2Introduction The increasing demand for accuracy of machined parts is being
fueled by economics because
it reduces assembly,
warranty, and ownership
costs. Traditionally, manufacturers have ensured accuracy of parts with linear
calibration of each axis of the machine
tools. But linear calibration is inadequate for ensuring accuracy of three
dimensional parts.
The conventional definition of the 3D volumetric positioning
error is the root mean square of the 3 axes
displacement error. 20 years ago, this definition is okay as long
as the dominate errors are the displacement
errors. Now the displacement errors are reduced considerably and the dominate errors are straightness
and squareness errors. Using a conventional laser interferometer to measure the
straightness and squareness errors is
rather difficult and costly. It usually takes days of machine down time
and experienced operator to
perform these measurements. For those
reasons the body diagonal
displacement error defined in the ASME B5.54 or ISO 230-6 standard is a
good quick check of
the volumetric error. However, it is
not clear, what is the relation between the body diagonal displacement errors and the
true 3D positioning errors.
Currently, both the ASME B5(TC52)
and ISO 230(TC39) are working on a
new definition of volumetric
accuracy. There are many possible definitions, such as the
root mean square of the 3 axes displacement
errors, the root mean square of the total errors in the 3-axis directions,
the maximum 4 body diagonal displacement
errors without squareness
and the maximum 4 body diagonal
displacement errors with squareness errors.Below are
some definitions of 3D
volumetric positioning errors
and some measurements on the volumetric
positioning errors. Based on these
measurement results, various
definitions of 3D volumetric errors can be calculated. It is concluded
that the 4 body diagonal displacement
errors with squareness errors correlate with the true 3D volumetric errors very well. II.
Basic 3D volumetric positioning errors
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 [1] 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,
