3.5 FEM Model of Laser Bending and Straightening
3.5.3 Mesh sensitivity and time increment analysis
Numerical simulation of laser bending process has been carried out to determine bend angle, and edge effect. A sequential thermo-mechanical process was conducted to simulate the laser assisted bending process by developing a moving heat source along scanning line. The laser scan was conducted at the middle along the length of the workpiece. Appropriate mesh refinement and time-increment is essential for obtaining the accurate results within rational computational time. Zhang
et al. (2004) used a 20-node brick element and also suggested 4 elements in a beam diameter and 3 elements in thickness direction as suitable for the better result. The mesh size depends upon the size of workpiece thickness and laser beam diameter.
Mesh refinement was carried out accordingly.
Preliminary simulation results show that simulation time increased as the laser power increased due to increase in temperature at high power which causes high thermal gradient. Zhang et al. (2004) reported that temporal discretization requires at least four time increments per radius. The scan speed was chosen during experimental work as in a manner that the time increment should be less than t1/4.
Where t1 is the duration of laser beam irradiation equal to the ratio of laser beam diameter to scan speed. Hence simulations were carried out with time-increments of 0.01 and 0.005 second and it was observed that at these two conditions, almost the same predictions were obtained. Hence, 0.01 second time-increment was selected as appropriate.
FEM simulations were carried out with eight-node thermally coupled brick element (C3D8T) using ABAQUS package. The entire domain was divided in three regions. In each region, the mesh size was uniform. The mesh was the finest in the region containing the laser irradiation path. Region between laser irradiated line and free side also region from fixed end to laser irradiated line were made of larger elements. Fine mesh size was used in the laser irradiated zone and coarse biased mesh was used at rest of the places. Fetene et al. (2017) observed that during laser assisted bending; mostly the deformation took place between the scan line and point of the application of the load. The zone between the clamped side and laser irradiated zone, the mesh sensitivity was low and it was considered few divisions along the length in this zone as good enough. A relatively finer mesh was used in the zone between laser scan line and free edge
.
As a compromise between computational time and accuracy, the mesh sizes were selected in a suitable manner.Mesh sensitivity was performed in a systematic manner for laser bending, laser assisted bending by electromagnetic force and laser assisted straightening by permanent magnetic force as follows.
A) Mesh sensitivity for laser bending
For laser bending 60 mm 40 mm 2 mm workpiece size was used. As shown in Figure 3.14 the meshing has been made in a systematic manner. For specimen of dimension 60 mm×40 mm× 2 mm, three clear divisions can be observed as explained previously. The laser irradiated region has been meshed with fine element while the other two regions are meshed with coarse element. Table 3.1 shows that in case of laser irradiated region element size of 0.5 × 0.5 × 0.5 are suitable considering accuracy in result and computational time. While region along clamp has 2 element and region along free end has 4 elements as shown. The results for this simulation have been discussed in chapter 4.
Table 3.1 Effect of fine mesh element size on bend angle for laser power of 900 W and scan speed of 800 mm/min
Element size in refined zone (mm3) Bend angle (Degree) Screen time (s)
2 × 2 × 0.5 4.17° 2124
1 × 1 × 0.5 7.42° 5011
0.5 × 1 × 0.5 11.71° 8019
0.5 × 0.5 × 0.5 14.8° 14437
0.25 × 0.25 × 0.25 15.09° 25121
Figure 3.14 Coarse and fine meshing for this simulation in laser bending
B) Mesh sensitivity for laser assisted bending
For laser assisted bending 100 mm 30 mm 2 mm workpiece size was used.
As shown in Figure 3.15 in the zone between the clamped side and laser irradiated zone, the mesh sensitivity was low and it was considered sufficient to have 4 divisions along the length. A relatively finer mesh was used in the zone between laser scan line and free edge and was decided to use 8 divisions along length in this zone. Table 3.3 presents the scheme for selection of proper element size in refined zone. It was observed that accuracy of the predicted bend angle increases with refined element size and high computational time. As shown in Table 3.3 as a compromise between computational time and accuracy, an element size 0.5 mm × 0.5 mm × 0.5 mm was found appropriate. The results for this simulation have been discussed in Chapter 7.
Table 3.2 Effect of element size on bend angle for laser power of 900 W, laser beam diameter 3.87 mm, scan speed 800 mm/min and current 5A
Element size in refined zone (mm3) Bend angle (Degree) Screen time (s)
2 × 2 × 0.5 2.43 5317
1 × 1 × 0.5 3.67 7441
0.5 × 1 × 0.5 4.03 15376
0.5 ×0.5 ×0.5 4.68 22567
0.25 × 0.25 × 0.5 4.71 37796
C) Mesh sensitivity for laser assisted straightening
For laser assisted straighten 100 mm 30 mm 2 mm workpiece size was used. As shown in Table 3.3, considering computational time and accuracy, an element size of 0.5 mm × 0.5 mm × 0.5 mm was taken in the heated region. On the magnet side, a coarse biased mesh comprising 20 elements was used. On the clamping side, mesh consisted of 5 elements. The largest element in the biased mesh was 5 times bigger than the smallest element in length direction. The size was same throughout the strip in the thickness and width directions. Figure 3.16 shows the coarse and fine meshing for this simulation. The results for this simulation have been discussed in chapter 6.
Figure 3.15 FEM simulations with coarse and fine meshing for the simulation and magnified view
Table 3.3 Effect of fine mesh element size on bend angle for laser power of 1000 W and scan speed of 800 mm/min
Element size in refined zone (mm3) Bend angle (Degree) Screen time (s)
2 × 2 × 0.5 0.67° 6105
1 × 1 × 0.5 0.72° 8020
0.5 × 1 × 0.5 13.3° 16906
0.5 × 0.5 × 0.5 12.8° 25460
0.25 × 0.25 × 0.25 13.0° 40906
Figure 3.16 Coarse and fine meshing for this simulation in laser assisted straightening by permanent magnet
In mechanical analysis, necessary constraints are added according to the experimental fixture used in real experiments. The boundary conditions are zero translation and rotation at one side of the work specimen, which is fully constrained.
The thermal load was given in the form of heat flux generated by the laser beam. It was applied only on the top surface of the sheet metal