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Table
2-2.
Calculation
of
Total Compensation
In
each
case
C
is
then
corrected
for
material
temnerature
with:
I
total
C
=
C-(TF-wwt)
x
~ t t .
or
total
C
=
C-(TC-20°C)
X
CEC.
where
TF
or
TC
=
material
temperature
in
O F
or
OC.
CEF
or
CEC
=
material
coefficient
of
expansion
in
ppm/OF
or
ppm/OC.
2.26
OPERATION
UNDER
CHANGING
TEMPERATURE
CONDITIONS.
It
is
very
im-
portant
to
realize
that
material
temperature
comoensation
is
completely
accurate
only
under
constant
nonstandard
conditions.
Relation
,
:an
be
used
to
compensate
for
thermal
ex-
pansion
of
the
part
only
if
the
part
and
thl
machine
are
at
thermal
equilibrium
with
their
surroundings.
Changing
temperature
can
result
in
changing
thermal
gradients
in
both
the
machine
and the
part.
In
this
case
the
primary
machine
errors
are
due
to
complex
bending
effects
which
distort
machine
geometry
instead
of
simple
thermal
expansion.
These
effects
are
extremely
difficult
if
not
impossible
to
describe
mathematically,
and
can
certainly
not
be
described
by
relation
.
Bending
effects
can
change
the
pitch,
yaw,
straightness,
paral-
lelism,
and
squareness
ot
the machine
slideways.
The
resulting
errors
are
not
a
function
of
the
positioning
transducer
used
on
the
machine.
Nor
are
they
a
function
of
material
tempera-
ture.
Therefore,
if
a
machine
is
operated
in
a
poor
environment,
its
accuracy
may
be
limited
by
its
own
geometry.
In
this
case,
the
practical
solution
is
to
either
improve
the
environment
or
make
the
machine
less
susceptible
to
environmental
changes.
There
is
no
rule-of-thumb
which
can
be
used
to
estimate
allowable
temperature
variation
during
a
machining
or
mea-
surement
cycle
to
obtain
a
given
tolerance.
One
can
only
predict
that
a
given
machine
will
be
most
accurate
when
operated
in
a
constant
temperature
environment.
If
the machine
environ-
ment
is
suspected
to
be
poor
it
is
best
to
run
"drift
tests"
on
the
machine
to
determine
environ-
ment
affects
on
the
machine tolerance.
2.27
WHERE
TO
S E N S E
MATERIAL
TEMPERATURE.
Even
when
a
machine
is
operated
at
thermal
equilibrium
in
a
constant
environment,
different
parts
of
the
machine
can
be
at
different
temperatures.
In
order
to
minimize
errors,
measure
material
temperature
at
a
point
a s
close
to
the
workpiece
a s
possible.
For
example,
on
a
milling
machine,
if
the
workpiece
is
clamped
to
a
table,
measure
the
table
temperature
since
the table
is
the
closest
available
point
to
the
workpiece.
Since
the
table
and
the
workpiece
are
in
close
contact,
they
will
tend
to
come
to
the
same
temperature.
Therefore,
the
table
temperature
will
be
indicative
of
the
temperature
of
the
workpiece.
On
turning
machines
this
may
not
be
possible
since
the
work-
piece
is
held
in
a
rotating
spindle.
In
cases
like
this,
it
is
necessary
to
determine
empirically
which
accessible
machine member
is
the
closest
in
temperature
to
the
workpiece.
2.28
Cosine Error
Misalignment of the laser beam path to the axis of motion of the machine tool will result in
an error between the measured distance and the actual distance traveled. This is referred to
a s cosine error because the magnitude of the error is proportional to the cosine of the angle
of misalignment.
Cosine error can be visualized a s shown in Figure 2-37. The laser beam consists of a number
of plane-parallel, equally-spaced wavefronts. The separation between wavefronts is the
laser wavelength which is approximately 25 microinches or 0.633 microns. Since the beam
diameter is quite large compared to the wavelength,
it
has been shown large in Figure 2-37.
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