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United States Patent Application 20030111206
Kind Code A1
Blejde, Walter N. ;   et al. June 19, 2003

Casting steel strip

Abstract

A method of producing strip comprising the steps of assembling a pair of casting rolls with a nip between them, introducing between the casting rolls to form a casting pool of molten carbon steel having a total oxygen content of at least 100 ppm and usually less than 250 ppm, counter rotating the casting rolls, solidifying the molten steel on the rolls to form metal shells with levels of oxide inclusions reflected by the total oxygen content of the molten steel, and forming thin steel strip through the nip between the casting rolls from the solidified shells. A unique steel strip may be obtained using the method having ductile properties.


Inventors: Blejde, Walter N.; (Brownsburg, IN) ; Mahapatra, Rama Ballav; (Indianapolis, IN) ; Strezov, Lazar; (New South Wales, AU)
Correspondence Address:
    BARNES & THORNBURG
    11 SOUTH MERIDIAN
    INDIANAPOLIS
    IN
    46204
Serial No.: 243699
Series Code: 10
Filed: September 13, 2002

Current U.S. Class: 164/480
Class at Publication: 164/480
International Class: B22D 011/06


Claims



1. A method of making a steel strip by continuous casting comprising the steps of: a. assembling a pair of cooled casting rolls having a nip between them and with confining closures adjacent the ends of the nip; b. introducing molten low carbon steel having a total oxygen content of at least 100 ppm between the pair of casting rolls to form a casting pool between the casting rolls; c. counter rotating the casting rolls and solidifying the molten steel to form metal shells on the surfaces of the casting rolls with levels of oxide inclusions reflected by the total oxygen content of the molten steel to promote the formation of thin steel strip; and d. forming solidified thin steel strip through the nip between the casting rolls from said solidified shells.

2. The method of making steel strip as claimed in claim 1 wherein the molten steel in the casting pool has carbon content in the range of 0.001% to 0.1% by weight, a manganese content in the range of 0.01% to 2.0% by weight, and a silicon content in the range of 0.01% to 10% by weight.

3. The method of making steel strip as claimed in claim 2 wherein the molten steel in the casting pool has an aluminum content on the order of 0.01% or less by weight.

4. The method of making steel strip as claimed in claim 2 wherein: the molten steel in the casting pool has an oxygen content between 100 ppm and 250 ppm.

5. The method of making steel strip as claimed in claim 1 wherein: the molten steel in the casting pool has an oxygen content between 100 ppm and 250 ppm.

6. The method of making steel strip as claimed in claim 1 wherein the molten steel contains oxide inclusions comprising any one or more of MnO, SiO.sub.2 and Al.sub.2O.sub.3 distributed through the steel at an inclusion density in the range 2 gm/cm.sup.3 to 4 gm/cm.sup.3.

7. The method of making steel strip as claimed in claim 1 wherein more than a majority of the inclusions range in size between 2 and 12 microns.

8. The method of making steel strip as claimed in claim 1 wherein the sulphur content of the molten steel is less than 0.01% by weight.

9. A method of making steel strip as claimed in claim 1 comprising the additional steps of: e. refining the molten steel prior to forming the casting pool by heating a steel charge and slag forming material to form molten steel covered by a slag containing silicon, manganese and calcium oxides, f. stirring the molten steel by injecting an inert gas into molten steel to cause desulphurization, and thereafter g. injecting oxygen to produce molten steel having the total oxygen content of greater than 100 ppm.

10. The method of making steel strip as claimed in claim 9 wherein the desulphurization reduces the sulphur content of the molten steel to less than 0.01% by weight.

11. The method of making a thin steel strip as claimed in claim 9 wherein the solidified steel is a silicon/manganese killed steel and the inclusions comprise any one or more of MnO, SiO.sub.2 and Al.sub.2O.sub.3.

12. The method of making a thin steel strip as claimed in claim 9 wherein more than a majority of the inclusions range in size between 2 and 12 microns.

13. The method of making a steel strip as claimed in claim 9 wherein the solidified steel has a total oxygen content in the range of 100 ppm to 250 ppm.

