Numerical simulation of friction in metal forming using a halfspace model

Sheet and bulk metal forming are widely used manufacturing methods. The industrial trend towards function integration leads to a demand for workpieces having features of both methods. The new forming technology sheet-bulk metal forming is a promising approach to manufacture workpieces with functional elements. Tribological aspects generally play an important role in metal forming processes. Especially for the formability of functional elements friction is very important. The coexistence of low and high contact pressures is characteristic of sheet-bulk metal forming and presents a challenge for the friction modelling. The surfaces of tool and workpiece are always rough, so that initial contact only occurs at the asperities of surface roughness. Consequently for small and moderate loads the real contact area is smaller than the apparent contact area. Surface traction can only occur in the real contact area, so that it is necessary to determine the real contact area in order to study the tribological behaviour of contact pairs. In order to get an accurate determination of the real contact area it is necessary to calculate the surface deformation in a three-dimensional model and to validate the simulation model by measurements. The halfspace approach has the significant advantage that only the surface has to be discretised, while in a Finite Element Analysis the whole bulk has to be discretised. Consequently the numerical effort, and thus the calculation time, in the halfspace model are much lower than in FE-modelling. The numerical solution scheme based on the halfspace theory is presented in this paper. Results of the calculation of the real contact area of rough surfaces are compared to experimental data from ultrasonic inspection. Friction coefficients calculated with the halfspace model are compared to results of strip drawing tests.