- Email: [email protected]
Experimental and finite element investigation of over-bending phenomenon in Double-Sided Incremental Forming (DSIF) of aluminium sheets
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect ScienceDirect
Available Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Procedia Manufacturing 00 (2018) 000–000 Procedia Manufacturing 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 29 (2019) 59–66 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
18th International Conference on Sheet Metal, SHEMET 2019 18th International Conference on Sheet Metal, SHEMET 2019
Experimental and finite element investigation of over-bending Experimental and finite element investigation of over-bending phenomenon in Double-Sided Incremental Forming (DSIF) ofJune Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30of phenomenon in Double-Sided Incremental Forming (DSIF) 2017, Vigo (Pontevedra), Spain aluminium sheets aluminium sheets a b Costing models capacity Industry Trade-off Wenxuan Peng a,for Meng Li b, Bin optimization Lu bb, Jun Chen bb, in Adib Becker aa, 4.0: Hengan Ou a,* Wenxuan Peng , Meng Li , Bin Lu , Jun Chen , Adib Becker , Hengan Ou a,* between usedandcapacity and operational efficiency Department of mechanical, Materials Manufacturing Engineering, University of Nottingham, Nottingham, NG9 2AR, UK a a
Plasticityand Technology, Shanghai Jiao Tong University, Shanghai, 200030, China NG9 2AR, UK Department ofbDepartment mechanical, of Materials Manufacturing Engineering, University of Nottingham, Nottingham, b a a,* Jiao Tong University, b b China Department of Plasticity Technology, Shanghai Shanghai, 200030,
A. Santana , P. Afonso , A. Zanin , R. Wernke a
University of Minho, 4800-058 Guimarães, Portugal
b Abstract Unochapecó, 89809-000 Chapecó, SC, Brazil Abstract Double-Sided Incremental forming (DSIF) is a flexible sheet forming method with increasing research interest in the last decade. Double-Sided Incremental forming (DSIF) is a flexible sheet forming with increasing research interest in the last decade. It offers improved formability and accuracy over the conventional singlemethod point incremental forming (SPIF) although it accompanies It offers andcontact accuracy over the forming conventional single point incremental forming (SPIF) it accompanies Abstract with the improved possibilityformability of tools losing during process. Mounting a pneumatic supporting toolalthough is an efficient solution. with the possibility tools losingand contact during the the material forming process. Mounting pneumatic supporting tool isreason an efficient solution. However, the tools of may squeeze over-bend when forming for aa high wall angle. A possible may be due to However, tools may squeeze and over-bend the material when forming for a pushed high wall angle. A finite possible reason may be due to inaccurate prediction ofofmaterial thinning or the effect of tool deflection. This work uses a to modified element (FE) model with Under thethe concept "Industry 4.0", production processes will be be increasingly interconnected, inaccurate toolpath prediction of material thinning orand, the effect ofstiffness tool deflection. This work usesIn a modified finite element model with dedicated incorporated with simplified of tools andefficient. machine in order to reproduce the (FE) effect of system information baseddesign on a real time basis necessarily, much more this context, capacity optimization dedicated toolpath design incorporated with simplified stiffness of tools and the machine in orderoftothe reproduce the effect of value. system elasticity to the process with supporting tool and evaluate over-bending problem. The goes beyond theDSIF traditional aim ofhydraulic capacity maximization, contributing alsoroot for causes organization’s profitability and elasticity to the DSIF process with hydraulic supporting tool and evaluate the root causes of the over-bending problem. numerical results are compared experimentally produced components, focusing on the thickness evaluation and development Indeed, lean management and continuous improvement approaches suggest capacity optimization instead The of numerical are throughout compared with experimentally produced demonstrates components, focusing the evaluation development of the tool results deflection the process. This comparison the effecton thethickness tool deflection upon and formed parts, maximization. The study of capacity optimization and costing models is an of important research topicthethat deserves of the toolthe deflection throughout process. deformation This comparison demonstrates effect of the tool deflection upon formed parts, including geometric error andthe excessive on the wall region.the The conclusion suggests a need forthe a compensation contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical including the geometric errorof and excessive deformation onsystems. the wall region. The conclusion suggests a need for a compensation based approach in the design DISF toolpath and machine model for capacity on and different costing models (ABC and TDABC). A generic model has been based approach in themanagement design of DISFbased toolpath machine systems. developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s © 2018 The Authors. Published by Elsevier B.V. © 2019The The Authors. Published bymaximization Elsevier B.V. vs operational efficiency is highlighted and it is shown that capacity value. trade-off capacity © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an openmight accesshide article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) optimization operational inefficiency. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the organizing committee of of SHEMET SHEMET 2019. 2019. Selection and peer-review under responsibility of the organizing committee © 2017 The Authors. Published Elsevier B.V. Selection and peer-review underby responsibility of the organizing committee of SHEMET 2019. Peer-review under responsibility ofFinite the scientific committee of the Engineering Keywords: Incremental sheet forming; element; Forming errors; ToolManufacturing deflection; System elasticity. Society International Conference 2017. Keywords: Incremental sheet forming; Finite element; Forming errors; Tool deflection; System elasticity.
Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction * Corresponding author. Tel.: +44-0115 8467391;
address: author. [email protected] *E-mail Corresponding Tel.: +44-0115 8467391; The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789 © 2018 The Authors. Published by Elsevier B.V. in several ways: tons of production, available hours of manufacturing, etc. The management of the idle capacity This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2351-9789 © 2018 Thearticle Authors. Published by Elsevier B.V. * Paulo Tel.: article +351 253 510 +351 604 741 Selection and under responsibility of the 253 organizing committee of SHEMET 2019. This is anAfonso. openpeer-review access under the761; CCfax: BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail address: [email protected] Selection and peer-review under responsibility of the organizing committee of SHEMET 2019.
