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Inside bead forming of aluminum tube by electro-magnetic forming
Journal of Materials Processing Technology 80 – 81 (1998) 695 – 699
Inside bead forming of aluminum tube by electro-magnetic forming Yoichi Murakoshi a,*, Masaharu Takahashi a, Toshio Sano a, Kotaro Hanada b, Hideaki Negishi c a
Mechanical Engineering Laboratory, AIST, MITI Namiki 1 -2, Tsukuba, Ibaraki 305, Japan b JST fellow, Namiki 1 -2, Tsukuba, Ibaraki 305, Japan c Electro Communication Uni6ersity, Chofu ga oka 1 -5 -1, Chofu, Tokyo 182, Japan
Abstract In this paper, the inside bead forming of aluminum tube (A6063TD) by electro-magnetic forming (EMF) is reported experimentally and numerically. The shape of the bead was affected by the change of the discharge voltage and the dimensions of a groove at a beading die which have a width and a shoulder radius. With the increase of the discharge voltage and the shoulder radius, the bead height increased due to the increasing of the bending moment. On the discharge voltage of over 4 kV (400 mF), the bead height rapidly increased so that the aluminum tube entered the groove at the beading die from both sides. Therefore the thickness strain at the top of the bead increased, the longitudinal strain of the aluminum tube saturated, and a necking appeared at the bead near the shoulder part of the beading die. Also, the simulation of the bead forming was carried out by using MARC and compared with the experimental results. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Bead forming; Electro-magnetic forming; Aluminum tube
1. Introduction High energy rate forming (HERF) processes [1,2] such as explosive forming, electro-hydraulic forming and electro-magnetic forming (EMF), have some attractive characteristics [3]. These are the extremely high ductility under high velocity conditions, the low spring back after the unloaded condition, and the one-sided die which is a male or a female die. Although HERF processes have many useful characteristics as shown above, there are only a few practical examples, so that in the HERF process it is difficult to control the energy and to make a lot of parts with complicated shapes. Therefore much research has been carried out to obtain the optimal process and to produce the practical examples which are used in the automobile and aerospace industry. Compared with other HERF processes, in EMF it is very easy to control the energy, little time is needed to deform the products, and it needs no transfer medium to transfer the deformation force [4]. But EMF * Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00217-9
cannot be used for ferrous materials, as the magnetic pressure which occurs between the ferrous material and the forming coil is smaller than the aluminum and copper material. The magnetic pressure is affected by the induced current in the ferrous material and the flux density which is made by the forming coil. Therefore the resistance of the materials is important. However expanding, shrinking, joining, straightening and cutting of the tube can be carried out by the EMF [5–11]. Bead forming is one of the tube forming processes carried out by EMF. It is possible to make the bead on the inside or on the outside of the tube by using a compressive or an expansive coil. According to whether the bead is deformed inside or outside the tube, the tube may have a higher stiffness. In this paper, the inside bead forming of an aluminum tube by using a compressive coil is carried out experimentally and numerically. The influence of the discharge voltage and the dimensions of the groove at the beading die are investigated. These influences are compared with the results of the simulation which used MARC.
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
696
3. Results and discussion
3.1. Estimated magnetic pressure
Fig. 1. Schematic diagram of the inside bead forming.
2. Experimental procedure Fig. 1 shows a schematic diagram of the inside bead forming of an aluminum tube by using a compressive coil. The schematic diagram shows the compressive coil, the groove at the beading die and the aluminum tube as a workpiece. The characteristics of the compressive coil are shown in Table 1. It is connected to a capacitor bank which has the maximum capacitance (C) of 400 mF, the total inductance (L) of 1.7 mH, and the total resistance (R) of 17.2 mV. To control the forming energy, the discharge voltage (V) was varied from 2 to 6 kV. The beading die was made from the polyacetal to decrease the friction force which acts between the aluminum tube and the beading die. The dimensions of the groove at the beading die were a width (w), a depth (d) and a shoulder radius (r). The shoulder radius was varied from 0 to 7 mm. But the width, the depth and the value of the capacitor were fixed at 5 mm, 9 mm and 400 mF, respectively. The aluminum tube (A6063TD) was annealed at 673 K for 1 h. The dimensions and the mechanical properties of the aluminum tube are shown in Table 2. These properties are also used to simulate the bead forming.
