Revised and Presented in the 6th LAMDAMAP Conference in Huddersfield, England, on
July 4, 2003 2
1.
Introduction The measurement
and compensation of 3D volumetric
positioning accuracy becomes
more important for quality assurance and to achieve higher accuracy.
The introduction
of B5.54 and
ISO230-6 machine tool
performance measurement
standards [1,2] are increasing the popularity of laser interferometer
diagonal, sequential step
diagonal or vector technique [3,4] for
the calibration and
compensation of machine
tool errors. The
B5.54 body diagonal
displacement tests have
been used by Boeing Aircraft Company
and many others for
many years with very good results and
success. This is due to the
reduction in calibration time
these methods can provide over the conventional laser interferometer based
measurement taken along lines
parallel to the machine’s X, Y and Z axes. Here a theoretical analysis on
the relations between the 21 rigid
body positioning errors and the 4
body diagonal displacement measurement; and the sequential step diagonal displacement errors; and the 3 axis
linear displacement measurement; has
been performed. It is concluded that
the 4 body diagonal displacement measurement can be used
for a quick check on the volumetric
positioning accuracy. The
sequential step diagonal measurement can be used to determine the volumetric
positioning errors, 3
displacement errors, 6 straightness errors and 3 squareness
errors. The 3 axis linear
displacement measurement can be used
to determine the 3 displacement errors, 3 pitch angular errors and 3 yaw angular errors. Using these measurements, all 21 rigid body positioning
errors, except roll angular errors, can all
be measured. The measurement accuracy is limited by
the repeatability of the
machine. The performance of these
measurements is relatively
simple and straight forward. A single laser interferometer with linear
displacement capability can
be used to perform all these
measurement. Now, manufacturing can migrate from one-dimensional linear to 3D
laser volumetric measurement without
incurring high costs and long machine tool down time. 2.
Positioning errors of a 3-axis machine For a 3-axis machine, there are 6 errors per axis or a total of
18 errors plus 3 squareness errors.
These 21 rigid body errors [5]
can be expressed as the following. Linear displacement
errors: Dx(x), Dy(y), and Dz(z) Vertical
straightness errors: Dy(x), Dx(y), and Dx(z) Horizontal straightness errors: Dz(x), Dz(y), and Dy(z)
Roll angular errors: Ax(x), Ay(y), and
Az(z) Pitch angular errors: Ay(x),Ax(y),
and Ax(z) Yaw angular errors: Az(x), Az(y),
and Ay(z) Squareness errors: Øxy, Øyz, Øzx,
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