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Deep spinning of sheet metals
International Journal of Machine Tools & Manufacture 97 (2015) 72–85
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International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Deep spinning of sheet metals Khaled I. Ahmed a,n, Mohamed S. Gadala a,b, Mohamed G. El-Sebaie c a b c
Department of Mechanical Engineering, University of British Columbia (UBC), Vancouver, BC V6T 1Z4, Canada Abu Dhabi University, Abu Dhabi, UAE Mechanical Engineering Department, Assiut University, Assiut 71516, Egypt
art ic l e i nf o
a b s t r a c t
Article history: Received 7 April 2015 Received in revised form 13 July 2015 Accepted 27 July 2015 Available online 29 July 2015
Spinning of sheet metals into cylindrical cups is an important sheet metal forming process for its advantages of flexible tooling and very small forming loads. The most challenging aspect in this process is its low formability due to wrinkling formation in the free flange. In this work, a new deep spinning process with roller set aided with blank-holder of constant clearance is proposed aiming to suppress the wrinkling formation in the deformation zone. Experimental work on annealed and hard aluminum sheet metals is carried out to assess the new process. The proposed spinning process has shown rapid increase in the formability of the sheet metals as the roller feed increases. On the other hand, significant increase in the roller feed worsens the formability of sheet metals in conventional spinning. The Limiting Spinning Ratios, LSRs; or the blank to mandrel diameters ratios, have increased from 1.75 using the conventional spinning to 2.40 using the deep spinning with annealed aluminum sheets in one pass. Also, the LSRs have increased from 1.67 using the conventional spinning to 2.24 using the deep spinning with hard aluminum sheets in one pass. New failure modes of flange jamming and wall fracture have been presented and discussed. In addition, the formability limitations, thickness strains, and spun cup form features at different process parameters are experimentally investigated and discussed. Further, a finite element model for the new process is presented and verified showing the limitation of the available shell elements offered by ANSYS Mechanical APDL in modeling the new process. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Spinning Sheet metal forming Cylindrical cups Spinning roller Blank-holder Aluminum Finite element ANSYS APDL
1. Introduction Sheet metal spinning of cylindrical cups is a traditional forming process, however, due to the flexibility of the process; it has undergone a renaissance in recent years and has developed into a versatile process for producing lightweight components [1–3]. In this process, a rotating sheet metal disk is deformed over a cylindrical mandrel into a cup by applying incremental small forces using an axially moving roller. Several attempts have been accomplished to study the challenging aspects of this process, particularly, failure modes, geometrical and thickness profiles of the final spun cup, and formability of the spinning process. Failure of a circular blank to be successfully spun into a cup usually results from either flange wrinkling or wall fracture [1,2]. Studies have reported that blank parameters and working conditions are two main reasons for wrinkling formations in the unsupported part of the blank during conventional spinning of sheet metals. Conventional spinning process has shown increasing n
Corresponding author. E-mail addresses: [email protected] (K.I. Ahmed), [email protected] (M.S. Gadala), [email protected] (M.G. El-Sebaie). http://dx.doi.org/10.1016/j.ijmachtools.2015.07.005 0890-6955/& 2015 Elsevier Ltd. All rights reserved.
tendency to wrinkling formation with small modulus of plastic buckling, large mandrel diameter, and thin original blank sheet metals [4]. In addition, wrinkling formation tendency increases significantly with higher roller feeds and higher roller angles [5– 8]. Furthermore, studies have shown that spinning of thicker sheet metals will fail due to wrinkling formation at higher roller feeds [8–11]. Fracture failure in conventional spinning not only occurs with oversized blanks but is also evident with smaller roller feeds, larger roller angles and smaller roller nose radii and this normally increases the tendency of tangential cracks in the partially deformed cup wall [5–11]. The wall thickness of conventionally spun cup is not uniform [6–8]. The cup edge is much thicker than the original blank thickness and the cup wall has two adjacent necks. The first neck is at the cup bottom and the second one is at the cup wall. Cup wall fractures occur due to oversized blanks at the location of the second neck. Conventional spinning process produces thinner cup wall with smaller roller feeds [6–8], smaller roller nose radii [6,7], higher roller angles [7] and smaller radial clearances [6]. The inner profile of the final spun cup is larger than the mandrel profile due to spring back [7]. This difference gets wider with smaller roller nose radii, higher roller feeds, and higher conical roller angles [7].
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The final spun cup by conventional single roller doesn't closely fit to the forming mandrel. The cup is rather shaped with bulged form having a gap between the cup inner diameter and the mandrel. This gap is not uniform and increases with cup height with its minimum at the cup bottom [7]. Also, it is shown that spinning with conical roller produces cups with bulged gap as high as 3.0 mm larger than the mandrel stem diameter [7] and the out of roundness of the spun cup is found to be as high as 0.5 mm [7]. Spinning formability is measured by the Limiting Spinning Ratio, LSR, which is the ratio of the maximum original blank diameter that can be successfully spun forming a cup, in a single pass, to the mandrel diameter [5–8]. Based on overcoming the wrinkling and fracture failure modes, many attempts have investigated flat [5,6], conical [7] and D-shape rollers [8] with various working conditions to enhance the spinning formability of conventional spinning. This formability limit is highly dependent on the ratio of mandrel diameter to blank thickness dm/tb [5,6]. At high ratios, dm /tb 430, failure due to wrinkling formation is generally dominant. On the other hand at small ratios, dm/tb o30, failure due to cup wall fracture is generally dominant. Sieble and Droge [5] have used flat roller in spinning of mild steel cups achieving LSR of 1.7 for dm/tb ¼40. However, this formability level decreased rapidly to about 1.5 as dm/tb increased to 70.0. On the same hand, Hayama, and Murota (1963) [6] have also used flat roller in spinning of annealed aluminum cups achieving slightly lower LSR of 1.67 at dm/tb ¼ 40 and LSR of 1.48 at dm/tb ¼70. They have extended their work to lower values of dm/t b ¼20 achieving LSR of 1.86. In these attempts, the maximum LSR was achieved by searching for optimum roller feed, which was bounded by the flange wrinkling formation and the cup wall fracture. El-Khabeery et al. [7] have used conical rollers achieving LSR of 1.9 at dm/tb ¼28 using conical roller with face angle of 45° in spinning of annealed aluminum cups. Xia et al. [8] have used D-shape roller in spinning of steel and aluminum cups achieving LSR of 1.68 at dm/tb ¼ 50. It is worth noting that in these studies [5– 8], the roller movement was in the axial direction parallel to the mandrel axis. In earlier work, Terada et al. [12] have presented a numerical study of a convex roller shape moving in radial direction perpendicularly to the mandrel axis instead of the conventional roller axial motion. However, the maximum LSR achieved was 1.65 for thick sheet metals with dm/tb ¼18.5. In a recent attempt, Lossen and Homberg [13] have proposed a new technique to achieve higher formability for complex shapes. In this technique, the blank elements are heated up by friction with roller, and then the roller is moved axially to create the cup wall. This technique has achieved LSR of 1.82 at dm/tb ¼13.5, which is lower than that achieved using flat, conical and D-shape rollers. Currently, high LSRs are achievable by multi-pass spinning [15,16]. Furthermore, multi-pass spinning is more favorable than multi-stage deep drawing for its flexibility and significant lower tool cost. Fig. 1 summarizes the maximum achieved LSRs of conventional spinning of commercial pure aluminum sheet metals for the previous studies [5–8,12,13] and that for conventional deep drawing [14] at various mandrel diameter to blank thickness ratios dm/tb. The achieved LSRs for small values of (dm/tb) are lower than those obtained in conventional deep drawing, which is usually higher than 2.0 [14]. Furthermore, for higher values of (dm/tb) the difference becomes much wider. It may be noted that the achieved LSRs of single pass spinning are banded in a very narrow region implying that the above investigations have not significantly improved the formability limitations of the sheet metal spinning process. Based on the above discussion, the problem persists in the flange wrinkling formation at high roller feeds. The formability of the conventional deep drawing is superior to that in conventional
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Fig. 1. Limiting spinning ratios at various dm/tb ratios with different roller profiles and conventional deep drawing process [adapted from: 5-8,12-14].
spinning due to the suppression of the flange wrinkling by the aid of a blank-holder. The main objective of the current work is to implement a new roller aided with constant clearance blank holder. The new roller is experimentally evaluated to define its ability in suppressing the wrinkling formation to improve the spinning formability. Also, the geometry and thickness distribution of the final produced cups will be measured at different working conditions. Further, the new process will be simulated by finite element method to get more understanding of the process kinematics and deformation mechanism.
2. Experimental setup The new proposed deep spinning process considers a blank holder to be fixed on the roller shaft as shown in Fig. 2. A hardened spacer with thickness Ch controls the distance between the roller and the blank-holder. The considered process parameters, as shown in Fig. 2, are geometrical and working conditions parameters. The variable geometrical parameters are the radial clearance Cr and the blank diameter Db. The considered variable working condition is the roller feed Sv. All other parameters are fixed throughout the course of experiments. The full construction of the new proposed deep spinning process with all components is shown in Fig. 3. The experimental work is carried out on a manually controlled conventional center lathe with a specially designed holder, replaced the tool post, to support the new roller setup. Fine finished flat-headed mandrel with diameter, 48 mm is used. The fillet profile radius of the mandrel is 6 mm, which is one eighth of its external diameter. The tested mandrel is supported on the lathe chuck using a special holder that ensure minimum run out errors. The blank holder and roller have the same diameter Dr ¼180.0 mm. They are made of hardened alloy tool steel [0.3% C, 0.66% Mn and 0.35% Si], with surface hardness of about 60– 62 HRC. The rollers and the blank holder are ground and then polished reaching surface roughness of Ra¼0.19–0.21 μm with minimum Rz ¼1.18 μm.
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tb
Sv
N Dm Rr Db tb Cr Rr Sv Dr Ch
: Rotational Speed : Mandrel Diameter : Mandrel Nose Radius : Blank Diameter : Blank Thickness : Radial Clearance : Roller Nose Radius : Roller Feed : Roller Diameter : Blank Holder Clearance
30.0 rpm 48.0 mm 6.0 mm Variable 1.5 mm Variable Variable Variable 180.0 mm 2.0 mm
Fig. 2. Schematic drawing of the deep spinning process showing the controlling parameters.
In the current study, a roller nose radius Rr is initially chosen to be 9.0 mm, which is six times the original blank thickness. This nose radius size is slightly less than the recommended die profile in deep drawing [14] to ensure spinning ratio for the free flange less than 1.4. Then two rollers with larger and smaller nose radii of 12.0 mm and 6.0 mm, respectively are tested to investigate the effect of roller nose radii on the formability of the new deep spinning process. The constant clearance between the roller and the blank-holder is chosen to be 2.0 mm, which is 1.33 times the nominal blank thickness. This is slightly wider than that in deep drawing [14] to ease the flange relative rotation inside the deformation zone. The tests are carried out at N ¼ 30 rpm to eliminate dynamic effects and to have adequate and safe control on the lathe carriage axial displacements at high feed rates of 43 mm/rev. It is worth noting that investigations on the rotational speed of the mandrel [6–8] have shown no effects on the spinning process outcomes. A continuous flow rate of lubricating oil is concentrated into the deformation zone to decrease the frictional forces generated between the blank and both the roller and the blank holder interfaces. The radial clearance is adjusted using the lathe cross vernier with accuracy of 0.01 mm. The tested blanks are held between the mandrel, held on the lathe chuck, and the blank fixture, held on the lathe tailstock, using centering device with accuracy of 0.05 mm.
