A non-rigid registration method for the efficient analysis of shape deviations in production engineering applications

Abstract

A common requirement in production engineering applications is the comparison of designed and as-built parts. Due to manufacturing influences and geometric changes incorporated during physical prototyping, there may exist significant deviations between these shapes. In order to compensate the manufacturing influences and to incorporate geometric changes into the virtual design, a detailed analysis of the deviations is required. The designed (or reference) shape is usually given in terms of a CAD data set, while the as-built (or test) geometry is acquired by digitization of the physically manufactured prototype. Given these two geometries, one is faced with the problem of determining points of correspondence between them. This is also referred to as registration. In rigid registration, correspondences are determined by first aligning the two geometries rigidly using a best-fit approach. Subsequently, the correspondences between the aligned geometries are determined by finding for a point of one shape the closest surface point on the other. While several efficient rigid registration methods exist, they do not account for shape deviations, resulting in inaccurate correspondences when applied to such geometries. Non-rigid registration methods, conversely, do not search for a global best-fit alignment, but instead affect a deformation of the one geometry onto the other, allowing for an improved correspondence calculation. Most published state-of-the-art non-rigid registration methods are not necessarily applicable to production engineering scenarios due to, among others, the typical data sizes and the required level of accuracy in the correspondence determination. A further hindrance is their lack of shop-floor applicability, attributable to their calculation times as well as to the expertise that their application requires on behalf of the user. This paper presents a non-rigid registration method for the efficient calculation of correspondences in production engineering scenarios. By combination of several established methods from the field of geometric modeling, the test shape is iteratively deformed onto the reference shape. When the deformed test shape satisfiably approximates the reference geometry, correspondences are determined by projection. The procedure is applied to the problem of springback behavior, which arises in sheet metal forming. A validation of the method is achieved by comparing the calculated correspondences with the ideal correspondences, as determined by finite element simulation.