CN103406505B - Slab crystallizer taper design method - Google Patents

Abstract

The invention relates to a method for designing the taper of a slab crystallizer, which belongs to the field of steelmaking-continuous casting. The taper of the slab mold designed by the invention can fully compensate the shrinkage of the billet shell in the crystallizer, and effectively restrain the billet shell from being trapped in the crystallizer. The deformation of the initial solidification slab shell prevents the frequent occurrence of continuous casting slab surface and subcutaneous cracks caused by excessive deformation in the upper part of the mold; the taper of the slab mold designed by the invention can effectively eliminate the wide and narrow slab shell. The "hot spot" in the area near the corner of the face realizes the uniform growth of the slab shell in the crystallizer; the taper of the slab crystallizer designed by the present invention can maximize the reduction of the wear of the copper plate of the crystallizer and prolong the service life of the crystallizer; the use of the present invention The designed taper of the slab mold can accelerate the heat transfer between the corner and the narrow surface of the slab shell, increase the strength of the slab shell when it exits the mold, and reduce the bulging of the narrow surface of the slab shell.

Description

A kind of Slab crystallizer taper design method

Technical field

The invention belongs to steel smelting-continuous casting field, be specifically related to a kind of Slab crystallizer taper design method.

Background technology

Crystallizer, as the high-efficient heat exchanger of conticaster, carries the task of the base that to congeal at the beginning of high-temperature molten steel, and base shell stress within it directly determines the surface of continuous casting billet and subcutaneous quality with heat transfer uniformity.In actual steel continuous casting is produced, base shell progressively solidifies in crystallizer, and then, leptoprosopy center position wide along it occurs significantly shrink and depart from crystallizer.In this process, owing to lacking copper plate of crystallizer to its supporting role, initial set base shell produces distortion under the effect of ferrostatic pressure in crystallizer, causes base shell solidification front to produce remarkable tension.Meanwhile, the contraction strong by base shell and metamorphosis, base shell-crystallizer interfacial gap is also uneven along the distribution of base shell circumference, causes flux film and air gap to cause continuous casting billet uneven heat transfer in crystallizer to this gap Nonuniform filling thus.By the impact of this two effect, continuous casting billet often takes place frequently surface and subcrack.In order to effectively suppress base shell in the distortion of crystallizer and the heat transfer of homogenising base shell in crystallizer; normal introducing mould reverse taper method in actual steel continuous casting production process; at utmost contact base shell by changing crystallizer internal cavity outline line to realize copper plate of crystallizer, thus reach effective support initial set base shell and suppress the object that the gentle gap of the uneven inflow of covering slag is formed.

Sheet billet continuous casting has the feature of big flakiness ratio, and base shell is to the contraction of contraction significantly in it to leptoprosopy center position of wide center position.In order to effective compensation base shell is to the contraction in wide direction, in current actual sheet billet continuous casting is produced, often use leptoprosopy with 0.5%-1.5% linear taper and wide face does not arrange the crystallizer of tapering.But, research shows, use this kind of crystallizer continuous casting to produce slab and fail to take into full account initial set base shell in crystallizer along the characteristic of its short transverse contraction change, often cause at crystallizer top tapering insufficient and in the excessive phenomenon of crystallizer bottom tapering compensation rate to base shell shrinkage-compensating.Cause base shell thus and in base shell-crystallizer interface, produce base shell deflecting angle " focus " along the circumferential skewness of base shell with air gap because being out of shape excessive and flux film on crystallizer top, cause continuous casting billet to take place frequently surface and subcrack.Meanwhile, the tapering compensation rate due to crystallizer bottom is greater than base shell amount of contraction, adds the wearing and tearing of crystallizer leptoprosopy bottom copper coin, greatly reduces the service life of crystallizer.Therefore, this conical degree of crystallizer is used to be unfavorable for that sheet billet continuous casting is produced.

In recent years, along with domestic and international researcher gos deep into the research of base shell solidification shrinkage and deformation rule in plate slab crystallizer, also start to possess some special knowledge for Slab crystallizer taper design.Be entitled as " optimization of austenite stainless steel plate blank continuous casting crystallizer tapering " and have studied the solidification shrinkage rule of stainless steel in plate slab crystallizer with the article of " research of austenite and martensitic stainless steel base shrinking law and conical degree of crystallizer in crystallizer ", and propose a kind of two-part shaped form leptoprosopy tapering adopting large compensation amount on crystallizer top, adopt little compensation rate in crystallizer bottom.Adopt this tapering continuous casting to produce stainless steel slab, more effectively can compensate base shell on crystallizer top to the contraction at its Kuan Mian center and the wearing and tearing reducing crystallizer bottom copper coin.But this taper design only considers the shrinkage-compensating effect of narrow face copper plate of crystallizer to base shell, do not consider that Wide-surface copper plate of crystallizer structure is conducted heat in crystallizer on base shell the impact of uniformity.And continuous casting produces reality and research all shows, wide of crystallizer lacks the taper design of base shell to its leptoprosopy center position shrinkage-compensating effect, very remarkable with the impact growing uniformity on the heat transfer in base shell wide deflecting angle region.The article being entitled as " research of copper plate taper of slab mold " and " research of Baosteel copper plate taper of slab mold " have studied that base shell is wide along crystallizer, the shrinking law of leptoprosopy center position, proposes wide of crystallizer and arranges Small Taper, leptoprosopy according to the different tapering viewpoint of different casting condition setting.But this research does not make a change crystallizer leptoprosopy tapered configuration, only based on original linear crystallizer leptoprosopy integrated regulation tapering size.Thus, it is failed to change traditional crystallizer and compensates at top leptoprosopy tapering insufficient and in the excessive phenomenon of bottom magnitude of recruitment.In addition, it increases unified tapering to wide of crystallizer entirety, adds the friction between crystallizer wide Middle face region copper coin and base shell, causes Wide-surface copper plate of crystallizer to wear and tear and aggravates, greatly shorten the service life of crystallizer.In addition, publication number is the Chinese invention patent of CN102328037A, and what disclose a kind of effective elimination strand transverse corner crack line carries tapering plate blank chamfering crystallizer.In this crystallizer, only fillet surface is achieved to fillet surface carry taper design by changing its width from top to bottom, and wide of the crystallizer except fillet surface and leptoprosopy tapering are not made new advances and design.Therefore, cannot overcome equally crystallizer leptoprosopy tapering at an upper portion thereof insufficient to base shell shrinkage-compensating, in the excessive difficult problem of bottom compensation rate.Meanwhile, this invention lacks the design to the wide face cone degree of copper coin equally.Publication number is the Chinese invention patent of CN1559722A, discloses a kind of technology based on crystallizer leptoprosopy and wide hot-fluid ratio On-line Control plate slab crystallizer leptoprosopy tapering.Equally, this technology, also only based on the size of its leptoprosopy tapering of existing crystallizer linear copper coin structure integrated regulation, thus also cannot overcome base shell and solidify run into problem in traditional crystallizer.

Therefore, based on the actual solidification shrinkage rule of base shell in crystallizer, exploitation one can fully compensate base shell crystallizer adduction contract homogenising base shell heat transfer and growth, the tapering alleviating copper coin wearing and tearing can be maximized again, be all of great practical significance service life to improving continuous casting billet quality and improving crystallizer.

Summary of the invention

For the deficiencies in the prior art, the present invention proposes a kind of Slab crystallizer taper design method, both the amount of contraction that narrow face copper plate of crystallizer fully compensates base Ke Xiangkuanmian center is met to reach, and do not increase the requirement of its wear extent, reach again that homogenising base shell is wide, the object of the heat transfer of leptoprosopy adjacent corner region and growth, thus solve the difficult problem that base shell easily produces continuous casting billet surface and subcrack under traditional conical degree of crystallizer.

A kind of Slab crystallizer taper design method, comprises the steps:

Step 1: according to C in conticaster institute continuous casting main flow steel grade, Si, Mn, P, the content of S, Ni, Cr and Al main component, determine the density of institute's continuous casting steel grade, thermal conductivity factor, specific heat and thermal linear expansion coefficient, set up for base shell-crystallizer system heat/couple of force closes finite element numerical computation model the high temperature physical parameter providing base shell to solidify;

Step 2: according to the high temperature physical parameter of crystallizer copper plate structure and Cross Section of CC Billet size and institute's continuous casting steel grade, to set up with 1/4 base shell-crystallizer cross section system be calculating object, and Two Dimensional Transient Heat Transfer/couple of force closes finite element numerical computation model, calculate determine base shell whole crystallizer along the contraction on its height and circumference be out of shape distribute, covering slag thickness distribution;

Step 2.1: according to the high temperature physical parameter of crystallizer copper plate structure, Cross Section of CC Billet size and institute's continuous casting steel grade, the Two Dimensional Transient Heat Transfer that foundation is calculating object with 1/4 base shell-crystallizer cross section system/couple of force closes solid finite element model, and to physical model grid division;

Step 2.2: determine copper plate of crystallizer initial temperature field and base shell-initial hot-fluid in crystallizer interface; Getting arbitrary temperature close to copper coin true temperature value is copper coin hot-face temperature, and suppose that base shell initial surface temperature is molten steel pouring temperature, in base shell-crystallizer interface, meniscus place, flux film is evenly distributed, according to Cross Section of CC Billet size and covering slag consumption, calculate the thickness of flux film in interface, and with above-mentioned base shell surface temperature, slag film thickness and copper coin hot-face temperature for parameter, calculate ejection shell-initial hot-fluid in crystallizer interface;

This base shell-initial hot-fluid in crystallizer interface and the copper coin hot-face temperature got are closed copper coin hot side hot-fluid boundary condition and the copper coin initial temperature of finite element numerical computation model as 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force, and only calculate copper plate temperature field, obtain new copper coin hot-face temperature;