Fig. 2 shows the estimated flux density (B/Tesla) and the estimated magnetic pressure (P/MPa), which appeared at the area between the aluminum tube and the compressive coil. The estimated magnetic pressure reaches about 100 MPa on the 6 kV. The estimated magnetic pressure was calculated by the equation of P= B 2/2m0 where m0 is 1.257× 10 − 6. The estimated flux density is calculated by the equation of B=A B0/A0 where A is the area between the compressive coil and the aluminum tube, A0 is inside area of the compressive coil, and B0 is the flux density which was measured at the central point of the compressive coil without the aluminum tube. The flux density was measured by a search coil, which is 7.07 mm2 in area and has 20 turns of copper wire.
3.2. Influence of some parameters on the bead 3.2.1. Bead shape Fig. 3 shows a photograph of a typical shape of the bead. This is deformed at the 4 kV of the discharge voltage, 3 mm of the shoulder radius and 5 mm of the width. Fig. 4 (a) and (b) show the influence of the discharge voltage and the shoulder radius on the bead shape. The bead shape is affected by the increasing of the discharge voltage and the shoulder radius, because the bending moment on the shoulder part at the beading die increases. But, the influence of the discharge voltage on the bead shape is bigger than the effect of the change of the bead shape on the shoulder radius. Increasing the discharge voltage from 5 to 6 kV causes a large change in the bead shape and the bead height so that the balance between the friction force and the forming force was suddenly collapsed by the increasing of the discharge voltage. The friction force which acts between the aluminum tube and the beading die depends on the magnetic pressure, the friction coefficient
Table 1 Characteristics of the compressive coil Length (L0/mm)
Inside diameter (Din/mm)
Inductance (L/mH)
Resistance (R/mV)
50
36.5
12.5
24
Table 2 Characteristics of the annealed A6063TD Young’s modulus (E/Gpa)
Poisson ratio (y)
Yield stress (s0/MPa)
Plastic coefficient (C/MPa)
Strain-hardening exponent (n)
70
0.33
50
78
0.27
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
697
Fig. 2. Estimated flux density and magnetic pressure.
Fig. 3. Typical bead shape.
and the contacted area of the aluminum tube and the beading die. The forming force depends on the magnetic pressure and the area which the aluminum tube and the beading die does not contact. Therefore the aluminum tube enters the groove at the beading die. The influence of the length of the aluminum tube on the bead shape was investigated. As the length of the aluminum tube became shorter, a necking appeared at the lower discharge voltage. This has a similar explanation as for the effects of increasing the discharge voltage to 6 kV.
3.2.2. Influence of the discharge 6oltage and the shoulder radius on the bead height Fig. 5(a) and (b) show the influence of the discharge voltage and the shoulder radius on the bead height. The bead height is normalized by the width of the beading die. The bead height increases with an increase of the discharge voltage and the shoulder radius as shown in Fig. 5(a) and (b). In Fig. 5(a), the bead height on the shoulder radius of 3 mm is higher than it is on the shoulder radius of 0 mm and it reaches 1.2 on 6 kV of the discharge voltage. In Fig. 5(b), the bead height increases with the increase of the shoulder radius and it reaches about 0.8 with the shoulder radius of 7 mm. The difference of the bead height on the shoulder radius of 0 and 3 mm is due to the bending moment. The bending moment became big, with the increasing of the shoulder radius. 3.2.3. Thickness strain at the top of the bead Fig. 6(a) and (b) show the influence of the discharge voltage and the shoulder radius on the thickness strain at the top of the bead. The thickness strain increases with an increase of the discharge voltage and the shoulder radius as shown in Fig. 6(a) and (b). In Fig. 6(a), the sudden change of the thickness strain can be seen at 4 kV for the 0 mm and at 5 kV for the 3 mm shoulder radius. In the experiment, the thickness change was found at the top of the bead and the shoulder part of the aluminum tube. The thickness at the top of the bead increases so that a compressive force acts on the
material which enters the groove from both sides. On the other hand, the thickness at the shoulder part decreases so that the material at the shoulder part was expanded. In Fig. 6(b), the influence of the shoulder radius on the thickness strain at the shoulder part increases with an increase of the shoulder radius.
