Gear Cutting Tools

Axial feed f a
[mm/workpiece rotation]
The axial feed is specified in mm
per workpiece rotation.
Owing to the large number of parameters
which influence the machining
process during hobbing,
experience has shown that the axial
feed is best specified as a function
of the tip chip thickness.
Workpiece
h 1 max
h 1 max = 4.9 · m · Z (9.25 · 10 –3 · β 0 – 0.542)
2 · e –0.015 · β0 ·
r a0
· e –0.015 · xp (–8.25 · 10 –3 · β 0 – 0.225)
·
· i –0.877 ·
m
f 0.511 a a 0.319
·
m
· [mm]
m
Centre of hob
The tip chip thickness is the theoretical
maximum chip thickness removed
by the tips of the hob teeth.
The tip chip thickness is regarded
as a criterion for the hob stress;
high tip chip thicknesses mean
high cutting forces and short tool
life.
The tip chip thicknesses are increased
when the module, axial
feed, cutting depth and number of
starts are increased. The tip chip
thicknesses are reduced when the
number of gear teeth, hob diameter
and number of gashes are increased.
Example:
m = 4
Z 2 = 46
Cutting depth
ß 0 = 16
x P = 0,2
r a0
i
= 55
= 12/2
r a0
f a
a
m
Z 2
ß 0
x P
r a0
i
f a
a
e
= 4
= 9
Module
Number of teeth
Helix angle (radian)
Profile displacement factor
Half hob diameter
Number of gashes/number
of starts
Axial feed
Cutting depth
2,718282
h 1 = 0,3659 Dissertation by Bernd Hoffmeister 1970
Maximum tip chip thickness
=
=
=
=
=
=
=
=
=
Hoffmeister [2] has devised a formula
for the maximum tip chip
thickness.
If this formula is transposed, the
axial feed can be calculated as a
function of the other gear parameters.
Experience has shown a tip
chip thickness of 0.2 to 0.25 mm
to be a realistic value.
For economic reasons, as high an
axial feed as possible is aimed for,
as the machining time is reduced
proportional to the increase in
feed.
Note however that the depth of the
feed markings increases quadratically
with the axial feed, and that
different maximum feed marking
depths are permissible according
to the machining step such as finish-milling,
rough-hobbing prior to
shaving, or rough-hobbing prior to
grinding, depending upon the gear
quality or the allowance.
If carbide hobs are employed for
machining from the solid, the maximum
tip chip thickness must be
between 0.12 and 0.20 mm. For
carbide hobbing without cooling
Z
t h = 2 · d a0 · π · (E + b + A)
[min]
Z 0 · f a · V c · 1000
t h [min]
Z 2
d a0 [mm]
E
b
A
Z 0
[mm]
[mm]
[mm]
f a [mm/WU]
V c [m/min]
=
=
=
=
=
=
=
=
=
Machining time
Number of teeth of
the gear to be cut
Tip circle diameter
of the hob
Lead length
of the hob
Tooth width of the
gear to be cut
Idle travel distance
of the hob
Number of starts
of the hob
Axial feed
Cutting speed
Machining time (production time)
for hobbing
lubricant, in particular, 80% of the
heat generated by the cutting process
must be dissipated by the
chips. Adequate chip cross-sections
are therefore required. For
this reason, the tip chip thickness
should not be less than 0.12 mm.
δ x
d
δ x [mm] =
f a
2
fa
·
cos β 0
sin α n
4 · d a0
δ x [mm] = Depth of the feed
marking
f a [mm/wr] = Axial feed
β 0
= Helix angle
α n
d a0 [mm]
= Profile angle
= Tip circle diameter
of the hob
Depth on the feed markings
159