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Radial-axial Force Controlled Electromagnetic Sheet Deep Drawing: Electromagnetic Analysis
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 81 (2014) 2505 – 2511
11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014, Nagoya Congress Center, Nagoya, Japan
Radial-axial force controlled electromagnetic sheet deep drawing: electromagnetic analysis Zhipeng Laia,b, Quanliang Caoa,b, Xiaotao Hana,b, Zhongyu Zhoua,b, Qi Xionga,b, Xiao Zhanga,b,Qi Chena,b, Liang Lia,b, * a Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China
b
Abstract
A new approach, radial-axial force controlled (RAFC) electromagnetic sheet forming (EMF), has been developed for hard-form metal sheet deep drawing. Different to the traditional EMF, an additional radial Lorentz force was introduced at the flange region of workpiece to improve the material flow and reduce the maximum strain of workpiece. For this purpose, an EMF system with two coils has been designed. The two coils were used to generate the axial Lorentz force (Fz) on the workpiece region (D1) above the cavity and the radial force (Fr) on the flange region (D2), respectively. The Fz was used to accelerate the D1 region’s material in axial direction to shape the workpiece into the die, while the Fr was used to accelerate the D2 region’s material in negative radial direction to improve the material flow of the flange. In this paper the electromagnetic analysis of the system has been carried out. As a proof of concept, the variation characteristics of Fr and Fz under different discharging energies and schedules of the coils were simulated and analyzed. The results show that the magnitudes and the action time of the Fr and the Fz can be well controlled, which indicates that the forming can be flexibly controlled. © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and and peer-review peer-reviewunder underresponsibility responsibilityofofthe Nagoya University and Toyohashi of Technology. Selection Department of Materials ScienceUniversity and Engineering, Nagoya University Keywords: Electromagnetic sheet forming; Material flow; Radial-axial force controlled; Strain distribution
* Corresponding author. Tel.: +86-027-87792331; fax: +86-027-87792333. E-mail address: [email protected]
1877-7058 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi:10.1016/j.proeng.2014.10.358
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Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
1. Introduction Due to high strength/weight ratio, lightweight alloy, such as aluminum alloy, magnesium alloy, and titanium alloy, sheets have a great application potential for the weight reduction in the aerospace and automobile industries. However, the formability of these materials is poor at room temperature, which seriously limits their applications. Lots of investigations have indicated that electromagnetic forming (EMF) as a high velocity forming method can significantly improve the formability of some these materials due to the following main factors: inertia effects, changes in constitutive behavior, impact, and dynamic failure mode etc. [1, 2]. Hence the EMF may have a good application prospect in the forming of the hard-form metal sheet. However, by now, EMF’s applications on metal sheet forming are rather rare, especially for the deep drawing. Manish, Daehn [3], Manish, Shang et al. [4] used the uniform pressure electromagnetic actuator for forming a depression and embossing. Lai, Han, Cao et al. [5] used a 200 kJ electromagnetic forming system to flange a sheet with the thickness, the outer diameter, and the inner diameter of 5, 640 and 180 mm, respectively. For the deep drawing, the major issue should be the non-uniform thickness reduction in the forming process. The failure generally occurs at the region where thickness reduction is maximum. To realize the deep drawing, the thickness reduction should be well controlled. In conventional sheet forming, the method to alter the thickness distribution (or strain distribution) may be to control the material flow at the flange region of the sheet, such as painting lubricant, using multi-point blank holder, and applying hydraulic pressure on the periphery of the flange (called fluid-pressure-assisted deep drawing)[6], etc. The electromagnetically assisted sheet metal stamping (EMAS) is based on the idea of directly delivering the deformation where it is required and then controlling the strain distribution [7-9]. By EMAS the AA2219-O sheet with the diameter and the thickness of 101.6 and 0.83 mm was drawn into the cup with height of 34.5 mm while the no failure cup height made by conventional deep drawing is only 10.4 mm [9]. Compared with other methods, both the fluid-pressure-assisted deep drawing and the EMAS are to directly deliver the deformation where it is required and thus can control the material flow more actively. In the EMF, especially the electromagnetic deep drawing, the methods to alter the strain distribution are few studied. Different to the traditional quasi-static forming processing, the high inertia force on the flange region of the sheet in EMF would significantly restrict the material flow on the flange. Inspired by the fluid-pressure-assisted deep drawing and EMAS, the approach by introducing an additional negative Fr on the flange of the sheet was studied in this paper. The preliminary experimental studies used an electromagnetic coil, whose outer diameter is larger than the diameter of the workpiece thus the Lorentz force distributions are significantly changed, to form a circular aluminum alloy sheet. The results show that the material flow of the flange was significantly improved. The reason may be the changes of Lorentz force distribution. Electromagnetic analysis indicates that the major difference between the larger and smaller diameter is that the Fr on the flange. It indicates that the negative Fr would affect the material flow and then affects the maximum no failure forming depth. However, the Fz and the Fr generated by one coil are coupled each other, the magnitudes and the action-time sequences of the Fr and Fz may not be optimal. Thus, for further investigation, a more flexible EMF system should be designed. In this paper, the concept of radial-axial force controlled (RAFC) EMF was introduced, where two coils are used to generate the Fz and the Fr, respectively. The key issue is focus on the electromagnetic design of the RAFC EMF system. The electromagnetic design principle of the system and the control of the Fz and the Fr were discussed in detail. 