3.2.4. Longitudinal strain of the aluminum tube Fig. 7(a) and (b) show the influence of the discharge voltage and the shoulder radius on the longitudinal strain. The longitudinal strain shows the change of the whole length of the aluminum tube. Therefore it does not show only the change of the bead. With increasing discharge voltage, the longitudinal strain on the shoulder radius of 3 mm increases as shown in Fig. 7(a). But it peaks at 4 kV and then decreases. This is the same reason as in Section 3.2.1 and Section 3.2.3. Therefore the thickness strain at the top of the bead rapidly increased (Fig. 6(a)) and the longitudinal strain in Fig. 7(a) decreased on 6 kV. Change between the longitudinal strain and the shoulder radius in Fig. 7(b) also shows the increasing and the saturation on the shoulder radius of 5 mm. 3.3. Simulation of the bead forming Influence of the discharge voltage and the shoulder radius on the deformation process of the bead forming was predicted by an FEM simulation and compared with the experimental results. In this simulation, MARC was used with MENTAT as a pre-post processor.
3.3.1. Analytical conditions Fig. 8 shows a quarter of the finite element model which is used to simulate the bead forming. L0, w and r were 50, 5 and 3 mm, respectively. The dimensions and the properties of the aluminum tube which are shown in Table 2 were used in this simulation. But strain rate hardening coefficient was not used. The
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Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
Fig. 6. Influence of the discharge voltage and the shoulder radius on the thickness strain at the top of the bead.
Fig. 4. Influence of the discharge voltage and the shoulder radius bead shape on the bead shape.
shear friction coefficient (m) was 0.1. Although the magnetic pressure is a dynamic pressure, the static simulation was carried out by using the magnetic pressure equation of P(t) =Pm e − dt sin2vt where d and v were 500 and 13300. The magnetic pressure was applied to the aluminum tube uniformly
3.3.2. Deformation beha6ior Fig. 9 shows the displacement of the top at the bead on the deformation time. With the increasing of the time and the discharge voltage, the displacement shows the increasing and the saturation at 120 ms. This time was almost the same as the time when the magnetic pressure became the maximum. 3.3.3. Comparison with the experimental results Fig. 10(a) and (b) show the influence of the discharge voltage on the bead height and the longitudinal strain. Compared with the experiment, the calculated bead height in Fig. 10(a) shows the same tendency for discharge voltage up to 4 kV. But in the experiment the bead height increases with increasing discharge voltage over 4 kV. On the other hand, the calculated longitudinal strain increases with increasing discharge voltage over 4 kV as shown in Fig. 10(b). This calculated
Fig. 5. Influence of the discharge voltage and the shoulder radius on the bead height.
results show that the thickness strain at the shoulder part was expanded. But the experimental results do not show it in Fig. 10(b). From these calculated results, this simulation is possible to explain up to 4 kV discharge voltage. But it does not explain over 4 kV discharge voltage so that the aluminum tube enter the groove of the beading die.
4. Conclusions The inside bead forming of the aluminum tube by the EMF was carried out experimentally and numerically. From these results, some of the conclusions were obtained as shown below. 1. The bead shape, the bead height, the thickness strain at the top of the bead and the longitudinal strain of the aluminum tube were affected by the discharge voltage and the dimensions of the groove at the beading die. 2. Over 4 kV, the bead shape, the bead height, the thickness strain at the top of the bead and the longitudinal strain of the aluminum tube increased rapidly, because the aluminum tube entered into the groove so that the balance of the friction force and the forming force collapsed. 3. Results of the simulation were almost the same as the experimental results for discharge voltage of 4 kV. But we need to try the FEM simulation and the friction under dynamic conditions.
Fig. 7. Influence of the discharge voltage and the shoulder radius on the longitudinal strain.
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
Fig. 8. Finite element model of the bead forming.
Fig. 9. Displacement of the top at the bead.
Acknowledgements The authors would like to thank Mr. Tonozuka and Mr. Sakuraba, from the Electro Communication University, for supporting the simulation.
References [1] E. J. Bruno (Ed.), High Velocity Forming of Metals, ASTME, 1968. [2] Japan Society for Technology of Plasticity (JSTP), High Energy Rate Forming, Corona, 1993. [3] G.S. Daehn, M. Altynova, V.S. Balanethiram, G. Fenton, M. Padmanabhan, A. Tamhane, E. Winnard, High-velocity metal forming — an old technology addresses a new problem, J.
