Effect of the hot-coil profile on the flatness and profile of cold-rolled strip

Journal of Materials Processing Technology, 41 (1994) 349-360 Elsevier

349

Effect of the hot-coil profile on the flatness and profile of cold-rolled strip H.D. P a r k a, I.J. Kim b , J.J. Yi a and J.K. Kim a aSystem Research Department, Research Institute of Industrial Science and Technology (RIST), Pohang 790-600, South Korea b Cold Rolling Department, Kwangyang Steel Works, Pohang Iron and Steel Co. Ltd. (POSCO), South Korea

(Received November 26, 1992; accepted July 7, 1993)

Industrial Summary The effect of the profile of the hot coil on the flatness and the profile of cold-rolled strip has been studied by means of samples from a tandem cold mill of Pohang Iron and Steel Co., South Korea. Using geometrical relationships between the factors, measured values of the flatness and the profile were evaluated and theoretical correlation between the steepness values and the change in crown ratios were confirmed experimentally. As for coil build-up, it was established that a very small trace of a high spot in the hot-coil profile gave rise to a wavy shape in the uncoiled strip. Although the crown ratio of the cold strip became larger than that of the hot strip as the measurement point approached the strip edge, the influence of the profile of the mother strip remained even to a point 15 mm from the edge. Based on the results, the height limit of a high spot for good flatness and hot-strip crown values for uniform thickness over the width of the cold-rolled strip have been discussed.

1. Introduction C u s t o m e r d e m a n d for more precise g e o m e t r y in the t h i c k n e s s and flatness of cold-rolled flat p r o d u c t s has r e c e n t l y become s t r i c t e r in the market. M a n y steel m a k e r s h a v e therefore c o n c e n t r a t e d on d e v e l o p i n g t e c h n o l o g i e s for dimensional c o n t r o l and on i n v e s t i n g in new types of d i m e n s i o n a l - c o n t r o l systems. In addition, t h e r e h a v e been a r g u m e n t s for m a n a g i n g strictly the d i m e n s i o n a l q u a l i t y of the p r o d u c t from c a s t i n g to hot-strip rolling in order to be able to supply good m a t e r i a l for the cold mill [1]. Especially, a u n i f o r m hot-coil profile is essential to the o b t a i n i n g of good d i m e n s i o n a l properties with cold-rolled flat

Correspondence to: Dr. Joon-Jeong Yi, Head of the Rolling Research Laboratory, System Research Department, Research Institute of Industrial Science and Technology (RIST), P.O. Box 135, Pohang 790-600, South Korea.

0924-0136/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved. SSDI 0924-0136(93)E0076-S

350

H.D. Park et al. / Effect of the hot-coil profile

products, but the optimum condition of the hot-coil profile is often debatable between engineers from different mills. To ensure good flatness of cold-rolled strip, it is necessary to have exactly the same pattern of the roll-gap profile to the incoming-sheet profile over the width of the strip: that is, a constant crown ratio (the ratio of the strip crown to the strip center thickness) should be maintained during cold rolling. For this, depending on the characteristics of the rolling mill facility, the optimum strip crown of the hot coil and the permissible value of the high spot (or ridge) in the hot-coil profile must necessarily be determined. In the present work, the correlation between the hot-coil profile and the cold-coil profile has been pursued experimentally making use of samples from a tandem cold mill (TCM) of Pohang Iron and Steel Co. Ltd. (POSCO). Further, the permissible height of the high spot and the optimum profile characteristics of the hot strip have been discussed. 2. G e o m e t r i c a l c a l c u l a t i o n s 2.1. Expression of flatness Bad flatness or shape of a cold-rolled sheet is caused by differential elongation over its width. Practically, the differential elongation can be found by slitting the strip into narrow ribbons and subsequently measuring their length. The differential elongation, AL per unit length, L can be expressed as differential strain, A~=AL/L. Since the differential strain is very small, a kind of normalized parameter, such as the /-unit, is used practically to express outof-flatness in the strip:

/-unit = A~ x 105 = L L x 105

(1)