Be parameter by base shell surface temperature, covering slag thickness and the above-mentioned new copper coin hot-face temperature value calculated, calculate new base shell-crystallizer interface heat flux, and this new base shell-crystallizer interface heat flux and the copper plate temperature field calculated are closed the new copper coin hot side hot-fluid boundary condition of finite element numerical computation model and initial temperature as 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force, again only calculate copper plate temperature field, to obtain hot-face temperature and the base shell-crystallizer interface heat flux of more approaching to reality copper plate temperature; Repeat this computational process, until copper coin hot-face temperature twice iteration difference is less than 0.5 DEG C; Last tried to achieve copper plate temperature field and base shell-crystallizer interface heat flux are closed the initial temperature field of finite element numerical computation model copper coin and base shell surface and copper coin hot side hot-fluid boundary condition as final 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force;

Step 2.3: calculate base shell-crystallizer system heat transfer; Namely based on base shell initial temperature field and copper coin initial temperature field, with fixed base shell-crystallizer interface heat flux for base shell surface and copper coin hot side hot-fluid boundary condition, calculate the temperature field of base shell and copper plate of crystallizer, base shell surface and copper coin hot-face temperature parameter are provided for determining that base shell-crystallizer interface heat flux of next crystallizer height calculates and calculate 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force and close base shell needed for finite element numerical computation model and copper coin initial temperature field;

Step 2.4: calculate base shell solidification shrinkage and deformational behavior; Namely based on the thermo parameters method of the base shell of having tried to achieve and copper coin, base shell is calculated along the contraction of crystallizer Kuan Mian center and leptoprosopy center position and deflection; Calculate the displacement difference between base shell surface and copper coin hot side, to determine base shell-crystallizer interfacial gap width, for determining that next crystallizer height base shell-crystallizer interface heat flux provides base shell-crystallizer interfacial gap width parameter simultaneously;

Step 2.5: according to base shell surface temperature, copper coin hot-face temperature and base shell-crystallizer gap width, the base shell-crystallizer interface heat flux changed along crystallizer circumference under determining next crystallizer height;

Step 2.5.1: form according to base shell surface temperature and covering slag setting temperature relation determination base shell-crystallizer interface resistance, if base shell surface temperature is higher than covering slag setting temperature, Gu then base shell-crystallizer interface resistance is composed in series by liquid slag layer, solid slag blanket and crystallizer-slag interface resistance, perform step 2.5.2; If base shell surface temperature is less than or equal to covering slag setting temperature, Gu then base shell-crystallizer interface resistance is composed in series by air gap layer, solid slag blanket and crystallizer-slag interface resistance, perform step 2.5.3;

Step 2.5.2: regulation covering slag gross thickness equals base shell-crystallizer interfacial gap width, Gu according to the hot-fluid principle by liquid slag layer, admittedly slag blanket and crystallizer-slag interface, Gu calculate liquid slag layer thermal resistance, solid slag blanket thermal resistance, crystallizer-slag interface resistance and flux film gross thickness along the distribution of crystallizer circumference, perform step 2.5.4;

Step 2.5.3: Gu according to the hot-fluid principle by air gap layer, admittedly slag blanket and crystallizer-slag interface, Gu calculate air gap layer thermal resistance, admittedly slag blanket thermal resistance, crystallizer-slag interface resistance and flux film along the distribution of crystallizer circumference;

Step 2.5.4: according to base shell surface and the relation between copper coin hot-face temperature difference and base shell-crystallizer interface entire thermal resistance, determine the heat flux distribution along crystallizer circumference;

Step 2.6: step 2.3 is calculated the base shell of gained and mould temperature field and the determined base shell-crystallizer interface heat flux of step 2.5.4 and be set as that 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force under next crystallizer height closes the base shell of finite element numerical computation model and copper coin initial temperature field and base shell surface and copper coin hot side hot-fluid boundary condition, and repeated execution of steps 2.3 to step 2.6, until continuous casting billet goes out crystallizer, thus try to achieve whole crystallizer along its height and circumference on base shell shrink be out of shape distribute, covering slag thickness distribution;

Step 3: according to flux film in the thickness distribution of wide of crystallizer with leptoprosopy, determine that Boundary is submitted in wide face and leptoprosopy submits Boundary, and on setting wide, boundary line side is wedge shape tapering district, wide bight, opposite side is wide Middle face zero draft district; On leptoprosopy, boundary line side is wedge shape tapering district, leptoprosopy bight, and opposite side is curve tapering district in the middle part of leptoprosopy;

Described boundary line position is determined as follows:

In base shell-crystallizer interface in crystallizer exit, determine in the middle part of wide of crystallizer or leptoprosopy to bight direction protection slag thickness increment slope first time be greater than 0.002 position, by this position and perpendicular on crystallizer or the straight line of end opening be boundary line;

Step 4: according to the amount of contraction to crystallizer wide center position in the middle part of the base shell leptoprosopy that step 2.3 ~ 2.6 are tried to achieve, its expression formula along the distribution of crystallizer short transverse of matching, and then determine that it is the tapering in curve tapering district in the middle part of crystallizer leptoprosopy;

Step 5: according to step 2.3 ~ 2.6 try to achieve contraction from base shell leptoprosopy bight to crystallizer wide center position with distortion distribute, determine bight and central region to the contraction of crystallizer wide center position and deflection poor, and then the maximum of difference both obtaining, and in the middle part of leptoprosopy curve tapering district tapering compensation rate basis on, the tapering compensation rate in design crystallizer leptoprosopy bight exports from meniscus to crystallizer and is linearly increased to above-mentioned maximum by 0; The tapering compensation rate in bight is reduced to 0 along bight to boundary line dimension linear simultaneously, make crystallizer leptoprosopy folding corner region become wedge shape structure;

Step 6: base shell wide the bight of trying to achieve according to step 2.3 ~ 2.6 distributes to the contraction of crystallizer leptoprosopy center position with distortion, determine that the maximum with distortion is shunk in bight, the tapering compensation rate in design crystallizer wide bight exports from meniscus to crystallizer and is linearly increased to above-mentioned maximum by 0, the tapering compensation rate in bight is reduced to 0 along bight to boundary line dimension linear simultaneously, make crystallizer wide folding corner region become wedge shape structure.

Described in step 2.1 with 1/4 base shell-crystallizer cross section system refer to set up according to the actual continuous casting crystallizer copper plate structure of steel mill and institute's continuous-cast blank cross dimensions with continuous casting billet and 1/4 continuous casting billet that crystallizer is wide, leptoprosopy center is the plane of symmetry-crystallizer cross section.

The Two Dimensional Transient Heat Transfer of the continuous casting billet described in step 2-crystallizer cross section system/couple of force closes the heat transfer of FEM model and mechanic boundary condition is: set base shell and copper plate of crystallizer plane of symmetry hot-fluid equals 0; Base shell-crystallizer interface heat flux that base shell surface calculates gained with copper plate of crystallizer hot side hot-fluid by previous step applies to realize along corresponding circumference; The heat transfer of copper plate of crystallizer tank is set as and cooling water convection heat transfer' heat-transfer by convection; Continuous casting billet is wide, the mechanic boundary condition of the leptoprosopy plane of symmetry is set as that the displacement along strand leptoprosopy and wide direction is 0 respectively; Wide-surface copper plate of crystallizer maintains static, and narrow copper plate moves in parallel to wide center position by tapering side-play amount size; The ferrostatic pressure of base shell solidification front vertically puts on the limit of base shell solidification front unit in the mode rejecting the non-solidification liquid core unit of continuous casting billet; The touching act of continuous casting billet and copper plate of crystallizer adopted just-and soft contact analysis algorithm imposes restriction;

The heat transfer governing equation of continuous casting billet and crystallizer is: two-dimensional transient heat transfer differential equation;

Continuous casting billet mechanics governing equation is elected Anand as and is led constitutive equation of being correlated with.

Entire thermal resistance described in step 2.5.4, computational process is:

In base shell-crystallizer interface, the thermal resistance of liquid slag layer, solid slag blanket and air gap layer is formed by thermal conduction resistance is in parallel with radiation thermal resistance, and interface entire thermal resistance then forms according to the heat transfer medium of its inside, in series by each heat transfer medium layer thermal resistance.

Calculating base shell described in step 2.2-initial hot-fluid in crystallizer interface, is realized by formula (1) ~ (5):

Liquid slag layer thermal resistance:

$\left\{\begin{array}{c}{R}_{\mathrm{liquid}}^c=d_{\mathrm{liquid}}/k_{\mathrm{liquid}}\\ R_{\mathrm{liquid}}^{\mathrm{rad}}=\frac{{0.75E}_{\mathrm{liquid}}\·d_{\mathrm{liquid}}+(1/{\mathrm{\ϵ}}_{\mathrm{shell}}+1/{\mathrm{\ϵ}}_f)-1}{\mathrm{\σ}\·n_{\mathrm{liquid}}^2\·({(T_{\mathrm{sol}}+273)}^2+{(T_{\mathrm{shell}}+273)}^2)\·((T_{\mathrm{sol}}+273)+(T_{\mathrm{shell}}+273))}\\ 1/R_{\mathrm{liquid}}=1/R_{\mathrm{liquid}}^c+1/R_{\mathrm{liquid}}^{\mathrm{rad}}\end{array}\right.---\left(1\right)$

In formula, for liquid slag layer thermal conduction resistance, m ²dEG C/W, for liquid slag layer radiation thermal resistance, m ²dEG C/W, R _liquidfor liquid slag layer thermal resistance, m ²dEG C/W, d _liquidliquid slag layer thickness, m, k _liquidfor the thermal conductivity factor of melt cinder, W/ (m DEG C) σ is Boltzmann's constant, E _liquidfor the extinction coefficient of melt cinder, n _liquidfor the refractive index of melt cinder, ε _shellfor the emissivity of base shell, ε _ffor the emissivity of covering slag, T _shellfor base shell surface temperature, DEG C, T _solfor covering slag setting temperature, DEG C;

Gu slag blanket thermal resistance:

