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1

Upper bound analysis of bimetallic rod extrusion process through rotating conical dies

Haghighat H., Mahdavi M. M.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

627--637

EN

In this paper, an upper bound approach is used to analyze the bimetallic rod extrusion process through rotating conical dies. By extending the kinematically admissible velocity field for mono-metal rod extrusion to the bimetallic rod extrusion process, the internal power and the power dissipated on frictional and velocity discontinuity surfaces are evaluated. Then, by equating the total power with the external power produced by axial movement of the punch and the power induced by rotation of the die, the relative extrusion pressure is determined. The extrusion process of bimetallic rods composed of a copper sleeve layer and an aluminium core layer through a conical rotating die is also simulated by using the finite element code ABAQUS. The analytical results are compared with the results given by the finite element method. These comparisons show a good agreement.

2

A generalized upper bound solution for extrusion of bi-metallic rectangular cross-section bars through dies of any shape

Haghighat H., Amjadian P.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 1

105--116

EN

In this paper, a generalized upper bound solution is developed for extrusion of bi-metallic rectangular cross-section bars through dies of any shape. The internal, shearing and frictional power terms are derived and they are used in the upper bound model. By using the developed upper bound model, the extrusion pressures for two types of die shapes, an optimum wedge shaped die as a linear die profile and an optimum streamlined die shape as a curved die profile, are determined. The corresponding results for those two die shapes are also determined by using the finite element code and compared with the upper bound results. These comparisons show a good agreement.

PL

W pracy wyprowadzono uogólnione rozwiązanie ograniczenia górnego problemu wytłaczania bimetalowych belek o przekroju prostokątnym za pomocą tłoczników o dowolnym kształcie. Wyznaczono wyrażenia potęgowe opisujące wewnętrzne, ścinające oraz tarciowe obciążenia i zastosowano je w modelu matematycznym omawianego zagadnienia. Zaproponowana metoda badań pozwoliła na określenie nacisku podczas wytłaczania elementów przy użyciu dwóch typów tłocznika – optymalnego klinowego o profilu liniowym oraz tłocznika o zarysie krzywoliniowym, opływowym. W obydwu przypadkach obliczenia porównano z wynikami uzyskanymi z metody elementów skończonych. Porównanie to wykazało dobrą zgodność rozwiązania ograniczenia górnego z rezultatami MES.

3

A simple analytical model of asymmetric rolling

Halloumi A., Desrayaud Ch., Bacroix B., Rauch E., Montheillet F.

Archives of Metallurgy and Materials

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2012

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Vol. 57, iss. 2

425-435

EN

An original analytical method is proposed for modeling asymmetric rolling (ASR) of metal sheet. It is based on a uniform strain field depending on a single optimization parameter, viz. the entry velocity of the sheet. The shear and normal strains associated with an ASR pass are derived analytically. Moreover, it is shown that the entry velocity almost coincides with the outer linear velocity of the slower roll, as far as ASR is sufficiently asymmetric. In that case, closed form formulae are available for the main rolling parameters such as the overall power dissipated and the two rolling torques. These results can be straighforwardly used for practical applications.

PL

Zaproponowano oryginalną metodę analityczną do modelowania asymetrycznego walcowania blachy. Model jest oparty na jednolitym obszarze odkształcenia zależnym od jednego parametru optymalizacji tj. prędkości wejścia arkusza. Naprężenia ścinanające i normalne związane z przebiegiem asymetrycznego walcowania wyprowadzone są analitycznie. Co więcej pokazano, że prędkość wejścia niemal zbiega się z zewnętrzną prędkością liniową wolniejszego walca, o ile asymetryczne walcowanie jest wystarczająco asymetryczne. W takim przypadku zamknięte równania są dostępne dla głównych parametrów walcowania takich jak całkowita moc rozpraszania i dwa momenty obrotowe walcowania. Wyniki te mogą być bezpośrednio wykorzystywane do zastosowań praktycznych.

4

Analytical methods application to the study of tube drawing processes with fixed conical inner plug: Slab and Upper Bound Methods

Rubio M. E.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 14, nr 1-2

119--130

EN

Purpose: The paper analyses the thin-walled tube drawing processes made in conical converging dies with fixed inner plugs. Design/methodology/approach: The analysis has been made by analytical methods. Concretely, the Slab Method (SM), with and without friction effects, and the Upper Bound Method (UBM) have been appliced. In this last case, the plastic deformation zone has been modelled by Triangular Rigid Zones (TRZ). The friction between the out surface of the tube and the die, and between the inner surface of the tube and the plug has been modelled by Coulomb friction. Besides, the change in the diameter of the tube has been considered negligible during the process, then, the forming process can be assumend that it is made under a state of plane strain. Findings: The results obtained by each method have been compared between them and, besides, with the obtained ones by the Finite Element Method (FEM) and the experimental ones extract from the literature about the theme. It has been able to be proven that all of them are reasonably close to a value for a certain set of parameters values. Research limitations/implications: This work is a first approache to the problem. As suggestion for future researches it is possible to remark a study of the different triangular rigid zones configurations in order to identify the TRZ pattern that requires smaller energy consumption. Practical implications: Unless it was needed to know a great number of outputs, the analytical method scan be a good option and, especially, the Upper Bound Method since, besides of completing and improving the classical analysis of other metal forming processes previously. Originality/value: The paper is orginal since the bibliographical review has allowed testing that previous works about the tubes drawing analysis made by the Upper Bound Method under plane strain and Coulomb friction conditions did not exist until the moment.