CN102039385A - Method for determining thicknesses of solid-liquid slag lubricating films on basis of temperature measuring continuous-casting mold of thermoelectric couple - Google Patents

Abstract

The invention relates to a method for determining the thicknesses of solid-liquid slag lubricating films on the basis of a temperature measuring continuous-casting mold of a thermoelectric couple, belonging to the field of mathematical model application of ferrous metallurgical continuous casting process, comprising the following steps: step 1, acquiring initial data; step 2, determining the thickness of the solid slag lubricating film and the thickness of the liquid slag lubricating film at a meniscus area of the mold; and step 3, displaying a result of the thickness of the solid slag lubricating film and the thickness of the liquid slag lubricating film in an online manner. The method has the advantages that on the basis of mass balance and heat flow balance, an equation for calculating the thicknesses of the lubricating films at the meniscus of the continuous casting mold is deduced, and under the premise of installing the thermoelectric couple at the meniscus area, temperature data detected in real time is imported to a mathematical model so as to realize real-time calculation of the thicknesses of the lubricating films.

Description

Definite method based on thermocouple temperature measurement continuous cast mold solid-liquid slag lubrication film thickness

Technical field

The invention belongs to Ferrous Metallurgy casting process Mathematical Modeling application, particularly a kind of definite method based on thermocouple temperature measurement continuous cast mold solid-liquid slag lubrication film thickness.

Background technology

During continuous casting steel machine, the covering slag of sprawling on the molten steel in mold liquid level absorbs the heat that high-temperature molten steel provides, on liquid steel level, form liquid slag layer rapidly, covering slag near liquid slag layer does not reach melt temperature yet, then form the sinter layer of interim form, then be the slag layer that maintains the original state on the sinter layer, be the three-decker of covering slag on the molten steel in mold liquid level; On the other hand, liquid slag constantly penetrates into air gap and the lubricated slag film of formation between crystallizer wall and initial solidification base shell with crystallizer periodicity double vibrations in the liquid slag layer, the liquid slag of wherein pressing close to crystallizer wall forms the solid lubricant film of the nature of glass and crystalline coexistence under cooling effect, the liquid slag of pressing close to base shell surface then forms the hydrodynamic lubrication film.Fig. 1 is a casting situation in the continuous cast mold, based on received mixed film friction theory in the metallurgical continuous casting field, the frictional force that produces between vibrating crystallizer wall and solidified shell surface is divided into two classes: contact the static friction that causes with solid because of solid between (1) solid slag film and solidified shell; (2) fluid friction that causes by the stickiness Newtonian fluid in the melt cinder film.Although the contact condition between crystallizer wall and solidified shell is subjected to the influence of two class frictional force simultaneously, and total frictional force is sum of the two, and the effect that two class frictional force are brought into play at the crystallizer diverse location is also inequality.Studies show that, occupy absolute leading position in crystallizer upper liquid frictional force, the crystallizer bottom is then mainly based on solid friction power.In addition, crystallizer upper meniscus district solidified shell is torn easily under the effect of fluid friction power and forms slab surface crack, even initiation bleed-out accident, cause heavy losses, the intermembranous friction of bottom crystallizer wall and solid slag has then caused the wearing and tearing of copper plate of crystallizer, make cost of equipment maintenance promote, and increased the possibility on strand generation surface.Therefore, no matter be fluid friction, or solid friction, all be the significant process parameters that should be monitored closely and control in the continuous casting steel machine, especially fluid friction power is directly being controlled the casting data that continuous casting direct motion and product quality are paid close attention to especially because of it.At present; at the monitoring of frictional force except that coming the Indirect evaluation by covering slag slag consumption; the means that adopted are by the detection to resistance of billet withdrawal mostly; the frictional force detection method that people such as Sahoo have developed based on multisensor is used for controlling frictional force to improve slab quality and casting stability; people such as Yao Man have developed the frictional force computation model based on power method; difference power during by detection crystallizer vibration platform load and zero load is estimated frictional force; all built-in frictional force detection module in the crystallizer system of international iron and steel technical research such as VAI and Da Nieli giant design; although solved the problem of the online detection of frictional force to a certain extent; its detected value and calculated value difference are bigger; and detecting mechanism is " black box ", still waits to further investigate and crack.The macroscopic view that these researchs all lay particular emphasis on frictional force detects, and be primarily aimed at the fluid friction power in meniscus district, and according to the Newtonian fluid theory of mechanics, fluid friction power is viscous fluid " internal friction ", can be calculated by equation (1), then should be the most direct and accurate means of its variation of monitoring in line computation fluid friction power.Based on equation (1) as can be known; fluid friction power depends on relative motion, covering slag viscosity and melt cinder film (lubricating film) thickness between crystallizer and solidified shell; the above two can be provided by conticaster setting value or covering slag supplier at the numerical value of stablizing under the casting condition; the melt cinder film thickness then is very difficult to determine; research up to now only can prove its order of magnitude in the 10-5-10-4m scope, thereby becomes the bottleneck of the online computation model of exploitation fluid friction power.

