ESTABLISHMENT OF 3D FEM MODEL OF MULTI-PASS SPINNING (2).doc

chinese journal of mechanical engineeringvol. 20, no. 4, 2007 19 zhan meizhou qiangyang hezhang jinhuicollege of materials scienceand engineering,northwestern polytechnical university,xian 710072, chinaestablishment of 3d fem model of multi-pass spinning*abstract: in order to improve the computational accuracy and efficiency, it is necessary to establish a reasonable 3d fem model for multi-pass spinning including not only spinning process but also springback and annealing processes. a numerical model for multi-pass spinning is established using the combination of explicit and implicit fem, with the advantages of them in accuracy and efficiency. the procedures for model establishment are introduced in detail, and the model is validated. the application of the 3d fem model to a two-pass spinning shows the following: the field variables such as the stress, strain and wall thickness during the whole spinning process can be obtained, not only during spinning process but also during springback and annealing processes, and the trends of their distributions and variations are in good agreement with a practical multi-spinning process. thus the 3d fem model for multi-pass spinning may be a helpfvi tooi for determination and optimization of process parameters of multi-pass spinning process. key words: multi-pass spinning 3d fem springback aniicsiing explicit implicit0introductionthe spinning process, as an important part of modern plastic working technology, has become one of prior forming processes for thin-walled axisymmetric workpieces, and plays an important role in fields of aeronautics, astronautics, weaponry, etj13. in spinning forming, the blank brings about continuous and partial plastic deformation, so it is very difficult to control the shape, size and precision of the finished parts. therefore a qualified spun part only can be obtained usually after multi-pass spinning processes. and after each-pass spinning process, springback is unavoidable and it is may be necessary to add the annealing process in order to soften the spun material and obtain a fine part. obviously, multi-pass spinning is one of complicated plastic forming processes, and springback and annealing processes have an important influence on spinning forming quality and processing efficiency. in recent years, fem has been one of main methods of studying spinning technology. but until now, only some models for single-pass spinning or multi-pass spinning without considering effects of springback and annealing have been established461. consequently, in order to improve the accuracy and efficiency, it is very essential to establish a reasonable 3d fem model for multi-pass spinning including not only spinning but also spring-back and annealing processes. in this paper, such a model for multi-pass spinning has been established using combined explicit and implicit fem with the advantages of them in accuracy and efficiency. the comparison between fem results using the model and experimental ones, and the application of the 3d fem model to a two-pass spinning show that the 3d fem model for multi-pass spinning may be a helpful tool for determination and optimization of process parameters of multi-pass spinning process.1research methodmulti-pass spinning is one of complex successive partial plastic forming technologies under multi-factors effects, with material nonlinearity, geometric nonlinearity and boundary non-linearity, so a 3d fem model is needed for simulating the multi-pass spinning process.springback is often an important part of a multi-pass spinning analysis because the springback analysis determines the shape of the final or interim, unloaded part. annealing is also an important part between adjacent pass spinning process or before the first passselected from proceedings of the 7th international conference on frontiers of design and manufacturing (1cfdm 2006). this project is supported by national natural science foundation of china (no. 50405039, no. 50575186), and national natural science foundation of china for distinguished young scholor (no. 50225518). received july 14, 2006; received in revised form march 21,2007; accepted march 29,2007spinning, because the annealing eliminates all the residual strain and stress to let the next pass spinning continue. while explicit fem is well-suited for forming and annealing simulations, springback poses some special difficulties. the main problem with performing springback simulations within explicit fem is the amount of time required to obtain a steady-state solution.since springback involves no contact and usually includes only mild nonlinearities, implicit fem can solve springback problems much faster than explicit fem can. therefore, the preferred approach to springback analyses is to import the completed forming model from explicit into implicit fem.for efficiency abaqus has the capability to import results back and forth between abaqus/explicit and abaqus/stan-dard, therefore, in this paper, abaqus/explicit has been chosen to simulate spinning and annealing processes, and springback analysis is carried out using abaqus/standard.2 establishment of fem model2.1 main flow chartbased on the implicit and explicit platform of abaqus, the flow chart of multi-pass spinning simulation is shown in fig. 1, in which, n pass is the total pass number of spinning. the key procedures of the simulation of multi-pass spinning are detailed as follows.