阅读说明：本技术 宽厚板连铸板坯轻压下过程最小理论压下量的确定方法 (Method for determining minimum theoretical reduction in soft reduction process of wide and thick plate continuous casting slab ) 是由 陈志平 朱苗勇 吴晨辉 张才贵 江中块 邓丽琴 宋景欣 祭程 于 2019-09-12 设计创作，主要内容包括：本发明公开了宽厚板连铸板坯轻压下过程最小理论压下量的确定方法,主要解决现有宽厚板连铸板坯轻压下过程最小理论压下量的确定精度低的技术问题。本发明提供的一种宽厚板连铸板坯轻压下过程最小理论压下量的确定方法,包括：S1采集板坯连铸机的浇铸工况参数；S2建立板坯的二维凝固传热有限元模型,根据连铸机的浇铸工况参数计算得到浇铸过程中的铸坯二维温度场；S3根据压下区间内由2.2所确定的宽厚板坯两相区形貌及其温度场变化等凝固传热规律,求解得到压下区间内宽厚板坯宽向不同位置最小理论压下量。本发明方法使得宽厚板连铸板坯的中心偏析评级≤1.0比例由现有工艺的67.2％提升至现在的95％。(The invention discloses a method for determining the minimum theoretical reduction of a wide and thick plate continuous casting slab in a soft reduction process, which mainly solves the technical problem of low determination precision of the minimum theoretical reduction of the wide and thick plate continuous casting slab in the soft reduction process. The invention provides a method for determining the minimum theoretical reduction in a soft reduction process of a wide and thick plate continuous casting slab, which comprises the following steps: s1, collecting casting condition parameters of the slab caster; s2, establishing a two-dimensional solidification heat transfer finite element model of the slab, and calculating according to casting condition parameters of a continuous casting machine to obtain a two-dimensional temperature field of the casting blank in the casting process; s3, solving to obtain the minimum theoretical reduction of the wide and thick plate blank in the width direction different positions in the reduction interval according to the two-phase region morphology of the wide and thick plate blank determined by 2.2 in the reduction interval, the temperature field change and other solidification heat transfer rules. The method of the invention ensures that the proportion of the center segregation rating of the continuous casting slab of the wide and thick plates being less than or equal to 1.0 is improved from 67.2 percent of the prior art to 95 percent of the prior art.)

1. A method for determining the minimum theoretical reduction in a soft reduction process of a wide and thick plate continuous casting slab is characterized by comprising the following steps:

s1, collecting casting condition parameters of the slab caster, wherein the casting condition parameters comprise the section size of a casting steel type, the components of the casting steel type, the casting temperature, the working casting speed, the water flow and backwater temperature difference of a crystallizer, secondary cooling zone division parameters and the water amount in each secondary cooling zone;

s2, establishing a two-dimensional solidification heat transfer finite element model of the slab, and calculating according to casting condition parameters of a continuous casting machine to obtain a two-dimensional temperature field of the casting blank in the casting process;

s3, solving to obtain the minimum theoretical reduction of the wide and thick plate blank in the reduction interval in different positions in the width direction according to the shape of the two-phase region of the wide and thick plate blank in the reduction interval and the solidification heat transfer rules such as the temperature field change and the like.

2. The method for determining the minimum theoretical reduction in a soft reduction process of a wide and thick continuous casting slab as claimed in claim 1, wherein said step S2 comprises the steps of:

s21, taking a slab cross section 1/4 as a calculation domain in the casting process, and establishing a two-dimensional solidification heat transfer finite element model; the solidification heat transfer control equation of the two-dimensional solidification heat transfer finite element model is shown as the formula (1):

in the formula (1), T is temperature, DEG C; rho is the density of steel, kg/m³(ii) a H is enthalpy, J/kg; k is the thermal conductivity, W/(m.DEG C); x and y are coordinates of the casting blank; t is the casting time, s;

s22, determining the cooling boundary condition of the two-dimensional solidification heat transfer finite element model according to the casting condition parameters of the continuous casting machine, and solving the two-dimensional solidification heat transfer finite element model to obtain a two-dimensional temperature field of the wide and thick plate blank in the casting process;

boundary conditions at different casting positions of the two-dimensional solidification heat transfer finite element model are respectively as follows:

taking the heat flux density of the casting blank in the crystallizer as the boundary condition of the crystallizer, as shown in formula (2):

