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The anisotropy of frictional resistances is often omitted in finite element method (FEM) based numerical modelling of industrial processes of sheet metal forming. The aim of this paper is to analyse the effect of anisotropy of frictional phenomena on the formability of drawpieces. As a benchmark experiment, the formability of cylindrical cups is carried out, and as a benchmark material the deep drawing quality (DDQ) steel sheets are used. The effect of friction phenomena on the formability of cylindrical cups is studied using finite element based program ABAQUS/Standard 3DExperience R2016x HF2. The results of predicted location and height of ears allow concluding that material and frictional anisotropy of sheet metals are the main factors that determine high conformity of the finite element based numerical simulation results with the experiments. Comparison of numerical results demonstrates great potential of Hill yield criterion incorporated with the anisotropic friction model in accurate prediction of earing.

Drawbeads are elements of the stamping die and they are used to compensate material flow resistance around the perimeter of the drawpiece or to change the stress state in specific regions of the drawpiece. This paper presents the results of experimental and numerical analyses of tests of sheet metal flowing through a drawbead. The tests have been carried out using a special tribological simulator of the drawbead. Experimental tests to determine the coefficient of friction (COF) have been carried out for three widths of sheet metal strip and two drawbead heights. The three-dimensional (3D) elastic-plastic numerical computations were performed using the MSC. Marc program. Special attention was given to the effect of material flow through the drawbead on the distribution of the normal stress on the tool-sheet interface. The mesh sensitivity analysis based on the value of the drawing force of the specimen being pulled through the drawbead allowed an optimal mesh size to be determined. The errors between the numerically predicted values of the COF and the values experimentally determined ranged from about 0.95% to 7.1% in the cases analysed. In the case of a drawbead height of 12 mm, the numerical model overestimated the value of the COF for all specimen widths analysed. By contrast, in the case of a drawbead height of 18 mm, all experimentally determined friction coefficients are underestimated by Finite Element Method (FEM). This was explained by the different character of sheet deformation under friction and frictionless conditions. An increase in the drawbead height, with the same sheet width, increases the value of the COF.Metals 2020, 10, 45 2 of 15 by Nine [9]. Nine's drawbead simulator mainly tests the friction condition between the blankholder and the die, which fails to reflect the change of coefficient of friction (COF) in each region caused by different stress modes. Several authors have conducted research to better understand the frictional phenomena in sheet metal forming [10][11][12][13] and mechanics of sheet deformation at the drawbeads [14-16] and over the years, analytical, semi-empirical and numerical approaches have been developed.

This article presents the results of an experimental investigation of the frictional resistance arising in a drawbead during sheet metal forming. The frictional characterization of DC04 deep drawing quality steels commonly used in the automotive industry is carried out using a friction simulator. The effects of some parameters of the friction process on the value of the coefficient of friction have been considered in the experimental investigations. The friction tests have been conducted on different strip specimens, lubrication conditions, heights of drawbead and specimen orientations in relation to the sheet rolling direction. The results of drawbead simulator tests demonstrate the relationship that the value of the coefficient of friction of the test sheets without lubrication is higher than in the case of lubricated sheets. The lubricant reduces the coefficient of friction, but the effectiveness of its reduction depends on the drawbead height and lubrication conditions. Moreover, the effectiveness of the reduction of the coefficient of friction by the lubricant depends on the specimen orientation according to the sheet rolling direction. In the drawbead test, the specimens oriented along the rolling direction demonstrate a higher value of coefficient of friction when compared to the samples cut transverse to the rolling direction. The smaller the width of the specimen, the lower the coefficient of friction observed. The difference in the coefficient of friction for the extreme values of the widths of the specimens was about 0.03–0.05. The use of machine oil reduced the coefficient of friction by 0.02–0.03 over the whole range of drawbead heights. Heavy duty lubricant even reduced the frictional resistances by over 50% compared to dry friction conditions. The effectiveness of friction reduction by machine oil does not exceed 30%.

This article reports a proposed approach to a frictional resistance description in sheet metal forming processes that enables the determination of the friction coefficient value under a wide range of friction conditions, without performing timeconsuming experiments. The motivation for this proposal is the fact that there exists a considerable amount of factors that affect the friction coefficient value and as a result building analytical friction model for specified process conditions is practically impossible. In this proposed approach, a mathematical model of friction behaviour is created using multiple regression analysis and artificial neural networks. The regression analysis was performed using a subroutine in MATLAB programming code and STATISTICA Neural Networks was utilized to build an artificial neural networks model. The effect of different training strategies on the quality of neural networks was studied. As input variables for regression model and training of radial basis function networks, generalized regression neural networks and multilayer networks, the results of strip drawing friction test were utilized. Four kinds of Al-Mg alloy sheets were used as a test material.