699
Fig. 10. Influence of the discharge voltage on the bead height and the longitudinal strain.
Organomet. Chem. 47 (7) (1995) 42 – 45. [4] K. Bains, J.L. Duncan, W. Johnson, Electromagnetic metal forming, Proc. Inst. Mech. Eng. 180 (4) (1965 – 66) 93 –110. [5] T. Sano, M. Takahashi, Y. Murakoshi, K. Matsuno, Impulsive forming of tube ends by electro-magnetic force, Advanced Technology of Plasticity 1st ICTP, vol. 1, JSTP, 1984, pp. 373–378. [6] T. Sano, M. Takahashi, Y. Murakoshi, K. Matsuno, High an experimental study on the generation of the electro-magnetic force by a spiral coil, Proceedings of the First International Conference on Experimental Mechanics, Science Press, Beijing, 1985, pp. 521 – 526. [7] Y. Murakoshi, M. Takahashi, M. Terasaki, T. Sano, K. Matsuno, High speed blanking of an amorphous alloy, Advanced Tech. of Plasticity 2nd ICTP, vol. 1, Springer, Berlin, 1987, pp. 323 – 328. [8] T. Sano, M. Takahashi, Y. Murakoshi, M. Terasaki, K. Matsuno, An analysis of electro-magnetic bulging of circular plates, Theor. Appl. Mech. 36 (1987) 367 – 377. [9] M. Takahashi, Y. Murakoshi, T. Sano, K. Matsuno, Accuracy improvement of thin-walled tubes by electro-magnetic force, Proc. Adv. Manuf. Technol., BDG, Hong Kong, 1989, pp. 275 – 282. [10] Y. Murakoshi, M. Takahashi, T. Sano, K. Matsuno, H. Takeishi, Powder forming by electro-magnetic sheath method, Advanced Tech. of Plasticity 3rd ICTP, vol. II, JSTP, 1990, pp. 939 – 944. [11] T. Sano, M. Takahashi, Y. Murakoshi, K. Matsuno, S. Fuchizawa, Punchless blanking of an amorphous alloy, Advanced Tech. of Plasticity 3rd ICTP, vol. III, JSTP, 1990, pp. 1447 – 1452.
.
Inside bead forming of aluminum tube by electro-magnetic forming Yoichi Murakoshi a,*, Masaharu Takahashi a, Toshio Sano a, Kotaro Hanada b, Hideaki Negishi c a
Mechanical Engineering Laboratory, AIST, MITI Namiki 1 -2, Tsukuba, Ibaraki 305, Japan b JST fellow, Namiki 1 -2, Tsukuba, Ibaraki 305, Japan c Electro Communication Uni6ersity, Chofu ga oka 1 -5 -1, Chofu, Tokyo 182, Japan
Abstract In this paper, the inside bead forming of aluminum tube (A6063TD) by electro-magnetic forming (EMF) is reported experimentally and numerically. The shape of the bead was affected by the change of the discharge voltage and the dimensions of a groove at a beading die which have a width and a shoulder radius. With the increase of the discharge voltage and the shoulder radius, the bead height increased due to the increasing of the bending moment. On the discharge voltage of over 4 kV (400 mF), the bead height rapidly increased so that the aluminum tube entered the groove at the beading die from both sides. Therefore the thickness strain at the top of the bead increased, the longitudinal strain of the aluminum tube saturated, and a necking appeared at the bead near the shoulder part of the beading die. Also, the simulation of the bead forming was carried out by using MARC and compared with the experimental results. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Bead forming; Electro-magnetic forming; Aluminum tube
1. Introduction High energy rate forming (HERF) processes [1,2] such as explosive forming, electro-hydraulic forming and electro-magnetic forming (EMF), have some attractive characteristics [3]. These are the extremely high ductility under high velocity conditions, the low spring back after the unloaded condition, and the one-sided die which is a male or a female die. Although HERF processes have many useful characteristics as shown above, there are only a few practical examples, so that in the HERF process it is difficult to control the energy and to make a lot of parts with complicated shapes. Therefore much research has been carried out to obtain the optimal process and to produce the practical examples which are used in the automobile and aerospace industry. Compared with other HERF processes, in EMF it is very easy to control the energy, little time is needed to deform the products, and it needs no transfer medium to transfer the deformation force [4]. But EMF * Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00217-9
cannot be used for ferrous materials, as the magnetic pressure which occurs between the ferrous material and the forming coil is smaller than the aluminum and copper material. The magnetic pressure is affected by the induced current in the ferrous material and the flux density which is made by the forming coil. Therefore the resistance of the materials is important. However expanding, shrinking, joining, straightening and cutting of the tube can be carried out by the EMF [5–11]. Bead forming is one of the tube forming processes carried out by EMF. It is possible to make the bead on the inside or on the outside of the tube by using a compressive or an expansive coil. According to whether the bead is deformed inside or outside the tube, the tube may have a higher stiffness. In this paper, the inside bead forming of an aluminum tube by using a compressive coil is carried out experimentally and numerically. The influence of the discharge voltage and the dimensions of the groove at the beading die are investigated. These influences are compared with the results of the simulation which used MARC.
