Streamlined wire drawing dies of minimum length

Abstract P revious work has established that ideal frictionless dies can be profiled to give perfect efficiency and strain uniformity in the reduction of ideal perfectly-plastic solids. The design principle for such dies, called die streamlining, requires that the principal stress directions be everywhere tangent to streamlines. This is not sufficient, however, to give a unique profile for each reduction. In the present work streamlined wire drawing profiles are determined which are believed to be the shortest possible for each reduction. These profiles have a generally concave shape with zero entrance angle, but finite exit angle. They are about half as long as the earlier sigmoidal streamlined dies which had zero exit as well as zero entrance angles. The shortest streamlined dies are believed to be advantageous for actual metal reduction since they tend to minimize the actual frictional force, thus approaching most nearly the theoretical frictionless model. The similarity of metal-forming die design and supersonic fluid nozzle design is briefly described.