2. Radial Lorentz Force on the flange Electromagnetic sheet forming is a high speed metal forming technology, which shapes the sheet by Lorentz forces generated by the pulsed magnetic field and eddy current induced by the pulsed magnetic field. The Lorentz forces have two components: radial Lorentz force (Fr) and axial Lorentz force (Fz). Commonly, the Fz is considered to play the leading role due to its effects on accelerating the material forming in axial direction, while the Fr is subjectively considered to be unimportant and is usually ignored. In our preliminary study, a coil whose outer diameter is larger than the diameter of sheet workpiece was used to form the sheet. The results in Fig. 1 show that the material flow of the flange was significantly improved. To explain the phenomenon, the electromagnetic analysis was carried out. Fig. 2 shows the Lorentz force distributions
Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
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in the cases of the smaller and the larger coil’s diameter. The major difference between the two distributions is that an additional negative Fr is introduced on the flange in the case of the coil with a larger diameter. Thus the negative Fr is the main reason of the improvement for the material flow on the flange. For the sake of simplicity, the workpiece region above the cavity and the corner of the die is denoted by D1, the flange region is denoted by D2. And unless noted otherwise, below the Fz and the Fr represent the axial force on the D1 and the radial force on the D2, respectively. As shown in Fig. 3, the Fz accelerates the workpiece in negative axial direction, while the Fr accelerates the flange material in negative radial direction. By introducing the Fr, the material flow can be enhanced, thus the strain and thickness distribution may be improved. However, in this method the Fz and the Fr are generated by the one coil, thus the Fz and the Fr are inter-coupling, couldn’t be controlled separately. A more flexible scheme maybe use two coils, which are energized by two capacitor banks separately, to generate the Fz and the Fr, respectively. And then the magnitudes and the action-time sequences of the Fz and Fr can be flexibly controlled.
Fig. 1. Comparison of the sheet formed by the coils with different outer diameters: (a) The outer diameter of the coil is smaller than the diameter of sheet; (b) the outer diameter of the coil is larger than the diameter of sheet.
Fig. 2. Comparison of the Lorentz force distribution of different outer diameter: (a) The outer diameter of the coil is smaller than the diameter of sheet; (b) the outer diameter of the coil is larger than the diameter of sheet.
Region D2
Region D1
Fr
Region D2 Fr
Sheet
Die
Fz Cavity
Fig. 3. Schematic of the roles of the Fz and the Fr: The Fz accelerates the material above the cavity in negative axial direction, while the Fr accelerates the flange material in negative radial direction.
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3. Radial-axial force controlled (RAFC) EMF 3.1. Electromagnetic design of system One simple and visualized approach to generate the Fz and the Fr separately is to split the coil shown in Fig. 2(b) into two coils. The coil with smaller diameter is used to generate the Fz on the D1, while the other is to generate the Fr on the D2. Since the distribution of the Fz and the Fr are directly related to the geometry parameters of the coils, the geometry design of the two coils is a key issue. As an illustrate, Fig. 4 gives one design to form an AA5083-O sheet with diameter and thickness of 130 mm and 1 mm, respectively. Fig. 4(a) shows the dimension parameters of the system, Fig. 4(b) shows the electrical connection of the coils and the capacitor banks. Table 1 lists the electrical parameters of the system. The Coil_1 has 12 layers copper conductors in radial direction, each layer has 5 turns, and thus the total turns of the Coil_1 is 60. The Coil_2 has 4 layers copper conductors in radial direction, each layer has 5 turns, the total turns thus is 20. To verify the design, the electromagnetic simulation was carried out. Fig. 5(a) shows the Lorentz force generated by Coil_1. It can be seen that the Fz is the major component Lorentz force. There is a radial force in positive radial direction on the flange which would block the material flow into the die. Fig. 5(b) shows that the Lorentz force generated by Coil_2. The Lorentz forces mainly focus on the flange, and have a considerable radial component Fr. The Fr is in negative radial direction that will be benefit to make the material flow into the die. The axial force on the flange region is also great, which would provide an additional blank hold force on the flange, and increase the frictional force between the workpiece and the die. The effects of this axial force need further investigations that would not be studied in this paper. Additionally, to bear the high mechanical load of the coils during the process, the reinforcement of the coils also should be well designed. However, this issue is beyond the main scope of this paper, readers may refers to Qiu, Han [10], where the nondestructive pulsed high field magnet technology was introduced into the design of the high strength coil used in EMF. Table 1. Electrical parameters of the system. Parameter
Magnitude
Unite
Description
n1
60
turn
Turns of Coil_1
n2
20
turn
Turns of Coil_2
Cp 1
160
ȝ)
Capacitance of C1
Cp 2
160
ȝ)
Capacitance of C2
Ȗ
59.5
QȍP
Resistivity of AA5083-O
RL1
10
Pȍ
Line resistance of circuit 1
RL2
10
Pȍ
Line resistance of circuit 2
Rd1
100
Pȍ
Crowbar resistance of circuit 1
Rd2
100
Pȍ
Crowbar resistance of circuit 2
L1
5
ȝ+
Line inductance of circuit 1
L2
5
ȝ+
Line inductance of circuit 2
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Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511 (a)
(b) 160 mm 85 mm
C2
S2
80 mm Coil_2
Coil_1
20 mm
20 mm
20 mm
Rd2
Epoxy board
C1
RL2
S1
1 mm 2 mm
5 mm
Rd1
Sheet 130 mm 40 mm
RL1
L2
L1
Die Coil_2
Coil_1_1
Fig. 4. RAFC EMF system: (a) the dimension parameters of the system; (b) the electrical connection of the system.