$\left\{\begin{array}{c}{R}_{\mathrm{solid}}^c=d_{\mathrm{solid}}/k_{\mathrm{solid}}\\ R_{\mathrm{solid}}^{\mathrm{rad}}=\frac{{0.75E}_{\mathrm{solid}}\·d_{\mathrm{solid}}+(1/{\mathrm{\ϵ}}_f+1/{\mathrm{\ϵ}}_{\mathrm{mold}})-1}{\mathrm{\σ}\·n_{\mathrm{solid}}^2\·({(T_{\mathrm{sol}}+273)}^2+{(T_{m/m}+273)}^2)\·((T_{\mathrm{sol}}+273)+(T_{m/m}+273))}\\ 1/R_{\mathrm{solid}}=1/R_{\mathrm{solid}}^c+1/R_{\mathrm{solid}}^{\mathrm{rad}}\end{array}\right.---\left(2\right)$

In formula, for solid slag blanket thermal conduction resistance, m ²dEG C/W, for solid slag blanket radiation thermal resistance, m ²dEG C/W, R _solidfor solid slag blanket thermal resistance, m ²dEG C/W, d _solidgu thickness of slag layer, m, k _solidfor the thermal conductivity factor of solid slag, W/ (m DEG C), E _solidfor the extinction coefficient of solid slag, n _solidfor the refractive index of solid slag, ε _moldfor the emissivity of copper plate of crystallizer, T _m/mgu be crystallizer hot side-slag interface temperature, DEG C;

Gu crystallizer-slag interface resistance:

$R_{\mathrm{int}}(\×{10}^{-4})={1.50d}_{\mathrm{flux}}^3-{7.53d}_{\mathrm{flux}}^2+{16.09d}_{\mathrm{flux}}+2.24---\left(3\right)$

In formula, R _intgu be crystallizer-slag interface resistance, m ²dEG C/W, d _fluxfor covering slag gross thickness;

According to the hot-fluid principle of hot-fluid by each dielectric layer in interface, formula (4) and formula (3) is utilized to try to achieve R _liquid, R _solidand R _int;

$\left\{\begin{array}{c}\frac{T_{\mathrm{shell}}-T_{\mathrm{sol}}}{R_{\mathrm{liquid}}}=\frac{T_{\mathrm{sol}}-T_{m/m}}{R_{\mathrm{solid}}}\\ \frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{liquid}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}=\frac{T_{m/m}-T_m}{R_{\mathrm{int}}}\\ d_{\mathrm{solid}}+d_{\mathrm{liquid}}=d_{\mathrm{flux}}\end{array}\right.---\left(4\right)$

In formula, T _mfor copper coin hot-face temperature, DEG C;

According to base shell surface and the temperature difference of copper coin hot side and the relation of interface entire thermal resistance, try to achieve interface heat flux:

$q=\frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{liquid}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}---\left(5\right)$

In formula, q is base shell-crystallizer interface heat flux, W/m ².

Gu the determination liquid slag layer thermal resistance described in step 2.5.2, solid slag blanket thermal resistance and crystallizer-slag interface resistance, process is: according to formula (1), formula (2), formula (3) and formula (4), Gu first calculate liquid slag layer thickness in base shell-crystallizer interface, solid thickness of slag layer and crystallizer-slag interface temperature, and above-mentioned result of trying to achieve is taken back formula (1), (2) and (3), Gu liquid slag layer thermal resistance, solid slag blanket thermal resistance and crystallizer-slag interface resistance can be obtained.

Gu Gu determination air gap layer thickness, air gap-slag interface temperature and the crystallizer-slag interface temperature described in step 2.5.3, formula (3) and following formula is adopted to determine:

$\left\{\begin{array}{c}{R}_{\mathrm{air}}^c=d_{\mathrm{air}}/k_{\mathrm{air}}\\ R_{\mathrm{air}}^{\mathrm{rad}}=0.5\mathrm{\σ}\·({\mathrm{\ϵ}}_{\mathrm{shell}}+{\mathrm{\ϵ}}_f)\·({(T_{a/m}+273)}^2+{(T_{\mathrm{shell}}+273)}^2)\·((T_{a/m}+273)+(T_{\mathrm{shell}}+273))\\ 1/R_{\mathrm{air}}=1/R_{\mathrm{air}}^c+1/R_{\mathrm{air}}^{\mathrm{rad}}\end{array}\right.---\left(6\right)$

In formula, for air gap layer thermal conduction resistance, m ²dEG C/W, for air gap layer radiation thermal resistance, m ²dEG C/W, R _airfor air gap layer thermal resistance, m ²dEG C/W, d _airair gap layer thickness, m, k _airfor the thermal conductivity factor of air gap, W/ (m DEG C), T _a/mgu be air gap-slag interface temperature, DEG C;

$\left\{\begin{array}{c}{R}_{\mathrm{solid}}^c=d_{\mathrm{solid}}/k_{\mathrm{solid}}\\ R_{\mathrm{solid}}^{\mathrm{rad}}=\frac{{0.75E}_{\mathrm{solid}}\·d_{\mathrm{solid}}+(1/{\mathrm{\ϵ}}_f+1/{\mathrm{\ϵ}}_{\mathrm{mold}})-1}{\mathrm{\σ}\·n_{\mathrm{solid}}^2\·({(T_{a/m}+273)}^2+{(T_{m/m}+273)}^2)\·((T_{a/m}+273)+(T_{m/m}+273))}\\ 1/R_{\mathrm{solid}}=1/R_{\mathrm{solid}}^c+1/R_{\mathrm{solid}}^{\mathrm{rad}}\end{array}\right.---\left(7\right)$

$\left\{\begin{array}{c}\frac{T_{\mathrm{shell}}-T_{a/m}}{R_{\mathrm{air}}}=\frac{T_{a/m}-T_{m/m}}{R_{\mathrm{solid}}}\\ \frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{air}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}=\frac{T_{m/m}-T_m}{R_{\mathrm{int}}}\\ d_{\mathrm{solid}}+d_{\mathrm{air}}=d_t\end{array}\right.---\left(8\right)$

In formula, d _tfor base shell-crystallizer interfacial gap width, m;

The above results is taken back formula (6) again, formula (7) and formula (3) are Gu can calculate air gap layer thermal resistance, solid slag blanket thermal resistance and crystallizer-slag interface resistance.

Advantage of the present invention:

(1) plate slab crystallizer tapering designed according to this invention fully can compensate the contraction of base shell in crystallizer, the distortion of effective suppression base shell in crystallizer, prevents initial set base shell to cause continuous casting billet surface and the taking place frequently of subcrack because deflection is excessive on crystallizer top;

(2) use plate slab crystallizer tapering designed by the present invention effectively to eliminate base shell is wide, " focus " in leptoprosopy adjacent corner region, realize base shell homoepitaxial in crystallizer;

(3) use the plate slab crystallizer tapering maximizing designed by the present invention to alleviate mold copper plate wear, extend the service life of crystallizer;

(4) use the plate slab crystallizer tapering designed by the present invention can accelerate the heat transfer of base shell bight and leptoprosopy, increase base shell goes out intensity during crystallizer, alleviates base shell leptoprosopy bulge.

Accompanying drawing explanation

Fig. 1 is that 1/2 crystallizer of one embodiment of the present invention is wide, narrow copper plate tapering schematic diagram;

Wherein, wedge shape tapering district, 1-crystallizer wide bight, 2-crystallizer wide Middle face zero draft district, wedge shape tapering district, 3-crystallizer leptoprosopy bight, curve tapering district in the middle part of 4-crystallizer leptoprosopy, height below h-crystallizer meniscus, l _wthe width of-crystallizer wedge shape tapering district, wide bight to bight and zero draft district, middle part boundary line, d _w-crystallizer wide total compensation rate of bight tapering, l _nthe width of-crystallizer leptoprosopy bight to wedge shape tapering district, bight and tapering district, middle part boundary line, d _nin the middle part of the total compensation rate of-crystallizer leptoprosopy bight tapering and leptoprosopy, the total compensation rate of tapering is poor;

Fig. 2 is the Slab crystallizer taper design method flow chart of one embodiment of the present invention;

Fig. 3 is the 1/4 base shell-crystallizer cross sectional representation of one embodiment of the present invention;

Fig. 4 is that the 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force of one embodiment of the present invention closes FEM model mechanical analysis boundary condition schematic diagram.

Detailed description of the invention

Below in conjunction with accompanying drawing, an embodiment of the present invention is described further.

Base shell solidifies to produce and shrinks and distortion in crystallizer, by amount of contraction in the inconsistent impact of crystallizer short transverse, often cause base shell crystallizer top compensate insufficient, in crystallizer bottom, compensation rate is excessive, thus cause base shell easily to cause crackle on crystallizer top, and a difficult problem for crystallizer bottom copper coin serious wear.In addition; because the contraction of base shell in crystallizer mainly concentrates on base shell adjacent corner region with distortion; base shell adjacent corner region is often caused significantly to reduce heat transfer rate at this region integrated distribution because of covering slag and air gap; produce base shell " focus ", be unfavorable for base shell homoepitaxial in crystallizer.For this reason; the present invention proposes following a kind of effective compensation base shell to shrink in crystallization; and maximize and alleviate the wearing and tearing of copper coin bottom, and distributed by homogenising base shell adjacent corner locality protection slag and air gap and realize the effective new tapering of plate slab crystallizer and the method for designing of eliminating base shell " focus ".

In the embodiment of the present invention, conical degree of crystallizer is made up of jointly leptoprosopy tapering and wide face cone degree:

As shown in Figure 1, described wide upper boundary line side is wedge shape tapering district, wide bight 1, and opposite side is wide Middle face zero draft district 2; Described wedge shape tapering district, wide bight 1 is by the width l of the h of height below crystallizer meniscus, wedge shape tapering district, wide bight 1 and wide Middle face zero draft district 2 boundary line _wand the total compensation rate d of bight tapering _wdetermine; Folding corner region tapering is: the tapering compensation rate in bight exports from meniscus to crystallizer and is linearly increased to the maximum d of base shell bight to crystallizer leptoprosopy center position amount of contraction by 0 _w, and along bight to boundary line l _wdimension linear reduces compensation rate to 0, makes crystallizer wide folding corner region become wedge shape structure.Keep native copper plate hot side motionless in the middle part of wide copper coin, make it form zero draft district.