14. A thin steel strip produced by twin roll casting to a thickness of less than 5 mm and formed of a solidified steel containing solidified oxide inclusions distributed such that surface regions of the strip to a depth of 2 microns from the surface contain such inclusions to a per unit area density of at least 120 inclusions/mm.sup.2.

15. The thin steel strip as claimed in claim 14 wherein the majority of the solidified steel is a silicon/manganese killed steel and the inclusions comprise any one or more of MnO, SiO.sub.2 and Al.sub.2O.sub.3.

16. The thin steel strip as claimed in claim 14 wherein the majority of the inclusions range in size between 2 and 12 microns.

17. The thin steel strip as claimed in claim 14 wherein the solidified steel has a total oxygen content in the range 100 ppm to 250 ppm.

18. The thin steel strip produced by twin roll casting to a thickness of less than 5 mm and formed of a solidified steel containing oxide inclusions distributed to reflect an oxygen content in the solidified steel in the range 100 ppm to 250 ppm.

19. The thin steel strip as claimed in claim 18 wherein the majority of the solidified steel is a silicon/manganese killed steel and the inclusions comprise any one or more of MnO, SiO.sub.2 and Al.sub.2O.sub.3.

20. The thin steel strip as claimed in claim 18 wherein the majority of the inclusions range in size between 2 and 12 microns.
Description



[0001] This application claims priority to, and the benefit of, U.S. Provisional Patent Application No. 60/322,261, filed Sep. 14, 2001, the disclosure of which is expressly incorporated herein by reference.

BACKGROUND AND SUMMARY OF THE INVENTION

[0002] This invention relates to the casting of steel strip. It has particular application to continuous casting of thin steel strip in a twin roll caster.

[0003] In twin roll casting, molten metal is introduced between a pair of contra-rotated horizontal casting rolls which are cooled so that metal shells solidify on the moving roll surfaces and are brought together at the nip between them to produce a solidified strip product delivered downwardly from the nip between the rolls. The term "nip" is used herein to refer to the general region at which the rolls are closest together. The molten metal may be poured from a ladle into a smaller vessel from which it flows through a metal delivery nozzle located above the nip so as to direct it into the nip between the rolls so forming a casting pool of molten metal supported on the casting surfaces of the rolls immediately above the nip and extending along the length of the nip. This casting pool is usually confined between side plates or dams held in sliding engagement with end surfaces of the rolls so as to dam the two ends of the casting pool against outflow, although alternative means such as electromagnetic barriers have also been proposed.

[0004] When casting thin steel strip in a twin roll caster the molten steel in the casting pool will generally be at a temperature of the order of 1500.degree. C. and above, and it is therefore necessary to achieve very high cooling rates over the casting surfaces of the rolls. It is particularly important to achieve a high heat flux and extensive nucleation on initial solidification of the steel on the casting surfaces to form the metal shells. U.S. Pat. No. 5,720,336 describes how the heat flux on initial solidification can be increased by adjusting the steel melt chemistry such that a substantial proportion of the metal oxides formed as deoxidation products are liquid at the initial solidification temperature so as to form a substantially liquid layer at the interface between the molten metal and each casting surface. As disclosed in U.S. Pat. Nos. 5,934,359 and 6,059,014 and International Application AU 99/00641, nucleation of the steel on initial solidification can be influenced by the texture of the casting surface. In particular International Application AU 99/00641 discloses that a random texture of peaks and troughs can enhance initial solidification by providing potential nucleation sites distributed throughout the casting surfaces. We have now determined that nucleation is also dependent on the presence of oxide inclusions in the steel melt and that surprisingly it is not advantageous in twin roll strip casting to cast with "clean" steel in which the number of inclusions formed during deoxidation has been minimized in the molten steel prior to casting.

