3.1 Forming force and temperature
Figure 4 shows the sheet surface temperature and vertical forming force corresponding to Experiments 1–8 in Table 3. It could be seen from Fig. 4 that the temperature increased and the forming force decreases as the effective current density increases. When the frequency of the electrical pulse remains constant, the effective current density increased, based on Eq. 2, the peak current density of the electrical pulse increased accordingly. It means that the current heating effect became more pronounced and the temperature of the sheet rose. Compared the surface temperature of the sheet under the assistance of EP and EP/U coupling field, it could be seen that EP/U coupling caused further temperature increase, and this phenomenon was more pronounced at conditions of lower effective current density, while the average percent of temperature rise reached a maximum of about 17% when effective current density was 21.1 A/mm2. Correspondingly, the forming force was further deceased in the EP/U coupling assisted forming process, while the average percent of forming force decrease reached a maximum of about 20% when effective current density was 33.4 A/mm2.
The influence of EP/U coupling on the forming force showed different characteristics with the forming depth increase, as shown in Fig. 4(b). Firstly, the evolution of the forming force decreased slightly at the initial stage, and then increased gradually; secondly, the forming force with EP/U coupling field is less than that of only EP condition due the higher temperature, especially at the later stage of forming process. AZ31B magnesium alloy sheet was softened under the assistance of EP or EP/U coupling field at the beginning of ISF forming, however, the effect of work hardening was gradually enhanced with the increasing of feeding depth, and the dynamic softening also played an important role at the later stage of forming process, which lead to vertical force decreasing.
The contact area temperature and variation of forming force with different current frequency were shown in Fig. 5. The contact area temperature was higher when high frequency was applied. Therefore, with the increase of the forming depth, the high frequency was more likely to cause heat accumulation than the low frequency, so the material exhibited more pronounced softening. Due to the above phenomenon, the forming force was significantly reduced at high frequency. The influence of ultrasonic vibration is mainly reflected in the early stage of forming. From Fig. 5 (a), ultrasonic vibration made the contact area temperature significantly increase in the initial stage of forming, which further softened the material and reduced the forming force. As the forming progressed, the temperature gap between EP assisted and EP/U assisted gradually decreased, so that the forming force tends to be consistent.
Figure 6 shows the effect of step depth on temperature and forming force when the effective current density was 29.9 A/mm2 and frequency was 400 Hz. Under the premise of the same forming height, larger step depth could effectively shorten the forming time. The temperature rise trend was basically the same with Fig. 5. Meanwhile, increasing the step depth led to a larger contact area between the tool head and the sheet during the feeding process, and resulted in an increase in the forming force. In addition, it could be seen from Fig. 6 (b) that when the step depth was set to 0.1 mm, the reduction of forming force caused by the EP/U coupling effect in the initial stage was more significantly.
3.2 Surface quality
Selected the area corresponding to the forming depth of 5 mm (sampling point B in Fig. 3) as the control area, surface morphology and roughness of the EP assisted and EP/U assisted forming parts under different effective current densities was shown in Fig. 7. Compared Fig. 7 (a), (c), (e), (g), it could be seen that the increase of the current density makes surface gullies more obvious and the roughness increase. After superimposing ultrasonic vibration, as shown in Fig. 7 (b), (d), (f), (h), the surface roughness all showed a downward trend, except when the effective current density was 33.3A/mm2.
In order to analyze the variation law of surface quality with forming depth, take the formed parts under the condition of electric pulse frequency of 400 Hz and effective current density of 29.9 A/mm2, and observed the surface morphology of sampling points A and C, as shown in Fig. 8. Combined with the surface morphology of the sampling point B shown in Fig. 7 (e), it could be seen that the surface quality deteriorated with the increase of the forming depth at the condition of EP assisted, the corresponding value of Sa increases from 0.653 (Point A) to 1.190 (Point C). However, the application of ultrasonic vibration made the surface quality no longer decrease sharply with the increase of forming depth and Sa remained around 0.7.
Figure 9 shows the effect of current frequency on surface topography of the formed parts when the current density was 30 A/mm2 and step depth was 0.1 mm. Compared with Fig. 7 (e) (f) which conducted at current frequency of 400 Hz, it was clearly seen that when the effective current density remained constant, low frequency conditions resulted in an increasing of Sa which means deterioration of the surface quality. When the effective current density remained constant, increasing the electric pulse frequency caused peak current density decreased, which showed a negative correlation with the frequency. Due to the contact area between the tool head and the plate was small, the current would concentrate on the surface of the plate and generate a high-density area due to the "skin effect"[30], so that the high peak current density which corresponding to low current frequency had a more significantly negative effect on the surface quality. For this reason, increasing current frequency can improve the surface quality. In addition, the application of ultrasonic vibration resulted in a substantial improvement in surface quality at each frequency, and the EP/U coupling effect was the most significant at 350 Hz, where the Sa reduced by about 50% compared with EP assisted.
