Predicting Geometric Errors and Failures in Additive Manufacturing

Additive manufacturing is a process that has facilitated the cost effective production of complicated designs. Objects fabricated via additive manufacturing technologies often suffer from dimensional accuracy issues and other part specific problems such as thin part robustness, overhang geometries that may collapse, support structures that cannot be removed, engraved and embossed details that are indistinguishable. In this work we present an approach to predict the dimensional accuracy per vertex and per part. Furthermore, we provide a framework for estimating the probability that a model is fabricated correctly via an additive manufacturing technology for a specific application. This framework can be applied to several 3D printing technologies and applications. In the context of this paper, a thorough experimental evaluation is presented for binder jetting technology and applications.Comment: This version has been published in the Rapid Prototyping Journal (2023

Tree-decomposable and underconstrained geometric constraint problems

Preprin

String Matching and 1d Lattice Gases

We calculate the probability distributions for the number of occurrences $n$ of a given $l$ letter word in a random string of $k$ letters. Analytical expressions for the distribution are known for the asymptotic regimes (i) $k \gg r^l \gg 1$ (Gaussian) and $k,l \to \infty$ such that $k/r^l$ is finite (Compound Poisson). However, it is known that these distributions do now work well in the intermediate regime $k \gtrsim r^l \gtrsim 1$. We show that the problem of calculating the string matching probability can be cast into a determining the configurational partition function of a 1d lattice gas with interacting particles so that the matching probability becomes the grand-partition sum of the lattice gas, with the number of particles corresponding to the number of matches. We perform a virial expansion of the effective equation of state and obtain the probability distribution. Our result reproduces the behavior of the distribution in all regimes. We are also able to show analytically how the limiting distributions arise. Our analysis builds on the fact that the effective interactions between the particles consist of a relatively strong core of size $l$, the word length, followed by a weak, exponentially decaying tail. We find that the asymptotic regimes correspond to the case where the tail of the interactions can be neglected, while in the intermediate regime they need to be kept in the analysis. Our results are readily generalized to the case where the random strings are generated by more complicated stochastic processes such as a non-uniform letter probability distribution or Markov chains. We show that in these cases the tails of the effective interactions can be made even more dominant rendering thus the asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The lattice gas analogy has been worked out in full, including virial expansion and equation of state. This constitutes the main part of the paper now. Connections with existing work is made and references should be up to date now. To be submitted for publicatio

On the effects of the fix geometric constraint in 2D profiles on the reusability of parametric 3D CAD models

