Luca Pagani

Curvature based sampling of curves and surfaces

Efficient sampling methods enable the reconstruction of a generic surface with a limited amount of points. The reconstructed surface can therefore be used for inspection purpose. In this paper a sampling method that enables the reconstruction of a curve or surface is proposed. The input of the proposed algorithm is the number of required samples. The method takes into account two factors: the regularity of the sampling and the complexity of the object. A higher density of samples is assigned where there are some significant features, described by the curvature. The analysed curves and surfaces are described through the B-splines spaces. The sampling of surfaces generated by two or more curves is also discussed.

Design of Deformable Tools for Sheet Metal Forming

Traditionally, industrial sheet metal forming technologies use rigid metallic tools to plastically deform the blanks. In order to reduce the tooling costs, rubber or flexible tools can be used together with one rigid (metallic) die or punch, in order to enforce a predictable and repeatable geometry of the stamped parts. If the complete tooling setup is built with deformable tools, the final part quality and geometry are hardly predictable and only a prototypal production is generally possible. The aim of this paper is to present the development of an automatic tool design procedure, based on the explicit FEM simulation of a stamping process, coupled to a geometrical tool compensation algorithm. The FEM simulation model has been first validated by comparing the experiments done at different levels of the process parameters. After the experimental validation of the FEM model, a compensation algorithm has been implemented for reducing the error between the simulated component and the designed one. The tooling setup is made of machined thermoset polyurethane (PUR) punch, die, and blank holder, for the deep drawing of an aluminum part. With respect to conventional steel dies, the plastic tools used in the test case are significantly more economic. The proposed procedure is iterative. It allows, already after the first iteration, to reduce the geometrical deviation between the actual stamped part and the designed geometry. This methodology represents one step toward the transformation of the investigated process from a prototyping technique into an industrial process for small and medium batch sizes.

Hierarchical Metamodeling: Cross Validation and Predictive Uncertainty

At Esaform 2013 a hierarchical metamodeling approach had been presented, able to combine the results of numerical simulations and physical experiments into a unique response surface, which is a “fusion” of both data sets. The method had been presented with respect to the structural optimization of a steel tube, filled with an aluminium foam, intended as ananti-intrusion bar. The prediction yielded by a conventional way of metamodeling the results of FEM simulations can be considered trustworthy only if the accuracy of numerical models have been thoroughly tested and the simulation parameters have been sufficiently calibrated. On the contrary, the main advantage of a hierarchical metamodel is to yield a reliable prediction of a response variable to be optimized, even in the presence of non-completely calibrated or accurate FEM models. In order to demonstrate these statements, in this paper the authors wish to compare the prediction ability of a “fusion” metamodel based on under-calibrated simulations, with a conventional approach based on calibrated FEM results. Both metamodels will be cross validated with a “leave-one-out” technique, i.e. by excluding one experimental observation at atime and assessing the predictive ability of the model. Furthermore, the paper will demonstrate how the hierarchical metamodel is able to provide not only an average estimated value for each excluded experimental observation, but also an estimation of uncertainty of the prediction of the average value.

Metamodeling Based on the Fusion of FEM Simulations Results and Experimental Data

In this Paper an Innovative Multistage Metamodeling Technique is Proposed for Linking Datacoming from Two Different Sources: Simulations and Experiments. the Model is Hierarchical, in Thesense that One Set of Data (the Experiments) is Considered to be more Reliable and it is Labeled as“high-Resolution” and the other Set (the Simulations) is Labeled as “low-Resolution”. the Results Ofexperiments is Obviously Fully Accurate, Except for the only Approximation due to the Measurementsystem and Given the Intrinsically Aleatory Nature of all Real Experiments. in the Proposed Approach,Gaussian Models are Used to Describe Results of Computer Experiments because they are Flexible Andthey can Easily Interpolate Data Coming from Deterministic Simulations. A Second Stage Model is Used,in Order to Link the Prediction of the First Model to the Real Experimental Data. for the Linkage Model,as in the First Stage, a Gaussian Process is Used. in this Second Stage a Random Parameter can be Addedto the Model, Known as Nugget, in Order to take into Account the Process Variability. this Kind Ofmetamodeling can have Different Purposes: Adjusting or Tuning the Simulations, Having a Better Tool Todrive the Design Process, Making an Optimization of a Parameter of Interest. in the Paper, its use Foroptimization of a Single Responsey with Two Design Variables x1 and x2 is Demonstrated. the Approachis Applied for Modeling the Crash Behavior in Three Point Bending of Metal Foam Filled Tubes.