Optimizing Reverse-Engineered Finite Element Models for Accurate Predictions of Experimental Measurements

This study investigates the challenges of reverse engineering in finite element modelling of sheet metal forming, specifically for the Volvo XC90 front door inner component. Advanced models incorporating anisotropic behaviour of steel and non-linear friction are compared against actual real-world measurements. The methodology involves simplifying complex continuous parameters into more manageable representative data sets and assessing model accuracy under both uniform and varied blank holder force settings, guided by measured contact pressure distributions. Although the results indicate an improvement in accuracy, they underscore the need for additional methodological improvements and more accurate replication of tooling effects to enhance the fidelity and effectiveness of these models.


Introduction
Accurate finite element modelling has emerged as a strategy to enhance cost-efficiency and streamline the development of forming tools and series production within the automotive sector.Achieving significant improvement in overall accuracy involves using advanced models that describe the anisotropic behaviour of steel sheet metal [1] and incorporate non-linear friction models [2,3].To verify model accuracy, it is essential to compare simulation predictions with actual measurements of drawn-in and strain distributions in parts produced under typical series production conditions [4].
Despite these advancements, a significant challenge remains in the field of reverse engineering: the creation of realistic models that accurately replicate existing processes.While incorporating the geometries of existing stamping tools through 3D surface scans is a relatively direct task, accurately capturing the elastic behaviour reported in actual tools and press structures adds a layer of complexity [5].Current efforts focus on developing methods that efficiently simulate these elastic effects [6,7,8], though the prevalent approach still relies on models assuming rigid tooling.This approach necessitates adjustments, particularly in modelling of the restraining effect exerted by the blank holder, as well as the simulation of material stretching in the punch area of the tool set.This is usually achieved through a series of detailed optimization iterations.These iterations are crucial for aligning model predictions IOP Publishing doi:10.1088/1757-899X/1307/1/012040 2 with actual measurements, thereby achieving models with sufficient accuracy to quantitatively describe real-world observations.
In industrial sheet metal forming it is observed that simulations align well with experimental outcomes when considering specific settings of the blank holder force.However, when the range of evaluated blank holder force settings is limited, predictions for series production scenarios outside this calibrated range may require extrapolation.To enhance the model prediction accuracy and reliability, it is essential to incorporate a wider array of blank holder force settings into these assessments.Furthermore, when experiments are conducted on industrial parts, the resulting volume of data is substantial.Consequently, an effective data reduction process is imperative, facilitating both qualitative and quantitative analyses without losing critical information.
This paper studies the first forming operation of the Volvo XC90 front door inner component [4].The proposed approach aims to simplify the complex continuous parameters describing the part drawin and part holes geometry modifications into a more manageable representative data set.The model accuracy is evaluated by comparing the model prediction with measurements performed on parts pressed in the production line at various blank holder force settings.Elastic tooling effects are approximated by adjusting the blank holder contract pressure distribution with information from measurements on trapped blanks.The reduced data set enables quantitative comparisons of experimental and model sensitivities to blank holder force adjustments.Pair correlation analysis reveals particularities of the experimental data and of the methodology to model the blank holder contact pressure.

Materials, experimental methods and finite element models
The material used in this paper is a 0.7 mm zinc coated mild steel CR4-ZM grade according to VDA 239-100 [9].Mechanical properties were used according to data from Tata Steel Aurora® Online material data base [10].ZM represents the MagiZinc Auto zinc coating containing additional magnesium and aluminium.The blanks were oiled with Anticorit PLS100T [11].
The finite element model was reverse engineered from measurements of an existing automotive part manufacturing process.The surfaces of the tools of the finite element model of the door inner automotive panel were based on 3D tool surface digitization using a HandySCAN 700 from Creaform.The trapped blank and draw panels were stamped at the stamping plant of Volvo Cars in Olofström.The model incorporates the tooling kinematics of the used mechanical press.The draw-in measurements were performed using the same HandySCAN 700.The tribology system was modelled using the TriboForm friction model.All finite element simulations were performed using AutoForm plus R10.
The pressure distribution was measured using a Fujifilm Prescale pressure measurement foil with a pressure range between 0.5 and 2.5 MPa.

