Abstract
Abstract. The framework of the single point uncertainty developed at the Institute of Manufacturing Metrology (FMT) presents a methodology to determine and evaluate the local measurement uncertainty for a measurement setup by local comparison of a measurement series with an associated reference geometry. This approach, which was originally developed and optimized for the processing of complete areal measurements of work pieces using industrial X-ray computed tomography, was now also extended to line scans found in dimensional testing using tactile coordinate measuring machines (CMMs). The targets of the investigation are spur (involute) steel gear wheels, which can be dimensionally characterized by both helix and profile scans using a CMM in scanning mode in combination with a rotatory table. A second measurement procedure is characterized by a single scan of the complete gear profile without the usage of a rotatory table, using the “free-form scan” CMM functionality. The modification of the single point uncertainty framework in order to determine the single point precision of repeated gear wheel measurements was implemented successfully for gear measurements using the Zeiss Gear Pro evaluation software in combination with a rotatory table as well as unassisted free-form scans of the same gear. The examinations yielded abnormally high random measurement errors, which could not fully be explained within our examinations and was for the most part caused by the accuracy of the used rotatory table of the CMM. The alternative measurement method showed that the CMM system is capable of measuring very precisely in scanning mode if the changes in the curvature of the scan trajectory are favourable.
Highlights
With respect to gear wheel inspection, the VDI/VDE 2612 guideline states that “Unless agreed otherwise, the profile is measured in a transverse plane approximately in the middle of the face width.” (VDI/VDE, November 2018) The profile measurement is complemented by the helix measurement: “The helix preferably is measured on the diameter of the Vcylinder.” (VDI/VDE, November 2018) Summarizing, each gear flank is described by one profile scan and one helix scan
The observed precision values represent the superimposition of the geometric work piece deviations and all uncorrected measurement error contributions along the complete measurement chain
The target of the following investigations was to determine whether the error characteristics of the rotatory table could account for the observed single point precision values
Summary
The framework of the single point uncertainty describes a methodology to statistically evaluate the local measurement uncertainty of a measurement series consisting of n repeated single measurements with respect to an associated reference geometry in the sense of the International Vocabulary of Metrology (VIM) (Brinkmann, 2012). The core routine used in this former work at the Institute of Manufacturing Metrology (FMT) provided accurate results under most conditions (Fleßner et al, 2016) This algorithm computes the distance from each sampling point of the reference/nominal geometry in the direction of the vertex normal vectors of these sampling points to the triangulated measurement geometry. Subsequent development efforts resulted in the introduction of an alternative sampling strategy, which solved the problematic sampling of edge regions associated with the sampling in the direction of the surface normal vector (Müller and Hausotte, 2019a) This sampling strategy calculates the shortest distance from a sampling point to the target surface and is called shortest distance (Fig. 1). These are mainly CT and structured-light scanning (Müller et al, 2019a)
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