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the organizing committee of SHEMET 2019. 10.1016/j.promfg.2019.02.106
60 2
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
Introduction Incremental sheet forming (ISF) is a relative new sheet metal forming process. The key concept is to use a specific tool traveling along pre-defined toolpath on a clamped sheet to generate local deformation to form the sheet to the desired shape. During the process, the movement of the tools replaces dies which leads to the enhanced flexibility and reduced cost as compared with the conventional sheet forming methods, e.g. deep drawing and stamping. Extensive research on ISF in the past two decades has shown the potential of applications in automotive and aerospace industries [1]. Single point incremental forming (Fig.1 (a)) and two point incremental forming (TPIF) (Fig.1 (b)), separately using single tool and a tool with a partial die are two ISF variations of mainstream studies. Double-sided incremental forming is another variant of ISF, which gives benefit of improved formability and geometric accuracy. The supporting tool is implemented in the DSIF process on the other side of the workpiece, providing additional controllability and stability (Fig. 1(c)). A core question to DSIF focused research is how to avoid the loss of contact problem, described as the support tool separates from the bottom surface of the workpiece due to the continuous material thinning during the forming process [2]. Two solutions are developed based on the position control or use of flexible support. The position control method optimises the toolpath of the support tool according to the error prediction by using such as FE or the feedback of force sensors to monitoring the contacting condition [3-7]. The flexible support method is generally conducted by using a pneumatic system, which automatically compensates for the gap between the sheet and the supporting tool on the vertical direction [8-10]. The toolpath optimisation is a mainstream in DSIF, whilst the method using flexible supporting tool is barely studied. The objective of this paper is to investigate the characteristics and the causes of the “over-bending” phenomenon, based on a series of experiments on a dedicated DSIF machine using a pneumatic cylinder. FE simulation is used to verify the experimental data through specifically defined toolpath incorporating the effect of machine deflection. Potential ways for improvement are discussed and suggestions are made for future design of DSIF of toolpath and machine systems.
Fig. 1. Schematics of ISF processes (a) SPIF (b) TPIF (c) DSIF.
Assumption of the “over-bending” phenomenon in DSIF The enhancement of formability in the DSIF process is regarded as a contribution from the stabilisation effect brought by the additional support. However, there are few investigation about the negative effect led by the disposition of the support tool. In pneumatic-assisted DSIF process, the excessive bending, referred as “over-bending” phenomenon, could happen due to the forming error including the clearances and deflection of machine and tools. In this study, the deflection of the slave tool is neglected due to the force on the bottom tool is totally generated by the compression of the sheet material and is relatively small compared with the forming force [6]. Fig. 2 shows the generation and evolution of the “over-bending” phenomenon. Due to the sheet thinning (∆𝛿𝛿𝑠𝑠 ) and tools deformation ([∆𝛿𝛿𝑡𝑡 ]), the distance between tools should keep increasing during the forming process as the forming forces increase. Thus the support tool moves upward and generates a bending effect (Fig. 2(a)). Consequently the slave tool no longer squeezes the workpiece but takes friction and stretching force, and works as a secondary forming tool. However, the relatively rigid fixture in the horizontal direction forces the support tool to continuously bend the formed region when it travels towards the cone centre along the pre-defined tool path (Fig. 2(b)). As a result, a vertical wall shape is formed in the end of the process, which shows as the “over-bending” phenomenon.
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng / Procedia Manufacturing 00 (2018) 000–000
61 3
Fig. 2. Assumption for the occurrence of "over-bending" problem: (a) master tool deflection result in excessive compensation of the support tool (b) "over-bending" occurs by the slave tool moving towards cone centre.
Experiment parameters 3.1.Experimental equipment and material The DSIF processes with pneumatic supporting system were conducted by using a dedicated machine [9]. The working space was limited to a fixture size of 158 mm x 158 mm. Semi-spherical tools of 10mm radius were used for both master and slave tool. The support force was provided by an air cylinder and determined by the pressure of compress air set at 300 N. Aluminium 5052-O was chosen as the test material. The sheet size was 180 mm x 180 mm with thickness of 1.0 mm. A truncated cone of 100 mm upper diameter was the designed shape to be formed. The lower diameter and forming depth was determined by the wall angle. Two sets of tests (45°wall angle for 32.5 mm depth and 60°wall angle for 35.5mm depth) were selected. For each wall angle, there were two samples to be made separately with and without support force for the sake of comparison. The helical tool paths were generated by MATLAB code with the step depth of 0.5 mm when the overall feed speed was fixed to 800 mm/min. Rocol Rtd cutting compound was used for lubrication during the forming process. 3.2. FE modelling As the metal sheet was assumed to be fully fixed, a 156mm x 156mm x 1mm sheet model was created with encastre boundary condition on the fringe area (Fig.3(a)). Both tools were defined as 10mm radius semi-spherical shell of analytical rigid property to avoid unexpected distortion during the forming process. A connector element was connected to the support tool, defined by non-linear elasticity and offering a constant upward force of 300 N also alldirection constraint besides the vertical direction. The density of the material was defined to be 2.68 g/cc, when young’s modulus was set at 7.03 GPa and poission’s ratio at 0.33. The plasticity definition followed swift’s strain hardening law for 𝜎𝜎 = 𝑘𝑘(𝜀𝜀0 + 𝜀𝜀)𝑛𝑛 , where 𝜀𝜀0 = 0.0416, 𝑘𝑘 = 315 and 𝑛𝑛 = 0.173. The interaction between the tools and workpiece was created as frictionless contact to reduce the simulation time. 4-layer solid brick element (C3D8R) with enhanced hourglassing control was used to define the workpiece. The whole model was separated to the forming and resting region and meshed based on sweep strategy with different mesh density in order to improve the simulation efficiency. The whole model contains 46,320 nodes and 36,764 elements. Mass scaling technique was also used as the minimum step length was limited to 2 × 10−5 s. The simulation was conducted by using ABAQUS/Explicit. The forming process control was made by the modification of toolpaths.
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
62 4
Fig. 3. FE model schematics: (a) Assembly and (b) Modification of toolpath.