The sheet metals used are hard and annealed commercially pure aluminum Al 99.5 sheets with nominal thickness of 1.5 mm. The annealed aluminum is chosen to represent easy to spin sheet metals and the hard aluminum is chosen to represent hard to spin sheet metals. Tensile tests are carried out to determine the directional mechanical properties of the investigated sheet metals. The tested specimens, five from each direction, are cut from different locations on the sheets at three orientations of 0°, 45°, and 90° to the rolling direction. The measured material properties are; yield strength, work-hardening exponent “n”, material strength coefficient constant “K”, and the plastic normal anisotropy at these three directions. The measured stress–strain relation for all specimens of the two sheet metals are shown in Fig. 4. These measured properties are summarized and listed in Table 1.
3. Experimental procedures, results and discussion For each spinning experimental test, three blanks were cut from the aluminum sheet with 10 mm greater in diameter than the required finished size, to ensure that work hardening effect due to blanking process will be eliminated after the turning operation. Then these blanks were turned down using a specially designed fixture to the designated final size. This turning operation was carried out using a special carbide tip with its designated
1- Lathe holder 2- Oil Seal Ring 3- Roller Bearings 4- Locking Nut 5- Locking Cover 6- Clearance Spacer 7- Blank-Holder 8- Mandrel
9- Partially spun cup 10- Blank Fixture 11- Spinning Roller 12- Roller holder 13- Locking cover 14- Axle 15- Oil Seal Ring 16- Mounting Fork
Fig. 3. Assembly drawings of the deep spinning apparatus and its experimental installation on the testing lathe.
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Fig. 4. Measured stress–strain relations of the tested specimens of hard and annealed aluminum sheet metals in three directions; 0°, 45°, and 90° from rolling direction.
optimum cutting conditions that ensure no work hardening would be added to the blank outer rim. For thickness measurements of the spun cups, a grid of concentric circles in a step of 2.0 mm are scratched on the blank external face. Also, the directions of 0°, 45°, and 90° to the rolling direction are marked. The final spun cup is then cut at these directions and the thickness strains are measured at the scratched circles to be related to its original position. For obtaining the limiting spinning ratio at particular working conditions, a series of blanks with diameter step of 4.0 mm are produced and tested. If the test case switches from fail to success or from success to fail, this step size is reduced to 2.0 mm then to 1.0 mm. The limiting spinning ratio is determined when three successful spun cups are achieved at blank diameter 1.0 mm less than that of three failed cups. 3.1. Failure modes The observed failure modes of the conventional spinning process are correlated with that reported in the literature; flange wrinkling at high roller feeds, Fig. 5a, and wall fracture at low roller feeds, Fig. 5b. The new deep spinning roller set with blank holder has successfully suppressed the wrinkling formations with extremely high roller feeds up to 4.0 mm/rev. The suppression of wrinkling formation leads to very deep cups with annealed and hard aluminum sheet metals. Wall-fracture failure mode of oversized blanks at smaller roller feeds becomes the main failure mode of the new deep spinning process as shown in Fig. 6a. However, increasing the roller feeds with wrinkling suppression is limited by another new failure mode, which is flange jamming as shown
Fig. 5. Failure modes of conventional spinning process. (a) Flange wrinkling. (b) Wall fracture failure.
in Fig. 6b. This failure mode occurs due to the sever curvatures in the cup flange just before entering the deformation zone resisting its rotation into the deformation zone. 3.2. Deep spun cups and thickness distribution Experimental results showed that the new deep spinning process has successfully achieved very high spinning ratios for annealed and hard aluminum sheet metals. Annealed aluminum sheet metal has been successfully spun to spinning ratio of 2.38 at roller feed 3.5 mm/rev as shown in Fig. 7a–c whereas for hard aluminum sheet metal a ratio of 2.21 has been achieved at roller feed 4.0 mm/rev as shown in Fig. 8a–c. The spun cup is not perfectly cylinder due to the diametral growth of the formed cup wall as shown in Figs. 7 and 8a.
Table 1 Material properties of the tested sheet metals. Hard aluminum Thickness tb ¼ 1.5 mm Angle to rolling direction (deg) Yield stress (MPa) Hardening exponent ‘n’ Strength coefficient ‘K’ (MPa) Normal anisotropy ‘R’ Average yield stress (MPa) Average hardening exponent ‘navg’ Average strength coefficient ‘Kavg’ (MPa) Normal anisotropy ‘Ravg’ Planar anisotropy ‘ΔR’
0 112.7 0.026 132.5 0.324 107.2 0.0363 134.3 0.540 0.182
45 103.8 0.049 143.5 0.631
Annealed aluminum Thickness tb ¼1.5 mm 90 105.2 0.021 117.6 0.574
0 27.1 0.23 113.1 0.980 28.8 0.22 113 0.592 0.464
45 26.8 0.22 105.4 0.360
90 36.9 0.20 127.9 0.667
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Fig. 6. Failure modes of deep spinning process. (a) Wall fracture failure. (b) Flange jamming failure.
Furthermore, the final cup profile has shown significant diametral variations due to the planar anisotropic nature of the sheet metal. The differences between the minimum and maximum radii is maximum at the middle third of the cup height as shown in Figs. 7b and 8b. These differences are reduced and the cup profile is mostly uniform at the lower third of the cup due stretching over the mandrel and at the upper third of the cup due to the roller back spinning of the cup wall. The deeply spun cups have significant ears due to the planar anisotropy of the sheet metals. The cup heights of both cases with respect to the rolling direction are presented in Fig. 7c for annealed aluminum and in Fig. 8c for hard aluminum. Two necks have been observed in both spun sheet metals as shown in Fig. 9. Neck I occurs at cup bottom curvature, and neck II occurs at the cup wall. In all failed cases, the fractures correlate perfectly with neck II location. Neck I in hard aluminum cup located at the cup bottom curvature quite close to the cup bottom than that in annealed aluminum. The thickness strain of this neck is almost equal for both sheet metals. Neck II in hard aluminum located at the cup wall quite close to the cup bottom curvature than that in annealed aluminum. The thickness of the cup wall at neck II is significantly thinner in annealed aluminum than that in hard aluminum. Furthermore, the fracture of the oversized hard aluminum cups occurs as soon as the roller nose passes the neck II locations. On the other hand, the fracture of the annealed aluminum cup occurs quite late after the roller nose passes neck II locations. In some cases, the fracture of the oversized annealed aluminum cups have been observed after the cup is fully spun. In such case, the blank size is count in the failed group. It is worth noting that the cup edge is slightly thinner than the neighbor elements due to the over ironing and rolling by the roller nose and its conical back. 3.3. Limiting spinning ratios The limitation of the conventional spinning is tested at different roller feeds for both sheet metals. The radial clearance between the roller nose and the mandrel stem is set equal to the original blank
thickness to reduce the wrinkling tendency. In all cases the conventional spinning is limited by wrinkling formation except the case of annealed aluminum at roller feed 0.5 mm/rev. In this case, small wrinkles are observed towards the end of the roller stroke that increases the forming loads and consequently causes wall fracture. In conventional spinning of both sheet metals, as the roller feed increases, the limiting spinning ratio, LSR, dramatically decreases as shown in Fig. 10. Annealed aluminum has shown better LSRs. In deep spinning, the wrinkles are fully suppressed leading to significant increase in the LSR of both sheet metals at roller feed 0.5 mm/rev. As the roller feed increases, the LSRs significantly increases up to 3.5 mm/rev in spinning of annealed sheet metals and up to 4.0 mm/rev in spinning of hard aluminum sheet metals. Further increase of the roller feed is limited by the new failure mode, flange jamming, as shown in the above section. Lower LSRs have been tested with higher roller feed with no success to overcome the flange jamming. The deep spinning of sheet metals with radial clearance equal to the original thickness has increased the LSR for annealed aluminum from 1.76 at roller feed 0.5 mm/rev to 2.2 at roller feed 3.5 mm/rev. Also, it has increased the LSR for hard aluminum from 1.67 at roller feed 0.5 mm/rev to 2.14 at roller feed 4.0 mm/rev. A comparison between the achieved LSR for both conventional and deep spinning processes is shown in Fig. 10. Suppression of flange wrinkling helps in increasing the radial clearance between the roller nose and the mandrel stem. Similar to that used in deep drawing, a radial clearance of (Cr ¼2.25 mm), which is 50% more than the original blank thickness has been adjusted and tested. The LSRs have increased significantly for both sheet metals, as shown in Fig. 11. The new deep spinning process has achieved a LSR of 2.38 for annealed aluminum and LSR of 2.21 for hard aluminum. It is worth noting that the increase of the radial clearance has neither enhanced nor worsened the flange jamming limitations. Deep spinning with larger roller nose radius (Rr ¼12.0 mm) has shown further increase in the LSR of the annealed and hard aluminum sheets as shown in Fig. 12. At small roller feeds, the increase in the LSR is quite significant, about 0.07, however
Fig. 7. Annealed aluminum successfully spun cup at SR ¼ 2.38 at Sv ¼3.5 mm/rev and Cr ¼ 2.25 mm. (a) Spun cup photo. (b) Cup radii variations through cup height. (c) Cup height variation w.r.t. rolling direction.
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Fig. 8. Hard aluminum successfully spun cup at SR ¼2.21 at Sv ¼ 4.0 mm/rev and Cr ¼2.25 mm. (a) Spun cup photo. (b) Cup radii variations through cup height. (c) Cup height variation w.r.t. rolling direction.
LSR are presented in Fig. 13. It is noted that deep spinning with smaller roller nose radius produces deep spun cups with less bulge and smaller feed marks. Smaller roller nose radius reduces the deep spinning formability similar to that of the die profile in deep drawing at small roller feeds due to added bending stresses. However, deep spinning at high roller feeds compensates these effects on the deep spinning formability showing insignificant reduction in the limiting spinning ratios especially with annealed aluminum. This can be explained by assuming a partially spun cup that is perfectly fit over the mandrel as shown in Fig. 14. The spinning loads created within the deformation zone are transferred to the mandrel through grading areas with smallest under the roller nose and the largest at the cup bottom. This critical area under the roller nose is proportional to the contact length between the roller nose and the partially spun cup. This contact length, for the assumed perfectly plastic deformed cup, can be calculated based on the schematic diagram in Fig. 14 as follows:
Lc =
Fig. 9. Thickness strain distribution of successfully spun cups at Cr ¼ 2.25 mm. (a) Annealed aluminum blank at SR ¼ 2.38, Sv ¼3.5 mm/rev (b) Hard aluminum blank at SR ¼ 2.21, Sv ¼4.0 mm/rev.
increasing the roller feed up to the jamming limit decreases these differences to 0.02. On the other hand, decreasing the roller nose radius (Rr ¼6.0 mm) has shown significant decrease in the LSR at small roller feeds of both sheet metals as shown in Fig. 12. In the same way, these differences are reduced with the increase of the roller feeds. Deep spinning with roller nose radius 6.0 mm has suffered from earlier flange jamming by 0.5 mm/rev for both sheet metals. Successful and failed spun cups at the maximum possible
⎛ Rr − Dr ⎜ . cos−1⎜ 1 − ⎜ 2 ⎝
2 ⎞ − ( Sv ) ⎟ ⎟⎟ Dr /2 ⎠ 2
( Rr )
(1)
The variation of the contact length Lc with the roller feed Sv at different roller nose radii Rr is shown in Fig. 15. This increase of the contact length Lc with the increase of the roller feed Sv is reflected into proportional increase of the load carrying area, which explains the significant increase of the LSR with the increase of the roller feed. It is worth noting, that the rate of increase of the contact length Lc at roller nose radius 6.0 mm is significantly higher than that at roller nose radius of 12.0 mm. This is similarly observed as shown in Fig. 12, that the rate of increase of the LSRs at deep spinning with roller nose radius 6.0 mm is significantly higher than that obtained at deep spinning with roller nose radius 12.0 mm. It is consistently reported in the literature [5–10] that the smaller roller feed produce thinner cup wall without giving a scientific reason of this observation. The main objective of conventional spinning was achieving the higher possible roller feed without wrinkling. It is worth noting that conventional spinning tests of the current work have achieved similar results of previously achieved limiting spinning ratios as shown in Fig. 16. Comparing to other achieved spinning ratios, deep spinning not only surpassed the previously achieved spinning ratios, but also, significantly surpassed the deep drawing process [14] as shown in Fig. 16.