As shown in Figure 1, on described leptoprosopy, boundary line side is wedge shape tapering district, leptoprosopy bight 3, and opposite side is curve tapering district 4 in the middle part of leptoprosopy; Described crystallizer leptoprosopy central region (in the middle part of leptoprosopy curve tapering district 4) tapering is determined to the distribution of amount of contraction on crystallizer height of crystallizer wide center position according in the middle part of base shell leptoprosopy; Described crystallizer leptoprosopy folding corner region (wedge shape tapering district, leptoprosopy bight 3) tapering is: on described leptoprosopy central region tapering basis, the tapering compensation rate in bight exports from meniscus to crystallizer and is linearly increased to maximum d by 0 _n(described maximum is: base shell leptoprosopy bight is to the amount of contraction of crystallizer wide center position and its central region to the maximum of wide center position amount of contraction difference), and along bight to boundary line l _ndimension linear reduces compensation rate to 0, makes crystallizer leptoprosopy folding corner region become wedge shape structure, forms wedge shape tapering, and regulation removes bight wedge shape with the tapering of exterior domain for curve tapering district, middle part.

To the distribution of amount of contraction on crystallizer height of crystallizer wide center position in the middle part of described base shell leptoprosopy, base shell leptoprosopy bight is to the amount of contraction of crystallizer wide center position and its central region to the maximum of wide center position amount of contraction difference, the boundary line position of crystallizer leptoprosopy folding corner region tapering and central region tapering, base shell wide bight to crystallizer leptoprosopy center position amount of contraction maximum and crystallizer folding corner region tapering and in the middle part of it boundary line position in zero draft region close finite element numerical computation model provide by the base shell in following method for designing-crystallizer system heat/couple of force.

A kind of Slab crystallizer taper design method, flow chart as shown in Figure 2, comprises the steps:

Step 1: according to C in conticaster institute continuous casting main flow steel grade, Si, Mn, P, the content of S, Ni, Cr and Al main component, determine the density of institute's continuous casting steel grade, thermal conductivity factor, specific heat and thermal linear expansion coefficient, set up for base shell-crystallizer system heat/couple of force closes finite element numerical computation model the high temperature physical parameter providing base shell to solidify;

(1) density

Density due to steel is main relevant with temperature and C content, its solid Density ρ _sdetermined by formula (1):

${\mathrm{\ρ}}_s=\frac{100\×(8245.2-0.51(T+273))}{(100-(\mathrm{wt}\%C)){(1+0.008(\mathrm{wt}\%C))}^3}---\left(9\right)$

Wherein, the temperature of T residing for current steel, DEG C; Wt%C is the percentage composition of C.

The density p of liquid steel _ldetermined by formula (2):

ρ _l=7100-73(wt%C)-(0.8-0.09(wt%C))(T-1550) (10)

Due to the two-phase section density p of steel _s/lbetween therebetween, and relevant with solid phase fraction, therefore it determined by formula (3):

ρ _s/l=f _sρ _s+(1-f _s)ρ _l (11)

Wherein, f _sfor solid phase fraction, provided by formula (4):

$f_s\left(T\right)=\frac{T_l-T+\frac{2}{\mathrm{\π}}(T_s-T_l)\{1-\cos \left(\frac{\mathrm{\π}(T-T_l)}{2(T_s-T_l)}\right)\}}{(T_l-T_s)(1-\frac{2}{\mathrm{\π}})}---\left(12\right)$

In formula, T _swith T _lbe respectively solidus temperature and the liquidus temperature of steel, DEG C.

T _stried to achieve by formula (5) ~ (7):

When wt%C≤0.09:

T _s=1538.0-478.0(wt%C)-20.5(wt%Si)-6.5(wt%Mn)-500(wt%P)-700(wt%S)

-11.5(wt%Ni)-2.0(wt%Cr)-5.5(wt%Al) (13)

When 0.09 < wt%C≤0.17:

T _s=1495.0-20.5(wt%Si)-6.5(wt%Mn)-500(wt%P)-700(wt%S)

-11.5(wt%Ni)-2.0(wt%Cr)-5.5(wt%Al) (14)

As wt%C > 0.17:

T _s=1527.0-187.5(wt%C)-20.5(wt%Si)-6.5(wt%Mn)-500(wt%P)-700(wt%S)

-11.5(wt%Ni)-2.0(wt%Cr)-5.5(wt%Al) (15)

T _ltried to achieve by formula (8):

T _l=1536.0-78.0(wt%C)-7.6(wt%Si)-4.9(wt%Mn)-34.4(wt%P)-38(wt%S)

-3.1(wt%Ni)-1.3(wt%Cr)-78(wt%Al) (16)

Wherein, wt%Si, wt%Mn, wt%P, wt%S, wt%Ni, wt%Cr, wt%Al are respectively Si, the percentage composition of Mn, P, S, Ni, Cr and Al.

(2) thermal conductivity coefficient

The thermal conductivity factor k of solid steel _sbe taken as 33.0W/ (m DEG C); In view of Mold convection current is on the impact of heat conduction, molten steel thermal conductivity factor k _lbe taken as k _sm doubly.

Two-phase section thermal conductivity factor k _s/lrequired by formula (9).It is 6.0 that the present invention gets m value.

k _s/l=f _sk _s+(1-f _s)mk _s (17)

(3) specific heat

The specific heat c of solid-state and liquid steel _sand c _lbe taken as 669.44 and 824.62J/ (kg DEG C) respectively.The specific heat of two-phase section is taken as equivalent specific heat c _eff, shown in (10).

$c_{\mathrm{eff}}=c_{s/l}-L\frac{{\&PartialD;f}_s}{\&PartialD;T}---\left(18\right)$

In formula, c _efffor equivalent specific heat, J/ (kg DEG C); c _s/lfor solid-liquid phase region specific heat, 772J/ (kg DEG C); L is latent heat of solidification, 272140J/kg.Solid rate f _svalue is such as formula shown in (4).

(4) thermal linear expansion coefficient

In the present invention, the instantaneous linear thermalexpansioncoefficientα (T) of the steel under arbitrary temp is tried to achieve by formula (11):

$\mathrm{\&alpha;}\left(T\right)=\frac{{\mathrm{d\&epsiv;}}^{\mathrm{th}}}{\mathrm{dT}}---\left(19\right)$

In formula, ε ^thfor thermal strain, tried to achieve by formula (12):

${\mathrm{\&epsiv;}}^{\mathrm{th}}=\sqrt[3]{\frac{\mathrm{\&rho;}\left(T_{\mathrm{ref}}\right)}{\mathrm{\&rho;}\left(T\right)}-1}---\left(20\right)$

Wherein, T _reffor reference temperature, DEG C.

Step 2: according to the high temperature physical parameter of crystallizer copper plate structure and Cross Section of CC Billet size and institute's continuous casting steel grade, set up as shown in Figure 3 with base shell and 1/4 base shell-crystallizer cross section system that crystallizer is wide, leptoprosopy center line is the plane of symmetry be calculating object Two Dimensional Transient Heat Transfer/couple of force closes finite element numerical computation model, calculate determine base shell whole crystallizer along the contraction on its height and circumference be out of shape distribute, covering slag thickness distribution;

Step 2.1: according to the high temperature physical parameter of crystallizer copper plate structure, Cross Section of CC Billet size and institute's continuous casting steel grade, Two Dimensional Transient Heat Transfer/couple of force that the foundation of Ansys finite element software is calculating object with 1/4 base shell-crystallizer cross section system is utilized to close solid finite element model, and to physical model grid division;

Step 2.2: determine copper plate of crystallizer initial temperature field and base shell-initial hot-fluid in crystallizer interface.Getting arbitrary temperature close to copper coin true temperature value is copper coin hot side initial temperature (desirable 275 DEG C of such as conventional plate blank continuous casting); and suppose that base shell initial surface temperature is molten steel pouring temperature (getting tundish temperature), in base shell-crystallizer interface, meniscus place, flux film is evenly distributed.According to Cross Section of CC Billet size and covering slag consumption parameter, calculate the thickness of flux film in ejection shell-crystallizer interface.Such as, in conventional plate blank continuous casting, first according to width and the thickness size of continuous casting billet, calculate the steel transportation amount of 1 second time crystallizer, can obtain divided by this steel transportation amount the covering slag weight that 1 second time flowed into base shell-crystallizer interface by the on-the-spot slag consumption of continuous casting; Again by the density of this weight divided by covering slag, covering slag volume can be obtained; In addition, can calculate by pulling speed of continuous casting the height that 1 second guardtime slag continuously flows into base shell; Thus, by covering slag volume divided by this height and the girth of continuous casting billet cross section, the thickness of slag film can be obtained.Base shell surface temperature due to meniscus place is enough to provide the heat needed for covering slag fusing; Gu the heat transfer resistance therefore in base shell-crystalizing interface is configured to liquid slag layer thermal resistance, solid slag blanket thermal resistance and crystallizer-slag interface resistance, corresponding thermal resistance calculation formula is provided by formula (13), formula (14) and formula (15).According to passing through liquid slag layer, Gu Gu the hot-fluid principle at slag blanket and crystallizer-slag interface, set up equation group (16), and with above-mentioned base shell surface temperature, slag film thickness and copper coin hot-face temperature are parameter, adopt Monte Carlo Solving Nonlinear Systems of Equations method solving equation group (16), calculate liquid slag layer thickness, Gu thickness of slag layer, Gu crystallizer-slag interface temperature value, and respective value takes back formula (13), formula (14) and formula (15), calculate liquid slag layer thermal resistance, Gu Gu slag blanket thermal resistance and crystallizer-slag interface resistance, finally calculate the ejection shell-initial hot-fluid in crystallizer interface distribution circumferentially by formula (17).

