The inspection of deformable bodies using curvature estimation and Thompson-Biweight test

Abstract

Dimensioning and tolerancing standards assume inspection operation, unless otherwise specified, must be done in Free State. This can be problematic when dealing with compliant parts. The inspection of compliant parts needs specialized fixtures because in Free State they may have a significantly different form than their nominal model (CAD) due to inherent variations in the manufacturing process, gravity loads, and residual strains. These specialized fixtures pose difficulties, bear significant costs to industry, and the process is very time-consuming. To address these challenges, this paper proposes a new method for quantifying flexibility/rigidity of the mechanical parts. Subsequently, a novel approach named IDB-CTB is proposed to fixtureless inspection of deformable bodies by curvature estimation and Thompson-Biweight test. This approach combines the Gaussian curvature properties of manufactured compliant parts, one of the intrinsic properties of the geometry, with the Thompson-Biweight statistical test based on the extreme value notion as an identification method. The aim is to distinguish profile deviation due to the manufacturing process from a part’s deformation due to its flexibility in order to determine whether the tolerance fits the CAD model or not. The IDB-CTB approach is tested on two sets of case studies. Three simulated, typical industrial sheet metal case studies were performed in the first set, and an experimental case study in the second one. The low percentage of errors in defect areas and in the profile deviations estimated compared with their reference ones in most cases reflects the effectiveness of the proposed approach.