Fig. 5. The Lorentz force distribution: (a) generated by Coil_1; (b) generated by the Coil_2.
3.2. Control of Fr and Fz The discharging energies of the Coil_1 and the Coil_2 are denoted by E1 and E2, respectively. The energy ratio is defined as E2/E1, which represents the different work patterns of the system. In the following, the Fr and the Fz in the cases of different energy ratios will be discussed. To be more visualized, the total axial Lorentz force (Fz) on the region D1 and the total radial Lorentz force (Fr) on the region D2 were calculated. The results in the case that only Coil_1 is discharged are shown in Fig. 6, where the initial voltage is 20 kV, the peak values of the current, Fz and Fr are 23.7 kA, -0.241 MN, and 0.037 MN, respectively. The results in the cases of different energies ratios are shown in Fig. 7. To make the conclusion more universal, the forces were normalized by the magnitude of the axial force (0.241 MN) on the region D1 in the case of only Coil_1 is discharged. And the E1 is constant in all the cases. Fig. 7 (a) shows the normalized Fz on the D1 region in the cases of the energy ratios increase from 0 to 2 with the interval of 0.25. The magnitude of peak value of the Fz increases with the increase of the energy ratio, while the variation are less than 7%, which indicates that the Coil_2 almost has no influence on the Fz on the D1 region. In other words, the Fz on the D1 region is determined by the energy of the Coil_1. Fig. 7 (b) shows the normalized Fr on the flange in the cases of different energy ratios. In the case of the 0 energy ratio, the Fr is positive which means that the Coil_1 would generate a positive radial Lorentz force, thus blocks the flange material flow into the cavity. With the increase of the energy ratio the Fr changes to be negative which improves the material flow of the D2 region, and the Fr increases near proportion to the energy ratio, which indicates that the Fr on the D2 region is linearly determined by the energy of the Coil_2. Thus the magnitudes of the Fz and the Fr are controlled separately, flexibly and linearly by the two coils.
(a) x 104 3
(b) x 105 1 Lorenz force (N)
Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
Magnitude (V or A)
2510
2 1
Current of Coil_1 Voltage of Capacitor 1
0 -1 0
1
2 3 Time (s)
4
-1
Fr Fz
-2 -3 0
5 x 10
0
-4
1
2 3 Time (s)
4
5 x 10
-4
Fig. 6. Simulation results in the case that only Coil_1 discharged at 32 kJ: (a) the current and voltage curves; (b) the Fr on the D2 region and the Fz on the D1 region.
(b)
(a)
0 E2/E1=0 E2/E1=0.25 E2/E1=0.5 E2/E1=0.75 E2/E1=1 E2/E1=1.25 E2/E1=1.5 E2/E1=1.75 E2/E1=2
-0.5
-1 Increasing the energy ratio
0
2
Time (s)
4
Normalized Fr
Normalized Fz
0
-2 -3 -4 0
6 x 10
E2/E1=0 E2/E1=0.25 E2/E1=0.5 E2/E1=0.75 E2/E1=1 E2/E1=1.25 E2/E1=1.5 E2/E1=1.75 E2/E1=2
-1
Increasing the energy ratio
2
-4
Time (s)
4
6 x 10
-4
Fig. 7. Energy ratio’s influence on the Fz on the D1 region and the Fr on the D2 region: (a) the Fz on the D1 region in the cases of different energy ratios; (b) the Fr on the D2 region in the cases of different energy ratios.
