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Numerical simulation of single and dual pass conventional spinning processes

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Due to the complex nature of sheet metal spinning processes, recent trends in analysis of the process are moving toward numerical techniques. These numerical methods, for instance finite element modelling, enable the study of parameters that can not
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  ORIGINAL RESEARCH Numerical simulation of single and dual pass conventionalspinning processes Khamis Essa  &  Peter Hartley Received: 11 March 2009 /Accepted: 29 June 2009 /Published online: 30 July 2009 # Springer/ESAFORM 2009 Abstract  Due to the complex nature of sheet metalspinning processes, recent trends in analysis of the processare moving toward numerical techniques. These numericalmethods, for instance finite element modelling, enable thestudy of parameters that can not easily be measured directlysuch as transient strains and stresses. Additionally, it allowsa prediction of dynamic instabilities that may be used tocontrol and achieve better product quality. In this investi-gation, a finite element dynamic explicit model has beenused to simulate single and dual pass conventional spinning processes. The initial models are validated against pub-lished experimental data and show very good correlation. Avariety of roller feed rates, roller passes and roller configurations are then simulated. Effects of roller feedrate on the axial force, radial force and thickness strain areestablished. The effect of roller pass and roller configura-tion on the axial force and thickness strain are alsoassessed. Keyword  Conventionalspinning.Finiteelementanalysis.ABAQUS/Explicit .Loadratescaling.Dualpass.Rollerconfiguration Introduction In conventional spinning, a circular sheet is clamped between a rotating mandrel and supporting holder and thesheet is gradually shaped over this rotating mandrel throughthe action of a roller that produces a localised pressure andmoves axially over the outer surface of the sheet to producea symmetrical product.Metal spinning is one of a number of flexible sheet forming processes in which the sheet deformation isimparted incrementally through a localised contact region between the deforming sheet and forming tools. Theattention of research into sheet metal spinning has increasedover recent years largely due to an increase in the demandfor parts in the transportation industries [1]. The trends in these industries are aimed at producing parts manufacturedwith very high strength to weight ratios and with low cost.For axi-symmetric components spinning processes are veryefficient in achieving these characteristics. There is arelatively low cost of the spinning tools and the inherent flexibility of the process lends itself to rapid changes tomanufacture different geometries of components. Sheet metal spinning has a wide variety of applications including parts for the automotive and aerospace industries, musicalinstruments, art objects and kitchenware. Some typicalexamples of these parts are components of jet engines andturbines, radar reflectors, satellite nose cones and homeutensils. The products produced by spinning have diametersranging from 0.003 m to 10 m and thicknesses rangingfrom 0.4 mm to 25 mm [2].Despite the extensive use of numerical modellingtechniques for the simulation of metal forming processes,it is still rarely used in sheet metal spinning when comparedto experimental achievements. This is most likely due tonumerical complexities associated with the localised con-tact between the tool and workpiece and the need for a fullthree-dimensional model to simulate the process. Thesedifficulties however, no longer present a major obstacle asmodern commercial finite-element software and high- K. Essa : P. Hartley ( * )School of Mechanical Engineering,College of Engineering and Physical Sciences,University of Birmingham,Edgbaston,Birmingham B15 2TT, UK e-mail: p.hartley@bham.ac.uk Int J Mater Form (2009) 2:271  –  281DOI 10.1007/s12289-009-0602-x   power computing facilities can overcome such problems. It is now possible to complete full three-dimensional simu-lations of the process, including the non-linear geometricand material effects, much more quickly than for anexperimental assessment. The principal requirements of any numerical simulation are to ensure that the materialdata, tool motion, surface interaction and lubricationconditions are reproduced accurately in the model in order to provide process data that are realistic. A numericalmodelling approach can be a very efficient tool for reducingthe cost of tool design and manufacturing development time by providing a detailed insight into the deformationcharacteristics of the sheet that is not obvious, or obtainable,from experimental observation. The computer models of the process permit a systematic study of the influence of important process parameters such as feed rate, lubrication,tool design and workpiece material.The