Bulging between Rolls in Continuously-cast Slabs

Transcription

1 Bulging between Rolls in Continuously-cast Slabs Lan Yu Department of Mechanical & Industrial Engineering University of Illinois at Urbana-Champaign September 25, 2

2 Acknowledgments Allegheny Ludlum Corp. AK Steel Columbus Stainless Steel Inland Steel LTV Steel Stollberg, Inc. National Center for Supercomputing Applications (NCSA)

3 Outline Introduction Modeling methodology Multiple-roll pitch model Effect of roll misalignment Effect of sudden roll pitch change Parametric study Plain carbon steel Stainless steel Evaluation of empirical bulging prediction equations Applications

4 Introduction Bulging of continuously cast steel slabs between supporting rolls is caused by internal ferrostatic pressure acting on the solidifying strand shell due to the weight of liquid steel and the height from the meniscus. Bulging is directly responsible for internal cracks, centerline segregation, and permanent deformation, which lead to poor quality of the continuously cast products. The bulging of slabs can also cause an increase of the load transmitted to the rolls and enhance their rate of wear. In practice, it is important to estimate bulging quantitatively in continuous caster design and set-up of secondary cooling conditions, especially in high-speed casting.

5 Background Solidifying Shell Liquid Steel Ferrostatic Pressure Casting Speed, Vc dn dp FEM Domain Y X 2D FEM single roll pitch model for bulging The Continuous Casting Process (Acknowledgement to Prof. Brian G. Thomas) FEM Domain with 6x16 mesh Periodic B.C. on two ends (coupled X & Y displacement)

6 Key Phenomena Roll pitch and shell thickness have a paramount effect on bulging Negative bulging Slab movement Transient behavior due to roll pitch changes Effect of temperature profile on bulging Material property at high temperature Creep behavior

7 Modeling Methodology 2-D Finite Element Method thermal stress model with Lagrangian approach is developed using commercial FEM package ABAQUS. Stress analysis Nonlinear problem Simplifying Assumptions: 2-D elastic-plastic model with plane stress assumption Constant solidified shell thickness Uniform ferrostatic pressure along x Constant temperature gradient across the shell thickness with uniform temperature profile along x

8 Define the Problem Liquid Steel Ferrostatic Pressure Solidifying Shell Casting Speed, Vc FEM Domain Multiple roll pitch bulging model (with at least 4 roll pitches) Objectives: 1. Suddenly drop one roll and keep other rolls moving as usual, what is the difference from uniform roll pitch model? 2. What is the effect of roll misalignment on bulging? 3. Reproduce the simulation done by Gancarz, Lamant, et al. Is their simulation correct? Experimental bulging profile on Sumitomo and Calculations over 9 rolls done by Gancarz, Lamant, et al.

9 Wunnenberg Conditions for Bulging Calculation Wunnenberg Conditions Slab width = 135 mm Roll pitch = 86 mm Shell thickness = 79 mm T Liquidus = 15 C T Surface = 1 C Liquid steel density = 7 kg / m 3 Distance from meniscus = 3.9 m Ferrostatic pressure =.26 MPa Casting speed =.85 m/min ( 14.2 mm/s ) Wunnenberg Measurements - The bulging profile is asymmetric with maximum deflection of 6.5mm at 75% from upstream roll. Distance from @75% Displacement (mm) (max)

10 Strain contour plot for a typical single roll pitch model Total Strain in X direction E11 VALUE -1.33E-2-1.2E-2-9.E-3-6.E-3-3.E E E-3 +6.E-3 +9.E E E E E E-2 Tension Compression Compression Tension DISPLACEMENT MAGNIFICATION FACTOR = 8. RESTART FILE = c2 STEP 157 INCREMENT 1 TIME COMPLETED IN THIS STEP 1.1 TOTAL ACCUMULATED TIME 34. ABAQUS VERSION: DATE: 5-APR-2 TIME: 17:16:27

11 Strain contour plot for an 8-roll 43mm pitch model with one roll missing Total Strain in X direction E11 VALUE -1.73E-2-1.4E-2-1.6E E E E E E E E E E E E-2 8-roll 43mm pitch model with one roll missing DISPLACEMENT MAGNIFICATION FACTOR = 2. RESTART FILE = miss4 STEP 187 INCREMENT 11 TIME COMPLETED IN THIS STEP 1.1 TOTAL ACCUMULATED TIME 334. ABAQUS VERSION: DATE: 1-NOV-1999 TIME: 15:59:7

12 1 Comparison of Bulging Profile between uniform roll pitch and sudden roll pitch change 5 Surface Displacement (mm) % % Uniform 86mm roll pitch 43mm roll pitch with one roll missing X (mm) Maximum bulge Negative bulge Max strain on sol. front Uniform 86mm roll pitch 1.61 mm 2.9 mm 2.32 % 43mm roll pitch with one roll missing mm 7.3 mm 2.62 % Difference 75 % 152 % 12.9 % Sudden roll pitch change leads to larger Max bulge and much larger Negative bulge, but the change in Max tensile strain on solidification front is not as significant as that of Max bulge and Neg bulge. Maximum bulge is at about 6% of the roll pitch from the upstream roll. Transient effect of sudden roll pitch change settles down in the following 4~5 roll pitches.