(a)
(b) 0.5
0
Normalized Fr
Normalized Fz
Coil_1 leads
-0.5
-1 Coil_1 delays
-1.5 0
2
Coil_1 delays 50 Ps Coil_1 delays 50 Ps Simultaneously Coil_1 leads 25 Ps Coil_1 leads 50 Ps
Time (s)
4
6 x 10
-4
0 -0.5
Coil_1 leads
-1 -1.5 -2 0
Coil_1 delays
2
Coil_1 delays 50 Ps Coil_1 delays 25 Ps Simultaneously Coil_1 leads 25 Ps Coil_1 leads 50 Ps
Time (s)
4
6 x 10
-4
Fig. 8. Discharging sequences’ influences on the Fz and the Fr: (a) the Fz in the cases of the different sequences; (a) the Fr in the cases of the different sequences.
Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
Furthermore, due to the fact that the electromagnetic forming is a high speed forming technology, the discharging sequence of the coils may be also very important, thus the sequence’s influence on the Fz and the Fr should be studied. Fig. 8(a) and (b) shows the waves of the Fz and the Fr in five discharging sequences, respectively. And in all of the cases, the energy ratio is 1. It can be seen that the Coil_1’s discharging delay would increases the Fz significantly, while its influence on the magnitude of the Fr can be ignored. The sequence’s influence on the force may be relevant to the phenomenon of the magnetic diffusion on the metal. Compared with the energy’s influence on the Lorentz force, the discharging sequence’s influence is much smaller. The main discharging sequences’ influences may lie in the action-time of the Fz and the Fr, which is very important in EMF due to the high speed dynamic processing. Thus the energy and the discharging sequence are two main degree of freedom to be controlled in the RAFC EMF. 4. Conclusions In this paper, the RACF EMF, where Fr and Fz are controlled separately, was introduced. Different to the traditional EMF, an additional negative radial Lorentz force has been introduced at the flange region of workpiece to improve the material flow behavior and increase the limit forming ability of the EMF. The electromagnetic analysis of the approach was discussed in detail. The analysis shows that the Fz and the Fr are determined by the discharging energies of the Coil_1 and the Coil_2, respectively, which indicates the two components of the forces can be well controlled through adjusting the energies of the two coils. Meanwhile, the discharging sequence has certain impact on the Fz and the Fr. By the analysis the feasibility of the RAFC EMF has been preliminary verified. However, all of the analysis is based on the numerical model only electromagnetic field was considered, the actual forming results should be checked out through the multi-physics simulation of the RAFC EMF, and the experiments. And the effects of the discharging energies and the sequences on the forming behavior should be further investigated. References [1] Mala Seth Dehra, High velocity formability and factors affecting it, Ph.D., The Ohio State University, Ann Arbor, 2006. [2] Glenn S. Daehn, Vincent J. Vohnout, and Subrangshu Datta, Hyperplastic forming: process potential and factors affecting formability, in The 1999 MRS Fall Meeting - Symposium W 'GaN and Related Alloys', November 29, 1999 - December 1, 1999, Boston, MA, USA, 2000, pp. 247-252. [3] Manish Kamal and Glenn S. Daehn, A Uniform Pressure Electromagnetic Actuator for Forming Flat Sheets, Journal of Manufacturing Science and Engineering, 2007, 129, 369. [4] Manish Kamal, Jianhui Shang, V. Cheng, S. Hatkevich, and G. S. Daehn, Agile manufacturing of a micro-embossed case by a two-step electromagnetic forming process, Journal of Materials Processing Technology, 2007, 190, 41-50. [5] Zhipeng Lai, Xiaotao Han, Quanliang Cao, Li Qiu, Zhongyu Zhou, and Liang Li, The Electromagnetic Flanging of a Large-Scale Sheet Workpiece, Applied Superconductivity, IEEE Transactions on, 2014, 24, 1-5. [6] S. Thiruvarudchelvan and M. J. Tan, Fluid-pressure-assisted deep drawing, Journal of Materials Processing Technology, Oct 1 2007, 192, 8-12. [7] Glenn S. Daehn, Jianhui Shang, and Vincent J. Vohnout, Electromagnetically assisted sheet forming: Enabling difficult shapes and materials by controlled energy distribution, in Proceedings of the Technical Sessions presented by the Materials Processing and Manufacturing Division of TMS, March 2, 2003 - March 6, 2003, San Diego, CA, United states, 2003, 117-128. [8] Jianhui Shang and G. Daehn, Electromagnetically assisted sheet metal stamping, Journal of Materials Processing Technology, 05/01 2011, 211, 868-874. [9] Jianhui Shang, Electromagnetically assisted sheet metal stamping, Ph.D., The Ohio State University, Ann Arbor, 2006. [10] Li Qiu, Xiaotao Han, Tao Peng, Hongfa Ding, Qi Xiong, Zhongyu Zhou, Chengxi Jiang, Yiliang Lv, and Liang Li, Design and experiments of a high field electromagnetic forming system, Applied Superconductivity, IEEE Transactions on, 2012, 22.