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
696
3. Results and discussion
3.1. Estimated magnetic pressure
Fig. 1. Schematic diagram of the inside bead forming.
2. Experimental procedure Fig. 1 shows a schematic diagram of the inside bead forming of an aluminum tube by using a compressive coil. The schematic diagram shows the compressive coil, the groove at the beading die and the aluminum tube as a workpiece. The characteristics of the compressive coil are shown in Table 1. It is connected to a capacitor bank which has the maximum capacitance (C) of 400 mF, the total inductance (L) of 1.7 mH, and the total resistance (R) of 17.2 mV. To control the forming energy, the discharge voltage (V) was varied from 2 to 6 kV. The beading die was made from the polyacetal to decrease the friction force which acts between the aluminum tube and the beading die. The dimensions of the groove at the beading die were a width (w), a depth (d) and a shoulder radius (r). The shoulder radius was varied from 0 to 7 mm. But the width, the depth and the value of the capacitor were fixed at 5 mm, 9 mm and 400 mF, respectively. The aluminum tube (A6063TD) was annealed at 673 K for 1 h. The dimensions and the mechanical properties of the aluminum tube are shown in Table 2. These properties are also used to simulate the bead forming.
Fig. 2 shows the estimated flux density (B/Tesla) and the estimated magnetic pressure (P/MPa), which appeared at the area between the aluminum tube and the compressive coil. The estimated magnetic pressure reaches about 100 MPa on the 6 kV. The estimated magnetic pressure was calculated by the equation of P= B 2/2m0 where m0 is 1.257× 10 − 6. The estimated flux density is calculated by the equation of B=A B0/A0 where A is the area between the compressive coil and the aluminum tube, A0 is inside area of the compressive coil, and B0 is the flux density which was measured at the central point of the compressive coil without the aluminum tube. The flux density was measured by a search coil, which is 7.07 mm2 in area and has 20 turns of copper wire.
3.2. Influence of some parameters on the bead 3.2.1. Bead shape Fig. 3 shows a photograph of a typical shape of the bead. This is deformed at the 4 kV of the discharge voltage, 3 mm of the shoulder radius and 5 mm of the width. Fig. 4 (a) and (b) show the influence of the discharge voltage and the shoulder radius on the bead shape. The bead shape is affected by the increasing of the discharge voltage and the shoulder radius, because the bending moment on the shoulder part at the beading die increases. But, the influence of the discharge voltage on the bead shape is bigger than the effect of the change of the bead shape on the shoulder radius. Increasing the discharge voltage from 5 to 6 kV causes a large change in the bead shape and the bead height so that the balance between the friction force and the forming force was suddenly collapsed by the increasing of the discharge voltage. The friction force which acts between the aluminum tube and the beading die depends on the magnetic pressure, the friction coefficient
Table 1 Characteristics of the compressive coil Length (L0/mm)
Inside diameter (Din/mm)
Inductance (L/mH)
Resistance (R/mV)
50
36.5
12.5
24
Table 2 Characteristics of the annealed A6063TD Young’s modulus (E/Gpa)
Poisson ratio (y)
Yield stress (s0/MPa)
Plastic coefficient (C/MPa)
Strain-hardening exponent (n)
70
0.33
50
78
0.27
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
697
Fig. 2. Estimated flux density and magnetic pressure.