[EN] In order to be reusable, history-based feature-based parametric CAD models must reliably allow for modifications while maintaining their original design intent. In this paper, we demonstrate that relations that fix the location of geometric entities relative to the reference system produce inflexible profiles that reduce model reusability. We present the results of an experiment where novice students and expert CAD users performed a series of modifications in different versions of the same 2D profile, each defined with an increasingly higher number of fix geometric constraints. Results show that the amount of fix constraints in a 2D profile correlates with the time required to complete reusability tasks, i.e., the higher the number of fix constraints in a 2D profile, the less flexible and adaptable the profile becomes to changes. In addition, a pilot software tool to automatically track this type of constraints was developed and tested. Results suggest that the detection of fix constraint overuse may result in a new metric to assess poor quality models with low reusability. The tool provides immediate feedback for preventing high semantic level quality errors, and assistance to CAD users. Finally, suggestions are introduced on how to convert fix constraints in 2D profiles into a negative metric of 3D model quality.The authors would like to thank Raquel Plumed for her support in the statistical analysis. This work has been partially funded by Grant UJI-A02017-15 (Universitat Jaume I) and DPI201784526-R (MINECO/AEI/FEDER, UE), project CAL-MBE. The authors also wish to thank the editor and reviewers for their valuable comments and suggestions that helped us improve the quality of the paper.González-Lluch, C.; Company, P.; Contero, M.; Pérez Lopez, DC.; Camba, JD. (2019). On the effects of the fix geometric constraint in 2D profiles on the reusability of parametric 3D CAD models. 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A comparison of manual vs. online grading for solid models. Paper presented at 120th ASEE annual conference and exposition, Atlanta, GA, June 23–26, 2013, Paper ID #7233.Barbero, B. R., Pedrosa, C. M., & Samperio, R. Z. (2016). Learning CAD at university through summaries of the rules of design intent. International Journal of Technology and Design Education. https://doi.org/10.1007/s10798-016-9358-z .Bodein, Y., Bertrand, R., & Caillaud, E. (2014). Explicit reference modeling methodology in parametric CAD system. Computers in Industry, 65(1), 136–147. https://doi.org/10.1016/j.compind.2013.08.004 .Bouma, W., Fudos, I., Hoffmann, C., Cai, J., & Paige, R. (1995). Geometric constraint solver. Computer-Aided Design, 27(6), 487–501. https://doi.org/10.1016/0010-4485(94)00013-4 .Briggs, J. C., Hepworth, A. I., Stone, B. R., Cobum, J. Q., Jensen, C. G., & Red, E. (2015). Integrated, synchronous multi-user design and analysis. Journal of Computing and Information Science in Engineering, 15(3), 031002. https://doi.org/10.1115/1.4029801 .Buckley, J., Seery, N., & Canty, D. (2017). Heuristics and CAD modelling: An examination of student behaviour during problem solving episodes within CAD modelling activities. International Journal of Technology and Design Education. https://doi.org/10.1007/s10798-017-9423-2 .Camba, J. D., & Contero, M. (2015). Assessing the impact of geometric design intent annotations on parametric model alteration activities. Computers in Industry, 71, 35–45. https://doi.org/10.1016/j.compind.2015.03.006 .Camba, J. D., Contero, M., & Company, P. (2016). Parametric CAD modeling: An analysis of strategies for design reusability. Computer-Aided Design, 74, 18–31. https://doi.org/10.1016/j.cad.2016.01.003 .Camba, J. D., Contero, M., & Company, P. (2017). CAD reusability and the role of modeling information in the MBE context. Model-based enterprise summit 2017. National Institute of Standards and Technology (NIST), Gaithersburg, MD, April 3–7. MBE17-020. https://www.nist.gov/file/361581 .Cheng, Z., & Ma, Y. (2017). A functional feature modeling method. Advanced Engineering Informatics, 33, 1–15. https://doi.org/10.1016/j.aei.2017.04.003 .Cheng, Z., Xie, Y., & Ma, Y. (2018). Graph centrality analysis of feature dependencies to unveil modeling intents. Computer-Aided Design and Applications. https://doi.org/10.1080/16864360.2018.1441236 .Chester, I. (2007). Teaching for CAD expertise. International Journal of Technology and Design Education, 17, 23–35. https://doi.org/10.1007/s10798-006-9015-z .Company, P., Contero, M., Otey, J., & Plumed, R. (2015). Approach for developing coordinated rubrics to convey quality criteria in CAD training. Computer-Aided Design, 63, 101–117. https://doi.org/10.1016/j.cad.2014.10.00 .Company, P., & González-Lluch, C. (2013). CAD 3D con SolidWorks ® Tomo I: Diseño básico. Publicacions de la Universitat Jaume I. (Colección Sapientia, Núm. 86). http://cad3dconsolidworks.uji.es .Contero, M., Company, P., Vila, C., & Aleixos, N. (2002). Product data quality and collaborative engineering. IEEE Computer Graphics Applications, 22(3), 32–42. https://doi.org/10.1109/MCG.2002.999786 .Dixon, B. M., & Dannenhoffer, J. F., III. (2014). Geometric sketch constraint solving with user feedback. Journal of Aerospace Information Systems, 11(5), 316–325. https://doi.org/10.2514/1.I010110 .Fudos, I., & Hoffmann, C. M. (1997). A graph-constructive approach to solving systems of geometric constraints. ACM Transactions on Graphics, 16(2), 179–216. https://doi.org/10.1145/248210.248223 .Ge, J. X., Chou, S. C., & Gao, X. S. (1999). Geometric constraint satisfaction using optimization methods. Computer-Aided Design, 31(14), 867–879. https://doi.org/10.1016/S0010-4485(99)00074-3 .González-Lluch, C., Company, P., Contero, M., Camba, J. D., & Colom, J. (2017a). A case study on the use of model quality testing tools for the assessment of MCAD models and drawings. International Journal of Engineering Education, 33(5), 1643–1653.González-Lluch, C., Company, P., Contero, M., Camba, J. D., & Plumed, R. (2017b). A survey on 3D CAD model quality assurance and testing tools. Computer-Aided Design, 83, 64–79. https://doi.org/10.1016/j.cad.2016.10.003 .Hamade, R. F. (2009). Profiling the desirable CAD trainee: Technical background, personality attributes, and learning preferences. Journal of Mechanical Design, 131(12), 121009–121019. https://doi.org/10.1115/1.4000455 .Hekman, K. A., & Gordon, M. T. (2013). Automated grading of first year student CAD work. Paper presented at the 120th ASEE annual conference and exposition 2013, Atlanta, GA, June 23–26. Paper ID #6379.Hepworth, A., Tew, K., Trent, M., Ricks, R., Jensen, C. G., & Red, E. R. (2014). Model consistency and conflict resolution with data preservation in multi-user computer aided design. Journal of Computing and Information Science in Engineering, 14(2), 021008. https://doi.org/10.1115/1.4026553 .Jackson, C., & Buxton, M. (2007). The design reuse benchmark report: Seizing the opportunity to shorten product development. Boston: Aberdeen Group.Joan-Arinyo, R., Soto-Riera, A., Vila-Marta, S., & Vilaplana-Pastó, J. (2003). Transforming an under-constrained geometric constraint problem into a well-constrained one. Paper presented at proceedings of ACM SM03, Seatle, June 16–20.Kirstukas, S. J. (2016). Development and evaluation of a computer program to assess student CAD models. Paper presented at ASEE annual conference and exposition, New Orleans, June 26.Kramer, G. (1991). Using degrees of freedom analysis to solve geometric constraint systems. Paper presented at proceedings of the first ACM symposium on solid modeling foundations and CAD/CAM applications 1991, Austin, June 05–07.Kwon, S., Kim, B. C., Mun, D., & Han, S. (2015). Graph-based simplification of feature-based three-dimensional computer-aided design models for preserving connectivity. Journal of Computing and Information Science in Engineering, 15(3), 031010. https://doi.org/10.1115/1.4030748 .Leea, J. Y., & Kimb, K. (1998). A 2-D geometric constraint solver using DOF-based graph reduction. Computer-Aided Design, 30(11), 883–896. https://doi.org/10.1016/S0010-4485(98)00045-1 .Mata Burgarolas, N. (1997). Solving incidence and tangency constraints in 2D. Technical report LSI-97-3R, Departament LiSI, Universitat Politècnica de Catalunya.Petrina, S. (2003). Two cultures of technical courses and discourses: The case of computer aided design. International Journal of Technology and Design Education, 13, 47–73.Race, P. (2001). The lecturers toolkit—A practical guide to learning, teaching and assessment. Great Britain: Glasgow.Red, E., French, D., Jensen, G., Walker, S. S., & Madsen, P. (2013). 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Over-constraints detection and resolution in geometric equation systems