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Fig. 10. Limiting spinning ratios, LSRs, for conventional and deep spinning processes at Cr ¼ 1.5 mm and various roller feeds for both annealed, with photo, and hard aluminum sheet metals.
LSR=2.21, Sv = 4.0 mm/rev.
Cr = tb = 1.50 mm
LSR=2.14, Sv = 4.0 mm/rev.
Ann. Aluminum
Hard Aluminum
Cr= 2.25 mm tb = 1.50 mm
LSR=2.38, Sv = 3.5 mm/rev.
LSR=2.20, Sv = 3.5 mm/rev.
Fig. 11. Limiting spinning ratios, LSRs, for deep spinning processes at Cr ¼ 1.50 mm and Cr ¼2.25 mm and various roller feeds for both annealed and hard aluminum sheet metals.
Fig. 12. Limiting spinning ratios, LSRs, for deep spinning process at different roller nose radii for both annealed and hard aluminum sheet metals at radial clearance Cr ¼ 2.25 mm.
K.I. Ahmed et al. / International Journal of Machine Tools & Manufacture 97 (2015) 72–85
Rr = 6.0 mm
LSR=2.24, S = 4.0 mm/rev.
LSR=2.1, S = 3.5 mm/rev.
LSR=2.40, S = 3.5 mm/rev.
LSR=2.20, S = 3.0 mm/rev.
Annealed Aluminum
Hard Aluminum
Rr = 12.0 mm
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Fig. 13. Obtained spun cups at the limiting spinning ratios, LSRs, for deep spinning process at Cr ¼2.25 mm and roller nose radii 12.0 mm and 6.0 mm for both annealed and hard aluminum sheet metals.
4. Finite element model 4.1. Model components Several attempts have been made to simulate conventional sheet metal spinning using both solid elements [17,18] and shell elements, [15,19]. Due to convergence difficulty with modeling with solid elements that arises due to deformation severity in the new deep spinning process, shell element is considered for the simulation modeling of the current work. ANSYS [20], Mechanical APDL offers two shell elements for nonlinear analysis, SHELL181, and SHELL43. The main difference is that SHELL43 considers the shear stresses through the element thickness whereas SHELL181 ignores shear deformation. In the current work, both elements have been used in modeling the new deep spinning process. Fig. 17 shows the components of the deep spinning process. These components are the blank, mandrel, blank fixture, roller, and blank-holder. All of these components, except the blank, are non-deformable bodies, therefore, they are modeled as rigid surfaces. The motion of each of these surfaces is controlled using a pilot node element, which is an element with one node, whose motion governs the motion of the entire rigid surface. The mandrel and the blank fixture are associated with two independent pilot nodes, while the roller and the blank-holder share the association of one pilot node. The mandrel, the blank fixture, and the blank inner circle are given the rotating motion around the mandrel axis and supported in all other degrees of freedom. The roller and blank-holder set is given the axial feed motion and is left free to rotate only around its
Fig. 15. Relation between the contact length and the roller feed and roller nose radius.
axis based on the kinematics of the process. The other degrees of freedom of the roller and the blank holder are fully constrained. The blank material is assumed isotropic with the averaged values shown in Table 1 and plastically obeys the isotropic hardening model MISO, which considers Von Misses yield criterion. The assumption of isotropic material is thought to be a good approximation and starting point to assess the overall behavior of the proposed experimental setup. The objective is not to verify or optimize process parameters but rather to have some qualitative assessment of the process and its limitation. In addition, the finite element model will be a good tool to have insight investigations into the deformation mechanism of the new deep spinning process. The coefficient of friction is generally varied during the forming process [21,22], however, in the current study it will be assumed constant through the operation to focus on the objectives of the model. Based on the experimental measurements of the coefficient of friction according to the roller surface roughness [21], the suitable value is about 0.1 for the current roller surface roughness of
Fig. 14. Schematic of the projected contact length between the spun cup and the roller under the roller nose.
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Table 2 Process parameters of the evaluation test cases. Test case #1 #2 Mesh density test
Cr mm 1.125 1.50 2.00
SR
Mesh density
Element type
1.9 2.16 2.18
48 16 48 16 Varies
43/181 43/181 SHELL43 only
Table 3 Mesh schemes for testing the model sensitivity to mesh density. Scheme
#1 #2 #3 #4 #5
Mesh density
24 8 36 12 42 14 48 16 60 20
Circum. elem.
24 36 42 48 60
Radial elem.
8 12 14 16 20
Total blank elements
192 432 672 768 1200
Rigid surfaces elements 772 1696 2398 2980 4324
Total nodes
632 1232 1688 2024 2888
Fig. 16. Comparison of the achieved limiting spinning ratios in the current work and that previously achieved from [5–8,12–14].
Rz ¼ 1.18 μm. Also, based on the experimental measurements of coefficient of friction according to oil lubrication [22], the average value is about 0.1. The model is solved using static implicit time scheme with full Newton Raphson nonlinear solver. Initial trials was performed with the recommended and default tolerance limits in ANSYS; 1.0E-3. All these trials have failed to converge very small deformation of the axial roller full displacement. Accordingly, the model is aided with especial subroutine to detect the convergence behavior and to adopt the solution tolerances accordingly. This tolerance starts at 5E 5 and is increased by steps of 1E 5 each time the model faces convergence difficulties to a maximum allowed tolerance of 1E 3. 4.2. Finite element model equations The formulation of the finite element formulation is obtained by the virtual work principle [23]. In this derivation, only linear differential terms are kept while all higher order terms are ignored to obtain a set of linear equations.
δW =
∫V σij δeij dV = ∫V fiB δui dV + ∫S fiS δui dS
(2)
where W is the internal virtual work
Fig. 18. Comparison between the form of the experimentally produced cup and those obtained by the FE simulation for test case #1.
sij is the Cauchy stress component 1 eij is the deformation tensor such that eij = 2 (∂ui /∂xj + ∂uj /∂xi ) ui is the displacement vector. xi is the spatial position vector of the particle in deformed configuration. f iS and fiB are the surface traction and body force components, respectively. The integration in Eq. (2) is carried out over the deformed volume and the surface on which the traction is applied. The constitutive law, which relates the stress increments to the strain increments, should be frame invariant and able to separate the rigid body rotations. To fulfill this requirement, the Jaumann rate of Cauchy stress is considered such that
Roller Blank
Blank
Roller Blank Holder Mandrel
Blank Fixture
Mandrel
Blank Holder
Fig. 17. Finite element model of the deep spinning showing half of the model in different views.
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Fig. 19. Comparison between thickness strains of the experimentally produced cup and those obtained by the FE simulation for test case #2.
Fig. 20. Plastic shear strains comparisons for test case #2. (a) In-plane plastic shear strain εxy (SHELL181), (b) in-plane plastic shear strain εxy (SHELL43), (c) throughthickness plastic shear strain εxz (SHELL43), (d) through-thickness plastic shear strain εxy (SHELL43).
σij̇ J = σij̇ − σik ω̇ jk − σjk ω̇ ik
(3)
stress rate and material constitutive tensor can be shown as
σij̇ = Cijkl Dkl + σik ω̇ jk + σjk ω̇ ik
where σ̇ijJ is the Jaumann rate of Cauchy stress 1
ω̇ ij is the spin tensor such that; ω̇ ij = 2 (∂vi/∂xj − ∂vj /∂xi ) σ̇ij is the time rate of Cauchy stress The constitutive law of materials undergoing large deformation, which describes stress change due to strain, can be expressed, using Jaumann rate of Cauchy stress, as
σij̇ J = σij̇ − Cijkl Dkl
(4)
where Cijkl is the fourth order material constitutive tensor 1
Dij is the rate of deformation such that; Dij = 2 (∂vi/∂xj + ∂vj /∂xi ) vi is the velocity in direction i. Then, from Eqs. (3) and (4) the relation between the Cauchy
(5)
where the elastoplastic constitutive matrix for isotropic material with isotropic hardening rule is given by [21]
Cijkl =
⎛ ⎞ 3σ ′ij σ ′kl ν E ⎜ ⎟ δik δjl + δij δkl − 2H 1 + ν 1 + ν ⎜⎝ 1 − 2ν 2σ 2 (1 + 3 ( E )) ⎟⎠
where: H: is the strain hardening modulus, σ¯ : is the effective stress, σ′ij : are the deviatoric stress components, ν: Poisson's ratio, E: Young' s modulus, δ ij : is the Kronecker delta.
(6)
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K.I. Ahmed et al. / International Journal of Machine Tools & Manufacture 97 (2015) 72–85
Fig. 21. Comparison between the final form of the experimentally spun cup and the simulated ones using five different mesh densities.
starting the finite element solution with very small tolerance allowance ( 5E 5) significantly reduces the divergence possibilities and consumes lower CPU time especially with SHELL43. On the other hand starting the solution with tolerance allowance higher than (1E 3) shows significant convergence difficulties with SHELL43 and the model fails to get a converged solution towards the end of the process in both cases In test case #1, final form of the predicted spun cup with SHELL43 is much closer to the experimentally obtained cup, as shown in Fig. 18. As for test case #2, also, the predicted thickness strain distribution of the spun cup with SHELL43 is much closer to the experimentally obtained cup as shown in Fig. 19. Furthermore, modeling with SHELL43 is able to predict both observed cup wall necks; however, modeling with SHELL181 is able to predict only the second neck with overestimated strain. As for the shear strains, both elements have shown similar behavior in plane shear strain. However, SHELL43 element has shown significant thickness shear strains that are ignored in SHELL181 as shown in Fig. 20. Five mesh densities are evaluated using SHELL43. The five test cases have successfully completed the simulation until the end of the deep spinning process. The predicted final form of the spun cup is close to the experimentally obtained cup as shown in Fig. 21. However, cases of #3, #4, and #5 are much closer than the coarser ones. As shown in Fig. 22. mesh density #4(48 16) shows lower CPU time than mesh #3(42 14) because mesh #4(48 16) shows better convergence regime and uses much lower total number of iterations.
Fig. 22. CPU time comparison for simulating 1 mm of the roller displacement using five different mesh densities using element SHELL43.
Utilizing Eq. (3) into Eq. (2), the incremental updated Lagrangian formulation of the problem takes the form [21]
∫V
∂δui [(σij•J ∂xj
−
δui fiB dV V
= ∫
σ ip ∂vj 2
( ∂x + p
∂vp ∂xj
)+
σ jp ∂vi ( 2 ∂xp
−
∂vp ∂xi
∂vp
) + σij ∂x ] dV p
δui fiS dS S
+ ∫
Both shell elements SHELL43 and SHELL181 have been evaluated with test cases #1 and #2 as listed in Table 2. Test case #1 is evaluating cup profile and test case #2 is evaluating cup wall thickness. Then the mesh sensitivity test is carried out on SHELL43 as shown in Table 3. For all test cases, the tested material is hard aluminum and the roller feed is Sv ¼4.0 mm/rev.
