Investigating Reliability of Variable Blank Holder Force Control in Sheet Drawing Under Process Uncertainties

Abstract

The blank holder force (BHF), which regulates the amount of metal drawn into the die cavity, has been used effectively to draw defect-free sheet parts. It has been shown that a properly designed variable BHF profile can provide greater drawability as compared to constant BHF. Extensive research has been carried out in the past to determine this optimal profile. However, these deterministic efforts neglect the sensitivity of this optimal BHF design to unintended process variations inherent in sheet forming. This paper investigates the reliability of optimal variable BHF in the presence of process uncertainties by minimizing the magnitude of wrinkling and fracture defects under probabilistic constraints. To demonstrate the efficacy of this approach, it analyzes the conical cup drawing of an aluminum killed deep-drawing quality steel under process uncertainties including sheet thickness, punch speed, interface friction at the punch surface, and interface friction at the die surface. The results show that probabilistic design improves the yield (probability of good parts) to 99.98% as compared to the 48.04% yield realized by the traditional deterministic design. In addition, Monte Carlo simulations verify that the probabilistic design handles the uncertainties better due to its inherent robustness. This is primarily due to the design moving away from the process constraints and at the same time balancing the probability of failure between the two failure modes.