(start)simulating the initial rnnwllng and the fint pass spinning using abaqus/explicit/ pass=2, afpassispringback analysis using abaqus/standard1annealing and the next passspinning analyub usingabaqus/explicit/ pass=/pass+ln 1 =ct / pass=/vpassispringback analysispost-processing analysisi(finish ) fig. 1 flow chart of multi-pass spinning analysis2.2 establishment of fem model for first pass spinningthe 3d fem model for the first pass spinning of multi-pass9 -2020*zhan mei, et al: establishment of 3d fem model of multi-pass spinningspinning should be built using abaqus/explicit, as shown in fig. 2. the billet (blank), the mandrel, and the rollers are modeled as separate parts.blankroller roller jmnmk mandrelfig. 2 fem model of the first pass spinningthe contact between the blank and the rigid mandrel, the blank and the rigid rollers is modeled with the contact pair option. the mechanical interaction between the contact surfaces is assumed to be frictional contact.since an analytical rigid surface provides a more smooth representation of the surface than a discrete rigid body, it is preferred to use analytic rigid surface for the rigid tools. in the model, the rollers are modeled with analytic rigid bodies. but for the mandrel, a discrete rigid body has been used in order to make it easy to tie the blank with the bottom of the mandrel.since the blank is a deformed body during spinning, the blank is discretized as quadrilateral reduced integral element s4r.it is should noticed that, the rigid surfaces should be as clow as possible to the blank without any overclosure at the start of the forming step. since abaqus/explicit includes the thickness of shell elements when detenririfng contact; therefore, the midplane of the blank must be at isast one-half of the shell thickness away from the rigid tools above and below it. prior to the first step abaqus/explicit will attempt to resolve overclosures in a strain-free manner, and the resulting nodal location changes may distort the elements.2.3procedures of springback analysisafter the forming analysis of the first pass spinning using abaqus/explicit, springback analysis can be conducted using abaqus/standard as the following procedures.(1) copy the old model (for the first pass spinning) as a new model.(1) delete all pans except the blank, and delete the set, the surface and interaction definition with them.(1) delete all step definition, and then add a new static general step.(1) delete all boundary definition, and then add a new fixed boundary condition to avoid the rigid motion during the spring-back step.(1) in load module, add a new field, select initial state, and fill the job name of the first pass spinning analysis into the dialog box of job name.(1) set up a new job based on the new model and submit it to compute.it is should notice that, geometric nonlinearity should be included in springback analysis because we do not always know whether or not geometric nonlinearities will affect the results.2.4establishment of fem model for annealing and nextpass spinningnow that the results for the first spinning and its corresponding springback have been obtained, the simulation with annealing and the next pass spinning using abaqus/explicit can be continued. since annealing and the succeeding spinning analysis both are performed using abaqus/explicit, a model including annealing and the next pass spinning can be set up at the same time, as shown in fig. 3.workpieceroller rollert ft mandrelfig. 3 fem model for annealing and the second spinningthe procedures of annealing and succeeding spinning analysis after springback analysis are as following.(1) create a new model which includes the blank part after springback, mandrel and rollers needed during the succeeding spinning step.(1) create an annealing step, in step manager module select the step and conduct create-anneal-ok.(1) create a succeeding spinning step using the same method as that used for the first pass spinning.(1) set up a new job based on the model and submit it to compute.since an anneal step cannot be the first step in an abaqus/explicit analysis, an additional step by moving the rigid tools into position must be added before the annealing step. the difficulty in moving the tools into position is positioning the tools properly, given the unknown shape of the blank following springback. at the end of the first spinning forming stage the position of the blank is known hov ev.;r during springback the blank is no longer constrained by vhe rigd tools, and it deforms freely to m.niroize it? interna strain energy. usually, before positioning the rigid took for the succeeding spinning stage, viewing fhe displaced sharx following springback will make it easy to position toois properly.and it is important that the velocity is zero at the end of the positioning step since the final velocity in the positioning step is the initial velocity in the second forming stage.2.5 validation of the modelin order to validate the fem model established above, the comparisons between fem simulation results using the model and experimental6 ones about the influence of feed ratio of roller and deviation ratio on flange angle are carried out. the computation conditions are the same as those in ref. 6, the results are shown in table. from the table, it can be shown that, the fem simulation results are in good accordance with those from experiment with the maximum relative error of 17.37%, thus it shows the 3d fem model for multi-pass spinning is practical and reasonable.table flange angle from fem simulation and experimentflange angle*relative error s/%experimentfemfeed ratio deviation /(mm r) ratio a30.441 -0.341 -4.833 -8.9858.249.1517.371.830.5 0.5 0.6 0.8-0.2 0 0 028.125 -0.313 -4.118 -8.235note: *positive value of flange angle indicates the flange bends toward the deadstock, and a negative value means the flange bends toward the tailstock3 example of applicationhere, a two-pass spinning process is analyzed using the above fem model.in the first