3.1. Technological window of WJSF for different thicknesses
Yield pressure and final pressure are the most effective parameters in sheet metal forming processes. The yield pressure is a pressure that causes plastic deformation in sheet metal and the final pressure is a pressure that brings the sheet about tearing during the forming. The yield and final working pressures are specified to select the pressure parameters to evaluate the effect of pressure on WJIF. Therefore, the yield pressure and final pressure for the copper sheets of 0.1, 0.15, and 0.2 mm thickness with the same forming conditions in Table.1, and the rotary velocity (VT) of 1000 RPM were examined experimentally. The formed specimens to obtain the yield pressure and final pressure with thicknesses of 0.1 and 0.2 are shown in Fig. 6.
As it can be seen from Fig. 6 there are several wrinkles on the specimens that were formed by the low pressure around the yield pressure whereas there are no wrinkles for those specimens that were formed with high pressure near to the final pressure. Therefore, the quality of the final surface increases by increasing the forming pressures. The results of the experiments to specify the yield pressure, final pressure, obtained final depths, and wall angles for the different sheet thicknesses are given in Table 2.
Table. 2 Yield pressure, final pressure, final depth, and wall angle for different sheet thicknesses
Parameters

Value

Initial thickness (mm)

0.1

0.15

0.2

Yield pressure (MPa)

2

3.4

5

Final depth for yield pressure (mm)

2.7

3.4

3.1

Final pressure (MPa)

10.5

19

28

Final depth for final pressure (mm)

38.3

38.6

39.1

Wall angle for yield pressure (q)

3.86

4.86

4.43

Wall angle for final pressure (q)

