This paper presents analysis methods utilizing the Finite Element Method for spinner straightening, and shows a guideline for optimum conditions. Two types of analysis methods were composed. Model [F-Expl], “full actual model with explicit scheme”, considers the rotational movement of dies as the actual process using the explicit scheme. Model [BndCr], “a model carrying out fundamental analysis on one cross section based on simple bending in the Finite Element Method (FEM)”, uses the FEM only for calculation of simple bending without rotation for obtaining the deformed bar shape. A series of experiments were conducted in an actual production line as well as the analyses by Model [F-Expl] and [BndCr]. The examination mainly focused upon the eﬀect of straightening intensity by changing the die positions. The experimental and analytical results show some mechanism of straightening and a basic guideline for the optimum working condition

Kajikawa, Shohei

Kawasaki, Keiichiro

Kuboki, Takashi

Matsumura, Hiromichi

Ono, Tetsushi

Seimiya, Hikaru

English

UPCommons. Portal del coneixement obert de la UPC

INVITED SESSIONSIS-Applications of Computational Methods to Product and Process De-sign for IndustryAnalysis of Spinner Straightening utilizi g the Finite Element MethodK. Taka hi, K. Keiichi o, K. Shohei, M. Hiromichi, O. Tetsushi and S. HikaruXV International Conference on Computational Plasticity. Fundamentals and ApplicationsCOMPLAS 2019E. On˜ate, D.R.J. Owen, D. Peric, M. Chiumenti & Eduardo de Souza Neto (Eds)ANALYSIS OF SPINNER STRAIGHTENING UTILIZINGTHE FINITE ELEMENT METHODTAKASHI KUBOKI∗, KEIICHIRO KAWASAKI†, SHOHEI KAJIKAWA†,HIROMICHI MATSUMURA††, TETSUSHI ONO†† and HIKARUSEIMIYA††∗ Department of Mechanical Engineering & Intelligent SystemsThe University of Electro-Communications1-5-1 Chofu Gaoka, Chofu-shi, Tokyo, 182-8585, Japane-mail: kuboki@mce.uec.ac.jp - web page: http://www.mt.mce.uec.ac.jp/† Department of Mechanical Engineering & Intelligent SystemsThe University of Electro-Communications1-5-1 Chofu Gaoka, Chofu-shi, Tokyo, 182-8585, Japan†† Shimomura Tokushu Seiko Co.,Ltd.668-1 Matsuomachi Kashikehongo, Sammu-shi, Chiba, 289-1537, Japanweb page: http://www.sts-shimomura.com/Key words: Spinner, Straightener, Straightness, Warp, Moment, CurvatureAbstract. This paper presents analysis methods utilizing the Finite Element Methodfor spinner straightening, and shows a guideline for optimum conditions. Two typesof analysis methods were composed. Model [F-Expl], “full actual model with explicitscheme”, considers the rotational movement of dies as the actual process using the explicitscheme. Model [BndCr], “a model carrying out fundamental analysis on one cross sectionbased on simple bending in the Finite Element Method (FEM)”, uses the FEM only forcalculation of simple bending without rotation for obtaining the deformed bar shape. Aseries of experiments were conducted in an actual production line as well as the analysesby Model [F-Expl] and [BndCr]. The examination mainly focused upon the effect ofstraightening intensity by changing the die positions. The experimental and analyticalresults show some mechanism of straightening and a basic guideline for the optimumworking condition.1 INTRODUCTIONStraightening is located at the end of manufacturing process for bars and wire rods,and determines the quality of the final product. The requirement to the dimensional pre-cision of bars and wire rods are getting stricter due to the recent trend of requirementsto the final products which use the bars and wire rods, and then the role of straightening121T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiyaprocess is getting more important. Figure 1 shows the process line of bars. The initial baris unwound from the coils on the supply stand, and drawn before the line of straiteningprocesses. The straightening line is composed of a couple of processes, which includesspinner, polishing and two-roll straighteners. These straightening processes would collab-oratively determine the quality of the bars, and the spinner is located at the first of thethree processes.There are few research works for spinner, though there are many for the final process,like two-roll straighter. Yanagihashi et al. [1] and Mutrux et al. [2] tried to apply theFEM to solid-bar straightening with deciding the deformed shape in advance. Furugencomposed a fundamental analysis for tube straightening considering axial deformationat first, followed by the consideration of cross-sectional deformation [3]. Kuboki et al.composed a FEM model applying the implicit scheme for three-stand tube straightening[4]. Wu et al. carried out theoretical approach for analyzing the mechanism of two-rollstraightener [5]. However, all the above works focused upon the final process in the pro-duction line without knowing phenomena in the first process, that