On the Development of a Surrogate Modelling Toolbox for Virtual Assembly
Abstract
:1. Introduction
1.1. Integration in the Context of Industry 4.0
1.2. Problem Setting
1.3. Scope and Aims
2. State of the Art
- Detection (of key points in order to reduce the number of points to register),
- Description (of the shape by local shape descriptors),
- Searching (of corresponding points) and
- Refinement (in an iterative optimization).
2.1. Methods for Relative Positioning
2.2. Prior Work for Surrogate Modelling for Joining Processes
3. Development of a Surrogate Modelling Toolbox
- Operations for detecting relevant subsets of points (Point set selection),
- Operations for describing and manipulating the surface morphology (Point set morphology),
- Operations concerning point correspondence search and assembly position determination (Objective function constraints) and
- Technological properties such as point set refinement or simplification operations, which are not further discussed in this work.
4. Use Case Study for a Laser Welding Assembly
4.1. Surrogate Model Composition
- Coarse Pre-Alignment according to the CAD assembly,
- Patch Selection of primary datum A (guiding pegs A1 and A2 at the cover and corresponding holes in the housing, see technical drawing in Figure 7) and secondary datum B (alignment of cover face in flush with the housing), and
- Virtual Intersection of the parts by using a penalty-based optimization approach as in [68].
4.2. Validation against the Physical Assembly
4.2.1. Comparison of Variation Distributions
4.2.2. Comparison of Single Point Deviations
5. Conclusions
6. Outlook
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
CPS | Cyber-Physical Systems |
CT | Computed Tomography |
GD&T | Geometrical Dimensioning and Tolerancing |
ICT | Information and Communication Technology |
PA | Physical Assembly |
SMS | Skin Model Shape |
SMT | Surrogate Modelling Toolbox |
SO | Surrogate Operation |
VA | Virtual Assembly |
Appendix A
Surrogate Operation | Description | Reference | Level of Detail |
---|---|---|---|
Point set selection | Detection of relevant subsets of points | ||
Coarse Matching | Determine initial position before assembly closely to the final position [35] | ||
Unconstrained Best Fit A | Alignment as provided by Iterative Closest Point-Algorithm (ICP) | [71] | |
Constrained Regular Geometries A | Alignment as provided by the ISO System for Geometrical Product Specification (GPS) datum definition in ISO 5459 [28] | [28] | |
Segmentation of contact faces A | Determination of subsets and that are by mechanical design provided as contact faces | ||
Local shape descriptors A | Determination of hypothetically corresponding, salient key features in and , such as Principal Curvature or Harris Algorithm [72] | [35,72] | |
Semantic segmentation A | Determination of subsets corresponding to geometrical primitives | [73] | |
Patch Selection (CAD based) A | Determination of subsets corresponding to a maximal distance to a nominal geometry such as a CAD file | [74] | |
Point set morphology | Description and manipulation of the surface morphology | ||
Definition of Offset and Intersection A | Definition of a certain offset between faces (e.g., to simulate adhesive gap) or of an intersection (virtual penetration) to simulate surface flattening or material loss (e.g., due to melting welding bead) | [41] | |
Morphological Filtering A | Manipulate surfaces locally to simulate surface flattening due to mechanical load | [51,52] | |
Hertzian Contact Formulation A | [41] | ||
Method of Influence Coefficients (MIC) A | Linearized computation of elastic deformation due to mechanical load | [50,57] | |
Linear Finite Element Analysis (FEA) A | Computation of elastic deformation due to mechanical load | [75,76] | |
Nonlinear FEA A | Computation of elastic and plastic deformation due to mechanical load | [65,66] | |
Objective Function | Searching of correspondences and the assembly position | ||
Modalities for Distance Computation | Approaches to compute distances between and | ||
Point to Point B | Distance computation discretized on single points | [71] | |
Point to Plane or Triangle B | Triangle-based algorithms for distance calculation that more precisely represent the physical distance | [77] | |
Point correspondence metric | Metric considered to determine corresponding points recreating the physical contact scenario [38] | ||
Euclidean distance B | Only sufficient, when point clouds are relatively dense | [38] | |
Ray Casting in Normal Direction B | Improved correspondence for surfaces that are sufficiently coarse aligned | [38] | |
Ray Casting in Assembly Direction B | Most accurate representation of the physical assembly contact correspondence | [38] | |
Distance Metric | Metric considered to determine the discrepancy between and | ||
Convex Hull of Gap Volume B | Minimization of the convex hull of the gap volume between and | [38] | |
Euclidean distance B | Minimization of local distances in corresponding points | [38] | |
Collision behavior | Collision behaviour stating an elastic or stiff contact | ||
Penalize Intersection B | Allows a certain virtual intersection | [41] | n/a |
Hard-Constrained Intersection B | Strict compliance to non-intersection | [41] | n/a |
Collision detection | Determination and quantification of a collision between and | ||
Sign of signed distances B | Negative signed distances represent a local intersection | [38] | |
Simplex-based B | Fast, approximative collision detection, only applicable for convex geometries, e.g., the GJK algorithm [78] | [78,79] | |
Bounding Volume Hierarchy B | More precise method applicable for closely positioned objects and initial collision | [79] | |
Datum Hierarchy | Representation of primary, secondary, tertiary datum hierarchy as per [28] | ||
Datum Weighting B | Weighting factors applied to the objective values derived from primary, secondary and tertiary patches | [38] | |
Contact and Force Equilibrium B | Allow contact configurations only, where the contact triangle of the primary datum is maximized and intersected by the assembly force vector. The secondary datum constitutes a line contact and the tertiary datum a point contact. | [51] |
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Kaufmann, M.; Effenberger, I.; Huber, M.F. On the Development of a Surrogate Modelling Toolbox for Virtual Assembly. Appl. Sci. 2021, 11, 1181. https://doi.org/10.3390/app11031181
Kaufmann M, Effenberger I, Huber MF. On the Development of a Surrogate Modelling Toolbox for Virtual Assembly. Applied Sciences. 2021; 11(3):1181. https://doi.org/10.3390/app11031181
Chicago/Turabian StyleKaufmann, Manuel, Ira Effenberger, and Marco F. Huber. 2021. "On the Development of a Surrogate Modelling Toolbox for Virtual Assembly" Applied Sciences 11, no. 3: 1181. https://doi.org/10.3390/app11031181