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ScienceDirect Procedia Engineering 81 (2014) 2505 – 2511
11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014, Nagoya Congress Center, Nagoya, Japan
Radial-axial force controlled electromagnetic sheet deep drawing: electromagnetic analysis Zhipeng Laia,b, Quanliang Caoa,b, Xiaotao Hana,b, Zhongyu Zhoua,b, Qi Xionga,b, Xiao Zhanga,b,Qi Chena,b, Liang Lia,b, * a Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China
b
Abstract
A new approach, radial-axial force controlled (RAFC) electromagnetic sheet forming (EMF), has been developed for hard-form metal sheet deep drawing. Different to the traditional EMF, an additional radial Lorentz force was introduced at the flange region of workpiece to improve the material flow and reduce the maximum strain of workpiece. For this purpose, an EMF system with two coils has been designed. The two coils were used to generate the axial Lorentz force (Fz) on the workpiece region (D1) above the cavity and the radial force (Fr) on the flange region (D2), respectively. The Fz was used to accelerate the D1 region’s material in axial direction to shape the workpiece into the die, while the Fr was used to accelerate the D2 region’s material in negative radial direction to improve the material flow of the flange. In this paper the electromagnetic analysis of the system has been carried out. As a proof of concept, the variation characteristics of Fr and Fz under different discharging energies and schedules of the coils were simulated and analyzed. The results show that the magnitudes and the action time of the Fr and the Fz can be well controlled, which indicates that the forming can be flexibly controlled. © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and and peer-review peer-reviewunder underresponsibility responsibilityofofthe Nagoya University and Toyohashi of Technology. Selection Department of Materials ScienceUniversity and Engineering, Nagoya University Keywords: Electromagnetic sheet forming; Material flow; Radial-axial force controlled; Strain distribution
* Corresponding author. Tel.: +86-027-87792331; fax: +86-027-87792333. E-mail address: [email protected]
1877-7058 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi:10.1016/j.proeng.2014.10.358
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Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
1. Introduction Due to high strength/weight ratio, lightweight alloy, such as aluminum alloy, magnesium alloy, and titanium alloy, sheets have a great application potential for the weight reduction in the aerospace and automobile industries. However, the formability of these materials is poor at room temperature, which seriously limits their applications. Lots of investigations have indicated that electromagnetic forming (EMF) as a high velocity forming method can significantly improve the formability of some these materials due to the following main factors: inertia effects, changes in constitutive behavior, impact, and dynamic failure mode etc. [1, 2]. Hence the EMF may have a good application prospect in the forming of the hard-form metal sheet. However, by now, EMF’s applications on metal sheet forming are rather rare, especially for the deep drawing. Manish, Daehn [3], Manish, Shang et al. [4] used the uniform pressure electromagnetic actuator for forming a depression and embossing. Lai, Han, Cao et al. [5] used a 200 kJ electromagnetic forming system to flange a sheet with the thickness, the outer diameter, and the inner diameter of 5, 640 and 180 mm, respectively. For the deep drawing, the major issue should be the non-uniform thickness reduction in the forming process. The failure generally occurs at the region where thickness reduction is maximum. To realize the deep drawing, the thickness reduction should be well controlled. In conventional sheet forming, the method to alter the thickness distribution (or strain distribution) may be to control the material flow at the flange region of the sheet, such as painting lubricant, using multi-point blank holder, and applying hydraulic pressure on the periphery of the flange (called fluid-pressure-assisted deep drawing)[6], etc. The electromagnetically assisted sheet metal stamping (EMAS) is based on the idea of directly delivering the deformation where it is required and then controlling the strain distribution [7-9]. By EMAS the AA2219-O sheet with the diameter and the thickness of 101.6 and 0.83 mm was drawn into the cup with height of 34.5 mm while the no failure cup height made by conventional deep drawing is only 10.4 mm [9]. Compared with other methods, both the fluid-pressure-assisted deep drawing and the EMAS are to directly deliver the deformation where it is required and thus can control the material flow more actively. In the EMF, especially the electromagnetic deep drawing, the methods to alter the strain distribution are few studied. Different to the traditional quasi-static forming processing, the high inertia force on the flange region of the sheet in EMF would significantly restrict the material flow on the flange. Inspired by the fluid-pressure-assisted deep drawing and EMAS, the approach by introducing an additional negative Fr on the flange of the sheet was studied in this paper. The preliminary experimental studies used an electromagnetic coil, whose outer diameter is larger than the diameter of the workpiece thus the Lorentz force distributions are significantly changed, to form a circular aluminum alloy sheet. The results show that the material flow of the flange was significantly improved. The reason may be the changes of Lorentz force distribution. Electromagnetic analysis indicates that the major difference between the larger and smaller diameter is that the Fr on the flange. It indicates that the negative Fr would affect the material flow and then affects the maximum no failure forming depth. However, the Fz and the Fr generated by one coil are coupled each other, the magnitudes and the action-time sequences of the Fr and Fz may not be optimal. Thus, for further investigation, a more flexible EMF system should be designed. In this paper, the concept of radial-axial force controlled (RAFC) EMF was introduced, where two coils are used to generate the Fz and the Fr, respectively. The key issue is focus on the electromagnetic design of the RAFC EMF system. The electromagnetic design principle of the system and the control of the Fz and the Fr were discussed in detail. 