As another way to express the out-of-flatness, the percentage steepness, ~, is convenient for manual measurement since the parameter is expressed by visual lengths such as the peak height, H, and the peak-to-peak length, P, of the waves. That is,

,~(%)= H× 100(%)

(2)

If the wave is assumed to be sinusoidal, t h e / - u n i t and the steepness can be correlated as follows: i_unit=A~ x 105 =

x 10s=\2]

x 105=10x

(2)

~2

(3)

2.2. Change in strip crown ratio and flatness Strip crown means the differential thickness between the strip center and the strip edge, whilst the crown ratio is defined as the ratio of the strip crown to

H.D. Park et al. / Effect of the hot-coil profile

351

the strip center thickness. Thus, the crown ratios of the hot strip and the cold strip are expressed as follows:

rhot=(Hc-Ho)lHo F¢o,d= ( h e - h~) ~he

(4)

Here, F means crown ratio and H, h mean thicknesses, whilst subscripts c and e mean center and edge, respectively. In the cold rolling of wide strip, since the thickness is very thin compared to the strip width, two-dimensional deformation of thinning and lengthening where lateral plastic flow is ignored can be assumed. If a dead flat sheet is changed into a wavy sheet, as shown in Fig. 1, after rolling and allowing the case of edge wave when Ae > 0, the following expression is obtained [2]: F 2 -F

A~---

1 --F2

1

~ F2-F1 =AF

(5)

Here, subscripts 1 and 2 mean before and after rolling, respectively. From eqns. (3) and (5),

~,. = + 2x/larl

(6)

where, the ' + ' sign means edge wave and the ' - ' sign means center wave, as shown in Fig. 2. In practice, however, even in the case of cold rolling there should be some lateral plastic flow in the strip edge region. Thus, this ideal case may not fit well with actual data, but the conceptional steepness can be evaluated experimentally from measured data. 2.3. Wavy shape caused by the a m o u n t of coil build-up In the hundreds of wraps of the coiled strip, high spots in the strip profile, even though only very slightly thicker than the bulk of the strip, can account

Dead Flat

Fig. 1. Even dead fiat strip will be changed into wavy strip when the incoming strip crown ratio does not suit the roll gap profile.

352

H.D. Park et al. / Effect of the hot-coil profile

0.2 Steepness, ),

0.1 Edge Wave I

-0.05

i

I

i

I

- 0 . 0 3 -0.01

I

i

i

i

!

0.0! 0.03 0.05 Change of Crown Ratio, hF

-0.2 Fig. 2. Relationship between steepness and change in strip crown ratio.

Fig. 3. Coil build-up and flatness of uncoiled strip.

for a build-up of the coil. T h e y m a y c o n t r i b u t e to a b r a s i o n damage in the s u b s e q u e n t h a n d l i n g of the coil, or cause a w a v y shape in the u n c o i l e d sheet. Since c u s t o m e r s h a v e r e c e n t l y r e q u i r e d s t r i c t e r c o n t r o l of the flatness property, a s t a n d a r d i z e d limit of build-up a m o u n t against such needs is necessary. As shown in Fig. 3, w h e n the build-up a m o u n t is Bt the o u t e r d i a m e t e r of the coil is (Do + 2Bt) at the build-up point. Here, Do is the o u t e r d i a m e t e r in the bulk of the coil. Thus, in the o u t e r m o s t wrap of the coil, the differential e l o n g a t i o n at the build-up point is 2uBt. In total differential s t r a i n A~t- 2~Bt nDo

(7)

H.D. Park et al. / Effect of the hot-coil profile

353

When elastic strain is removed from this, the remaining plastic strain, Aep, may cause a wavy shape, as Aep = A~t- 0.002 = ~ -

0.002 = 2.47~ 2 x 10

4

(8)