[0005] Steel for continuous casting is subjected to deoxidation treatment in the ladle prior to pouring. In twin roll casting the steel is generally subjected to silicon manganese ladle deoxidation although it is possible to use aluminum deoxidation with calcium addition to control the formation of solid Al.sub.2O.sub.3 inclusions that can clog the fine metal flow passages in the metal delivery system through which molten metal is delivered to the casting pool. It has hitherto been thought desirable to aim for optimum steel cleanliness by ladle treatment to minimize the total oxygen level in the molten steel. However we have now determined that lowering the steel oxygen level reduces the volume of inclusions and if the total oxygen content of the steel is reduced below a certain level the nature of the initial contact between the steel and roll surfaces can be adversely effected to the extent that there is insufficient nucleation to generate rapid initial solidification and high heat flux. Molten steel is trimmed by deoxidation in the ladle such that the total oxygen content falls within a range which ensures satisfactory solidification on the casting rolls and production of a satisfactory strip product. The molten steel contains a distribution of oxide inclusions (typically MnO, CaO, SiO.sub.2 and/or Al.sub.2O.sub.3) sufficient to provide an adequate density of nucleation sites on the roll surfaces for initial solidification and the resulting strip product exhibits a characteristic distribution of solidified inclusions.

[0006] There is provided a method of casting steel strip comprising:

[0007] assembling a pair of cooled casting rolls having a nip between them and confining closures adjacent the ends of the nip;

[0008] introducing molten low carbon steel between said pair of casting rolls to form a casting pool between the casting rolls with said closures confining the pool adjacent the ends of the nip, with the molten steel having a total oxygen content in the casting pool of at least 100 ppm and usually less than 250 ppm;

[0009] counter rotating the casting rolls and solidifying the molten steel to form metal shells on the casting rolls with levels of oxide inclusions reflected by the total oxygen content of the molten steel to promote the formation of thin steel strip; and

[0010] forming solidified thin steel strip through the nip between the casting rolls to produce a solidified steel strip delivered downwardly from the nip.

[0011] The total oxygen content of the molten steel in the casting pool may be about 200 ppm. The low carbon steel may have a carbon content in the range 0.001% to 0.1% by weight, a manganese content in the range 0.01% to 2.0% by weight and a silicon content in the range 0.01% to 10% by weight. The steel may have an aluminum content of the order of 0.01% or less by weight. The aluminum may for example be as little as 0.008% or less by weight. The molten steel may be a silicon/manganese killed steel.

[0012] The oxide inclusions are solidification inclusions and deoxidation inclusions. The solidification inclusions are formed during cooling and solidification of the steel in casting, and deoxidation inclusions are formed during deoxidation of the molten steel before casting. The solidified steel may contain oxide inclusions usually comprised of any one or more of MnO, SiO.sub.2 and Al.sub.2O.sub.3 distributed through the steel at an inclusion density in the range 2 gm/cm.sup.3 and 4 gm/cm.sup.3.

[0013] The molten steel may be refined in a ladle prior to introduction between the casting rolls to form the casting pool by heating a steel charge and slag forming material in the ladle whereby to form molten steel covered by a slag containing silicon, manganese and calcium oxides. The molten steel may be stirred by injecting an inert gas into it to cause desulphurization, and with steels such as a silicon/manganese killed steel, then injecting oxygen, to produce steel having the desired total oxygen content of at least 100 ppm and usually less than 250 ppm. The desulphurization may reduce the sulphur content of the molten steel to less than 0.01% by weight.

[0014] The thin steel strip produced by continuous twin roll casting as described above has a thickness of less than 5 mm and is formed of a solidified steel containing solidified oxide inclusions. The distribution of the inclusions may be such that the surface regions of the strip to a depth of 2 microns from the outer faces contain solidified inclusions to a per unit area density of at least 120 inclusions/mm.sup.2.

[0015] The solidified steel may be a silicon/manganese killed steel and the oxide inclusions may comprise any one or more of MnO, SiO.sub.2 and Al.sub.2O.sub.3 inclusions. The inclusions typically may range in size between 2 and 12 microns, so that at least a majority of the inclusions are in that size range.