2. Radial Lorentz Force on the flange Electromagnetic sheet forming is a high speed metal forming technology, which shapes the sheet by Lorentz forces generated by the pulsed magnetic field and eddy current induced by the pulsed magnetic field. The Lorentz forces have two components: radial Lorentz force (Fr) and axial Lorentz force (Fz). Commonly, the Fz is considered to play the leading role due to its effects on accelerating the material forming in axial direction, while the Fr is subjectively considered to be unimportant and is usually ignored. In our preliminary study, a coil whose outer diameter is larger than the diameter of sheet workpiece was used to form the sheet. The results in Fig. 1 show that the material flow of the flange was significantly improved. To explain the phenomenon, the electromagnetic analysis was carried out. Fig. 2 shows the Lorentz force distributions
Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
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in the cases of the smaller and the larger coil’s diameter. The major difference between the two distributions is that an additional negative Fr is introduced on the flange in the case of the coil with a larger diameter. Thus the negative Fr is the main reason of the improvement for the material flow on the flange. For the sake of simplicity, the workpiece region above the cavity and the corner of the die is denoted by D1, the flange region is denoted by D2. And unless noted otherwise, below the Fz and the Fr represent the axial force on the D1 and the radial force on the D2, respectively. As shown in Fig. 3, the Fz accelerates the workpiece in negative axial direction, while the Fr accelerates the flange material in negative radial direction. By introducing the Fr, the material flow can be enhanced, thus the strain and thickness distribution may be improved. However, in this method the Fz and the Fr are generated by the one coil, thus the Fz and the Fr are inter-coupling, couldn’t be controlled separately. A more flexible scheme maybe use two coils, which are energized by two capacitor banks separately, to generate the Fz and the Fr, respectively. And then the magnitudes and the action-time sequences of the Fz and Fr can be flexibly controlled.
Fig. 1. Comparison of the sheet formed by the coils with different outer diameters: (a) The outer diameter of the coil is smaller than the diameter of sheet; (b) the outer diameter of the coil is larger than the diameter of sheet.
Fig. 2. Comparison of the Lorentz force distribution of different outer diameter: (a) The outer diameter of the coil is smaller than the diameter of sheet; (b) the outer diameter of the coil is larger than the diameter of sheet.
Region D2
Region D1
Fr
Region D2 Fr
Sheet
Die
Fz Cavity
Fig. 3. Schematic of the roles of the Fz and the Fr: The Fz accelerates the material above the cavity in negative axial direction, while the Fr accelerates the flange material in negative radial direction.
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3. Radial-axial force controlled (RAFC) EMF 3.1. Electromagnetic design of system One simple and visualized approach to generate the Fz and the Fr separately is to split the coil shown in Fig. 2(b) into two coils. The coil with smaller diameter is used to generate the Fz on the D1, while the other is to generate the Fr on the D2. Since the distribution of the Fz and the Fr are directly related to the geometry parameters of the coils, the geometry design of the two coils is a key issue. As an illustrate, Fig. 4 gives one design to form an AA5083-O sheet with diameter and thickness of 130 mm and 1 mm, respectively. Fig. 4(a) shows the dimension parameters of the system, Fig. 4(b) shows the electrical connection of the coils and the capacitor banks. Table 1 lists the electrical parameters of the system. The Coil_1 has 12 layers copper conductors in radial direction, each layer has 5 turns, and thus the total turns of the Coil_1 is 60. The Coil_2 has 4 layers copper conductors in radial direction, each layer has 5 turns, the total turns thus is 20. To verify the design, the electromagnetic simulation was carried out. Fig. 5(a) shows the Lorentz force generated by Coil_1. It can be seen that the Fz is the major component Lorentz force. There is a radial force in positive radial direction on the flange which would block the material flow into the die. Fig. 5(b) shows that the Lorentz force generated by Coil_2. The Lorentz forces mainly focus on the flange, and have a considerable radial component Fr. The Fr is in negative radial direction that will be benefit to make the material flow into the die. The axial force on the flange region is also great, which would provide an additional blank hold force on the flange, and increase the frictional force between the workpiece and the die. The effects of this axial force need further investigations that would not be studied in this paper. Additionally, to bear the high mechanical load of the coils during the process, the reinforcement of the coils also should be well designed. However, this issue is beyond the main scope of this paper, readers may refers to Qiu, Han [10], where the nondestructive pulsed high field magnet technology was introduced into the design of the high strength coil used in EMF. Table 1. Electrical parameters of the system. Parameter
Magnitude
Unite
Description
n1
60
turn
Turns of Coil_1
n2
20
turn
Turns of Coil_2
Cp 1
160
ȝ)
Capacitance of C1
Cp 2
160
ȝ)
Capacitance of C2
Ȗ
59.5
QȍP
Resistivity of AA5083-O
RL1
10
Pȍ
Line resistance of circuit 1
RL2
10
Pȍ
Line resistance of circuit 2
Rd1
100
Pȍ
Crowbar resistance of circuit 1
Rd2
100
Pȍ
Crowbar resistance of circuit 2
L1
5
ȝ+
Line inductance of circuit 1
L2
5
ȝ+
Line inductance of circuit 2
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Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511 (a)
(b) 160 mm 85 mm
C2
S2
80 mm Coil_2
Coil_1
20 mm
20 mm
20 mm
Rd2
Epoxy board
C1
RL2
S1
1 mm 2 mm
5 mm
Rd1
Sheet 130 mm 40 mm
RL1
L2
L1
Die Coil_2
Coil_1_1
Fig. 4. RAFC EMF system: (a) the dimension parameters of the system; (b) the electrical connection of the system.