4.4. Numerical investigations The finite element model is used to investigate the deformation mechanism and the stress pattern of the spun part during deep spinning process. The numerical investigations are carried on hard aluminum sheet metal due to its much shorter simulation time. In failed cases, fracture of oversized blanks in hard aluminum sheet metal occurs much earlier than that for annealed aluminum. Also, successful cases are obtained at lower spinning ratios with higher roller feeds, which require much shorter simulation time than that for annealed aluminum. In the current investigation, the onset of
4.3. Finite element model evaluation results Both shell elements, mentioned above, are capable of simulating the deep spinning process successfully with full integration schemes. The CPU time for the model with SHELL43 is four times of that with SHELL181 in both test cases. It is worth noting that, Table 4 Working conditions for the first test group. Material
SR (Db/Dm)
HHAL
2.1, 2.2, 2.3 and 2.4
Sv (mm/rev) 4.0
μ 0.1
Rr (mm)
Dm (mm)
Rm (mm)
to (mm)
Cr (mm)
9.0
48.0
7.0
1.50
2.25
K.I. Ahmed et al. / International Journal of Machine Tools & Manufacture 97 (2015) 72–85
83
Fig. 23. Thickness strains distribution in the successful cups and the failed cups at the instant of failure. [HHAL, SR ¼ Varies, Sv ¼ 4.0 mm/rev, Dm ¼ 48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼1.5 mm, Cr ¼ 2.25 mm].
Radial Stresses
Hoop Stresses
C – Fillet End
B – Bottom Neck
A – Cup Bottom
Element Strength
E – Cup Edge
wall fracture is assumed at thickness strains εt o 0.45 (at thickness reduction 4 36%), which is observed at the fracture sections of the experimentally failed cups. It is worth noting that wall fracture in deep spinning occurs due to localized necking, which allows further thinning after necking before rupture than that for diffused necking [24]. In deep spinning, two necks are usually observed in the successful cups, cup bottom neck, neck I, and cup wall neck, neck II. Experiments have shown that, failure usually occurs due to cup wall fracture at the location of the cup wall neck rather than the location of the cup bottom neck. Four spinning ratios are numerically examined; 2.1, 2.2, 2.3 and 2.4 with the working conditions listed in Table 4. The first two ratios; 2.1 and 2.2, produce successful cups, while the other two ratios; 2.3 and 2.4 produce failed cups due to wall fracture, see Fig. 23. The figure shows that the thinning in both necks; the bottom neck and the wall neck, increases as the spinning ratio increases. Although the bottom neck showed more thinning in the successful cups, the wall neck dominated the deformation and cause failure in the failed cups at oversized blanks. Also, it is observed that the failure starts with SR ¼2.4 earlier than that with SR ¼ 2.3, however the neck locations of the failed cups as well as that of the successful cups locate at the same initial radial location as shown in Fig. 24.
D - Wall Neck
Fig. 24. Average thickness strains related to the initial radial positions for the successful cups and the failed cups at the instant of failure. [HHAL, Sv ¼4.0 mm/rev, Dm ¼48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼1.5 mm, Cr ¼ 2.25 mm].
Fig. 25. Radial and hoop stresses history for the five selected locations from the cup bottom till the cup edge for SR ¼ 2.2. [HHAL, Sv ¼ 4.0 mm/rev, Dm ¼48 mm, Rr ¼9.0 mm, Rm ¼7.0 mm, to ¼ 1.5 mm, and Cr ¼ 2.25 mm], N.P. Roller side lies at halves of the turns, while roller opposite side lies at integers. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
For more understanding of the failure mechanism, the stress history of the mid layer of an element on the selected five points “A”, “B”, “C”, “D”, and “E” at radial locations described in Fig. 24 are plotted against the blank rotations as shown in Figs. 25–27. The solid red line represents the strength state of the investigated element due to the induced plastic strains, the solid magneto line represents the radial stress, and the dashed blue line represents the hope stress. The recording of the stresses at each investigated
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Element Strength
Radial Stresses
Hoop Stresses
SR = 2.10
SR = 2.20
SR = 2.30
SR = 2.40
Fig. 26. Radial and hoop stresses history for bottom neck, location “B”, at various spinning ratios. [HHAL, Sv ¼4.0 mm/rev, Dm ¼ 48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼ 1.5 mm, and Cr ¼ 2.25 mm], N.P. Roller side lies at halves of the turns, while roller opposite side lies at integers. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Element Strength
Radial Stresses
Hoop Stresses
SR = 2.10
SR = 2.20
SR = 2.30
SR = 2.40
Fig. 27. Radial and hoop stresses history for wall neck, location “D”, at various spinning ratios. [HHAL, Sv ¼4.0 mm/rev, Dm ¼ 48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼ 1.5 mm, and Cr ¼ 2.25 mm], N.P. Roller side lies at halves of the turns, while roller opposite side lies at integers. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
element starts at the opposite side of the roller. In other words, the roller nose locates at halves of the turns and the opposite side locates at the full turns.
The generated radial and the hoop stresses during the deep spinning process for the critical spinning ratio SR ¼2.2 at the selected five radial locations are plotted against the mandrel turns as shown in Fig. 25. Hoop and radial stresses at the locations “A” and “B” are both tensile due to stretching over the mandrel profile. This deformation pattern at the roller side is similar to that of the conventional deep drawing [14]. Location “C” at the connection between the mandrel profile and the cup wall experiences uniaxial tension with lower stress level. It is worth noting that the width of the stressing cycle at location “C” is narrower than that at location “B”, which confirms the previous discussion of the grading of the load carrying area from under the roller nose to the cup bottom. The critical location “D” passes through three stages; radial drawing towards the mandrel up to seventh cycle, bending and unbending over the roller profile through cycles 7 and 8, and carrying loads from the flange to the cup bottom from the ninth cycle to the end of deformation. In the first stage, the element experiences uniaxial tensile radial stresses preceded with uniaxial compressive hoop stresses at the entrance of the deformation zone. The element is then stretched over the roller profile up to the ninth cycle, after which it locates over the mandrel stem. During the ninth and tenth cycles, the element experiences the maximum radial stresses. The element, at the last stage, experiences consistent pattern of uniaxial radial stresses due to carrying the spinning loads and a preceded and followed uniaxial compressive radial stresses due to the effect of the roller back. The edge location “E” experiences uniaxial compressive hoop stresses as it passes over the roller profile and enters the deformation zone due to the radial drawing of the element. Then it experiences uniaxial tensile hoop stresses due to pulling its neighbor elements into the deformation zone. The effect of the spinning ratio on the stress levels at locations “B” and “D” are presented in Figs. 26 and 27. It is clear from these graphs that the bottom neck at location “B” has slight dependency on the spinning ratio. The stress pattern in this region is close to be bi-axial tension, which is due to the stretching of the blank over the mandrel fillet. For oversized spinning ratios, the forming loads are dissipated at the wall neck creation and fracture, so the carried stresses to the cup bottom are lower in spinning ratio 2.3 and above than that at spinning ratio 2.2 and lower. As for the cup wall neck at location “D”, it is clear that the positive radial stresses increase as the spinning ratio increases. At the point that the radial stresses are attaining the material strength, the fracture begins and the spinning of the cup fails.
5. Conclusions Low formability of sheet metal spinning is not significantly overcome through previous attempts in the literature due to wrinkling formation in the free flange. In the current work, a new deep spinning process is developed and experimentally and numerically evaluated. In the new process, a blank holder with constant clearance has been added to the spinning roller to suppress the wrinkling formation in the deformation zone. The deep spinning process has shown rapid increase in the formability of the sheet metals as the roller feed increases. On the other hand, the increase in the roller feed drastically worsens the formability of sheet metals in conventional spinning. The limiting spinning ratios, LSRs; blank to mandrel diameters ratios, have increased from 1.76 using the conventional spinning to 2.40 using the deep spinning with annealed aluminum sheets in one pass. Also, the LSRs have increased from 1.67 using the conventional spinning to 2.24 using the deep spinning with hard aluminum sheets in one pass. This formability level is a breakthrough especially with the hard aluminum sheet metal that is difficult to be achieved even with multi-pass spinning process.
K.I. Ahmed et al. / International Journal of Machine Tools & Manufacture 97 (2015) 72–85
The deep spinning process is limited with new failure modes of wall fracture at low roller feeds and flange jamming at high roller feeds. Two necks have been observed in the successfully spun cup at the LSR. Neck I is observed at the cup bottom curvature and neck II is observed at the partially formed cup wall. Failure due to wall fracture correlate with neck II in both annealed and hard aluminum sheet metals. Localized forming nature of the spinning process results in diametral growth of the cup wall, which produces a bulged cup with significant out of cylindricity cup form. The deep spinning process is a newly developed process that requires more investigation and development to achieve its optimum conditions. Comparing to other achieved spinning ratios, deep spinning not only surpassed the previously achieved spinning ratios, but also, significantly surpassed the conventional deep drawing process. Roller nose radius has shown significant effect on the LSRs at small roller feeds similar to those observed in deep drawing due to die profile. However, deep spinning at high roller feeds achieve almost same LSRs with insignificant differences at different roller nose radii in case they have the same flange jamming limits. The significant increase in the LSRs with the increase of the roller feeds is due to the increase of the load carrying area from the deformation zone to the cup bottom. Finite element modeling of the deep spinning process is achieved using shell elements offered by ANSYS Mechanical APDL; SHELL43 and SHELL181. SHELL181 shows significantly, lower CPU cost and smoother convergence patterns than that achieved by SHELL43. However, capabilities of thickness shear consideration that is offered by SHELL43 is very crucial in modeling deep spinning of sheet metals. The finite element model has shown that the wall neck location experiences the highest radial tensile stresses under the roller nose. Also, it shows that the stresses at the bottom neck location are due to stretching over the mandrel profile. At the fracture conditions, all radial tensile stresses are dissipated at the wall neck location rather than at the cup bottom.