Results 4.1.Overall profiles and “over-bending” phenomenon All samples were formed by DSIF without fracture happening (Fig. 4). The outer surface finish indicates the contact condition during the process. It can be seen that the contact ends near the upper flange of the parts made without supporting force, which means that the tool has lost contact to the workpiece in the early stage of the process. Fig. 5 presents the comparison between part profiles and the designed shape. 45°cone parts are closer to the desired geometry than parts of 60°cone. For the 45°cone, the transfer from unformed to formed region is more apparent on the samples made with flexible support. However, a sudden change of curvature is specifically noticeable in the wall area on the part of 60°wall angle, fabricated with supporting force, which may be noted as the “over-bending” phenomenon. The “over-bending” characteristic is barely reported in the past literatures of either SPIF or DSIF field. The investigation to the causes of this phenomenon is beneficial to improve the forming accuracy of the DSIF process with flexible support.
Fig. 4. Parts formed with or without the supporting force.
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng / Procedia Manufacturing 00 (2018) 000–000
63 5
4.2.Thickness distribution The excessive thinning of workpiece during the forming process is a main reason of geometric error and the loss of contact. There is possibility that the sheet thinning releases space for the support tool traveling upward under the force of pneumatic system. This assumption also explains the “over-bending” phenomenon occurring on the part with the steeper wall due to the larger thickness reduction. The thickness distribution along radius for parts of 60° is plotted in Fig. 5 (b). The “over-bending” phenomenon shows a minor shift and the concentration of the thickness reduction in the bending and vertical wall area. However, the peak values of the thickness in both parts are close to 0.4mm and only 0.1mm difference from the sine law predicted value of 0.5 mm, which is barely sufficient to result in such geometry error. The tool and machine deflection due to forming forces needs to be involved in consideration as a potential cause of the forming error. 35
1,3
desired profile Profile-45deg without support force Profile-45deg with support force Thickness-45deg without support force Thickness-45deg with support force
30
1,2 1,1
25
40
Profile-60deg without support force Profile-60deg with support force Desired Profile Thickness-60deg without support force Thickness-60deg with support force
35 30
0,7
0,9
20
0,8 0,7
15
0,6
10
0,5 5 0 0
10
20
30
40
50
60
Distance to cone centre /mm
(a)
70
80
90
0,6
10
0,4
5
0,3
0
1,1
Thickness /mm
0,8
15
25
Depth /mm
Thickness /mm
Depth /mm
0,9
1,2
1
1
20
1,3
0,5 0,4 0,3 0
10
20
30
40
50
60
Distance to cone centre /mm
70
80
90
(b)
Fig. 5. Overall geometry profiles and thickness distribution along the radius direction (a) 45 deg cones (b) 60 deg cones.
4.3.FE simulation To verify the effect of tool displacement, FE simulation was conducted with the consideration of possible tool shift and deformation under DSIF processing conditions. A specific toolpath was defined and applied on the top tool to simulate the machine deflection (Fig. 3(b)). This toolpath was extracted based on the geometry of the 60° cone part made without the support force. There are two reasons for choosing the part formed by the DSIF without supporting force as a reference of tool deflection. First, the additional bending changed the geometry of the part formed with flexible tool which could no longer reflect the traveling path of the master tool during the process. Then, the distinction between the forming forces of SPIF and DSIF is equal to the force given by the support tool [6]. In this test, the supporting force was defined as a constant value at about 300 N. Comparing to the major forming forces, the additional displacement caused by the supporting force could be negligible in the simulation. The geometry and thickness results from the FE simulation is plotted and compared with the 60° sample appearing “over-bending” phenomenon in Fig. 5. The FE result and the experimental test agree well on the thickness distribution and the position of the over-bending. Meanwhile, the current FE model still has some differences especially on the region of the cone top and bottom. There are still some discrepancies on the thickness prediction from FE simulation. These errors may be contributed to the reduction of system stiffness and stability due to the artificially increased feed rate, coarse mesh or the differences of material properties. However, this comparison can be an evidence of the aforementioned assumption that the “over-bending” phenomenon is caused by the deflection of the master tool. The accurately predicted bending location also gives a hint that the completed geometry is only determined by the
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
64 6
trajectory and supporting force on the support tool since “over-bending” has started. It means the FE may predict whether and where the “over-bending” issue will happen even though the actual movement of the master tool is approximately defined in this FE simulation.
(a) 35 30
Depth /mm
1,3
Geometry by simulation Profile-60deg with support force Thickness by simulation Thickness-60deg with support force
1,2 1,1 1
25
0,9 0,8
20
0,7
15
0,6
10
Thickness /mm
40
0,5
5
0,4
0
0,3 0
10
20
30
40
50
60
Distance to cone centre /mm
70
80
90
(b) Fig. 6. (a) Equivalent strain result in FE model (b) Comparison of geometry and thickness result from FEA and experiments.