$f_l={\mathrm{\μ}}_f\frac{v_m-v_c}{d_l}---\left(1\right)$

In the formula, fl is a fluid friction power, Pa; μ f is the covering slag viscosity, Pas; Vm is a mold oscillation speed, mms-1; Vc is the strand pulling rate, mms-1; Dl is the melt cinder film thickness, mm.

Summary of the invention

Lubrication film thickness can comparatively intuitively reflect in the casting cycle lubricated in the crystallizer, friction and heat transfer conditions between vibrating crystallizer and solidified shell, lubrication film thickness should maintain in the stability range helping and keep the continuous casting direct motion and guarantee slab quality in the actual pouring operation, otherwise can cause a series of negative consequences.1. solid slag and melt cinder are lubricated lepthymenia, show that then the covering slag consumption reduces, and not only reduce lubricant effect, and make vibrating crystallizer inwall and solidified shell inter-surface friction to aggravate, thereby produce slab surface crack, even cause the bleed-out accident to take place; Gu slag and melt cinder 2. lubricating films are blocked up, make that heat transfer resistance increases between crystallizer inwall and solidified shell surface, be unfavorable for release and the transmission of the latent heat of solidification of liquid metal and sensible heat to water mold, cause the attenuation of base shell, more easily under vibrating machine external force and thermal stress effect, produce distortion, produce the strand underbead crack; 3. solid slag and melt cinder lubrication film thickness instability (promptly can't maintain in the fixing scope, frequent blocked up or thin excessively), easily cause the instability of heat flux, both made the base shell solidify the growth inhomogeneous, the stable row that influence heat is again transmitted, can cause surface or underbead crack in vibrating machine external force or thermal stress effect row equally, even the bleed-out accident.

For solving the problem that continuous cast mold meniscus district's melt cinder film thickness calculating means lack, the present invention proposes a kind of definite method based on thermocouple temperature measurement continuous cast mold solid-liquid slag lubrication film thickness, reaching in line computation meniscus district solid slag and melt cinder lubrication film thickness, and calculate for fluid friction power process data is provided.Wherein thermocouple is installed in meniscus surface area.The present invention is based on two angles and consider the calculating of lubrication film thickness: the continuity of (1) slag consumption, i.e. mass balance; (2) continuity of the vertical throwing direction heat transfer of molten steel, the instant heating mobile equilibrium.

A kind of continuous crystallizer protecting slag lubrication film thickness based on the meniscus thermocouple temperature measurement is determined method, carries out as follows:

Step 1, obtain primary data

1. determine meniscus level H

Meniscus level is slag road length, is obtained by capillary constant equation (15);

$H=\sqrt{\frac{{2\mathrm{\σ}}_{s-f}}{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_f)g}}---\left(15\right)$

In the formula, g is an acceleration of gravity, g=9.8ms-2; ρ s is a molten steel density, kgm-3; σ s-f is an interfacial tension between initial set base shell and covering slag, and Nm-1 is calculated by Girifalco-Good equation (16).

${\mathrm{\σ}}_{s-f}={\mathrm{\σ}}_s+{\mathrm{\σ}}_f-2\mathrm{\φ}\sqrt{{\mathrm{\σ}}_s{\mathrm{\σ}}_f}---\left(16\right)$

In the formula, σ s, σ f are respectively initial set base shell and covering slag surface tension, and Nm-1, covering slag comprise melt cinder and solid slag; Φ is the contact interface characteristic value.

