TPT May 2009

Once at this stage of the theoretical parabolic contour, there is a 1.39° deflection of the reflected light of the formed section’s outset point. However, the reflected light can only be reflected to the effective decalescence position. According to the marginal ray principle [4] , all of the parallel light arrives at the effective decalescence position after reflection by the formed section, which shows that the spotlight performances of formed section and parabolic contour are closed to a considerable degree. 4. Finite element analysis simulation For practical engineering, the required parabolic parameters and experimental model cannot be fully in accordance. The method involves an extensive application of the feasibility of the forming parabolic using rollforming and the accuracy of roll design. Therefore, finite element analysis was used for the forming process of the parabolic section in this study. Rollforming is a complicated non-linear problem. Therefore, the forming process for the parabolic section was simulated by the commercial FEA software MSC Marc. 4.1 Finite element analysis simulation of forming process experiments Because the rollforming process is very complicated, the FEA model used in simulation should be simplified according to the practical condition. In this study, during setup of the simulation forming model, sheet material is deformable and the roll is rigid, and friction force is not considered. Sheet material fed through the rolling tool is replaced with a quarter roll sliding on the strip, and the entire long sheet material is replaced by precut pieces of strip. The centre distance between two stations is 250mm, and the length of precut strip material is 300mm and the width 120mm. The strip is divided equally to 60 elements in X-axis (transverse direction) and 50 elements in Z axis (forming direction). There are 3,000 elements in total, and the element thickness is the practical thickness of forming aluminium sheet (0.48mm). The element type

Transverse unfolding coordinate of section (mm)

Formed section in Z coordinate (mm)

Sample No.

X=0 X=10 X=20 X=30 X=40 X=50 X=60

Z=400 Z=500 Z=600 Z=400 Z=500 Z=600 Z=400 Z=500 Z=600

0 0.16 0.22 0.25 0.37 0.49 0.55

1

0

0 -0.04 0.21 0.31 0.10 -0.15

0 0.16 0.18 0.43 0.50 0.28 0.07 0 -0.07 -0.19 0.04 0.2 0.14 0.11 0 -0.06 -0.10 0.25 0.36 0.2 -0.04 0 -0.11 -0.20 0.10 0.35 0.38 0.44 0 -0.11 -0.23 0 0.13 0.01 -0.11 0 -0.01 -0.1 0.12 0.25 0.15 0.07

2

3

4.2 Simulation result analysis The formed section can be compared with the simulation result. For analysis, the experiment results had 3 corresponding sections that keep the distance respectively of 400mm, 500mm and 600mm to the beginning of the formed strip. For this reason, 3 sections were picked that keep the respective distances of 100mm, 150mm and 200mm to the start of strip simulation. Firstly, coordinates are based in the unfolding centre of the formed section. Because of the symmetry, only the positive half axle of transversely unfolding section coordinates is taken into account. Then, this strip is divided equally into 6 parts, and on the divided point, the normal error between formed section and simulation section is shown in table 2. In the table, the positive value shows that the simulation section is blow formed section on the divided point, and the negative value shows that the simulation section is formed from above on the divided point. The mean value of normal errors of every divided point is shown in figure 11. Given the data of table 2, the maximum error is 0.3mm. It is observed that simulation section and formed section are basically identical, and simulation results in high precision, so that simulating results are reliable for engineering design. 4.3 Finite element simulation of aluminium sheet forming process with the thickness of 0.5mm In order to establish the thickness difference of material and roll design setting, 0.5mm thickness aluminium sheet is used for finite element simulation. The error is compared with a simulation strip thickness of 0.48mm. 0 -0.18 -0.27 0.05 0.27 0.20 0.05  Table 2 : A normal error between simulation section and formed section (mm)  Table 3 : A normal error between simulation section and idea parabolic section (mm) Formed Transverse unfolding coordinate of section (mm)

is No.139 with 4 nodes of thin shell. The simulation geometric model is shown in figure 9.

 Figure 9 : Simulation

geometric model

Boundary conditions comprise the fixed displacement at the beginning and end of the forming strip in Z direction, and all fixed displacement areas on the centre point of the end strip in X direction. The Von Misses yield and isotropic hardening criterion were used. In the simulation result of the forming strip, displacement in Y axis (vertical direction) is shown as figure 10. Here different colours have been used to represent different displacement. It can be observed that Y displacements of the forming strip are always shown as the same colour, which means that the length of the forming direction of the parabolic section is uniform and the forming of the parabolic section is comparative.

section in Z coordinate (mm)

X=0 X=10 X=20 X=30 X=40 X=50 X=60

Z=100 Z=150 Z=200

0 0 0

-0.12 -0.2 -0.33 -0.35 -0.56 -0.95 -0.17 -0.17 -0.31 -0.38 -0.5 -0.88 -0.11 -0.21 -0.29 -0.36 -0.54 -0.89

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M ay 2009

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