Thus, Bt = (1.235~ 2 x 10- * + 0.001) Do 3. E x p e r i m e n t a l

(9)

measurements

Sampling was done twice per coil, once for the hot coil at entry to the welding machine and once for the cold coil at the delivery side of the TCM, the samples being sheared from immediately adjacent positions in the coil. For every coil sampled, the waviness of the strip at the sampled position was measured by the peak height and the pitch of the waves, using a convex rule and a height gauge, on the inspection table of the TCM. The sampled coils were of two gauge groups, thinner and thicker, other parameters such as width and steel grade being similar, as shown in Table 1. For each respective size, three times of sampling were done from the different coils. The sampled specimens were first degreased and then their strip profiles were measured at every 10 mm span of the strip width using a point micrometer with a 1 ~m scale. From the measured data, the correlation between the strip profile and the flatness was evaluated. 4. R e s u l t s

and discussion

4.1. Steepness caused by crown-ratio change The steepness values caused by the change in crown ratio during cold rolling was calculated according to eqn. (6) for the respective sample, after which the measured steepness values at the delivery side of the TCM were compared to the calculated values as shown in Fig. 4. Very good linearity is found between the ideal steepness and the measured steepness. The slopes were dependent only on the gauge group, as follows:

'~act=0.14715 "~th (for thinner gauge)

(10)

~act=0-08152 ~th (for thicker gauge)

(11)

It was very interesting to find that the slopes were very small, which means that the constraining force serving to prevent the elongation of local bands against the bulk of the strip is strong. There might be also some effect of lateral deformation at the strip-edge region on the small value of the observed slope. This relationship can be expressed in general form as the following equation, Aact = (1 - ~) Ath

(12)

H.D. Park et al. / Effect of the hot.coil profile

354 Table 1

Kinds of samples in size and grade Thickness (mm) Hot coil

Cold coil

2.0a 2.3 2.5

0.3~ 0.4 0.5

3.5 3.5

1.0 1.2

a In following tables denoted as 2.0/0.3, etc. Strip width = 1000 1050 nun; steel grade = 20-24 kgf/mm 2 (1 kgf/mm2= 9.81 MPa).

1.5 ~kac t

~< 1.2

--

(1-~)Xth e ~ / J f

.

0.9

~ 0.3 0.0

0

2 Calculated

4

6 Steepness

8

10

~th,

Fig. 4. Linear relationship between the measured steepness values and the calculated steepness values.

w h e r e ~ is a c o n s t r a i n i n g r a t i o r e p r e s e n t i n g the efficiency of the c o n s t r a i n i n g force n o t to e l o n g a t e locally a g a i n s t the bulk of strip.

4.2. Effect of a high spot on the flatness of the product 4.2.1. Deformation of a high spot during cold rolling A h i g h spot of w h i c h the b a n d width is small will cause local buckles after cold rolling since the spot will be e l o n g a t e d more. Also, the r e m a i n d e r of the high spot after cold rolling will c a u s e the build-up defect in the coil product. It is quite n a t u r a l to expect t h a t the a v e r a g e cold-reduction r a t i o c a n be applied to the h i g h spot also. A l o n g with this, the h i g h spot will be r e d u c e d

H.D. Park et al. / Effect of the hot-coil profile

Hot Coil Profile at TCM Entry

355

Cold Coil Profile at TCM Delivery

Thickness

~ Wldth

Pz = ~(1-Rt) PI

Fig. 5. Relationship between the height of high spot in hot-coil profile and that in cold-coil profile. further by locally concentrated contact stress on the projecting point against the work roll of mill. On the other hand, lateral plastic flow will be constrained highly due to its character of being a narrow band at the center of width. There is no good reference by means of which to predict what proportion of the height will be transformed into waves. However, if the constraining ratio, ~, of eqn. (12) is taken, some guidelines on the high spot of the hot-coil profile could be laid down. Then, as shown in Fig. 5, the height of the high spot after rolling, P2, can be expressed by the equation P2 = ~ ( 1 - R t ) P1

