Verification and validation methods based on ASME recornmendations

Rigid registration

The primary step in a CAl method for non-rigid parts is a rigid registration. Rigid registration brings the CAD and scan models as close as possible in a common coordinate system without deforming the models. In fact, rigid registration uses an optimal transformation matrix to translate and rotate the models without making any changes to their shapes. Among different rigid registration methods such as those described by (Li and Gu 2004, Savio, De Chiffre et al. 2007), the Iterative Closest Point (lCP) algorithm (Besl and Mckay 1992) is widely applied in different domains and well-known as a robust and efficient rigid registration. For example, a rigid registration for inspection of aircraft parts is presented in (Ravishankar, Dutt et al. 2010) for which the modified lCP method is applied. Among all rigid registration methods, lCP algorithm is known as a statistically robust and efficient method. The optimal transformation (translation and rotation) matrix in lCP registration is estimated at each iteration to minimize the distance between two models.

To this end, the Hausdorff distance (Henrikson 1999) between CAD mesh and acquired point clouds of scan model measures how far these two models are from each other. As illustrated in Equation 2-1 , the Hausdorff distance (dH (X, Y) between two non51 empty subsets (X, Y) of a metric space can be defmed as the maximum distance between every point of either set to sorne point of the other set. The lCP has been modified and developed to improve the calculation time as weIl as the minimization strategy (Rusinkiewicz and Levoy 2001), and sorne of these improvements are presented here. The improvements on decreasing the calculation time of lCP is presented in (Ma sud a and Y okoya 1995) by proposing a robust method applying random sampling of the point clouds. (Greenspan and Godin 2001) proposed an improvement in searching closest points by using corresponding points of previous iterations of the lCP and searching only in their smaIl neighborhood. (Zhu, Barhak et al. 2007) applied a mixture of techniques that accelerate the registration process and improve the efficiency of the lCP method. Many variant techniques of lCP have been investigated by (Rusinkiewicz and Levoy 2001) and (Bentley 1975). However, it should be pointed out that lCP-based algorithms are not capable of dealing with non-rigid parts where flexible deformations need to be taken into consideration.

Fixtureless inspection of non-rigid parts (non-rigid registration)

Applying only the rigid registration methods such as lCP method (Ravishankar, Dutt et al. 2010) is not sufficient for inspection ofnon-rigid parts in a free-state. Rigid registration methods do not permit any modification on the shape of CAD or scan models to compensate for the flexible deformation of non-rigid parts during the inspection process in a free-state. Meanwhile, inspection methods for non-rigid parts need to distinguish between the flexible deformation of non-rigid parts in a free-state with defects such as geometrical deviations due to faulty manufacturing. Conventional CAl methods apply restraining non-rigid parts in physical fixtures (Ascione and Polini 2010) during the inspection process. However, these sophisticated and expensive fixtures have significant drawbacks for which the setup and repeatability of the fixtures are costly.

Therefore, the fixtureless inspection methods are required to eliminate these costly fixtures. Fixtureless inspection of non-rigid parts based on CAl methods is able to evaluate the geometrical deviation of manufactured parts with respect to the assigned tolerance by taking into consideration the flexible deformation of non-rigid parts in a free-state. A categorization of fixtureless inspection methods based on literature is presented in (Abenhaim, Desrochers et al. 2012). The fixtureless CAl methods are c1assified into four approaches as l) automated vision inspection, In metric characteristic, III) boundary reconstruction and IV) simulated displacement. Fixtureless inspection of non-rigid parts can be performed by non-rigid registration methods c1assified as simulated displacement. These methods are essentially based on compensating for flexible deformation of non-rigid parts in a free-state by virtual displacement. The core idea of the fixtureless methods is to enable a comparison between the scan and CAD models by virtually compensating for the flexible deformation of the part whereas leaving the defect areas intact. The inspection methods presented in section 2.4.2.1 are based on virtually deforming the scan model towards the CAD model, while the non-rigid inspection methods presented in section 2.4.2.2 are based on virtually deforming the CAD models. Studying the displacement simulation for fixtureless inspection methods, this simulation can be performed based on FEA or graduaI iterative displacement methods.

