Journal of Materials Processing Technology 80–81 (1998) 325–329

FE simulations of camber in hot strip rolling

Annika Nilsson *MEFOS, Box 812, S-971 25 Lulea, Sweden

Abstract

In this work, finite-element simulations have been made to model camber and lateral movement (strip walk) during hot rolling.Experiments have been performed in a pilot plant rolling mill to verify the results. The FE model used to determine strip camberand strip walk was developed using the explicit code Dyna3d. The roll in the FE model was modelled partly stiff, to avoidgenerating an excessively large model. Roll deflection and roll flattening was calculated with MEFOS’s profile and flatnessprogram Crown426. The results show fairly good agreement between the FE simulations and the experiments. © 1998 ElsevierScience S.A. All rights reserved.

Keywords: FE simulation; Hot rolling; Camber; Strip walk

1. Introduction

Strip tracking problems have increased in recentyears due to the improved crown control systems in themills. Tracking problems cause the strip to move side-ways in the roll gap. This causes strip wedges andcamber, which lowers the product quality. Sometimesthe strip crashes into the side guides and this picks upparticles that often damage the roll surface. Stablerolling conditions are important for a good mill yield.Generally it is accepted that a small positive crown isneeded for good tracking of a strip. A positive stripcrown has a stabilising effect on the process. Severalpapers have been written studying the cause of camber,and include models or corrections to improve the striptracking [1–4]. Several factors cause camber, as seen inthese papers. Some work has been done to measurecamber and correct it in the following rolling pass [5,6].The problem has also been analysed empirically in [7]where the necessary strip crown for good tracking wascalculated. A detailed three-dimensional analyticalmodel calculating strip shape that accounts for mill andstrip deformations and asymmetric rolling conditionswas presented in [8]. That model was verified for coldrolling. In this work, the problem is analysed using thefinite-element method.

2. Description of the experiments and FE calculations

2.1. Pilot plant experiments

Pilot plant trials were performed according to anexperimentally designed plan, to verify the calculations.The experiments were planned so that a large camberwould be obtained. A total of 20 strips were rolled inMEFOS’s four-high pilot mill. The mill specificationand the conditions for the experiments are listed inTable 1. Two pairs of work rolls were used, one pairhad a 0.3-mm convex crown and the other pair wascylindrical. To keep track of the strip in the mill, thework rolls were marked which left prints on the rolledstrips. Strip width, reduction, positioning, tilt of themill and work roll shape were varied according to anexperimentally designed plan. The variables with theirhigh and low values are shown in Table 2.

Table 1Mill specification and rolling conditions

Type of mill 4 HiWork roll diameter (mm) 249Back-up roll diameter (mm) 545

840Work roll barrel length (mm)Material Stainless steel

1Rolling speed (m s)Initial strip thickness (mm) 6Strip length (mm) 2000

950Rolling temperature (°C)* Fax: +46 920 99309.

0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.

PII S0924-0136(98)00144-7

A. Nilsson / Journal of Materials Processing Technology 80–81 (1998) 325–329326

Table 2Parameters varied with their high and low values

Variable Abbreviation Low and highvalues

Width (mm) 300, 400WiCrWork roll crown (mm) 0, 0.3

20, 30ReReduction (%)TiTilted mill (difference in gap 0, 0.7

between chocks) (mm)Initial strip off-centre in roll Of 0, 30

gap (mm)

Fig. 1. Results from the statistical evaluation of the experiments. Allparameters that were included in the study affected the resultssignificantly. The error bars show the 95% confidence intervals.

Fig. 2. The model fits very well with the experimental results. The 19dots corresponds to the 19 strips rolled in the mill. The model canpredict both camber and side shift with a high degree of accuracy.

elastic-plastic material model has been used. Due tosymmetry, only the upper part of the mill was mod-elled. Only the outer part of the roll was modelled withone or two layers of elements. The boundary conditionscontrolling the rotation of the roll are applied at theinner boundary. Roll deflection and roll flattening wascalculated with MEFOS’s profile and flatness programCrown426. The deformed shape (calculated) of the rollwas used in the FE model. Coulomb friction was usedbetween the roll and the strip and a coefficient offriction of 0.3 was used. One drawback with the modelis that it cannot handle how the deflection and rollflattening change as the strip moves sideways. Someflattening was included by using two elastic layers ofelements in the roll skin. (When two layers of elements

2.2. Finite-element simulations

The FE model to determine strip camber and stripwalk was developed using the explicit code dyna3d. An

Fig. 3. Rolling of a 400 mm wide strip with an initial wedge profile. The thickness difference at the entry side was 0.5 mm. Reduction on thethicker side (lower) is larger, resulting in increased elongation and cambering at the delivery side. At the entry side, the incoming strip rotates.The letters mark positions along the center of the strip for which the sideways movement is plotted in Fig. 4.

