Quantification of Profile Measurement Data
Analytics
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Abstract
Parts with complicated freeform shapes have been attracting more attention in industrial applications in recent decades. In most systems, the functional performance of these parts is directly related to the conformity of their profile with the designed position, form, shape and size of the part surface. Traditional profile measurement methods were primarily developed for parts with simple prismatic shapes; the increased use of freeform profiles has highlighted the need for new rapid measurement methods to validate these profiles with an acceptable level of uncertainty. Metrological uncertainty is a task-specific parameter that quantifies the variability of a measurement, and is influenced by numerous factors. To analyze the effect of these factors, it is necessary to have both a well-quantified metric to describe the profile measurement error, as well as a quantification of errors in the measurement data.This research has two main components. In the first stage, the common Least Squares (LS) fitting method is extended to two different fitting algorithms identified as Weighted Least Squares (WLS) and Highly Weighted Least Squares (HWLS). These algorithms can accommodate variable density in the point distribution, are developed to analyze the effect of non-uniform point cloud density on the fitting process, which is more likely with newer, optical measuring systems. In these algorithms, the weight of individual point deviations is defined based on distances from surrounding points. These algorithms are implemented in Matlab software, and are applied to simulated theoretical data sets as well as experimental data sets obtained by tactile and optical measurement methods. In the second stage of this work, a convolution averaging filter is proposed as a method for quantification of profile measurement data. By applying this filter to the point deviation data, the Mean Local Deviation (MLD) of every profile segment is calculated. This quantified local error can be used as a criterion for comparing different profile scans performed with one or multiple measurement methods. The point clouds—fitted by WLS and HWLS algorithms—are filtered and then their MLDs are compared with MLDs of data fitted by LS method. Primary results of this stage show that the proposed filtering method can effectively be used to compare measurement data with very different density, and can also remove the negative effect of noise in data. With effective filtering, the MLD values of a part are almost constant (they are independent of the measurement method).