is spinner straightening.Although Tsurumi et al. conducted a study on a spinner-like machine, the material wasa very thin wire and the study is not so general [6].The present study focuses upon the spinner straightening, which is the first processand may plays an important role in the production line. Analysis methods are composedutilizing the Finite Element Method for proposing a guideline for optimum conditions.Two types of analysis methods are shown. Model 1, ”full actual model with explicitscheme [F-Expl]”, considers the rotational movement of dies as the actual process usingthe explicit scheme. Model 2, ”a model carrying out fundamental analysis on one crosssection based on simple bending in FEM [BndCr]”, uses the FEM only for calculationof simple bending without rotation for obtaining the deformed bar shape. A series ofexperiments were conducted in an actual production line as well as the analyses by Model[F-Expl] and [BndCr]. The examination mainly focused upon the effect of straighteningintensity by changing the die positions for showing mechanism in spinner straighteningand a guideline for the optimum working condition.Supply standPreliminarystraighteningShot blastDrawingSpinner-1 Spinner-2CuttingPolishing straightenerTwo-roll straightenerBar/wire rodFigure 1: Process line for bars and wire rods2 CONDITION FOR SPINNERFigure 2 shows a schematic illustration of spinner. Only the second spinner [Spinner-2](see Fig. 1) was used in this study. The die positions hi (i = 1 · · · 5) was defined so222T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiyathat the hi should be zero when the dies contact with a completely straight bar withoutany load. The sign (positive/negative) of hi was defined as shown in the figure. The diepositions hi determine the bending intensity during straightening. The detailed conditionon the die positions are shown in Table 1. Condition [A] is intuitively expected to havethe strongest straightening effect.Table 2 shows the drawing condition in advance of spinner straightening. Coils of lead-free free-cutting steel was annealed, and drawn. Two-pass drawing was conducted underthe condition [a], and the area reduction at the second pass was set to be around 1 %so that the residual stress should be leveled to almost zero as clarified in the literature[7]. Conventioal one-pass drawing was employed for (b) so that the residual stress mightgenerate. The difference between conditions [a] and [b] would show the effect of residualstresses on straightening. Table 3 shows other working conditions.Figure 2: Composition of spinner straightenerTable 1: Die position for spinner straight-eningPosition hi/mm (i = 1 · · · 5)[A] 0 -2.25 11.0 -2.25 0[B] 0 -1.875 10.0 -1.875 0[C] 0 -1.55 9.0 -1.55 0[D] 0 -1.3 8.0 -1.3 0[E] 0 -1.1 7.0 -1.1 0[F] 0 -0.97 6.0 -0.97 0[G] 0 -0.92 5.5 -0.92 0Table 2: Drawing condition before spinner straight-eningInitial Die inside diameterDiameter Heat 1st 2ndd0/mm treat d1/mm db/mm[a] 7.0 Anneal 6.08 6.05[b] 7.0 Anneal - 6.05Material: Lead-free free-cutting steelFlow stress (after spinner straightening):σ = 855(ε+ 0.11)0.089Table 3: Working conditionFeed pitch f/mm · rev−1 9.52Initial cuvature c0/mm−1 8.8 ×10−5323T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiya3 ANALYTICAL MODELS3.1 Full explicit scheme model [F-Expl]Two analytical models were composed, and the detailed settings are explained in thissection. Figure 3 shows the composition of spinner in the Finite Element Analysis (FEA).Guides and rollers were introduced as well as the bar and the dies. Residual stresses areassumed to be zero in the analyses in this study.Figure 3: Model in FEAFigure 4: Analysis steps in model [F-Expl]The first model (F-Expl, full explicit) almost fully reproduced the movement of spinnerstraightening using the explicit scheme. The analysis was carried out by two steps asshown in Figure 4. The bar was set through Guide 1 to roller 2 via dies #1 – #5, andthe front tension T was applied. The dies gradually moved to the target position ofhi(i = 1, · · · , 5) at Step 1. At Step 2, the rotational movement was given to the dies,while feeding movement was given to the bar end. Although Model [F-Expl] would not beas precise as a model with the implicit scheme, it can consider the centrifugal force andthe convergence would be stable. An initial curvature c0 was given to the bar betweenthe Roller 1 and Die #1, and the curvature was evaluated at the same portion of the barduring and after the spinner straightening.The FEA was carried out using the commercial code ELFEN, which was developedby Rockfield Software Limited, Swansea. A von Mises’ yield criterion was adopted, and424T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiyathe normality principle was applied to the flow rule. Constraints were dealt with by thepenalty function method. 