Determination of forces at the bending of perforated plates with slotted holes through experimental and FEM.

Pascu, Adrian ; Oleksik, Valentin ; Curtu, Ioan 等

1. INTRODUCTION

Plane perforated plates (Figure 1) are used as strength elements for numerous machines and installations, both in machine manufacturing industry and in civil engineering.

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The analytical strength calculus is very difficult, both from the mathematical point of view and from the workload volume, so very often, and with results close to reality, the stress state is determined with experimental methods and/or with numerical methods.

2. EXPERIMENTAL RESULTS

For the experimental tests carried out, there was used the electrical transducer presented in Figure 2, which has as elastic element two identical semi-rings, fastened in a stiff intermediary body, which serves also as positioning base.

The electrical transducer is composed of the lower plate (3) and the upper plate (2), between which the two elastic elements (1) and (4) are mounted. Their centring and fastening is done by means of the pins (6) and of the screws (5).

An optimization calculus for the transducer (using the ANSYS software) was also realized in order to increase its sensitivity while maintaining its resistance.

The base plate has wedges for centring on the employed hydraulic press table, while the upper plate has T-slots for the centring and fastening of the experimental die on which the "V"-bending of the studied perforated plates was carried out.

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The strain gauges were positioned in complete bridge, the displacement manner being presented in Figure 3 (Iliescu, 2006).

It thus became possible to determine forces on three directions, both under static conditions and under dynamic conditions. The sections where gauges were placed were chosen so that the vertical force FV and the horizontal force [F.sub.H], had no mutual influence from the point of view of bending moment.

After calibrating the electrical transducer, a sub-assembly was realized from a V-bending die and the transducer (Figure 4), later mounted on a hydraulic press of 450 N.

The test samples employed for these tests were realized from steel sheet of 1.2 mm thickness. Dimensions of slotted holes are 2 mm width and 24.2 lengths. Also, forces on a direction perpendicular to the plane of the dynamometric table (further on called vertical direction) and on the direction parallel to the samples' large edge (further on called horizontal) were determined for a sheet of the same thickness, but without holes.

Figure 5a presents the variation charts of the forces on horizontal direction, while Figure 5b shows the variation charts of the forces on horizontal direction during the bending process (Test Point user's guide, 1995).

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3. NUMERICAL SIMULATION RESULTS

For this numerical simulation was used the Ansys Ls-Dyna software package. In the case of this loading type, the active elements are also described discreetly and not analytically. Thus, the active part of the V-type bending die is generated as having the thickness equal to the one of the perforated plate. The punch was generated as a plane, bent surface (Figure 6), positioned in linear contact with the part, so that by its displacement relative to the latter one the contact should be established on an extended contact surface (Bathe, 2007).

For the part (here part is the generic name used to define the assembly consisting of the geometry, the finite elements network, the real constants and the materials for each of the forming system's elements) that defines the die, all degrees of freedom were canceled and for the one defining the punch, all rotations and translations along Ox and Oz directions (both in the perforated plate's initial plane) being maintained only the translation on Oy direction (perpendicular to the plate's plane).

Figure 7 presents the way in which the force on vertical direction (Oy) varies during the loading (Pascu, 2005).

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Type of material items associated perforated plate is elastoplastic. Flow condition is considered to Hill, the flow is given Swift's law and hardening type is anisotropic defined Barlat. Elastic modulus is considered E = 210 GPa, Poisson's coefficient is v = 0.28, and yield stress for plate material [[sigma].sub.c] = 195 MPa.

Also, using the same software package we determined the equivalent stress for two different type of perforation with slotted holes (Figure 8) (Pascu, 2005).

4 SUMMARY AND CONCLUSIONS

Analyzing the previously presented charts, it can be remarked that:

--On horizontal direction the force is about 10% of the value of the force on vertical direction;

--The force on horizontal direction has at first a slight decrease, after which it increases quite rapidly during the punch's movement and at the punch's pullback it has again a slightly decreasing slope;

--Te forces on vertical direction also has a slightly decreasing tendency at the beginning of the bending process, after which its value increases much more rapidly and to a value higher than for the horizontal force, then it decreases equally fast and towards the end of the bending process it has again a very slight tendency to increase.

--The maximum value of the equivalent stress (von Mises) for two different perforated cases (52.80 MPa for parallel perforation and 48.44 MPa for "zig-zag" perforation, respectively) do not exceed the yield stress of the material considered for this perforated plate.

Based on the obtained results, a good concordance between numerical and experimental results can be noticed. Thus, the numerical method can be applied with good precision for the simulation of similar cases.

5 ACKNOWLEDGEMENTS

This work was carried out within the framework of the research laboratory of "Lucian Blaga" University from Sibiu (www.ulbsibiu.ro) and "Transinlvania" University from Brasov (www.unitbv.ro).

6 REFERENCES

Bathe, K.J. (2007). Finite Element Procedures, Prentice Hall, ISBN 0-13-301458-4, Engelwood Cliffs.

Iliescu, N., Atanasiu C.; (2006). Metode tensometrice in inginerie, Editura AGIR, ISBN 973-720-078-0, Bucuresti.

Pascu, A. (2005). Researches regarding the loading of mesh type and perforated plate type structures realised from different materials (in Romanian). PhD Thesis, "Transilvania" University of Brasov, Romania.

*** (1998) LabVIEW Data Acquisition Basics Manual, National Instruments.

*** (1995) Test Point user's guide. Vol. 1, 2, 1995.