Approximation by the Lamé-Gielis formula of the shell contours at superplastic forming of sheet blanks

The paper shows that the contour of a sheet blank at all stages of superplastic forming can be described using universal formulas known as a «superformula» Gielis and «superellipse» Lamé. The work provides information on the values range of the coefficients entering into these formulas. The paper shows the results of approximation by means of the proposed formulas of shell contours manufactured by superplastic forming by different methods. The application of the «superformula» to approximate the spherical shell contours in the first stage of molding has been tested. The graphs that show the ratio of the ordinates of the contours of the spherical shells and the hemisphere are given. It is shown that the contours of the shells from the AlMg5 and Pb-38%Sn alloys are rejected in the direction of the formation of parabolas. It was found that the deviations increase with decreasing the coefficient of high-speed hardening of the alloy of the shell. The contour of AMg6 alloy shells and blanks of variable thickness, with maximum in the central zone, is diverted from the hemisphere towards the ellipse. The first stage of forming in a non-uniform temperature field forms a contour of shells, similar to an ellipse. Forming shells with the ratio of the height (H) and the radius (R) as H = 0,6R in the angular zones of the matrix forms intermediate contours of different shapes. This shape depends on the presence of lubricant between the shell and the bottom of the matrix