43.76

43.98

44.35

The relation between the sheet thickness and WJ pressure for the three different thicknesses of the copper sheet was experimentally examined. It can be found from the table that the final depth and the wall angle for the yield pressure and final pressure of the sheets are approximately equal with thicknesses of 0.1, 0.15, and 0.2 mm. It is clear that as the sheet thickness increases, the yield pressure and final pressure also are increased. Therefore, by increasing pressure at each thickness; the final depth and wall angle also are increased.
The relation between relative jet diameter (Ƙ) and WJ pressure for the three different sheet thicknesses was also investigated. The relative jet diameter (Ƙ) is a nondimensional parameter that depends on the WJ diameter and the initial thickness of the sheet (t0) as defined in Eq.(1) which was extracted by Jurisevic et al. [5].
Ƙ was calculated using Eq. (1) for each thickness as shown in Table. 3. It can be found that, for the lowest initial thickness of the sheet, Қ is the highest value and the Қ decreased with increasing sheet thickness. On the other hand, when the initial thickness is low, the difference between the yield pressure and the final pressure is low, and as the thickness increases, the pressure difference increases.
Table. 3 The calculated relative jet diameter (Ƙ) for different thicknesses
As it is mentioned by Jurisevic et al. [5] a technological window can be presented to obtain process parameters as shown in Fig. 7, which is a schematic diagram of this process. This diagram is one of the important typical diagrams in designing the process of WJIF that is based on two parameters, Ƙ and WJ pressure (PW).
The upper area of the technological window is limited by the erosion starting line, and the lower area of the technological window is limited by the yield start curve as shown in Fig. 7. In this research, the technological window of this process is obtained experimentally that composed of three parts and separated by two curved lines. Below the bottom line is the area where plastic deformation doesn’t occur on the sheet. Between the bottom curve and the top line is the technological window area for WJS process which forming process is completely performed in this area.
Fig. 8 shows the obtained experimental technological window of WJSF of different thicknesses. In this diagram, the lower bound shows the yield pressure boundary, and the upper bound shows the boundary margin of tear pressure of the sheet with different thicknesses. There are two values for each Қ, one for the minimum pressure (yield pressure) and the other for the maximum pressure (final pressure) that can be seen on the bottom and top lines, respectively. The intermediate region between the lower bound and the upper bound is a technological process window to perform a successful forming by WJSF. It can be seen, the variation of the boundary curve of yield pressure is less than that for the tearing boundary curve while the variations of both curves become constant for the larger relative jet values.
In the proposed schematic diagram by Jurisevic et al. [5], a tearing boundary was not presented in the technological window and only the erosion boundary was illustrated, while in the obtained graph in this research, tearing boundary is presented.
3.2. Effect of water jet pressure at different rotational speed on deformation
WJ pressure is one of the effective parameters in the WJIF process. Therefore, the WJ pressure parameter for three different rotational speeds of sheets was investigated. To perform this study, the parameters of WJ pressure and sheet rotation speed were examined. Thus, different water jet pressures of 4, 6, and 8 MPa were initially examined with a constant rotary speed. Subsequently, the same pressures were reexamined after changing the rotary speed for the other specimens. The deformed parts using WJSF with rotational speeds of 1000 RPM, 90 RPM, and 22 RPM for copper sheets with a thickness of 0.1 mm with different pressures are illustrated in Figs. 9, 10, 11.
The specimens which formed using a rotational speed of 1000 RPM with the pressures of 4, 6, and 8 MPa were not formed appropriately and several wrinkles can be observed on the deformed parts. It can be concluded that as the WJ pressure increases, the wrinkles in the parts decrease. The forming time was about 6 seconds for the speed of 1000 RPM.
As shown in Fig. 10, three other experiments have been carried out at a speed of 90 RPM for the same pressures of 4, 6, and 8 MPa to investigate the effect of WJ pressure during the WJSF process. As it can be seen from the figure, several small grooves were formed on the deformed parts. The forming time for the speed of 90 RPM was about 66 seconds. It can be found that, while WJ pressure is high, despite the reduction in the forming time, the quality of the formed sheet and also surface roughness is improved.
As shown in Fig. 11, three specimens were formed with a rotational speed of 22 RPM and WJ pressures of 4, 6, and 8 MPa. Unlike previous speeds where several wrinkles and grooves were formed on the specimens, no wrinkle or groove occurred on the specimens using a rotational speed of 22 RPM with different WJ pressures. It is mentioned that the forming time was about 273 seconds for this rotational speed.
Focusing on Fig. 9 and Fig. 10 reveals an interesting phenomenon which is the effect of pressure on orientations of wrinkles and grooves. It can be seen that in Figs (9a) and (9c) wrinkles are clockwise and in Fig. (9b) the wrinkles have no orientation and several radial wrinkles can be seen. Similarly, the orientation of the grooves in Fig. (10a) is clockwise and in Fig. (10b) is radial, whereas grooves in Fig. (10c) are counterclockwise.
3.3. Effect of water jet pressure on final depth and crosssectional shape
The final depths of the deformed parts with the rotational speed of 22, 90, and 1000 RPM for the pressures of 4, 6, and 8 MPa are shown in Fig. 12. The final depth obtained using the WJ pressure of 4 MPa is approximately equal at all three speeds of 1000, 90, and 22 RPM. Although the speed of 22 RPM slightly increased the final depth, the speed of 1000 RPM led to the lowest final depth in the formed specimens.
It is clear that for all three speeds the final depth obtained by the pressure of 6 MPa is greater than for the pressure of 4 MPa whereas the effect of the rotational speed on final depth at pressures of 6 and 8 MPa is greater than that of the pressure of 4 MPa. It is observed that with increasing WJ pressure the effect of the rotational speed on the final depth increases. At the beginning of the forming, the rotational speed does not have large effect on the deformation, whereas as the plastic area develops and the forming time becomes longer, the rate of plastic deformation increases.