Results
Figure 1 illustrates qualitatively the contact pressure distribution status of the trapped blank, a stage in the forming operation where the blank holder presses against the die under nominal force.At this moment of the forming operation the draw beads are fully engaged with the blank, yet the punch has not made contact.The forming tools utilised in this study are dimensionally precise and the 3D alignment of the blank holder and die surfaces ensures a consistent uniform gap that results in a uniform pressure distribution, as predicted by the FE model in figure 1b, hereinafter referred to as "FEM uniform".Experimental observations indicate some regions in the blank holder that exhibit partial contact as demonstrated in figure 1a.A qualitative mapping of the experimental contact pressure distribution using the "non-bearing area" option in AutoForm was realized.The contact pressure distribution of this second model (hereafter referred to as "FEM mapped") is provided in figure 1c.
Figure 2a outlines the XY plane positions of the equalizer blocks of the die set used to stamp the part.For each block, points on the trapped blank outer edge were defined as the local closest point to the centre of the block.Draw-in was calculated as the distance in a perpendicular direction from the trapped blank edge selected point towards the formed part edge (figure 2b).For the analysis in this paper, the draw-in values corresponding to these 16 points on the trapped blank were considered.The blank has four holes of different initial sizes.They were labelled with capital letters in figure 2a.In the final formed part, the hole shape and dimension change.The average diameter of the deformed hole and the absolute relative displacement of the hole centre relative to the undeformed hole centre, were determined.Examples of measured and FE element models predictions of several points on the trapped blank edge and parameters of the holes are presented in figure 3. The title of the subfigures indicates with a number the locations along the trapped blank edges, respectively, with letters combination, the parameters of the holes as labelled in figure 2a.The average diameter of hole A is labelled as A_d, etc.The relative displacement of the hole centre of hole A is labelled as A_c, etc. Increasing the blank holder force results in higher restraining of the material flow into the die cavity and consequently the draw-in decreases and the diameters of the holes increases.The expected trend of the blank holder effect on draw-in and hole diameters can be observed in both experimental and numerical generated data in figure 3. The locations 3, 7 and 13 shows a well-defined decreases rate of the draw-in for both experiments and simulations, however the absolute values and the rate of decrease can be significantly different.The FEM mapped model predicts well the absolute draw-in values and the draw-in rate change at locations 3 and 13, while the prediction accuracy of the FEM uniform model at these two locations is significantly lower.The two models predict well the size of the holes are blank holder force up to 1500 kN.At higher blank holder force settings, the models predict significantly larger average holed diameters as compared to experimental measurements.Hole positions exhibit a varied response; experimental results show negligible effects of blank holder force on hole centre positioning, while both models predict noticeable shifts.Figure 4 summarizes the predictive accuracy of the two reverse-engineered models, at a blank holder force setting equal to 1800 kN, by presenting the relative deviations from experimental results in percentage terms for each parameter.The FEM Mapped model delivers more accurate draw-in predictions compared to the FEM uniform model.The accuracy of both models is similar for average hole diameters, but predictions for hole centre shifts are less precise, although the FEM mapped model performs better.
A linear regression analysis was used to gauge the sensitivity to blank holder force variations of the draw-in and the hole parameters.For experimental data a blank holder interval between 1200 and 2200 kN was used.For the FE models 2500 kN was used for the upper limit of the blank holder force interval.In figure 5 the sensitivities of the parameters experimentally measured and calculated using FEM are presented as millimetre changes for 100 kN blank holder force adjustment.For most parameters the experimental sensitivity is smaller as compared to model predictions.Some regions of the pressed parts (locations 6, 9, 10, 11 and 12) and the diameter and locations of the deformed holes are almost insensitive to blank holder force variations.The rocker side of the pressed parts (locations 12, 14 and 15) are more sensitive as compared to the predictions of the models.In the b-pillar area (locations 0 to 3) the FEM uniform model predicts a higher sensitivity as compared to FEM mapped model.In the window frame and a-pillar side (locations 5 to 11) the FEM mapped model predicts higher sensitivity as compared to FEM uniform model.The pair correlation plots of the experimental and numerical data are presented in figure 6.The global control parameter of the process, the blank holder force was also considered in the set (labelled as BHF in figure 6).Strong correlation (above 0.8 and below -0.8) are highlighted in black or dark grey, while moderate and weak correlations appear in light grey.Experimental data (Figure 6a) reveal a heterogeneous correlation pattern, with some parameters like the 0 to 3, 13 to 15 locations, and diameters of holes B and D strongly linked to BHF.A significant number of the considered parameters are relatively weak correlated with the blank holder force and to each other (the light grey) areas in figure 6a.The FEM uniform model (figure 6b) show a very strong pair correlation between almost all considered parameters.A reduced pair correlation is observed between the position of the holes (e.g., A_c, etc.) and some draw-in parameters (12, 13 or 14).The FEM mapped model exhibits a more nuanced correlation pattern as compared to FEM uniform model.Most of the draw in parameters are strongly linked to the blank holder force and consequently to each other.Parameters that are not influenced by the blank holder force (e.g., draw-in locations 1 and 15 or the position of the holes B and C) are also weaker correlated with the rest of the parameters.

