3.1 Forming limit analysis
"Orthogonal experiment design" is a scientific method of analyzing multi-factor experiments, which can greatly reduce the number of experiments and will not reduce the feasibility of experiments. The orthogonal experiment design was used to study the influence of forming parameters on the forming ability of the sheet metal. The three factors are the rotational speed, vertical step size, tool diameter, the level of the orthogonal experiment factors as shown in Table 4, and the angle and temperature when the sheet material was broken were recorded. The table of orthogonal experiment results was got, then the experimental data was analyzed, the impact of each process parameter on the forming performance was observed, and the relatively good set of process parameters for later test analysis was got.
Table 4 Orthogonal experimental factor level table
Forming
parameters
|
Factor
|
Level
|
1
|
2
|
3
|
4
|
5
|
6
|
Rotational speed(rpm)
|
A
|
500
|
1000
|
1500
|
2000
|
2500
|
3000
|
Vertical step size(mm)
|
B
|
1
|
1.5
|
2
|
|
|
|
Tool diameter(mm)
|
C
|
8
|
12
|
16
|
|
|
|
In the HFIF, the angle α between the forming sheet and the vertical direction was the forming angle, as shown in Fig. 8. The thickness of the deformation zone conforms to the law of cosine t=t0 × cosα. From this rule, it can be seen that the larger the forming angle, the smaller the thickness t of the deformation zone, the higher the thinning rate, and the easier it is to break. When α reaches a certain value, the deformation zone was cracked. At this time, the angle α can be used as a judgment value of whether the sheet metal was broken. The larger the forming limit angle, the greater the amount of deformation that the sheet can produce, and the higher the forming performance. In the experiment, the forming limit angle was used as the standard for the forming performance of the material[25-27].
After orthogonal experiment, the forming limit angle αmax(°) and temperature T(°C) were obtained (Table 5).
Table 5 Orthogonal test data table
Run
|
A
|
B
|
A×B
|
C
|
A×C
|
B×C
|
αmax
|
T
|
1
|
500
|
1
|
3
|
12
|
3
|
1
|
29
|
52
|
2
|
500
|
2
|
1
|
8
|
1
|
2
|
23
|
61
|
3
|
500
|
1.5
|
2
|
16
|
2
|
3
|
27
|
60
|
4
|
1000
|
1
|
1
|
12
|
1
|
1
|
36
|
87
|
5
|
1000
|
2
|
2
|
8
|
2
|
2
|
41
|
90
|
6
|
1000
|
1.5
|
3
|
16
|
3
|
3
|
13
|
110
|
7
|
1500
|
1.5
|
2
|
12
|
1
|
1
|
59
|
80
|
8
|
1500
|
1
|
3
|
8
|
2
|
2
|
47
|
100
|
9
|
1500
|
2
|
1
|
16
|
3
|
3
|
56
|
112
|
10
|
2000
|
2
|
2
|
16
|
3
|
1
|
71
|
140
|
11
|
2000
|
1.5
|
3
|
12
|
1
|
2
|
62
|
110
|
12
|
2000
|
1
|
1
|
8
|
2
|
3
|
49
|
95
|
13
|
2500
|
2
|
3
|
12
|
2
|
1
|
59
|
120
|
14
|
2500
|
1.5
|
1
|
8
|
3
|
2
|
51
|
100
|
15
|
2500
|
1
|
2
|
16
|
1
|
3
|
55
|
120
|
16
|
3000
|
1.5
|
1
|
8
|
2
|
1
|
64
|
130
|
17
|
3000
|
1
|
2
|
16
|
3
|
2
|
65
|
125
|
18
|
3000
|
2
|
3
|
12
|
1
|
3
|
52
|
135
|
Table 5 was imported into SPSS software for orthogonal test variance analysis. The results are shown in Table 6.
Table 6 Orthogonal test results data analysis
Factor
|
Mean difference
|
Degrees of freedom
|
F
|
Sig
|
Distinctiveness
|
A
|
560.633
|
5
|
21.425
|
0.045
|
Important
|
B
|
33.500
|
2
|
1.280
|
0.439
|
Not important
|
C
|
32.000
|
2
|
1.223
|
0.450
|
Not important
|
A×B
|
4.081
|
2
|
0.156
|
0.865
|
Not important
|
B×C
|
80.082
|
2
|
3.061
|
0.246
|
Not important
|
A×C
|
0.333
|
2
|
0.013
|
0.987
|
Not important
|
According to the data analysis table of the orthogonal test results, the effects of the three main factors and their interaction on the forming limit angle are A>B×C>B>C>A×B>A×C. the rotational speed has the most significant effect on the forming angle, and other factors have less effect. It can be seen from Fig. 9 that the forming limit angle is gradually increased sharply from 500prm to 2000prm with the spindle speed is increased, but after 2000prm, the forming limit angle is basically unchanged, the forming ability of magnesium alloy has been greatly improved compared with 500prm. Generally speaking, the forming ability is increased with the rotational speed is increased. After rotational speed is reached a certain speed, the forming ability is basically unchanged. The forming limit angle gradually is decreased with the vertical step size is increased, but the change range is small. The forming limit angle is also increased only slightly with the tool diameter is increased, with a change of about 5°, the forming ability is basically unchanged. According to the optimal parameters, rotational speed is 2000prm, vertical step size is 1mm, and the tool diameter is 16mm, the forming limit angle can be up to 76°.
It can be seen from the influence of each process parameter on the temperature at the forming limit angle that the rotational speed, vertical step size, and the tool diameter is increased will increase its temperature. The most important factor is the rotational speed. As the speed is increased, the temperature is doubled, and the trend of temperature increase is roughly the same as the trend of forming ability. The vertical step size and tool diameter have little effect on the temperature, and the change is about 10°C.
