of the
linear axis. Hence, the measured displacement errors are sensitive to the errors both parallel and perpendicular
to the direction of the linear axis. More
precisely, the
measured volumetric
positioning error is
the displacement error (parallel to the
linear axis), the vertical straightness error (perpendicular to the linear axis), and the
horizontal straightness error
(perpendicular to the linear axis and the vertical
straightness error
direction) projected to
the direction of the laser beam (see
Figure 2). Because the
errors of each axis of motion are the
vectors with three
perpendicular error
components, we call this
measurement a
"vector" measurement technique. In
practice, first point the laser beam in one
of the body diagonal directions, similar
to the
body diagonal displacement
measurement in the ASME B5.54 standard (see Fig- ure 3). However, instead of
program-ming the machine
to move x, y and z continuously to the next increment, stop and take a measurement, the machine is now programmed to move the
x-axis, stop and
take a measurement, then
move the
y-axis, stop and
take a measurement, then move the
z-axis, stop and take a
measurement (see Figure 4).
As compared to
the conventional body diagonal measurement where only one data point is
collected at each increment in the diagonal direction, the vector measurement collects three data
points, after each axis
movement, such that three times
more data is collected. Then point the
laser beam in another body diagonal
direction and repeat the same until all four-body diagonals
are measured. Because
each body diagonal measurement collected three
sets of data, there
are 12 sets of
data, enough to solve
the three displacement errors,
six straightness errors
and the three
squareness errors. For conventional
body diagonal measurement,
the displacement is
a straight line along the
body diagonal; so a laser interferometer with a retroreflector as target can
be used to
do the measurement. However, for the vector
measurement, the
displacements are along the three axes. The
trajectory of the
target or the retroreflector
is not parallel
to the diagonal direction. The deviations from the body diagonal
are proportional to the size of the
increment X, Y or Z. A conventional laser
interfer-ometer will
be way out of
alignment even with
an increment of a few mil-limeters. To
tolerate such large lateral devia-tions, a Laser
Doppler Displacement Meter (LDDM) using a single-aperture
laser head and a flat mirror as the target
can be
used. Because
any lateral movement or movement perpendicular
to the normal direction of the flat mirror
will not
displace the
laser beam, alignment is maintained.
After three movements, the flat-mirror
target will move
back to the center of the diagonal again,
hence, the size of the flat mirror
has only to be
larger than the largest increment. Advantages and applications The major advantages of
the vector measurement technique are
simplicity and
efficiency. Data collection is auto-matic and three
times more data are
collected in a
single setup, with the
calculations done using a notebook PC.
The results can be plotted or
tabulated. On a machine
with a work volume of one cubic meter, all four
diagonals can be
measured in two to four hours. The
vector measurement technique has made
high-accuracy volumetric calibration
affordable. Because
a machinist can
operate it, it makes laser calibration and
compensation possible for
shops with fewer employees and
modest budgets. There are
many advanced controls where the squareness errors and FIGURE 2. What is the vector (3-dimensional)
measurement?
