Comparison of Volumetric Analysis Methods for Machine Tools with Rotary Axes

Confidence in the ability of a production machine to meet manufacturing
tolerances requires a full understanding of the accuracy of the machine.
However, the definition of “the accuracy of the machine” is open to
interpretation. Historically, this has been in terms of linear positioning accuracy
of an axis with no regard for the other errors of the machine. Industry awareness
of the three-dimensional positioning accuracy of a machine over its working
envelope has slowly developed to an extent that people are aware that
“volumetric accuracy” gives a better estimation of machine performance.
However, at present there is no common standard for volumetric errors of
machine tools, although several researchers have developed models to predict
the effect of the combined errors.
The error model for machines with three Cartesian axes has been well
addressed, for example by the use of homogenous transformation matrices.
Intuitively, the number of error sources increases with the number of axes
present on the machine. The effect of the individual axis geometric errors can
become increasingly significant as the chain of dependent axes is extended.
Measurement of the “volumetric error” or its constituents is often restricted
to a subset of the errors of the Cartesian axes by solely relying on a laser
interferometer for measurement. This leads to a volumetric accuracy figure that
neglects the misalignment errors of rotary axes. In more advanced models the
accuracy of the rotary axes are considered as a separate geometric problem
whose volumetric accuracy is then added to the volumetric accuracy of the
Cartesian axes.
This paper considers the geometric errors of some typical machine
configurations with both Cartesian and non-Cartesian axes and uses case studies
to emphasise the importance of measurement of all the error constituents.
Furthermore, it shows the misrepresentation when modelling a five-axis
machine as a three-plus-two error problem. A method by which the five-axis
model can be analysed to better represent the machine performance is
introduced.
Consideration is also given for thermal and non-rigid influences on the
machine volumetric accuracy analysis, both in terms of the uncertainty of the
model and the uncertainty during the measurement. The magnitude of these
errors can be unexpectedly high and needs to be carefully considered whenever
testing volumetric accuracy, with additional tests being recommended.