13 Bulging Profile on Surface and Strain Profile on Solidification Front 1 4 Surface Displacement (mm) mm roll pitch with one roll missing (infinity misalignment) - + Surface displacement Strain on solidification front (+ tension, - compression) Strain on Solidification Front (%) X (mm) -8 Negative bulge is important to tensile strain on solidification front, which is responsible for internal crack. Maximum tensile strain is located between maximum bulge and negative bulge, but not on maximum negative bulge point.

14 Effect of Misalignment on Bulging 1 5 Roll Pitch = 43 mm Surface Displacement (mm) mm 1mm misalignment 2mm misalignment 3mm misalignment 5mm misalignment 1mm misalignment 15mm misalignment infinity misalignment maximum bulging effective max misalignment X (mm) Effective Maximum Misalignment = mm

15 Max bulge for 86mm roll pitch Neg bulge for 86mm roll pitch Max bulge for 43mm roll pitch with misalignment Neg bulge for 43mm roll pitch with misalignment Max strain for 86mm roll pitch Max strain on solidification front for 43mm roll pitch with misalignment Effect of Misalignment on Bulge and Max Strain on Solidification Front 2 4 Bulge (mm) Max Strain on Solidification Front (%) -1 Small roll spacing 43mm (no misalignment) Misalignment (mm) mm Effective max misalignment -2 Double roll spacing 86mm (infinity misalignment) Max bulge, Negative bulge and Max strain on solidification front are almost linear functions of misalignment till effective maximum misalignment (17.43mm). When actual misalignment is larger than effective maximum misalignment, it behaves like one roll is missing.

16 Effect of Misalignment on Bulging Misalignment (mm) (Roll spacing 43mm) Maximum bulge(mm) Position from upstream roll Negative bulge(mm) Ratio of neg. bulge to max bulge Max strain on solidification front (%) % % % % % % % (One roll missing) Double roll spacing 86mm % %

17 Sumitomo Conditions Pilot caster at Sumitomo Metals in Japan 4 x 1 mm 2 slab Casting Speed = 1.65 m/min Caster Radius (R) = 3 m Mold Length =.7 m Roll Pitch (L) = 31 mm Shell Thickness (D) = mm Height from Meniscus (H) = 2.65 m Ferrostatic Pressure =.18 MPa Surface Temperature = 122 o C => Distance from Meniscus = 3.25 m # of rolls = 8, the point of interest is around 8-9 rolls down the mold..31 Measurement: 1. Maximum bulging of 3.2 mm is at 6~65% of the roll pitch from the upstream roll. 2. There is a negative bulging at the vicinity of the supporting rolls. 3. The ratio between negative bulging and positive bulging is around.4. R=3m m Cutoff Point

18 Strain contour plot for roll pitch changing from 25mm to 31mm Total Strain in X direction E11 VALUE -1.33E-2-1.6E E E E E E E E E E E E E-2 Roll pitch changing from 25mm to 31mm DISPLACEMENT MAGNIFICATION FACTOR = 7. RESTART FILE = continue7 STEP 266 INCREMENT 8 TIME COMPLETED IN THIS STEP 1.1 TOTAL ACCUMULATED TIME 463. ABAQUS VERSION: DATE: 18-JAN-2 TIME: 1:32:46

19 4 Comparison of Bulging Profile between uniform roll pitch and sudden roll pitch change Surface Displacement (mm) Sudden roll pitch change from 25mm to 31mm Uniform 31mm roll pitch Distance x (mm)

20 Bulging Profile on Surface and Strain Profile on Solidification Front Surface Displacement (mm) -2 Surface displacement -2 Strain on Solidification Front (%) -4 Strain on solidification front Distance x (mm)

21 Observations Current model qualitatively matches Sumitomo measurements and simulation by J. Gancarz, et al. Sudden change of roll pitch from 25mm to 31mm Uniform 31mm roll pitch Increase (sudden/uniform) Sumitomo measurements 4.6 mm 3.2 mm 44% J. Gancarz et al. model 3.6 mm 2. mm 8% Our model * 5.96 mm 3.67 mm 62% * Surface temperature changed from 122 o C to 1 o C to account for property uncertainty. Sudden roll pitch change leads to a larger bulge and bigger tensile strain on solidification front. Uniform 25mm Sudden change from 25mm to 31mm Uniform 31mm Increase (sudden/uniform) Maximum bulge.34 mm 5.96 mm 3.67 mm 62% Negative bulge mm 1.78 mm.93 mm 91% Max strain on sol. front.2% 2.1% 1.75% 2% Disturbance from upstream rolls settles down (within 2%) after 4 roll pitches. Maximum tensile strain on solidification front is located on top of the rolls, instead of maximum negative bulge.