The crosssectional shapes of the deformed parts with a rotational speed of 1000 RPM for different pressures are illustrated in Fig. 13. As can be seen, the final depths of the deformed specimens are different and it indicates the increase of pressure proportionally increases the depth of the deformed part.
The specimens formed using a speed of 1000 RPM with pressures of 4 and 8 MPa have a final depth of 14.3 and 24.7 mm, respectively, so with an increase in pressure of 4 MPa, the final depth is 10.4 mm increased. The specimens formed using a speed of 90 RPM with pressures of 4 and 8 MPa have a final depth of 14.9 and 33.8 mm, respectively, so with an increase in pressure of 4 MPa, the final depth is 18.9 mm increased. The specimens formed using a speed of 22 RPM with pressures of 4 and 8 MPa have a final depth of 15.8 and 39.1 mm, respectively, so with an increase in pressure of 4 MPa, the final depth is 23.3 mm increased.
3.4. Effect of rotational speed on deformation and depth
Nozzle displacement speed or sheet rotation is another effective parameter in this process. Fig.14 illustrates the formed specimens using a pressure of 8 MPa and different rotational speeds for copper sheets with a thickness of 0.1 mm. The rotation speed of the sheet was the only changing parameter in this section that varied from 22 to 1000, so the other effective parameters in this process were constant.
The WJSF process was performed with each speed of 1000, 500, 90, and 22 RPM. The forming time for each of the mentioned speeds was about 6, 12, 66, and 273 seconds, respectively.
As can be seen from Fig. 14, for the speed of 1000 RPM, relatively large wrinkles have occurred on the specimen while for the speeds of 500 and 90 RPM, many small grooves or waviness appeared. The surface smoothness of the specimen, which is formed at a speed of 22 RPM, looks excellent because it is free of any wave or groove. Fig. 15, shows the final depth of the specimens formed at different speeds for the WJ pressure of 8 MPa. As the sheet rotation speed increases, the final depth decreases and more importantly, the final depth increases exponentially.
The specimens were formed using the speeds of 22 and 1000 RPM and pressures of 8 MPa have a final depth of 39.1 and 24.7, respectively. Thus, by reducing the speed from 1000 to 22 RPM, the final depth increases about 14.4 mm.
3.5. Effect of water jet pressure and rotational speed of sheet on wall angle
The wall angle is also one of the important results in investigation of deformed cone specimens. To evaluate the effect of the parameters on the cone specimens, this output was studied. Based on the final depth of the specimens in the previous sections, the wall angle was obtained. Fig. 16 shows the measured wall angles for pressures of 4, 6, and 8 MPa and speeds of 22, 90, and 1000 RPM. The results indicate, as the pressure increases, the wall angle of the specimens’ increases linearly.
It is also can be seen from the figure that a slight difference between the wall angles of specimens formed using speeds of 1000 RPM and with pressures of 4 and 8 MPa, whereas a large difference between the wall angles of specimens formed at speeds of 22 at pressures 4 and 8 can be observed.
On the other hand, at the pressures of 4 MPa, for speeds of 22, 90, and 1000 RPM, the wall angles of the specimens are very close to each other. At the pressures of 6 and 8 MPa, the differences between the wall angles of the specimens are greater than that for the pressures of 4 MPa.
The wall angles of the deformed specimens with the pressure of 8 MPa for different sheet rotation speeds of 22, 90, 500, and 1000 RPM are compared in Fig. 17. It can be seen that by increasing the rotation speeds of the sheets, the wall angles are reduced. The wall angles of the formed specimens by pressure of 8 MPa and speeds of 22, 90, 500, and 1000 are about 44.35, 40.19, 34.7, and 31.68, degrees respectively. The lowest wall angle is related to the formed specimen with a speed of 1000 RPM and the maximum wall angle is related to the rotation speed of 22 RPM. The difference between the minimum and maximum wall angles is about 12.67 degrees.
3.6. Effect of rotational speed and WJ pressure on surface quality
The effect of WJ pressure and rotational speed on surface roughness, waviness and grooves of deformed parts were investigated. The maximum surface roughness of the deformed parts with the rotational speed of 22, 90, and 1000 RPM for the pressures of 4, 6, and 8 MPa were measured by a digital roughness tester. The maximum roughness depth (Rmax) is the largest roughness depth within the evaluated specimens to evaluate the surface quality. The next three figures (1820) show the surface roughness of the specimens formed at different speeds for the WJ pressure of 4, 6 and 8 MPa respectively. As can be seen from these figures, with increasing the rotational speeds of sheets, the maximum surface roughness has been increased.
In addition, to perform a qualitative surface investigation, several macroscopic photographs with different magnifications were prepared and compared. The macroscopic images for different pressures and rotational speeds are shown in Figs. 21 to 23.
Fig. 21 shows that the deformed specimens with the speed of 1000 RPM by different pressures have a few large wrinkles. The wrinkles formed on the specimens started from the centre of the cone and reaches to the outer area of the deformed area by the water jet.
Microscopic images of the formed specimens using a speed of 90 RPM and pressures of 4, 6, and 8 MPa are shown in Fig. 22. It is obvious that the many small wrinkles were formed at this speed and these small wrinkling lead the medium size grooves with different directions and paths on the deformed surfaces. Wrinkles in a specimen formed at a pressure of 4 MPa appear to be slightly smaller than those specimens formed at a pressure of 6 and 8 MPa.
Fig. 23 shows the microscopic images using a speed of 22 RPM and pressures of 4, 6, and 8 MPa. It is interesting that the deformed specimens with a speed of 22 RPM at all pressures have a better surface quality without any wrinkles or grooves. It means that, the wrinkles and grooves were decreased and even disappeared by the reduction of rotational speed of the rotating sheet during the process of WJSF.
To evaluate the effect of rotational speed on surface quality, two rotational speeds of 1000 and 22 RPM at the pressure of 4 MPa were selected and the required images were obtained using a scanning electron microscope (SEM) by the magnification of 50x. These two results are shown in Fig. 24 and it is illustrated that, there is a wrinkle on the formed specimen using the speed of 1000 RPM whereas there is not any surface defect or waviness on the formed specimen by the speed of 22 RPM and a very smooth and uniform surface occurred at the low speed of sheet rotation during the forming process.