Liquid slag layer thermal resistance:

$\left\{\begin{array}{c}{R}_{\mathrm{liquid}}^c=d_{\mathrm{liquid}}/k_{\mathrm{liquid}}\\ R_{\mathrm{liquid}}^{\mathrm{rad}}=\frac{{0.75E}_{\mathrm{liquid}}\&CenterDot;d_{\mathrm{liquid}}+(1/{\mathrm{\&epsiv;}}_{\mathrm{shell}}+1/{\mathrm{\&epsiv;}}_f)-1}{\mathrm{\&sigma;}\&CenterDot;n_{\mathrm{liquid}}^2\&CenterDot;({(T_{\mathrm{sol}}+273)}^2+{(T_{\mathrm{shell}}+273)}^2)\&CenterDot;((T_{\mathrm{sol}}+273)+(T_{\mathrm{shell}}+273))}\\ 1/R_{\mathrm{liquid}}=1/R_{\mathrm{liquid}}^c+1/R_{\mathrm{liquid}}^{\mathrm{rad}}\end{array}\right.---\left(1\right)$

In formula, for liquid slag layer thermal conduction resistance, m ²dEG C/W, for liquid slag layer radiation thermal resistance, m ²dEG C/W, R _liquidfor liquid slag layer thermal resistance, m ²dEG C/W, d _liquidliquid slag layer thickness, m, k _liquidfor the thermal conductivity factor of melt cinder, W/ (m DEG C) σ is Boltzmann's constant, E _liquidfor the extinction coefficient of melt cinder, n _liquidfor the refractive index of melt cinder, ε _shellfor the emissivity of base shell, ε _ffor the emissivity of covering slag, T _shellfor base shell surface temperature, DEG C, T _solfor covering slag setting temperature, DEG C;

Gu slag blanket thermal resistance:

$\left\{\begin{array}{c}{R}_{\mathrm{solid}}^c=d_{\mathrm{solid}}/k_{\mathrm{solid}}\\ R_{\mathrm{solid}}^{\mathrm{rad}}=\frac{{0.75E}_{\mathrm{solid}}\&CenterDot;d_{\mathrm{solid}}+(1/{\mathrm{\&epsiv;}}_f+1/{\mathrm{\&epsiv;}}_{\mathrm{mold}})-1}{\mathrm{\&sigma;}\&CenterDot;n_{\mathrm{solid}}^2\&CenterDot;({(T_{\mathrm{sol}}+273)}^2+{(T_{m/m}+273)}^2)\&CenterDot;((T_{\mathrm{sol}}+273)+(T_{m/m}+273))}\\ 1/R_{\mathrm{solid}}=1/R_{\mathrm{solid}}^c+1/R_{\mathrm{solid}}^{\mathrm{rad}}\end{array}\right.---\left(2\right)$

In formula, for solid slag blanket thermal conduction resistance, m ²dEG C/W, for solid slag blanket radiation thermal resistance, m ²dEG C/W, R _solidfor solid slag blanket thermal resistance, m ²dEG C/W, d _solidgu thickness of slag layer, m, k _solidfor the thermal conductivity factor of solid slag, W/ (m DEG C), E _solidfor the extinction coefficient of solid slag, n _solidfor the refractive index of solid slag, ε _moldfor the emissivity of copper plate of crystallizer, T _m/mgu be crystallizer hot side-slag interface temperature, DEG C;

Gu crystallizer-slag interface resistance:

$R_{\mathrm{int}}(\&times;{10}^{-4})={1.50d}_{\mathrm{flux}}^3-{7.53d}_{\mathrm{flux}}^2+{16.09d}_{\mathrm{flux}}+2.24---\left(3\right)$

In formula, R _intgu be crystallizer-slag interface resistance, m ²dEG C/W, d _fluxfor covering slag gross thickness;

According to the hot-fluid principle of hot-fluid by each dielectric layer in interface, formula (4) and formula (3) is utilized to try to achieve R _liquid, R _solidand R _int;

$\left\{\begin{array}{c}\frac{T_{\mathrm{shell}}-T_{\mathrm{sol}}}{R_{\mathrm{liquid}}}=\frac{T_{\mathrm{sol}}-T_{m/m}}{R_{\mathrm{solid}}}\\ \frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{liquid}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}=\frac{T_{m/m}-T_m}{R_{\mathrm{int}}}\\ d_{\mathrm{solid}}+d_{\mathrm{liquid}}=d_{\mathrm{flux}}\end{array}\right.---\left(4\right)$

In formula, T _mfor copper coin hot-face temperature, DEG C;

According to base shell surface and the temperature difference of copper coin hot side and the relation of interface entire thermal resistance, try to achieve interface heat flux:

$q=\frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{liquid}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}---\left(5\right)$

In formula, q is base shell-crystallizer interface heat flux, W/m ².

Based on above-mentioned tried to achieve base shell-initial hot-fluid in crystallizer interface, it is applied mode by node and puts on copper coin hot side along crystallizer circumference, the copper coin hot side conductive heat flow boundary condition of FEM model is closed as 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force, and set that copper plate of crystallizer is wide, the hot-fluid in leptoprosopy Central Symmetry face is 0, namely for crystallizer wide Central Symmetry face crystallizer leptoprosopy Central Symmetry face the heat transfer of copper plate of crystallizer tank is the convection heat transfer' heat-transfer by convection with cooling water; Set the initial temperature of above-mentioned given copper coin hot-face temperature (275 DEG C) as copper plate of crystallizer, utilize Ansys finite element analysis software only to make Steady-State Thermal Field to copper plate of crystallizer to calculate (continuous casting billet part does not participate in calculating), thus try to achieve new copper plate of crystallizer temperature field and hot-face temperature thereof.Wherein, copper plate of crystallizer heat transfer governing equation is as follows:

${\mathrm{\&rho;}}_m{c}_m\frac{\&PartialD;T}{\&PartialD;t}=\frac{\&PartialD;}{\&PartialD;x}\left({\mathrm{\&lambda;}}_m\frac{\&PartialD;T}{\&PartialD;x}\right)+\frac{\&PartialD;}{\&PartialD;y}\left({\mathrm{\&lambda;}}_m\frac{\&PartialD;T}{\&PartialD;y}\right)---\left(21\right)$

In formula, ρ _m, c _mwith λ _mbe respectively the density of copper, specific heat and thermal conductivity factor; T, t are respectively temperature and time.Wherein, the heat transfer of copper plate of crystallizer tank is calculated by formula (19) with cooling water convective heat-transfer coefficient to be determined, the cooling water temperature under different crystallizer height is determined by formula (20), and namely coolant water temperature linearly increases from bottom to top along crystallizer height.

$\frac{h_w{d}_w}{{\mathrm{\&lambda;}}_w}0.023{\left(\frac{{\mathrm{\&rho;}}_w{u}_w{d}_w}{{\mathrm{\&mu;}}_w}\right)}^{0.8}{\left(\frac{c_w{\mathrm{\&mu;}}_w}{{\mathrm{\&lambda;}}_w}\right)}^{0.4}---\left(22\right)$

In formula, h _wfor the convective heat-transfer coefficient of tank and cooling water, W/ (㎡ DEG C); T is copper coin tank temperature, DEG C; T _wfor cooling water temperature, DEG C; λ _wfor cooling water thermal conductivity factor, W/ (m DEG C); d _wfor tank equivalent diameter, m; ρ _wfor cooling water density, kg/m ³; u _wfor cooling water flow velocity, m/s; μ _wfor cooling water viscosity, Pas; c _wfor cooling water specific heat, J/ (kg DEG C).

T _w=T _out-n×(T _in+T _out)/N (23)

In formula, T _infor crystallizer cooling water inlet temperature, DEG C; T _outfor crystallizer cooling water outlet temperature, DEG C; N is the step number that current continuous casting billet moves down, and is taken as 0; N to export the total step number of movement for continuous casting billet from meniscus to crystallizer.In order to ensure computational accuracy, reduce amount of calculation as far as possible again, to the plate slab crystallizer of 800mm effective length, N gets 400 simultaneously.

Bring base shell surface temperature (being still now molten steel pouring temperature), covering slag thickness and new copper coin hot-face temperature value into formula (13) ~ (17), calculate new base shell-crystallizer interface heat flux, and this new base shell-crystallizer interface heat flux and the copper plate temperature field that newly calculates are closed the new copper coin hot side conductive heat flow boundary condition of FEM model and initial temperature as 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force, again only calculate copper plate temperature field, to obtain copper plate temperature field and the base shell-crystallizer interface heat flux of more approaching to reality; Repeat this computational process, until terminate when copper coin hot-face temperature twice iteration difference is less than 0.5 DEG C to calculate; Last tried to achieve copper plate of crystallizer temperature field and base shell-crystallizer interface heat flux are closed the initial temperature field of FEM model copper coin and base shell surface and copper coin hot side conductive heat flow boundary condition as final 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force.