2. pouring operation parameter

(1) determines wide of continuous cast mold and leptoprosopy length L and W by design drawing;

(2) stablize under the casting state statistics by the scene and determine unit plane accumulated slag consumption Q;

(3) by design drawing determine thermocouple imbed the position apart from the crystallizer hot side apart from d;

(4) The real time measure electric thermo-couple temperature T _c

(5) calculate initial set base shell surface temperature T in real time by casting process simulation system in-circuit emulation model _s

3. covering slag physical parameter

(1) determines melt cinder lubricating film density p f by the covering slag technical manual;

(2) determine covering slag fusing point T by the covering slag technical manual _f

4. material thermal conductivity

(1) sets melt cinder film and solid slag film thermal conductivity factor λ s and λ l;

(2), set the copper thermal conductivity factor according to meniscus copper coin hot-face temperature;

Step 2, determine solid slag lubrication film thickness in crystallizer meniscus district and melt cinder lubrication film thickness

Set up solid slag lubrication film thickness model (13) in crystallizer meniscus district and melt cinder lubrication film thickness model (14) based on mass balance and hot-fluid equilibrium principle, determine the solid slag lubrication film thickness d in crystallizer meniscus district _sWith melt cinder lubrication film thickness d _l

$d_s=\frac{(A-\sqrt{A^2-4B})D-2E}{2(C+D)}---\left(13\right)$

$d_l=\frac{(A-\sqrt{A^2-4B})C+2E}{2(C+D)}---\left(14\right)$

In the formula

D=λ _sλ _m

L and W are respectively wide of crystallizer and leptoprosopy length; Q is a unit plane accumulated slag consumption; ρ f is a melt cinder lubricating film density; λ _lThermal conductivity factor for the melt cinder lubricating film; λ _sThermal conductivity factor for solid slag lubricating film; λ _mThermal conductivity factor for copper plate of crystallizer; T _sTemperature for the solidified shell surface; T _fTemperature for the covering slag melting point; T _mTemperature for the copper plate of crystallizer hot side; T _cTemperature for thermocouple location; D is that thermocouple is imbedded the position apart from crystallizer hot side distance;

The result of step 3, the solid slag lubrication film thickness of online demonstration and melt cinder lubrication film thickness;

It is as follows wherein to set up the method for solid slag lubrication film thickness model (13) in crystallizer meniscus district and melt cinder lubrication film thickness model (14) based on mass balance and hot-fluid equilibrium principle:

1. mass balance

Usually estimate the slag consumption according to the covering slag that consumes on the unit are in the produced on-site, i.e. the slag consumption rate of covering slag, covering slag comprises melt cinder and solid slag, its unit is kgm ^-2, then meniscus district slag consumption can be expressed as equation (2).In addition, (commerical test and theoretical calculating prove that all its order of magnitude is 10 as thin as a wafer owing to meniscus district lubricating film ^-5-10 ^-4The m scope), then can be thought of as normal value with stablizing solid slag lubricating film in when casting meniscus district and melt cinder lubricating film, the another kind that then obtains meniscus district slag consumption is represented mode, equation (3).

M＝2H(L+W)Q (2)

In the formula, M is a meniscus district slag consumption, kg; L and W are respectively wide of crystallizer and leptoprosopy length, m; H is a meniscus district height; Q is unit plane accumulated slag consumption (is slag consumption rate, can provides by produced on-site is actual), kgm ^-2d _sAnd d _lBe respectively solid slag lubricating film and melt cinder lubrication film thickness, m; ρ f is melt cinder lubricating film density (can be provided by the continuous casting covering slag technical data), kgm ^-3, then obtain comprising solid slag lubrication film thickness d by equation (2) and equation (3) _sWith melt cinder lubrication film thickness d _lEquation (4), because of the present invention is directed to solid slag lubrication film thickness in meniscus district and melt cinder lubrication film thickness, and the solid slag lubrication film thickness and the melt cinder lubrication film thickness order of magnitude are minimum in should the zone, consider that along solid slag lubrication film thickness of throwing direction and melt cinder lubrication film thickness be definite value, obtain

(d _s+d _l) ²-A(d _s+d _l)+B＝0 (4)

Wherein,

$A=\frac{L+W}{2}---\left(5\right)$

$B=\frac{L+W}{2}\frac{Q}{{\mathrm{\ρ}}_f}---\left(6\right)$

2. hot-fluid balance

Characteristics of the present invention rely on its detected temperature data that solid slag lubrication film thickness and melt cinder lubrication film thickness are calculated just.Based on the numerical heat transfer theory as can be known, heat flow density is identical on the vertical throwing direction, and promptly synchronization transfers to the heat flow unanimity of crystallizer cooling water by molten steel, so can set up the thermocouple location equation of heat balance.