The influence of various process parameters on the forming ability and temperature is analyzed, and the conclusion is that the forming ability and temperature change trend is basically the same as the temperature is increased, but the vertical step size is different, as the vertical step size is increased, the forming capacity gradually decreases, but the temperature is increased. The main reason is that the vertical step size is increased within this range, the pressure of the sheet is increased, causing the sheet is broken, and the forming ability is reduced. At this time, the influence of pressure on the plate is greater than the influence of temperature increase on the sheet forming capacity.
The rotational speed is the biggest factor affecting the forming limit angle. When the speed is increased above 2000prm, the forming ability is not changed basically. When the speed is increased, the temperature will increase, reducing the service time of the forming tool. In the experiment, it was also found that when the temperature is increased, the outer surface of the parts will have "ripple marks", which makes the surface quality poor, as shown in Fig. 10. 2000prm is the best choice for other deformation characteristics experiments.
Vertical step size is an important factor that affects forming efficiency. As the vertical step size is increased, the processing time is reduced and the production efficiency is improved, but at the same time the surface roughness will be increased. The vertical step size is small, which is helpful to reduce the surface roughness of the parts, but the processing time will be increased.
The tool diameter has little effect on the forming ability. The tool diameter is increased will increase the contact area between the forming tool and the sheet, the temperature will be increased, and the forming ability will be increased. The lower tool diameter will cause more serious damage to the plate, thus forming capacity is reduced. On the other hand, the tool diameter is too large and the corners of the formed parts are not easy to form, therefore, the choice of forming tool diameter depends on the complexity of the forming part.
3.2 Deformation and geometrical accuracy in FHIF
In order to better understand the deformation characteristics and geometrical accuracy of the early, intermediate and final forming stages, the ideal model and the contour drawing of the actual part cross section were extracted from CATIA for comparison, as shown in Fig. 11. Due to the symmetry of the part, only the half-part contour is analyzed. When the part is above the CAD model, it is "+", otherwise it is "﹣".
It can be seen from the comparison of the cross-sectional views of the CAD model and the part that the edge area of the part will be bended to varying degrees in each period, which is caused by the blank holder. This mainly depends on the distance between the clamping edge and the contact position of the forming tool. The bend is particularly obvious in the early stage, and the 45° sidewall area is not obvious, there are no obvious upper and lower corners, this is the shortcoming of no lower mold. Through analysis, it is found that there are defect in the lower corners in each period, which is left during the last round of the forming tool. The forming tool squeezes the metal and flows to the side edge, so that the metal is not deformed piled up, so the thickness of this part will be thicker. And the bottom of the part is not flat, and the center position is higher than the edge position, this is because during the local plastic deformation process, the bottom edge position is subjected to more downward pressure on the tool head, so that the center of the bottom is always higher than the position where the forming tool is being processed during the entire process.
3.3 Thickness distribution in FHIF
Comparing the simulated thickness results with the actual results, it can be seen from Fig. 12 that the thickness of the sidewall area is not uniform in the early stage of forming, and the uniform thickness is 0.99mm in the intermediate and final stages of forming, which is 11% thinner than the theoretical thickness of 1.13mm. Friction heating requires rotating contact friction between the tool head and the plate, material loss occurs, and it is impossible to use 100%, from the overall error analysis above, it can be seen that the thickness of the side wall region is partially thinned because part of the side wall material is squeezed into the bottom region. The experiment found that the thinning rate is basically the fixed value is 11%, so 89% of the theoretical sidewall thickness is the thickness of the actual FHIF sidewall uniform area.
It is found that the designed simulation model can accurately predict the thinning trend, but because the metal flow in the entire process cannot be accurately simulated, the trend can only be predicted, and the thickness and the true value are somewhat different. In the simulated parts, the thickness of the corners found during the experimental research was rapidly reduced. Due to the symmetry of the parts, the thickness profile (Fig. 13) only studies half-sections. In the unformed area, the sheet thickness is about 1.6 mm, and the sheet thickness was decreased rapidly in the upper fillet area, in the side wall area, as the forming depth was increased, the thickness of the plate gradually was stabilized. The stable thickness is about 1.13mm, which is not much different from the theoretical thickness, which is in accordance with the cosine law of the plate.
The measured thickness distribution along the forming depth in the final forming is as shown in Fig.14, it can be seen that the side wall area of the part does not reach a stable thickness at the beginning, but the thickness reaches a minimum after a certain forming depth. Through experiments, it is found that the forming thickness reaches a stable thickness when the forming depth is about 15mm, and the temperature also reaches a stable value, so in the forming process, special attention should be paid to forming depth 0-15mm, which is the easiest to break.
3.4 Strain and stress distribution in FHIF
Due to the nature and complexity of the process, it is impossible to obtain the stress state in the FHIF process. Therefore, the equivalent stress was evaluated by the finite element method. The stress evolution at each forming stage of the forming process is shown in Fig. 15. It can be observed that the maximum stress value was increased as the forming stage was increased. For the early forming stage, the value is 165.1MPa, 171.1MPa in the intermediate stage, and 174.2MPa in the final forming stage. The maximum strain of the part in the early forming stage is 0.437, while the plastic strain of the part in the intermediate forming stage and the final forming stage has increased but has not changed much, both are around 0.471. The strain measured in the side wall area is basically fixed by grid experiment.
The plastic strain value increases from the early stage to the middle stage of forming, but the plastic deformation does not change much from the middle stage to the final stage of forming, because the sidewall region at this stage is the maximum equivalent strain value, and the thickness of the sidewall region basically does not occur variety. The amount of strain changes from the beginning to the early stage is large, and then basically unchanged. Corresponding to the existence of a depth in the above experiment, after this depth the sheet will be basically not break.