Modelling and parameter identification of coefficient of friction for deep-drawing quality steel sheets using the CatBoost machine learning algorithm and neural networks

Abstract

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.