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J. Mater. Process. Technol. 210 (1) (2010) 3–23. [3] Qinxiang Xia, Gangfeng Xiao, Hui Long, Xiuquan Cheng, Xiangfei Sheng, A review of process advancement of novel metal spinning, Int. J. Mach. Tools Manuf. 85 (2014) 100–121. [4] S. Kobayashi, Instability in conventional spinning of cones, J. Eng. Ind. 85 (1963) 44–48. [5] E. Sieble, K.H. Dröge, Krafte und MateriatfluB beim Druken, Werkstantstechnick und Maschinenbau 45 (1) (1955) 6–9. [6] M. Hayama, T. Murota, On the study of metal spinning, Bull. Fac. Eng. 12 (1963) 53–88 , Youkohama National University. [7] M.M. El-Khabeery, M. Fattouh, M.N. El-Sheikh, O.A. Hamed, On the conventional simple spinning of cylindrical aluminium cups, Int. J. Mach. Tools Manuf. 31 (2) (1991) 203–219. [8] Q. Xia, S. Shima, H. Kotera, D. Yasuhuku, A study of the one-path deep drawing spinning of cups, J. Mater. Process. Technol. 159 (3) (2005) 397–400. [9] L. Wang, H. Long, D. Ashley, M. Roberts, P. White, Effects of the roller feed ratio on wrinkling failure in conventional spinning of a cylindrical cup, Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf. 225 (11) (2011) 1991–2006. [10] Michael Watson, Hui Long, Wrinkling failure mechanics in metal spinning, Procedia Eng. 81 (2014) 2391–2396. [11] L. Wang, H. Long, Roller path design by tool compensation in multi-pass conventional spinning, Mater. Des. 46 (2013) 645–653. [12] K. Terada, S. Takahasi, C. Taguchi, K. YisiGawa, The simulation of the deep drawing spin-forming, in: Proceedings of the 2000 Japanese Spring Conference for the Technology of Plasticity, 2000, p. 639. [13] Benjamin Lossen, Werner Homberg, Friction-spinning – interesting approach to manufacture of complex sheet metal parts and tubes, Procedia Eng. 81 (2014) 2379–2384. [14] M.G. El-Sebaie, P.B. Mellor, Plastic instability conditions in the deep-drawing of a circular blank of sheet metal, Int. J. Mech. Sci. 14 (9) (1972) 535–540. [15] Lin Wang, Hui Long, Investigation of material deformation in multi-pass conventional metal spinning, Mater. Des. 32 (5) (2011) 2891–2899. [16] Abdullah Özer, Akio Sekiguchi, Hirohiko Arai, Experimental implementation and analysis of robotic metal spinning with enhanced trajectory tracking algorithms, Robot. Comput.-Integr. Manuf. 28 (4) (2012) 539–550. [17] E. Quigley, J. Monaghan, Enhanced finite element models of metal spinning, J. Mater. Process. Technol. 121 (1) (2002) 43–49. [18] Hamed Zoghi, Alireza Fallahi Arezoodar, Mojtaba Sayeaftabi, Enhanced finite element analysis of material deformation and strain distribution in spinning of 42CrMo steel tubes at elevated temperature, Mater. Des. 47 (2013) 234–242. [19] Jinhui Zhang, Mei Zhan, He Yang, Zhiqiang Jiang, Dong Han, 3D-FE modeling for power spinning of large ellipsoidal heads with variable thicknesses, Comput. Mater. Sci. 53 (1) (2012) 303–313. [20] ANSYS Theory Manual, Release 8.0, ANSYS Inc., USA, 2003. [21] L. Figueiredo, A. Ramalho, M.C. Oliveira, L.F. Menezes, Experimental study of friction in sheet metal forming, Wear 271 (9) (2011) 1651–1657. [22] M.A. Hassan, C.J. Tan, K. Yamaguchi, A developed friction test for sheet metal stretch forming processes, Int. J. Surf. Sci. Eng. 7 (2) (2013) 152–170. [23] M.S. Gadala, J. Wang, Simulation of metal forming processes with finite element methods, Int. J. Numer. Methods Eng. 44 (10) (1999) 1397–1428. [24] Jagabandhu Chakrabarty, Problems in Plane Stress, Second Edition, Springer, US (2010), p. 49–135.
Contents lists available at ScienceDirect
International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Deep spinning of sheet metals Khaled I. Ahmed a,n, Mohamed S. Gadala a,b, Mohamed G. El-Sebaie c a b c
Department of Mechanical Engineering, University of British Columbia (UBC), Vancouver, BC V6T 1Z4, Canada Abu Dhabi University, Abu Dhabi, UAE Mechanical Engineering Department, Assiut University, Assiut 71516, Egypt
art ic l e i nf o
a b s t r a c t
Article history: Received 7 April 2015 Received in revised form 13 July 2015 Accepted 27 July 2015 Available online 29 July 2015
Spinning of sheet metals into cylindrical cups is an important sheet metal forming process for its advantages of flexible tooling and very small forming loads. The most challenging aspect in this process is its low formability due to wrinkling formation in the free flange. In this work, a new deep spinning process with roller set aided with blank-holder of constant clearance is proposed aiming to suppress the wrinkling formation in the deformation zone. Experimental work on annealed and hard aluminum sheet metals is carried out to assess the new process. The proposed spinning process has shown rapid increase in the formability of the sheet metals as the roller feed increases. On the other hand, significant increase in the roller feed worsens the formability of sheet metals in conventional spinning. The Limiting Spinning Ratios, LSRs; or the blank to mandrel diameters ratios, have increased from 1.75 using the conventional spinning to 2.40 using the deep spinning with annealed aluminum sheets in one pass. Also, the LSRs have increased from 1.67 using the conventional spinning to 2.24 using the deep spinning with hard aluminum sheets in one pass. New failure modes of flange jamming and wall fracture have been presented and discussed. In addition, the formability limitations, thickness strains, and spun cup form features at different process parameters are experimentally investigated and discussed. Further, a finite element model for the new process is presented and verified showing the limitation of the available shell elements offered by ANSYS Mechanical APDL in modeling the new process. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Spinning Sheet metal forming Cylindrical cups Spinning roller Blank-holder Aluminum Finite element ANSYS APDL
1. Introduction Sheet metal spinning of cylindrical cups is a traditional forming process, however, due to the flexibility of the process; it has undergone a renaissance in recent years and has developed into a versatile process for producing lightweight components [1–3]. In this process, a rotating sheet metal disk is deformed over a cylindrical mandrel into a cup by applying incremental small forces using an axially moving roller. Several attempts have been accomplished to study the challenging aspects of this process, particularly, failure modes, geometrical and thickness profiles of the final spun cup, and formability of the spinning process. Failure of a circular blank to be successfully spun into a cup usually results from either flange wrinkling or wall fracture [1,2]. Studies have reported that blank parameters and working conditions are two main reasons for wrinkling formations in the unsupported part of the blank during conventional spinning of sheet metals. Conventional spinning process has shown increasing n
Corresponding author. E-mail addresses: [email protected] (K.I. Ahmed), [email protected] (M.S. Gadala), [email protected] (M.G. El-Sebaie). http://dx.doi.org/10.1016/j.ijmachtools.2015.07.005 0890-6955/& 2015 Elsevier Ltd. All rights reserved.
tendency to wrinkling formation with small modulus of plastic buckling, large mandrel diameter, and thin original blank sheet metals [4]. In addition, wrinkling formation tendency increases significantly with higher roller feeds and higher roller angles [5– 8]. Furthermore, studies have shown that spinning of thicker sheet metals will fail due to wrinkling formation at higher roller feeds [8–11]. Fracture failure in conventional spinning not only occurs with oversized blanks but is also evident with smaller roller feeds, larger roller angles and smaller roller nose radii and this normally increases the tendency of tangential cracks in the partially deformed cup wall [5–11]. The wall thickness of conventionally spun cup is not uniform [6–8]. The cup edge is much thicker than the original blank thickness and the cup wall has two adjacent necks. The first neck is at the cup bottom and the second one is at the cup wall. Cup wall fractures occur due to oversized blanks at the location of the second neck. Conventional spinning process produces thinner cup wall with smaller roller feeds [6–8], smaller roller nose radii [6,7], higher roller angles [7] and smaller radial clearances [6]. The inner profile of the final spun cup is larger than the mandrel profile due to spring back [7]. This difference gets wider with smaller roller nose radii, higher roller feeds, and higher conical roller angles [7].
K.I. Ahmed et al. / International Journal of Machine Tools & Manufacture 97 (2015) 72–85
The final spun cup by conventional single roller doesn't closely fit to the forming mandrel. The cup is rather shaped with bulged form having a gap between the cup inner diameter and the mandrel. This gap is not uniform and increases with cup height with its minimum at the cup bottom [7]. Also, it is shown that spinning with conical roller produces cups with bulged gap as high as 3.0 mm larger than the mandrel stem diameter [7] and the out of roundness of the spun cup is found to be as high as 0.5 mm [7]. Spinning formability is measured by the Limiting Spinning Ratio, LSR, which is the ratio of the maximum original blank diameter that can be successfully spun forming a cup, in a single pass, to the mandrel diameter [5–8]. Based on overcoming the wrinkling and fracture failure modes, many attempts have investigated flat [5,6], conical [7] and D-shape rollers [8] with various working conditions to enhance the spinning formability of conventional spinning. This formability limit is highly dependent on the ratio of mandrel diameter to blank thickness dm/tb [5,6]. At high ratios, dm /tb 430, failure due to wrinkling formation is generally dominant. On the other hand at small ratios, dm/tb o30, failure due to cup wall fracture is generally dominant. Sieble and Droge [5] have used flat roller in spinning of mild steel cups achieving LSR of 1.7 for dm/tb ¼40. However, this formability level decreased rapidly to about 1.5 as dm/tb increased to 70.0. On the same hand, Hayama, and Murota (1963) [6] have also used flat roller in spinning of annealed aluminum cups achieving slightly lower LSR of 1.67 at dm/tb ¼ 40 and LSR of 1.48 at dm/tb ¼70. They have extended their work to lower values of dm/t b ¼20 achieving LSR of 1.86. In these attempts, the maximum LSR was achieved by searching for optimum roller feed, which was bounded by the flange wrinkling formation and the cup wall fracture. El-Khabeery et al. [7] have used conical rollers achieving LSR of 1.9 at dm/tb ¼28 using conical roller with face angle of 45° in spinning of annealed aluminum cups. Xia et al. [8] have used D-shape roller in spinning of steel and aluminum cups achieving LSR of 1.68 at dm/tb ¼ 50. It is worth noting that in these studies [5– 8], the roller movement was in the axial direction parallel to the mandrel axis. In earlier work, Terada et al. [12] have presented a numerical study of a convex roller shape moving in radial direction perpendicularly to the mandrel axis instead of the conventional roller axial motion. However, the maximum LSR achieved was 1.65 for thick sheet metals with dm/tb ¼18.5. In a recent attempt, Lossen and Homberg [13] have proposed a new technique to achieve higher formability for complex shapes. In this technique, the blank elements are heated up by friction with roller, and then the roller is moved axially to create the cup wall. This technique has achieved LSR of 1.82 at dm/tb ¼13.5, which is lower than that achieved using flat, conical and D-shape rollers. Currently, high LSRs are achievable by multi-pass spinning [15,16]. Furthermore, multi-pass spinning is more favorable than multi-stage deep drawing for its flexibility and significant lower tool cost. Fig. 1 summarizes the maximum achieved LSRs of conventional spinning of commercial pure aluminum sheet metals for the previous studies [5–8,12,13] and that for conventional deep drawing [14] at various mandrel diameter to blank thickness ratios dm/tb. The achieved LSRs for small values of (dm/tb) are lower than those obtained in conventional deep drawing, which is usually higher than 2.0 [14]. Furthermore, for higher values of (dm/tb) the difference becomes much wider. It may be noted that the achieved LSRs of single pass spinning are banded in a very narrow region implying that the above investigations have not significantly improved the formability limitations of the sheet metal spinning process. Based on the above discussion, the problem persists in the flange wrinkling formation at high roller feeds. The formability of the conventional deep drawing is superior to that in conventional
73
Fig. 1. Limiting spinning ratios at various dm/tb ratios with different roller profiles and conventional deep drawing process [adapted from: 5-8,12-14].
spinning due to the suppression of the flange wrinkling by the aid of a blank-holder. The main objective of the current work is to implement a new roller aided with constant clearance blank holder. The new roller is experimentally evaluated to define its ability in suppressing the wrinkling formation to improve the spinning formability. Also, the geometry and thickness distribution of the final produced cups will be measured at different working conditions. Further, the new process will be simulated by finite element method to get more understanding of the process kinematics and deformation mechanism.
2. Experimental setup The new proposed deep spinning process considers a blank holder to be fixed on the roller shaft as shown in Fig. 2. A hardened spacer with thickness Ch controls the distance between the roller and the blank-holder. The considered process parameters, as shown in Fig. 2, are geometrical and working conditions parameters. The variable geometrical parameters are the radial clearance Cr and the blank diameter Db. The considered variable working condition is the roller feed Sv. All other parameters are fixed throughout the course of experiments. The full construction of the new proposed deep spinning process with all components is shown in Fig. 3. The experimental work is carried out on a manually controlled conventional center lathe with a specially designed holder, replaced the tool post, to support the new roller setup. Fine finished flat-headed mandrel with diameter, 48 mm is used. The fillet profile radius of the mandrel is 6 mm, which is one eighth of its external diameter. The tested mandrel is supported on the lathe chuck using a special holder that ensure minimum run out errors. The blank holder and roller have the same diameter Dr ¼180.0 mm. They are made of hardened alloy tool steel [0.3% C, 0.66% Mn and 0.35% Si], with surface hardness of about 60– 62 HRC. The rollers and the blank holder are ground and then polished reaching surface roughness of Ra¼0.19–0.21 μm with minimum Rz ¼1.18 μm.
