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A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch
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CIRP-1121; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch Takashi Kuboki a,*, Armad Azrie a, Yingjun Jin b a b
Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Tokyo, Japan Amada Co., Ltd., Kanagawa, Japan
Submitted by Manabu Kiuchi (1), Tokyo, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Incremental sheet forming Cold forming Bending
This paper proposes an innovative incremental in-plane bending of thin metal sheets for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile is used. The beating face enables the punch to bend thin metal sheets in in-plane manner. Working conditions, including indentation and feeding pitch, can easily and flexibly control the bending radius and even the bending direction. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments. ß 2014 CIRP.
1. Introduction Microstructural components have diversely been used as parts in medical devices, precision machines, optical MEMS (Micro Electro-Mechanical Systems), Bio MEMS and so on. In many cases, these micro-components are fabricated by technologies using radiated lights such as LIGA (Lithographie, Galvanoformung, Abformung) processes. LIGA processes would be effective and suitable for the fabrication of components which require high precision, such as micro gears. On the other hand, technology of plasticity would be suitable for the fabrication of miniature chassis or boxes for mounting micro gears and other components which do not require high precision, as technology of plasticity would realize high productivity and reasonable production costs. Incremental forming would have the potential ability of fabricating microstructural components. Saotome et al. [1] developed a process called ‘‘incremental forming by hammering’’ for fabrication of microstructural chassis. Incidentally, incremental forming has been used for forming in ordinary scales as well. Matsubara [2] controlled toll paths by computer numerical control. Malhotra et al. [3] improved formability by tool path optimization. Martins et al. [4] applied incremental forming for the fabrication of polymers. All the above forming utilizes point beating. On the other hand, the authors proposed incremental in-plane bending with tilted punch for sheet metal with 2 mm thickness [5]. The method utilized line beating, which would realize higher productivity than point beating. However, it was not applicable for bending thinner sheet metals in micro scales.
* Corresponding author.
This paper proposes an innovative incremental forming for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile is used. The beating face enables the punch to give thickness distribution. This mechanism would be applicable for micro forging. It gives local slopes on material’s top surface or makes a large tilted surface flexibly. In this paper, the mechanism was applied for in-plane bending of thin sheet metal as an example. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments. 2. In-plane-bending using a tiltable punch 2.1. Mechanism of in-plane bending of thin sheet metals The proposed method bends thin sheet metals in in-plane manner by introducing a new movement mechanism of tiltable punch. The method was invented based on the authors’ previous research on in-plane bending with a tilted punch for 2 mm-thick sheet metal [5]. However, the previous tilted punch is not applicable for thinner sheet metals as the tilt angle should be adjusted precisely in a small amount for thinner metals. In the present method, the punch is gradually and automatically tilted during each beating. The movement is shown in Fig. 1. The tilting motion generates a small bending deformation at each beating, and a repeat of beatings bends the sheet metal at a radius. If out-of-plane deviation should be prevented, a gate-shaped jig would be effective, though it was not used in this research. Fig. 2 describes the mechanism of tilting motion caused by the tiltable punch having a beating face with trapezoidal profile. The trapezoidal profile is composed of toe and heel sides. When the
http://dx.doi.org/10.1016/j.cirp.2014.03.010 0007-8506/ß 2014 CIRP.
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
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T. Kuboki et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
Furthermore, it is noteworthy that the sheet metal would be bent in the opposite way by just increasing feed pitch p. When feed pitch p is large enough, some area of the sheet metal would be unbeaten on the toe side, resulting in opposite-way bending as shown in Fig. 3(c). Therefore, the bending radius and direction would flexibly be changed by changing feed pitch during the process as shown in Fig. 3(d). 2.2. Possible final products More complicated final products for miniature and micro machines can be manufactured from the bent sheet metals, which are shown in Fig. 3. Some examples of final products are shown in Fig. 4.
Fig. 1. In-plane bending with tiltable punch.
Fig. 3. Schematic illustration of effect of working condition on bending curve of sheet metal.
Fig. 2. Punch geometry and mechanism of tilt motion.
punch is pushed downwards to beat the sheet metal, the toe side indents the sheet metal deeper than the heel side. If the tilt angle a is assumed to be zero as shown in Fig. 2(b), the resistant load on the heel side FH must be larger than that on the toe side FT, because the heel side has a larger area. As a result, a tilting moment is generated. When this moment inclines the punch as shown in Fig. 2(c), the pressure on the toe side increases due to the work hardening, leading to the increase of resistant force at the toe side FT. When the moment, which is generated by FT and FH, is zero, the tilting motion stops and an equilibrium state is obtained. The tilting motion of the punch generates the thickness distribution along the sheet metal breadth, which bends the sheet metal due to volumetric constancy. After lifting up the punch, the sheet metal is fed in longitudinal direction, followed by the second beating. Repeated forming of incremental beating bends the sheet metal in in-plane manner as shown in Fig. 1(c). As the toe side of the sheet is thinner than the heel side, the toe side becomes extrados and the heel side becomes intrados of the bending arc. The toe angle u, set indentation ds and feed pitch p are the dominant parameters in the process. In particular, the bending radius r would flexibly and freely be controlled by changing the set indentation ds and feed pitch p, even during the in-plane bending process. The effect of the parameters is schematically explained in Fig. 3. The sheet metal would be bent following the mechanism explained above. When the indentation d is large, the bending radius is small because of the larger tilting angle a as shown in Fig. 3(b). The smaller feed pitch p would also result in smaller bending radius, because smaller p would decrease the contact area and the punch load F, and the elastic deformation of the machine would decrease, leading to the larger actual indentation da.
Fig. 4. Possible final products.
Some of them may be used in medical or biomedical fields. Recently, surgical manipulators have been developed for reducing damage to patients during surgical operation of internal organs, because the manipulators need only small holes in the abdomen. Kawashima et al. have developed a new manipulator using spring-
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
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CIRP-1121; No. of Pages 4 T. Kuboki et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
type joints with a cross section of high rectangle ratio instead of mechanical joints. The usage of the spring is the key technology to reduce the size of the joints, which will make the seize of holes on the abdomen minimal [6]. The springs with a cross section of high rectangle ratio would be manufactured by the present beating method as shown in Fig. 4(a). This type of spring could also be used as a tail of a swimming robot [7]. Micro forceps and grippers, which are now fabricated by LIGA process [8], are another possibility. Nozzles for micro-droplets [9] could also be fabricated from the quarter sector formed by the present bending method. If the bending process is applied to the angle sheet metals, they could be used as a bush of micro machines as shown in Fig. 4(d). The S-shape-bent sheet metals could be fabricated into two-way angular bearings in micro machines. 3. Examination of effectiveness of the proposed method 3.1. Prototype machine and forming conditions Fig. 5 shows the prototype machine, which was fabricated for the verification of the effectiveness of the proposed method. The rotation of the motor was reduced by the decelerator to rotate the cam, which pushes down the punch for beating the sheet metals. After beating, the punch is lifted up to the initial position by the spring, which is mounted in the punch holder. The sheet metal is fed along the linear guide after every beating.
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stiffness of the machine. The feed pitch is assumed to be so small that no unbeaten area should appear on the toe side. The calculation procedure is explained as follows: (1) The actual indentation da and the tilt angle a are assumed. (2) The thickness distribution t is calculated as the function of breadth position x from a. (3) The stress distribution s(x) is estimated assuming that the plastic equivalent strain should be equal to the thickness strain -log(t/t0), considering work hardening. (4) The moment M around the punch joint is calculated from s(x). If M is not zero, the assumed value of a should be modified. (5) If M is zero, the punch load F is calculated by integration of s(x). Here, the integrated value is multiplied by a coefficient g, because the actual punch load should be much larger than the integrated value because of friction and constraints from material of the unbeaten area [10]. (6) Elastic deformation of machine de is calculated from stiffness k as F/k. If de + da is not equal to ds, da should be modified. The value of g/k is estimated in a preliminary comparison between analytical and laboratory results. Once da and a are obtained, the bending radius is calculated using equations in the authors’ previous research [5]. Fig. 7 shows the analysis results. While the actual indentation da increases with increase of ds, da is much less than ds. Tilt angle a increases with increase of ds as intended. These tendencies strengthen with increase of toe angle a.
Fig. 5. Prototype machine of in-plane bending with a tiltable punch.
Table 1 shows the beating condition. Aluminium A1050 was used as the sheet metal with a thickness of 0.5 mm and a breadth of 5 mm. The beating face of the punch had a trapezoidal shape, the two sides of which were positioned from the centre at w = 0.75 mm as shown in Fig. 2. The toe angle u ranged from 15 to 45 degrees. While the set indentation ds ranged from 0.2 to 0.5 mm to the sheet metal thickness t of 0.5 mm, the actual indentation da would be much less than the set indentation ds due to elastic deformation of the machine. The feed pitch ranged from 0.25 to 1.5 mm. Table 1 Beating conditions. Sheet metal
Material Thickness t0/mm Breadth B0/mm
A1050 aluminium 0.5 5
Punch
Material Tip Outside diameter d/mm Distance between centre to sides w/mm Toe angle u/8
Medium carbon steel 5 0.75
Operation
Set indentation ds/mm Feed pitch p/mm
0.2, 0.3, 0.4, 0.5 0.25–1.5
15, 30, 45
3.2. Genuine deformation under ideal condition The genuine deformation under ideal condition was examined by numerical analysis before the experiment. The flow chart of the analysis is shown in Fig. 6. The analysis calculates the actual indentation da and the tilt angle a from the set indentation ds and the toe angle u, considering work hardening of the material and the
Fig. 6. Flow chart for calculation of actual indentation and tilt angle.
3.3. Bent sheet metals in experiment Fig. 8 shows the bent sheet metals under the condition of feed pitch p = 0.25 mm/beat and set indentation ds = 0.5 mm. The sheet metal is bent successfully by the punch with the toe angle u of 30 degrees. Although the numerical results showed that the higher toe angle u should result in larger tilt angle, the bending radius of u = 45 degrees was larger than that of u = 30 degrees. This was
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
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contact area increases with increase of p, which results in larger punch load leading to smaller actual indentation. Secondly, the unbeaten area appears and expands with increase of p. This effect of feed pitch could be utilized in the positive manner in the forming process, as the pitch is able to be easily controlled. A bent sample is shown in Fig. 10(b). The shape of the bent sheet was successfully controlled as intended so that it might have an S shape 3.4. Envisaged defects and possible solutions Fig. 7. Results of numerical analysis. (a) Actual indentation. (b) Tilt angle.
Fig. 8. Bent sheet metal. (feed pitch p = 0.25 mm/beat, set indentation ds = 0.5 mm). (a) Toe angle u = 158. (b) u = 308. (c) u = 458.
attributed to the appearance of unbeaten area which is schematically shown in Fig. 3. Fig. 9 shows the effect of toe angle u and set indentation ds on intrados radius ri in the expression of inverse, i.e. curvature, with the numerical prediction. There was a large difference between experimental and numerical results for u = 45 degrees because of the appearance of unbeaten area in experiments. The curvatures of experiments were smaller than those of numerical analysis. This was attributed to the deflection of sheet metal in horizontal direction, breadth increase, effect of friction, and so on, which were not taken into account in the analysis.
Although precise thickness value is difficult to obtain, the bending radius would be controlled by feed-back using in-situ observation of the bending shape. The surface irregularities due to incremental pressing were suppressed by reducing the feed pitch in this study. The irregularities could also be reduced by improving the punch geometry as proposed by Tajul et al. [11], who added an extra inclined surface to the beating punch surface in the sheetmetal’s longitudinal direction. If further flatness and smooth surface are needed, other processes like polishing should be introduced. When the specimen thickness becomes as small as several times of the grain size, the effect of grain size could appear leading to surface irregularity or variation of bending radius due to the crystal anisotropy. There was also a forming limit on bending radius in the present method. When the bending radius was near or less than the size of the sheet metal breadth, some cracks were observed at the extrados of the bending arc. 4. Conclusions This paper proposed an innovative incremental in-plane bending of thin metal sheets for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile was used. The beating face enabled the punch to bend thin metal sheets in in-plane manner. The toe angle of the beating face of 30 degrees was the most effective among the tried conditions in this paper. Working conditions, including indentation and feeding pitch, can easily and flexibly control the bending radius. In particular, the feeding pitch, which is easily changed during forming, was able to control the bending direction. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments. References
Fig. 9. Effect of toe angle and set indentation on bending radius. (a) Experiment. (b) Numerical analysis.
Fig. 10. Effect of pitch on bending radius in experiment (set indentation ds = 0.5 mm). (a) Curvature. (b) S-shaped metal sheet.
The effect of feed pitch p is shown in Fig. 10 for toe angle u = 30 degrees. A negative value of curvature means that sheet metal is bent in the opposite direction. The curvature decreased with increase of feed pitch p because of two phenomena. Firstly, the
[1] Saotome Y, Okamoto T (2001) An In-situ Incremental Microforming System for Three-dimensional Shell Structures of Foil Materials. Journal of Materials Processing Technology 113:636–640. [2] Matsubara S (1994) CNC Incremental Forming. Japan Society for Technology of Plasticity 35–406:1258–1263. (in Japanese). [3] Malhotra R, Bhattacharya A, Kumar A, Reddy N, Cao J (2011) A New Methodology for Multi-pass Single Point Incremental Forming with Mixed Tool Paths. CIRP Annals – Manufacturing Technology 60(1):323–326. [4] Martins P, Kwiatkowski L, Franzen V, Tekkaya A, Kleiner M (2009) Single Point Incremental Forming of Polymers. CIRP Annals – Manufacturing Technology 58(1):229–232. [5] Jin Y, Kuboki T, Murata M (2005) Influence of Strip Materials on Behavior of Incremental In-plane Bending. Journal of Materials Processing Technology 162– 163:190–195. [6] Tadano K, Kawashima K, Kojima K, Tanaka N (2010) Development of a Pneumatic Surgical Manipulator IBIS IV. Journal of Robotics and Mechatronics 22(2):179–188. [7] Tottori S, Sugita N, Kometani R, Ishihara S, Mitsuishi M (2011) Selective Control Method for Multiple Magnetic Helical Microrobots. Journal of Micro-Nano Mechatronics 6:89–95. [8] Mackay R, Le H, Keatch R (2011) Design Optimisation and Fabrication of su-8 Based Electro-thermal Micro-grippers. Journal of Micro-Nano Mechatronics 6:13–22. [9] Hirata S, Hirose K, Irie Y, Aoyama H (2012) Improvement of the Needle-type Dispenser for Precise Micro-droplet Dispensation-gap Measurement Between the Needle Tip and the Target Surface Based on Needle Vibration. Journal of Robotics and Mechatronics 24(2):284–290. [10] Kuboki T, Takahashi K, Sanda K, Moriya S, Ishida K (2012) Development of a Tube-spinning Machine for Thin Tubes with a Large Diameter. Materials Transactions 53(5):853–861. [11] Tajul L, Maeno T, Mori K, Kinoshita T (2013) Successive forging of long plate having inclined cross-section. The Proceedings of the 64th Japanese Joint Conference for the Technology of Plasticity, Osaka, 347–348.
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
CIRP-1121; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch Takashi Kuboki a,*, Armad Azrie a, Yingjun Jin b a b
Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Tokyo, Japan Amada Co., Ltd., Kanagawa, Japan
Submitted by Manabu Kiuchi (1), Tokyo, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Incremental sheet forming Cold forming Bending
This paper proposes an innovative incremental in-plane bending of thin metal sheets for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile is used. The beating face enables the punch to bend thin metal sheets in in-plane manner. Working conditions, including indentation and feeding pitch, can easily and flexibly control the bending radius and even the bending direction. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments. ß 2014 CIRP.