Discussion The pneumatic supporting system provides automatic compensation and also the ability of forming to the support tool. This characteristic may also enlarge the misplacement of the tools’ relative position. Fig. 7 shows the potential positional deflection in the forming process. According to the sine law, the relative position of two tools in DSIF process can be defined as the equations below: 𝑡𝑡𝑓𝑓 = 𝑡𝑡0 ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(1)
𝑆𝑆 = (2𝑟𝑟 + 𝑡𝑡𝑓𝑓 ) ∙ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
(3)
𝐷𝐷 = (2𝑟𝑟 + 𝑡𝑡𝑓𝑓 ) ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(2)
Wenxuan Peng et al. / Procedia Manufacturing (2019) 59–66 Wenxuan Peng / Procedia Manufacturing 00 (2018)29 000–000 𝑆𝑆
657
𝛽𝛽 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎( )
(4)
𝐹𝐹𝑐𝑐 = 𝐹𝐹2𝑧𝑧 ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(5)
∆𝐷𝐷 = (∆𝛿𝛿 + 𝑆𝑆) ∙ 𝑡𝑡𝑡𝑡𝑡𝑡(𝛽𝛽) − 𝐷𝐷
(6)
𝐷𝐷
Where 𝑡𝑡𝑓𝑓 represents the thickness of the formed wall and 𝑟𝑟 is the tool radius. 𝛽𝛽 is the angle between the connecting line 𝑂𝑂1 𝑂𝑂2 and the vertical direction. D and S are respectively the distance between tools in the vertical and horizontal direction. The support force 𝐹𝐹2𝑧𝑧 and the reaction force due to compression 𝐹𝐹𝑐𝑐 following the equation (5), which is:
In ideal condition, β is equal to pre-defined wall angle α and 𝑂𝑂1 𝑂𝑂2 is normal to the sheet surface during the forming process. Thus, the support force generates compression and leads to formability improvement. However, the machine deflection increases 𝑆𝑆 and decreases 𝐷𝐷 due to the automatic compensation of the support tool. According to equations (4-5), 𝛽𝛽 rises and 𝐹𝐹𝑐𝑐 reduces which means the compressive effect is reduced as well. Additionally, the support tool causes a moment with the master tool in the local deformation area due to 𝑂𝑂1 𝑂𝑂2 is no longer perpendicular to the sheet plane. The horizontal rigidity of the support tool generates increasing reaction force 𝐹𝐹2𝑟𝑟 when tools moving towards cone centre. Therefore, the formability is decreased because of the disposition of tools and the bending occurs on the region between tools. It can also be inferred that the “over-bending” is more likely to happen when forming parts with higher wall angle due to the larger defection caused by the increased forming force. The steeper wall enlarges the effect of positional errors to the auto-compensation of the support tool, where the displacement for compensation equals to ∆𝐷𝐷 and can be calculated by the horizontal deflection ∆𝛿𝛿: ∆𝐷𝐷 rises as 𝛽𝛽 increases. The minimum value of 𝛽𝛽 equals to the desired wall angle 𝛼𝛼, which indicates the steeper the formed shape is, the easier the “over-bending” would occur during the process. In conclusion, the adjustment to avoid the reduction of formability by “over-bending” effect needs to be configured in the DSIF process using flexible support. A possible solution is to increase the machine and tool stiffness to reduce the defection (∆𝛿𝛿) on the master tool. Alternatively, a compensated toolpath can be considered based on the determined system stiffness and clearances, associated with the prediction given by FE simulation. This positional correction is expected to be effective to avoid the negative effect of the support tool to the process formability.
Fig. 7. Forces and tools’ relative positions in local deformation area in DSIF: (a). Ideal condition (b). “Over-bending”.
66 8
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
Conclusions This study discussed a geometric error, called “over-bending” phenomenon, specifically occurring in the DSIF process with constant support and contact when forming parts with large wall angles. A hypothesis was made about the potential formability reduction, activated by system stiffness and caused by the flexible support tool. There were overall 4 tests being conducted by using a dedicated DSIF machine. The surface finishing comparison exhibits that the pneumatic-assisted processes could efficiently prevent the loss of contact. However, the sudden change of crosssection curvature was particularly observed on the part of high wall angle formed through the DSIF with the support force. The results are presented and compared in terms of thickness distribution, which shows 0.1 mm difference between the measured and sine law predicted values. Thus, the continuous decrease of thickness is expected from the main factor causing such a geometric error. Comparing the results obtained from experiments and FE simulation, the “over-bending” phenomenon is initially caused by the deformation of the tool and machine, then being amplified by the supporting force and spirally inward movement of the slave tool. This conclusion leads to discussions for the initial condition of the “over-bending” phenomenon and the methods of prevention. The “over-bending” is caused by the deflection of machine and tools, which is more likely to occur in DSIF forming high wall angle parts or the system has insufficient stiffness, e.g. with a robotic system. It is suggested that improving the machine stiffness or incorporating the machine deflection into the toolpath design is sufficient to avoid the occurrence of the “overbending” phenomenon in DSIF.
Reference [1] W.C. Emmens, G. Sebastiani, A.H. van den Boogaard, The technology of Incremental Sheet Forming—A brief review of the history, Journal of Materials Processing Technology 210(8) (2010) 981-997. [2] E. Maidagan, J. Zettler, M. Bambach, P.P. Rodríguez, G. Hirt, A New Incremental Sheet Forming Process Based on a Flexible Supporting Die System, Key Engineering Materials 344 (2007) 607-614. [3] L. Rakesh, S. Amit, N.V. Reddy, Deflection Compensations for Tool Path to Enhance Accuracy During Double-Sided Incremental Forming, Journal of Manufacturing Science and Engineering 138(9) (2016) 091008. [4] E. Ndip-Agbor, K. Ehmann, J. Cao, Automated Flexible Forming Strategy for Geometries With Multiple Features in Double-Sided Incremental Forming, Journal of Manufacturing Science and Engineering 140(3) (2017) 031004. [5] R. Lingam, A. Bhattacharya, J. Asghar, N.V. Reddy, Compensations for tool path to enhance accuracy during double sided incremental forming, ASME 2015 International Manufacturing Science and Engineering Conference, American Society of Mechanical Engineers, 2015, pp. V001T02A094-V001T02A094. [6] H. Ren, F. Li, N. Moser, D. Leem, T. Li, K. Ehmann, J. Cao, General contact force control algorithm in double-sided incremental forming, CIRP Annals 67(1) (2018) 381-384. [7] H. Meier, B. Buff, R. Laurischkat, V. Smukala, Increasing the part accuracy in dieless robot-based incremental sheet metal forming, CIRP Annals - Manufacturing Technology 58(1) (2009) 233-238. [8] B. Lu, Y. Fang, D.K. Xu, J. Chen, S. Ai, H. Long, H. Ou, J. Cao, Investigation of material deformation mechanism in double side incremental sheet forming, International Journal of Machine Tools and Manufacture 93 (2015) 37-48. [9] H. Wang, R. Zhang, H. Zhang, Q. Hu, J. Chen, Novel strategies to reduce the springback for double-sided incremental forming, The International Journal of Advanced Manufacturing Technology 96(1-4) (2018) 973-979. [10] B. Lu, D.K. Xu, R.Z. Liu, H.A. Ou, H. Long, J. Chen, Cranial Reconstruction Using Double Side Incremental Forming, Key Engineering Materials 639 (2015) 535-542.
