Application of G. Lame’s and J. Gielis’ formulas for description of shells superplastic forming

¹ Pryazovskyi State Technical University, Universytetska, 7, Mariupol, 87555, Ukraine
² Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, St. Petersburg, 195251, Russia
³ Tyumen Industrial University, Volodarskogo str., 38, Tyumen, 625000, Russia

^* Corresponding author: artiukh@mail.ru

Abstract

The paper shows that the contour of a sheet blank at all stages of superplastic forming can be described by application of the universal equations known as a "superformula" and "superellipse". The work provides information on the ranges of values of the coefficients entering these equations and shows that their magnitudes make it possible to additionally determine the level of superplastic properties of the workpiece metal, the shape of the shell being manufactured, the stage of superplastic forming, and the presence of additional operations to regulate the flow of the deformable metal. The paper has the results of approximation by the proposed equations of shell contours that manufactured by superplastic forming by different methods.