in the formula (2), q_(z)The heat flow density of the crystallizer is the distance between a two-dimensional solidification heat transfer finite element model and the meniscus in the crystallizer is z, MW/m²(ii) a l is the distance between each unit of the two-dimensional solidification heat transfer finite element model and a meniscus, m and v are working pulling speeds, m/s, A is an empirical value of 2.64, and B is determined according to water flow and return water temperature difference of a crystallizer during on-site casting by the following formula (3) and formula (4):

in the formulae (3) and (4),is the uniform heat flux density in the crystallizer, MW/m²，ρ_wFor the density of cooling water, kg/m³，V_wFor cooling the water flowAmount, m³/s；C_wCooling water heat capacity is 4200J/(kg. DEG C.), delta t is return water temperature difference in the crystallizer, A_sIs the area of the heat transfer surface of the crystallizer, m²，t_moldThe cooling time in the crystallizer is calculated according to the effective height h of the crystallizer and the working pulling speed v, t_mold＝h/v，q_(t)The heat flux density, MW/m, of the casting blank entering the crystallizer at different moments²(ii) a By combining the two formulas, the expression of B is finally obtained as shown in formula (5):

a, B finally formulated by combining the relevant working condition parameters of the crystallizer and the formula (5);

(II) taking an equivalent heat exchange coefficient determined by actually measuring the water flow density of the secondary cooling area as a boundary condition of the secondary cooling area, wherein the equivalent heat exchange coefficient of the secondary cooling area is as shown in the formula (6):

hⁱ＝αⁱwⁱ _(x) ^0.55(1-0.0075T_w)(6)

in the formula (6), hⁱIs the equivalent heat exchange coefficient of the ith secondary cooling zone, W/(m)²·℃)；w_(x)The density L/(m) of the water flow at the position X of the width surface of the ith secondary cooling area is measured²S) the density of the water flow is obtained through actual measurement according to the nozzles and the water flow in the corresponding secondary cooling area; alpha is alpha_iThe correction coefficient in the ith secondary cooling area;

and (III) taking radiation heat dissipation in the air cooling area as a boundary condition of the air cooling area, wherein the radiation heat dissipation heat flow density of the casting blank surface of the air cooling area is as shown in a formula (7):

q_B＝σε((T+273)⁴-(T_amb+273)⁴)(7)

in the formula (7), q_BIs the heat radiation heat flow density of W/m on the surface of the casting blank in an air cooling area²；σ＝5.67×10^-8W/(m²·K⁴) The constant is Stefan-Boltzmann constant, and the radiation coefficient is epsilon 0.8; t is_surfThe surface temperature of the casting blank is DEG C; t is_ambIs a ringAmbient temperature in deg.C.

3. The method for determining the minimum theoretical reduction in the soft reduction process of the wide and thick continuous casting slab as claimed in claim 1, wherein in the step S2 of solving the solidification heat transfer model, the distance from each integral point to the meniscus is calculated in real time in units of each integral point on the outer surface of the wide and narrow surface units of the casting slab, and the cooling boundary condition at the corresponding casting position is applied to each integral point according to the distance and the secondary cooling zone division parameters of the continuous casting machine.

4. The method for determining the minimum theoretical reduction in a soft reduction process of a wide and thick continuous casting slab as claimed in claim 1, wherein said step S3 comprises the steps of:

s31, determining the minimum theoretical reduction required by each unit for feeding based on the density change of each unit in the two-phase region calculated by the two-dimensional solidification heat transfer model in the reduction interval; in the pressing process, the calculation formula of the minimum theoretical pressing amount required by each unit is as follows:

in the formula (8), Δ h_iAnd h_iRespectively representing the minimum theoretical pressing amount and the height of the unit i in the feeding two-phase region; rho_i ⁰And rho_iRespectively representing the cell density at the pressing start position and the pressing end position; the density of each unit element in the formula (8) is determined based on the corresponding unit temperature and steel grade components calculated in the two-dimensional solidification heat transfer model and the formula (9):

in the formula (9), ρ_s、ρ_lAnd rho (T) is the density of steel grades under solidus line, liquidus line temperature strip and other temperature T pieces respectively; wt% C is the percentage of carbon content in steel; t is_s、T_lThe solidus temperature and the liquidus temperature of the steel are respectively; f. of_sThe solid phase ratio of each unit; in the formula (9), f_s、ρ_s、ρ_lAnd ρ (T) and may be determined by equations (10) to (13), respectively,

ρ_l＝7100-73(wt％C)-(0.8-0.09(wt％C))(T_l-1550)(11)

ρ(T)＝ρ_sf_s+(1-f_s)f_L(12)

s32, determining the minimum theoretical reduction required by different positions in the width direction of the casting blank based on the minimum theoretical reduction required by each unit in the two-phase region; in the reduction interval, the minimum theoretical reduction required at different positions in the width direction of the casting blank can be determined by accumulating the minimum theoretical reduction of each unit in a two-phase area at the corresponding position in the width direction,

in the formula (14), Δ H is the minimum theoretical reduction, mm, required at a certain position in the width direction of the casting blank; and N is the number of units in the two-phase region of the casting blank at the corresponding wide position, and the shape of the two-phase region of the casting blank is determined by calculation of a two-dimensional solidification heat transfer model.