modelling of conventional spinning using multi-domain finite element (FE) models has been proposed byQuigley and Monaghan [3]. The principal motivation of  this investigation was to reduce the simulation time bysharing the computational requirements of the FE model between numbers of machines called domains to solve theentire model. They concluded that the use of multi-domainfinite element models will encourage an increase in thesimulation of incremental forming processes. Liu [4] simulated multi-pass and die-less conventional spinning processes by applying the dynamic explicit LS-DYNAfinite element software. Die-less conventional spinningwith multiple passes can be effectively applied if the sheet material has sufficient rigidity to retain the formed shapeduring the process and has lower tool costs than spinningwith a specific mandrel. Liu applied different combinationsof roller types, element numbers and adaptive mesh control.While the element size is determined principally by themesh thickness, Liu concluded that the element size of thesheet must be less than that in the tools in order to ensure areasonable model of contact between them. Long andHamilton [5] developed a three dimensional FE model for single-pass conventional spinning of cylindrical cups usingthe ABAQUS/Explicit formulation. They presented thestrain distribution in three perpendicular directions, i.e.thickness, hoop and radial directions. For the conventionalspinning process, the radial stress component which leadsto material flow in the axial direction along the mandrel,causes thinning of the sheet. However, this thinning iscompensated by thickening caused by the hoop compres-sive stress. They showed that the magnitude of radial strainis greater than the magnitude of hoop strain and as a result of this difference, a thinning of the spun part takes placenear to the round corner of the mandrel. In further analysisof this model, Hamilton and Long [6] applied different  values of load rate scaling and mass scaling factors in theExplicit FE model, in order to reduce the simulation time.They concluded that both techniques demonstrated asignificant reduction in the simulation time with acceptableaccuracy.These finite element investigations were all concernedwith the spinning of cylindrical cup geometries. Alternativecomponent geometries have been also considered to solve particular problems. For example Zhan et al. [7] constructed a finite element model for cone spinning in order to analysethe effect of feed rate on the forming forces. Theyconcluded that as feed rate increases, all force componentsincrease but the precision of the shape and size decreases.Qian et al. [8] used a finite element model of spinning of  thin-walled shells with an inner rib using the ABAQUS FEsoftware, in order to analyse the springback of the spun product. They found a significant change in the product geometry after removing the tools but with a uniformdistribution of residual stresses after springback. Theyconcluded that the finite element model considering elasticdeformation is very useful to study the deformationmechanism, to determine the correct working parametersand to analyse springback of the workpiece. Liang et al. [9] studied the effect of material parameters in the productionof aluminium alloy automotive wheels and pulleys usingthe  ‘ splitting spinning ’  process by constructing a FE modelusing ABAQUS/Explicit. An increase in the spinning forceand moment was observed as a result of increasing themechanical properties such as modulus of elasticity, yieldstress and strain hardening exponent. They also observedthat an increase in the elastic modulus and a decrease in theyield stress lead to an increase in the degree of inhomoge-neous deformation.The aim of much of the previous finite element modelling work was to study the stresses and strainsgenerated in the process and to investigate means of reducing the simulation time. Other investigations focussedon a specific spinning product. In the investigation presented here, a general dynamic explicit finite element model for single and dual pass conventional spinning processes is developed and used to study the effect of roller feed rate on the axial force, radial force and thicknessstrain during the spinning of cylindrical aluminium cups.Additionally, it shows the effect of using additional passesand different types of roller on the axial force and thicknessstrain which has not been considered previously. Explicit dynamic finite element modelling In this investigation, the commercial ABAQUS/Explicit software [10] is used to simulate the conventional spinning process. The Explicit code uses a central difference methodto integrate the equation of motion explicitly through time. 272 Int J Mater Form (2009) 2:271  –  281  During each increment, the initial kinematic conditions areused to calculate the kinematic conditions for the next increment. The nodal acceleration ( u ) can be calculated at the beginning of time increment ( t  ) based on dynamicequilibrium through Eq. 1 [10].  