Investigation of Lateral Surface Contour at Forging of Billets with Upsetting Ratio Above 2.5

Abstract

List of the most used functions (circle, parabola, ellipse, hyperbola, cosine, hyperbolic cosine), which are applied to approximate of billets contours at upsetting and pointed to the lack of a universal equation for these purposes, was analyzed. The advantages and disadvantages of each type of equations are pointed. The paper presents the results of upsetting of lead cylindrical specimens with a upsetting ratio 2.0-4.0. The experiment shows the stages of a “double barrel” forming on the lateral surface of a billet and its subsequent transition to a single one. The authors propose to use the “superformula” recently invented by Johan Gielis as a universal equation that allows to approximate the contour of the lateral surface of a billet at all stages of upsetting. The paper presents comparative initial data necessaries to determine upsetting force and pressure, taking into account the barrel-shape calculated by the superformula, and the coefficient of friction determined by Gubkin’s method. The equations coefficients have find, which give approximately the same results comparables to upsetting of specimens from lead, and these equations proposed for the calculation of the forming at upsetting from double-barrel to single-barrel workpiece.