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