Application of the Gradient-Boosting with Regression Trees to Predict the Coefficient of Friction on Drawbead in Sheet Metal Forming

Correct design of the sheet metal forming process requires knowledge of the friction phenomenon occurring in various areas of the drawpiece. Additionally, the friction at the drawbead is decisive to ensure that the sheet flows in the desired direction. This article presents the results of experimental tests enabling the determination of the coefficient of friction at the drawbead and using a specially designed tribometer. The test material was a DC04 carbon steel sheet. The tests were carried out for different orientations of the samples in relation to the sheet rolling direction, different drawbead heights, different lubrication conditions and different average roughnesses of the countersamples. According to the aim of this work, the Features Importance analysis, conducted using the Gradient-Boosted Regression Trees algorithm, was used to find the influence of several parameter features on the coefficient of friction. The advantage of gradient-boosted decision trees is their ability to analyze complex relationships in the data and protect against overfitting. Another advantage is that there is no need for prior data processing. According to the best of the authors' knowledge, the effectiveness of gradient-boosted decision trees in analyzing the friction occurring in the drawbead in sheet metal forming has not been previously studied. To improve the accuracy of the model, five MinLeafs were applied to the regression tree, together with 500 ensembles utilized for learning the previously learned nodes, noting that the MinLeaf indicates the minimum number of leaf node observations. The least-squares-boosting technique, often known as LSBoost, is used to train a group of regression trees. Features Importance analysis has shown that the friction conditions (dry friction of lubricated conditions) had the most significant influence on the coefficient of friction, at 56.98%, followed by the drawbead height, at 23.41%, and the sample width, at 11.95%. The average surface roughness of rollers and sample orientation have the smallest impact on the value of the coefficient of friction at 6.09% and 1.57%, respectively. The dispersion and deviation observed for the testing dataset from the experimental data indicate the model's ability to predict the values of the coefficient of friction at a coefficient of determination of R2 = 0.972 and a mean-squared error of MSE = 0.000048. It was qualitatively found that in order to ensure the optimal (the lowest) coefficient of friction, it is necessary to control the friction conditions (use of lubricant) and the drawbead height.