The melt cinder lubricating film equates with the solid slag lubricating film hot-fluid of correspondence position:

${\mathrm{\λ}}_l\frac{T_s-T_f}{d_l}={\mathrm{\λ}}_s\frac{T_f-T_m}{d_s}---\left(7\right)$

The melt cinder lubricating film equates with correspondence position copper plate of crystallizer hot-fluid:

${\mathrm{\λ}}_l\frac{T_s-T_f}{d_l}={\mathrm{\λ}}_m\frac{T_m-T_c}{d}---\left(8\right)$

In the formula, T is a temperature, ℃, T _s, T _f, T _mAnd T _cRepresent the temperature on solidified shell surface, the temperature of covering slag melting point, the temperature of copper plate of crystallizer hot side and the temperature of thermocouple location respectively; λ is a material thermal conductivity, Wm ^-1℃ ^-1, λ _l, λ _sAnd λ _mRepresent the thermal conductivity factor of melt cinder lubricating film, the thermal conductivity factor of solid slag lubricating film and the thermal conductivity factor of copper plate of crystallizer respectively; D is that thermocouple is imbedded the position apart from crystallizer hot side distance, m.Then release equation (9) and equation (10) respectively by equation (7) and equation (8).

$(T_s-T_f)\frac{{\mathrm{\λ}}_l}{d_l}\frac{d_s}{{\mathrm{\λ}}_s}=T_f-T_m---\left(9\right)$

$(T_s-T_f)\frac{{\mathrm{\λ}}_l}{d_l}\frac{d}{{\mathrm{\λ}}_m}=T_m-T_c---\left(10\right)$

Here because copper plate of crystallizer hot-face temperature T _mBe difficult to determine, then with equation (7) and equation (8) addition, put in order equation (9) to equation (12).

Cd _s-Dd _l+E＝0 (9)

$C={\mathrm{\λ}}_l{\mathrm{\λ}}_m\frac{T_s-T_f}{T_f-T_c}---\left(10\right)$

D＝λ _sλ _m (11)

$E={\mathrm{\λ}}_l{\mathrm{\λ}}_{s}d\frac{T_s-T_f}{T_f-T_c}---\left(12\right)$

3, determine solid slag lubrication film thickness in crystallizer meniscus district and melt cinder lubrication film thickness

Simultaneous solution equation (4) and equation (9), and cast out unnecessary separating based on the actual slag film thickness order of magnitude, promptly obtain solid slag lubrication film thickness and melt cinder lubrication film thickness such as equation (13) and equation (14) respectively.

$d_s=\frac{(A-\sqrt{A^2-4B})D-2E}{2(C+D)}---\left(13\right)$

$d_l=\frac{(A-\sqrt{A^2-4B})C+2E}{2(C+D)}---\left(14\right)$

Advantage of the present invention: be to derive continuous cast mold meniscus lubrication film thickness accounting equation based on mass balance and hot-fluid balance, and be equipped with in the meniscus district under the prerequisite of thermocouple, its real-time detected temperature data is imported Mathematical Modeling, realize the real-time calculating of lubrication film thickness.

Description of drawings

Casting situation signal in Fig. 1 continuous cast mold;

The signal of Fig. 2 continuous cast mold physical model size;

Fig. 3 continuous cast mold meniscus district physical model;

Fig. 4 meniscus lubrication film thickness calculation flow chart;

The real-time result of calculation of Fig. 5 crystallizer meniscus slag film thickness.

The specific embodiment

The present invention is based on above-mentioned derivation equation, set up Mathematical Modeling, and be implemented in line computation meniscus district covering slag lubrication film thickness in conjunction with meniscus district thermocouple detection gained temperature, existing at cast-in-place mild steel situation detailed description embodiment.