Fixtureless inspection based on virtually deforming the scan model

The fixtureless inspection methods based on virtually deforming the scan model apply boundary conditions (BCs) via Finite Element Analysis (FEA) to deform the scan mesh towards the corresponding CAD model. The BCs in the virtual fixation concept (Weckenmann and Weickmann 2006) are imposed on fixation features of the scan mesh such as inspection fixations and assembly mounting holes and edges on the part. These features can automatically be identified using feature extraction techniques (Weckenmann, Gall et al. 2004). The virtual fixation method consists of processing scanned data, simulation (virtual fixation) and then comparing the models. The process of this inspection method, as presented in Figure 2-5, starts with data acquisition from visible surfaces of a part using an optical surface measuring system (e.g. fringe projection measuring system). These 3D measuring devices provide sorne millions of point c10uds per measurement. This scan data (with huge data size) is then reduced into 30 to 50 thousand point clouds, using a curvature-based method, which allow performing finite element calculation.

To reduce the size of scan mesh, the points in the flat area are removed but the points associated with curved features are kept to preserve the geometrical properties of the part. An approximation of the surface as triangulations with linear elements is then performed on the point clouds. Applying triangulation techniques su ch as Delaunay-based (Borouchaki, George et al. 1996) approaches on the point clouds generate a representative geometrical shape of the part as scan mesh. The data processing continues with removing the noise of the measured surface by applying mesh smoothing and filtering techniques. In the examples performed by (Weckenmann and Gabbia 2006), the local sphere assumption proposed in (Karbacher and Hausler 1998) is applied for smoothing the scanned data. In order to utilize the finite element analysis, the material properties (such as Young’ s modulus and Poisson’ s ratio and density in addition to the wall thickness ofthe triangulated mesh) are defmed for the inspecting model. In this step, the extracted features (such as fixation holes) are used to fmd the correspondence (for registration process) between the CAD model and scan mesh. Then, BCs (such as imposed displacements) are applied on fixation features of scan mesh to displace these features towards the corresponding features on the CAD model via FEA. The ·FEA applied in this method uses updated Lagrange algorithm, which is a nonlinear large displacement FEA resolution. Then, a geometrical comparison between the deformed scan mesh (after applying FEA) and CAD model identifies defects on the scan model (inspection of part).

However, imposing BCs on aIl fixation features to displace them into their design location for non-rigid parts is not always possible and may result in geometrical deviations in the part. To this end, (Gentilini and Shimada 2011) proposed an alternative for applying BCs directly on fixation features. In this method, an optirnization method is used to rninimize the location and orientation of fixation features between the defonned scan mesh and CAD model. The specific displacement BCs that satisfies the optimization method can predict the functional shape of the part. Applying these BCs on the scan mesh via FEA, a virtual inspection is perfonned on the defonned scan mesh in its assembly-state. The geometrical comparison between the defonned scan mesh and CAD model evaluates defects on the scan model. Considering the application of movable datum targets for restraining non-rigid parts during inspection and an industrial inspection technique (see Figure 1-2) as restraining loads, a virtualfixture method is presented in (Abenhaim, Desrochers et al. 2015). In this fixtureless CAl method as depicted in Figure 2-6, the scan mesh is virtuaIly restrained by a combination of forces located only on datum targets to minimize the weighted average of distances at specific points (constrained regions) between the deformed scan mesh and CAD model. The restraining forces, which are limited to the defined permissible assembly loads, are estimated through an optimization method that minimizes the distance at constrained regions between the scan and CAD models. Applying these optimized restraining forces on the scan mesh, the functional shape of the part in assembly-state can be retrieved. The inspection result in this method is performed on datum targets evaluating the difference between the deformed scan mesh and nominal position of datum targets. The advantages of applying fixtureless inspection based on virtual deforming the scan model can be outlined as: