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The mechanics of multi-point sandwich forming
ARTICLE IN PRESS International Journal of Machine Tools & Manufacture 48 (2008) 1495– 1503
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International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
The mechanics of multi-point sandwich forming Q. Zhang a,, Z.R. Wang a, T.A. Dean a,b a b
School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China Mechanical and Manufacturing Engineering, School of Engineering, University of Birmingham, Birmingham B15 2TT, UK
a r t i c l e in fo
abstract
Article history: Received 24 January 2008 Received in revised form 31 March 2008 Accepted 1 April 2008 Available online 16 April 2008
Multi-point sandwich forming (MPSF) is a sheet metal forming process of recent innovation, in which a reconfigurable bottom die and a rubber top die are used. Also, a reusable die sheet is placed on the pins of the reconfigurable die to form a continuous surface. Because a simple press may be used and the cost of altering the tooling to make a new part shape is small, MPSF is a suitable method for forming smallbatch quantities of a particular part. However, the basic deformation mechanics of MPSF have not yet been investigated and thus the best configuration of tool components to make a given part shape has to be determined by trial and error, which detracts from the low-cost aspect of the process. Therefore, in this paper, the results of investigation of the effect of workpiece and tool component dimensions and workpiece properties on the characteristics of the formed part shapes are presented. To enable the effect of tool and process parameters to be revealed more readily, plane strain deformation is used and a cylindrically shaped die surface was chosen for the bottom die. Three kinds of metal sheet and two kinds of rubber were used in the experiments. Experimental results show that for the die sheet, forming force increases and dimple size reduces with increase in the thickness of the sheet. Dimples occur on the surface of 1 mm LF21 aluminum sheet workpieces, however no dimples are formed on 2-mm-thick Q235B and ST12 steel sheet workpieces. The stiffness of the interpolator has an effect on the final shape accuracy. Also, the forming force of the workpiece reduces and shape accuracy increases, when lubrication is used in the surfaces of a workpiece. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Multi-point sandwich forming (MPSF) Die sheet Interpolator Dimple Sheet forming
1. Introduction Conventional sheet-forming tools are costly and take a long time to manufacture and they utilize large amounts of storage space when not in production mode [1–6]. The high cost of these tools makes them suitable for only large quantity production. Nowadays, often, small quantities of parts are required, which has led to the development of reconfigurable tooling. This tooling can be used to make a number of different part shapes. Usually, a reconfigurable tool consists of a large number of adjustable pins, the ends of which form the workpiece/tool contact region and define the specified part shape. Several designs of reconfigurable tooling have been developed [1–8]. Papazian et al. [4,5] developed a reconfigurable discrete die and a closed-loop shape control system for stretch forming sheet-metal parts for aircraft. The surface of the die was made up of the hemispherical ends of individual pins of square cross-section. The position of the ends could be adjusted by a servo system. The full-scale tool working space was 1800 mm 1200 mm, and contained 2688 pins. Socrate
Corresponding author. Tel./fax: +86 45186414751.
E-mail address: [email protected] (Q. Zhang). 0890-6955/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2008.04.003
and Boyce [6] investigated the reconfigurable stretch-forming process and the necessary compensation of the tool shape, for springback, using FE simulation. Walczyk et al. [7] developed a reconfigurable tool to manufacture composite aircraft parts, as such parts, with complex shapes, have been required for aerospace applications with increasing frequency, in recent years. The tooling shape could be changed incrementally during composite forming. Li et al. [8] developed a 2000 kN multi-point forming machine, which included 560 pins on upper and lower dies with a forming area of 840 mm 600 mm. The height of pins could be adjusted automatically by electric motors. Till now, the most widely known successful applications of multi-point forming seem to be, for the manufacture of skins for locomotives, aerospace panels and architectural facades. The reconfigurable dies, referred to above, have been composed of close-packed pins located within a container. This type of reconfigurable die, although versatile, is still relatively expensive. One feature contributing to the high cost is the large number of pins, each one often having a dedicated hydraulic or electric operating system. The multi-point sandwich forming (MPSF) tool configuration, with which the work described in this paper is concerned, is designed to reduce tool cost to a significantly lower value, compared with that for conventional reconfigurable tools.
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Nomenclature R R0 E E0 t tel n
radius of curvature before springback radius of curvature after springback elastic modulus plane strain modulus thickness of sheet thickness of elastic core in sheet during bending poisson’s ratio
Pins are used only in the bottom die and the space between them is large, so that fewer of them are required to span a given area and their height is adjusted manually using their threaded shanks. The top die is composed of urethane, which has the ability to deform to conform to virtually any bottom die shape while deforming a workpiece. To provide a continuous surface for the bottom die, a steel sheet is deformed between the appropriately positioned pins and the urethane top die. The sheet remains in place on the pins for subsequent forming of workpieces. When a different shape is to be formed the pins are adjusted and a new die sheet deformed, then production commences. Because of the wide pin spacing, and consequent high local pressure, often, dimples are formed on the die sheet when it is deformed. To stop these being imprinted on the workpiece, a rubber interpolator sheet is placed on top of the die sheet and it this that the workpiece contacts, as it is forced into the bottom die cavity. The assembled workpiece and tool set has a sandwich like structure, and therefore this process is called MPSF. In 2002, this process was successfully used to form steel panels for a structural feature on a slow speed wind tunnel [9–12]. Fig. 1 is a schematic illustration of an MPSF tool assembly. At the current stage of development of MPSF the shape of the formed workpiece cannot be predicted with accuracy because the effect of individual process and tool factors is not known. These
n K s0 s¯ ¯ sXX sXX0
strain-hardening exponent material strength coefficient initial yield stress effective stress effective strain stress along the length of sheet residual stress along the length of sheet after springback
factors include: thickness of die sheet, thickness and hardness of interpolator, the thickness and mechanical properties of the workpiece, shape and mechanical properties of the urethane top die and workpiece/die friction. Therefore, to overcome, this problem, in part at least, these factors are investigated, in the work presented in this paper. Using a bottom die shape of cylindrical section, enables the deformation mechanism to be examined in two dimensions.
2. Experimental procedure 2.1. Equipment A multi-point bottom die, consisting of 28 pins (7 rows 4 columns), was manufactured to the design and dimensions shown in Fig. 1. The complete tooling, consisting of pin array, die sheet, workpiece, interpolator and rubber top die, was mounted on a 100 ton hydraulic press. A two-dimensional coordinate measuring device, including two digital gauges and a measuring base with moveable bearings, was designed and constructed to measure the formed part shape along a section. Before measurement, the workpiece was fixed on the measuring table. One gauge, mounted on a carriage which can be translated in the X direction, was used to measure the Z direction coordinate; another one was used to record the X direction coordinate. 2.2. Materials Table 1 lists details of tool and workpiece components used in experiments. Workpieces comprised sheets of either Q235B or ST12 steel or LF21 aluminum alloy, of various thicknesses, cut into blanks of dimensions, 400 mm 116 mm. Die sheets with three different thicknesses, were of Q235B steel 400 mm 200 mm. Tensile stress–strain relations obtained for these three alloys are shown in Fig. 2. Two types of elastomer were used for the interpolator, either polyurethane or a black rubber. Compressive engineering stress–strain relations obtained for the elastomers are given in Fig. 3. 2.3. Experimental method
Fig. 1. Schematic illustration of MPSF. (a) set up for deformation of die sheet and (b) set up for deformation of workpiece.
In all operations the deformation stroke of the press was terminated on contact of the die sheet with the central pin in the bottom die. This was signaled by completion of an electric circuit containing a battery and light bulb. The chosen die shape was a cylindrical surface with radius 300 mm, which was produced by setting the pin heights in the bottom die. A rectangular polyurethane pad was chosen as the top die. The first operation was to place a flat die sheet on the bottom die and deform it into the pins with the top die, as shown in Fig. 1(a). Finally, an interpolator sheet and the chosen workpiece were placed on top of the die sheet and deformed by the top
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Table 1 The size and material type of each part in MPSF Part name
Material
Thickness (mm)
Length and width (mm)
Workpiece
Q235B ST12 LF21 Polyurethane (Shore A hardness 85) Q235B Polyurethane (Shore A hardness 85) Black rubber (Shore A hardness 54)
2 2 1 80 2, 3.7,5.5 10, 20, 30 20
400 116
Top die Die sheet Interpolator
500 250 400 200 400 150
600 Q235 T=5.5mm
550
Q235 T=2mm
500
Q235 T=3.7mm
True stress (MPa)
450 400 ST12 T=2mm
350 300 250 200
LF21 T=1mm
150 100 50 0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Fig. 4. Coordinate system for analysis of bending.
Natural strain Fig. 2. True stress–natural strain curves of die sheet and workpiece alloys.
10
Engineering Stress (MPa)
Polyurethane with Shore A hardness 85 Black Rubber with Shore A hardness 54
8
6
4
2
0 0.0
0.1
0.2 0.3 Engineering Strain
0.4
Fig. 3. Engineering stress–strain relation for elastomers.
die, in one continuous stroke of the press, as shown in Fig. 1(b). Forming load and stroke were recorded automatically. To measure the deformation of the interpolator during deformation, plasticene was used as a gauge block between workpiece and die sheet.
workpieces is significantly larger than their thickness, so the deformation can be considered as plane strain. The theory of bending has been presented by researchers such as, Johnson and Mellor [13], Chakrabarty, [14] and Hosford and Caddell [15]. In this paper, a simple derivation for bending and springback presented by Hosford [15] is used to analyze the bending deformation of both die sheet and workpiece. This is the bending of a flat sheet of a work-hardening material (Power law hardening rule:s¯ ¼ K ¯ n ). Fig. 4 shows the coordinate system for analysis of bending. For pure bending, the mid-plane is the same as the neutral plane whose length is unchanged. R is the radius of curvature of the mid-plane. As bending continues, yielding begins at the outer sheet and gradually spreads towards the center, but central elastic region still exists near the midplane, the thickness of which is tel. The relationship of radius of curvature between fully loaded condition and after springback can be written as 0 " nþ2 nþ2 # 1 1 1 t el 3 24 K t t ¼ þ el 0 R R0 R t 2 2 ðn þ 2ÞRn t 3 E where E0 ¼ E=ð1 n2 Þ;
t el ¼ 2s0 R=E0 ;
K0 ¼ K
ðnþ1Þ=2 4 3
After bending, the stress sXX along the length of sheet can be express as
3. Theoretical analysis of forming process sXX To gain a basic understanding of the deformation of the workpiece, classical bending theory was utilized. Bending is the main mode of workpiece deformation in the experiment, because a cylindrical die shape and no blank holder are used. The width of
(1)
z t t E0 el ozo el R 2 2 ¼ z n t t t t > el 0 > > ozo ; el ozo :K R 2 2 2 2 8 > > > <
(2)
where z is the distance from the mid-plane of sheet. After springback, the resulting residual stress along the sheet length is
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sXX0 ¼ sXXDsXX and can be written as
s0XX
z t t E0 0 el ozo el 2 2 R ¼ n 1 1 t t t t > 0 z 0 > > ozo el ; el ozo : K R E z R R0 2 2 2 2 8 > > > <
(3)
4. Numerical simulation of MPSF In order to analyze the deformation mechanisms, which are complicated by the interactions of die sheet, interpolator, workpiece and rubber die and enable the prediction of springback and hence further develop the process, finite element simulation was undertaken. An FE process model was built which included different material models (elastic–plastic and hyperelastic) and friction between each tool/workpiece element. Considering the complicated non-linear contact, the code ABAQUS/Explicit was used. However, ABAQUS/Standard was used to simulate springback. The simulation results of a deformed mesh and its associated material state can be transformed easily between ABAQUS/Standard and ABAQUS/Explicit [16]. For improving the accuracy of results, seven Gauss integration points were set along the thickness of shell elements S4R in the die sheet and workpiece. The elastic top die and interpolator were meshed with solid elements C3D8R. The press slide and pins in the lower die
Fig. 5. Deformed 3.7-mm-thick Q235B die sheet.
were considered rigid bodies, and rigid shell elements R3D4 and analytical rigid surfaces were assigned to them, respectively. The elastic–plastic material model was applied to workpiece and die sheet. The top die and interpolator were elastomers, therefore the Moony–Rivalin hyperelastic material model was used. The whole simulation of workpiece manufacture was separated into four steps. Firstly, ABAQUS/Explicit was used to simulate the forming process of the die sheet. Secondly, ABAQUS/Standard was used to simulate springback of die sheet. Then, the workpiece forming simulation was undertaken using ABAQUS/Explicit with the die sheet after springback. Finally, workpiece springback was simulated using ABAQUS/ Standard. 5. Results and discussion 5.1. Die sheet thickness The role of the die sheet is to provide a continuous surface in the bottom die. When the die sheet was given its initial shape the pressure of the pins (usually the outermost ones) caused dimples to form in it. Possibly there is a sheet thickness that can be deformed without dimple formation, but this is likely to require high press load, and in addition it will reduce the accuracy of the bottom die shape. Fig. 5 is a photograph of the deformed 3.7-mmthick Q235B die sheet. The maximum height of dimple on die sheet was obtained by measuring the profile of a section that contacted the outermost pins. Section B-B is shown, for example, in Fig. 5. In order to investigate the effect of die sheet thickness on the forming force and dimple, three Q235B die sheets with 2, 3.7 and 5.5 mm thicknesses were used in the experiment. And also six thicknesses of die sheet 1, 2, 3, 3.7, 5.5 and 6.5 mm were chosen for the simulation. Fig. 6 shows relationships between thickness of die sheet, forming force and maximum height of dimple. Experimental and simulation results indicate that forming force and maximum height of dimple respectively, increase and decease nearly linearly, with increase in sheet thickness. Therefore, to reduce the possibility of dimple arising on the workpiece, the thicken die sheet should be chosen under the capacity of press and multi-point die.
600
3.0 Forming force
550
The maximum height of dimples
Experimental results Simulation results
Forming force (KN)
500
2.8
Experimental results Simulation results
2.6 2.4
450
2.2
400
2.0 350 1.8 300
1.6
250
1.4
200
1.2
Maximum height of dimples
150
1.0
100
Maximum height of dimples in die sheet (mm)
1498
0.8 0.5
1.0
1.5
2.0
2.5 3.0 3.5 4.0 4.5 5.0 5.5 The thickness of die sheet (mm)
6.0
6.5
7.0
Fig. 6. Relationships between thickness of die sheet, forming force and maximum height of dimple.
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Fig. 7. Three different deformed workpieces.
Q235B 2mm ST12 2mm LF21 1mm Multi-point die shape
Height (mm)
30 20 10 0 -10 0
25
50
75
100
125
150
175
200
Distance from center (mm)
least although the elastic modulus of the light alloy is the lowest. Dimples in Q235B and ST12 workpieces are nearly the same height, but the dimple on the LF21 workpiece is significantly larger as shown in Fig. 8(b). That is because the LF21 sheet is thinner and has a lower yield point. According to the experimental results, forming force of Q235B, ST12 and LF21 sheet were 288, 283 and 273 KN, respectively. The difference between them is not large, because the forming force is not only due to workpiece deformation, but also deformation of the die sheet, which is thicker than workpiece and does not fit the multi-point die shape before workpiece-forming process, due to springback. Fig. 9 shows the simulated distribution of longitudinal stress sXX, at different z heights, on the centerline of Q235B and ST12 sheets. It can be seen that the stress distribution along the thickness of sheets is not symmetrical about the mid-plane. The stress at the mid-plane becomes plastic at high values of press stroke, showing that the deformation is not pure bending but has a superposed tension through stretching. The stress on the midplane of ST12 sheet is larger than that on the Q235B sheet, so plastic deformation due to stretching is greater than for the Q235B sheet. However, the stress on the mid-plane of Q235B sheet is small, the deformation can be considered as close to pure bending. In order to determine whether stress distribution derived by simulation agrees with that calculated from theoretical analysis, the theoretical pure bending stress distribution of sXX, using Eqs. (2) and (3) and that predicted by simulation are shown in Fig. 10. It can be seen that the simulated and theoretical results are similar both for full loading and after pressing for a Q235B workpiece.
5.3. Interpolator thickness and hardness
3.0 Q235B 2mm ST12 2mm LF21 1mm
2.5 2.0 Height (mm)
1499
1.5 1.0 0.5 0.0 -0.5
Dimples
-1.0 -50
-25
0
25
50
Distance from center along section B-B (mm) Fig. 8. The effect of workpiece alloy and sheet thickness on deformation (interpolator: 10 mm polyurethane, die sheet: 3.7 mm Q235B): (a) deformed profile on section O-A and (b) profile of dimples on section B-B.
5.2. Workpiece alloy Measurements of features on the deformed workpieces, were made along two sections: OA and BB, as shown in Fig. 7. Three different workpieces, 2 mm Q235B, 2 mm ST12 and 1 mm LF21, were manufactured and shapes of them are shown in Fig. 8. Experimental results illustrate that curved shape and dimple profile are different for different materials and different thicknesses. The springback of the Q235B workpiece is larger than that of the ST12 workpiece having the same thickness, because the yield point of Q235B has a higher value than that of ST12 (See Fig. 2). The plastic deformation arising in the sheet of the latter alloy occupies a greater proportion of the section than that of the former alloy, so springback is less in ST12 sheet as shown in Fig. 8(a). Moreover, the thickness and yield point of LF21 sheet is less than that of both Q235B and ST12, so springback of LF21 is
The function of the interpolator is to prevent dimples on the die sheet from being transferred to the workpiece, but the effective die shape is changed by using different thicknesses of interpolator. Also the forming force is changed. Fig. 11 shows experimental forming forces of the 2 mm Q235B workpiece using different interpolators. According to experimental results it can be seen that the greater the thickness of interpolator, the larger is the effective radius of curvature in the die and therefore, the lower is the forming force. Moreover, the forming force is reduced by reducing the hardness of the interpolator by using black rubber instead of polyurethane. To investigate the influence of interpolator on the shape of workpiece, bending experiments with different interpolators and workpieces were carried out. The results are shown in Fig. 12. It is seen that for the steel workpiece the thicker and softer an interpolator is, the shallower the formed workpiece is. But the interpolator characteristic has no significant influence on workpiece shape in the central region. In Fig. 12(c) it appears that for the LF21 workpiece dimples are reduced by reducing the stiffness of the interpolator, as they are nearly obviated with thicker polyurethane or black rubber and 20 mm rubber produces smaller dimples than 20 mm polyurethane. It is because the black rubber is softer and forming force is lower than polyurethane, the pressure acting on the surface of workpiece is more uniform than with polyurethane. An interpolator can induce a change in a workpiece due to its own deformation. During experiments, interpolator deformation was measured by placing pieces of plasticene between workpiece and die sheet and measuring its reduction in height. The results show that the thickness of an interpolator changes along its length under load, and becomes greater at mid-length and less at the ends, as shown in Fig. 13. During forming, the end region of the
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Z
500
Mid-plane Plastic Zone
400 300
Z=0.94911
200 xx (MPa)
Z=0.74153 Z=0.40585
100
Z=0 Z=-0.40585 Z=-0.74153
0 Elastic Zone
Z=-0.94911
-100 -200 -300 -400
Plastic Zone
-500 0
10
20 30 40 The displacement of press slide (mm)
50
Z
250
Mid-plane Plastic Zone
200 150 100 xx (MPa)
Z=0.94911
50
Z=0.74153 Z=-0.40585
0
Elastic Zone
Z=0 Z=-0.40585
-50
Z=-0.74153 Z=-0.94911
-100 -150 -200
Plastic Zone
-250 0
10 20 30 The displacement of press slide (mm)
40
Fig. 9. Simulated distribution of sXX along thickness at middle point in 2-mm-thick workpiece (interpolator: 10 mm polyurethane, die sheet: 3.7 mm Q235B). (a) Q235B sheet and (b) ST12 sheet.
interpolator, where it is located upon the outermost pins of the die, suffers a high normal pressure from the large compression deformation of elastic top die, so its thickness is reduced greatly. Meanwhile, interpolator material flows towards the middle of the die due to the smaller normal pressure on this region. Therefore, the middle of the interpolator thickens. The difference in thickness from end to middle decreases with interpolator thickness. Black rubber deforms more than polyurethane when a 20-mm-thick interpolator is used, therefore the shape of workpiece is shallower when the former material is used, as shown in Fig. 12. To identify the relevance of springback and interpolator in producing malformed parts, 2 mm Q235B sheet was chosen as a workpiece to simulate forming and springback. Also classical analysis was used to calculate the shape change due to springback. It can be seen from Fig. 14 that the difference between the workpiece shape and the die shape at maximum slide displacement
is due to interpolator deformation, and the difference between workpiece shape at maximum slide displacement and after die parting is due to springback. Therefore, the shape error from springback is larger than that of interpolator in this forming process. This is the reason why the differences in final shapes of workpiece are not large when different interpolators are used (see Fig. 12).
5.4. The effect of lubrication In order to research the effect of friction condition on the forming force and formed part shape, solid Teflon-lubricating films were applied to workpiece/interpolator and workpiece/top die interfaces during forming process. In experiments, LF21 was chosen as a workpiece and polyurethane pads with thickness 10, 20 and 30 mm were used as interpolator. With lubricant, the
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1501
1.2 1.0
Before springback After springback
25
0.6 Simulation results
0.4
Before springback After springback
0.2 0.0 -0.2
Polyurethane T= 10mm Polyurethane T= 20mm Polyurethane T= 30mm Black Rubber T= 20mm Multi-point die shape
30 Height (mm)
Distance on Zcoordinate (mm)
35
Theoretical results
0.8
20 15 10 5 0
-0.4
-5
-0.6
-10
-0.8
0
-1.0
25
50 75 100 125 150 175 Displacement from center (mm)
-1.2 -400
-300
-200
-100
0
100
200
300
400
xx (MPa)
35
Black rubber
Polyurethane T= 10mm Polyurethane T= 20mm Polyurethane T= 30mm Black Rubber T= 20mm Multi-point die shape
30 Height (mm)
Fig. 10. Theoretical and simulated height distribution of stress sXX on the centerline of a Q235B workpiece before and after springback (interpolator: 10 mm polyurethane, die sheet: 3.7 mm Q235B).
300
200
25 20 15 10 5
250
0 200
0
25
50 75 100 125 150 Distance from the center (mm)
175
200
150
100
50
0 10
20
30
40
Thickness of interpolator (mm) Fig. 11. Effect of different interpolator on forming force for 2 mm thickness Q235B workpiece (die sheet: 3.7 mm Q235B, workpiece: 2 mm Q235B).
forming force decreases for all process conditions as shown in Fig. 15. Experimental results show that shape error of a workpiece is reduced when lubrication is used, as shown in Fig. 16. This is because a lubricated workpiece flows into the die cavity and is stretched less than an unlubricated one. Also the forming force is smaller with lubrication, and the compression of the interpolator is more uniform (see Fig. 17), thus it effectively retains most of its original profile. Fig. 17 shows shape of the interpolator upper surface under 212 and 264 kN loads by using simulation. Simulated results indicate a shallower die for a higher force.
6. Conclusions Forming parameters existing in MPSF have been investigated in this work for die shapes of cylindrical form. Based on the results obtained, the following conclusions are drawn: 1. With an increase in thickness of the die sheet, the die sheet forming force increases but the maximum height of dimples on the die sheet decreases, nearly linearly.
Height (mm)
Forming force for workpiece (KN)
Polyurethane
6 5 4 3 2 1 0 -1 -2 -3
Polyurethane T=30mm Polyurethane T=20mm Polyurethane T=10mm Black Rubber T=20mm
Dimples
-60
-40
-20 0 20 Distance from center (mm)
40
60
Fig. 12. The effect of interpolator on formed workpiece shape (die sheet: 3.7 mm Q235B): (a) 2 mm Q235B workpiece on section O-A, (b) 1 mm LF21 workpiece on section O-A, (c) 1 mm LF21 workpiece on section B-B.
2. The forming force required for a workpiece decreases with increase in the thickness of interpolator. Softer interpolator material can suppress dimples effectively, but the shape error of a workpiece became large. Dimples on the workpiece can be obviated when a suitable thickness of interpolator is chosen. The interpolator is another factor introducing shape error in addition to workpiece springback, because of its non-uniform deformation. But the shape error of a workpiece due to interpolator distortion is less than that from springback, due to the larger bending deformation in the cylindrical die. 3. Workpiece springback is low when a low-yield stress sheet is used. The dimples on the 2 mm Q235B and ST12 sheet are not significant, but on the 1 mm LF21 sheet were seen to be larger when 10 mm polyurethane interpolator is used.
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40 Polyurethane T=20mm Polyurethane T=10mm Black rubber T=20mm
Polyurethane T=40mm Polyurethane T=30mm
40
with lubrication Polyurethane T=10mm Polyurethane T=20mm Polyurethane T=30mm
35 30 Height (mm)
The thickness of interpolator (mm)
50
30
20
without lubrication Polyurethane T=10mm Polyurethane T=20mm Polyurethane T=30mm Multi-point die shape
25 20 15 10 5
10
0 0 0
20
40
60 80 100 120 Distance from center (mm)
140
Fig. 13. The deformation of interpolator during forming (workpiece: 2 mm Q235B, Die sheet: 3.7 mm Q235B).
30 Height (mm)
25
Height (mm)
Multi-point die shape After springback (experiment) Before springback (simulation) After springback (simulation) After springback (theory)
35
50
20
75 100 125 150 Distance from center (mm)
175
200
Fig. 16. Effects of lubrication and thickness of interpolator on the shape of a formed workpiece along section O-A (workpiece: 1 mm LF21, die sheet: 3.7 mm Q235B).
F=212KN F=264KN
25 40
25
160
20 15 10 5
15 10
0
5
0
50
100
150
200
250
Distance along section O-A (mm)
0 -5
Fig. 17. Shape of interpolator upper surface along section O-A under different forming forces (workpiece: 1 mm LF21, die sheet: 3.7 mm Q235B, interpolator: 30 mm polyurethane).
Forming range
-10 0
20
40
60
80
100
120
140
160
180
200
220
Distance from center (mm) Fig. 14. Shape of workpiece before and after springback (workpiece: 2 mm Q235B, Interpolaotor: 10 mm polyurethane, Die sheet: 3.7 mm Q235B).
Acknowledgment
290 Without lubrication With lubrication
280 270
Forming force (KN)
4. The forming force and shape error of workpieces decrease when lubrication is applied on both the surfaces of workpiece.
260 250
The authors would like to express their sincere appreciation for the financial support of the National Natural Science Foundation of China (its number 50435010). Reference
240 230 220 210 200 190 180 10
15 20 25 The thickness of interpolator (mm)
30
Fig. 15. The effect of lubrication on the forming force (workpiece: 1 mm LF21, die sheet: 3.7 mm Q235B).
[1] J.A. Knapke, Evaluation of a variable-configuration-die sheet metal forming machine, M.S. Thesis, Department of Mechanical Engineering Massachusetts Institute of Technology, 1988. [2] K.B. Ousterhout, Design and control of a flexible process for threedimensional sheet metal forming, Ph.D. Thesis, Dept. of Mechanical Engineering Massachusetts Institute of Technology, 1991. [3] J.W. Park, Y.S. Hong, S.H. Lim, Dieless forming apparatus, US Patent No. 6,151,938, 2000. [4] J.M. Papazian, Tools of change, Mechanical Engineering 124 (2002) 52–55. [5] J.M. Papazian, E.L. Anagnostou, R.J. Christ, et al., Tooling for rapid sheet metal parts production, in: sixth Joint FAA/DoD/NASA Conference on Aging Aircraft, San Francisco, CA, USA, September 2002, pp. 16–19. [6] S. Socrate, M.C. Boyce, A finite element based die design algorithm for sheetmetal forming on reconfigurable tools, ASME Journal of Engineering Material Technology 123 (2001) 489–495.
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[7] D.F. Walczyk, J.F. Hosford, J.M. Papazian, Using reconfigurable tooling and surface heating for incremental forming of composite aircraft parts, Journal of Manufacturing Science and Engineering 125 (2003) 333–343. [8] M.Z. Li, Z.Y. Cai, Z. Sui, Q.G. Yan, Multi-point forming technology for sheet metal, Journal of Materials Processing Technology 129 (2002) 333–338. [9] Q. Zhang, T.A. Dean, Z.R. Wang, Numerical simulation of deformation in multipoint sandwich forming, International Journal of Machine Tools and Manufacture 46 (2006) 699–707. [10] Q. Zhang, Z.R. Wang, T.A. Dean, Experimentation and numerical simulation of the manufacture of an ellipsoidal workpiece by multi-point sandwich forming, in: Proceedings of the International Technology and Innovation Conference 2006, Hangzhou, China.
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[11] Q. Zhang, Z.R. Wang, T.A. Dean, Multi-point sandwich forming of a spherical sector with tool-shape compensation, Journal of Materials Processing Technology 194 (2007) 74–80. [12] Z.R. Wang, B.G. Teng, Q. Zhang, Multi-point sandwich forming, Advanced Technology of Plasticity (2005) 563–564. [13] W. Johnson, P.B. Mellor, Engineering Plasticity, Van Nostrand Reinhold, London, 1973. [14] J. Chakrabarty, Theory of Plasticity, McGraw-Hill, New York, 1987. [15] W.F. Hosford, R.M. Caddell, Metal Forming Mechanics and Metallurgy, Prentice-Hall Inc., Englewood Cliffs, 1983. [16] ABAQUS Analysis User’s Manual, ABAQUS, Inc., Version 6.5, 2004.
Contents lists available at ScienceDirect
International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
The mechanics of multi-point sandwich forming Q. Zhang a,, Z.R. Wang a, T.A. Dean a,b a b
School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China Mechanical and Manufacturing Engineering, School of Engineering, University of Birmingham, Birmingham B15 2TT, UK
a r t i c l e in fo
abstract
Article history: Received 24 January 2008 Received in revised form 31 March 2008 Accepted 1 April 2008 Available online 16 April 2008
Multi-point sandwich forming (MPSF) is a sheet metal forming process of recent innovation, in which a reconfigurable bottom die and a rubber top die are used. Also, a reusable die sheet is placed on the pins of the reconfigurable die to form a continuous surface. Because a simple press may be used and the cost of altering the tooling to make a new part shape is small, MPSF is a suitable method for forming smallbatch quantities of a particular part. However, the basic deformation mechanics of MPSF have not yet been investigated and thus the best configuration of tool components to make a given part shape has to be determined by trial and error, which detracts from the low-cost aspect of the process. Therefore, in this paper, the results of investigation of the effect of workpiece and tool component dimensions and workpiece properties on the characteristics of the formed part shapes are presented. To enable the effect of tool and process parameters to be revealed more readily, plane strain deformation is used and a cylindrically shaped die surface was chosen for the bottom die. Three kinds of metal sheet and two kinds of rubber were used in the experiments. Experimental results show that for the die sheet, forming force increases and dimple size reduces with increase in the thickness of the sheet. Dimples occur on the surface of 1 mm LF21 aluminum sheet workpieces, however no dimples are formed on 2-mm-thick Q235B and ST12 steel sheet workpieces. The stiffness of the interpolator has an effect on the final shape accuracy. Also, the forming force of the workpiece reduces and shape accuracy increases, when lubrication is used in the surfaces of a workpiece. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Multi-point sandwich forming (MPSF) Die sheet Interpolator Dimple Sheet forming
1. Introduction Conventional sheet-forming tools are costly and take a long time to manufacture and they utilize large amounts of storage space when not in production mode [1–6]. The high cost of these tools makes them suitable for only large quantity production. Nowadays, often, small quantities of parts are required, which has led to the development of reconfigurable tooling. This tooling can be used to make a number of different part shapes. Usually, a reconfigurable tool consists of a large number of adjustable pins, the ends of which form the workpiece/tool contact region and define the specified part shape. Several designs of reconfigurable tooling have been developed [1–8]. Papazian et al. [4,5] developed a reconfigurable discrete die and a closed-loop shape control system for stretch forming sheet-metal parts for aircraft. The surface of the die was made up of the hemispherical ends of individual pins of square cross-section. The position of the ends could be adjusted by a servo system. The full-scale tool working space was 1800 mm 1200 mm, and contained 2688 pins. Socrate
Corresponding author. Tel./fax: +86 45186414751.
E-mail address: [email protected] (Q. Zhang). 0890-6955/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2008.04.003
and Boyce [6] investigated the reconfigurable stretch-forming process and the necessary compensation of the tool shape, for springback, using FE simulation. Walczyk et al. [7] developed a reconfigurable tool to manufacture composite aircraft parts, as such parts, with complex shapes, have been required for aerospace applications with increasing frequency, in recent years. The tooling shape could be changed incrementally during composite forming. Li et al. [8] developed a 2000 kN multi-point forming machine, which included 560 pins on upper and lower dies with a forming area of 840 mm 600 mm. The height of pins could be adjusted automatically by electric motors. Till now, the most widely known successful applications of multi-point forming seem to be, for the manufacture of skins for locomotives, aerospace panels and architectural facades. The reconfigurable dies, referred to above, have been composed of close-packed pins located within a container. This type of reconfigurable die, although versatile, is still relatively expensive. One feature contributing to the high cost is the large number of pins, each one often having a dedicated hydraulic or electric operating system. The multi-point sandwich forming (MPSF) tool configuration, with which the work described in this paper is concerned, is designed to reduce tool cost to a significantly lower value, compared with that for conventional reconfigurable tools.
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Nomenclature R R0 E E0 t tel n
radius of curvature before springback radius of curvature after springback elastic modulus plane strain modulus thickness of sheet thickness of elastic core in sheet during bending poisson’s ratio
Pins are used only in the bottom die and the space between them is large, so that fewer of them are required to span a given area and their height is adjusted manually using their threaded shanks. The top die is composed of urethane, which has the ability to deform to conform to virtually any bottom die shape while deforming a workpiece. To provide a continuous surface for the bottom die, a steel sheet is deformed between the appropriately positioned pins and the urethane top die. The sheet remains in place on the pins for subsequent forming of workpieces. When a different shape is to be formed the pins are adjusted and a new die sheet deformed, then production commences. Because of the wide pin spacing, and consequent high local pressure, often, dimples are formed on the die sheet when it is deformed. To stop these being imprinted on the workpiece, a rubber interpolator sheet is placed on top of the die sheet and it this that the workpiece contacts, as it is forced into the bottom die cavity. The assembled workpiece and tool set has a sandwich like structure, and therefore this process is called MPSF. In 2002, this process was successfully used to form steel panels for a structural feature on a slow speed wind tunnel [9–12]. Fig. 1 is a schematic illustration of an MPSF tool assembly. At the current stage of development of MPSF the shape of the formed workpiece cannot be predicted with accuracy because the effect of individual process and tool factors is not known. These
n K s0 s¯ ¯ sXX sXX0
strain-hardening exponent material strength coefficient initial yield stress effective stress effective strain stress along the length of sheet residual stress along the length of sheet after springback
factors include: thickness of die sheet, thickness and hardness of interpolator, the thickness and mechanical properties of the workpiece, shape and mechanical properties of the urethane top die and workpiece/die friction. Therefore, to overcome, this problem, in part at least, these factors are investigated, in the work presented in this paper. Using a bottom die shape of cylindrical section, enables the deformation mechanism to be examined in two dimensions.
2. Experimental procedure 2.1. Equipment A multi-point bottom die, consisting of 28 pins (7 rows 4 columns), was manufactured to the design and dimensions shown in Fig. 1. The complete tooling, consisting of pin array, die sheet, workpiece, interpolator and rubber top die, was mounted on a 100 ton hydraulic press. A two-dimensional coordinate measuring device, including two digital gauges and a measuring base with moveable bearings, was designed and constructed to measure the formed part shape along a section. Before measurement, the workpiece was fixed on the measuring table. One gauge, mounted on a carriage which can be translated in the X direction, was used to measure the Z direction coordinate; another one was used to record the X direction coordinate. 2.2. Materials Table 1 lists details of tool and workpiece components used in experiments. Workpieces comprised sheets of either Q235B or ST12 steel or LF21 aluminum alloy, of various thicknesses, cut into blanks of dimensions, 400 mm 116 mm. Die sheets with three different thicknesses, were of Q235B steel 400 mm 200 mm. Tensile stress–strain relations obtained for these three alloys are shown in Fig. 2. Two types of elastomer were used for the interpolator, either polyurethane or a black rubber. Compressive engineering stress–strain relations obtained for the elastomers are given in Fig. 3. 2.3. Experimental method
Fig. 1. Schematic illustration of MPSF. (a) set up for deformation of die sheet and (b) set up for deformation of workpiece.
In all operations the deformation stroke of the press was terminated on contact of the die sheet with the central pin in the bottom die. This was signaled by completion of an electric circuit containing a battery and light bulb. The chosen die shape was a cylindrical surface with radius 300 mm, which was produced by setting the pin heights in the bottom die. A rectangular polyurethane pad was chosen as the top die. The first operation was to place a flat die sheet on the bottom die and deform it into the pins with the top die, as shown in Fig. 1(a). Finally, an interpolator sheet and the chosen workpiece were placed on top of the die sheet and deformed by the top
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Table 1 The size and material type of each part in MPSF Part name
Material
Thickness (mm)
Length and width (mm)
Workpiece
Q235B ST12 LF21 Polyurethane (Shore A hardness 85) Q235B Polyurethane (Shore A hardness 85) Black rubber (Shore A hardness 54)
2 2 1 80 2, 3.7,5.5 10, 20, 30 20
400 116
Top die Die sheet Interpolator
500 250 400 200 400 150
600 Q235 T=5.5mm
550
Q235 T=2mm
500
Q235 T=3.7mm
True stress (MPa)
450 400 ST12 T=2mm
350 300 250 200
LF21 T=1mm
150 100 50 0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Fig. 4. Coordinate system for analysis of bending.
Natural strain Fig. 2. True stress–natural strain curves of die sheet and workpiece alloys.
10
Engineering Stress (MPa)
Polyurethane with Shore A hardness 85 Black Rubber with Shore A hardness 54
8
6
4
2
0 0.0
0.1
0.2 0.3 Engineering Strain
0.4
Fig. 3. Engineering stress–strain relation for elastomers.
die, in one continuous stroke of the press, as shown in Fig. 1(b). Forming load and stroke were recorded automatically. To measure the deformation of the interpolator during deformation, plasticene was used as a gauge block between workpiece and die sheet.
workpieces is significantly larger than their thickness, so the deformation can be considered as plane strain. The theory of bending has been presented by researchers such as, Johnson and Mellor [13], Chakrabarty, [14] and Hosford and Caddell [15]. In this paper, a simple derivation for bending and springback presented by Hosford [15] is used to analyze the bending deformation of both die sheet and workpiece. This is the bending of a flat sheet of a work-hardening material (Power law hardening rule:s¯ ¼ K ¯ n ). Fig. 4 shows the coordinate system for analysis of bending. For pure bending, the mid-plane is the same as the neutral plane whose length is unchanged. R is the radius of curvature of the mid-plane. As bending continues, yielding begins at the outer sheet and gradually spreads towards the center, but central elastic region still exists near the midplane, the thickness of which is tel. The relationship of radius of curvature between fully loaded condition and after springback can be written as 0 " nþ2 nþ2 # 1 1 1 t el 3 24 K t t ¼ þ el 0 R R0 R t 2 2 ðn þ 2ÞRn t 3 E where E0 ¼ E=ð1 n2 Þ;
t el ¼ 2s0 R=E0 ;
K0 ¼ K
ðnþ1Þ=2 4 3
After bending, the stress sXX along the length of sheet can be express as
3. Theoretical analysis of forming process sXX To gain a basic understanding of the deformation of the workpiece, classical bending theory was utilized. Bending is the main mode of workpiece deformation in the experiment, because a cylindrical die shape and no blank holder are used. The width of
(1)
z t t E0 el ozo el R 2 2 ¼ z n t t t t > el 0 > > ozo ; el ozo :K R 2 2 2 2 8 > > > <
(2)
where z is the distance from the mid-plane of sheet. After springback, the resulting residual stress along the sheet length is
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sXX0 ¼ sXXDsXX and can be written as
s0XX
z t t E0 0 el ozo el 2 2 R ¼ n 1 1 t t t t > 0 z 0 > > ozo el ; el ozo : K R E z R R0 2 2 2 2 8 > > > <
(3)
4. Numerical simulation of MPSF In order to analyze the deformation mechanisms, which are complicated by the interactions of die sheet, interpolator, workpiece and rubber die and enable the prediction of springback and hence further develop the process, finite element simulation was undertaken. An FE process model was built which included different material models (elastic–plastic and hyperelastic) and friction between each tool/workpiece element. Considering the complicated non-linear contact, the code ABAQUS/Explicit was used. However, ABAQUS/Standard was used to simulate springback. The simulation results of a deformed mesh and its associated material state can be transformed easily between ABAQUS/Standard and ABAQUS/Explicit [16]. For improving the accuracy of results, seven Gauss integration points were set along the thickness of shell elements S4R in the die sheet and workpiece. The elastic top die and interpolator were meshed with solid elements C3D8R. The press slide and pins in the lower die
Fig. 5. Deformed 3.7-mm-thick Q235B die sheet.
were considered rigid bodies, and rigid shell elements R3D4 and analytical rigid surfaces were assigned to them, respectively. The elastic–plastic material model was applied to workpiece and die sheet. The top die and interpolator were elastomers, therefore the Moony–Rivalin hyperelastic material model was used. The whole simulation of workpiece manufacture was separated into four steps. Firstly, ABAQUS/Explicit was used to simulate the forming process of the die sheet. Secondly, ABAQUS/Standard was used to simulate springback of die sheet. Then, the workpiece forming simulation was undertaken using ABAQUS/Explicit with the die sheet after springback. Finally, workpiece springback was simulated using ABAQUS/ Standard. 5. Results and discussion 5.1. Die sheet thickness The role of the die sheet is to provide a continuous surface in the bottom die. When the die sheet was given its initial shape the pressure of the pins (usually the outermost ones) caused dimples to form in it. Possibly there is a sheet thickness that can be deformed without dimple formation, but this is likely to require high press load, and in addition it will reduce the accuracy of the bottom die shape. Fig. 5 is a photograph of the deformed 3.7-mmthick Q235B die sheet. The maximum height of dimple on die sheet was obtained by measuring the profile of a section that contacted the outermost pins. Section B-B is shown, for example, in Fig. 5. In order to investigate the effect of die sheet thickness on the forming force and dimple, three Q235B die sheets with 2, 3.7 and 5.5 mm thicknesses were used in the experiment. And also six thicknesses of die sheet 1, 2, 3, 3.7, 5.5 and 6.5 mm were chosen for the simulation. Fig. 6 shows relationships between thickness of die sheet, forming force and maximum height of dimple. Experimental and simulation results indicate that forming force and maximum height of dimple respectively, increase and decease nearly linearly, with increase in sheet thickness. Therefore, to reduce the possibility of dimple arising on the workpiece, the thicken die sheet should be chosen under the capacity of press and multi-point die.
600
3.0 Forming force
550
The maximum height of dimples
Experimental results Simulation results
Forming force (KN)
500
2.8
Experimental results Simulation results
2.6 2.4
450
2.2
400
2.0 350 1.8 300
1.6
250
1.4
200
1.2
Maximum height of dimples
150
1.0
100
Maximum height of dimples in die sheet (mm)
1498
0.8 0.5
1.0
1.5
2.0
2.5 3.0 3.5 4.0 4.5 5.0 5.5 The thickness of die sheet (mm)
6.0
6.5
7.0
Fig. 6. Relationships between thickness of die sheet, forming force and maximum height of dimple.
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Fig. 7. Three different deformed workpieces.
Q235B 2mm ST12 2mm LF21 1mm Multi-point die shape
Height (mm)
30 20 10 0 -10 0
25
50
75
100
125
150
175
200
Distance from center (mm)
least although the elastic modulus of the light alloy is the lowest. Dimples in Q235B and ST12 workpieces are nearly the same height, but the dimple on the LF21 workpiece is significantly larger as shown in Fig. 8(b). That is because the LF21 sheet is thinner and has a lower yield point. According to the experimental results, forming force of Q235B, ST12 and LF21 sheet were 288, 283 and 273 KN, respectively. The difference between them is not large, because the forming force is not only due to workpiece deformation, but also deformation of the die sheet, which is thicker than workpiece and does not fit the multi-point die shape before workpiece-forming process, due to springback. Fig. 9 shows the simulated distribution of longitudinal stress sXX, at different z heights, on the centerline of Q235B and ST12 sheets. It can be seen that the stress distribution along the thickness of sheets is not symmetrical about the mid-plane. The stress at the mid-plane becomes plastic at high values of press stroke, showing that the deformation is not pure bending but has a superposed tension through stretching. The stress on the midplane of ST12 sheet is larger than that on the Q235B sheet, so plastic deformation due to stretching is greater than for the Q235B sheet. However, the stress on the mid-plane of Q235B sheet is small, the deformation can be considered as close to pure bending. In order to determine whether stress distribution derived by simulation agrees with that calculated from theoretical analysis, the theoretical pure bending stress distribution of sXX, using Eqs. (2) and (3) and that predicted by simulation are shown in Fig. 10. It can be seen that the simulated and theoretical results are similar both for full loading and after pressing for a Q235B workpiece.
5.3. Interpolator thickness and hardness
3.0 Q235B 2mm ST12 2mm LF21 1mm
2.5 2.0 Height (mm)
1499
1.5 1.0 0.5 0.0 -0.5
Dimples
-1.0 -50
-25
0
25
50
Distance from center along section B-B (mm) Fig. 8. The effect of workpiece alloy and sheet thickness on deformation (interpolator: 10 mm polyurethane, die sheet: 3.7 mm Q235B): (a) deformed profile on section O-A and (b) profile of dimples on section B-B.
5.2. Workpiece alloy Measurements of features on the deformed workpieces, were made along two sections: OA and BB, as shown in Fig. 7. Three different workpieces, 2 mm Q235B, 2 mm ST12 and 1 mm LF21, were manufactured and shapes of them are shown in Fig. 8. Experimental results illustrate that curved shape and dimple profile are different for different materials and different thicknesses. The springback of the Q235B workpiece is larger than that of the ST12 workpiece having the same thickness, because the yield point of Q235B has a higher value than that of ST12 (See Fig. 2). The plastic deformation arising in the sheet of the latter alloy occupies a greater proportion of the section than that of the former alloy, so springback is less in ST12 sheet as shown in Fig. 8(a). Moreover, the thickness and yield point of LF21 sheet is less than that of both Q235B and ST12, so springback of LF21 is
The function of the interpolator is to prevent dimples on the die sheet from being transferred to the workpiece, but the effective die shape is changed by using different thicknesses of interpolator. Also the forming force is changed. Fig. 11 shows experimental forming forces of the 2 mm Q235B workpiece using different interpolators. According to experimental results it can be seen that the greater the thickness of interpolator, the larger is the effective radius of curvature in the die and therefore, the lower is the forming force. Moreover, the forming force is reduced by reducing the hardness of the interpolator by using black rubber instead of polyurethane. To investigate the influence of interpolator on the shape of workpiece, bending experiments with different interpolators and workpieces were carried out. The results are shown in Fig. 12. It is seen that for the steel workpiece the thicker and softer an interpolator is, the shallower the formed workpiece is. But the interpolator characteristic has no significant influence on workpiece shape in the central region. In Fig. 12(c) it appears that for the LF21 workpiece dimples are reduced by reducing the stiffness of the interpolator, as they are nearly obviated with thicker polyurethane or black rubber and 20 mm rubber produces smaller dimples than 20 mm polyurethane. It is because the black rubber is softer and forming force is lower than polyurethane, the pressure acting on the surface of workpiece is more uniform than with polyurethane. An interpolator can induce a change in a workpiece due to its own deformation. During experiments, interpolator deformation was measured by placing pieces of plasticene between workpiece and die sheet and measuring its reduction in height. The results show that the thickness of an interpolator changes along its length under load, and becomes greater at mid-length and less at the ends, as shown in Fig. 13. During forming, the end region of the
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Z
500
Mid-plane Plastic Zone
400 300
Z=0.94911
200 xx (MPa)
Z=0.74153 Z=0.40585
100
Z=0 Z=-0.40585 Z=-0.74153
0 Elastic Zone
Z=-0.94911
-100 -200 -300 -400
Plastic Zone
-500 0
10
20 30 40 The displacement of press slide (mm)
50
Z
250
Mid-plane Plastic Zone
200 150 100 xx (MPa)
Z=0.94911
50
Z=0.74153 Z=-0.40585
0
Elastic Zone
Z=0 Z=-0.40585
-50
Z=-0.74153 Z=-0.94911
-100 -150 -200
Plastic Zone
-250 0
10 20 30 The displacement of press slide (mm)
40
Fig. 9. Simulated distribution of sXX along thickness at middle point in 2-mm-thick workpiece (interpolator: 10 mm polyurethane, die sheet: 3.7 mm Q235B). (a) Q235B sheet and (b) ST12 sheet.
interpolator, where it is located upon the outermost pins of the die, suffers a high normal pressure from the large compression deformation of elastic top die, so its thickness is reduced greatly. Meanwhile, interpolator material flows towards the middle of the die due to the smaller normal pressure on this region. Therefore, the middle of the interpolator thickens. The difference in thickness from end to middle decreases with interpolator thickness. Black rubber deforms more than polyurethane when a 20-mm-thick interpolator is used, therefore the shape of workpiece is shallower when the former material is used, as shown in Fig. 12. To identify the relevance of springback and interpolator in producing malformed parts, 2 mm Q235B sheet was chosen as a workpiece to simulate forming and springback. Also classical analysis was used to calculate the shape change due to springback. It can be seen from Fig. 14 that the difference between the workpiece shape and the die shape at maximum slide displacement
is due to interpolator deformation, and the difference between workpiece shape at maximum slide displacement and after die parting is due to springback. Therefore, the shape error from springback is larger than that of interpolator in this forming process. This is the reason why the differences in final shapes of workpiece are not large when different interpolators are used (see Fig. 12).
5.4. The effect of lubrication In order to research the effect of friction condition on the forming force and formed part shape, solid Teflon-lubricating films were applied to workpiece/interpolator and workpiece/top die interfaces during forming process. In experiments, LF21 was chosen as a workpiece and polyurethane pads with thickness 10, 20 and 30 mm were used as interpolator. With lubricant, the
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1.2 1.0
Before springback After springback
25
0.6 Simulation results
0.4
Before springback After springback
0.2 0.0 -0.2
Polyurethane T= 10mm Polyurethane T= 20mm Polyurethane T= 30mm Black Rubber T= 20mm Multi-point die shape
30 Height (mm)
Distance on Zcoordinate (mm)
35
Theoretical results
0.8
20 15 10 5 0
-0.4
-5
-0.6
-10
-0.8
0
-1.0
25
50 75 100 125 150 175 Displacement from center (mm)
-1.2 -400
-300
-200
-100
0
100
200
300
400
xx (MPa)
35
Black rubber
Polyurethane T= 10mm Polyurethane T= 20mm Polyurethane T= 30mm Black Rubber T= 20mm Multi-point die shape
30 Height (mm)
Fig. 10. Theoretical and simulated height distribution of stress sXX on the centerline of a Q235B workpiece before and after springback (interpolator: 10 mm polyurethane, die sheet: 3.7 mm Q235B).
300
200
25 20 15 10 5
250
0 200
0
25
50 75 100 125 150 Distance from the center (mm)
175
200
150
100
50
0 10
20
30
40
Thickness of interpolator (mm) Fig. 11. Effect of different interpolator on forming force for 2 mm thickness Q235B workpiece (die sheet: 3.7 mm Q235B, workpiece: 2 mm Q235B).
forming force decreases for all process conditions as shown in Fig. 15. Experimental results show that shape error of a workpiece is reduced when lubrication is used, as shown in Fig. 16. This is because a lubricated workpiece flows into the die cavity and is stretched less than an unlubricated one. Also the forming force is smaller with lubrication, and the compression of the interpolator is more uniform (see Fig. 17), thus it effectively retains most of its original profile. Fig. 17 shows shape of the interpolator upper surface under 212 and 264 kN loads by using simulation. Simulated results indicate a shallower die for a higher force.
6. Conclusions Forming parameters existing in MPSF have been investigated in this work for die shapes of cylindrical form. Based on the results obtained, the following conclusions are drawn: 1. With an increase in thickness of the die sheet, the die sheet forming force increases but the maximum height of dimples on the die sheet decreases, nearly linearly.
Height (mm)
Forming force for workpiece (KN)
Polyurethane
6 5 4 3 2 1 0 -1 -2 -3
Polyurethane T=30mm Polyurethane T=20mm Polyurethane T=10mm Black Rubber T=20mm
Dimples
-60
-40
-20 0 20 Distance from center (mm)
40
60
Fig. 12. The effect of interpolator on formed workpiece shape (die sheet: 3.7 mm Q235B): (a) 2 mm Q235B workpiece on section O-A, (b) 1 mm LF21 workpiece on section O-A, (c) 1 mm LF21 workpiece on section B-B.
2. The forming force required for a workpiece decreases with increase in the thickness of interpolator. Softer interpolator material can suppress dimples effectively, but the shape error of a workpiece became large. Dimples on the workpiece can be obviated when a suitable thickness of interpolator is chosen. The interpolator is another factor introducing shape error in addition to workpiece springback, because of its non-uniform deformation. But the shape error of a workpiece due to interpolator distortion is less than that from springback, due to the larger bending deformation in the cylindrical die. 3. Workpiece springback is low when a low-yield stress sheet is used. The dimples on the 2 mm Q235B and ST12 sheet are not significant, but on the 1 mm LF21 sheet were seen to be larger when 10 mm polyurethane interpolator is used.
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40 Polyurethane T=20mm Polyurethane T=10mm Black rubber T=20mm
Polyurethane T=40mm Polyurethane T=30mm
40
with lubrication Polyurethane T=10mm Polyurethane T=20mm Polyurethane T=30mm
35 30 Height (mm)
The thickness of interpolator (mm)
50
30
20
without lubrication Polyurethane T=10mm Polyurethane T=20mm Polyurethane T=30mm Multi-point die shape
25 20 15 10 5
10
0 0 0
20
40
60 80 100 120 Distance from center (mm)
140
Fig. 13. The deformation of interpolator during forming (workpiece: 2 mm Q235B, Die sheet: 3.7 mm Q235B).
30 Height (mm)
25
Height (mm)
Multi-point die shape After springback (experiment) Before springback (simulation) After springback (simulation) After springback (theory)
35
50
20
75 100 125 150 Distance from center (mm)
175
200
Fig. 16. Effects of lubrication and thickness of interpolator on the shape of a formed workpiece along section O-A (workpiece: 1 mm LF21, die sheet: 3.7 mm Q235B).
F=212KN F=264KN
25 40
25
160
20 15 10 5
15 10
0
5
0
50
100
150
200
250
Distance along section O-A (mm)
0 -5
Fig. 17. Shape of interpolator upper surface along section O-A under different forming forces (workpiece: 1 mm LF21, die sheet: 3.7 mm Q235B, interpolator: 30 mm polyurethane).
Forming range
-10 0
20
40
60
80
100
120
140
160
180
200
220
Distance from center (mm) Fig. 14. Shape of workpiece before and after springback (workpiece: 2 mm Q235B, Interpolaotor: 10 mm polyurethane, Die sheet: 3.7 mm Q235B).
Acknowledgment
290 Without lubrication With lubrication
280 270
Forming force (KN)
4. The forming force and shape error of workpieces decrease when lubrication is applied on both the surfaces of workpiece.
260 250
The authors would like to express their sincere appreciation for the financial support of the National Natural Science Foundation of China (its number 50435010). Reference
240 230 220 210 200 190 180 10
15 20 25 The thickness of interpolator (mm)
30
Fig. 15. The effect of lubrication on the forming force (workpiece: 1 mm LF21, die sheet: 3.7 mm Q235B).
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