Discussion
The results presented in figure 2 and figure 3 illustrate a practical methodology to extract a manageable representative set of parameters from the continuous functions representing draw-in variations and hole edge modifications.The selected draw-in locations, adjacent to the positions of the equalizer blocks in the tool, are most affected by the common practice of shimming in press shops.These locations display the highest sensitivity to adjustments in local restraint.The irregular shape of holes in the deformed parts, differing from perfect circles was approximated by two parameters, an average diameter increase and the relative position of the corresponding centre.This reduced set of parameters provides a good estimate of the average in-plane dimensions of the deformed part.The reverse engineering effort is primarily aimed at predicting this set of parameters.Accurate prediction is a critical step before analysing plastic strain distribution and comparing strain measurements to simulations.For both drawin and hole diameter, as well as position predictions, further refinement is needed to enhance accuracy (an example of accuracy status is illustrated in figure 4), which is essential for qualitative strain comparison of measured strains and strains predicted by the models.
Incorporating measured contact pressure distribution (figure 1) into the analysis alters the restraint on material flow and improves accuracy, though further refinement is needed for a closer alignment between measurements and simulations.The discrepancy between experimental draw-in sensitivity and model predictions (figure 5) necessitates additional examination of methods to emulate the elastic effects of actual tooling, which is typically present in real-world forming tools but absent in rigid virtual tooling models.While the models can capture major trends, finer interpolation or empirical scaling may be necessary to reconcile measured and predicted values.It is interestingly to note that the consistently lower sensitivity to draw-in variations observed in practice suggests that the actual process might be less affected by fluctuations than the models imply.
Pair correlation analysis indicates significant differences between finite element model outcomes and experimental data.In the case of the finite element model featuring a uniform contact pressure distribution, there is almost a complete correlation, as shown in figure 6b.This suggests a high level of predictability across various parameters, indicating that a single parameter might be sufficient to predict the overall behaviour.However, this stands in stark contrast to what is observed experimentally (figure 6a), where the correlations are considerably weaker.The diminished correlations in the experimental data suggest the necessity of monitoring multiple parameters, possibly even all, to gain a comprehensive understanding of the forming process.Incorporating more realistic pressure distributions into the finite element model results in a decrease in correlation strength, as seen in figure 6c.Despite these adjustments, the model's outcomes still significantly differ from the experimental observations, indicating a need for further refinement of the finite element model to more accurately mirror the experimental data.
The data discussed are based on a limited set of experimental observations which were gathered using panels from the production line.To enhance the understanding of the actual process, more extensive experimental data is required.This could be achieved by employing an optical monitoring system that operates non-intrusively during series production.Collecting such data is crucial for the advancement of monitoring and control strategies, both empirical and model-based, within the process control field.

Conclusions
In this paper, challenges associated with the reverse engineering of an existing sheet metal forming process for serial production of automotive parts are highlighted.A methodology has been introduced for simplifying complex continuous parameters, which enhances the efficiency of data analysis.The limited accuracy of reverse-engineered models under relatively large variations of blank holder force settings has been revealed.The incorporation of measured contact pressure distributions into the model qualitatively enhances its overall accuracy.A more realistic contact pressure distribution has led to a weakening in correlation strength, aligning more closely with experimental observations.The emphasis on accuracy improvement underscores the need for realistic contact pressure data to enhance predictive abilities.
However, key discrepancies in experimental model predictions, particularly in draw-in sensitivity and pair correlations, have been identified.Several strategies could address these in the short term.One approach involves enhancing local restraining through iterative tuning using available FEM capabilities for location-specific adjustments.Additionally, creating distinct models for interpolation of smaller blank holder intervals could achieve greater precision in data analysis, aligning more closely with serial production practices.Empirical scaling offers another short-term solution, allowing adjustments based on observed data and practical outcomes.
In the long term, the development of methodologies to accurately replicate the elastic effects observed in actual tooling is identified as a crucial need.These effects, common in real-world forming tools, are challenging to approximate with current rigid tooling models and are labour-intensive.This underscores the necessity for innovation in tooling model development to more closely mirror realworld conditions.
A more realistic guidance for improving the model necessitates additional experimental data.The importance of gathering this data extends beyond model enhancement; it deepens the understanding of the forming process as a whole.This understanding is crucial for advancing the development of process monitoring and control strategies, ultimately leading to more efficient, safer, and cost-effective automotive manufacturing processes.

Figure 1 .
Figure 1.Qualitative visualisations of the trapped blank contact pressure distribution corresponding to (a) experimental observation, (b) FE model prediction with a uniform gap (termed "FEM uniform"), and (c) FE model with experimentally mapped contact pressures (termed "FEM mapped).

Figure 2 .
Figure 2. (a) Projection on the XY plane of the equalizer blocks, selected reference points and experimentally measured contours of the trapped blank and formed part (BHF 1800kN).(b) Detail illustrating the position of the normal segments used to characterize the local draw-in.

Figure 3 .
Figure 3. Examples of measurements and simulation results for local draw-in at several locations along the part outer contours and parameters of the holes as specified in figure 2. The figure titles indicate the corresponding locations along the outer contours and the average diameter (e.g.A_d.etc.) respectively hole centre relative displacement (e.g.A_c, etc.) of the four holes.

Figure 4 .
Figure 4. Relative differences between experiments and model predictions at 1800 kN blank holder force setting for the two FE models.

Figure 5 .
Figure 5. Experimentally measured and FE models predictions of the sensitivity to blank holder force variation for the draw-in parameters and parameters of the holes, relative positions and average diameters expressed as mm effect for 100 kN blank holder force variation.

Figure 6 .
Figure 6.Pair correlation plots of the draw-in, parameters of the holes and blank holder force (BHF) for: (a) experiments, (b) FEM uniform model and (c) FEM mapped model.