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REVIEW OF SCIENTIFIC INSTRUMENTS
VOLUME 71, NUMBER 10
OCTOBER 2000
Laser
vector measurement technique for the determination and
compensation of
volumetric positioning errors. Part I: Basic theory Charles Wang Optodyne, Incorporated 1180 Mahalo Place,
Compton, California 90220 (Received
2 May 2000; accepted for publication 8 July 2000) A new laser vector method for the measurement of the volumetric
positioning errors of a computer numerically controlled machine or a precision instrument is described here.
Compared with conventional laser interferometer measurement, the laser vector method
measures the vector errors, namely, the
displacement error, vertical straightness error, and horizontal straightness error, rather
than the displacement error only. The key to the laser vector method is that the measurement direction or the laser
beam direction is not parallel to the displacement direction. With four setups, all
three displacement, six straightness, and
three squareness errors can be determined. Once the volumetric
positioning errors are measured, they can
be used to compensate for the
repeatable positioning errors of the
machine or instrument. The basic concept, theory, and measurement errors
are described. Experimental verification of
the vector method is in the Part II of this article. © 2000
American Institute
of Physics. [S0034-6748(00)04010-7]
I.
INTRODUCTION parallel to the motion
of the linear axis and the position The linear displacement
errors, straightness errors, errors are
measured at each increment. Since the measure squareness errors, angular errors, and nonrigid body errors
ment direction is parallel to the direction
of movement, the determine the performance
or accuracy of a computer nu- measured
displacement errors are not sensitive to the merically controlled (CNC) machine tool, a coordinate mea-
straightness errors which are perpendicular
to the displace suring machine (CMM), or a
precision instrument. Charac- ment
direction. terization of a machine movement
is very complex. For each It is noted that for a
quick check of volumetric position axis of
motion, there are six errors, three linear errors, and ing accuracy linear displacement measurement along four
pitch, yaw, and roll angular errors in the
X, Y, and Z direc- body diagonals is
recommended by the B5.57 standard1 This
tions. For a three-axis machine, there are
18 errors plus 3 for is because the body
diagonal measurements are sensitive to squareness, a total of 21 errors. Complete measurement of
all the errors such as the displacement
errors, straightness these errors is very
time consuming. Body diagonal measure- errors, squareness errors, and angular errors. Hence it is a
ments have been recommended1 for a quick check of the good check of volumetric accuracy. However, if the mea
volumetric accuracy. This is because it is
sensitive to all the sured errors are
large, there are not enough data to identify error components. However, if the errors measured are large,
the sources of the errors.
there is not enough information to identify
the error sources. The basic concept of the laser vector measurement tech
Machine accuracy can be improved by measuring all
nique is that the laser beam direction (or
the measurement these errors and then
compensating for these errors, provided direction) is not parallel to the motion of the linear axis.
that the machine is
repeatable. 2-4 The key is how to measure Hence, the measured displacement errors are sensitive to the
these errors accurately and quickly. There
are many methods errors both parallel and
perpendicular to the direction of the by
which to measure these errors. Zhang et al.5 measured the
linear axis. More precisely, the measured
linear errors are the displacement errors
along 22 lines in the machine work zone vector sum of errors, namely, the displacement errors (paral
to determine the volumetric errors.
Beckwith6 used a com-
lel to the linear axis), the vertical
straightness errors (perpen plex five laser
beam system, in which two of the laser beams dicular to the linear axis), and horizontal straightness errors
were used for displacement interferometers
and three of the (perpendicular to the
linear axis and the vertical straightness laser beams were used for lateral displacements with quad-
error direction), projected to the
direction of the laser beam. rant
photodetectors. However, all of these methods are very Furthermore, by collecting data with the laser beam pointing
complex and time consuming.
in three different diagonal directions, all
nine error compo Described here is a laser vector measurement technique.
nents can be determined. Since the errors
of each axis of It can measure all these
errors using a simple and portable motion
are the vector sum of the three perpendicular error laser interferometer or a laser Doppler displacement meter
components, we call this measurement a
"vector" measure (LDDMTM),7 in four
setups and within a few hours. ment
technique. In practice, first point the laser beam in one of the body
11. BASIC
CONCEPT diagonal directions,
the same as in the body diagonal mea To measure the
displacement accuracy of a linear axis, a surement. Instead of moving x, y, and z continuously to the
laser interferometer can be used. The
laser beam is aligned next increment R,
stop and take a measurement. Now, move 0034-6748/2000/71(10)/3933/5/$17.00 3933 © 2000 American Institute of Physics
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