Comparison of Computer Extended Descriptive Geometry (CeDG) with CAD in the Modeling of Sheet Metal Patterns

Abstract

The emergence of computer-aided design (CAD) has propelled the evolution of the sheet metal engineering field. Sheet metal design software tools include parameters associated to the part’s forming process during the pattern drawing calculation. Current methods avoid the calculation of a first pattern drawing of the flattened part’s neutral surface, independent of the forming process, leading to several methodological limitations. The study evaluates the reliability of the Computer Extended Descriptive Geometry (CeDG) approach to surpass those limitations. Three study cases that cover a significative range of sheet metal systems are defined and the associated solid models and patterns’ drawings are computed through Geogebra-based CeDG and two selected CAD tools (Solid Edge 2020, LogiTRACE v14), with the aim of comparing their reliability and accuracy. Our results pointed to several methodological lacks in LogiTRACE and Solid Edge that prevented to solve properly several study cases. In opposition, the novel CeDG approach for the computer parametric modeling of 3D geometric systems overcame those limitations so that all models could be built and flattened with accuracy and without methodological limitations. As additional conclusion, the success of CeDG suggests the necessity to recover the relevance of descriptive geometry as a key core in graphic engineering.

Surfaces Intersection and Flattening in 3D Models Through Computer Extended Descriptive Geometry (CeDG)

“…The fail of Solid Edge 2023 to achieve the flat pattern of a particular surfaces' configuration agrees with other comparative studies [13]. Although a more complete analysis of this lack exceeds the scope of this paper, the strategy of current CAD technology for surfaces' flattening seems limited to a set of configurations previously defined in the software.…”

“…The usual procedure used in DG to calculate the intersection between two surfaces consists of defining it by means of their projections, which are obtained through interpolation on a set of points belonging to them. The points are obtained by means of DG techniques, which are applied iteratively, so that the accuracy and complexity of the resulting curve is proportional to the number of points attained [13]. The CeDG approach uses an extension of the DG procedures, taking advantage of the existence of an exact algebraic function that defines the sought intersection curve, which represents the algebraic calculation of a general point of this curve.…”

“…In the case of the latter, a demolding operation has also been added to ensure the desired conicity in each case. Once the two solids were created, a thickness of 0.0001 mm was applied because Solid Edge 2023 does not allow to work with the neutral surface (fiber) of the hopper, as indicated in the methodology pointed out in Prado-Velasco and Ortiz-Marín [13] and the minimum thickness value allowed by this software is the one indicated above. In figure 15, D u cylinder is shown together with the intersection curve between it and the previous D f straight truncated cone.…”

“…The integrity of geometrical objects (i.e. handle without approximation) that characterizes CEDG [10,13] is kept also in this method.…”

Intersection and Flattening of Surfaces in 3D Models through Computer-Extended Descriptive Geometry (CeDG)

“…The usual procedure used in DG to calculate the intersection between two surfaces consists of defining it by means of their projections, which are obtained through interpolation on a set of points belonging to them. The points are obtained by means of DG techniques, which are applied iteratively so that the accuracy and complexity of the resulting curve are proportional to the number of points attained [17]. The CEDG approach extends the DG procedures to find a parametric mathematical function that defines the sought intersection curve.…”