Step 2.3: apply mode by node hot-fluid, base shell-crystallizer the interface heat flux applying to have tried to achieve is the heat transfer boundary condition of base shell surface and copper plate of crystallizer hot side, setting base shell and copper plate of crystallizer is wide, the heat transfer boundary condition in leptoprosopy Central Symmetry face be hot-fluid is 0, namely for base shell and crystallizer wide Central Symmetry face leptoprosopy Central Symmetry face copper plate of crystallizer tank is the convection heat transfer' heat-transfer by convection with cooling water, and convection transfer rate determined by formula (7), (the base shell at meniscus place and copper coin initial temperature are respectively the copper coin initial temperature of molten steel pouring temperature and above-mentioned calculating for setting base shell and copper coin initial temperature, base shell below meniscus and copper coin initial temperature by previous step 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force closes FEM model result of calculation provide), utilize the calculating of Ansys finite element analysis software to make transient state temperature field to base shell and copper plate of crystallizer to calculate, with provide next crystallizer height base shell-crystallizer interface heat flux calculate needed for base shell surface and copper coin hot-face temperature parameter, and calculate 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force and close base shell needed for FEM model and copper coin initial temperature field.Wherein, copper coin heat transfer governing equation is such as formula shown in (18), and base shell heat transfer governing equation is as follows:

${\mathrm{\&rho;}}_s{c}_s\frac{\&PartialD;T}{\&PartialD;t}=\frac{\&PartialD;}{\&PartialD;x}\left({\mathrm{\&lambda;}}_s\frac{\&PartialD;T}{\&PartialD;x}\right)+\frac{\&PartialD;}{\&PartialD;y}\left({\mathrm{\&lambda;}}_s\frac{\&PartialD;T}{\&PartialD;y}\right)---\left(24\right)$

In formula, ρ _s, c _swith λ _sbe respectively the temperature variant density of steel, specific heat and thermal conductivity factor.

Step 2.4: calculate the base shell of gained and copper plate temperature field for primary condition with step 2.3, the mechanic boundary condition of base shell and copper coin is set as shown in Figure 4: continuous casting billet is wide, the leptoprosopy plane of symmetry is set as being respectively 0 along the displacement in strand leptoprosopy and wide direction respectively; Ferrostatic pressure vertically puts on the limit of base shell solidification front unit in the mode rejecting the non-solidification liquid core unit of continuous casting billet, that is: according to the setting temperature relation of base shell temperature field and institute's continuous casting steel, judge the unit of temperature higher than this setting temperature, delete these unit, the limit of the unit be connected with these delete cellses is base shell solidification front, is directly applied by ferrostatic pressure with on these limits; Base shell and copper coin touching act adopted just-and soft contact analysis algorithm arranges; Wide-surface copper plate of crystallizer maintains static; In order to simulate crystallizer leptoprosopy tapering to the shrinkage-compensating effect of base shell along wide center position, narrow face copper plate of crystallizer moves in parallel to wide center position by tapering side-play amount size, that is: base shell often moves down a step, and the displacement amount of movement of narrow copper plate is l _taper/ N, l _taperfor crystallizer leptoprosopy tapering total drift amount, N is the same gets 400, thus calculate the deflection of base shell and crystallizer, obtaining base shell-crystallizer interfacial gap width by the displacement difference between base shell surface and copper coin hot side again, providing base shell-crystallizer interfacial gap width parameter for determining that next crystallizer height base shell-crystallizer interface heat flux calculates.

Wherein, copper coin mechanics governing equation adopts Elastic-plastic Constitutive equation, and base shell process of setting in crystallizer is attended by creep generation, thus base shell mechanics governing equation adopts formula (22) to lead relevant constitutive equation to the Anand shown in formula (23):

${\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}}_{\mathrm{ie}}=\mathrm{A\; exp}(-\frac{Q_A}{T}){\left[\sinh \left(\mathrm{\&xi;}\frac{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}{s}\right)\right]}^{1/m}---\left(25\right)$

Wherein, the differentiation formula of s is:

$\stackrel{\&CenterDot;}{s}={\left(h_0{|1-\frac{s}{\tilde{s}{\left[\frac{{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}}_{\mathrm{ie}}}{A}\exp \left(\frac{Q_A}{(T+273)}\right)\right]}^n}|}^{\mathrm{\&alpha;}}\mathrm{sign}(1-\frac{s}{\tilde{s}{\left[\frac{{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}}_{\mathrm{ie}}}{A}\exp \left(\frac{Q_A}{(T+273)}\right)\right]}^n})\right)}^{{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}}_{\mathrm{ie}}}---\left(26\right)$

In formula, s is deformation resistance, MPa; Q _afor the ratio of viscoplastic deformations activation energy and gas constant, K; A is pre-exponential factor, 1/s; ξ is stress multiplier; M is strain sensitive index; h ₀for sclerosis/softening constant, MPa; for give fixed temperature and strain rate time S saturation value, MPa; N answers the strain rate sensitivity of impedance saturation value; α is and hardens/soften relevant strain rate Sensitivity Index.Wherein, the initial value of s is 43MPa, Q _aget 32514K, A gets 1.0 × 1011 1/s, and ξ gets 1.15, m and gets 0.147, h ₀get 1329MPa, get 147.6MPa, n gets 0.06869, α and gets 1.

Step 2.5: according to base shell surface temperature, copper coin hot-face temperature and base shell-crystallizer gap width, calculates the base shell-crystallizer interface heat flux along the distribution of crystallizer circumference;

Step 2.5.1: form according to tried to achieve base shell surface temperature and covering slag setting temperature relation determination base shell-crystallizer interface resistance.Regulation: if base shell surface temperature is higher than covering slag setting temperature, Gu then base shell-crystallizer interface resistance is composed in series by liquid slag layer, solid slag blanket and crystallizer-slag interface resistance, this process is heat transfer modes I, performs step step 2.5.2; If base shell surface temperature is less than or equal to covering slag setting temperature, Gu then base shell-crystallizer interface resistance is composed in series by air gap layer, solid slag blanket and crystallizer-slag interface resistance, this process is heat transfer modes II, performs step 2.5.3.

Step 2.5.2: because now base shell-crystallizer interface is filled completely by melt cinder and solid slag, thus specifies that covering slag gross thickness (liquid slag layer thickness and solid thickness of slag layer sum) equals base shell-crystallizer interfacial gap width.Liquid slag layer is passed through according to heat, Gu Gu the hot-fluid principle at slag blanket and crystallizer-slag interface, with step 2.2, based on step 2.3 determined base shell surface temperature and copper coin hot-face temperature and step 2.4 determined base shell-crystallizer interfacial gap width, liquid slag layer thickness in ejection shell-crystallizer interface is calculated according to formula (13) ~ (16), Gu Gu thickness of slag layer and crystallizer-slag interface temperature, and tried to achieve result correspondence is taken back formula (13) ~ (15) calculate liquid slag layer thermal resistance respectively, Gu Gu slag blanket thermal resistance and crystallizer-slag interface resistance, perform step 2.5.4,

Step 2.5.3: because air gap layer thickness and solid thickness of slag layer sum equal base shell-crystallizer interfacial gap width, and pass through air gap layer according to heat, Gu Gu the hot-fluid principle at slag blanket and crystallizer-slag interface, set up equation group (26), and based on step 2.3 determined base shell surface temperature and copper coin hot-face temperature and step 2.4 determined base shell-crystallizer interfacial gap width, adopt Monte Carlo Solving Nonlinear Systems of Equations method solving equation group (26), calculate air gap layer thickness, Gu Gu thickness of slag layer and crystallizer-slag interface temperature value, and these value correspondences are taken back formula (24), formula (25) and formula (15), calculate air gap layer thermal resistance, Gu Gu slag blanket thermal resistance and crystallizer-slag interface resistance,

Air gap layer thermal resistance:

$\left\{\begin{array}{c}{R}_{\mathrm{air}}^c=d_{\mathrm{air}}/k_{\mathrm{air}}\\ R_{\mathrm{air}}^{\mathrm{rad}}=0.5\mathrm{\&sigma;}\&CenterDot;({\mathrm{\&epsiv;}}_{\mathrm{shell}}+{\mathrm{\&epsiv;}}_f)\&CenterDot;({(T_{a/m}+273)}^2+{(T_{\mathrm{shell}}+273)}^2)\&CenterDot;((T_{a/m}+273)+(T_{\mathrm{shell}}+273))\\ 1/R_{\mathrm{air}}=1/R_{\mathrm{air}}^c+1/R_{\mathrm{air}}^{\mathrm{rad}}\end{array}\right.---\left(6\right)$

In formula, for air gap layer thermal conduction resistance, m ²dEG C/W, for air gap layer radiation thermal resistance, m ²dEG C/W, R _airfor air gap layer thermal resistance, m ²dEG C/W, d _airair gap layer thickness, m, k _airfor the thermal conductivity factor of air gap, W/ (m DEG C), T _a/mgu be air gap-slag interface temperature, DEG C;

$\left\{\begin{array}{c}{R}_{\mathrm{solid}}^c=d_{\mathrm{solid}}/k_{\mathrm{solid}}\\ R_{\mathrm{solid}}^{\mathrm{rad}}=\frac{{0.75E}_{\mathrm{solid}}\&CenterDot;d_{\mathrm{solid}}+(1/{\mathrm{\&epsiv;}}_f+1/{\mathrm{\&epsiv;}}_{\mathrm{mold}})-1}{\mathrm{\&sigma;}\&CenterDot;n_{\mathrm{solid}}^2\&CenterDot;({(T_{a/m}+273)}^2+{(T_{m/m}+273)}^2)\&CenterDot;((T_{a/m}+273)+(T_{m/m}+273))}\\ 1/R_{\mathrm{solid}}=1/R_{\mathrm{solid}}^c+1/R_{\mathrm{solid}}^{\mathrm{rad}}\end{array}\right.---\left(7\right)$

$\left\{\begin{array}{c}\frac{T_{\mathrm{shell}}-T_{a/m}}{R_{\mathrm{air}}}=\frac{T_{a/m}-T_{m/m}}{R_{\mathrm{solid}}}\\ \frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{air}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}=\frac{T_{m/m}-T_m}{R_{\mathrm{int}}}\\ d_{\mathrm{solid}}+d_{\mathrm{air}}=d_t\end{array}\right.---\left(8\right)$

In formula, d _tfor base shell-crystallizer interfacial gap width, m;

Step 2.5.4: when base shell surface temperature is higher than covering slag setting temperature, determines the base shell-crystallizer heat flow density of current base shell position according to formula (17); When base shell surface temperature is equal to or less than covering slag setting temperature, determine the heat flow density of base shell current location according to formula (27), thus obtain the heat flux distribution along crystallizer circumference;

$q=\frac{T_{\mathrm{shell}}-T_m}{R_{\mathrm{air}}+R_{\mathrm{solid}}+R_{\mathrm{int}}}---\left(27\right)$

Step 2.6: step 2.3 is calculated the base shell of gained and mould temperature field and the determined base shell-crystallizer interface heat flux of step 2.5.4 and be set to 1/4 base shell-crystallizer cross section system Two Dimensional Transient Heat Transfer/couple of force under next crystallizer height and close the base shell of finite element numerical computation model and copper coin initial temperature field and base shell surface and copper coin hot side conductive heat flow boundary condition; and repeated execution of steps 2.3 to step 2.6; until continuous casting billet goes out crystallizer, thus try to achieve to shrink along its height and circumference distribution base shell at whole crystallizer distribute with distortion, covering slag thickness distribution.

