Local geometric deviations of free-form surfaces are determined as normal deviations of measurement points from the nominal surface. Different sources of errors in the manufacturing process result in deviations of different character, deterministic and random. The different nature of geometric deviations may be the basis for decomposing the random and deterministic components in order to compute deterministic geometric deviations and further to introduce corrections to the processing program. Local geometric deviations constitute a spatial process. The article suggests applying the methods of spatial statistics to research on geometric deviations of free-form surfaces in order to test the existence of spatial autocorrelation. Identifying spatial correlation of measurement data proves the existence of a systematic, repetitive processing error. In such a case, the spatial modelling methods may be applied to fitting a surface regression model representing the deterministic deviations. The first step in model diagnosing is to examine the model residuals for the probability distribution and then the existence of spatial autocorrelation.

JO - Metrology and Measurement Systems L1 - http://www.czasopisma.pan.pl/Content/107080/PDF/Journal10178-VolumeXVII+Issue4_08+paper.pdf L2 - http://www.czasopisma.pan.pl/Content/107080 IS - No 4 EP - 610 KW - geometric deviations KW - free-form surface KW - coordinate measurements KW - spatial modelling KW - spatial autocorrelation ER - A1 - Poniatowska, MaĆgorzata A1 - Werner, Andrzej PB - Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation JF - Metrology and Measurement Systems SP - 599 T1 - Fitting Spatial Models of Geometric Deviations of Free-Form Surfaces Determined in Coordinate Measurements UR - http://www.czasopisma.pan.pl/dlibra/docmetadata?id=107080 DOI - 10.2478/v10178-010-0049-x