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tb
Sv
N Dm Rr Db tb Cr Rr Sv Dr Ch
: Rotational Speed : Mandrel Diameter : Mandrel Nose Radius : Blank Diameter : Blank Thickness : Radial Clearance : Roller Nose Radius : Roller Feed : Roller Diameter : Blank Holder Clearance
30.0 rpm 48.0 mm 6.0 mm Variable 1.5 mm Variable Variable Variable 180.0 mm 2.0 mm
Fig. 2. Schematic drawing of the deep spinning process showing the controlling parameters.
In the current study, a roller nose radius Rr is initially chosen to be 9.0 mm, which is six times the original blank thickness. This nose radius size is slightly less than the recommended die profile in deep drawing [14] to ensure spinning ratio for the free flange less than 1.4. Then two rollers with larger and smaller nose radii of 12.0 mm and 6.0 mm, respectively are tested to investigate the effect of roller nose radii on the formability of the new deep spinning process. The constant clearance between the roller and the blank-holder is chosen to be 2.0 mm, which is 1.33 times the nominal blank thickness. This is slightly wider than that in deep drawing [14] to ease the flange relative rotation inside the deformation zone. The tests are carried out at N ¼ 30 rpm to eliminate dynamic effects and to have adequate and safe control on the lathe carriage axial displacements at high feed rates of 43 mm/rev. It is worth noting that investigations on the rotational speed of the mandrel [6–8] have shown no effects on the spinning process outcomes. A continuous flow rate of lubricating oil is concentrated into the deformation zone to decrease the frictional forces generated between the blank and both the roller and the blank holder interfaces. The radial clearance is adjusted using the lathe cross vernier with accuracy of 0.01 mm. The tested blanks are held between the mandrel, held on the lathe chuck, and the blank fixture, held on the lathe tailstock, using centering device with accuracy of 0.05 mm.
The sheet metals used are hard and annealed commercially pure aluminum Al 99.5 sheets with nominal thickness of 1.5 mm. The annealed aluminum is chosen to represent easy to spin sheet metals and the hard aluminum is chosen to represent hard to spin sheet metals. Tensile tests are carried out to determine the directional mechanical properties of the investigated sheet metals. The tested specimens, five from each direction, are cut from different locations on the sheets at three orientations of 0°, 45°, and 90° to the rolling direction. The measured material properties are; yield strength, work-hardening exponent “n”, material strength coefficient constant “K”, and the plastic normal anisotropy at these three directions. The measured stress–strain relation for all specimens of the two sheet metals are shown in Fig. 4. These measured properties are summarized and listed in Table 1.
3. Experimental procedures, results and discussion For each spinning experimental test, three blanks were cut from the aluminum sheet with 10 mm greater in diameter than the required finished size, to ensure that work hardening effect due to blanking process will be eliminated after the turning operation. Then these blanks were turned down using a specially designed fixture to the designated final size. This turning operation was carried out using a special carbide tip with its designated
1- Lathe holder 2- Oil Seal Ring 3- Roller Bearings 4- Locking Nut 5- Locking Cover 6- Clearance Spacer 7- Blank-Holder 8- Mandrel
9- Partially spun cup 10- Blank Fixture 11- Spinning Roller 12- Roller holder 13- Locking cover 14- Axle 15- Oil Seal Ring 16- Mounting Fork
Fig. 3. Assembly drawings of the deep spinning apparatus and its experimental installation on the testing lathe.
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Fig. 4. Measured stress–strain relations of the tested specimens of hard and annealed aluminum sheet metals in three directions; 0°, 45°, and 90° from rolling direction.
optimum cutting conditions that ensure no work hardening would be added to the blank outer rim. For thickness measurements of the spun cups, a grid of concentric circles in a step of 2.0 mm are scratched on the blank external face. Also, the directions of 0°, 45°, and 90° to the rolling direction are marked. The final spun cup is then cut at these directions and the thickness strains are measured at the scratched circles to be related to its original position. For obtaining the limiting spinning ratio at particular working conditions, a series of blanks with diameter step of 4.0 mm are produced and tested. If the test case switches from fail to success or from success to fail, this step size is reduced to 2.0 mm then to 1.0 mm. The limiting spinning ratio is determined when three successful spun cups are achieved at blank diameter 1.0 mm less than that of three failed cups. 3.1. Failure modes The observed failure modes of the conventional spinning process are correlated with that reported in the literature; flange wrinkling at high roller feeds, Fig. 5a, and wall fracture at low roller feeds, Fig. 5b. The new deep spinning roller set with blank holder has successfully suppressed the wrinkling formations with extremely high roller feeds up to 4.0 mm/rev. The suppression of wrinkling formation leads to very deep cups with annealed and hard aluminum sheet metals. Wall-fracture failure mode of oversized blanks at smaller roller feeds becomes the main failure mode of the new deep spinning process as shown in Fig. 6a. However, increasing the roller feeds with wrinkling suppression is limited by another new failure mode, which is flange jamming as shown
Fig. 5. Failure modes of conventional spinning process. (a) Flange wrinkling. (b) Wall fracture failure.
in Fig. 6b. This failure mode occurs due to the sever curvatures in the cup flange just before entering the deformation zone resisting its rotation into the deformation zone. 3.2. Deep spun cups and thickness distribution Experimental results showed that the new deep spinning process has successfully achieved very high spinning ratios for annealed and hard aluminum sheet metals. Annealed aluminum sheet metal has been successfully spun to spinning ratio of 2.38 at roller feed 3.5 mm/rev as shown in Fig. 7a–c whereas for hard aluminum sheet metal a ratio of 2.21 has been achieved at roller feed 4.0 mm/rev as shown in Fig. 8a–c. The spun cup is not perfectly cylinder due to the diametral growth of the formed cup wall as shown in Figs. 7 and 8a.
Table 1 Material properties of the tested sheet metals. Hard aluminum Thickness tb ¼ 1.5 mm Angle to rolling direction (deg) Yield stress (MPa) Hardening exponent ‘n’ Strength coefficient ‘K’ (MPa) Normal anisotropy ‘R’ Average yield stress (MPa) Average hardening exponent ‘navg’ Average strength coefficient ‘Kavg’ (MPa) Normal anisotropy ‘Ravg’ Planar anisotropy ‘ΔR’
0 112.7 0.026 132.5 0.324 107.2 0.0363 134.3 0.540 0.182
45 103.8 0.049 143.5 0.631
Annealed aluminum Thickness tb ¼1.5 mm 90 105.2 0.021 117.6 0.574
0 27.1 0.23 113.1 0.980 28.8 0.22 113 0.592 0.464
45 26.8 0.22 105.4 0.360
90 36.9 0.20 127.9 0.667
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Fig. 6. Failure modes of deep spinning process. (a) Wall fracture failure. (b) Flange jamming failure.
Furthermore, the final cup profile has shown significant diametral variations due to the planar anisotropic nature of the sheet metal. The differences between the minimum and maximum radii is maximum at the middle third of the cup height as shown in Figs. 7b and 8b. These differences are reduced and the cup profile is mostly uniform at the lower third of the cup due stretching over the mandrel and at the upper third of the cup due to the roller back spinning of the cup wall. The deeply spun cups have significant ears due to the planar anisotropy of the sheet metals. The cup heights of both cases with respect to the rolling direction are presented in Fig. 7c for annealed aluminum and in Fig. 8c for hard aluminum. Two necks have been observed in both spun sheet metals as shown in Fig. 9. Neck I occurs at cup bottom curvature, and neck II occurs at the cup wall. In all failed cases, the fractures correlate perfectly with neck II location. Neck I in hard aluminum cup located at the cup bottom curvature quite close to the cup bottom than that in annealed aluminum. The thickness strain of this neck is almost equal for both sheet metals. Neck II in hard aluminum located at the cup wall quite close to the cup bottom curvature than that in annealed aluminum. The thickness of the cup wall at neck II is significantly thinner in annealed aluminum than that in hard aluminum. Furthermore, the fracture of the oversized hard aluminum cups occurs as soon as the roller nose passes the neck II locations. On the other hand, the fracture of the annealed aluminum cup occurs quite late after the roller nose passes neck II locations. In some cases, the fracture of the oversized annealed aluminum cups have been observed after the cup is fully spun. In such case, the blank size is count in the failed group. It is worth noting that the cup edge is slightly thinner than the neighbor elements due to the over ironing and rolling by the roller nose and its conical back. 3.3. Limiting spinning ratios The limitation of the conventional spinning is tested at different roller feeds for both sheet metals. The radial clearance between the roller nose and the mandrel stem is set equal to the original blank
thickness to reduce the wrinkling tendency. In all cases the conventional spinning is limited by wrinkling formation except the case of annealed aluminum at roller feed 0.5 mm/rev. In this case, small wrinkles are observed towards the end of the roller stroke that increases the forming loads and consequently causes wall fracture. In conventional spinning of both sheet metals, as the roller feed increases, the limiting spinning ratio, LSR, dramatically decreases as shown in Fig. 10. Annealed aluminum has shown better LSRs. In deep spinning, the wrinkles are fully suppressed leading to significant increase in the LSR of both sheet metals at roller feed 0.5 mm/rev. As the roller feed increases, the LSRs significantly increases up to 3.5 mm/rev in spinning of annealed sheet metals and up to 4.0 mm/rev in spinning of hard aluminum sheet metals. Further increase of the roller feed is limited by the new failure mode, flange jamming, as shown in the above section. Lower LSRs have been tested with higher roller feed with no success to overcome the flange jamming. The deep spinning of sheet metals with radial clearance equal to the original thickness has increased the LSR for annealed aluminum from 1.76 at roller feed 0.5 mm/rev to 2.2 at roller feed 3.5 mm/rev. Also, it has increased the LSR for hard aluminum from 1.67 at roller feed 0.5 mm/rev to 2.14 at roller feed 4.0 mm/rev. A comparison between the achieved LSR for both conventional and deep spinning processes is shown in Fig. 10. Suppression of flange wrinkling helps in increasing the radial clearance between the roller nose and the mandrel stem. Similar to that used in deep drawing, a radial clearance of (Cr ¼2.25 mm), which is 50% more than the original blank thickness has been adjusted and tested. The LSRs have increased significantly for both sheet metals, as shown in Fig. 11. The new deep spinning process has achieved a LSR of 2.38 for annealed aluminum and LSR of 2.21 for hard aluminum. It is worth noting that the increase of the radial clearance has neither enhanced nor worsened the flange jamming limitations. Deep spinning with larger roller nose radius (Rr ¼12.0 mm) has shown further increase in the LSR of the annealed and hard aluminum sheets as shown in Fig. 12. At small roller feeds, the increase in the LSR is quite significant, about 0.07, however
Fig. 7. Annealed aluminum successfully spun cup at SR ¼ 2.38 at Sv ¼3.5 mm/rev and Cr ¼ 2.25 mm. (a) Spun cup photo. (b) Cup radii variations through cup height. (c) Cup height variation w.r.t. rolling direction.
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Fig. 8. Hard aluminum successfully spun cup at SR ¼2.21 at Sv ¼ 4.0 mm/rev and Cr ¼2.25 mm. (a) Spun cup photo. (b) Cup radii variations through cup height. (c) Cup height variation w.r.t. rolling direction.
