Creating a Virtual Shadow of the Manufacturing of Automotive Components

Within the automotive industry, there is an increasing demand for a paradigm shift in terms of which materials are used for the manufacturing of the automotive body. Global climate goals are forcing a rapid adaption of new, advanced, sustainable material grades such as the fossil free steels and materials containing higher scrap content. With the introduction of these new and untested materials, methods for accounting for variation in material properties are needed directly in the press lines. The following study will focus on creating an initial virtual shadow of the manufacturing of a Volvo XC90 inner door panel through the application of Artificial Neural Networks (ANN). The virtual shadow differs from the concept of the digital twin by only being a virtual representation of the production line, with training data generated exclusively by numerical simulations, and having no automated communication with the physical press line control system. The virtual shadow can be used as an assistance to the press line operators to see how different press line settings and material parameter variations will impact the quality of the stamped component. The study aims to validate the virtual shadow through accurate predictions of the material draw-in measured in the physical press line.


Introduction
Within the automotive industry, there is an increasing demand for a paradigm shift in terms of which materials are used for the manufacturing of an automotive body.Global climate challenges are forcing a rapid adaption of new, advanced, sustainable material grades such as the fossil free steels and materials containing higher scrap content, where especially the latter is suspected to increase the in-coil variation of material parameters [1].The in-coil variation of material parameters of existing materials already forces manufacturing engineers to perform conservative evaluations of Finite Element simulations, where the Forming Limit Curve (FLC) is often lowered by a 10% offset or more to be on the safe side [2].With this reduction in FLC, the material is underutilized and an optimal process design cannot be achieved.Early attempts to combat this challenge was made by Sigvant & Carleer [3] and Sigvant et al. [4] running large stochastic simulations with focus on variations of material and process parameters to replicate issues that presented themselves in production of automotive body components, but did not show up in the Finite Element simulations used for the process design.These studies added another dimension to the discussion of scatter -that of process parameters such as friction and clamping force.The big issue that presents itself with running large stochastic simulation models is that it is currently only manufacturing CAE engineers that create and use the data, but the data is not available on the production floor for the operators to use directly where it is most needed.Therefore, in order to account for in-coil material parameter variation, and drifts in the process window, this study aims to create an early virtual shadow of a sheet metal forming process using an Artificial Neural Network (ANN), that can be used by the operators on the production floor.The study presented in this paper will focus on the first forming operation of the Volvo XC90 front door (inner) component.The focus will be on an accurate prediction of the draw-in of the trapped blank in 15 predefined points.The geometry of the component after the first forming operation can be seen in Figure 1 (left) and the 15 predefined points can be seen on Figure 1 (right).The ANN will be trained on data obtained from Finite Element simulations and later validated through measurements from the production line.

Data Generation
To train the ANN, data were generated through stochastic simulations using the AutoForm sigma-module.A total of five different parameters were chosen to vary to align with the needs specified in the previous section: the initial yield strength (σ 0 ), the tensile strength (R m ), the average Lankford coefficient (r m ), the lubrication amount, and the cushion force.Since the material used for the component is a VDA239 CR4 mild steel, the base Finite Element model was build using the Vegter 2017 material model.The Full Vegter material model was disregarded as it does not allow for variation of the average Lankford coefficient in the sigma-module.The base model was set up to run with a stroke rate of 14.00 [1/min], which is why the strain rate sensitive hardening behaviour of the material was considered.The hardening curves and yield surface for the CR4 mild steel can be found in Figure 2.
To investigate the impact of friction, the lubrication amount on the sheet was varied, and not the friction coefficient itself.This is due to the fact that a standard Coulomb friction model is not used, but a pressure, velocity, and strain dependent friction model is applied.The behaviour of the friction is modelled in the TriboForm software, where scans of the actual sheet and tool surfaces are used as input.These surfaces are illustrated in Figure 3  To determine the ranges which within the material parameters (σ 0 , R m , and r m ) can vary, the VDA 239-100 standard [6] was consulted.The material used for the component being a CR4 mild steel, the acceptable ranges within the VDA standard were used as the upper and lower limits of the variation.The selected values can be found in Table 1.
For the determination of the ranges of the process parameters (lubrication amount and cushion force), a more observation-based approach was taken.For the lubrication amount, measurements of the oil film on a full coil with a strip length of approximately 1550 [m] was observed.The measurement for the upper side of the coil is presented in Figure 4, where it can be seen that the lubrication amount varies between 1.00 and 2.50 [g/m 2 ].In the modelling of the base model, it was decided to use a uniformly distributed lubrication amount, why a value of 1.50 [g/m 2 ] was chosen.For the variation, the extreme values reaching 2.50 [g/m 2 ] was disregarded and the variation was chosen to be ± 0.5 [g/m 2 ].For the range of the cushion force, observations from running production were made.The applied cushion force for the batch made from the coil presented in Figure 3 was monitored, and a range between 1200 and 1800 [kN] was determined.Subsequent simulations were run to ensure that no failure occurred when applying the maximum and minimum cushion force values.
All the ranges for the parameter variation of the stochastic simulation can be found in Table 1.
The stochastic simulation was set to run 500 realizations, with the cushion force and lubrication amount being controllable variables, and the initial yield stress, tensile strength, and average Lankford coefficient being uncontrollable variables.Furthermore, a positive interaction (85%) was set between the initial yield stress and tensile strength to ensure that when initial yield stress increases, the tensile strength will not decrease.
To validate the Artificial Neural Network trained on the simulation data, measurements of three components from a production line were made.The three different components were stamped from the same coil (i.e.same material parameters and lubrication) with a variation in the cushion force used (values presented in Table 2).The measurements were taken after the first forming operation, with the press running in single-stroke mode to avoid temperature effects in the tooling.Figure 5(a) presents the complete blank outline for the three measurements, and

Methodology
An artificial neural network approach was employed in this research to predict draw-in values for the 15 measurement points.The ability of neural networks to learn and predict output values from the input data makes them a powerful tool to solve numerous real-world applications [7].The neural network architecture consists of three fundamental components: an input layer, hidden layers, and an output layer, all functioning within a feedforward framework.The neural network architecture was modeled to predict 15 measurement points based on five input parameters.The primary objective was to construct a neural network model proficient in capturing the complex relationships between these input parameters and the output measurement points.The neural network architecture can be seen in Figure 6.