[0016] The method described above produces a unique steel high in oxygen content distributed in oxide inclusions. Specifically, the combination of the high oxygen content in the molten steel and the short residence time of the molten steel in the casting pool results in a thin steel strip with improved ductility properties.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order that the invention may be described in more detail, some specific examples will be given with reference to the accompanying drawings in which:

[0018] FIG. 1 shows the effect of inclusion melting points on heat fluxes obtained in twin roll casting trials using silicon/manganese killed steels;

[0019] FIG. 2 is an energy dispersive spectroscopy (EDS) map of Mn showing a band of fine solidification inclusions in a solidified steel strip;

[0020] FIG. 3 is a plot showing the effect of varying manganese to silicon contents on the liquidus temperature of inclusions;

[0021] FIG. 4 shows the relationship between alumina content (measured from the strip inclusions) and deoxidation effectiveness;

[0022] FIG. 5 is a ternary phase diagram for MnO SiO.sub.2 Al.sub.2O.sub.3;

[0023] FIG. 6 shows the relationship between alumina content inclusions and liquidus temperature;

[0024] FIG. 7 shows the effect of oxygen in a molten steel on surface tension; and

[0025] FIG. 8 is a plot of the results of calculations concerning the inclusions available for nucleation at differing steel cleanliness levels.

DETAILED DESCRIPTION OF THE DRAWINGS

[0026] While the invention will be illustrated and described in detail in the drawings and following description, the same is to be considered as illustrative and not restrictive in character, it being understood that one skilled in the art will recognize, and that it is desired to protect, all aspects, changes and modifications that come within the spirit of the invention.

[0027] We have conducted extensive casting trials on a twin roll caster of the kind fully described in U.S. Pat. Nos. 5,184,668 and 5,277,243 to produce steel strip of the order of 1 mm thick and less. Such casting trials using silicon manganese killed steel have demonstrated that the melting point of oxide inclusions in the molten steel have an effect on the heat fluxes obtained during steel solidification as illustrated in FIG. 1. Low melting point oxides improve the heat transfer contact between the molten metal and the casting roll surfaces in the upper regions of the pool, generating higher heat transfer rates. Liquid inclusions are not produced when the melting point is greater than the steel temperature in the casting pool. Therefore, there is a dramatic reduction in heat transfer rate when the inclusion melting point is greater than approximately 1600.degree. C.

[0028] Casting trials with aluminum killed steels have shown that in order to avoid the formation of high melting point alumina inclusions (melting point 2050.degree. C.) it is necessary to have calcium treatment to provide liquid CaO.Al.sub.2O.sub.3 inclusions.

[0029] The oxide inclusions formed in the solidified metal shells and in turn the thin steel strip comprise inclusions formed during cooling and solidification of the steel, and deoxidation inclusions formed during refining in the ladle.

[0030] The free oxygen level in the steel is reduced dramatically during cooling at the meniscus, resulting in the generation of solidification inclusions near the surface of the strip. These solidification inclusions are formed predominantly of MnO.SiO.sub.2 by the following reaction:

Mn+Si+3O.dbd.MnO.SiO.sub.2

[0031] The appearance of the solidification inclusions on the strip surface, obtained from an Energy Dispersive Spectroscopy (EDS) map, is shown in FIG. 2. It can be seen that solidification inclusions are extremely fine (typically less than 2 to 3 .mu.m) and are located in a band located within 10 to 20 .mu.m from the surface. A typical size distribution of the inclusions through the strip is shown in FIG. 3 of our paper entitled Recent Developments in Project M the Joint Development of Low Carbon Steel Strip Casting by BHP and IHI, presented at the METEC Congress 99, Dusseldorf Germany (Jun. 13-15, 1999)

[0032] The comparative levels of the solidification inclusions are primarily determined by the Mn and Si levels in the steel. FIG. 3 shows that the ratio of Mn to Si has a significant effect on the liquidus temperature of the inclusions. A manganese silicon killed steel having a carbon content in the range of 0.001% to 0.1% by weight, a manganese content in the range 0.1% to 2.0% by weight and a silicon content in the range 0.1% to 10% by weight and an aluminum content of the order of 0.01% or less by weight can produce such oxide inclusions during cooling of the steel in the upper regions of the casting pool. In particular the steel may have the following composition, termed M06:

1 Carbon 0.06% by weight Manganese 0.6% by weight Silicon 0.28% by weight Aluminium 0.002% by weight.

[0033] Deoxidation inclusions are generated during deoxidation of the molten steel in the ladle with Al, Si and Mn. Thus, the composition of the oxide inclusions formed during deoxidation is mainly MnO.SiO.sub.2.Al.sub.2O.sub.3 based. These deoxidation inclusions are randomly located in the strip and are coarser than the solidification inclusions near the strip surface.