Fig. 3. Typical bead shape.
and the contacted area of the aluminum tube and the beading die. The forming force depends on the magnetic pressure and the area which the aluminum tube and the beading die does not contact. Therefore the aluminum tube enters the groove at the beading die. The influence of the length of the aluminum tube on the bead shape was investigated. As the length of the aluminum tube became shorter, a necking appeared at the lower discharge voltage. This has a similar explanation as for the effects of increasing the discharge voltage to 6 kV.
3.2.2. Influence of the discharge 6oltage and the shoulder radius on the bead height Fig. 5(a) and (b) show the influence of the discharge voltage and the shoulder radius on the bead height. The bead height is normalized by the width of the beading die. The bead height increases with an increase of the discharge voltage and the shoulder radius as shown in Fig. 5(a) and (b). In Fig. 5(a), the bead height on the shoulder radius of 3 mm is higher than it is on the shoulder radius of 0 mm and it reaches 1.2 on 6 kV of the discharge voltage. In Fig. 5(b), the bead height increases with the increase of the shoulder radius and it reaches about 0.8 with the shoulder radius of 7 mm. The difference of the bead height on the shoulder radius of 0 and 3 mm is due to the bending moment. The bending moment became big, with the increasing of the shoulder radius. 3.2.3. Thickness strain at the top of the bead Fig. 6(a) and (b) show the influence of the discharge voltage and the shoulder radius on the thickness strain at the top of the bead. The thickness strain increases with an increase of the discharge voltage and the shoulder radius as shown in Fig. 6(a) and (b). In Fig. 6(a), the sudden change of the thickness strain can be seen at 4 kV for the 0 mm and at 5 kV for the 3 mm shoulder radius. In the experiment, the thickness change was found at the top of the bead and the shoulder part of the aluminum tube. The thickness at the top of the bead increases so that a compressive force acts on the
material which enters the groove from both sides. On the other hand, the thickness at the shoulder part decreases so that the material at the shoulder part was expanded. In Fig. 6(b), the influence of the shoulder radius on the thickness strain at the shoulder part increases with an increase of the shoulder radius.
3.2.4. Longitudinal strain of the aluminum tube Fig. 7(a) and (b) show the influence of the discharge voltage and the shoulder radius on the longitudinal strain. The longitudinal strain shows the change of the whole length of the aluminum tube. Therefore it does not show only the change of the bead. With increasing discharge voltage, the longitudinal strain on the shoulder radius of 3 mm increases as shown in Fig. 7(a). But it peaks at 4 kV and then decreases. This is the same reason as in Section 3.2.1 and Section 3.2.3. Therefore the thickness strain at the top of the bead rapidly increased (Fig. 6(a)) and the longitudinal strain in Fig. 7(a) decreased on 6 kV. Change between the longitudinal strain and the shoulder radius in Fig. 7(b) also shows the increasing and the saturation on the shoulder radius of 5 mm. 3.3. Simulation of the bead forming Influence of the discharge voltage and the shoulder radius on the deformation process of the bead forming was predicted by an FEM simulation and compared with the experimental results. In this simulation, MARC was used with MENTAT as a pre-post processor.
3.3.1. Analytical conditions Fig. 8 shows a quarter of the finite element model which is used to simulate the bead forming. L0, w and r were 50, 5 and 3 mm, respectively. The dimensions and the properties of the aluminum tube which are shown in Table 2 were used in this simulation. But strain rate hardening coefficient was not used. The
698
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
Fig. 6. Influence of the discharge voltage and the shoulder radius on the thickness strain at the top of the bead.
Fig. 4. Influence of the discharge voltage and the shoulder radius bead shape on the bead shape.
shear friction coefficient (m) was 0.1. Although the magnetic pressure is a dynamic pressure, the static simulation was carried out by using the magnetic pressure equation of P(t) =Pm e − dt sin2vt where d and v were 500 and 13300. The magnetic pressure was applied to the aluminum tube uniformly
3.3.2. Deformation beha6ior Fig. 9 shows the displacement of the top at the bead on the deformation time. With the increasing of the time and the discharge voltage, the displacement shows the increasing and the saturation at 120 ms. This time was almost the same as the time when the magnetic pressure became the maximum. 3.3.3. Comparison with the experimental results Fig. 10(a) and (b) show the influence of the discharge voltage on the bead height and the longitudinal strain. Compared with the experiment, the calculated bead height in Fig. 10(a) shows the same tendency for discharge voltage up to 4 kV. But in the experiment the bead height increases with increasing discharge voltage over 4 kV. On the other hand, the calculated longitudinal strain increases with increasing discharge voltage over 4 kV as shown in Fig. 10(b). This calculated
Fig. 5. Influence of the discharge voltage and the shoulder radius on the bead height.
results show that the thickness strain at the shoulder part was expanded. But the experimental results do not show it in Fig. 10(b). From these calculated results, this simulation is possible to explain up to 4 kV discharge voltage. But it does not explain over 4 kV discharge voltage so that the aluminum tube enter the groove of the beading die.
