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

The laser step-diagonal measurement modifies the diagonal displacement measurement 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, including linear errors, straightness and squareness errors, in three-dimensional space. In this paper, we show that the conventional formulation of the step-diagonal measurement is valid only when implicit assumptions related to the configuration of laser and mirror setups are met, and that its inherent problem is that it is generally not possible to guarantee these conditions when volumetric errors of the machine is unknown. To address these issues, we propose a new formulation of the step-diagonal measurement, in order to accurately identify volumetric errors even under the existence of setup errors. To simplify the discussion, this paper only considers the two-dimensional version of laser step-diagonal measurement to estimate volumetric errors on the XY plane. The effectiveness of the proposed modified identification scheme is experimentally investigated by an application example of two-dimensional laser step diagonal measurement to a high-precision machine tool.