8-node hexahedral elements were employed.3.2 One cross section analysis following FE bending [BndCr]The second model (BndCr, bending and cross section) was also composed of two stepsas shown in Figure 5. Step 1 is the same to that of Model [F-Expl], and the distributionof axial strains εu(z) on the upper side and εd(z) on the down side were extracted andtransferred to Step 2. Step 2 calculated curvature distribution c(z), axial strain distribu-tion εax(x,y,z), axial stress distribution σax(x,y,z), and Moment distribution M(z) in order.The detailed procedure is shown in Figure 6, and the meanings of the symbols are shownin Table 4. This model assumed that the bar shape should be kept just as the bentshape at Step 1, and calculated the strain and stress history. Kinematic hardening andBauschinger effect were not taken into account. The curvatures cex and cey after spinnerstraightening were determined so that the moment, which is the integration value of axialstress σax, should be zero.Figure 5: Analysis steps in model [BndCr]Table 4: Notationϕ(k)initial curvaturedirectionz axial position zst start positionzend end position c curvature εel elongation straincx curvature in x cy curvature in y εax axial strainσax axial stress Mx moment around x axis My moment around y axiscex curvature around x axis cey curvature around y axis cS short-span curvaturecL long-span curvature db bar diameter525T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. SeimiyaFigure 6: Flow chart for 2nd step in model [BndCr]Figure 7: Curvature3.3 Evaluation of straightnessCurvature was used for the evaluation of straightness, and was defined as shown inFigure 7. Model [F-Expl] can show curvature distribution. The curvature was calculatedfor each node as shown in Figure 7(a). When the value was positive, the node was placedon the extrados of the bar arc. When it was negative, the node was on the intrados. Thechord lengths Lsp were set to be 9.52 mm (feed pitch f) and 190.4 mm (10f) for evaluationof short-span curvature cS and long-span curvature cL. In Model [BndCr], the short-span626T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiyacurvature cS and long-span curvature cL were calculated by equations in Figure 6. Theimage of cS and cL are shown in Figure 7(b). The long span curvature cE was measuredin the experiment as shown in Figure 7(c).4 ANALYTICAL AND EXPERIMENTAL RESULTS4.1 Results in full explicit scheme model (F-Expl)Model [F-Expl] shows the dynamic shape change during spinner straightening. Figure8 shows the curvature distribution during spinner straightening under the condition ofTable 1[B]. ”Initially intrados line”in (a) means the intrados line of the curved bar withcurvature of c0 in Figure 3. The bar started to be twisted at Die #3. The short-spancurvatures periodically generated at Die #3.Figure 8: Spiral and warp during spinner straightening under the condition of Table 1[B]Figure 9 shows the curvature distribution after spinner straightening under the condi-tion of Table 1[B]. It is noteworthy that the extrados (red part) and the intrados (bluepart) are found to be inconsistent before and after spinner straightening by comparing(a) and (c). In other words, the initial curvature was eliminated by spinner straightening.On the other hand, short-span curvatures periodically exist as shown in (b). If thesecurvatures cS cancel each other, the long-span curvature cL should be leveled to zero.However, the cS did not cancel each other, and then cL appeared.Figure 10 shows the effect of Die #3 position h3 on the curvature after spinner straight-ening. The curvatures cL and cE increased with increase of h3. The model [F-Expl] andexperimental results qualitatively show the same results. The spinner conditions in Table1 might be strong enough for the elimination of the initial curvature, and these conditionswould be called as “over straightening”. As the result, the large h3 caused large short-span curvature cS, resulting in large long-span curvature cL. The experimental resultsalso showed that the effect of residual stress before spinner straightening on straighteningeffect was small as the difference between [a] (2-pass drawing: very small residual stresses)and [b] (1-pass drawing) was small. Figure 11 shows the effect of Die #3 position h3 ontwist in spinner straightening. The bars were twisted at Die #3. The spiral angle ϕ727T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. SeimiyaFigure 9: Spiral and warp after spinner straightening under the condition of Table 1[B]increased with increase of h3.Figure 10: Effecti of die position on curvaturesin [F-Expl] and experimentFigure 11: Effect of die position on twist inbar bar obtained by [F-Expl]4.2 Results in one cross section analysis following FE bending [BndCr]Model [BndCr] shows the results, which is obtained based on the statically bent bar.Figure 12 shows the effect of Die #3 position