[0034] The alumina content of the inclusions has a strong effect on the free oxygen level in the steel. FIG. 4 shows that with increasing alumina content, free oxygen in the steel is reduced. With the introduction of alumina, MnO.SiO.sub.2 inclusions are diluted with a subsequent reduction in their activity, which in turn reduces the free oxygen level, as seen from the reaction below:

Mn+Si+3O+Al.sub.2O.sub.3(Al.sub.2O.sub.3).MnO.SiO.sub.2.

[0035] For MnO--SiO.sub.2--Al.sub.2O.sub.3 based inclusions, the effect of inclusion composition on liquidus temperature can be obtained from the ternary phase diagram shown in FIG. 5.

[0036] Analysis of the oxide inclusions in the thin steel strip has shown that the MnO/SiO.sub.2 ratio is typically within 0.6 to 0.8 and for this regime, it was found that alumina content of the oxide inclusions had the strongest effect on the inclusion melting point (liquidus temperature), as shown in FIG. 6.

[0037] We have determined that it is important for casting in accordance with the present invention to have the solidification and deoxidation inclusions such that they are liquid at the initial solidification temperature of the steel and that the molten steel in the casting pool have an oxygen content of at least 100 ppm to produce metal shells with levels of oxide inclusions reflected by the total oxygen content of the molten steel to promote nucleation and high heat flux during the initial solidification of the steel on the casting roll surfaces. Both solidification and deoxidation inclusions are oxide inclusions and provide nucleation sites and contribute significantly to nucleation during the metal solidification process, but the deoxidation inclusions are ultimately rate controlling in that their concentration can be varied. The deoxidation inclusions are much bigger, typically greater than 4 microns, whereas the solidification inclusions are generally less than 2 microns and are MnO.SiO.sub.2 based and have no Al.sub.2O.sub.3 whereas the deoxidation inclusions also have Al.sub.2O.sub.3.

[0038] It has been found in casting trials using the above M06 grade of silicon/manganese killed steel that if the total oxygen content of the steel is reduced in the ladle refining process to low levels of less than 100 ppm, heat fluxes are reduced and casting is impaired whereas good casting results can be achieved if the total oxygen content is at least above 100 ppm and typically on the order of 200 ppm. The total oxygen content may be measured by a "Leco" instrument and is controlled by the degree of "rinsing" during ladle treatment, i.e. the amount of argon bubbled through the ladle via a porous plug or top lance, and the duration of the treatment. The total oxygen content was measured by conventional procedures using the LECO TC-436 Nitrogen/Oxygen Determinator described in the TC 436 Nitrogen/Oxygen Determinator Instructional Manual available from LECO (Form No. 200-403, Rev. Apr. 96, Section 7 at pp. 7-1 to 7-4.

[0039] In order to determine whether the enhanced heat fluxes obtained with higher total oxygen contents was due to the availability of oxide inclusions as nucleation sites, casting trials were carried out with steels in which deoxidation in the ladle was carried out with calcium silicide (Ca-Si) and the results compared with casting with the low carbon Si-killed steel known as M06 grades of steel. The results are set out in the following table:

2TABLE 1 Heat flux differences between M06 and Ca--Si grades. Casting Pool speed, Height, Total heat Cast No. Grade (m/min) (mm) Removed (MW) M 33 M06 64 171 3.55 M 34 M06 62 169 3.58 O 50 Ca--Si 60 176 2.54 O 51 Ca--Si 66 175 2.56

[0040] Although Mn and Si levels were similar to normal Si-killed grades, the free oxygen level in Ca--Si heats was lower and the oxide inclusions contained more CaO. Heat fluxes in Ca--Si heats were lower despite a lower inclusion melting point (See Table 2).

