Application of Artificial Neural Networks to the Analysis of Friction Behaviour in a Drawbead Profile in Sheet Metal Forming

Abstract

Drawbeads are used when forming drawpieces with complex shapes to equalise the flow resistance of a material around the perimeter of the drawpiece or to change the state of stress in certain regions of the drawpiece. This article presents a special drawbead simulator for determining the value of the coefficient of friction on the drawbead. The aim of this paper is the application of artificial neural networks (ANNs) to understand the effect of the most important parameters of the friction process (sample orientation in relation to the rolling direction of the steel sheets, surface roughness of the counter-samples and lubrication conditions) on the coefficient of friction. The intention was to build a database for training ANNs. The friction coefficient was determined for low-carbon steel sheets with various drawability indices: drawing quality DQ, deep-drawing quality DDQ and extra deep-drawing quality EDDQ. Equivalents of the sheets tested in EN standards are DC01 (DQ), DC03 (DDQ) and DC04 (EDDQ). The tests were carried out under the conditions of dry friction and the sheet surface was lubricated with machine oil LAN46 and hydraulic oil LHL32, commonly used in sheet metal forming. Moreover, various specimen orientations (0° and 90°) in relation to the rolling direction of the steel sheets were investigated. Moreover, a wide range of surface roughness values of the counter-samples (Ra = 0.32 μm, 0.63 μm, 1.25 μm and 2.5 μm) were also considered. In general, the value of the coefficient of friction increased with increasing surface roughness of the counter-samples. In the case of LAN46 machine oil, the effectiveness of lubrication decreased with increasing mean roughness of the counter-samples Ra = 0.32–1.25 μm. With increasing drawing quality of the sheet metal, the effectiveness of lubrication increased, but only in the range of surface roughness of the counter-samples in which Ra = 0.32–1.25 μm. This study investigated different transfer functions and training algorithms to develop the best artificial neural network structure. Backpropagation in an MLP structure was used to build the structure. In addition, the COF was calculated using a parameter-based analytical equation. Garson partitioning weight was used to calculate the relative importance (RI) effect on coefficient of friction. The Bayesian regularization backpropagation (BRB)—Trainbr training algorithm, together with the radial basis normalized—Radbasn transfer function, scored best in predicting the coefficient of friction with R2 values between 0.9318 and 0.9180 for the training and testing datasets, respectively.