CN106670413B - A kind of computational methods of determining continuous cast mold slag film thickness - Google Patents
A kind of computational methods of determining continuous cast mold slag film thickness Download PDFInfo
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- CN106670413B CN106670413B CN201710140299.4A CN201710140299A CN106670413B CN 106670413 B CN106670413 B CN 106670413B CN 201710140299 A CN201710140299 A CN 201710140299A CN 106670413 B CN106670413 B CN 106670413B
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- 239000002893 slag Substances 0.000 title claims abstract description 125
- 238000000205 computational method Methods 0.000 title abstract 2
- 230000005499 meniscus Effects 0.000 claims abstract description 18
- 239000007787 solid Substances 0.000 claims abstract description 14
- 238000005266 casting Methods 0.000 claims abstract description 12
- 238000004364 calculation method Methods 0.000 claims abstract description 10
- 238000004458 analytical method Methods 0.000 claims abstract description 6
- 230000010355 oscillation Effects 0.000 claims abstract description 6
- 230000004907 flux Effects 0.000 claims abstract description 5
- 238000009749 continuous casting Methods 0.000 claims description 27
- 229910000831 Steel Inorganic materials 0.000 claims description 19
- 239000010959 steel Substances 0.000 claims description 19
- 230000001133 acceleration Effects 0.000 claims description 15
- 238000000034 method Methods 0.000 claims description 14
- 230000008569 process Effects 0.000 claims description 8
- 230000003068 static effect Effects 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 5
- 239000000843 powder Substances 0.000 claims description 5
- 230000035882 stress Effects 0.000 claims description 5
- 230000009471 action Effects 0.000 claims description 4
- 238000012546 transfer Methods 0.000 claims description 4
- 230000008642 heat stress Effects 0.000 claims description 3
- 238000009851 ferrous metallurgy Methods 0.000 abstract description 2
- 238000005461 lubrication Methods 0.000 abstract description 2
- 230000007246 mechanism Effects 0.000 abstract description 2
- 238000004088 simulation Methods 0.000 abstract description 2
- 238000013459 approach Methods 0.000 abstract 1
- 239000007788 liquid Substances 0.000 description 8
- 230000007547 defect Effects 0.000 description 4
- 230000001050 lubricating effect Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000001816 cooling Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000012466 permeate Substances 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000007711 solidification Methods 0.000 description 1
- 230000008023 solidification Effects 0.000 description 1
Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
- B22D11/10—Supplying or treating molten metal
- B22D11/11—Treating the molten metal
- B22D11/111—Treating the molten metal by using protecting powders
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
- B22D11/16—Controlling or regulating processes or operations
- B22D11/166—Controlling or regulating processes or operations for mould oscillation
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Continuous Casting (AREA)
Abstract
The invention belongs to Ferrous Metallurgy casting process mathematical simulation application field, more particularly to a kind of computational methods of determining continuous cast mold slag film thickness.The present invention simplifies continuous cast mold meniscus slag road shape, and Solidified Flux Film is thought of as planar solid slag film and is adhered on crystallizer wall with mold oscillation.Wherein, x-axis is parallel to throwing direction, and y-axis is perpendicular to throwing direction, R (x) is Solidified Flux Film curvilinear equation, S (x) is solidified shell contour curve equation, and slag road is divide into upper part and lower part by line of demarcation, and upper part uses Bikerman meniscus shape equations.The present invention to the determining of continuous cast mold slag film thickness is proposed based on green shell force analysis, by the vibration of crystallizer, this key factor is considered into, new approaches are provided for lubrication mechanism in vibrating crystallizer, makes result of calculation more closing to reality, more has directive significance to practical operation.
Description
Technical Field
The invention belongs to the field of mathematical simulation application of ferrous metallurgy continuous casting process, and particularly relates to a calculation method for determining the thickness of a slag film of a continuous casting crystallizer.
