Keywords: bending, experiments, finite element method, spring-back.

Because of the low cost of the blank, sheet metal forming is a very popular process and is widely used by the sheet metal industry to create a large number of products. Bending is a forming process by which a variety of different shapes can be manufactured. Unconstrained cylindrical bending is a process in which a punch bends a metal sheet pressing it to the bottom of the die. In this process there is no blank holder so that deformation is bending dominant [1].

In the bending process the stress state is extremely complex. When the forming punch is retracted, the elastic components of the stress cause spring-back that increases the angle of the bent part.

In this paper, a series of experiments have been performed on a laboratory special apparatus realized for bending testing. The machining has been performed through a spindle that moves along three axes X, Y, Z. The spindle performs the movements, along the axes X and Y, necessary to locate the punch in axis with the matrix and it performs the bending operation by effecting the punch stroke along the axis Z. With this test apparatus, a very accurate punch force registration is possible. The experiments were carried out using a 2024-T3 aluminium alloy rectangular blank at constant velocity of punch. In order to study the influence of punch velocity, a range of five different velocities is used. For every set of test three repetitions have been carried out. The repeatability of the tests is resulted satisfactory, since the errors in the determination of the forces as to the average percentage are not superior to 5%. The tests have been followed by the bending angle measurement. The average percentage is resulted equal to 107 with errors inferior to 1%. The time of load application is also considered. The results of the tests have not found out any influence of the duration of the load application on the magnitude of the elastic recovery.

In this paper the possibility of simulating the unconstrained cylindrical bending with the finite element method is presented. The possibility of controlling the bend angle by using finite element method allows to bend sheets to different angles varying the geometry of the tools. The main goal of the finite element simulation of the bending process is to calculate the required punch force and the spring-back of formed parts. The spring-back is studied in this paper by using a 2D elasto-plastic finite element program and quadrilateral elements in plane-strain state are employed [2].

The first simulation modelled to demonstrate the robustness of the finite element method showed very good agreement with the experimental results. The spring-back amount varies largely and almost linearly from 69^o to 81^o within the examination range of sheet thickness. Furthermore, the effect of die corner radius change shows the insignificant variation in the spring-back amount within the examination range.

1

J.A. Schey, "Introduction to Manufacturing Processes", McGraw-Hill Book Company, 1987.

2

Marc Analysis Research Corporation, USA, MARC-MENTAT Manuals, 1994.

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