This paper proposes an original decision-support approach to address over-constrained geometric configurations in Computer-Aided Design. It focuses particularly on the detection and resolution of redundant and conflicting constraints when deforming free-form surfaces made of NURBS patches. Based on a series of structural decompositions coupled with numerical analyses, the proposed approach handles both linear and non-linear constraints. The structural decompositions are particularly efficient because of the local support property of NURBS. Since the result of this detection process is not unique, several criteria are introduced to drive the designer in identifying which constraints should be removed to minimize the impact on his/her original design intent. Thus, even if the kernel of the algorithm works on equations and variables, the decision is taken by considering the user-specified geometric constraints. The method is illustrated on academic and industrial examples realized with our prototype software

Correctness Proof of a Geometric Constraint Solver

We present a correctness proof of a graph-directed variational geometric constraint solver. First, we prove that the graph reduction that establishes the sequence in which to apply the construction steps defines a terminating confluent reduction system, in the case of well-constrained graphs. For overconstrained problems there may not be a unique normal form. Underconstrained problems, on the other hand, do have a unique normal form. Second, we prove that all geometric solutions found using simple root-selection rules must place certain triples of elements in the same topological order, no matter which graph reduction sequence they are based on. Moreover, we prove that this implies that the geometric solutions derived by different reduction sequences must be congruent. Again, this result does not apply to overconstrained problems. Keywords: geometric constraint solving, computer aided design 1. Introduction Geometric constraint solving has broad applications in a wide range of subje..

On Pattern Occurrences in a Random Text

Consider a given pattern H and a random text T of length n. We assume that symbols in the text occur independently, and various symbols have different probabilities of occurrence (i.e., the so called asymmetric Bernoulli model). We are concerned with the probability of exactly r occurrences of H in the text T. We derive the generating function of this probability, and show that asymptotically it behaves as ffn r ae n\Gammar\Gamma1 H , where ff is an explicitly computed constant, and ae H ! 1 is the root of an equation depending on the structure of the pattern. We then extend these findings to random patterns. Key Words: Pattern occurrence, Bernoulli model, autocorrelation polynomial, generating functions, asymptotic analysis. Research of this author was supported by NSF Grants CCR-9201078 and NCR-9206315, and NATO Collaborative Grant CGR.950060. 1. INTRODUCTION Repeated patterns and related phenomena in words (sequences, strings) are known to play a central role in many facets..

Editable Representations for 2D Geometric Design

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vii 1. INTRODUCTION AND RELATED WORK : : : : : : : : : : : : : : : : 1 1.1 Trends in two dimensional sketching : : : : : : : : : : : : : : : : : : : 2 1.1.1 The descriptive approach : : : : : : : : : : : : : : : : : : : : : 2 1.1.2 The constructive approach : : : : : : : : : : : : : : : : : : : : 2 1.1.3 The declarative approach : : : : : : : : : : : : : : : : : : : : : 3 1.2 Constraint solving methods : : : : : : : : : : : : : : : : : : : : : : : 5 1.2.1 Numerical constraint solvers : : : : : : : : : : : : : : : : : : : 5 1.2.2 Constructive constraint solvers : : : : : : : : : : : : : : : : : : 6 1.2.3 Propagation methods : : : : : : : : : : : : : : : : : : : : : : : 7 1.2.4 Symbolic constraint solvers : : : : : : : : : : : : : : : : : : : : 9 1.2.5 Solvers using hybrid methods : : : : : : : : : : : : : : : : : : 9 1.2.6 Other methods : : : : : : : : : : : : : : : : : : : : : : : : : : 10 1.3 The repertoire of con..