u j ð t  Þ  ¼  M ð Þ  1 P    I ð Þ  ð t  Þ  ð 1 Þ Where ( M ) is the nodal mass matrix, ( P ) is the vector of the external applied forces and ( I ) is the vector of internalelement forces. Therefore, without the need to solvesimultaneous equations, the acceleration at any nodal point is determined only through its mass and net acting force.From a knowledge of the accelerations, the velocities (   u )and displacements ( u ) are advanced  “ explicitly ”  througheach time increment ( ∆ t  ), as shown in Eqs. 2 and 3 [10].  u j t  þ Δ t  = 2 ð Þ  ¼  u j t   Δ t  = 2 ð Þ  þ Δ t  j t  þ Δ t  ð Þ  þ Δ t  j Δ t  ð Þ   2  u j ð t  Þ  ð 2 Þ u j t  þ Δ t  ð Þ  ¼  u j ð t  Þ  þ  Δ t  j t  þ Δ t  ð Þ  u j ð t  þ Δ t  = 2 Þ  ð 3 Þ In order to obtain accurate results, the time increment ( ∆ t  ) must be quite small so that the accelerations are nearlyconstant during an increment. As the time increment decreases, the analysis will require an unacceptable number of increments and computational time. In order to reducethe computational time, either   “ load rate scaling ”  or   “ massscaling ”  may be introduced. Both techniques show asignificant reduction in the processing times with accept-able computational accuracy [6, 8, 11]. In conventional spinning, the load rate scaling reduces the simulation time by increasing the linear velocity of the roller and therotational speed of the mandrel by the same factor in order to maintain the specified feed rate. Mass scaling reduces thesimulation time by increasing the material density. Neither load rate scaling nor mass scaling must be set too large(which would cause the inertia forces to dominate) and thusaffect the computational accuracy. Numerical models of conventional spinning process As described earlier, conventional spinning involves theforming of a circular sheet which is clamped between arotating mandrel and supporting holder. The sheet isgradually shaped over this rotating mandrel through theaction of a roller that produces a localised pressure andmoves axially over the outer surface of the sheet. In theexample here the mandrel has a diameter of 118 mm androtates with a constant rotational speed of 200 rpm. Analuminium sheet blank with an srcinal diameter of 192 mmand thickness of 3 mm is attached to the mandrel. The holder has a diameter of 112 mm. At the beginning of the FEsimulation, the holder pushes the sheet forward to themandrel with a small constant load of 100 kN in order tokeep the sheet secure between the mandrel and the holder.Thus, the sheet and holder will rotate with the same mandrelspeed. The sheet is spun into a cylindrical cup with aninternal nominal diameter of 118 mm by the conventionalspinning process for three different cases (A, B, C) as shownin Table 1.Case A investigates the influence of feed rate in single pass spinning. Case B considers the effect of introducing asecond pass in the process and case C examines theinfluence of changing the roller geometry in the second pass.The geometries and dimensions of the mandrel, sheet and type 1 roller are taken from Xia et al. [12]. These conditions are also presented in two other investigations byLiu [4] and Long and Hamilton [5]. The dimensions of the type 2 roller are taken from Liu [4] and the holder  dimensions are taken from Long and Hamilton [5]. Thesedetails are shown in Fig. 1.The Mandrel, holder and roller are modelled as rigid bodies, while the sheet is modelled as an elastic-plasticdeformable body using the material properties of purealuminium (A-1100-O). The stress strain curve for thisaluminium is described by,  σ  =148 ε 0.233 , with an initialyield stress of 100 MPa and a mass density of 2,700 kg/m 3 .Isotropic elasticity is assumed with a Young ’ s modulus of 70 GPa and Poisson ’ s ratio 0.3 [5]. The material data are taken from Long and Hamilton [5], srcinally presented inKalpakjian and Schmid [13]. Thermal and rate effects are not included in the present model. Coulomb friction is set with a friction coefficient of 0.2, 0.5 and 0.05 between thesheet and the mandrel, holder and roller respectively asassumed in [5]. Xia et al. [12] did not indicate the lubrication used in their experimental study. The massinertia of the roller is defined so that the roller can rotateabout its axis when contacting the sheet. Three-dimensional8-node linear hexahedral elements are used to mesh thesheet. The number of elements in an annular region inwhich the sheet will contact the round corner of the mandrel Table 1  The cases simulated and corresponding process conditionsCaseConditions A B CRoller type 1 1 2 No. of passes 1 2 2Feed rate (mm/rev) (0.5  –  1.0  –  2.0) 1.0 1.0Rotational speed (rpm) 200 200 200Int J Mater Form (2009) 2:271  –  281 273  is increased as shown in Fig. 2, in order to provide smoothcontact between the mandrel and sheet and enhance the plastic bending deformation in this area. The number of elements in the thickness direction is two, this is theminimum number of elements required to properlyreproduce the bending deformation around the mandrelcorner without excessive