The Mechanics of Drawing Polygonal Tube from Round on a Plug

Abstract

The mechanics of plug-drawing of regular polygonal tube directly from round through a single die, has been studied, theoretically and practically. Both upper and lower bound solutions were derived and solved numerically, using an especially developed computer programme to establish draw force and other data for a range of variables. In the upper bound solution, which combined the energy and apparent strain methods, the concept of a tube of circular section equivalent to a polygonal section was employed. The concept of the die or plug semi-angle used in axi-symmetric drawing was replaced by the notion of an equivalent semi-angle to enable account to be taken of the transformation of the circular tube to the complex shape of the polygon. The lower bound solution proved to be unreliable in predicting the draw force at larger equivalent die semi-angles. Experiments were conducted to evaluate the optimum geometrical drawtool profile including those employed in conventional industrial processes. The process of the direct drawing of round tube to any regular polygonal shape through a single die proved to be technically feasible. It was shown that an elliptical die was most efficient, and that it is unnecessary to use a profiled plug. The optimised drawtools, based on the theoretical results, were shewn to be most successful in minimising the draw force and producing well defined sections with sharp corners. The effect of diameter/thickness ratio of the undrawn tube and the reduction of area on the draw stress, were investigated experimentally for several polygonal sections. Generally, both the experimental and the theoretical results were in good agreement and draw forces could be predicted within close limits. The proven ‘technological approach’ to designing optimised section drawtools is proposed as a replacement to the current 'trial and error' methods adopted in industry.