Figure 10 shows the surface topography of the parts with different step depths when current density was 30 A/mm2 and frequency was 400 Hz. As can be seen from Fig. 10, increasing the step depth resulted in increase of surface roughness, however, the surface quality of parts can be improved under ultrasonic vibration condition. The surface of magnesium alloy incremental formed parts is periodically distributed along the depth direction with "gully" formed by the action of the tool head, which is one of the main reasons for the poor surface quality of parts. The reasons for these "gully" can be concluded as follow: (1) Due to the hemispherical shape of the tool head, feeding along discrete layers will leave unformed protrusions between layers. Theoretically, the height of protrusions, also known as residual wave crest height, is equal to the vertical height from the intersection of the tool head contour to the theoretical contour, as shown in Fig. 11, in which the hs is the residual height, r is the radius of the tool head, h is the interlayer feed in depth direction and α is the wall angle of truncated cone. (2) Due to the extrusion and friction of the tool head, the surface material flowing lead to local accumulation on both sides of the feeding direction of the tool head, and a furrow effect is generated at the top of the ball head. (3) The mechanical wear and grinding particles also occurred in the process of tool head feeding, and the effect of oxidative wear would become much more serious with surface temperature increasing. The increasing of the step depth would increase the theoretical residual height, resulting in the increase of surface roughness. However, the dynamic softening and impact effects caused by ultrasonic vibration could enhance the formability of materials, which resulted in the decreasing of Sa and improvement of surface quality with assistance of EP/U coupling field.
3.3 Line roughness in different directions
The line roughness of the workpiece under different effective current density was shown in Fig. 12, and the position of the reference line for line roughness measurement was shown in Fig. 3 (b). In this study, \(\Delta Ra\)(the difference between the linear roughness of the EP assisted part minus the linear roughness of the EP/U assisted part) was used to characterize the influence of the coupling effect on the roughness.
From Fig. 12, the line roughness perpendicular to the feeding direction of the EP assisted and EP/U assisted forming parts showed the same trend, they both increased with the increase of the effective current density. The main factor affected the line roughness perpendicular to the feed direction was surface gully. The increase of surface temperature caused by the increasing of effective current density led to the surface material soften, and more serious mechanical wear and oxidative wear generated. For this reason, the roughness in parallel direction also increased with the increasing of effective current density in both EP assisted and EP/U assisted ISF process. As for the\(\Delta Ra\)in perpendicular direction, it showed a trend of initial increased and then decreased with the increasing of the effective current density. \(\Delta Ra\)reached a maximum at the effective current density of 25.6 A/mm2, which means that the influence of EP/U coupling effect was the most significant under this condition. When the effective current density reached 33.3 A/mm2, \(\Delta Ra\)was less than zero, which means that the EP/U coupling effect further increased the line roughness in this direction. After applying ultrasonic vibration, the superimposed ultrasonic energy can further soften the surface material. Meanwhile, with the up and down movement of the tool head in the axial direction, more local surface materials will participate as the deformation continued, thereby effectively improving the flow of surface materials. However, the impact caused by ultrasonic vibration enhances the rolling action of the tool head on the sheet surface. On the premise of improving the formability of the surface material, the repeated rolling of the sheet by the tool head is conducive to the rearrangement of the surface gully, makes the surface profile height distribution relatively uniform. Under the combined effect of the above factors, when effective current density was lower than 30A/mm2, EP/U composite field assistance effectively reduced the roughness perpendicular to the direction of the feed direction. Nevertheless, when the effective current density was higher than 30 A/mm2, the surface temperature was too high and would cause excessive softening of the surface material. In this case, the dynamic impact caused by ultrasonic vibration leads to more severe adhesive wear, oxidative wear and local surface quality deterioration.
The\(\Delta Ra\)in parallel direction showed a different trend, with the corresponding maximum value reached 0.32 when effective current density is 29.9 A/mm2. Same as above, this trend could be partly attributed to the combined effect of material softening and surface wear caused by higher temperature. In addition, it was also affected by the "jumping" of the tool head and the ultrasonic dynamic impact. Figure 13 shows the morphology of the EP/U assisted forming parts under the conditions of effective current of 21.1 A/mm2 and 33.4 A/mm2. Due to the “jumping” action of the tool head on the surface of the sheet, a continuous arrangement of “fish scale” ripples were formed in the surface gullies at condition of effective current of 21.1 A/mm2, as shown in Fig. 13(a). The reason for its formation is shown in Fig. 14.
