## 4 Conclusions  
In this article, the authors put emphasis on modelling the friction phenomenon in SMF using RBF ANNs. Since it is analytically difficult to find complex interactions between input parameters and the COF value, ANNs can acquire the ability to predict the COF from a set of training data. The main conclusions from the experimental research and neural modelling are as follows:  
* Under lubrication with both oils considered (S100+ and S300), the value of the COF increased with decreasing oil pressure. This relation is observed for the whole range of nominal pressures analysed. * The higher the nominal pressure value, the smaller the difference between the COF determined for different oil pressures. So, in the case of pressurised lubrication, the viscosity of the oil becomes less important in SMF under high pressures. * The developed concept of pressurised lubrication is most effective at relatively small nominal pressures of 2-4 MPa. This range of nominal pressures corresponds to the actual rip pressures when forming deep-drawing steel sheets. * Under conditions of dry friction, the values obtained for the COF rise above 0.3, while under lubrication conditions, even without pressure-assisted lubrication, the COF values are reduced by at least 50%. Figure 15: (**a**) Comparison of the actual and predicted values of the COF and (**b**) values of the MSE during the training process of the RBF-8-9-1-1 network. * As the nominal pressure increases, the value of the coefficient of lubrication effectiveness decreases exponentially. Moreover, the lubrication efficiency clearly decreases with the value of the oil pressure. * Several combinations of input parameters were tested using RBF ANNs. Among the sheet surface roughness parameters considered (Sa, Sq, Ssk, and Sku), the root mean square height Sq was found to be the most sensitive in relation to the COF. * The smallest error for the test set (0.000292) was characteristic of the RBF network with nine neurons in the hidden layer. The ANN prediction value for the training set, determined by the coefficient of determination R2, was 0.989. * ANN response surfaces showed very good agreement with the experimental data, and the main experimental observations are also confirmed by the RBF ANN predictions. The experimental results show that pressure-assisted lubrication in the blankholder area in sheet metal forming allows for a reduction of COF compared with conventional lubrication conditions. This confirms the correctness of the concept of the device for reducing friction in the flange area of the drawpiece. The use of channels in the construction of the die to supply lubricant to the zone of contact between the sheet metal and the surface of the stamping tool under the appropriate pressure, by reducing the value of the COF, will enable obtaining greater strains on the sheet metal without risk of fracture. Further research is required for the optimal arrangement of the supply channels and the selection of a lubricant with an appropriate viscosity and appropriate lubricant pressure for the specific conditions of forming various grades of sheet metal. One of the basic limitations of neural networks is the possibility of predicting output parameters only in the range of input parameters used to train the RBF ANN. The second limitation of the neural network model is the strong relationship between the amount of training data and the quality of prediction. Therefore, it is planned to extend the variability range of input parameters and conduct more experiments for oils with different viscosities. In this paper, only four surface roughness parameters were considered, which, according to the literature, are the most representative in the analysis of the friction phenomenon in sheet metal forming. It is planned to check the correlation of the COF with other roughness parameters. The influence of pressure-assisted lubrication on the final surface roughness of the drawpieces also requires further research. Conceptualization, T.T., K.S. and M.S. ; methodology, T.T., K.S.