Step 3: according to flux film in the thickness distribution of wide of crystallizer with leptoprosopy, determine that Boundary is submitted in wide face and leptoprosopy submits Boundary, and on setting wide, boundary line side is wedge shape tapering district, wide bight, opposite side is wide Middle face zero draft district; On leptoprosopy, boundary line side is wedge shape tapering district, leptoprosopy bight, and opposite side is curve tapering district in the middle part of leptoprosopy;

Described boundary line position is determined as follows:

In base shell-crystallizer interface in crystallizer exit, determine in the middle part of wide of crystallizer or leptoprosopy to bight direction protection slag thickness increment slope first time be greater than 0.002 position, by this position and perpendicular on crystallizer or the straight line of end opening be boundary line; As the AB line in the figure (a) of Fig. 1 and the CD line in figure (b);

Step 4: according to the amount of contraction to crystallizer wide center position in the middle part of the base shell leptoprosopy that step 2.3 ~ 2.6 are tried to achieve, its expression formula along the distribution of crystallizer short transverse of matching, and then determine the tapering in curve tapering district in the middle part of crystallizer leptoprosopy;

In the embodiment of the present invention; adopting at pulling rate is 1.2m/min ~ 1.6m/min; crystallizer cooling water flow is wide 2550L/min ~ 3050L/min, leptoprosopy 450L/min ~ 540L/min; molten steel overheat 20 DEG C ~ 35 DEG C; crystallizer total length 900mm; working depth 800mm, covering slag consumption is 0.40 ~ 0.55kg/ ton steel, setting temperature is when under 1136 DEG C of conditions, continuous casting section is 1280mm × 220mm section casting blank

Its expression formula along the distribution of crystallizer short transverse of matching is:

$T_{\mathrm{slope}}=\left\{\begin{array}{cc}0.00805h& h\&le;90\mathrm{mm}\\ -12.856\&times;\exp (-h/1339.07)-1.9815\&times;\exp (-h/63.4912)+13.2226& h>90\mathrm{mm}\end{array}\right.---\left(28\right)$

Wherein, T _slopefor tapering in the middle part of crystallizer leptoprosopy, mm; H is apart from meniscus level, mm.

Step 5: according to step 2.3 ~ 2.6 try to achieve contraction from base shell leptoprosopy bight to crystallizer wide center position with distortion distribute, determine bight and central region to the contraction of crystallizer wide center position and deflection poor, the maximum 1mm of both acquisitions difference, and in the middle part of leptoprosopy on tapering basis, curve tapering district, the tapering compensation rate in crystallizer leptoprosopy bight is exported from meniscus to crystallizer and is linearly increased to 1mm thickness along height h from 0mm; And the thickness in respective heights is linearly reduced to 0mm along bight to the boundary line apart from its 70mm, make crystallizer leptoprosopy folding corner region become wedge shape structure;

Step 6: according to step 2.3 ~ 2.6 try to achieve contraction from base shell wide bight to crystallizer leptoprosopy center position with distortion distribute, determine bight and central region to the contraction of crystallizer leptoprosopy center position and deflection poor, the maximum 1mm of both acquisitions difference, the tapering compensation rate in wide for a crystallizer bight is exported from meniscus to crystallizer and is linearly increased to 1mm thickness along height h from 0mm, and the thickness in respective heights is reduced to 0mm along bight to the boundary line position linearity apart from its 120mm, make crystallizer wide folding corner region become wedge shape structure.

In the embodiment of the present invention, after applying this tapering, crystallizer base shell is wide, " focus " of leptoprosopy deflecting angle is all eliminated; The wear rate of copper coin is by 1.041 × 10 when adopting traditional tapering ^-4mm/ ton steel is reduced to 2.507 × 10 ^-5mm/ ton steel, the service life of crystallizer is greatly improved; Continuous casting billet is wide, the average subcutaneous cracking breakout of leptoprosopy drops to 0.103% and 0.068% by with 17.338% under traditional tapering and 10.916% respectively, greatly improves continuous casting billet surface and subcutaneous quality.

Claims (7)