The tool head was subjected to the reaction force of the sheet during the feeding process, so it can be regarded as a fully constrained cantilever beam. At the condition of lower current density (≤ 30.0 A/mm2) or frequency (≤ 400 Hz) of electric pulse, the deformation resistance of the sheet was larger, tool head and fixtures did not guarantee an ideal rigid connection. Therefore, elastic bending deformation in the horizontal direction occurred during the feeding process. On one hand, there was no relative movement between the tool head and sheet at the moment, and the friction mode was static friction. With the position offset of the tool head, the actual contact area between the tool head and the sheet became smaller, which reduced the amount of material involved in the deformation and reduced the corresponding forming force, then the tool head had a certain degree of elastic recovery. This phenomenon caused alternating static and dynamic friction between the tool head and the sheet, which made the tool head “jumping” in the feed direction. At the same time, the sheet was elastically deformed, resulted in residual bulges in the feed path. On the other hand, at lower current density, the material flow ability was poor, surface material accumulated in front of the tool head, and increased tool head deflection. These accumulated materials will be destroyed under the pressure of the tool head, which cause the tool head elastically recover in a short period time in the case of sudden resistance changes and cause an impact on the front surface material and left a residue “hollow” in the original position, as Fig. 14 (a) showed.
Ultrasonic vibration would have different effects on the above phenomena. As shown in Fig. 14 (b), the tool head moves up and down along the axial direction under the action of ultrasonic vibration, which would form a hollow on the surface of the sheet. This hallow would be superimposed with the "jumping" of the tool head, causing a greater impact on the front surface material, resulting in further accumulation of the material in front of the tool head. At the same time, the upward movement helps the tool head to pass over the material accumulated in front, which will effectively avoid material damage, and reduced the elastic bending degree, weaken the impact caused by “jumping”. However, the accumulated material is not peeled off, it means high residual height. The above reasons lead to the fact that the roughness parallel to the feeding direction increased after ultrasonic vibration was applied under the condition of low effective current density. The primary cause of the above phenomenon was the limited flow ability of the surface material and the high deformation resistance. When the effective current density increased, the plastic deformation ability of the surface material was improved by temperature increasing and electroplastic effect, and the “fish scale” ripples also disappeared, as shown in Fig. 13 (b).
Figure 15 (a) (b) show the line roughness for different forming depths, which correspond to the position of A, B and C, as shown in Fig. 3 (b). It can be seen that the line roughness in both directions showed an increasing trend with depth increasing. The larger the tool head feed depth, the shorter feed cycle between layers. That meant the interval between the tool head running along the contour line was shorter, heat accumulation faster, then the actual temperature of the sheet increased further. The increase of temperature would lead to further softening and wear of the material at the position, which resulted in increasing of roughness. Meanwhile, compared the\(\Delta Ra\)in the two directions, it was found that the surface quality improvement effect caused by ultrasonic vibration was most significant at the forming depth of 5 mm (Position B), where the\(\Delta Ra\)reached a maximum 0.2 in perpendicular direction and 0.07 in parallel direction. Therefore, with the increasing of forming depth, the line roughness in both directions will increase due to the material softening caused by temperature rise. Moreover, EP/U coupling field could decrease the line roughness and improve the surface quality compared with EP assisted forming. It should be noted that the parallel direction\(\Delta Ra\)was less than zero at a forming depth of 2 mm (Position A), which was due to significant dynamic impact effect of the tool head and the lateral “jumping” caused by the low temperature and limited deformation ability of magnesium alloy sheet.
It can be seen from Fig. 15 (c) (d) that the roughness in both directions of the EP and EP/U assisted forming parts basically showed a trend of decrease with the increasing of frequency. This is because the high peak current density corresponding to the low frequency would cause excessive softening and wear of the surface material. For the perpendicular direction, the line roughness decreased by 0.42, 0.28 and 0.18 corresponding to the frequency was 300 Hz, 350 Hz and 400Hz under the action of ultrasonic vibration. The higher peak current density caused by lower frequency led to stronger electroplastic effect and better plasticity of surface material. Under the impact effect caused by ultrasonic vibration, the gullies were partially filled, so that the roughness perpendicular to the feed direction was significantly reduced. However, the line roughness in the parallel direction increased due to the higher forming force and more material accumulating and flaking caused by ultrasonic vibration at low frequency. With the increasing of frequency, the line roughness decreased with the action of EP/U coupling effect, and \(\Delta Ra\) reached a maximum of 0.09 when current frequency was 350 Hz, which means that the surface quality was significantly improved. Therefore, the line roughness in both directions of perpendicular and parallel to feed direction could be reduced by EP/U coupling effect.