Data Preprocessing
Prior to model training, the data set underwent essential pre-processing steps.This includes partitioning the data set into input and output variables and standardizing the data through the normalization process.The 'min-max' scaling method was employed for normalization, leading to data values confined within the 0 and 1 range.This normalization procedure was instrumental in ensuring consistent scaling across all the parameters, thus enhancing the models robustness.

Data Splitting
The dataset was methodically divided into two distinct subsets to facilitate model development and evaluation: • Training Set: This segment comprises 80% of the dataset and was exclusively used to model training.During this phase, the neural network model acquired the ability to understand and model the complex relationships existing between the input parameters and the output measurement points.• Testing Set: The remaining 20% of the data served as a benchmark for evaluating the model's performance.This evaluation process follows the principle of "out-of-sample" validation, offering insights into the model's predictive accuracy when applied to previously unseen data.

Out-of-sample Evaluation
To evaluate the models performance, standard evaluation metrics were utilized in the form of the Mean Squared Error (MSE) and R-squarred (R 2 ) values.The MSE measures the average magnitude of prediction errors.It is a measure of the average squared difference between predicted and actual values.Lower MSE values indicate better predictive accuracy [8], and is defined as: where n is the number of samples, y pred is the predicted value, and y true is the actual value.The R 2 quantifies the proportion of variance in the measurement points that is explained by the model.A higher R 2 indicates a better fit to the data [9] and is defined as: where y pred is the predicted value, y true is the actual value, and y mean is the mean value.

Validation with Experimental Data set
To further assess the model's prediction ability to new, unseen data, an independent experimental data set was introduced.This data set incorporated different input values entirely distinct from the training and testing data sets.The pre-trained neural network model was applied to predict the 15 output variables for these new input values.

Evaluation Metrics
The performance of the model was evaluated using two metrics: R-squared and MSE.These metrics were calculated for both the testing data set and the experimental data set, as depicted in Figure 7.The assessment outcomes provided insights into the model's capacity to predict the 15 output measurements accurately and its adaptability to new, previously unseen data.Figure 9 presented the models predictions of the experimental observations.Even though a good performance of the trained model is seen for the test and validation data, variations were observed for the predictions of the experimental observations.

Discussion
The results presented in Figure 9 shows a discrepancy between the predicted and measured values in draw-in.For the validation, the only parameter varied was the cushion force, indicating the model to be relatively insensitive to this parameter.Observing Figure 8 the test of the ANN showed an acceptable accuracy why the root cause for the discrepancy is most likely to be found in the generated data used for training.
An area assumed to be the cause of the discrepancy is the tribology model.A decision was made to set up the stochastic simulation with a uniform lubrication amount over the blank.The largest discrepancies are seen between points 4-7 and 12-14.These points are aligned with the top and bottom edges of the component, which could indicate a migration of lubrication towards these areas (slight indication of this is seen in Figure 4).It is assumed that by increasing the model complexity with respect to the lubrication distribution, a more accurate prediction can be made.

Conclusion
The presented study aimed to create a virtual shadow of the Volvo XC90 front door (inner) with focus on accurately predicting the draw-in in 15 points along the trapped blank during the first forming operation.A feedforward Artificial Neural Network (ANN) was chosen as the model base, with the training data being generated from a stochastic Finite Element simulation with 500 realizations varying three material parameters (σ 0 , R m , and r m ) and two process parameters (lubrication amount and cushion Force).The ANN was successfully trained using the simulated data and presented a good accuracy during testing.Three physical measurements with variations in the cushion force only were used to validate the ANN.The ANN was not able to accurately predict the draw-in in all 15 points for the three measurements, and showed particular bad performance around the points located along the top and bottom of the component.This discrepancy between model and measurement is expected to be caused by the assumption of uniform lubrication distribution across the blank used for the stochastic simulation, thereby disregarding the oil migration occurring in reality.

Figure 1 .
Figure 1.Volvo XC90 Front Door after first forming operation (left), and illustration of trapped blank and final component contours displayed with the 15 measurement points used in the study (right).

Figure 4 .
Figure 4. In-line measurement of lubrication amount for full coil of CR4 mild steel used for the XC90 Front Door (inner) component.

Figure 5 (
Figure 5(b) presents the draw-in values in the 15 measurement points for the three measurements.
Full component outline measurements from production run.(b) Draw-in values of the 15 measurement points.

Figure 5 .
Figure 5. Results of three draw-in measurements made in production.

Figure 8
Figure8display the models predictions for measurement points for three random observations based on the testing dataset and validation dataset.These visual representations showcase the model's predictive capabilities for the testing and validation datasets.The model demonstrated favorable performance when applied to new, un-encountered data (out-of-sample accuracy).Figure9presented the models predictions of the experimental observations.Even though a good performance of the trained model is seen for the test and validation data, variations were observed for the predictions of the experimental observations.

Figure 8 .
Figure 8. Testing of the trained Artificial Neural Network using the allocated training data.

Figure 9 .
Figure 9. Prediction of draw-in for the three measurements compared to actual measurements.

Table 1 .
Parameter variation used in the stochastic simulation.

Table 2 .
Values used in production for the three measured components.