ScienceDirect ScienceDirect
Available Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Procedia Manufacturing 00 (2018) 000–000 Procedia Manufacturing 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 29 (2019) 59–66 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
18th International Conference on Sheet Metal, SHEMET 2019 18th International Conference on Sheet Metal, SHEMET 2019
Experimental and finite element investigation of over-bending Experimental and finite element investigation of over-bending phenomenon in Double-Sided Incremental Forming (DSIF) ofJune Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30of phenomenon in Double-Sided Incremental Forming (DSIF) 2017, Vigo (Pontevedra), Spain aluminium sheets aluminium sheets a b Costing models capacity Industry Trade-off Wenxuan Peng a,for Meng Li b, Bin optimization Lu bb, Jun Chen bb, in Adib Becker aa, 4.0: Hengan Ou a,* Wenxuan Peng , Meng Li , Bin Lu , Jun Chen , Adib Becker , Hengan Ou a,* between usedandcapacity and operational efficiency Department of mechanical, Materials Manufacturing Engineering, University of Nottingham, Nottingham, NG9 2AR, UK a a
Plasticityand Technology, Shanghai Jiao Tong University, Shanghai, 200030, China NG9 2AR, UK Department ofbDepartment mechanical, of Materials Manufacturing Engineering, University of Nottingham, Nottingham, b a a,* Jiao Tong University, b b China Department of Plasticity Technology, Shanghai Shanghai, 200030,
A. Santana , P. Afonso , A. Zanin , R. Wernke a
University of Minho, 4800-058 Guimarães, Portugal
b Abstract Unochapecó, 89809-000 Chapecó, SC, Brazil Abstract Double-Sided Incremental forming (DSIF) is a flexible sheet forming method with increasing research interest in the last decade. Double-Sided Incremental forming (DSIF) is a flexible sheet forming with increasing research interest in the last decade. It offers improved formability and accuracy over the conventional singlemethod point incremental forming (SPIF) although it accompanies It offers andcontact accuracy over the forming conventional single point incremental forming (SPIF) it accompanies Abstract with the improved possibilityformability of tools losing during process. Mounting a pneumatic supporting toolalthough is an efficient solution. with the possibility tools losingand contact during the the material forming process. Mounting pneumatic supporting tool isreason an efficient solution. However, the tools of may squeeze over-bend when forming for aa high wall angle. A possible may be due to However, tools may squeeze and over-bend the material when forming for a pushed high wall angle. A finite possible reason may be due to inaccurate prediction ofofmaterial thinning or the effect of tool deflection. This work uses a to modified element (FE) model with Under thethe concept "Industry 4.0", production processes will be be increasingly interconnected, inaccurate toolpath prediction of material thinning orand, the effect ofstiffness tool deflection. This work usesIn a modified finite element model with dedicated incorporated with simplified of tools andefficient. machine in order to reproduce the (FE) effect of system information baseddesign on a real time basis necessarily, much more this context, capacity optimization dedicated toolpath design incorporated with simplified stiffness of tools and the machine in orderoftothe reproduce the effect of value. system elasticity to the process with supporting tool and evaluate over-bending problem. The goes beyond theDSIF traditional aim ofhydraulic capacity maximization, contributing alsoroot for causes organization’s profitability and elasticity to the DSIF process with hydraulic supporting tool and evaluate the root causes of the over-bending problem. numerical results are compared experimentally produced components, focusing on the thickness evaluation and development Indeed, lean management and continuous improvement approaches suggest capacity optimization instead The of numerical are throughout compared with experimentally produced demonstrates components, focusing the evaluation development of the tool results deflection the process. This comparison the effecton thethickness tool deflection upon and formed parts, maximization. The study of capacity optimization and costing models is an of important research topicthethat deserves of the toolthe deflection throughout process. deformation This comparison demonstrates effect of the tool deflection upon formed parts, including geometric error andthe excessive on the wall region.the The conclusion suggests a need forthe a compensation contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical including the geometric errorof and excessive deformation onsystems. the wall region. The conclusion suggests a need for a compensation based approach in the design DISF toolpath and machine model for capacity on and different costing models (ABC and TDABC). A generic model has been based approach in themanagement design of DISFbased toolpath machine systems. developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s © 2018 The Authors. Published by Elsevier B.V. © 2019The The Authors. Published bymaximization Elsevier B.V. vs operational efficiency is highlighted and it is shown that capacity value. trade-off capacity © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an openmight accesshide article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) optimization operational inefficiency. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the organizing committee of of SHEMET SHEMET 2019. 2019. Selection and peer-review under responsibility of the organizing committee © 2017 The Authors. Published Elsevier B.V. Selection and peer-review underby responsibility of the organizing committee of SHEMET 2019. Peer-review under responsibility ofFinite the scientific committee of the Engineering Keywords: Incremental sheet forming; element; Forming errors; ToolManufacturing deflection; System elasticity. Society International Conference 2017. Keywords: Incremental sheet forming; Finite element; Forming errors; Tool deflection; System elasticity.
Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction * Corresponding author. Tel.: +44-0115 8467391;
address: author. [email protected] *E-mail Corresponding Tel.: +44-0115 8467391; The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789 © 2018 The Authors. Published by Elsevier B.V. in several ways: tons of production, available hours of manufacturing, etc. The management of the idle capacity This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2351-9789 © 2018 Thearticle Authors. Published by Elsevier B.V. * Paulo Tel.: article +351 253 510 +351 604 741 Selection and under responsibility of the 253 organizing committee of SHEMET 2019. This is anAfonso. openpeer-review access under the761; CCfax: BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail address: [email protected] Selection and peer-review under responsibility of the organizing committee of SHEMET 2019.
