axis position, drawn with dotted lines. The original gear pitch line
moves to the new gear pitch line location. The pre-corrected shaft angle between
pinion and gear is:

S 2 = S 1 – xg 1 – xg 2 (13)
whereas:
S 1… initial and final required shaft angle
S 2… temporary shaft angle for pre-correction

After the pre-correction of the shaft angle, the initial pitch angles g and g 2I are
1I
now meaningless. New pitch angles have to be calculated according to the
kinematic rule of cones rolling without slippage:

Z1/Z2 = sin g 1 / sin g 2 (14)
With: g 2 = S 2 – g 1 (15)
(15) plugged in (14) and solved for g 1:

= arctan(sin(S 2) / (Z2 / Z1 + cos(S 2))) (16)
g
1

whereas:
Z1… pinion number of teeth
Z2… gear number of teeth

At this point, a gearset with the correct number of teeth and a pre-corrected shaft
angle and with pitch angles, adjusted to the pre-corrected shaft angle is the result.

After the pre-correction of the shaft angle and the pitch angles, the pinion and gear
profile shifts are applied in a second step which moves the pinion reference pitch
line away from the original common pitch line (see Figure 10). The pinion profile
shift X1*mn will increase the pinion diameter and create the pinion reference pitch.
In order to achieve congruent pinion and gear reference pitch lines, the pinion axis
is now rotated counterclockwise by the angle xj 1 to the original location, which
rotates the pinion reference pitch line to the location of the original pitch line.

The gear profile shift X2*mn will increase the gear diameter and create the gear
reference pitch line. The gear axis is now rotated clockwise by the angle xj 2 to the
original location, which rotates the gear reference pitch line to the location of the
original pitch line.

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