Background
The development of high-speed continuous casting puts higher demands on the lubricating action of a slag film between a crystallizer and a casting blank, and a plurality of defects of the continuous casting blank, particularly surface defects, are generated in the initial solidification stage of molten steel in the crystallizer and are expanded in the secondary cooling and straightening processes. The casting technology of the covering slag is adopted, the covering slag is added to the liquid level of the liquid steel of the crystallizer in the casting process and covers the liquid level of the liquid steel, and when the crystallizer regularly vibrates up and down, the covering slag permeates into a gap between the wall of the crystallizer and a casting blank shell to form a layer of slag film. The thickness of the slag film directly influences the heat transfer and lubrication between the molten steel and the wall of the crystallizer, and plays an important role in the smooth running of the continuous casting process and the surface quality of a casting blank. Therefore, to control the vibration mark defect as much as possible, the thickness of the slag film of the casting powder and the change rule of the slag film along with the vibration waveform need to be specified, so that the purposes of achieving good lubricating effect and reducing the vibration mark to the maximum extent are achieved.
The existing method for determining the thickness of the slag film is to predict the liquid state, the solid state and the respective thickness of the molten covering slag film through the temperature field distribution. The crystallizer is considered to be static, analysis on the influence of crystallizer vibration on the thickness of a slag film is lacked, and the crystallizer vibration is a significant factor which is not negligible in actual operation. Therefore, the existing slag film thickness determination method is not close to practice.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a calculation method for determining the thickness of a slag film of a continuous casting crystallizer, which analyzes the stress condition of a blank shell and considers the important factor of the vibration of the crystallizer so as to achieve the aim of making the result closer to the reality and have more guiding significance for the actual operation.
The technical scheme of the invention is realized as follows:
a calculation method for determining the thickness of a slag film of a continuous casting crystallizer comprises the following steps:
step 1: determining the shape of the meniscus of a continuous casting mould
Simplifying a slag channel in the meniscus area, wherein the shape of the slag channel depends on the surface contour of the solid slag film and the meniscus; the slag channel is divided into an upper part and a lower part along the billet drawing direction, and the upper part adopts a Bikerman equation:
in the formula, l is meniscus height mm; sigmasfIs the interfacial tension of steel slag, N.m-1；ρsIs the density of molten steel, kg.m-3；ρfAs the density of the mold flux, kg.m-3；
Because the shape of the slag channel is that the air gap is gradually increased along the direction of drawing, the lower part of the slag channel model determines the outline of the solid slag film and the outline of the blank shell by a crystallizer heat transfer model and a heat-stress model, R (x) and S (x) are respectively the equations of the outline of the solid slag film and the outline of the blank shell, and the equations are as follows:
determining initial value, selecting slag film at the boundary of upper and lower parts of slag channel as initial slag film thickness d0Mm; oscillation speed v of the mold0，m·s-1；
Step 2: determining the pressure of the slag channel of a continuous casting mold
The formula for determining the slag channel pressure of the continuous casting crystallizer is as follows:
wherein,
in the formula, pfIs a pressure variable, Pa; v. ofmM.s. the oscillation speed of the mold-1；vcIs the pulling speed, m.s-1η is the viscosity of the casting powder, Pa.s, p1Is the slag channel inlet pressure, p1＝ρfgd, Pa; d is the depth of the molten pool, m;
and step 3: determining acceleration
The stress analysis of the blank shell shows that the blank shell is subjected to the total pressure of a slag channel and the static pressure of molten steel, and the acceleration of the blank shell in the direction vertical to a drawing blank is calculated by a Newton's second law under the combined action of the two pressures, wherein the formula is as follows:
F＝ma (8)
wherein F is a resultant force, i.e., F ═ Fd-Fs，Fd、FsRespectively is total pressure of the slag channel and static pressure of molten steelForce, N; m is the shell mass, kg, a is the acceleration, m/s2；
And 4, step 4: determining the thickness of slag film of continuous casting crystallizer
Determining the acceleration of the blank shell and the initial speed of the blank shell according to the step 3, and calculating the moving distance of the blank shell in a short period of time; adopting an iteration method, taking a short period of time as an iteration step length, and according to the initial slag film thickness d0And t1Calculating total pressure F of slag channel by using vibration speed at moment1Thereby obtaining an acceleration a1Calculating the moving distance s of the shell according to the formula (9)1：
Wherein v is the moving speed of the shell, i.e. v is at, and the initial speed is zero;
thereby obtaining the thickness d of the slag film1Is d1＝d0+s1According to d1And t2Calculating total pressure F of slag channel by using vibration speed at moment2Repeating the steps until the vibration period is finished; therefore, the change rule of the thickness of the corresponding covering slag film along with the vibration waveform in the vibration process of the continuous casting crystallizer is calculated.