h3 on the curvature after spinner straight-ening. The analytical long-span curvature cL decreased with increase of h3 against theexperimental one cE. On the other hand, the analytical short-span curvature cS qualita-tively show the same tendency to cE. 0.06 times cS might be used for the prediction of theexperimental long-span curvature cE. In the static model [BndCr], the local curvatureswould cancel each other, and then the long-span curvature cL decreased with increase ofh3. However, in the experiment, the local curvature do not completely cancel each other,excessive h3 lead to large curvature cE.The mechanism in spinner straightening would be depicted as in Figure 13. When Die#3 position h3 is small, the initial long-span curvature should exist as (a). When h3 isappropriate, short-span curvatures or waves periodically appears eliminating the initiallong-span curvature as (b). When h3 is excessively large, the short-span curvatures are828T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiyalarge as (c). If the short-span curvatures cancel each other, the long-span curvature wouldbe kept at the small value as (c1). However, they do not cancel each other in practice,and then the long-span curvature becomes large as (c2).The residual axial stresses are shown in Figure 14. Under the conditions in this study,the residual stress increased with increase of Die #3 position h3. In other words, theresidual stress increased with increase of long-span curvature cE in the experiment.These results show a fundamental guideline for spinner straightening, i.e. it is impor-tant to give minimum bare bending intensity to the bent part. Excessive intensity leadsto secondary increase of long-span curvature as well as residual stresses.Figure 12: Curvatures in [BndCr] and experimentFigure 13: Mechanism for curvature gen-erationFigure 14: Residual stress after spinner straightening5 CONCLUSIONS- This paper presents two analytical models. One is Model [F-Expl] and the other isModel [ExplCr].- [F-Expl] almost fully reproduced the movement of spinner straightening using theexplicit scheme.- [F-Expl] shows the distribution of both short and long span curvatures in a visualway.929T. Kuboki, K. Kawasaki, S. Kajikawa, H. Matsumura, T. Ono and H. Seimiya- [F-Expl] showed that long-span curvature increased with increase of Die #3 position,or the increase of the intensity of straightening under the conditions of this study.This analytical tendency is qualitatively the same to that in experiment.- [ExplCr] analyzed one-cross section based on the simple and static bending of thebar.- [ExplCr] showed that 0.06 times calculated short-span curvature is the same level oflong-span curvature in the experiment. Therefore, the 0.06 times the value might beused for prediction of the experimental curvature for the optimization of straight-ening condition.- [ExplCr] showed residual stress might increase with increase of curvature in theexperiment.- Experimental curvature increased with increase of the bending intensity in thisstudy. It would be attributed to the increase of short-span curvatures, which do notcancel each other.- A fundamental guideline for spinner straightening was obtained, i.e. it is importantto give minimum bare bending intensity to the bent part. Excessive intensity leadsto secondary increase of long-span curvature as well as residual stresses.REFERENCES[1] Yanagihashi, T., Hama, T., Onoda, Y., Asakawa, M. Effect of plastic ratio andrepeat bending on straightness in two-roll straightening - higher straightening andlower residual stress technology of bar products 3 -, J. Jpn. Soc. Technol. Plast.,(2005), 46-537:972-976,in Japanese.[2] Mutrux, A., Berisha, B., Weber, M., Hora, P. Fe simulation of cross roll straighten-ing:, COMPLAS X, (2009) Barcelona, 23 in Index.[3] Furugen, M., Hayashi, C. Proc. 3rd. Int. Conf. Steel Rolling, (1985) Tokyo, 497.[4] Kuboki, T., Huang, H., Murata, M., Yamaguchi, Y., Kuroda, K. Fem analysis oftube straightener adopting implicit scheme, Steel Research Int., (2010) 81-9:584-587.[5] Wu, B., Chan, L., Lee, T., Ao, L. A study on the precision modeling of the barsproduced in two cross-roll straightening, J. Mater. Process. Technol., (2000) 99:22-206.[6] Tsurumi, K., Asakawa, M., Kato, N., Urabe, M., Yoshida, M., Sakumoto, K., Kanno,T. J. Jpn. Soc. Technol. Plast., (2014), 55-640:435-439,in Japanese.[7] Kuboki, T., Akiyama, M., Neishi, Y., Kuroda, K. Effect of final drawing with lightreduction on the levelling of residual stress distribution in cold bar drawing, Proc.Instn Mech. Engrs, Part C, J. of Mech. Eng. Sci., (2000) 214-12:1389-1400.1030

Analysis of spinner straightening utilizing the finite element method

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Analysis of spinner straightening utilizing the finite element method

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