1. a slab crystallizer taper design method, is characterized in that: comprise the steps: Step 1: According to the content of C, Si, Mn, P, S, Ni, Cr and Al in the mainstream steel grades continuously cast by the continuous casting machine, determine the density, thermal conductivity, specific heat and linear thermal expansion coefficient of the continuously cast steel grades , to provide the high-temperature physical parameters of shell solidification for the establishment of thermal/mechanical coupling finite element numerical calculation model of the shell-crystallizer system; Step 2: According to the copper plate structure of the mold, the cross-sectional size of the continuous casting slab, and the high-temperature physical parameters of the continuously cast steel, establish a two-dimensional transient thermal/mechanical coupling with the 1/4 billet shell-mold cross-section system as the calculation object The finite element numerical calculation model calculates and determines the shrinkage and deformation distribution of the billet shell along its height and circumferential direction, and the mold slag thickness distribution in the entire crystallizer; Step 2.1: According to the copper plate structure of the mold, the cross-sectional size of the continuous casting slab and the high-temperature physical parameters of the continuously cast steel, establish a two-dimensional transient thermal/mechanical coupling with the 1/4 billet shell-mold cross-section system as the calculation object Finite element solid model, and mesh the solid model; Step 2.2: Determine the initial temperature field of the copper plate of the crystallizer and the initial heat flow at the billet shell-mold interface; take any temperature close to the real temperature value of the copper plate as the hot surface temperature of the copper plate, and assume that the initial surface temperature of the billet shell is the pouring temperature of the molten steel. The mold slag film is evenly distributed in the billet shell-mold interface at the lunar surface. According to the cross-sectional size of the continuous casting billet and the mold slag consumption, the thickness of the mold slag film in the interface is calculated, and the above billet shell surface temperature, slag film thickness and The temperature of the hot surface of the copper plate is used as a parameter, and the initial heat flow at the shell-crystallizer interface is calculated; The initial heat flow at the shell-mold interface and the temperature of the hot surface of the copper plate are respectively used as the heat flow boundary of the copper plate hot surface of the 1/4 shell-mold cross-section system two-dimensional transient thermal/mechanical coupled finite element numerical calculation model conditions and the initial temperature of the copper plate, and only calculate the temperature field of the copper plate to obtain a new hot surface temperature of the copper plate; Use the shell surface temperature, mold flux thickness, and the calculated new copper plate hot surface temperature as parameters to calculate the new shell-mold interface heat flow, and combine the new shell-mold interface heat flow with the calculated copper plate temperature The field is used as a 1/4 billet shell-crystallizer cross-section system two-dimensional transient thermal/mechanical coupling finite element numerical calculation model, the new heat flow boundary condition and initial temperature of the hot surface of the copper plate, and only the temperature field of the copper plate is calculated again to obtain a closer approximation The hot surface temperature of the real copper plate temperature and the shell-mold interface heat flow; repeat the calculation process until the difference between the two iterations of the hot surface temperature of the copper plate is less than 0.5°C; the finally obtained copper plate temperature field and shell-mold The interface heat flow is used as the initial temperature field of the copper plate and the heat flow boundary conditions between the surface of the billet shell and the hot surface of the copper plate as the two-dimensional transient thermal/mechanical coupling finite element numerical calculation model of the final 1/4 billet shell-crystallizer cross-section system; Step 2.3: Calculate the heat transfer of the billet shell-mold system; that is, based on the initial temperature field of the billet shell and the initial temperature field of the copper plate, the heat flow at the billet shell-mold interface is determined as the heat flow boundary condition of the billet shell surface and the hot surface of the copper plate, and the calculation The temperature field of the billet shell and the copper plate of the crystallizer provides the temperature parameters of the billet shell surface and the hot surface of the copper plate and calculates the 1/4 billet shell-mold cross-section system for determining the heat flow calculation of the billet shell-mold interface at the next mold height The initial temperature field of the billet shell and copper plate required for the 3D transient thermal/mechanical coupled finite element numerical calculation model; Step 2.4: Calculate the solidification shrinkage and deformation behavior of the billet shell; that is, based on the obtained temperature field distribution of the billet shell and copper plate, calculate the shrinkage and deformation of the billet shell along the direction of the center of the wide surface and the center of the narrow surface of the crystallizer; at the same time calculate the billet The displacement difference between the surface of the shell and the hot surface of the copper plate is used to determine the gap width of the shell-mold interface, and to provide the gap width parameter of the shell-mold interface for determining the heat flow at the shell-mold interface at the next mold height; Step 2.5: According to the surface temperature of the billet shell, the temperature of the hot surface of the copper plate, and the width of the billet shell-mold gap, determine the heat flow at the billet shell-mold interface that changes along the circumferential direction of the mold at the next mold height; Step 2.5.1: According to the relationship between the surface temperature of the shell and the solidification temperature of the mold slag, the thermal resistance of the shell-mold interface is determined. If the surface temperature of the shell is higher than the solidification temperature of the mold slag, the thermal resistance of the shell-mold interface is determined by the The slag layer, the solid slag layer and the crystallizer-solid slag interface thermal resistance are connected in series, and the step 2.5.2 is performed; , The solid slag layer is connected in series with the crystallizer-solid slag interface thermal resistance, perform step 2.5.3; Step 2.5.2: The total thickness of mold slag is specified to be equal to the gap width of the billet shell-mold interface, and the thermal resistance of the liquid slag layer and the solid slag layer are calculated according to the principle of equal heat flow through the liquid slag layer, solid slag layer, and mold-solid slag interface. Layer thermal resistance, crystallizer-solid slag interface thermal resistance and the distribution of the total thickness of the mold slag film along the circumferential direction of the mold, perform step 2.5.4; Step 2.5.3: According to the principle of equal heat flow through the air gap layer, solid slag layer and mold-solid slag interface, calculate the thermal resistance of the air gap layer, solid slag layer, mold-solid slag interface thermal resistance and mold flux The distribution of the film along the circumference of the crystallizer; Step 2.5.4: According to the relationship between the temperature difference between the surface of the billet shell and the hot surface of the copper plate and the total thermal resistance of the billet shell-mold interface, determine the heat flux distribution along the circumferential direction of the mold; Step 2.6: Set the shell and crystallizer temperature field calculated in step 2.3 and the shell-mold interface heat flow determined in step 2.5.4 as 1/4 shell-mold cross section at the next mold height The initial temperature field of the billet shell and copper plate and the heat flow boundary conditions between the billet shell surface and the hot surface of the copper plate in the two-dimensional transient thermal/mechanical coupling finite element numerical calculation model of the system, and repeat steps 2.3 to 2.6 until the continuous casting billet exits the crystallizer , so as to obtain the shrinkage and deformation distribution of the billet shell along its height and circumferential direction, and the mold slag thickness distribution in the entire crystallizer; Step 3: According to the thickness distribution of the mold flux film on the wide and narrow surfaces of the mold, determine the position of the boundary line on the wide surface and the boundary line on the narrow surface, and set the side of the boundary line on the wide surface as the corner wedge of the wide surface In the shape taper area, the other side is the non-taper area in the middle of the wide face; on the narrow face, one side of the boundary line is the wedge-shaped taper area at the corner of the narrow face, and the other side is the curved taper area in the middle of the narrow face; The position of the boundary line is determined as follows: In the slab shell-mold interface at the exit of the mold, determine the position where the slope of the mold slag thickness increase is greater than 0.002 for the first time along the direction from the middle of the wide surface or narrow surface of the mold to the corner, pass through this position and be perpendicular to the mold The straight line of the upper or lower mouth is the boundary line; Step 4: According to the shrinkage from the middle of the narrow surface of the billet shell to the center of the wide surface of the mold obtained in steps 2.3 to 2.6, fit the expression for its distribution along the height direction of the mold, and then determine that it is the middle of the narrow surface of the mold the taper of the curve taper zone; Step 5: According to the distribution of shrinkage and deformation from the corners of the narrow face of the billet shell to the center of the wide face of the mold obtained in steps 2.3 to 2.6, determine the difference in shrinkage and deformation between the corner and the middle area toward the center of the wide face of the mold, Then obtain the maximum value of the difference between the two, and on the basis of the taper compensation amount of the taper area in the middle of the narrow face, design the taper compensation amount at the corner of the narrow face of the crystallizer to increase linearly from 0 to the above-mentioned value from the meniscus to the outlet of the mold. The maximum value; at the same time, the taper compensation amount of the corner is linearly reduced to 0 along the direction from the corner to the boundary line, so that the corner area of the narrow face of the crystallizer becomes a wedge-shaped structure; Step 6: According to the shrinkage and deformation distribution of the corner of the wide face of the billet shell to the center of the narrow face of the mold obtained in steps 2.3 to 2.6, determine the maximum value of shrinkage and deformation of the corner, and design the taper of the corner of the wide face of the mold The compensation amount is linearly increased from 0 to the above-mentioned maximum value from the meniscus to the mold outlet, and at the same time, the taper compensation amount of the corner is linearly reduced to 0 along the direction from the corner to the junction line, so that the corner area of the wide surface of the mold becomes a wedge shape structure. 2. The slab crystallizer taper design method according to claim 1, characterized in that: the 1/4 billet shell-mold cross-section system described in step 2.1 refers to the copper plate structure of the continuous casting mold according to the actual steel mill The 1/4 continuous casting slab-mold cross section established with the continuous casting slab and the center of the width and narrow face of the mold as the symmetrical plane established with the continuous casting slab section size. 3. The slab mold taper design method according to claim 1, characterized in that: the heat transfer of the two-dimensional transient thermal/mechanical coupling finite element model of the continuous casting slab-mold cross-section system described in step 2 The mechanical boundary conditions are as follows: set the heat flow on the symmetrical surface of the billet shell and the mold copper plate to be equal to 0; ; The heat transfer of the crystallizer copper plate water tank is set as convective heat transfer with the cooling water; the mechanical boundary conditions of the symmetrical planes of the width and narrow planes of the continuous casting slab are respectively set to be 0 for the displacement along the direction of the narrow and wide sides of the slab; The copper plate on the wide side of the device is fixed, and the copper plate on the narrow side moves parallel to the center of the wide side according to the taper offset; the hydrostatic pressure at the solidification front of the billet shell is applied vertically to the billet shell in the way of eliminating the unsolidified liquid core unit of the continuous casting billet On the edge of the solidification front unit; the contact behavior between the continuous casting slab and the mold copper plate is constrained by the rigid-flexible contact analysis algorithm; The governing equation of heat transfer between continuous casting slab and mold is: two-dimensional transient heat transfer differential equation; The governing equation of continuous casting slab mechanics is selected as Anand rate-related constitutive equation. 4. The slab crystallizer taper design method according to claim 1, characterized in that: the calculation process for the total thermal resistance described in step 2.5.4 is; The thermal resistance of the liquid slag layer, solid slag layer and air gap layer in the shell-crystallizer interface is composed of thermal conduction thermal resistance and radiation thermal resistance in parallel, and the total thermal resistance of the interface is composed of the internal heat transfer medium. The thermal resistance of the dielectric layer is formed in series. 5. The method for designing the taper of the slab crystallizer according to claim 1, characterized in that: the calculation of the initial heat flow at the slab shell-crystallizer interface in step 2.2 is realized by formulas (1) to (5): Liquid slag layer thermal resistance: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.75</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sol</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sol</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ In the formula, is the thermal conductivity of liquid slag layer, m ² ℃/W, is the radiation thermal resistance of the liquid slag layer, m ² ℃/W, R _liquid is the thermal resistance of the liquid slag layer, m ² ℃/W, d _liquid is the thickness of the liquid slag layer, m, k _liquid is the thermal conductivity of the liquid slag, W/( m℃), σ is Boltzmann's constant, E _liquid is the extinction coefficient of liquid slag, n _liquid is the refractive index of liquid slag, ε _shell is the emissivity of shell, ε _f is the emissivity of mold slag, T _shell is Shell surface temperature, °C, T _sol is solidification temperature of mold flux, °C; Solid slag layer thermal resistance: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.75</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; mold</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sol</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sol</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ In the formula, is the thermal conduction resistance of solid slag layer, m ² ℃/W, is the radiation thermal resistance of the solid slag layer, m ² ℃/W, R _solid is the thermal resistance of the solid slag layer, m ² ℃/W, d _solid is the thickness of the solid slag layer, m, k _solid is the thermal conductivity of the solid slag, W/( m℃), E _solid is the extinction coefficient of the solid slag, n _solid is the refractive index of the solid slag, ε _mold is the emissivity of the mold copper plate, T _m/m is the mold hot surface-solid slag interface temperature, °C; Crystallizer-solid slag interface thermal resistance: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; int</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.50</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; flux</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 7.53</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; flux</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 16.09</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; flux</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2.24</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ In the formula, R _int is the mold-solid slag interface thermal resistance, m ² ℃/W, and d _flux is the total thickness of mold slag; According to the principle of equal heat flow through each medium layer in the interface, R _liquid , R _solid and R _int can be obtained by using formula (4) and formula (3); $\left\{\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sol</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sol</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; int</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; int</span>}}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; flux</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ In the formula, T _m is the temperature of the hot surface of the copper plate, °C; According to the relationship between the temperature difference between the shell surface and the hot surface of the copper plate and the total thermal resistance of the interface, the interface heat flow is obtained: $\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; liquid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; int</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ In the formula, q is the shell-crystallizer interface heat flow, W/m ² . 6. The slab crystallizer taper design method according to claim 1, characterized in that: determining the liquid slag layer thermal resistance, the solid slag layer thermal resistance and the crystallizer-solid slag interface thermal resistance described in step 2.5.2, The process is: according to formula (1), formula (2), formula (3) and formula (4), first calculate the liquid slag layer thickness, solid slag layer thickness and mold-solid slag interface temperature in the billet shell-mold interface , and bring the above obtained results back to formulas (1), (2) and (3), the thermal resistance of the liquid slag layer, the thermal resistance of the solid slag layer and the thermal resistance of the crystallizer-solid slag interface can be obtained. 7. The slab crystallizer taper design method according to claim 1, characterized in that: determining the thickness of the air gap layer, the air gap-solid slag interface temperature and the crystallizer-solid slag interface temperature described in step 2.5.3, Use formula (3) and the following formula to determine: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ In the formula, is the thermal conduction resistance of the air gap layer, m ² ℃/W, is the radiation thermal resistance of the air gap layer, m ² ℃/W, R _air is the thermal resistance of the air gap layer, m ² ℃/W, d _air is the thickness of the air gap layer, m, k _air is the thermal conductivity of the air gap, W/( m℃), T _a/m is the air gap-solid slag interface temperature, ℃; $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.75</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; mold</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}^{\mathrm{<span\; class="notranslate">\; rad</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ $\left\{\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; shell</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; int</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; int</span>}}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; solid</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$ In the formula, d _t is the gap width of billet shell-mold interface, m; Then bring the above results back to formula (6), formula (7) and formula (3) can calculate the thermal resistance of air gap layer, thermal resistance of solid slag layer and thermal resistance of crystallizer-solid slag interface.