A kind of continuous crystallizer protecting slag lubrication film thickness based on the meniscus thermocouple temperature measurement is determined method, carries out as follows: as shown in Figure 4:

Step 1, obtain primary data

1. determine meniscus level H

Meniscus level is slag road length, is obtained by capillary constant equation (15);

$H=\sqrt{\frac{{2\mathrm{\σ}}_{s-f}}{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_f)g}}---\left(15\right)$

In the formula, g is an acceleration of gravity, g=9.8ms-2; ρ s is a molten steel density, kgm-3; σ s-f is an interfacial tension between initial set base shell and covering slag, and Nm-1 is calculated by Girifalco-Good equation (16).

${\mathrm{\σ}}_{s-f}={\mathrm{\σ}}_s+{\mathrm{\σ}}_f-2\mathrm{\φ}\sqrt{{\mathrm{\σ}}_s{\mathrm{\σ}}_f}---\left(16\right)$

In the formula, σ s, σ f are respectively initial set base shell and covering slag surface tension, Nm-1; Φ is the contact interface characteristic value.

2. pouring operation parameter

(1) determines wide of continuous cast mold and leptoprosopy length L and W by design drawing;

(2) stablize under the casting state statistics by the scene and determine unit plane accumulated slag consumption Q;

(3) by design drawing determine thermocouple imbed the position apart from the crystallizer hot side apart from d;

(4) The real time measure electric thermo-couple temperature Tc;

(5) calculate initial set base shell surface temperature Ts in real time by casting process simulation system in-circuit emulation model;

3. covering slag physical parameter

(1) melt cinder lubricating film density p f is taken as normal temperature (1300 ℃) measured value, can be determined by the covering slag technical manual;

(2) covering slag fusing point Tf is determined by the covering slag technical manual.

4. material thermal conductivity

(1) because of lubricating film as thin as a wafer, melt cinder film and solid slag film thermal conductivity factor λ s and λ l all are taken as 1.5Wm-1 ℃-1;

(2) because of meniscus copper coin hot-face temperature near 300 ℃, getting the copper thermal conductivity factor is 310Wm-1 ℃-1.

Step 2, determine solid slag lubrication film thickness in crystallizer meniscus district and melt cinder lubrication film thickness

Set up solid slag lubrication film thickness model (13) in crystallizer meniscus district and melt cinder lubrication film thickness model (14) based on mass balance and hot-fluid equilibrium principle, determine the solid slag lubrication film thickness d in crystallizer meniscus district _sWith melt cinder lubrication film thickness d _l

$d_s=\frac{(A-\sqrt{A^2-4B})D-2E}{2(C+D)}---\left(13\right)$

$d_l=\frac{(A-\sqrt{A^2-4B})C+2E}{2(C+D)}---\left(14\right)$

In the formula

D=λ _sλ _m

L and W are respectively wide of crystallizer and leptoprosopy length; Q is a unit plane accumulated slag consumption; ρ f is a melt cinder lubricating film density; λ _lThermal conductivity factor for the melt cinder lubricating film; λ _sThermal conductivity factor for solid slag lubricating film; λ _mThermal conductivity factor for copper plate of crystallizer; T _sTemperature for the solidified shell surface; T _fTemperature for the covering slag melting point; T _mTemperature for the copper plate of crystallizer hot side; T _cTemperature for thermocouple location; D is that thermocouple is imbedded the position apart from crystallizer hot side distance;

The result of step 3, the solid slag lubrication film thickness of online demonstration and melt cinder lubrication film thickness.Solid slag lubrication film thickness and melt cinder lubrication film thickness result such as Fig. 5 in the casting cycle of determining.

It is as follows wherein to set up the method for solid slag lubrication film thickness model (13) in crystallizer meniscus district and melt cinder lubrication film thickness model (14) based on mass balance and hot-fluid equilibrium principle:

1. mass balance

Usually estimate the slag consumption according to the covering slag that consumes on the unit are in the produced on-site, i.e. the slag consumption rate of covering slag, its unit is kgm ^-2, then meniscus district slag consumption can be expressed as equation (2).In addition, (commerical test and theoretical calculating prove that all its order of magnitude is 10 as thin as a wafer owing to meniscus district lubricating film ^-5-10 ^-4The m scope), then can be thought of as normal value with stablizing solid slag lubricating film in when casting meniscus district and melt cinder lubricating film, the another kind that then obtains meniscus district slag consumption is represented mode, equation (3).