LSR are presented in Fig. 13. It is noted that deep spinning with smaller roller nose radius produces deep spun cups with less bulge and smaller feed marks. Smaller roller nose radius reduces the deep spinning formability similar to that of the die profile in deep drawing at small roller feeds due to added bending stresses. However, deep spinning at high roller feeds compensates these effects on the deep spinning formability showing insignificant reduction in the limiting spinning ratios especially with annealed aluminum. This can be explained by assuming a partially spun cup that is perfectly fit over the mandrel as shown in Fig. 14. The spinning loads created within the deformation zone are transferred to the mandrel through grading areas with smallest under the roller nose and the largest at the cup bottom. This critical area under the roller nose is proportional to the contact length between the roller nose and the partially spun cup. This contact length, for the assumed perfectly plastic deformed cup, can be calculated based on the schematic diagram in Fig. 14 as follows:
Lc =
Fig. 9. Thickness strain distribution of successfully spun cups at Cr ¼ 2.25 mm. (a) Annealed aluminum blank at SR ¼ 2.38, Sv ¼3.5 mm/rev (b) Hard aluminum blank at SR ¼ 2.21, Sv ¼4.0 mm/rev.
increasing the roller feed up to the jamming limit decreases these differences to 0.02. On the other hand, decreasing the roller nose radius (Rr ¼6.0 mm) has shown significant decrease in the LSR at small roller feeds of both sheet metals as shown in Fig. 12. In the same way, these differences are reduced with the increase of the roller feeds. Deep spinning with roller nose radius 6.0 mm has suffered from earlier flange jamming by 0.5 mm/rev for both sheet metals. Successful and failed spun cups at the maximum possible
⎛ Rr − Dr ⎜ . cos−1⎜ 1 − ⎜ 2 ⎝
2 ⎞ − ( Sv ) ⎟ ⎟⎟ Dr /2 ⎠ 2
( Rr )
(1)
The variation of the contact length Lc with the roller feed Sv at different roller nose radii Rr is shown in Fig. 15. This increase of the contact length Lc with the increase of the roller feed Sv is reflected into proportional increase of the load carrying area, which explains the significant increase of the LSR with the increase of the roller feed. It is worth noting, that the rate of increase of the contact length Lc at roller nose radius 6.0 mm is significantly higher than that at roller nose radius of 12.0 mm. This is similarly observed as shown in Fig. 12, that the rate of increase of the LSRs at deep spinning with roller nose radius 6.0 mm is significantly higher than that obtained at deep spinning with roller nose radius 12.0 mm. It is consistently reported in the literature [5–10] that the smaller roller feed produce thinner cup wall without giving a scientific reason of this observation. The main objective of conventional spinning was achieving the higher possible roller feed without wrinkling. It is worth noting that conventional spinning tests of the current work have achieved similar results of previously achieved limiting spinning ratios as shown in Fig. 16. Comparing to other achieved spinning ratios, deep spinning not only surpassed the previously achieved spinning ratios, but also, significantly surpassed the deep drawing process [14] as shown in Fig. 16.
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Fig. 10. Limiting spinning ratios, LSRs, for conventional and deep spinning processes at Cr ¼ 1.5 mm and various roller feeds for both annealed, with photo, and hard aluminum sheet metals.
LSR=2.21, Sv = 4.0 mm/rev.
Cr = tb = 1.50 mm
LSR=2.14, Sv = 4.0 mm/rev.
Ann. Aluminum
Hard Aluminum
Cr= 2.25 mm tb = 1.50 mm
LSR=2.38, Sv = 3.5 mm/rev.
LSR=2.20, Sv = 3.5 mm/rev.
Fig. 11. Limiting spinning ratios, LSRs, for deep spinning processes at Cr ¼ 1.50 mm and Cr ¼2.25 mm and various roller feeds for both annealed and hard aluminum sheet metals.
Fig. 12. Limiting spinning ratios, LSRs, for deep spinning process at different roller nose radii for both annealed and hard aluminum sheet metals at radial clearance Cr ¼ 2.25 mm.
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Rr = 6.0 mm
LSR=2.24, S = 4.0 mm/rev.
LSR=2.1, S = 3.5 mm/rev.
LSR=2.40, S = 3.5 mm/rev.
LSR=2.20, S = 3.0 mm/rev.
Annealed Aluminum
Hard Aluminum
Rr = 12.0 mm
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Fig. 13. Obtained spun cups at the limiting spinning ratios, LSRs, for deep spinning process at Cr ¼2.25 mm and roller nose radii 12.0 mm and 6.0 mm for both annealed and hard aluminum sheet metals.
4. Finite element model 4.1. Model components Several attempts have been made to simulate conventional sheet metal spinning using both solid elements [17,18] and shell elements, [15,19]. Due to convergence difficulty with modeling with solid elements that arises due to deformation severity in the new deep spinning process, shell element is considered for the simulation modeling of the current work. ANSYS [20], Mechanical APDL offers two shell elements for nonlinear analysis, SHELL181, and SHELL43. The main difference is that SHELL43 considers the shear stresses through the element thickness whereas SHELL181 ignores shear deformation. In the current work, both elements have been used in modeling the new deep spinning process. Fig. 17 shows the components of the deep spinning process. These components are the blank, mandrel, blank fixture, roller, and blank-holder. All of these components, except the blank, are non-deformable bodies, therefore, they are modeled as rigid surfaces. The motion of each of these surfaces is controlled using a pilot node element, which is an element with one node, whose motion governs the motion of the entire rigid surface. The mandrel and the blank fixture are associated with two independent pilot nodes, while the roller and the blank-holder share the association of one pilot node. The mandrel, the blank fixture, and the blank inner circle are given the rotating motion around the mandrel axis and supported in all other degrees of freedom. The roller and blank-holder set is given the axial feed motion and is left free to rotate only around its
Fig. 15. Relation between the contact length and the roller feed and roller nose radius.
axis based on the kinematics of the process. The other degrees of freedom of the roller and the blank holder are fully constrained. The blank material is assumed isotropic with the averaged values shown in Table 1 and plastically obeys the isotropic hardening model MISO, which considers Von Misses yield criterion. The assumption of isotropic material is thought to be a good approximation and starting point to assess the overall behavior of the proposed experimental setup. The objective is not to verify or optimize process parameters but rather to have some qualitative assessment of the process and its limitation. In addition, the finite element model will be a good tool to have insight investigations into the deformation mechanism of the new deep spinning process. The coefficient of friction is generally varied during the forming process [21,22], however, in the current study it will be assumed constant through the operation to focus on the objectives of the model. Based on the experimental measurements of the coefficient of friction according to the roller surface roughness [21], the suitable value is about 0.1 for the current roller surface roughness of
Fig. 14. Schematic of the projected contact length between the spun cup and the roller under the roller nose.
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Table 2 Process parameters of the evaluation test cases. Test case #1 #2 Mesh density test
Cr mm 1.125 1.50 2.00
SR
Mesh density
Element type
1.9 2.16 2.18
48 16 48 16 Varies
43/181 43/181 SHELL43 only
Table 3 Mesh schemes for testing the model sensitivity to mesh density. Scheme
#1 #2 #3 #4 #5
Mesh density
24 8 36 12 42 14 48 16 60 20
Circum. elem.
24 36 42 48 60
Radial elem.
8 12 14 16 20
Total blank elements
192 432 672 768 1200
Rigid surfaces elements 772 1696 2398 2980 4324
Total nodes
632 1232 1688 2024 2888
Fig. 16. Comparison of the achieved limiting spinning ratios in the current work and that previously achieved from [5–8,12–14].
Rz ¼ 1.18 μm. Also, based on the experimental measurements of coefficient of friction according to oil lubrication [22], the average value is about 0.1. The model is solved using static implicit time scheme with full Newton Raphson nonlinear solver. Initial trials was performed with the recommended and default tolerance limits in ANSYS; 1.0E-3. All these trials have failed to converge very small deformation of the axial roller full displacement. Accordingly, the model is aided with especial subroutine to detect the convergence behavior and to adopt the solution tolerances accordingly. This tolerance starts at 5E 5 and is increased by steps of 1E 5 each time the model faces convergence difficulties to a maximum allowed tolerance of 1E 3. 4.2. Finite element model equations The formulation of the finite element formulation is obtained by the virtual work principle [23]. In this derivation, only linear differential terms are kept while all higher order terms are ignored to obtain a set of linear equations.
δW =
∫V σij δeij dV = ∫V fiB δui dV + ∫S fiS δui dS
(2)
where W is the internal virtual work
Fig. 18. Comparison between the form of the experimentally produced cup and those obtained by the FE simulation for test case #1.
sij is the Cauchy stress component 1 eij is the deformation tensor such that eij = 2 (∂ui /∂xj + ∂uj /∂xi ) ui is the displacement vector. xi is the spatial position vector of the particle in deformed configuration. f iS and fiB are the surface traction and body force components, respectively. The integration in Eq. (2) is carried out over the deformed volume and the surface on which the traction is applied. The constitutive law, which relates the stress increments to the strain increments, should be frame invariant and able to separate the rigid body rotations. To fulfill this requirement, the Jaumann rate of Cauchy stress is considered such that
Roller Blank
Blank
Roller Blank Holder Mandrel
Blank Fixture
Mandrel
Blank Holder
Fig. 17. Finite element model of the deep spinning showing half of the model in different views.
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Fig. 19. Comparison between thickness strains of the experimentally produced cup and those obtained by the FE simulation for test case #2.
Fig. 20. Plastic shear strains comparisons for test case #2. (a) In-plane plastic shear strain εxy (SHELL181), (b) in-plane plastic shear strain εxy (SHELL43), (c) throughthickness plastic shear strain εxz (SHELL43), (d) through-thickness plastic shear strain εxy (SHELL43).
σij̇ J = σij̇ − σik ω̇ jk − σjk ω̇ ik
(3)
stress rate and material constitutive tensor can be shown as
σij̇ = Cijkl Dkl + σik ω̇ jk + σjk ω̇ ik
where σ̇ijJ is the Jaumann rate of Cauchy stress 1
ω̇ ij is the spin tensor such that; ω̇ ij = 2 (∂vi/∂xj − ∂vj /∂xi ) σ̇ij is the time rate of Cauchy stress The constitutive law of materials undergoing large deformation, which describes stress change due to strain, can be expressed, using Jaumann rate of Cauchy stress, as
σij̇ J = σij̇ − Cijkl Dkl
(4)
where Cijkl is the fourth order material constitutive tensor 1
Dij is the rate of deformation such that; Dij = 2 (∂vi/∂xj + ∂vj /∂xi ) vi is the velocity in direction i. Then, from Eqs. (3) and (4) the relation between the Cauchy
(5)
where the elastoplastic constitutive matrix for isotropic material with isotropic hardening rule is given by [21]
Cijkl =
⎛ ⎞ 3σ ′ij σ ′kl ν E ⎜ ⎟ δik δjl + δij δkl − 2H 1 + ν 1 + ν ⎜⎝ 1 − 2ν 2σ 2 (1 + 3 ( E )) ⎟⎠
where: H: is the strain hardening modulus, σ¯ : is the effective stress, σ′ij : are the deviatoric stress components, ν: Poisson's ratio, E: Young' s modulus, δ ij : is the Kronecker delta.