22 Temperature dependent stress-strain curves for plain carbon steel Experimental data ( %C, strain rate(s -1 ), temperature) Wray data (.51%C, 2.4e-3, 95 C) Wray data (.51%C, 2.9e-3, 11 C) Wray data (.93%C, 2.3e-3, 12 C) Suzuki data (.25%C, 6.7e-3, 1 C) Suzuki data (.25%C, 6.7e-3, 11 C) Suzuki data (.25%C, 6.7e-3, 12 C) Suzuki data (.25%C, 6.7e-3, 13 C) Suzuki data (.25%C, 6.7e-3, 14 C) Suzuki data (.25%C, 6.7e-3, 15 C) Linear kinematic hardening model in ABAQUS This work (95 C) This work (11 C) This work (12 C) This work (14 C) This work (15 C) Stress (MPa) Plastic Strain

23 Roll Pitch Study 1 Bulging Displacement, d max (mm) d max = c1 * L 6.34 Bulging Displacement (mm) Standard Wunnenberg Condition Roll Pitch, L (mm)

24 Shell Thickness Study 1 4 Bulging Displacement, d max (mm) d max = c2 * D Bulging Displacement (mm) Standard Wunnenberg Condition Shell Thickness, D (mm)

25 Ferrostatic Pressure Study 1 Bulging Displacement, d max (mm) Bulging Displacement (mm) Standard Wunnenberg Condition d max = c3 * P Ferrostatic Pressure, P (MPa)

26 Surface Temperature Study 6 Bulging Displacement, d max (mm) Bulging Displacement (mm) Standard Wunnenberg Condition d max = c4 * T surf Surface Temperature, T surf ( C)

27 Bulging Prediction Equation 2-D shape factor from Okamura {( π W / 2L) tanh( πw / 2L) + 2} / 2cosh( πw / 2 ) F( W / L) = 1 L Bulging prediction equation based on the parametric study for plain carbon steel d mm = 32 max ( ) ( / ) F W L L ( mm) P ( MPa) o surf ( C ) ( mm) D T To be improved: Casting speed Material properties

28 Temperature dependent stress-strain curves for stainless steel Experimental data for stainless steel (43) at strain rate of 6.67x C 11 C 12 C 13 C 14 C [1] ABAQUS (1 C) ABAQUS (11 C) ABAQUS (12 C) ABAQUS (13 C) ABAQUS (>=14 C) 2 Stress (MPa) Plastic Strain (%) 1.Kyoto University, Nippon Steel Corp. et al., Data sheet of high temperature mechanical behavior of steel, in Metallurgy and Mechanics of Continuous Casting, ISIJ, Tokyo, Japan, 1985, pp

29 Armco Case Study Case 1 Case 2 Case 3 Roll pitch, L (mm) Shell thickness, D (mm) Ferrostatic pressure, P (MPa) Surface temperature, T surf ( o C) Plain carbon steel d max (mm) Stainless steel Our Equation Material property has a paramount effect on bulging

30 Case 1 (33mm roll pitch) Cold face strain (%) Strain Cold face strain rate (s -1 ) x1-4 s -1 Strain rate Strain rate magnitude Average strain rate Distance (mm) Distance (mm) Surface strain ranging from.8%~.4% Average strain rate is around 6.67x1-4 s -1

31 Evaluation of Empirical Bulging Prediction Equations Okamura Equation (based on FEM simulations): d, AF( W / L) D max ε b = j P k l m L Tsurf V n c Where, {( π W / 2L) tanh( πw / 2L) + 2} / 2cosh( πw / 2 ) F( W / L) = 1 L Palmaers Equation (based on beam bending analysis): d where, Lamant Equation (based on beam bending analysis): d = max.4623c( Tsurf ) V P c max = exp(.3866( Tsurf + 273)) L D 3.8 C( T surf.69 1 ) = L V c H D T T T surf surf surf = 9 C = 1 C = 11 C

32 Comparison of Different Models Wunnenberg case (86mm) Sumitomo case (31mm) Armco case 3 (165mm) Okamura Equation Palmaers Equation *.332 Lamant Equation Our Equation **.26 Our model (raw / adjusted) 1.61 / / 1.79 **.184 /.184 Measurement 5~7 3.2 N/A * Must use surface temperature = 11 o C instead of 122 o C, so prediction is really higher. ** Surface temperature of 1 o C is used instead of 122 o C. Conclusion: Okamura Equation is always much too low. Lamant Equation is ok except for Armco case 3 (too low). Palmaers Equation matches measurements and our model pretty well.

33 Future Work Need more appropriate material properties at high temperature for each individual case Results should be more quantitative Applications Crack formation Slab width prediction

34 Slab Width Prediction Possible slab distortion mechanisms Creep due to ferrostatic pressure Bulging ratcheting effect Ferrostatic pressure Roll distortion Roll friction / thermal shrinkage ratcheting Narrow face bulging

35 Bulging Calculation and Slab Width Change Roll number Predicted bulging Slab width change due to displacement (mm) bulging (mm) e e e e e e e e e e e e e e e e e e e e e e e e e Accumulated slab width change =.4978 mm Mold width = mm Measured slab width = mm Narrow face bulging = 7.9 mm Thermal shrinkage = 7.3 mm Accumulated slab width change due to bulging =.5 mm