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the organizing committee of SHEMET 2019. 10.1016/j.promfg.2019.02.106
60 2
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
Introduction Incremental sheet forming (ISF) is a relative new sheet metal forming process. The key concept is to use a specific tool traveling along pre-defined toolpath on a clamped sheet to generate local deformation to form the sheet to the desired shape. During the process, the movement of the tools replaces dies which leads to the enhanced flexibility and reduced cost as compared with the conventional sheet forming methods, e.g. deep drawing and stamping. Extensive research on ISF in the past two decades has shown the potential of applications in automotive and aerospace industries [1]. Single point incremental forming (Fig.1 (a)) and two point incremental forming (TPIF) (Fig.1 (b)), separately using single tool and a tool with a partial die are two ISF variations of mainstream studies. Double-sided incremental forming is another variant of ISF, which gives benefit of improved formability and geometric accuracy. The supporting tool is implemented in the DSIF process on the other side of the workpiece, providing additional controllability and stability (Fig. 1(c)). A core question to DSIF focused research is how to avoid the loss of contact problem, described as the support tool separates from the bottom surface of the workpiece due to the continuous material thinning during the forming process [2]. Two solutions are developed based on the position control or use of flexible support. The position control method optimises the toolpath of the support tool according to the error prediction by using such as FE or the feedback of force sensors to monitoring the contacting condition [3-7]. The flexible support method is generally conducted by using a pneumatic system, which automatically compensates for the gap between the sheet and the supporting tool on the vertical direction [8-10]. The toolpath optimisation is a mainstream in DSIF, whilst the method using flexible supporting tool is barely studied. The objective of this paper is to investigate the characteristics and the causes of the “over-bending” phenomenon, based on a series of experiments on a dedicated DSIF machine using a pneumatic cylinder. FE simulation is used to verify the experimental data through specifically defined toolpath incorporating the effect of machine deflection. Potential ways for improvement are discussed and suggestions are made for future design of DSIF of toolpath and machine systems.
Fig. 1. Schematics of ISF processes (a) SPIF (b) TPIF (c) DSIF.
Assumption of the “over-bending” phenomenon in DSIF The enhancement of formability in the DSIF process is regarded as a contribution from the stabilisation effect brought by the additional support. However, there are few investigation about the negative effect led by the disposition of the support tool. In pneumatic-assisted DSIF process, the excessive bending, referred as “over-bending” phenomenon, could happen due to the forming error including the clearances and deflection of machine and tools. In this study, the deflection of the slave tool is neglected due to the force on the bottom tool is totally generated by the compression of the sheet material and is relatively small compared with the forming force [6]. Fig. 2 shows the generation and evolution of the “over-bending” phenomenon. Due to the sheet thinning (∆𝛿𝛿𝑠𝑠 ) and tools deformation ([∆𝛿𝛿𝑡𝑡 ]), the distance between tools should keep increasing during the forming process as the forming forces increase. Thus the support tool moves upward and generates a bending effect (Fig. 2(a)). Consequently the slave tool no longer squeezes the workpiece but takes friction and stretching force, and works as a secondary forming tool. However, the relatively rigid fixture in the horizontal direction forces the support tool to continuously bend the formed region when it travels towards the cone centre along the pre-defined tool path (Fig. 2(b)). As a result, a vertical wall shape is formed in the end of the process, which shows as the “over-bending” phenomenon.
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng / Procedia Manufacturing 00 (2018) 000–000
61 3
Fig. 2. Assumption for the occurrence of "over-bending" problem: (a) master tool deflection result in excessive compensation of the support tool (b) "over-bending" occurs by the slave tool moving towards cone centre.
Experiment parameters 3.1.Experimental equipment and material The DSIF processes with pneumatic supporting system were conducted by using a dedicated machine [9]. The working space was limited to a fixture size of 158 mm x 158 mm. Semi-spherical tools of 10mm radius were used for both master and slave tool. The support force was provided by an air cylinder and determined by the pressure of compress air set at 300 N. Aluminium 5052-O was chosen as the test material. The sheet size was 180 mm x 180 mm with thickness of 1.0 mm. A truncated cone of 100 mm upper diameter was the designed shape to be formed. The lower diameter and forming depth was determined by the wall angle. Two sets of tests (45°wall angle for 32.5 mm depth and 60°wall angle for 35.5mm depth) were selected. For each wall angle, there were two samples to be made separately with and without support force for the sake of comparison. The helical tool paths were generated by MATLAB code with the step depth of 0.5 mm when the overall feed speed was fixed to 800 mm/min. Rocol Rtd cutting compound was used for lubrication during the forming process. 3.2. FE modelling As the metal sheet was assumed to be fully fixed, a 156mm x 156mm x 1mm sheet model was created with encastre boundary condition on the fringe area (Fig.3(a)). Both tools were defined as 10mm radius semi-spherical shell of analytical rigid property to avoid unexpected distortion during the forming process. A connector element was connected to the support tool, defined by non-linear elasticity and offering a constant upward force of 300 N also alldirection constraint besides the vertical direction. The density of the material was defined to be 2.68 g/cc, when young’s modulus was set at 7.03 GPa and poission’s ratio at 0.33. The plasticity definition followed swift’s strain hardening law for 𝜎𝜎 = 𝑘𝑘(𝜀𝜀0 + 𝜀𝜀)𝑛𝑛 , where 𝜀𝜀0 = 0.0416, 𝑘𝑘 = 315 and 𝑛𝑛 = 0.173. The interaction between the tools and workpiece was created as frictionless contact to reduce the simulation time. 4-layer solid brick element (C3D8R) with enhanced hourglassing control was used to define the workpiece. The whole model was separated to the forming and resting region and meshed based on sweep strategy with different mesh density in order to improve the simulation efficiency. The whole model contains 46,320 nodes and 36,764 elements. Mass scaling technique was also used as the minimum step length was limited to 2 × 10−5 s. The simulation was conducted by using ABAQUS/Explicit. The forming process control was made by the modification of toolpaths.
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
62 4
Fig. 3. FE model schematics: (a) Assembly and (b) Modification of toolpath.
