On the magnification of two-dimensional contouring errors by using contour-parallel offsets

The cross grid encoder is a diffraction grating type encoder to measure two-dimensional position of a optical head by using a grid plate, and is widely used in the industry to evaluate the two-dimensional contouring performance of a machine tool. In the graphical display of measured contouring error profiles, the error is often magnified to some given scale with respect to the reference trajectory. The conventional algorithm to compute the magnified contouring error profile, adopted in a commercial software to analyze an error profile measured by the cross grid encoder, makes the magnified trajectory discontinuous when the given reference trajectory is unsmooth, which makes it difficult to understand the magnified trajectory especially at corners. This paper proposes a new algorithm to compute the magnified trajectory of two-dimensional contouring error profiles such that the magnified trajectory becomes continuous even when the reference trajectory is unsmooth. Application examples are presented with error profiles obtained by using a cross grid encoder applied to a commercial machining center.