3TABLE 2 Slag compositions with Ca--Si deoxidation Inclusion Free melting Oxygen Slag Composition (wt %) temperature Grade (ppm) SiO.sub.2 MnO Al.sub.2O.sub.3 CaO (.degree. C.) Ca--Si 23 32.5 9.8 32.1 22.1 1399

[0041] Oxygen levels in Ca-Si grades were lower, typically 20 to 30 ppm compared to 40 to 50 ppm with M06 grades. Oxygen is a surface active element and thus reduction in oxygen level is expected to reduce the wetting between molten steel and the casting rolls and cause a reduction in the heat transfer rate. However, from FIG. 7 it appears that oxygen reduction from 40 to 20 ppm may not be sufficient to increase the surface tension to levels that explain the observed reduction in the heat flux.

[0042] It can be concluded that lowering the oxygen level in the steel reduces the volume of inclusions and thus reduces the number of oxide inclusions for initial nucleation. This has the potential to adversely impact the nature of the initial contact between steel and the roll surface. Dip testing work has shown that a nucleation per unit area density of about 120/mm.sup.2 is required to generate sufficient heat flux on initial solidification in the upper or meniscus region of the casting pool. Dip testing involves advancing a chilled block into a bath of molten steel at such a speed as to closely simulate the conditions at the casting surfaces of a twin roll caster. Steel solidifies onto the chilled block as it moves through the molten bath to produce a layer of solidified steel on the surface of the block. The thickness of this layer can be measured at points throughout its area to map variations in the solidification rate and therefore the effective rate of heat transfer at the various locations. It is thus possible to produce an overall solidification rate as well as total heat flux measurements. It is also possible to examine the microstructure of the strip surface to correlate changes in the solidification microstructure with the changes in observed solidification rates and heat transfer values and to examine the structures associated with nucleation on initial solidification at the chilled surface. A dip testing apparatus is more fully described in U.S. Pat. No. 5,720,336.

[0043] The relationship of the oxygen content of the liquid steel on initial nucleation and heat transfer has been examined using a model described in Appendix 1. This model assumes that all the oxide inclusions are spherical and are uniformly distributed throughout the steel. A surface layer was assumed to be 2 .mu.m and it was assumed that only inclusions present in that surface layer could participate in the nucleation process on initial solidification of the steel. The input to the model was total oxygen content in the steel, inclusion diameter, strip thickness, casting speed, and surface layer thickness. The output was the percentage of inclusions of the total in the steel required to meet a targeted nucleation per unit area density of 120/mm.sup.2.

[0044] FIG. 8 is a plot of the percentage of oxide inclusions in the surface layer required to participate in the nucleation process to achieve the target nucleation per unit area density at different steel cleanliness levels as expressed by total oxygen content, assuming a strip thickness of 1.6 mm and a casting speed of 80 m/min. This shows that for a 2 .mu.m inclusion size and 200 ppm total oxygen content, 20% of the total available oxide inclusions in the surface layer are required to achieve the target nucleation per unit area density of 120/mm.sup.2. However, at 80 ppm total oxygen content, around 50% of the inclusions are required to achieve the critical nucleation rate and at 40 ppm total oxygen level there will be an insufficient level of oxide inclusions to meet the target nucleation per unit area density. Accordingly when trimming the steel by deoxidation in the ladle, the oxygen content of the steel can be controlled to produce a total oxygen content in the range 100 to 250 ppm and typically about 200 ppm. This will have the result that the two micron deep layers adjacent the casting rolls on initial solidification will contain oxide inclusions having a per unit area density of at least 120/mm.sup.2. These inclusions will be present in the outer surface layers of the final solidified strip product and can be detected by appropriate examination, for example by energy dispersive spectroscopy (EDS).