M＝2H(L+W)Q (2)

In the formula, M is a meniscus district slag consumption, kg; L and W are respectively wide of crystallizer and leptoprosopy length, m; H is a meniscus district height; Q is unit plane accumulated slag consumption (is slag consumption rate, can provides by produced on-site is actual), kgm ^-2d _sAnd d _lBe respectively solid slag lubricating film and melt cinder lubrication film thickness, m; ρ f is melt cinder lubricating film density (can be provided by the continuous casting covering slag technical data), kgm ^-3, continuous cast mold size such as Fig. 2.Then obtain comprising solid slag lubrication film thickness d by equation (2) and equation (3) _sWith melt cinder lubrication film thickness d _lEquation (4), because of the present invention is directed to solid slag lubrication film thickness in meniscus district and melt cinder lubrication film thickness, and the solid slag lubrication film thickness and the melt cinder lubrication film thickness order of magnitude are minimum in should the zone, consider that along solid slag lubrication film thickness of throwing direction and melt cinder lubrication film thickness be definite value, obtain

(d _s+d _l) ²-A(d _s+d _l)+B＝0 (4)

Wherein,

$A=\frac{L+W}{2}---\left(5\right)$

$B=\frac{L+W}{2}\frac{Q}{{\mathrm{\ρ}}_f}---\left(6\right)$

2. hot-fluid balance

Fig. 3 provides thermograde signal between solidified shell and crystallizer, the thermocouple of wherein monitoring cast temperature in the crystallizer is placed in the meniscus district, and characteristics of the present invention rely on its detected temperature data that solid slag lubrication film thickness and melt cinder lubrication film thickness are calculated just.Based on the numerical heat transfer theory as can be known, heat flow density is identical on the vertical throwing direction, and promptly synchronization transfers to the heat flow unanimity of crystallizer cooling water by molten steel, so can set up the thermocouple location equation of heat balance.

The melt cinder lubricating film equates with the solid slag lubricating film hot-fluid of correspondence position:

${\mathrm{\λ}}_l\frac{T_s-T_f}{d_l}={\mathrm{\λ}}_s\frac{T_f-T_m}{d_s}---\left(7\right)$

The melt cinder lubricating film equates with correspondence position copper plate of crystallizer hot-fluid:

${\mathrm{\λ}}_l\frac{T_s-T_f}{d_l}={\mathrm{\λ}}_m\frac{T_m-T_c}{d}---\left(8\right)$

In the formula, T is a temperature, ℃, T _s, T _f, T _mAnd T _cRepresent the temperature on solidified shell surface, the temperature of covering slag melting point, the temperature of copper plate of crystallizer hot side and the temperature of thermocouple location respectively; λ is a material thermal conductivity, Wm ^-1℃ ^-1, λ _l, λ _sAnd λ _mRepresent the thermal conductivity factor of melt cinder lubricating film, the thermal conductivity factor of solid slag lubricating film and the thermal conductivity factor of copper plate of crystallizer respectively; D is that thermocouple is imbedded the position apart from crystallizer hot side distance, m.Then release equation (9) and equation (10) respectively by equation (7) and equation (8).

$(T_s-T_f)\frac{{\mathrm{\λ}}_l}{d_l}\frac{d_s}{{\mathrm{\λ}}_s}=T_f-T_m---\left(9\right)$

$(T_s-T_f)\frac{{\mathrm{\λ}}_l}{d_l}\frac{d}{{\mathrm{\λ}}_m}=T_m-T_c---\left(10\right)$

Here because copper plate of crystallizer hot-face temperature T _mBe difficult to determine, then with equation (7) and equation (8) addition, put in order equation (9) to equation (12).

Cd _s-Dd _l+E＝0 (9)

$C={\mathrm{\λ}}_l{\mathrm{\λ}}_m\frac{T_s-T_f}{T_f-T_c}---\left(10\right)$

D＝λ _sλ _m (11)

$E={\mathrm{\λ}}_l{\mathrm{\λ}}_{s}d\frac{T_s-T_f}{T_f-T_c}---\left(12\right)$

3, determine the solid slag lubrication film thickness in crystallizer meniscus district and melt cinder lubrication film thickness simultaneous solution equation (4) and equation (9), and cast out unnecessary separating based on the actual slag film thickness order of magnitude, promptly obtain solid slag lubrication film thickness and melt cinder lubrication film thickness such as equation (13) and equation (14) respectively.