Fig. 5. The Lorentz force distribution: (a) generated by Coil_1; (b) generated by the Coil_2.
3.2. Control of Fr and Fz The discharging energies of the Coil_1 and the Coil_2 are denoted by E1 and E2, respectively. The energy ratio is defined as E2/E1, which represents the different work patterns of the system. In the following, the Fr and the Fz in the cases of different energy ratios will be discussed. To be more visualized, the total axial Lorentz force (Fz) on the region D1 and the total radial Lorentz force (Fr) on the region D2 were calculated. The results in the case that only Coil_1 is discharged are shown in Fig. 6, where the initial voltage is 20 kV, the peak values of the current, Fz and Fr are 23.7 kA, -0.241 MN, and 0.037 MN, respectively. The results in the cases of different energies ratios are shown in Fig. 7. To make the conclusion more universal, the forces were normalized by the magnitude of the axial force (0.241 MN) on the region D1 in the case of only Coil_1 is discharged. And the E1 is constant in all the cases. Fig. 7 (a) shows the normalized Fz on the D1 region in the cases of the energy ratios increase from 0 to 2 with the interval of 0.25. The magnitude of peak value of the Fz increases with the increase of the energy ratio, while the variation are less than 7%, which indicates that the Coil_2 almost has no influence on the Fz on the D1 region. In other words, the Fz on the D1 region is determined by the energy of the Coil_1. Fig. 7 (b) shows the normalized Fr on the flange in the cases of different energy ratios. In the case of the 0 energy ratio, the Fr is positive which means that the Coil_1 would generate a positive radial Lorentz force, thus blocks the flange material flow into the cavity. With the increase of the energy ratio the Fr changes to be negative which improves the material flow of the D2 region, and the Fr increases near proportion to the energy ratio, which indicates that the Fr on the D2 region is linearly determined by the energy of the Coil_2. Thus the magnitudes of the Fz and the Fr are controlled separately, flexibly and linearly by the two coils.
(a) x 104 3
(b) x 105 1 Lorenz force (N)
Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
Magnitude (V or A)
2510
2 1
Current of Coil_1 Voltage of Capacitor 1
0 -1 0
1
2 3 Time (s)
4
-1
Fr Fz
-2 -3 0
5 x 10
0
-4
1
2 3 Time (s)
4
5 x 10
-4
Fig. 6. Simulation results in the case that only Coil_1 discharged at 32 kJ: (a) the current and voltage curves; (b) the Fr on the D2 region and the Fz on the D1 region.
(b)
(a)
0 E2/E1=0 E2/E1=0.25 E2/E1=0.5 E2/E1=0.75 E2/E1=1 E2/E1=1.25 E2/E1=1.5 E2/E1=1.75 E2/E1=2
-0.5
-1 Increasing the energy ratio
0
2
Time (s)
4
Normalized Fr
Normalized Fz
0
-2 -3 -4 0
6 x 10
E2/E1=0 E2/E1=0.25 E2/E1=0.5 E2/E1=0.75 E2/E1=1 E2/E1=1.25 E2/E1=1.5 E2/E1=1.75 E2/E1=2
-1
Increasing the energy ratio
2
-4
Time (s)
4
6 x 10
-4
Fig. 7. Energy ratio’s influence on the Fz on the D1 region and the Fr on the D2 region: (a) the Fz on the D1 region in the cases of different energy ratios; (b) the Fr on the D2 region in the cases of different energy ratios.