EXAMPLE

[0045]

4 INPUTS Critical nucleation per 120 This value has unit area density no/mm2 been obtained (needed to achieve sufficient from heat transfer rates) experimental dip testing work Roll width m 1 Strip thickness mm 1.6 Ladle tonnes t 120 Steel density, kg/m3 7800 Total oxygen, ppm 75 Inclusion density, kg/m3 3000 OUTPUTS Mass of inclusions, kg 21.42857 Inclusion diameter, m 2.00E-06 Inclusion volume, m3 0.0 Total no of 1706096451319381.5 inclusions Thickness of surface 2 layer, .mu.m (one side) Total no of 4265241128298.4536 These inclusions inclusions surface can participate only in the initial nucleation process Casting speed, m/min 80 Strip length, m 9615.38462 Strip surface area, m2 19230.76923 Total no of nucleating 2307692.30760 sites required % of available inclusions 54.10462 that need to participate in the nucleation process

[0046] Appendix 1

[0047] a. List of Symbols

[0048] w=roll width, m

[0049] t=strip thickness, mm

[0050] m.sub.s=steel weight in the ladle, tonne

[0051] .rho..sub.s=density of steel, kg/m.sup.3

[0052] .rho..sub.i=density of inclusions, kg/m3

[0053] O.sub.t=total oxygen in steel, ppm

[0054] d=inclusion diameter, m

[0055] v.sub.i=volume of one inclusions, m3

[0056] m.sub.i=mass of inclusions, kg

[0057] N.sub.t=total number of inclusions

[0058] t.sub.s=thickness of the surface layer, um

[0059] N.sub.s=total number of inclusions present in the surface (that can participate in the nucleation process)

[0060] u=casting speed, m/min

[0061] L.sub.s=strip length, m

[0062] A.sub.s=strip surface area, m2

[0063] N.sub.req=Total number of inclusions required to meet the target nucleation density

[0064] NC.sub.t=target nucleation per unit area density, number/mm2 (obtained from dip testing)

[0065] N.sub.av=% of total inclusions available in the molten steel at the surface of the casting rolls for initial nucleation process.

[0066] b. Equations

m.sub.i=(O.sub.t.times.m.sub.s.times.0.001)/0.42 (1)

[0067] Note: for Mn-Si killed steel, 0.42 kg of oxygen is needed to produce 1 kg of neclusions with a composition of 30% MnO, 40% SiO.sub.2 and 30% Al.sub.2O.sub.3.

[0068] For Al-killed steel (with Ca injection), 0.38 kg of oxygen is required to produce 1 kg of inclusions with a composition of 50% Al.sub.2O.sub.3 and 50% CaO.

v.sub.i=4.19.times.(d/2).sup.3 (2)

N.sub.t=m.sub.i/(.rho..sub.i.times.v.sub.i) (3)

N.sub.s=(2.0 t.sub.s.times.0.001.times.N.sub.t/t) (4)

L.sub.s=(m.sub.s.times.1000)/(.rho..sub.s.times.w.times.t/1000) (5)

A.sub.s=2.0.times.L.sub.s.times.w (6)

N.sub.req=A.sub.s.times.10.sup.6.times.NC.sub.t (7)

N.sub.av % =(N.sub.req/N.sub.s).times.100.0

[0069] Eq. 1 calculates the mass of inclusions in steel.

[0070] Eq. 2 calculates the volume of one inclusion assuming they are spherical.

[0071] Eq. 3 calculates the total number of inclusions available in steel.

[0072] Eq. 4 calculates the total number of inclusions available in the surface layer (assumed to be 2 .mu.m on each side). Note that these inclusions can only participate in the initial nucleation.

[0073] Eq. 5 and Eq. 6 are used to calculate the total surface area of the strip.

[0074] Eq. 7 calculates the number of inclusions needed at the surface to meet the target nucleation rate.

[0075] Eq. 8 is used to calculate the percentage of total inclusions available at the surface which must participate in the nucleation process. Note if this number is great than 100%, then the number of inclusions at the surface is not sufficient to meet target nucleation rate.

* * * * *

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