Page 212 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
190
and helical gear teeth can be cut by the same tools as spur gears by moving or feeding
the tool perpendicularly to the normal plane. The tangential plane or axial plane is tan-
gential to the pitch surface of the gear. The axial pitch p is measured in the axial plane,
a
which is the distance between corresponding points of adjacent teeth measured parallel
to the gear axis. The angle between the normal plane and transverse plane is the helix
angle .
By definition, the transverse circular pitch is the same as the circular pitch defined for
spur gears. Thus
d
p = p = (8.30)
t
c
z
From Figure 8.7, we can have the relations between normal circular pitch and trans-
verse circular pitch
p = p cos (8.31)
n
t
Therefore, the relation between the transverse module and normal module is
m n
m = (8.32)
t
cos
Also,fromFigure8.7,wehaveaxial pitch p expressed as
a
p t p n
p = = (8.33)
a
tan sin
Since the pitch diameter of a helical gear is calculated at transverse plane as
m z
n
d = m z = (8.34)
t
cos
Figure 8.7 Geometrical relationship of transverse,
normal and axial pitches.
β

β l

p n
B
β
B
p a
b
p n
p a
A p t C
A p t C
πd