The fundamental equations for the drawing of tubing with a moving mandrel have been solved for the simplified cases of both cold-drawing and hot-drawing of thin-walled tubing through a stationary die. For the solution of the fundamental equation, a method of successive improvement can be used for any contour of the tools and any shape of the stress-strain curve. Algebraic solutions were developed for tapered tools and for a metal exhibiting a constant flow stress in cold-working, and for a metal with the flow stress depending exponentially upon the strain rate in hot-working. The effects of the die and punch contours and the friction coefficients between the metal and the die and punch, respectively, on the stresses in the metal, the draw forces, and the limits of drawing were determined. The calculations reveal that, with a small die angle and high friction on the mandrel, the process resembles extrusion rather than drawing, the limit being determined by the strength of the die rather than by the tensile strength of the metal.

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