Results 4.1.Overall profiles and “over-bending” phenomenon All samples were formed by DSIF without fracture happening (Fig. 4). The outer surface finish indicates the contact condition during the process. It can be seen that the contact ends near the upper flange of the parts made without supporting force, which means that the tool has lost contact to the workpiece in the early stage of the process. Fig. 5 presents the comparison between part profiles and the designed shape. 45°cone parts are closer to the desired geometry than parts of 60°cone. For the 45°cone, the transfer from unformed to formed region is more apparent on the samples made with flexible support. However, a sudden change of curvature is specifically noticeable in the wall area on the part of 60°wall angle, fabricated with supporting force, which may be noted as the “over-bending” phenomenon. The “over-bending” characteristic is barely reported in the past literatures of either SPIF or DSIF field. The investigation to the causes of this phenomenon is beneficial to improve the forming accuracy of the DSIF process with flexible support.
Fig. 4. Parts formed with or without the supporting force.
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng / Procedia Manufacturing 00 (2018) 000–000
63 5
4.2.Thickness distribution The excessive thinning of workpiece during the forming process is a main reason of geometric error and the loss of contact. There is possibility that the sheet thinning releases space for the support tool traveling upward under the force of pneumatic system. This assumption also explains the “over-bending” phenomenon occurring on the part with the steeper wall due to the larger thickness reduction. The thickness distribution along radius for parts of 60° is plotted in Fig. 5 (b). The “over-bending” phenomenon shows a minor shift and the concentration of the thickness reduction in the bending and vertical wall area. However, the peak values of the thickness in both parts are close to 0.4mm and only 0.1mm difference from the sine law predicted value of 0.5 mm, which is barely sufficient to result in such geometry error. The tool and machine deflection due to forming forces needs to be involved in consideration as a potential cause of the forming error. 35
1,3
desired profile Profile-45deg without support force Profile-45deg with support force Thickness-45deg without support force Thickness-45deg with support force
30
1,2 1,1
25
40
Profile-60deg without support force Profile-60deg with support force Desired Profile Thickness-60deg without support force Thickness-60deg with support force
35 30
0,7
0,9
20
0,8 0,7
15
0,6
10
0,5 5 0 0
10
20
30
40
50
60
Distance to cone centre /mm
(a)
70
80
90
0,6
10
0,4
5
0,3
0
1,1
Thickness /mm
0,8
15
25
Depth /mm
Thickness /mm
Depth /mm
0,9
1,2
1
1
20
1,3
0,5 0,4 0,3 0
10
20
30
40
50
60
Distance to cone centre /mm
70
80
90
(b)
Fig. 5. Overall geometry profiles and thickness distribution along the radius direction (a) 45 deg cones (b) 60 deg cones.
4.3.FE simulation To verify the effect of tool displacement, FE simulation was conducted with the consideration of possible tool shift and deformation under DSIF processing conditions. A specific toolpath was defined and applied on the top tool to simulate the machine deflection (Fig. 3(b)). This toolpath was extracted based on the geometry of the 60° cone part made without the support force. There are two reasons for choosing the part formed by the DSIF without supporting force as a reference of tool deflection. First, the additional bending changed the geometry of the part formed with flexible tool which could no longer reflect the traveling path of the master tool during the process. Then, the distinction between the forming forces of SPIF and DSIF is equal to the force given by the support tool [6]. In this test, the supporting force was defined as a constant value at about 300 N. Comparing to the major forming forces, the additional displacement caused by the supporting force could be negligible in the simulation. The geometry and thickness results from the FE simulation is plotted and compared with the 60° sample appearing “over-bending” phenomenon in Fig. 5. The FE result and the experimental test agree well on the thickness distribution and the position of the over-bending. Meanwhile, the current FE model still has some differences especially on the region of the cone top and bottom. There are still some discrepancies on the thickness prediction from FE simulation. These errors may be contributed to the reduction of system stiffness and stability due to the artificially increased feed rate, coarse mesh or the differences of material properties. However, this comparison can be an evidence of the aforementioned assumption that the “over-bending” phenomenon is caused by the deflection of the master tool. The accurately predicted bending location also gives a hint that the completed geometry is only determined by the
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
64 6
trajectory and supporting force on the support tool since “over-bending” has started. It means the FE may predict whether and where the “over-bending” issue will happen even though the actual movement of the master tool is approximately defined in this FE simulation.
(a) 35 30
Depth /mm
1,3
Geometry by simulation Profile-60deg with support force Thickness by simulation Thickness-60deg with support force
1,2 1,1 1
25
0,9 0,8
20
0,7
15
0,6
10
Thickness /mm
40
0,5
5
0,4
0
0,3 0
10
20
30
40
50
60
Distance to cone centre /mm
70
80
90
(b) Fig. 6. (a) Equivalent strain result in FE model (b) Comparison of geometry and thickness result from FEA and experiments.