(6)
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Fig. 21. Comparison between the final form of the experimentally spun cup and the simulated ones using five different mesh densities.
starting the finite element solution with very small tolerance allowance ( 5E 5) significantly reduces the divergence possibilities and consumes lower CPU time especially with SHELL43. On the other hand starting the solution with tolerance allowance higher than (1E 3) shows significant convergence difficulties with SHELL43 and the model fails to get a converged solution towards the end of the process in both cases In test case #1, final form of the predicted spun cup with SHELL43 is much closer to the experimentally obtained cup, as shown in Fig. 18. As for test case #2, also, the predicted thickness strain distribution of the spun cup with SHELL43 is much closer to the experimentally obtained cup as shown in Fig. 19. Furthermore, modeling with SHELL43 is able to predict both observed cup wall necks; however, modeling with SHELL181 is able to predict only the second neck with overestimated strain. As for the shear strains, both elements have shown similar behavior in plane shear strain. However, SHELL43 element has shown significant thickness shear strains that are ignored in SHELL181 as shown in Fig. 20. Five mesh densities are evaluated using SHELL43. The five test cases have successfully completed the simulation until the end of the deep spinning process. The predicted final form of the spun cup is close to the experimentally obtained cup as shown in Fig. 21. However, cases of #3, #4, and #5 are much closer than the coarser ones. As shown in Fig. 22. mesh density #4(48 16) shows lower CPU time than mesh #3(42 14) because mesh #4(48 16) shows better convergence regime and uses much lower total number of iterations.
Fig. 22. CPU time comparison for simulating 1 mm of the roller displacement using five different mesh densities using element SHELL43.
Utilizing Eq. (3) into Eq. (2), the incremental updated Lagrangian formulation of the problem takes the form [21]
∫V
∂δui [(σij•J ∂xj
−
δui fiB dV V
= ∫
σ ip ∂vj 2
( ∂x + p
∂vp ∂xj
)+
σ jp ∂vi ( 2 ∂xp
−
∂vp ∂xi
∂vp
) + σij ∂x ] dV p
δui fiS dS S
+ ∫
Both shell elements SHELL43 and SHELL181 have been evaluated with test cases #1 and #2 as listed in Table 2. Test case #1 is evaluating cup profile and test case #2 is evaluating cup wall thickness. Then the mesh sensitivity test is carried out on SHELL43 as shown in Table 3. For all test cases, the tested material is hard aluminum and the roller feed is Sv ¼4.0 mm/rev.
4.4. Numerical investigations The finite element model is used to investigate the deformation mechanism and the stress pattern of the spun part during deep spinning process. The numerical investigations are carried on hard aluminum sheet metal due to its much shorter simulation time. In failed cases, fracture of oversized blanks in hard aluminum sheet metal occurs much earlier than that for annealed aluminum. Also, successful cases are obtained at lower spinning ratios with higher roller feeds, which require much shorter simulation time than that for annealed aluminum. In the current investigation, the onset of
4.3. Finite element model evaluation results Both shell elements, mentioned above, are capable of simulating the deep spinning process successfully with full integration schemes. The CPU time for the model with SHELL43 is four times of that with SHELL181 in both test cases. It is worth noting that, Table 4 Working conditions for the first test group. Material
SR (Db/Dm)
HHAL
2.1, 2.2, 2.3 and 2.4
Sv (mm/rev) 4.0
μ 0.1
Rr (mm)
Dm (mm)
Rm (mm)
to (mm)
Cr (mm)
9.0
48.0
7.0
1.50
2.25
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Fig. 23. Thickness strains distribution in the successful cups and the failed cups at the instant of failure. [HHAL, SR ¼ Varies, Sv ¼ 4.0 mm/rev, Dm ¼ 48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼1.5 mm, Cr ¼ 2.25 mm].
Radial Stresses
Hoop Stresses
C – Fillet End
B – Bottom Neck
A – Cup Bottom
Element Strength
E – Cup Edge
wall fracture is assumed at thickness strains εt o 0.45 (at thickness reduction 4 36%), which is observed at the fracture sections of the experimentally failed cups. It is worth noting that wall fracture in deep spinning occurs due to localized necking, which allows further thinning after necking before rupture than that for diffused necking [24]. In deep spinning, two necks are usually observed in the successful cups, cup bottom neck, neck I, and cup wall neck, neck II. Experiments have shown that, failure usually occurs due to cup wall fracture at the location of the cup wall neck rather than the location of the cup bottom neck. Four spinning ratios are numerically examined; 2.1, 2.2, 2.3 and 2.4 with the working conditions listed in Table 4. The first two ratios; 2.1 and 2.2, produce successful cups, while the other two ratios; 2.3 and 2.4 produce failed cups due to wall fracture, see Fig. 23. The figure shows that the thinning in both necks; the bottom neck and the wall neck, increases as the spinning ratio increases. Although the bottom neck showed more thinning in the successful cups, the wall neck dominated the deformation and cause failure in the failed cups at oversized blanks. Also, it is observed that the failure starts with SR ¼2.4 earlier than that with SR ¼ 2.3, however the neck locations of the failed cups as well as that of the successful cups locate at the same initial radial location as shown in Fig. 24.
D - Wall Neck
Fig. 24. Average thickness strains related to the initial radial positions for the successful cups and the failed cups at the instant of failure. [HHAL, Sv ¼4.0 mm/rev, Dm ¼48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼1.5 mm, Cr ¼ 2.25 mm].
Fig. 25. Radial and hoop stresses history for the five selected locations from the cup bottom till the cup edge for SR ¼ 2.2. [HHAL, Sv ¼ 4.0 mm/rev, Dm ¼48 mm, Rr ¼9.0 mm, Rm ¼7.0 mm, to ¼ 1.5 mm, and Cr ¼ 2.25 mm], N.P. Roller side lies at halves of the turns, while roller opposite side lies at integers. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
For more understanding of the failure mechanism, the stress history of the mid layer of an element on the selected five points “A”, “B”, “C”, “D”, and “E” at radial locations described in Fig. 24 are plotted against the blank rotations as shown in Figs. 25–27. The solid red line represents the strength state of the investigated element due to the induced plastic strains, the solid magneto line represents the radial stress, and the dashed blue line represents the hope stress. The recording of the stresses at each investigated
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Element Strength
Radial Stresses
Hoop Stresses
SR = 2.10
SR = 2.20
SR = 2.30
SR = 2.40
Fig. 26. Radial and hoop stresses history for bottom neck, location “B”, at various spinning ratios. [HHAL, Sv ¼4.0 mm/rev, Dm ¼ 48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼ 1.5 mm, and Cr ¼ 2.25 mm], N.P. Roller side lies at halves of the turns, while roller opposite side lies at integers. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Element Strength
Radial Stresses
Hoop Stresses
SR = 2.10
SR = 2.20
SR = 2.30
SR = 2.40
Fig. 27. Radial and hoop stresses history for wall neck, location “D”, at various spinning ratios. [HHAL, Sv ¼4.0 mm/rev, Dm ¼ 48 mm, Rr ¼ 9.0 mm, Rm ¼ 7.0 mm, to ¼ 1.5 mm, and Cr ¼ 2.25 mm], N.P. Roller side lies at halves of the turns, while roller opposite side lies at integers. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
element starts at the opposite side of the roller. In other words, the roller nose locates at halves of the turns and the opposite side locates at the full turns.
The generated radial and the hoop stresses during the deep spinning process for the critical spinning ratio SR ¼2.2 at the selected five radial locations are plotted against the mandrel turns as shown in Fig. 25. Hoop and radial stresses at the locations “A” and “B” are both tensile due to stretching over the mandrel profile. This deformation pattern at the roller side is similar to that of the conventional deep drawing [14]. Location “C” at the connection between the mandrel profile and the cup wall experiences uniaxial tension with lower stress level. It is worth noting that the width of the stressing cycle at location “C” is narrower than that at location “B”, which confirms the previous discussion of the grading of the load carrying area from under the roller nose to the cup bottom. The critical location “D” passes through three stages; radial drawing towards the mandrel up to seventh cycle, bending and unbending over the roller profile through cycles 7 and 8, and carrying loads from the flange to the cup bottom from the ninth cycle to the end of deformation. In the first stage, the element experiences uniaxial tensile radial stresses preceded with uniaxial compressive hoop stresses at the entrance of the deformation zone. The element is then stretched over the roller profile up to the ninth cycle, after which it locates over the mandrel stem. During the ninth and tenth cycles, the element experiences the maximum radial stresses. The element, at the last stage, experiences consistent pattern of uniaxial radial stresses due to carrying the spinning loads and a preceded and followed uniaxial compressive radial stresses due to the effect of the roller back. The edge location “E” experiences uniaxial compressive hoop stresses as it passes over the roller profile and enters the deformation zone due to the radial drawing of the element. Then it experiences uniaxial tensile hoop stresses due to pulling its neighbor elements into the deformation zone. The effect of the spinning ratio on the stress levels at locations “B” and “D” are presented in Figs. 26 and 27. It is clear from these graphs that the bottom neck at location “B” has slight dependency on the spinning ratio. The stress pattern in this region is close to be bi-axial tension, which is due to the stretching of the blank over the mandrel fillet. For oversized spinning ratios, the forming loads are dissipated at the wall neck creation and fracture, so the carried stresses to the cup bottom are lower in spinning ratio 2.3 and above than that at spinning ratio 2.2 and lower. As for the cup wall neck at location “D”, it is clear that the positive radial stresses increase as the spinning ratio increases. At the point that the radial stresses are attaining the material strength, the fracture begins and the spinning of the cup fails.
5. Conclusions Low formability of sheet metal spinning is not significantly overcome through previous attempts in the literature due to wrinkling formation in the free flange. In the current work, a new deep spinning process is developed and experimentally and numerically evaluated. In the new process, a blank holder with constant clearance has been added to the spinning roller to suppress the wrinkling formation in the deformation zone. The deep spinning process has shown rapid increase in the formability of the sheet metals as the roller feed increases. On the other hand, the increase in the roller feed drastically worsens the formability of sheet metals in conventional spinning. The limiting spinning ratios, LSRs; blank to mandrel diameters ratios, have increased from 1.76 using the conventional spinning to 2.40 using the deep spinning with annealed aluminum sheets in one pass. Also, the LSRs have increased from 1.67 using the conventional spinning to 2.24 using the deep spinning with hard aluminum sheets in one pass. This formability level is a breakthrough especially with the hard aluminum sheet metal that is difficult to be achieved even with multi-pass spinning process.
K.I. Ahmed et al. / International Journal of Machine Tools & Manufacture 97 (2015) 72–85
The deep spinning process is limited with new failure modes of wall fracture at low roller feeds and flange jamming at high roller feeds. Two necks have been observed in the successfully spun cup at the LSR. Neck I is observed at the cup bottom curvature and neck II is observed at the partially formed cup wall. Failure due to wall fracture correlate with neck II in both annealed and hard aluminum sheet metals. Localized forming nature of the spinning process results in diametral growth of the cup wall, which produces a bulged cup with significant out of cylindricity cup form. The deep spinning process is a newly developed process that requires more investigation and development to achieve its optimum conditions. Comparing to other achieved spinning ratios, deep spinning not only surpassed the previously achieved spinning ratios, but also, significantly surpassed the conventional deep drawing process. Roller nose radius has shown significant effect on the LSRs at small roller feeds similar to those observed in deep drawing due to die profile. However, deep spinning at high roller feeds achieve almost same LSRs with insignificant differences at different roller nose radii in case they have the same flange jamming limits. The significant increase in the LSRs with the increase of the roller feeds is due to the increase of the load carrying area from the deformation zone to the cup bottom. Finite element modeling of the deep spinning process is achieved using shell elements offered by ANSYS Mechanical APDL; SHELL43 and SHELL181. SHELL181 shows significantly, lower CPU cost and smoother convergence patterns than that achieved by SHELL43. However, capabilities of thickness shear consideration that is offered by SHELL43 is very crucial in modeling deep spinning of sheet metals. The finite element model has shown that the wall neck location experiences the highest radial tensile stresses under the roller nose. Also, it shows that the stresses at the bottom neck location are due to stretching over the mandrel profile. At the fracture conditions, all radial tensile stresses are dissipated at the wall neck location rather than at the cup bottom.
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