Technical Field

The invention relates to a slab continuous casting process, in particular to a method for determining the minimum theoretical reduction in a light reduction process of a wide and thick slab continuous casting, belonging to the technical field of steel continuous casting.

Background

Center segregation, shrinkage cavity and porosity are common internal quality defects of the continuous casting billet, and the production of the high-quality continuous casting billet is severely restricted, so that the mechanical property of a final rolled material is influenced. At present, a solidification tail end soft reduction process is one of the most effective process means for improving the internal quality defects of continuous casting billets.

The solidification tail end soft reduction process aims at applying a certain amount of mechanical reduction deformation to a continuous casting billet in a certain area before the solid tail end of the continuous casting billet through a casting roller, thereby effectively feeding the solidification shrinkage of residual molten steel in a two-phase area of the continuous casting billet, simultaneously inhibiting the segregation of molten steel rich in solute elements among dendrites in a central area of a casting flow to the central position of the casting billet, and effectively improving the central macro segregation of the casting billet.

The reduction interval and the reduction are core process parameters of the soft reduction process, and determine whether the soft reduction process can be successfully implemented. Wherein, the reduction interval represents a casting flow area (usually expressed by a solid fraction range of a central point of a casting blank) applied by a soft reduction process, and the reduction represents the mechanical reduction of the thickness direction of the casting blank in the reduction interval. In the process of setting the reduction, the minimum theoretical reduction required by solidification shrinkage of residual molten steel in a feeding two-phase region is determined on the basis of the shape of the two-phase region of a casting blank in a reduction region and the change of a temperature field, so that the final reduction of the surface of the casting blank is determined.

At present, the disclosed calculation method for the minimum theoretical reduction generally regards a two-phase region of a continuous casting billet in a reduction interval as a whole, and solves the minimum theoretical reduction through the appearance and temperature field change characteristics of the two-phase region in the reduction interval. For example, forest initiative and courage, etc. (theoretical model of reduction ratio in continuous casting slab light reduction process and analysis thereof. reports on metals, 2007,43(8): 847-85; regular analysis of continuous casting slab light reduction ratios of different steel grades. reports on metals, 2007,43(12): 1297-.

The Chinese patent application publication No. CN101658911A discloses an online control method for the rolling reduction of bloom continuous casting dynamic soft reduction, which takes a two-phase area in the whole transverse section of a bloom in a rolling reduction interval as an object, deduces the minimum theoretical rolling reduction required by shrinkage of the two-phase area of the bloom, and finally determines the rolling reduction required by the surface of the continuous casting billet on the basis of further solving the rolling reduction efficiency.

The application publication number CN105108096A discloses a method for determining dynamic soft reduction of continuous casting of heavy rail steel bloom. The method is characterized in that the whole two-phase area of the bloom in the reduction interval is taken as an object, the volume shrinkage of the whole two-phase area in the reduction interval is firstly obtained, and the actual reduction required to be applied to the surface of the bloom is finally determined by combining the actual volume change of the two-phase area in the reduction deformation process. The volume shrinkage of the two-phase region involved in the method substantially reflects the theoretical reduction required by the two-phase region solidification shrinkage of the feeding bloom.

It can be seen that the two-phase region is regarded as a whole by the method when the minimum theoretical reduction required by solidification shrinkage of the two-phase region of the feeding continuous casting billet in the reduction interval is calculated. However, for the wide and thick plate continuous casting billet, the water flow density in the secondary cooling zone is not uniformly distributed along the width direction of the wide and thick plate continuous casting billet, and the wide cooling solidification process also has obvious non-uniformity.

In the prior art, a two-phase region in a pressing interval is regarded as a whole, and the influence of the width-direction non-uniform solidification characteristic of the wide and thick plate blank on the minimum theoretical pressing amount required by the solidification shrinkage of the feeding two-phase region cannot be considered, so that the internal quality defects of center segregation, shrinkage porosity and the like of the wide and thick plate blank are not favorably and comprehensively improved.