$d_s=\frac{(A-\sqrt{A^2-4B})D-2E}{2(C+D)}---\left(13\right)$

$d_l=\frac{(A-\sqrt{A^2-4B})C+2E}{2(C+D)}---\left(14\right).$

Claims (2)

1. definite method based on thermocouple temperature measurement continuous cast mold solid-liquid slag lubrication film thickness is characterized in that: carry out as follows:

Step 1, obtain primary data

1), determines meniscus level H

Meniscus level is slag road length, is obtained by capillary constant equation (15);

$H=\sqrt{\frac{{2\mathrm{\σ}}_{s-f}}{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_f)g}}---\left(15\right)$

In the formula, g is an acceleration of gravity, g=9.8ms-2; ρ s is a molten steel density, kgm-3; σ s-f is an interfacial tension between initial set base shell and covering slag, and Nm-1 is calculated by Girifalco-Good equation (16);

${\mathrm{\σ}}_{s-f}={\mathrm{\σ}}_s+{\mathrm{\σ}}_f-2\mathrm{\φ}\sqrt{{\mathrm{\σ}}_s{\mathrm{\σ}}_f}---\left(16\right)$

In the formula, σ s, σ f are respectively initial set base shell and covering slag surface tension, and Nm-1, covering slag comprise melt cinder and solid slag; Φ is the contact interface characteristic value;

2), pouring operation parameter

(1) determines wide of continuous cast mold and leptoprosopy length L and W by design drawing;

(2) stablize under the casting state statistics by the scene and determine unit plane accumulated slag consumption Q;

(3) by design drawing determine thermocouple imbed the position apart from the crystallizer hot side apart from d;

(4) The real time measure electric thermo-couple temperature T _c

(5) calculate initial set base shell surface temperature T in real time by casting process simulation system in-circuit emulation model _s

3), covering slag physical parameter

(1) determines melt cinder lubricating film density p f by the covering slag technical manual;

(2) determine covering slag fusing point T by the covering slag technical manual _f

4), material thermal conductivity

(1) sets melt cinder film and solid slag film thermal conductivity factor λ s and λ l;

(2), set the copper thermal conductivity factor according to meniscus copper coin hot-face temperature;

Step 2, determine solid slag lubrication film thickness in crystallizer meniscus district and melt cinder lubrication film thickness

Set up solid slag lubrication film thickness model (13) in crystallizer meniscus district and melt cinder lubrication film thickness model (14) based on mass balance and hot-fluid equilibrium principle, determine the solid slag lubrication film thickness d in crystallizer meniscus district _sWith melt cinder lubrication film thickness d _l

$d_s=\frac{(A-\sqrt{A^2-4B})D-2E}{2(C+D)}---\left(13\right)$

$d_l=\frac{(A-\sqrt{A^2-4B})C+2E}{2(C+D)}---\left(14\right)$

In the formula

D=λ _sλ _m

L and W are respectively wide of crystallizer and leptoprosopy length; Q is a unit plane accumulated slag consumption; ρ f is a melt cinder lubricating film density; λ _lThermal conductivity factor for the melt cinder lubricating film; λ _sThermal conductivity factor for solid slag lubricating film; λ _mThermal conductivity factor for copper plate of crystallizer; T _sTemperature for the solidified shell surface; T _fTemperature for the covering slag melting point; T _mTemperature for the copper plate of crystallizer hot side; T _cTemperature for thermocouple location; D is that thermocouple is imbedded the position apart from crystallizer hot side distance;

The result of step 3, the solid slag lubrication film thickness of online demonstration and melt cinder lubrication film thickness.