1. Introduction Microstructural components have diversely been used as parts in medical devices, precision machines, optical MEMS (Micro Electro-Mechanical Systems), Bio MEMS and so on. In many cases, these micro-components are fabricated by technologies using radiated lights such as LIGA (Lithographie, Galvanoformung, Abformung) processes. LIGA processes would be effective and suitable for the fabrication of components which require high precision, such as micro gears. On the other hand, technology of plasticity would be suitable for the fabrication of miniature chassis or boxes for mounting micro gears and other components which do not require high precision, as technology of plasticity would realize high productivity and reasonable production costs. Incremental forming would have the potential ability of fabricating microstructural components. Saotome et al. [1] developed a process called ‘‘incremental forming by hammering’’ for fabrication of microstructural chassis. Incidentally, incremental forming has been used for forming in ordinary scales as well. Matsubara [2] controlled toll paths by computer numerical control. Malhotra et al. [3] improved formability by tool path optimization. Martins et al. [4] applied incremental forming for the fabrication of polymers. All the above forming utilizes point beating. On the other hand, the authors proposed incremental in-plane bending with tilted punch for sheet metal with 2 mm thickness [5]. The method utilized line beating, which would realize higher productivity than point beating. However, it was not applicable for bending thinner sheet metals in micro scales.
* Corresponding author.
This paper proposes an innovative incremental forming for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile is used. The beating face enables the punch to give thickness distribution. This mechanism would be applicable for micro forging. It gives local slopes on material’s top surface or makes a large tilted surface flexibly. In this paper, the mechanism was applied for in-plane bending of thin sheet metal as an example. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments. 2. In-plane-bending using a tiltable punch 2.1. Mechanism of in-plane bending of thin sheet metals The proposed method bends thin sheet metals in in-plane manner by introducing a new movement mechanism of tiltable punch. The method was invented based on the authors’ previous research on in-plane bending with a tilted punch for 2 mm-thick sheet metal [5]. However, the previous tilted punch is not applicable for thinner sheet metals as the tilt angle should be adjusted precisely in a small amount for thinner metals. In the present method, the punch is gradually and automatically tilted during each beating. The movement is shown in Fig. 1. The tilting motion generates a small bending deformation at each beating, and a repeat of beatings bends the sheet metal at a radius. If out-of-plane deviation should be prevented, a gate-shaped jig would be effective, though it was not used in this research. Fig. 2 describes the mechanism of tilting motion caused by the tiltable punch having a beating face with trapezoidal profile. The trapezoidal profile is composed of toe and heel sides. When the
http://dx.doi.org/10.1016/j.cirp.2014.03.010 0007-8506/ß 2014 CIRP.
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
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CIRP-1121; No. of Pages 4 2
T. Kuboki et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
Furthermore, it is noteworthy that the sheet metal would be bent in the opposite way by just increasing feed pitch p. When feed pitch p is large enough, some area of the sheet metal would be unbeaten on the toe side, resulting in opposite-way bending as shown in Fig. 3(c). Therefore, the bending radius and direction would flexibly be changed by changing feed pitch during the process as shown in Fig. 3(d). 2.2. Possible final products More complicated final products for miniature and micro machines can be manufactured from the bent sheet metals, which are shown in Fig. 3. Some examples of final products are shown in Fig. 4.
Fig. 1. In-plane bending with tiltable punch.
Fig. 3. Schematic illustration of effect of working condition on bending curve of sheet metal.
Fig. 2. Punch geometry and mechanism of tilt motion.
punch is pushed downwards to beat the sheet metal, the toe side indents the sheet metal deeper than the heel side. If the tilt angle a is assumed to be zero as shown in Fig. 2(b), the resistant load on the heel side FH must be larger than that on the toe side FT, because the heel side has a larger area. As a result, a tilting moment is generated. When this moment inclines the punch as shown in Fig. 2(c), the pressure on the toe side increases due to the work hardening, leading to the increase of resistant force at the toe side FT. When the moment, which is generated by FT and FH, is zero, the tilting motion stops and an equilibrium state is obtained. The tilting motion of the punch generates the thickness distribution along the sheet metal breadth, which bends the sheet metal due to volumetric constancy. After lifting up the punch, the sheet metal is fed in longitudinal direction, followed by the second beating. Repeated forming of incremental beating bends the sheet metal in in-plane manner as shown in Fig. 1(c). As the toe side of the sheet is thinner than the heel side, the toe side becomes extrados and the heel side becomes intrados of the bending arc. The toe angle u, set indentation ds and feed pitch p are the dominant parameters in the process. In particular, the bending radius r would flexibly and freely be controlled by changing the set indentation ds and feed pitch p, even during the in-plane bending process. The effect of the parameters is schematically explained in Fig. 3. The sheet metal would be bent following the mechanism explained above. When the indentation d is large, the bending radius is small because of the larger tilting angle a as shown in Fig. 3(b). The smaller feed pitch p would also result in smaller bending radius, because smaller p would decrease the contact area and the punch load F, and the elastic deformation of the machine would decrease, leading to the larger actual indentation da.
