UBC Theses and Dissertations

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UBC Theses and Dissertations

Evaluation of linear segment length and local curvature radius along airfoil leading and trailing edges Razive, Mohammad Nahid Islam


Airfoil is the basic profile geometry of impeller and turbine blades. The operational efficiency of these blades is governed by stringent tolerance specifications on the airfoils. The specified tolerances are commonly evaluated from discrete coordinate data collected in sections by a touch-probe coordinate measuring machine (CMM). These measurement data are subject to inspection inaccuracies associated with CMM measurement operation. Apart from well-known inspection parameters like profile tolerance, profile thickness and edge radius, the leading edge (LE) and trailing edge (TE) are specified with a unique set of geometric parameters like the maximum linear segment length restriction and the minimum curvature radius restriction. This thesis focuses on evaluating these two localized geometric restrictions along the leading edge and trailing edge of an airfoil. This thesis first presents a robust algorithm to identify the longest linear segment. The main feature of the proposed algorithm is the explicit consideration of measurement uncertainty. The algorithm starts by detecting relatively small linear segments and then merges these segments to determine the longest feasible linear segment under given measurement uncertainty. The effect of measurement uncertainty and data point resolution on the performance of the presented algorithm is demonstrated through case studies. Once the linear segments are identified and excluded, the remaining data points only belong to the non-linear segments. As minimum radius can occur at any location, curvature radius at each point along the non-linear segments is evaluated. Curvature radius at a specific point can only be estimated from its neighborhood. The chosen neighborhood size needs to be balanced between capturing local curvature attribute and effectively considering the effect of measurement uncertainty. An algorithm is thus proposed to evaluate radius via a rolling scheme of five consecutive data points in order to retrieve the local curvature information of the mid-point. A statistical approach is employed where all feasible radii are considered in order to reliably estimate the desired radius. Biarc construction is used as a tool to calculate radius. Compared with existing radius estimation methods, the proposed method has demonstrated to yield better accuracy with varying measurement uncertainty and data point resolution.

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