(13)

where P1 is the height of the high spot before rolling and R, is the total reduction ratio. Further, the portion ( 1 - ~ ) ( l - R , ) P1 will contribute to the differential elongation of the bulk of the strip width. 4.2.2. Effect of a high spot on coil build-up According to eqn. (8), the amount of build-up, Bt, can be plotted against the steepness value, depending on the coil outer diameter, as shown in Fig. 6. Even though the coiling tension is under the elastic limit, there can be much higher tension arising in the build-up band due to the projecting shape. It is worth noting that a very small change in the amount of build-up brings a very large change in the steepness value when once the strain caused by the build-up exceeds the elastic limit of the strip. In the case that the build-up is purely due to the high spot, it is possible to determine how the high spot in the hot coil will, in the last place, cause the coil build-up defect. Summarized in Table 2 are the observed parameters which may change the height of the high spot in the processing of the cold-rolled strip for the case where the limit of the steepness value is 0.4% in the uncoiled strip product and the coil diameter is 1210 mm. Based on these conditions, the height limit was calculated at each step of the processing, final results being summarized in Table 3. In all cases the height limit of the high spot was less than 10 tun, the limit becoming more severe the

356

H.D. Park et al. / Effect of the hot-coil profile

~ 3 Wavy Shape .-2

1510__.___~ 1210________ 910

Coil Diameters, mm

¥ I

I

I

0.2

0.0

I

0.4

I

I

0.6

I

I

I

0.8

1.0

Steepness of Uncoiled Strip, ;x, Fig. 6. Relationship between build-up amount of coil and steepness of uncoiled strip.

Table 2 Observed data in the processing of the cold-rolled strip Samples (mm)

Reduction ratio (%)

Coil packing (%)

Wraps in coil (No.)

Elongation by processing (%) (mm) CAL

SPM

RCL

2.0/0.3 2.3/0.4 2.5/0.5

85.0 82.6 80.0

96.5 96.7 97.0

1930.0 1450.5 1164.0

0.5 0.5 0.5

0.5 0.5 0.5

0.2 0.2 0.2

3.5/1.0 4.0/1.2

71.4 70.0

98.0 98.0

588.0 490.0

0.5 0.5

0.8 0.9

0.3 0.3

Constraining ratio ~ in first three experiments is 0.85285 and in last two experiments 0.91848.

t h i n n e r t h e final product. F o r the t h i n n e r gauge, e s p e c i a l l y for t h e 0.4 m m t h i c k strip, it w a s quite i n t e r e s t i n g to n o t e t h a t the h i g h spot h a v i n g a h e i g h t of a b o v e 6 ~m, was not allowable, this figure giving a s t r o n g m e s s a g e t h a t the m a i n t e n a n c e of the s u r f a c e s of t h e w o r k roll of t h e finishing s t a n d s of a hot strip mill is v e r y i m p o r t a n t , e s p e c i a l l y for t h i n n e r g a u g e s of h o t coil. T h a t is, r e d u c i n g the c a m p a i g n l e n g t h of w o r k rolls or k e e p i n g w o r k rolls f r o m local w e a r by m e a n s of a cyclic shifting of w o r k rolls in the hot-rolling o p e r a t i o n m i g h t be e s s e n t i a l for the q u a l i t y a s s u r a n c e of t h i n n e r g a u g e cold strips. 4.2.3.

Effect of a

h i g h spot on the s t e e p n e s s

of fully

hard strip

T h e w a v e s in a cold-rolled fully h a r d strip are often r e c o v e r a b l e in subs e q u e n t h i g h t e m p e r a t u r e a n n e a l i n g , w h e r e the e l o n g a t i o n effect is m u c h

357

H.D. Park et al. / Effect of the hot-coil profile Table 3 Permissible limit of high spot in hot-coil profile Samples (mm)

Permissible limit of high spot in the hot coil (~m)

2.0/0.3 2.3/0.4 2.5/0.5

5.2 6.0 6.5

3.5/1.0 4.0/1.2

8.3 9.5

Remarks: the calculating conditions were: (1) steepness of product = 0.4%; (2) coil outer diameter = 1210 ram.