Fig. 4. Possible final products.
Some of them may be used in medical or biomedical fields. Recently, surgical manipulators have been developed for reducing damage to patients during surgical operation of internal organs, because the manipulators need only small holes in the abdomen. Kawashima et al. have developed a new manipulator using spring-
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
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CIRP-1121; No. of Pages 4 T. Kuboki et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
type joints with a cross section of high rectangle ratio instead of mechanical joints. The usage of the spring is the key technology to reduce the size of the joints, which will make the seize of holes on the abdomen minimal [6]. The springs with a cross section of high rectangle ratio would be manufactured by the present beating method as shown in Fig. 4(a). This type of spring could also be used as a tail of a swimming robot [7]. Micro forceps and grippers, which are now fabricated by LIGA process [8], are another possibility. Nozzles for micro-droplets [9] could also be fabricated from the quarter sector formed by the present bending method. If the bending process is applied to the angle sheet metals, they could be used as a bush of micro machines as shown in Fig. 4(d). The S-shape-bent sheet metals could be fabricated into two-way angular bearings in micro machines. 3. Examination of effectiveness of the proposed method 3.1. Prototype machine and forming conditions Fig. 5 shows the prototype machine, which was fabricated for the verification of the effectiveness of the proposed method. The rotation of the motor was reduced by the decelerator to rotate the cam, which pushes down the punch for beating the sheet metals. After beating, the punch is lifted up to the initial position by the spring, which is mounted in the punch holder. The sheet metal is fed along the linear guide after every beating.
3
stiffness of the machine. The feed pitch is assumed to be so small that no unbeaten area should appear on the toe side. The calculation procedure is explained as follows: (1) The actual indentation da and the tilt angle a are assumed. (2) The thickness distribution t is calculated as the function of breadth position x from a. (3) The stress distribution s(x) is estimated assuming that the plastic equivalent strain should be equal to the thickness strain -log(t/t0), considering work hardening. (4) The moment M around the punch joint is calculated from s(x). If M is not zero, the assumed value of a should be modified. (5) If M is zero, the punch load F is calculated by integration of s(x). Here, the integrated value is multiplied by a coefficient g, because the actual punch load should be much larger than the integrated value because of friction and constraints from material of the unbeaten area [10]. (6) Elastic deformation of machine de is calculated from stiffness k as F/k. If de + da is not equal to ds, da should be modified. The value of g/k is estimated in a preliminary comparison between analytical and laboratory results. Once da and a are obtained, the bending radius is calculated using equations in the authors’ previous research [5]. Fig. 7 shows the analysis results. While the actual indentation da increases with increase of ds, da is much less than ds. Tilt angle a increases with increase of ds as intended. These tendencies strengthen with increase of toe angle a.
Fig. 5. Prototype machine of in-plane bending with a tiltable punch.
Table 1 shows the beating condition. Aluminium A1050 was used as the sheet metal with a thickness of 0.5 mm and a breadth of 5 mm. The beating face of the punch had a trapezoidal shape, the two sides of which were positioned from the centre at w = 0.75 mm as shown in Fig. 2. The toe angle u ranged from 15 to 45 degrees. While the set indentation ds ranged from 0.2 to 0.5 mm to the sheet metal thickness t of 0.5 mm, the actual indentation da would be much less than the set indentation ds due to elastic deformation of the machine. The feed pitch ranged from 0.25 to 1.5 mm. Table 1 Beating conditions. Sheet metal
Material Thickness t0/mm Breadth B0/mm
A1050 aluminium 0.5 5
Punch
Material Tip Outside diameter d/mm Distance between centre to sides w/mm Toe angle u/8
Medium carbon steel 5 0.75
Operation
Set indentation ds/mm Feed pitch p/mm
0.2, 0.3, 0.4, 0.5 0.25–1.5
15, 30, 45
3.2. Genuine deformation under ideal condition The genuine deformation under ideal condition was examined by numerical analysis before the experiment. The flow chart of the analysis is shown in Fig. 6. The analysis calculates the actual indentation da and the tilt angle a from the set indentation ds and the toe angle u, considering work hardening of the material and the
Fig. 6. Flow chart for calculation of actual indentation and tilt angle.
