Fitting Spatial Models of Geometric Deviations of Free-Form Surfaces Determined in Coordinate Measurements

Abstract

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.

An analysis of methods of measurement and evaluation of sphericity deviations

“…stitching), a zasadę tę przedstawiono na rys. 4. zwłaszcza w odniesieniu do danych pomiarowych uzyskanych ze współrzędnościowych maszyn pomiarowych [11][12][13]. Inną metodą obliczania elementów odniesienia w przypadku pomiarów kulistości jest zastosowanie techniki obliczeń zastępczych elementów geometrycznych, najczęściej z wykorzystaniem tzw.…”

Simulation Tests of the Method for Determining a CAD Model of Free-Form Surface Deterministic Deviations

“…The component connected with the deterministic deviations is spatially correlated. The random component, on the other hand, is weakly correlated and is considered to be of a spatially random character [4,8]. Deviations of random values may be spatially correlated which is reflected in their deterministic distribution on a surface and is indicative of the existence of a systematic source in the course of processing.…”

“…1) only represent surface irregularities which can be divided into three components of different length: form deviations, waviness, and roughness of the surface [10]. Spatial coordinates of each measurement point include all the three components in different proportions [4,8].…”

“…Deterministic deviations are spatially correlated, however a lack of spatial correlation indicates spatial randomness of deviations [4]. Spatial statistics methods are applied to research on dependency of spatial data [5][6][7][8] (Section 2.2).…”

The study on an influence of scanning speed on results of measurements of form deviations with the use of coordinate measuring machines

“…Chodzi tu głównie o łożyska toczne i ślizgowe, wrzeciona obrabiarek, a także o elementy wykonujące przemieszczenia liniowe (np. tłoki silników) [2][3][4]. W badaniach laboratoryjnych ocena odchyłek kształ-tuelementów obrotowych jest zwykle dokonywana za pomocą tzw.…”