Determination of size-dependent friction functions in sheet metal forming with respect to the distribution of the contact pressure

The aim of this paper is to optimize the analytical model developed in previous work (Hu et al. in Determination of the friction coefficient in deep drawing, process scaling. In: Vollertsen F, Hollmann F (eds) Proceeding of the 1st colloquium of DFG priority program process scaling. BIAS-Verlag, ISBN 3-933762-14-6, Bremen, pp 27–34, 2003; Hu and Vollertsen in J Technol Plast 29:1–9, 2004; Vollertsen and Hu in Annu CIRP 55(1):291–294, 2006) with respect to the distribution of the contact pressure at the drawing radius. A size-dependent friction function was acquired based on the experimentally measured punch force from strip drawing with deflection, which can identify the tribological size effects in sheet metal forming. This function was implemented in the FEM-simulation. The distribution of the contact pressure at the drawing radius was assumed to be uniform in the previous analytical model, which is not right, since the simulated punch force versus punch travel curve showed a difference of about 11% from the experimental curve (Vollertsen and Hu in Annu CIRP 55(1):291–294, 2006). In the new analytical model the non-uniform distribution of contact pressure between the work piece and the tools was taken into account. The simulated curve using the friction function from the new model shows a better agreement with the experimental curve.