The development of models for the coefficient of friction is difficult due to many factors influencing its value and many tribological phenomena that accompany contact between metals (i.e., flattening, ploughing, adhesion), the influence of which also depends on the friction conditions. Therefore, developing an analytical model of friction is difficult. In this article, the CatBoost machine learning algorithm, newly developed by Yandex researchers and engineers, is used for modelling and parameter identification of friction coefficients for three grades of deep-drawing quality steel sheets. Experimental tests to determine the friction coefficient were carried out using the strip drawing method with the use of a specially designed tribological device. Lubrication conditions, normal force, and the surface roughness of countersample surfaces were used as input parameters. The friction tests were conducted in dry friction and lubricated conditions with three grades of oils with a wide range of viscosities. Different transfer functions and various training algorithms were tested to build the optimal structure of the artificial neural networks. An analytical equation based on the parameters that were being investigated was created to calculate the COF of each material. Different methods of partitioning weight were employed for the expected COF to assess the relative importance (RI) and individual feature’s relevance. A Shapley decision plot, which uses cumulative Shapley additive explanations (SHAP) values, was used to depict models for predicting COF. CatBoost was able to predict the coefficient of friction with R² values between 0.9547 and 0.9693 as an average for the training and testing dataset, depending on the grade of steel sheet. When considering all the materials that were tested, it was discovered that the Levenberg–Marquardt training algorithm performed the best in predicting the coefficient of friction.

The article presents the results of investigations into the depth of the plastically deformed surface layer in the roller burnishing process. The investigation was carried out in order to obtain information on the dependence relationship between the depth of plastic deformation, the pressure on the roller and the braking torque. The research was carried out according to the original method developed by the authors, in which the depth of plastic deformation is increased by applying a braking torque to the burnishing roller. In this method, it is possible to significantly increase (up to 20%) the depth of plastic deformation of the surface layer. The tests were carried out on a specially designed device on which the braking torque can be set and the force of the rolling resistance of the roller during burnishing can be measured. The tests were carried out on specimens made of C45 heat-treatable carbon steel. The dependence of the depth of the plastically deformed surface layer was determined for a given pressure force and variable braking moments. The depth of the plastically deformed layer was measured on the deformed end face of the ring-shaped samples. The microhardness in the sample cross-section and the evolution of the microstructure were both analysed.

Measuring errors caused by deformation (flattening) of a measured object appear under the influence of pressure force and weight of the measured object. Plastic strain, arising at the contact of a measured object and an undeformable contact tip of a measuring device, can be calculated by applying the Hertz plastic solution and the hypothesis of plastic strain. In a small area of contact between two bodies pressing against one another with force F, there appears the so-called contact stress. It can sometime reach very high values, exceeding the yield point, even when the contact pressure is relatively small. In the present work, the authors describe a theoretical solution to the problem of plastic strain between two bodies. The derived relationships enable to calculate force F during measurements of a deformable object by means of an instrument with an undeformable, spherical measuring tip. By applying the τ_max hypothesis, a solution was obtained for the force F in an inexplicit form. The theoretical solution was verified with the digital simulation and experimental measurement. With the FEM method, the limit length gage was modeled in interaction with the measured shaft of a diameter d larger than the nominal one of Δl value.

This paper is devoted to the determination of the coefficient of friction (COF) in the drawbead region in metal forming processes. As the test material, AW-5251 aluminium alloys sheets fabricated under various hardening conditions (AW-5251-O, AW-5251-H14, AW-5251-H16 and AW-5251H22) were used. The sheets were tested using a drawbead simulator with different countersample roughness and different orientations of the specimens in relation to the sheet rolling direction. A drawbead simulator was designed to model the friction conditions when the sheet metal passed through the drawbead in sheet metal forming. The experimental tests were carried out under conditions of dry friction and lubrication of the sheet metal surfaces with three lubricants: machine oil, hydraulic oil, and engine oil. Based on the results of the experimental tests, the value of the COF was determined. The Random Forest (RF) machine learning algorithm and artificial neural networks (ANNs) were used to identify the parameters affecting the COF. The R statistical package software version 4.1.0 was used for running the RF model and neural network. The relative importance of the inputs was analysed using 12 different activation functions in ANNs and nine different loss functions in the RF. Based on the experimental tests, it was concluded that the COF for samples cut along the sheet rolling direction was greater than for samples cut in the transverse direction. However, the COF’s most relevant input was oil viscosity (0.59), followed by the average counter sample roughness Ra (0.30) and the yield stress R_p0.2 and strength coefficient K (0.05 and 0.06, respectively). The hard sigmoid activation function had the poorest R² (0.25) and nRMSE (0.30). The ideal run was found after training and testing the RF model (R² = 0.90 ± 0.028). Ra values greater than 1.1 and R_p0.2 values between 105 and 190 resulted in a decreased COF. The COF values dropped to 9–35 for viscosity and 105–190 for R_p0.2, with a gap between 110 and 130 when the oil viscosity was added. The COF was low when the oil viscosity was 9–35, and the Ra was 0.95–1.25. The interaction between K and the other inputs, which produces a relatively limited range of reduced COF values, was the least relevant. The COF was reduced by setting the R_p0.2 between 105 and 190, the Ra between 0.95 and 1.25, and the oil viscosity between 9 and 35.

This article concerns the application of the FEM method for the prediction of stress and deformation states in the workpiece during diamond sliding burnishing (DSB). An updated Lagrange (UL) description was used to describe the phenomena at a typical incremental step. The states of strain and strain rate are described by non-linear relationships without linearization. The material parameters were estimated during tensile tests to determine the characteristics of the 41Cr4 steel. Its hardness was also tested. Its aim was to prepare a table with the material properties of the above-mentioned steel and its implementation for numerical analyses. A Cowper–Symonds material model was used to model the displacement process of the wedge on an elastic/visco-plastic body reflecting the DSB process. The computer model was validated, and a good convergence of the results was obtained. Applications in the ANSYS/LS-Dyna program were developed to simulate the process of DSB. The results of numerical analyses were presented, among others, to explain the influence of the rake angle on the condition of the surface after machining, as well as the phenomenon of chip formation. The results of numerical simulations were verified experimentally on a test stand.

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.