Discussion The pneumatic supporting system provides automatic compensation and also the ability of forming to the support tool. This characteristic may also enlarge the misplacement of the tools’ relative position. Fig. 7 shows the potential positional deflection in the forming process. According to the sine law, the relative position of two tools in DSIF process can be defined as the equations below: 𝑡𝑡𝑓𝑓 = 𝑡𝑡0 ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(1)
𝑆𝑆 = (2𝑟𝑟 + 𝑡𝑡𝑓𝑓 ) ∙ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
(3)
𝐷𝐷 = (2𝑟𝑟 + 𝑡𝑡𝑓𝑓 ) ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(2)
Wenxuan Peng et al. / Procedia Manufacturing (2019) 59–66 Wenxuan Peng / Procedia Manufacturing 00 (2018)29 000–000 𝑆𝑆
657
𝛽𝛽 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎( )
(4)
𝐹𝐹𝑐𝑐 = 𝐹𝐹2𝑧𝑧 ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(5)
∆𝐷𝐷 = (∆𝛿𝛿 + 𝑆𝑆) ∙ 𝑡𝑡𝑡𝑡𝑡𝑡(𝛽𝛽) − 𝐷𝐷
(6)
𝐷𝐷
Where 𝑡𝑡𝑓𝑓 represents the thickness of the formed wall and 𝑟𝑟 is the tool radius. 𝛽𝛽 is the angle between the connecting line 𝑂𝑂1 𝑂𝑂2 and the vertical direction. D and S are respectively the distance between tools in the vertical and horizontal direction. The support force 𝐹𝐹2𝑧𝑧 and the reaction force due to compression 𝐹𝐹𝑐𝑐 following the equation (5), which is:
In ideal condition, β is equal to pre-defined wall angle α and 𝑂𝑂1 𝑂𝑂2 is normal to the sheet surface during the forming process. Thus, the support force generates compression and leads to formability improvement. However, the machine deflection increases 𝑆𝑆 and decreases 𝐷𝐷 due to the automatic compensation of the support tool. According to equations (4-5), 𝛽𝛽 rises and 𝐹𝐹𝑐𝑐 reduces which means the compressive effect is reduced as well. Additionally, the support tool causes a moment with the master tool in the local deformation area due to 𝑂𝑂1 𝑂𝑂2 is no longer perpendicular to the sheet plane. The horizontal rigidity of the support tool generates increasing reaction force 𝐹𝐹2𝑟𝑟 when tools moving towards cone centre. Therefore, the formability is decreased because of the disposition of tools and the bending occurs on the region between tools. It can also be inferred that the “over-bending” is more likely to happen when forming parts with higher wall angle due to the larger defection caused by the increased forming force. The steeper wall enlarges the effect of positional errors to the auto-compensation of the support tool, where the displacement for compensation equals to ∆𝐷𝐷 and can be calculated by the horizontal deflection ∆𝛿𝛿: ∆𝐷𝐷 rises as 𝛽𝛽 increases. The minimum value of 𝛽𝛽 equals to the desired wall angle 𝛼𝛼, which indicates the steeper the formed shape is, the easier the “over-bending” would occur during the process. In conclusion, the adjustment to avoid the reduction of formability by “over-bending” effect needs to be configured in the DSIF process using flexible support. A possible solution is to increase the machine and tool stiffness to reduce the defection (∆𝛿𝛿) on the master tool. Alternatively, a compensated toolpath can be considered based on the determined system stiffness and clearances, associated with the prediction given by FE simulation. This positional correction is expected to be effective to avoid the negative effect of the support tool to the process formability.
Fig. 7. Forces and tools’ relative positions in local deformation area in DSIF: (a). Ideal condition (b). “Over-bending”.
66 8
Wenxuan Peng et al. / Procedia Manufacturing 29 (2019) 59–66 Wenxuan Peng. / Procedia Manufacturing 00 (2018) 000–000
Conclusions This study discussed a geometric error, called “over-bending” phenomenon, specifically occurring in the DSIF process with constant support and contact when forming parts with large wall angles. A hypothesis was made about the potential formability reduction, activated by system stiffness and caused by the flexible support tool. There were overall 4 tests being conducted by using a dedicated DSIF machine. The surface finishing comparison exhibits that the pneumatic-assisted processes could efficiently prevent the loss of contact. However, the sudden change of crosssection curvature was particularly observed on the part of high wall angle formed through the DSIF with the support force. The results are presented and compared in terms of thickness distribution, which shows 0.1 mm difference between the measured and sine law predicted values. Thus, the continuous decrease of thickness is expected from the main factor causing such a geometric error. Comparing the results obtained from experiments and FE simulation, the “over-bending” phenomenon is initially caused by the deformation of the tool and machine, then being amplified by the supporting force and spirally inward movement of the slave tool. This conclusion leads to discussions for the initial condition of the “over-bending” phenomenon and the methods of prevention. The “over-bending” is caused by the deflection of machine and tools, which is more likely to occur in DSIF forming high wall angle parts or the system has insufficient stiffness, e.g. with a robotic system. It is suggested that improving the machine stiffness or incorporating the machine deflection into the toolpath design is sufficient to avoid the occurrence of the “overbending” phenomenon in DSIF.
Reference [1] W.C. Emmens, G. Sebastiani, A.H. van den Boogaard, The technology of Incremental Sheet Forming—A brief review of the history, Journal of Materials Processing Technology 210(8) (2010) 981-997. [2] E. Maidagan, J. Zettler, M. Bambach, P.P. Rodríguez, G. Hirt, A New Incremental Sheet Forming Process Based on a Flexible Supporting Die System, Key Engineering Materials 344 (2007) 607-614. [3] L. Rakesh, S. Amit, N.V. Reddy, Deflection Compensations for Tool Path to Enhance Accuracy During Double-Sided Incremental Forming, Journal of Manufacturing Science and Engineering 138(9) (2016) 091008. [4] E. Ndip-Agbor, K. Ehmann, J. Cao, Automated Flexible Forming Strategy for Geometries With Multiple Features in Double-Sided Incremental Forming, Journal of Manufacturing Science and Engineering 140(3) (2017) 031004. [5] R. Lingam, A. Bhattacharya, J. Asghar, N.V. Reddy, Compensations for tool path to enhance accuracy during double sided incremental forming, ASME 2015 International Manufacturing Science and Engineering Conference, American Society of Mechanical Engineers, 2015, pp. V001T02A094-V001T02A094. [6] H. Ren, F. Li, N. Moser, D. Leem, T. Li, K. Ehmann, J. Cao, General contact force control algorithm in double-sided incremental forming, CIRP Annals 67(1) (2018) 381-384. [7] H. Meier, B. Buff, R. Laurischkat, V. Smukala, Increasing the part accuracy in dieless robot-based incremental sheet metal forming, CIRP Annals - Manufacturing Technology 58(1) (2009) 233-238. [8] B. Lu, Y. Fang, D.K. Xu, J. Chen, S. Ai, H. Long, H. Ou, J. Cao, Investigation of material deformation mechanism in double side incremental sheet forming, International Journal of Machine Tools and Manufacture 93 (2015) 37-48. [9] H. Wang, R. Zhang, H. Zhang, Q. Hu, J. Chen, Novel strategies to reduce the springback for double-sided incremental forming, The International Journal of Advanced Manufacturing Technology 96(1-4) (2018) 973-979. [10] B. Lu, D.K. Xu, R.Z. Liu, H.A. Ou, H. Long, J. Chen, Cranial Reconstruction Using Double Side Incremental Forming, Key Engineering Materials 639 (2015) 535-542.