According to the calculation method for determining the thickness of the slag film of the continuous casting crystallizer, the iteration step length in the step 4 is preferably within the range of 0.01-0.03 s.
The invention has the advantages and beneficial effects that:
the determination of the thickness of the slag film of the continuous casting crystallizer is provided based on the stress analysis of the blank shell, and the important factor of the vibration of the crystallizer is taken into consideration, so that a new thought is provided for the lubricating mechanism in the vibration crystallizer, the calculation result is closer to the reality, and the method has more guiding significance for the actual operation.
Drawings
FIG. 1 is a flow chart of an embodiment of the calculation method for determining the thickness of the slag film of the continuous casting crystallizer according to the invention;
FIG. 2 is a schematic view of the meniscus region of a continuous casting mold according to an embodiment of the present invention;
FIG. 3 is a graph of slag film thickness as a function of vibration speed in accordance with an embodiment of the present invention. Wherein, 1 vibration speed and time curve; 2 thickness versus time curve.
In the figure, 1, the upper part of a slag channel; 2. the lower part of the slag channel; 3. initially solidifying the blank shell; 4. a solid slag film; 5. a meniscus.
Detailed Description
The following description of the embodiments will be made with reference to the accompanying drawings.
In the specific implementation process, the flow chart of the calculation method for determining the thickness of the slag film of the continuous casting crystallizer is shown in figure 1. For the sake of research, the meniscus region slag channel is simplified, its shape depending on both the solid slag film and the meniscus surface profile. The implementation process of the invention firstly simplifies the shape of the meniscus slag channel of the continuous casting crystallizer, and considers the solid slag film 4 as a plane solid slag film which is adhered on the wall of the crystallizer and vibrates with the crystallizer, as shown in figure 2. Wherein, the x-axis is parallel to the throwing direction, the y-axis is perpendicular to the throwing direction, R (x) is a solid slag film curve equation, S (x) is a solidified blank shell contour curve equation, and the slag channel is divided into an upper part and a lower part by a boundary line: the upper part 1 and the lower part 2 of the slag channel, a meniscus 5 is formed between the molten steel and the liquid slag on the upper part 1 of the slag channel, an initial solidified shell 3 is formed between the molten steel and the liquid slag on the lower part 2 of the slag channel, a solid slag film 4 is arranged outside the liquid slag, and the upper part adopts a Bikerman meniscus shape equation:
in the formula, l is meniscus height mm; sigmasfIs the interfacial tension of steel slag, N.m-1；ρsIs the density of molten steel, kg.m-3；ρfAs the density of the mold flux, kg.m-3. According to the technical index of casting SPHC, the density of the molten steel is 7400 kg.m-3The density of the casting powder is 2500 kg.m-3The interfacial tension between the steel slags is 1.35 N.m-1。
Because the shape of the slag channel is that the air gap is gradually increased along the direction of drawing, the profile of the slag film and the profile of the blank shell are determined by a crystallizer heat transfer model and a heat-stress model at the lower part of the slag channel model, R (x) and S (x) are respectively equations of the profile of the solid slag film and the profile of the blank shell, and the formula is as follows:
determining initial value, selecting slag film at the boundary of upper and lower parts of slag channel as initial slag film thickness d0Vibration velocity v of mold0. In this example, the slag film at the boundary of the slag passage (at 7mm of the slag passage) was selected as the initial thickness d of the slag film00.08mm, non-sinusoidal vibration waveform with vibration frequency of 2.0Hz, amplitude of 4.0mm, and non-sinusoidal vibration factor alpha of 0.20，0.045m·s-1。
And (3) calculating the pressure of the slag channel of the crystallizer according to the step 2, wherein the equation is as follows:
wherein,
in the formula, pfIs a pressure variable, Pa; v. ofmM.s. the oscillation speed of the mold-1；vcFor pull rate, 0.025 m.s-1η is the viscosity of the casting powder, 0.42 Pa.s1Is the slag channel inlet pressure, p1＝ρfgd; d is the depth of the molten pool of 0.01 m.
