Upper-bound estimate of reduced pressure and optimisation of scheme parameters for backward extrusion of parts with a conical cavity

Authors

DOI:

https://doi.org/10.20535/2521-1943.2026.10.2(109).356881

Keywords:

backward extrusion, part with a conical cavity, upper-bound method, reduced pressure, parametric scheme, optimisation, force regime, finite element method

Abstract

Backward extrusion of parts with a conical cavity is characterised by complex metal flow, sensitivity of the force regime to tool geometry and friction conditions, and a lack of generalised analytical models suitable for rapid engineering estimation.

The aim of this study is to develop a parametric computational scheme of the deformation zone in the backward extrusion of parts with a conical cavity and, on this basis, to obtain an analytical expression for reduced pressure by the upper-bound method.

The deformation zone was represented by a system of rigid triangular elements in the axial section, with separation of the bottom region and the wall reduction region. The reduced pressure was expressed as the sum of two components. Analytical expressions for the optimal scheme parameters were obtained for the compression and flow-turning zone, while for the wall region relationships were established between the subdivision parameters, the similarity coefficient, wall height, and the number of similar elements. Primary verification was performed using finite element method in QForm software package at an extrusion speed of 1 mm/s.

A generalised analytical expression for reduced pressure in the backward extrusion of parts with a conical cavity was obtained. It was shown that a specific feature of the backward process is a variable normalising quantity, which affects the shape of the plotted dependences and may lead to the appearance of gentle segments or local minima. The greatest influence on reduced pressure is exerted by the relative punch radius, especially in the region of its high values; the friction coefficient also significantly increases the level of reduced pressure. For the cases considered, the mean absolute relative error of the extrusion force was 12.6%.

The developed parametric model based on the upper-bound method is suitable for primary engineering estimation of the force regime in the backward extrusion of parts with a conical cavity within the considered parametric section.

Author Biographies

Anton Hranovskyi, Donbass State Engineering Academy

Donbass State Engineering Academy, Faculty of Integrated Technologies and Equipment, Department of Metal Forming by Pressure

Vitaliy Stankov, Donbass State Engineering Academy

Donbass State Engineering Academy, Faculty of Integrated Technologies and Equipment, Department of Metal Forming by Pressure

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Published

2026-06-18

How to Cite

[1]
A. Hranovskyi and V. Stankov, “Upper-bound estimate of reduced pressure and optimisation of scheme parameters for backward extrusion of parts with a conical cavity”, Mech. Adv. Technol., vol. 10, no. 2(109), Jun. 2026.

Issue

Vol. 10 No. 2(109) (2026): in progress

Section

Mechanics

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Copyright (c) 2026 Антон Грановський

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