Table 4 Calculation of the buckles of a fully hard strip due to surplus elongation at the band of the high spot Cases (ram)

( 1 - R,)

(1 - 4)

P1 (pro)

Ae ( × 10 s)

Steepness of the fully hard strip (%)

2.0/0.3

0.150

0.14715

12 10 8

94.30 73.58 58.86

2.08 1.73 1.38

2.3/0.4

0.174

0.14715

12 10 8

76.80 64.00 51.20

1.93 1.61 1.29

2.5/0.5

0.200

0.14715

12 10 8

70.63 58.86 47.09

1.85 1.54 1.23

3.5/1.0

0.286

0.08152

20 15 10

46.60 34.96 23.30

1.94 1.46 0.97

4.2/1.0

0.300

0.08152

20 15 10

40.76 30.57 20.38

1.82 1.37 0.91

greater than the observable amount of differential elongation in the cold-rolled s t r i p . H o w e v e r , w h e n t h e f u l l y h a r d s t r i p is u s e d f o r t h e p r o c e s s o f l o w t e m p e r a t u r e r e c o v e r y a n n e a l i n g a n d j u s t g a l v a n i z i n g , t h e f l a t n e s s is v e r y i m p o r t a n t , s i n c e t h e r e is v e r y l i t t l e e l o n g a t i o n e f f e c t i n t h e s u b s e q u e n t p r o c e s s .

358

H.D. Park et al. / Effect of the hot-coil profile 5o

~,~H~/

4o o

30 20

©

lO 0

o

~,

o

,

I

30

i

J

I

60

,

I

~ i

90

I

I

i

120

I

I

150

H o t Coil C r o w n , p m Fig. 7. Relationship between cold-coil crown values and hot-coil crown values.

In this case, the high spot, which may induce local buckles in the fully hard strip, is the critical defect of the hot-coil profile. Since the reduced height of the high spot by rolling will be accommodated by elongation in the rolling direction, the differential strain can be calculated using the principle of constant mass. The results are summarized in Table 4, from which it can be seen t ha t even though a very small proportion of the high spot contributed to the differential elongation, the resulting steepness values were very high. This calculation is not to determine any limit value, but to show the importance of the hot-coil profile, since the recovery of the manifested waves in fully hard strip may depend on the c h a r a c t e r of subsequent processes. 4.3. Effect of the hot-coil crown on the thickness profile of cold-rolled strip On account of the two-dimensional c h a r a c t e r of cold rolling, the cold-strip profile cannot be changed from t hat of the hot-coil profile: the cold-coil crown depends linearly on the hot-coil crown. In the present work, the relationship between hot-coil crown and cold-coil crown has also been studied experimentally, the results being shown in Fig. 7. Here, the crown values plotted were the measured values at both 15 and 25 mm from the strip edge. As expected, different gauge groups showed different degrees of effect, which means th at the degree of dependency may change with steel grade, the size, the draft schedule, and the c h a r a c t e r of the rolling mill. For t hi nner gauge strips, the requirement is for a thickness reduction of less t han 10 ~m over the width of the strip and a hot-coil crown of less than 40 ~m. Since for different gauges the crown value themselves cannot give an exact physical meaning, the crown ratios were plotted as in Fig. 8 and Fig. 9. It has been said [3] : th at the cold-strip crown in the region from the strip center to 75 mm from the edge changes at almost the same crown ratio as the mother

H.D. Park et al. / Effect of the hot-coil profile 7

/

f

• •

6

5 O

O

=

359

Thinner • •.'" OO~ Thicker • .; , /

/

4 3

.'rill

2

~Neasured

1 O

I

0

I

I

I

I

at 15ram from edge

'

I

2

,

3

I

,

4

I

,

5

I

i

6

7

Crown Ratio of Hot Strip, 7.

Fig. 8. Relationship between the crown ratio of the cold strip and that of the hot strip at 15 mm from the strip edge.

5, 6

• •

5~

¢.9

Thinner Thicker

5 4

o ~ ~

o~

0

1

"y

Measured at 25mm from edge

0 O

,

0

I

1 Crown

,

I

,

2 Ratio

t

3

i

I

,

4 of Hot

I

,

5

I

I

6

Strip,

~.