(a)
(b) 0.5
0
Normalized Fr
Normalized Fz
Coil_1 leads
-0.5
-1 Coil_1 delays
-1.5 0
2
Coil_1 delays 50 Ps Coil_1 delays 50 Ps Simultaneously Coil_1 leads 25 Ps Coil_1 leads 50 Ps
Time (s)
4
6 x 10
-4
0 -0.5
Coil_1 leads
-1 -1.5 -2 0
Coil_1 delays
2
Coil_1 delays 50 Ps Coil_1 delays 25 Ps Simultaneously Coil_1 leads 25 Ps Coil_1 leads 50 Ps
Time (s)
4
6 x 10
-4
Fig. 8. Discharging sequences’ influences on the Fz and the Fr: (a) the Fz in the cases of the different sequences; (a) the Fr in the cases of the different sequences.
Zhipeng Lai et al. / Procedia Engineering 81 (2014) 2505 – 2511
Furthermore, due to the fact that the electromagnetic forming is a high speed forming technology, the discharging sequence of the coils may be also very important, thus the sequence’s influence on the Fz and the Fr should be studied. Fig. 8(a) and (b) shows the waves of the Fz and the Fr in five discharging sequences, respectively. And in all of the cases, the energy ratio is 1. It can be seen that the Coil_1’s discharging delay would increases the Fz significantly, while its influence on the magnitude of the Fr can be ignored. The sequence’s influence on the force may be relevant to the phenomenon of the magnetic diffusion on the metal. Compared with the energy’s influence on the Lorentz force, the discharging sequence’s influence is much smaller. The main discharging sequences’ influences may lie in the action-time of the Fz and the Fr, which is very important in EMF due to the high speed dynamic processing. Thus the energy and the discharging sequence are two main degree of freedom to be controlled in the RAFC EMF. 4. Conclusions In this paper, the RACF EMF, where Fr and Fz are controlled separately, was introduced. Different to the traditional EMF, an additional negative radial Lorentz force has been introduced at the flange region of workpiece to improve the material flow behavior and increase the limit forming ability of the EMF. The electromagnetic analysis of the approach was discussed in detail. The analysis shows that the Fz and the Fr are determined by the discharging energies of the Coil_1 and the Coil_2, respectively, which indicates the two components of the forces can be well controlled through adjusting the energies of the two coils. Meanwhile, the discharging sequence has certain impact on the Fz and the Fr. By the analysis the feasibility of the RAFC EMF has been preliminary verified. However, all of the analysis is based on the numerical model only electromagnetic field was considered, the actual forming results should be checked out through the multi-physics simulation of the RAFC EMF, and the experiments. And the effects of the discharging energies and the sequences on the forming behavior should be further investigated. References [1] Mala Seth Dehra, High velocity formability and factors affecting it, Ph.D., The Ohio State University, Ann Arbor, 2006. [2] Glenn S. Daehn, Vincent J. Vohnout, and Subrangshu Datta, Hyperplastic forming: process potential and factors affecting formability, in The 1999 MRS Fall Meeting - Symposium W 'GaN and Related Alloys', November 29, 1999 - December 1, 1999, Boston, MA, USA, 2000, pp. 247-252. [3] Manish Kamal and Glenn S. Daehn, A Uniform Pressure Electromagnetic Actuator for Forming Flat Sheets, Journal of Manufacturing Science and Engineering, 2007, 129, 369. [4] Manish Kamal, Jianhui Shang, V. Cheng, S. Hatkevich, and G. S. Daehn, Agile manufacturing of a micro-embossed case by a two-step electromagnetic forming process, Journal of Materials Processing Technology, 2007, 190, 41-50. [5] Zhipeng Lai, Xiaotao Han, Quanliang Cao, Li Qiu, Zhongyu Zhou, and Liang Li, The Electromagnetic Flanging of a Large-Scale Sheet Workpiece, Applied Superconductivity, IEEE Transactions on, 2014, 24, 1-5. [6] S. Thiruvarudchelvan and M. J. Tan, Fluid-pressure-assisted deep drawing, Journal of Materials Processing Technology, Oct 1 2007, 192, 8-12. [7] Glenn S. Daehn, Jianhui Shang, and Vincent J. Vohnout, Electromagnetically assisted sheet forming: Enabling difficult shapes and materials by controlled energy distribution, in Proceedings of the Technical Sessions presented by the Materials Processing and Manufacturing Division of TMS, March 2, 2003 - March 6, 2003, San Diego, CA, United states, 2003, 117-128. [8] Jianhui Shang and G. Daehn, Electromagnetically assisted sheet metal stamping, Journal of Materials Processing Technology, 05/01 2011, 211, 868-874. [9] Jianhui Shang, Electromagnetically assisted sheet metal stamping, Ph.D., The Ohio State University, Ann Arbor, 2006. [10] Li Qiu, Xiaotao Han, Tao Peng, Hongfa Ding, Qi Xiong, Zhongyu Zhou, Chengxi Jiang, Yiliang Lv, and Liang Li, Design and experiments of a high field electromagnetic forming system, Applied Superconductivity, IEEE Transactions on, 2012, 22.
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