pass spinning stage, a tapered blank billet is deformed between a rotational mandrel and two feeding rollers into the shape of a cup. once the cup has been formed, the blank is removed from the first set of tools so that it can spring back to an unloaded configuration. it is then annealed to relieve the cold-working plastic strains generated during the first spinning stage. after annealing, the blank is placed into the second set of rigid tools, and it is deformed into the final shape, then unloading and springback again.the blank is made of lf2m that is assumed to satisfy the relation for true stress and logarithmic strain (as shown in eq. (1), with a reference stress value k of 275 mpa and a work-hardening exponent n of 0.245. isotropic elasticity is assumed, with a modulus of elasticity of 70 gpa and a poissons ratio of 0.3. the blank is taped, with an angle of 54.7, an initial thickness of 4 mm. the semi-angle of the first mandrel is 30; the semi-angle of the second mandrel is 7.897; and the fixed angles of rollers during the two spinning are both of 90.o = kewhere atrue strength94-20 7 ch n acade c journa el c n c p1 ights:/chinese journal of mechanical engineering21 elogarithonic strainnwork-hardening exponentfigs. 4-6 show the stress, strain distributions on the outside surface and wall thickness distributions on the midplane of the workpiece during the whole two-pass spinning process, including in the midst of the first pass spinning, after the first pass spinning, after springback, after annealing, in the midst of the second spinning, after the second pass spinning and after the succeeding springback.(a) in the midst of the first spinning262.700 0 229.900 0 197.000 0 164.200 0 131.400 098.510 065.680 032.840 0 0.001 3(b)aftei ic first s/nimiig207.900 182.600 157.400 132.200 106.90081.69056.46051.220 5.989(c)after the first springbackb(d) after annealing0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0218.600 0 191.300 0 164.000 0 136.600 0 109.300 0 81.980 0 54.660 0 27.330 0 0.000 2(e) in the midst of the second spinning265.700232.500199.200166.000132.80099.62066.42023.2100.000(f) after the second spinning237.00209.50181.90154.30126.8099.2071.6344.0716.50(g) after the second springback fig. 4 stress distributions (effective stress al mpa)0.591 0 0.517 1 0.443 2 0.369 4 0.295 5 0.221 6 0.147 7 0.073 9 0.000 0 (a) in the midst of the first spinning0.778 4 0.681 1 0.583 8 0.486 5 0.389 2 0.291 9 0.194 6 0.097 3 0.000 0(t) / iter the first spiriting0.778 4 0.s81 i j.ss3 8 0.486 5 0.389 2 0.291 9 0.194 6 0.097 3 0.000 0(c) after the first springback(d) after annealing267 9 234 4 200 9 167 4 133 9 100 4 067 0 033 5 0000 e) in the midst of the second spinning0.813 7 0.712 0 0.610 3 0 508 6 0 406 9 0.305 1 0.203 4 0.1017 0.000 0(f) after the second spinning0.813 9 0.712 2 0.610 5 0.508 7 0.407 0 0.305 2 0.203 5 0.101 7 0.000 0(g) after the second springbackfig. 5 strain distributions (effective strain e)1 9 -2 07 c a acade c j urnal elec osh.lrgtsev:/ni22zhan mei, et a): establishment of 3d fem model of multi-pass spinning4.036 3.992 3.948 3.905 3.861 3.817 3.773 3.729 3.686(a) in the midst of the first spinning(b) after the first spinning4.168 4.093 4.019 3.945 3.871 3.797 3.723 3,649 3.5754.1664.092 4.018 3.944 3 870(c) after the first spnngback3.574(f) after the second spinning4.472 4.346 4.220 4.094 3.968 3.842 3.716 3.590 3463(g) after the second springbackfig. 6 wall thickness distributions (wall thickness s/mm)from figs. 4 and s, it can be seen that, during the first pass spinning, the stress and strain increase, but then springback makes more even distribution in stress and strain. annealing step removes all stress and strain, which lets the workpiece soften tosome degree. during the second pass spinning, the stress and strain begin to increase from zero again. the variations of the stress, and strain during spinning, springbcak and annealing analysis accord with the practical multi-pass spinning process.the wall thickness distributes almost evenly along the hoop direction, as shown in fig. 6. in order to distinctly observe the variation of wall thickness of the workpiece during the whole two-pass spinning process, wall thickness variations of the work-piece along a given radial direction at different time are shown in fig. 7. with the processing of the spinning, the midst zone of the wall becomes more and more thinner, and wall thickness of the flange increases slowly. the springback and annealing after the first pass spinning brings about slight variation in wall thickness. during the second pass spinning, the thickness of the wall near the bottom decreases in the beginning, then the middle part of the wall continues to thin and the flange continues to thicken obviously. the distributions and variations wail thickness during spinning, springback and annealing ana/ysis accord with the practical multi-pass spinning process.-time is 33.3% of the first-pass spinning- tvnx is 50.0% of the first -pass spinning -alter the first-pass spinning -afterthe first springback- time is 50.0% of the second - pass spinning- after the second - pass spinning -after the second springback3.6 -3.40.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 spinning time r/s fig. 7 wall thickness variation during spinning process4 conclusions(1) a 3d fem model for multi-pass spinning is established. the model can be used to the whole process simulation, including not only spinning process but also springback and annealing processes, and the computation method for the model is explicit combined with implicit fem, which inheriting their advantages in accuracy and efficiency.(1) using the 3d fem model, distributions and variations of effective stress, effective strain and wal