2. by the described definite method based on thermocouple temperature measurement continuous cast mold solid-liquid slag lubrication film thickness of claim 1, it is characterized in that: it is as follows to set up the method for solid slag lubrication film thickness model (13) in crystallizer meniscus district and melt cinder lubrication film thickness model (14) based on mass balance and hot-fluid equilibrium principle in the described step 2:

(1.) mass balance

Meniscus district slag consumption can be expressed as equation (2), because meniscus district lubricating film is as thin as a wafer, then can be thought of as normal value with stablizing solid slag lubricating film in when casting meniscus district and melt cinder lubricating film, and the another kind that then obtains meniscus district slag consumption is represented mode, equation (3),

M＝2H(L+W)Q (2)

In the formula, M is a meniscus district slag consumption, kg; L and W are respectively wide of crystallizer and leptoprosopy length, m; H is a meniscus district height; Q is a unit plane accumulated slag consumption, kgm ^-2d _sAnd d _lBe respectively solid slag lubricating film and melt cinder lubrication film thickness, m; ρ f is a melt cinder lubricating film density, kgm ^-3, then obtain comprising solid slag lubrication film thickness d by equation (2) and equation (3) _sWith melt cinder lubrication film thickness d _lEquation (4), consider that along solid slag lubrication film thickness of throwing direction and melt cinder lubrication film thickness be definite value, obtain

(d _s+d _l) ²-A(d _s+d _l)+B＝0 (4)

Wherein,

$A=\frac{L+W}{2}---\left(5\right)$

$B=\frac{L+W}{2}\frac{Q}{{\mathrm{\ρ}}_f}---\left(6\right);$

(2.) hot-fluid balance

Based on the numerical heat transfer theory as can be known, heat flow density is identical on the vertical throwing direction, and promptly synchronization transfers to the heat flow unanimity of crystallizer cooling water by molten steel, so can set up the thermocouple location equation of heat balance;

The melt cinder lubricating film equates with the solid slag lubricating film hot-fluid of correspondence position:

${\mathrm{\λ}}_l\frac{T_s-T_f}{d_l}={\mathrm{\λ}}_s\frac{T_f-T_m}{d_s}---\left(7\right)$

The melt cinder lubricating film equates with correspondence position copper plate of crystallizer hot-fluid:

${\mathrm{\λ}}_l\frac{T_s-T_f}{d_l}={\mathrm{\λ}}_m\frac{T_m-T_c}{d}---\left(8\right)$

In the formula, T is a temperature, ℃, T _s, T _f, T _mAnd T _cRepresent the temperature on solidified shell surface, the temperature of covering slag melting point, the temperature of copper plate of crystallizer hot side and the temperature of thermocouple location respectively; λ is a material thermal conductivity, Wm ℃ ^-1, λ _l, λ _sAnd λ _mRepresent the thermal conductivity factor of melt cinder lubricating film, the thermal conductivity factor of solid slag lubricating film and the thermal conductivity factor of copper plate of crystallizer respectively; D is that thermocouple is imbedded the position apart from crystallizer hot side distance, m; Then release equation (9) and equation (10) respectively by equation (7) and equation (8);

$(T_s-T_f)\frac{{\mathrm{\λ}}_l}{d_l}\frac{d_s}{{\mathrm{\λ}}_s}=T_f-T_m---\left(9\right)$

$(T_s-T_f)\frac{{\mathrm{\λ}}_l}{d_l}\frac{d}{{\mathrm{\λ}}_m}=T_m-T_c---\left(10\right)$

Here because copper plate of crystallizer hot-face temperature T _mBe difficult to determine, then with equation (7) and equation (8) addition, put in order equation (9) to equation (12);

Cd _s-Dd _l+E＝0 (9)

$C={\mathrm{\λ}}_l{\mathrm{\λ}}_m\frac{T_s-T_f}{T_f-T_c}---\left(10\right)$

D＝λ _sλ _m (11)

$E={\mathrm{\λ}}_l{\mathrm{\λ}}_{s}d\frac{T_s-T_f}{T_f-T_c}---\left(12\right)$

(3) determine solid slag lubrication film thickness in crystallizer meniscus district and melt cinder lubrication film thickness

Simultaneous solution equation (4) and equation (9), and cast out unnecessary separating based on the actual slag film thickness order of magnitude, promptly obtain solid slag lubrication film thickness and melt cinder lubrication film thickness such as equation (13) and equation (14) respectively;

$d_s=\frac{(A-\sqrt{A^2-4B})D-2E}{2(C+D)}---\left(13\right)$

$d_l=\frac{(A-\sqrt{A^2-4B})C+2E}{2(C+D)}---\left(14\right).$

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