Mixed lubrication friction model including surface texture effects for sheet metal forming

In deep drawing processes, mixed lubrication friction regime is common in which the friction condition is governed by solid–solid asperity contacts and lubricant pressure. In this study, a friction model in the mixed lubrication regime is developed that accounts for the effect of the surface topographies of sheet and tool on the lubricant pressure distribution. The overall friction due to solid–solid asperity contacts and lubricant pressure is determined using a coupled hydrodynamic and boundary friction models. The model is utilized in an in-house FE code (DiekA) for deep drawing simulations. In the FE simulations, the lubricant pressure is determined by solving the average Reynolds equation. The flow factors required in the average Reynolds equation are determined separately using measured tool and sheet surface topographies. Cross-die experiments are performed at different lubricant amounts to validate the friction model at a component level. The results show that punch force vs. displacement and strain field from experiments and FE simulations (using the new friction model) correlate very well.