Theoretical considerations of drawing a round tube through a conical die and a polygonal plug

Abstract

Theoretical and practical investigations in the drawing of the following sections directly from an entirely round stock have been reported: polygonal bars, polygonal tubes with the outside and bore surfaces geometrically similar, and tubes with the outside polygonal surface and circular bore, The derived theoretical solutions enabled the industrialists to design tools to manufacture tubing or bar stocks directly from round with minimum amount of energy being dissipated in the drawing process; the resulting optimal tools also produced relatively superior polygonal stocks. This thesis extends the theoretical analysis to the manufacture of a polygonal tube by drawing an entirely round stock through a deformation passage formed by a conical die and a polygonal plug.Using a prescribed shape of the plug and a regular conical die, two solutions of the drawing loads were derived: the 10V\erbound and the upper bound. The laver bound load considered the homogenecusdefonnation and the friction work and ~,hus ignored the redundant work. The upper bound value • of the drawing force was derived fran the minimumenergy associated with the velocity pattern obtained by conformal mapping. Unlike the axisymnetric drawing on a mandrel, the plug profile was carplex; an equivalent plug semi-angle was therefore used to enable canparisons to be madebetween deformation passages formedby a knovn die profile and the polygonal plugs and also to facilit~te the optirr:rrzationof the process parameters. The graphs of the drawing forces drawn against the various parameterrs such as the die angle, 'the equivalent plug angle, the reduction of area as well as friction shewed trends s~lar to those tried practically and reported in the literature of polygonal tube drawing directly frcm round stock