A. Nilsson / Journal of Materials Processing Technology 80–81 (1998) 325–329 327

Fig. 4. Sideways movement of points A–E marked in Fig. 3, during rolling.

were used, the roll flattening was not modelled in theroll shape.) To speed up the calculations, the densitywas increased by 1000 times. The calculation time wasabout 1 week on a Sun Ultra1 workstation.

3. Results and discussion

3.1. Results from the pilot plant trials

The results from the pilot plant trials have beenevaluated statistically with the PC program MODDE.The statistical evaluation showed that all parametersstudied had a significant influence on the two responses,camber and strip walk. To differ between directions(movement and cambering to the left or to the right) anegative sign was used for one of the directions. Thesignificant parameters from the multiple linear regres-sion are shown in Fig. 1 and the model fit is shown inFig. 2.

3.2. Comparison between experiments and simulations

In the simulations, the behaviour of the asymmetri-cally rolled sheet can be observed. During rolling, thestrip at the entry side rotates due to the different entryvelocities. The strip at the exit side becomes cambereddue to the different elongation of the strip. The stripalso moves sideways in the roll gap towards the sidewhere the roll gap is largest. This behaviour is illus-trated in Fig. 3. The rotation of the strip at the entryside causes the strip to be fed into the roll gap moreand more off-center. The sideways movement is largestfor the rear end of the strip. This can be seen in the plotof sideways movement in Fig. 4.

A comparison between the experiments and the simu-lation is shown in Fig. 5(a) and (b). Fig. 6 shows howthe camber was measured. For strips d2807 and d2808,both camber and side shift agree well with the pilotplant experiments. For strip d2808, the calculated cam-ber was 11 mm and the measured camber was 11.8 mm..

A. Nilsson / Journal of Materials Processing Technology 80–81 (1998) 325–329328

Fig. 5. (a) Comparison between measured and calculated camber. (b)Comparison between measured and calculated side shift. For two ofthe strips where roll flattening was large, a model with an elastic rollsurface was tested. This improved the results considerably.

Fig. 7. Roll gap shape when roll flattening is large.

Fig. 8. Roll gap shape for a work roll with a crown, when the mill istilted.

underestimated. For strips d2807 and d2808, the influ-ence of roll flattening is smaller and therefore the FEsimulations corresponded better with the experimentalresults even though the strip moved. The roll gap froma strip with a large degree of roll flattening is shown inFig. 7. When the strip moves sideways in such a rollgap, the wedge decreases, since the roll gap is narrower,therefore the calculated camber and sideways move-ment become smaller than what was measured in theexperiments. Fig. 8 shows a roll gap shape that corre-lates well with the experimental results. The strip wedgeincreases when the strip moves sideways due to thework roll crown and the small roll flattening. To allowsome roll flattening in the model, two elements wereused in the roll skin for strips d2804 and d2811, whichimproved the results.

4. Conclusions

The rigid FE model of the deformed roll has thedrawback that roll flattening will not follow the strip asit moves sideways. Camber and sideways movementtherefore become underestimated for strips where rollflattening is large. A better estimation of sidewaysmovement is obtained when using two element layerswhich allow some flattening on the surface. It would bedesirable to include a model of the whole mill in theanalysis. In spite of the simplifications which were

The strip moved sideways by 77 mm whereas thesimulation gave 72 mm. The results for some otherstrips, for example d2804 and d2811, were not asaccurate. The reason is that roll flattening has gener-ated a groove that caused the sideways movement to be

Fig. 6. The camber was measured as the gap generated at the middleof a 1000 mm long ruler placed 500 mm from the head end of therolled plates. .

A. Nilsson / Journal of Materials Processing Technology 80–81 (1998) 325–329 329

made, the model gives fairly good results. The statisticalevaluation of the experiments resulted in a good modelwhere both camber and sideways movement can beaccurately described mathematically from linear termsand cross terms of the parameters varied.

References

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