And (4) determining the acceleration of the blank shell according to the slag channel pressure calculated in the step (2). Selecting a slag film at a position of 7mm of a slag channel as the initial slag film thickness, carrying out stress analysis on a blank shell, knowing that the blank shell is subjected to the total pressure of the slag channel and the static pressure of molten steel, and calculating the acceleration of the blank shell in the direction vertical to a drawing blank according to Newton's second law under the combined action of the two forces, wherein the formula is as follows:
F＝ma (16)
f is a resultant force, i.e. F ═ Fd-Fs，Fd、Fs(ii) a Respectively the total pressure of the slag channel and the static pressure of the molten steel, Fs7056N; m is the shell mass, 9800kg is taken, and a is the acceleration.
Finally, the thickness of the slag film of the continuous casting crystallizer is determined, and the moving distance of the blank shell in a short period of time can be calculated according to the acceleration of the blank shell and the initial speed of the blank shell. Adopting an iteration method, taking the time step length as 0.02s and according to the initial slag film thickness d0And t1Calculating the total pressure F of the slag channel1Thereby obtaining an acceleration a1Calculating the moving distance s of the shell according to the formula (17)1：
Where v is the shell moving speed, i.e., v ═ at, and the initial speed is zero.
Thereby obtaining the thickness d of the slag film1(mm) is d1＝d0+s1According to d1(mm) and t2(s) calculating total pressure F of slag channel by vibration speed at moment2And (N), and so on until the vibration period is finished. Therefore, the change rule of the thickness of the corresponding covering slag film along with the vibration waveform in the vibration process of the continuous casting crystallizer can be calculated.
FIG. 3 is a curve of the change of the slag film thickness at 7mm position of the slag channel along with the vibration speed in the non-sinusoidal vibration mode. When the upward vibration speed exceeds the pulling speed, the slag channel is narrowest at the moment, the positive pressure pushes away the blank shell quickly to widen the slag channel, the slag channel reaches the maximum at the initial stage of negative slip, then the slag channel contracts and narrows under the action of negative pressure, and the thickness of the slag film is changed periodically along with the vibration of the crystallizer.
The embodiments of the present invention have been described above, but it will be understood by those skilled in the art that the above is only illustrative and various changes or modifications may be made to the embodiments without departing from the principle and spirit of the present invention. The scope of the invention is only limited by the appended claims.