3.3. Bent sheet metals in experiment Fig. 8 shows the bent sheet metals under the condition of feed pitch p = 0.25 mm/beat and set indentation ds = 0.5 mm. The sheet metal is bent successfully by the punch with the toe angle u of 30 degrees. Although the numerical results showed that the higher toe angle u should result in larger tilt angle, the bending radius of u = 45 degrees was larger than that of u = 30 degrees. This was
Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010
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CIRP-1121; No. of Pages 4 4
T. Kuboki et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
contact area increases with increase of p, which results in larger punch load leading to smaller actual indentation. Secondly, the unbeaten area appears and expands with increase of p. This effect of feed pitch could be utilized in the positive manner in the forming process, as the pitch is able to be easily controlled. A bent sample is shown in Fig. 10(b). The shape of the bent sheet was successfully controlled as intended so that it might have an S shape 3.4. Envisaged defects and possible solutions Fig. 7. Results of numerical analysis. (a) Actual indentation. (b) Tilt angle.
Fig. 8. Bent sheet metal. (feed pitch p = 0.25 mm/beat, set indentation ds = 0.5 mm). (a) Toe angle u = 158. (b) u = 308. (c) u = 458.
attributed to the appearance of unbeaten area which is schematically shown in Fig. 3. Fig. 9 shows the effect of toe angle u and set indentation ds on intrados radius ri in the expression of inverse, i.e. curvature, with the numerical prediction. There was a large difference between experimental and numerical results for u = 45 degrees because of the appearance of unbeaten area in experiments. The curvatures of experiments were smaller than those of numerical analysis. This was attributed to the deflection of sheet metal in horizontal direction, breadth increase, effect of friction, and so on, which were not taken into account in the analysis.
Although precise thickness value is difficult to obtain, the bending radius would be controlled by feed-back using in-situ observation of the bending shape. The surface irregularities due to incremental pressing were suppressed by reducing the feed pitch in this study. The irregularities could also be reduced by improving the punch geometry as proposed by Tajul et al. [11], who added an extra inclined surface to the beating punch surface in the sheetmetal’s longitudinal direction. If further flatness and smooth surface are needed, other processes like polishing should be introduced. When the specimen thickness becomes as small as several times of the grain size, the effect of grain size could appear leading to surface irregularity or variation of bending radius due to the crystal anisotropy. There was also a forming limit on bending radius in the present method. When the bending radius was near or less than the size of the sheet metal breadth, some cracks were observed at the extrados of the bending arc. 4. Conclusions This paper proposed an innovative incremental in-plane bending of thin metal sheets for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile was used. The beating face enabled the punch to bend thin metal sheets in in-plane manner. The toe angle of the beating face of 30 degrees was the most effective among the tried conditions in this paper. Working conditions, including indentation and feeding pitch, can easily and flexibly control the bending radius. In particular, the feeding pitch, which is easily changed during forming, was able to control the bending direction. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments. References
Fig. 9. Effect of toe angle and set indentation on bending radius. (a) Experiment. (b) Numerical analysis.
Fig. 10. Effect of pitch on bending radius in experiment (set indentation ds = 0.5 mm). (a) Curvature. (b) S-shaped metal sheet.
The effect of feed pitch p is shown in Fig. 10 for toe angle u = 30 degrees. A negative value of curvature means that sheet metal is bent in the opposite direction. The curvature decreased with increase of feed pitch p because of two phenomena. Firstly, the
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Please cite this article in press as: Kuboki T, et al. A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.010