A new formulation of laser step diagonal measurement—Three-dimensional case

To ensure the motion accuracy of a machine tool over its entire three-dimensional workspace, it is important to evaluate all the volumetric errors associated with three linear axes including three linear displacement errors, six straightness errors and three squareness errors. The laser step diagonal measurement modifies the diagonal displacement measurement, described in the standard ISO 230-6, by executing a diagonal as a sequence of single-axis motions. It has been claimed that the step diagonal test enables the identification of all the volumetric error components by using a linear laser interferometer only. This paper first shows that the conventional formulation of step diagonal measurements is potentially subject to a significant estimation error caused by setup errors in mirror and laser directions. We then propose a new formulation of laser step diagonal measurement, in order to accurately identify three-dimensional volumetric errors even under the existence of setup errors. The effectiveness of the modified identification scheme is experimentally investigated by an application example of three-dimensional laser step diagonal measurements to a high-precision vertical machining center.