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tact conditions are shown in Figure 10.
The different curves showing the tangential
grinding forces versus the stock removal are
representative of contact conditions occurring
in the gear profile grinding process. The x-axis
has a second label indicating the number of gaps
being ground after removing a certain amount
of stock. This method is rather time consuming,
and it is only possible to determine the grinding
forces in areas of the profile, i.e., where the
contact conditions (stock ∆s and profile angle ϕ)
are known from the analogy process. Therefore,
the calculations of the local contact conditions
are used in order to calculate local grinding
forces, as opposed to using the process model.
The results of the calculations of the tangential
grinding forces related to the contour length of
l = 1 mm versus the workpiece radius are shown
d
in Figure 11.
Those results show that the lowest grinding
forces of F t min
/l = 1.2 N/mm can be found in
d
the area of the largest profile angle, which is
the tooth root. Along the profile geometry, the
grinding forces are increasing up to a maximum
of F t
max
/l = 2.3 N/mm in the area of the root
d
flank just below the root form radius, where the
minimum profile angle ϕ min
is found. The grinding
forces are then observed decreasing again, to
F t
/l = 1.5 N/mm in the area of the tip flank with
d
a rather high profile angle. Furthermore, these
calculations show that the grinding forces are
increasing most when machining multiple gaps
in the area with the maximum grinding forces.
In this area, initial grinding burn can be expected
for this process strategy. This has already been
shown by Schlattmeier (Ref. 2).
The most common process strategy in industrial
practice is the radial infeed of the grinding
wheel. In this case, the local stock ∆s varies
along the profile geometry. For typical trials, as
well as for these calculations, a pre-ground gap is
used in order to make sure that infeed a e
is constant
along the profile. The important geometric
values for a radial in-feed of a e
= 0.235 mm
versus the workpiece radius are shown in
Figure 12.
The local stock shows a maximum of
∆s max
= 0.235 mm = a e
in the area of the tooth
root, and lowers to a minimum short below the
root form diameter of ∆s min
= 0.02 mm. Towards
the tip flank, it increases again—to a local
maximum of ∆s = 0.2 mm. The contact length
l g
is constant along the profile, but the oriented
stock removal shows an absolute maximum in
the tooth root, a minimum short below the root
form radius, and a local maximum in the area of
the tip flank.
Figure 12—Local grinding conditions for a radial infeed of the grinding wheel.
Figure 13—Tangential grinding forces for a radial infeed of the grinding wheel.
With this data, it is now possible to calculate
the local grinding forces along the gear profile
geometry. The calculations of the tangential
grinding forces F t
versus the workpiece radius
are shown in Figure 13.
The grinding force F t
shows a maximum
in the tooth root and a minimum in the area of
the root flank, just below the root form radius.
Another local maximum can be observed in the
area of the tip flank. After grinding multiple gaps
in the area of the minimum forces, there is hardly
any increase. But in the areas of the tooth root
and the tip flank, grinding forces are increasing
with the number of ground gaps. Increased grinding
wheel wear can be expected, and grinding
burn is most likely to occur in these areas.
With these calculations, it is known that
in the areas found to be critical, grinding burn
occurs when using a radial infeed strategy in
gear profile grinding (Ref. 2). When grinding
the gear with a radial infeed including the tooth
root, a grinding burn occurs mostly at the tooth
root. When grinding the gear with a radial infeed
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