Fig. 9. Relationship between the crown ratio of the cold strip and that of the hot strip at 25 mm from the strip edge.

profile; t h a t the cold-strip c r o w n b e t w e e n 25 m m f r o m the edge a n d t h e e x t r e m e edge c h a n g e s w i t h t h e cold-rolling condition; a n d t h a t the cold-strip c r o w n in the r e g i o n b e t w e e n 75 m m a n d 25 m m f r o m t h e edge is subject to b o t h of t h e s e effects. It is i n t e r e s t i n g , h o w e v e r , t h a t t h e c r o w n r a t i o m e a s u r e d at e v e n 15 m m f r o m the edge s h o w e d a s t r o n g d e p e n d e n c y on the m o t h e r profile, as s h o w n in Fig. 8. T h a t is, e v e n t h o u g h t h e c r o w n r a t i o of t h e cold s t r i p b e c o m e s g r e a t e r t h a n t h a t of the h o t s t r i p t h e closer the m e a s u r i n g p o i n t to t h e strip edge, the basic p a t t e r n of the strip profile is i n h e r e n t to t h e m o t h e r profile. As i l l u s t r a t e d in Fig. 8 a n d Fig. 9, the c r o w n r a t i o of the cold strip w a s g r e a t e r by a b o u t 1.5% at 15 m m f r o m the edge a n d by a b o u t 0.75% a t 25 m m f r o m t h e edge. I t is w o r t h y

360

H.D. Park et al. / Effect of the hot-coil profile

of n o t e t h a t these values are smaller t h a n those of earlier work [3]. Since the edge drop is a replica of work-roll flattening a r o u n d the strip edge [4], the span subjected to edge drop might be smaller for the case of rolling in a mill using a small-diameter work roll, such as a six-high mill. By the same principle, w h e n the cold r e d u c t i o n is g r e a t e r the edge drop will be greater, as illustrated in Fig. 8 and Fig. 9, w h e r e the t h i n n e r gauge shows a slightly g r e a t e r cold-strip crown r a t i o t h a n the t h i c k e r gauge. To meet the r e c e n t m a r k e t d e m a n d for e l e c t r o n i c panel application, it is n e c e s s a r y to produce a strip crown ratio at 15 mm from the edge of less t h a n 1.5%. However, it is clear from Fig. 8 t h a t with the present rolling conditions t h e r e is no way but to have a m o t h e r profile of zero crown or to trim the strip edges after rolling. According to the results of a r e c e n t study [5] however, the edge drop was so m u c h r e d u c e d w h e n using a t a p e r e d work roll t h a t the cold-strip c r o w n ratio was a b o u t the same as the hot-strip crown ratio. Irrespective, it can be said t h a t a hot-strip profile of low crown and low edge drop is essential for t h i n n e r gauge cold strip. 5. C o n c l u s i o n s The effect of the hot-coil profile on the flatness and the profile of the cold-rolled strip has been studied experimentally, from the results of which the following c o n c l u s i o n s can be drawn. (1) The d i s c r e p a n c y in the c r o w n r a t i o between the hot-strip profile and the cold-strip profile causes out-of-flatness in the cold rolled strip in a r e g u l a r manner, so t h a t the observed steepness values c o r r e l a t e linearly with the c a l c u l a t e d values. (2) Coil build-up can be induced by a v e r y small t r a c e of high spot in the hot-strip profile, so that, for example, the h e i g h t limit of the high spot was found to be 6 ~m for the 0.4 mm thick cold strip. (3) The cold-strip c r o w n values c o r r e l a t e l i n e a r l y with the hot-strip values, but the degree of d e p e n d e n c y is different for each t h i c k n e s s group. (4) The c r o w n r a t i o of the cold strip became g r e a t e r t h a n t h a t of the hot strip as the m e a s u r i n g point b e c a m e closer to the strip edge, but the influence of the profile of the m o t h e r strip r e m a i n e d even at a point 15 mm from the edge. References [1] F. Hollander and A. Hurkmans, Dimensional control in rolling mills, Proc. 5th Int. Rolling Conf., September 1990, London, UK, pp. 33-45. [2] H. Hirano (Ed.), ISIJ, Theory and Practice in Flat Rolling, 1983, (in Japanese), p. 96. [3] M. Ikeda, J. Satoh, Y. Ohike and M. Ohkura, CAMP-ISIJ, 5 (1992) 487-490. [4] T. Ishikawa and N. Yukawa, CAMP-ISIJ, 5 (1992) 452-454. [5] M. Sihonmatsu, S. Inoue and K. Aoki, CAMP-ISIJ, 5 (1992) 491-494.