4. Conclusions The inside bead forming of the aluminum tube by the EMF was carried out experimentally and numerically. From these results, some of the conclusions were obtained as shown below. 1. The bead shape, the bead height, the thickness strain at the top of the bead and the longitudinal strain of the aluminum tube were affected by the discharge voltage and the dimensions of the groove at the beading die. 2. Over 4 kV, the bead shape, the bead height, the thickness strain at the top of the bead and the longitudinal strain of the aluminum tube increased rapidly, because the aluminum tube entered into the groove so that the balance of the friction force and the forming force collapsed. 3. Results of the simulation were almost the same as the experimental results for discharge voltage of 4 kV. But we need to try the FEM simulation and the friction under dynamic conditions.
Fig. 7. Influence of the discharge voltage and the shoulder radius on the longitudinal strain.
Y. Murakoshi et al. / Journal of Materials Processing Technology 80–81 (1998) 695–699
Fig. 8. Finite element model of the bead forming.
Fig. 9. Displacement of the top at the bead.
Acknowledgements The authors would like to thank Mr. Tonozuka and Mr. Sakuraba, from the Electro Communication University, for supporting the simulation.
References [1] E. J. Bruno (Ed.), High Velocity Forming of Metals, ASTME, 1968. [2] Japan Society for Technology of Plasticity (JSTP), High Energy Rate Forming, Corona, 1993. [3] G.S. Daehn, M. Altynova, V.S. Balanethiram, G. Fenton, M. Padmanabhan, A. Tamhane, E. Winnard, High-velocity metal forming — an old technology addresses a new problem, J.
699
Fig. 10. Influence of the discharge voltage on the bead height and the longitudinal strain.
Organomet. Chem. 47 (7) (1995) 42 – 45. [4] K. Bains, J.L. Duncan, W. Johnson, Electromagnetic metal forming, Proc. Inst. Mech. Eng. 180 (4) (1965 – 66) 93 –110. [5] T. Sano, M. Takahashi, Y. Murakoshi, K. Matsuno, Impulsive forming of tube ends by electro-magnetic force, Advanced Technology of Plasticity 1st ICTP, vol. 1, JSTP, 1984, pp. 373–378. [6] T. Sano, M. Takahashi, Y. Murakoshi, K. Matsuno, High an experimental study on the generation of the electro-magnetic force by a spiral coil, Proceedings of the First International Conference on Experimental Mechanics, Science Press, Beijing, 1985, pp. 521 – 526. [7] Y. Murakoshi, M. Takahashi, M. Terasaki, T. Sano, K. Matsuno, High speed blanking of an amorphous alloy, Advanced Tech. of Plasticity 2nd ICTP, vol. 1, Springer, Berlin, 1987, pp. 323 – 328. [8] T. Sano, M. Takahashi, Y. Murakoshi, M. Terasaki, K. Matsuno, An analysis of electro-magnetic bulging of circular plates, Theor. Appl. Mech. 36 (1987) 367 – 377. [9] M. Takahashi, Y. Murakoshi, T. Sano, K. Matsuno, Accuracy improvement of thin-walled tubes by electro-magnetic force, Proc. Adv. Manuf. Technol., BDG, Hong Kong, 1989, pp. 275 – 282. [10] Y. Murakoshi, M. Takahashi, T. Sano, K. Matsuno, H. Takeishi, Powder forming by electro-magnetic sheath method, Advanced Tech. of Plasticity 3rd ICTP, vol. II, JSTP, 1990, pp. 939 – 944. [11] T. Sano, M. Takahashi, Y. Murakoshi, K. Matsuno, S. Fuchizawa, Punchless blanking of an amorphous alloy, Advanced Tech. of Plasticity 3rd ICTP, vol. III, JSTP, 1990, pp. 1447 – 1452.
.