element distortion. The totalnumber of elements is 5968, with 9102 nodal points.Figure 3 shows the finite element model and arrangement of components for the single-pass conventional spinning process. All simulations were performed on an Intel®Core ™ Dual computer with a 3 GHz CPU. Several valuesof load rate scaling were applied to reduce the simulationtime. A maximum scaling factor of 21 was used, which provided a significant reduction in simulation time whilemaintaining a similar accuracy in the numerical results. Validation of the finite element model To determine the validity of the numerical models thesingle-pass conventional spinning process with a 1 mm/revfeed rate (case A) was selected and compared to theexperimental results of Xia et al. [12]. Figure 4 shows the  progressive state of deformation and Von Mises stressdistribution for this case. It can be seen that for a roller displacement less than 20 mm, where there is no contact  between the deforming sheet and the sides of themandrel, the deformation state is essentially free bending.For roller displacements more than 20 mm and less than40 mm, the geometry developed during deformationclosely resembles that in deep drawing. For roller displacements of more than 40 mm, the deformationstate is a combination of compression and bending,where the sheet is compressed between the roller andmandrel which occurs simultaneously with the bendingdeformation around the mandrel corner. Figure 5(a)shows the shape of the fully deformed cup and Fig. 5(b)shows a cross-section indicating the thickness distributionof the final cup. The local thinning in the corner region isevident. The distribution of Von Mises stress shown inFig. 5(a) reveals a reasonably uniform level for much of thedeformed wall of the cup, but with some variations,especially on the inner surface of the wall, towards theopen end. Figure 5(b) shows a typical distribution of wallthickness variations in which the base of the cup held between the mandrel and holder is almost constant, whilethere is local thinning around the mandrel corner and slight thickening near the open end.Two assessments of the finite element results arerequired in order to ensure the validity of these models.Firstly, an assessment of the stability of the numericalsolution must be undertaken to ensure that the solution isclose to quasi-static conditions, followed by a comparisonof the results to experimental data. Qian et al. [8] and Liang et al. [9] suggest that for the finite element model to be   An annular area with smallerelements 3 D 8-node hexahedral elements Fig. 2  The finite element mesh used to represent the sheet  MandrelHolder   Roller   Sheet Fig. 3  Finite element model of the single-pass conventional spinning process Unit: mm HolderMandrelRoller type 2Roller type 1Sheet Fig. 1  Geometries and dimensions of the models274 Int J Mater Form (2009) 2:271  –  281  reliable, the maximum kinetic energy of the deformedmaterial and the maximum artificial strain energy must both be less than 10% of the maximum internal energy. Also, thekinetic energy curve must be free of any sudden fluctua-tions. Figure 6 shows the history of internal energy,artificial strain energy and kinetic energy, and shows that the maximum kinetic energy is 7.9% of the internal energyand the maximum artificial strain energy is 9.5% of theinternal energy. Therefore, the maximum values of bothenergy parameters are within the suggested limit.Figures 7 and 8 show the simulation results for the roller  axial and radial forces compared to experimental resultsobtained by Xia et al. [12] at 1 mm/rev feed rate for the single-passconventionalspinningprocess(CaseA).Figure7displays the variation of axial force during the spinning process as the roller is moved axially from the initial position, at which point the roller starts to contact thesheet. As the plastic deformation increases, the axialforce increases. The maximum axial force correspondswith the maximum plastic deformation that takes placenear the round corner of the mandrel at approximately45 mm roller displacement. At this stage, the deforma-tion state is a combination of compression and bending.With further translation of the roller, the force decreasesas necking occurs at the corner of the mandrel under large axial tensile stresses. This large axial tensile stressthen decreases as the axial force decreases and neckingdoes not continue. If the sheet thickness could not support the maximum axial force, fracture could take place at this region. The maximum axial force of the FE  S=20mm S=40mm S=60mm S=100mm Fig. 4  Deformation states during single-pass conventional spinning, case (A). S is the linear, axial displacement of the roller  (a)   (b) Thickening at the open Thinning at round corner of the mandrel Constant thickness at cupbottom Fig. 5 a  Von Mises stress in thefully deformed cup, and  b  asection through the cup with theFE mesh superimposed reveal-ing the local thinningInt J Mater Form (2009) 2:271  –  281 275
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