Claims (1)
1. A calculation method for determining the thickness of a slag film of a continuous casting crystallizer is characterized by comprising the following steps:
step 1: determining the shape of the meniscus of a continuous casting mould
Simplifying a slag channel in the meniscus area, wherein the shape of the slag channel depends on the surface contour of the solid slag film and the meniscus; the slag channel is divided into an upper part and a lower part along the billet drawing direction, and the upper part adopts a Bikerman equation:
in the formula, l is meniscus height mm; sigmasfIs the interfacial tension of steel slag, N.m-1；ρsIs the density of molten steel, kg.m-3；ρfAs the density of the mold flux, kg.m-3；
Because the shape of the slag channel is that the air gap is gradually increased along the direction of drawing, the lower part of the slag channel model determines the outline of the fixed slag film and the blank shell by a crystallizer heat transfer model and a heat-stress model, R (x) and S (x) are respectively the equations of the outline of the solid slag film and the blank shell, and the equations are as follows:
determining initial value, selecting slag film at the boundary of upper and lower parts of slag channel as initial slag film thickness d0Mm; oscillation speed v of the mold0，m·s-1；
Step 2: determining the pressure of the slag channel of a continuous casting mold
The formula for determining the slag channel pressure of the continuous casting crystallizer is as follows:
wherein,
in the formula, pfIs a pressure variable, Pa; v. ofmM.s. the oscillation speed of the mold-1；vcIs the pulling speed, m.s-1η is the viscosity of the casting powder, Pa.s, p1Is the slag channel inlet pressure, p1＝ρfgd, Pa; d is the depth of the molten pool, m;
and step 3: determining acceleration
The stress analysis of the blank shell shows that the blank shell is subjected to the total pressure of a slag channel and the static pressure of molten steel, and the acceleration of the blank shell in the direction vertical to a drawing blank is calculated by a Newton's second law under the combined action of the two pressures, wherein the formula is as follows:
F＝ma (8)
wherein F is a resultant force, i.e., F ═ Fd-Fs，Fd、FsRespectively representing the total pressure of the slag channel and the static pressure of molten steel, N; m is the shell mass, kg, a is the acceleration, m/s2；
And 4, step 4: determining the thickness of slag film of continuous casting crystallizer
Determining the acceleration of the blank shell and the initial speed of the blank shell according to the step 3, and calculating the moving distance of the blank shell in a period of time; adopting an iteration method, taking the iteration step length range as 0.01-0.03 s, and obtaining the initial slag film thickness d0And t1Calculating total pressure F of slag channel by using vibration speed at moment1Thereby obtaining an acceleration a1Calculating the moving distance s of the shell according to the formula (9)1：
Wherein v is the moving speed of the shell, i.e. v is at, and the initial speed is zero;
thereby obtaining the thickness d of the slag film1Is d1＝d0+s1According to d1And t2Calculating total pressure F of slag channel by using vibration speed at moment2Repeating the steps until the vibration period is finished; therefore, the change rule of the thickness of the corresponding covering slag film along with the vibration waveform in the vibration process of the continuous casting crystallizer is calculated.
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| CN102039385A (en) * | 2010-11-29 | 2011-05-04 | 东北大学 | Method for determining thicknesses of solid-liquid slag lubricating films on basis of temperature measuring continuous-casting mold of thermoelectric couple |
| CN102672129A (en) * | 2012-05-23 | 2012-09-19 | 东北大学 | Method for determining pressure of residue channel of continuous casting crystallizer |
| CN104331629A (en) * | 2014-11-17 | 2015-02-04 | 大连理工大学 | Uneven distributed calculating method of liquid, solid powder film and air gap thickness of continuous casting crystallizer casting powder |
| CN104439142A (en) * | 2014-09-22 | 2015-03-25 | 中南大学 | Method used for detecting liquid level of liquid steel and protecting thickness of slag layer of slag liquid in crystallizer |
| CN106092020A (en) * | 2016-06-03 | 2016-11-09 | 中南大学 | The method of testing of melt cinder film thickness in a kind of continuous cast mold |
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Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5813456A (en) * | 1981-07-15 | 1983-01-25 | Nippon Kokan Kk <Nkk> | Monitoring device for ingot in continuous casting machine |
| CN102039385A (en) * | 2010-11-29 | 2011-05-04 | 东北大学 | Method for determining thicknesses of solid-liquid slag lubricating films on basis of temperature measuring continuous-casting mold of thermoelectric couple |
| CN102672129A (en) * | 2012-05-23 | 2012-09-19 | 东北大学 | Method for determining pressure of residue channel of continuous casting crystallizer |
| CN104439142A (en) * | 2014-09-22 | 2015-03-25 | 中南大学 | Method used for detecting liquid level of liquid steel and protecting thickness of slag layer of slag liquid in crystallizer |
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