Disclosure of Invention

The invention aims to provide a method for determining the minimum theoretical reduction of a wide and thick plate continuous casting slab in a soft reduction process, and mainly solves the technical problem of low determination precision of the minimum theoretical reduction of the wide and thick plate continuous casting slab in the soft reduction process.

The method fully considers the influence of the non-uniform solidification characteristic in the width direction of the wide and thick plate blank on the minimum theoretical reduction required by the solidification shrinkage of the feeding two-phase region, improves the determination precision of the minimum theoretical reduction, and can improve the center segregation and shrinkage porosity of the wide and thick plate blank to the maximum extent.

The technical idea of the invention is that a two-dimensional solidification heat transfer model of a wide and thick slab is established, and the non-uniform solidification heat transfer rules of the two-phase region morphology of the casting slab in a reduction interval, the temperature field change and the like are revealed; and finally determining the minimum theoretical reduction required by the wide-direction different positions of the continuous casting billet of the wide and thick plate in the reduction interval according to a solidification feeding principle.

The invention adopts the technical scheme that the method for determining the minimum theoretical reduction in the soft reduction process of the wide and thick plate continuous casting slab comprises the following steps:

s1, collecting casting condition parameters of the slab caster, wherein the casting condition parameters comprise the section size of a casting steel type, the components of the casting steel type, the casting temperature, the working casting speed, the water flow and backwater temperature difference of a crystallizer, secondary cooling zone division parameters and the water amount in each secondary cooling zone;

s2, establishing a two-dimensional solidification heat transfer finite element model of the slab, and calculating according to casting condition parameters of a continuous casting machine to obtain a two-dimensional temperature field of the casting blank in the casting process;

s3, solving to obtain the minimum theoretical reduction of the wide and thick plate blank in the reduction interval in different positions in the width direction according to the shape of the two-phase region of the wide and thick plate blank in the reduction interval and the solidification heat transfer rules such as the temperature field change and the like.

The step S2 includes the steps of:

s21, taking a slab cross section 1/4 as a calculation domain in the casting process, and establishing a two-dimensional solidification heat transfer finite element model; the solidification heat transfer control equation of the two-dimensional solidification heat transfer finite element model is shown as the formula (1):

in the formula (1), T is temperature, DEG C; rho is the density of steel, kg/m³(ii) a H is enthalpy, J/kg; k is the thermal conductivity, W/(m.DEG C); x and y are coordinates of the casting blank; t is the casting time, s;

s22, determining the cooling boundary condition of the two-dimensional solidification heat transfer finite element model according to the casting condition parameters of the continuous casting machine, and solving the two-dimensional solidification heat transfer finite element model to obtain a two-dimensional temperature field of the wide and thick plate blank in the casting process;

boundary conditions at different casting positions of the two-dimensional solidification heat transfer finite element model are respectively as follows:

taking the heat flow density of the casting blank in the crystallizer as a boundary condition of the crystallizer, and taking the heat flow density of the casting blank in the crystallizer measured by a method of Savage and Pritcard as a boundary condition, wherein the formula (2) is as follows:

in the formula (2), q_(z)The heat flow density of the crystallizer is the distance between a two-dimensional solidification heat transfer finite element model and the meniscus in the crystallizer is z, MW/m²(ii) a l is the distance between each unit of the two-dimensional solidification heat transfer finite element model and a meniscus, m and v are working pulling speeds, m/s, A is an empirical value of 2.64, and B is determined according to water flow and return water temperature difference of a crystallizer during on-site casting by the following formula (3) and formula (4):

in the formulae (3) and (4),is the uniform heat flux density in the crystallizer, MW/m²，ρ_wFor the density of cooling water, kg/m³，V_wFor cooling water flow, m³/s；C_wCooling water heat capacity is 4200J/(kg. DEG C.), delta t is return water temperature difference in the crystallizer, A_sIs the area of the heat transfer surface of the crystallizer, m²，t_moldThe cooling time in the crystallizer can be calculated according to the effective height h and the working pulling speed v of the crystallizer, and t_mold＝h/v，q_(t)The heat flux density, MW/m, of the casting blank entering the crystallizer at different moments²(ii) a By combining the two formulas, the expression of B is finally obtained as shown in formula (5):

a, B finally formulated by combining the relevant working condition parameters of the crystallizer and the formula (5);

(II) taking the equivalent heat exchange coefficient determined by actually measured water flow density of the secondary cooling area as the boundary condition of the secondary cooling area, and taking the equivalent heat exchange coefficient of the secondary cooling area determined by Figelow and island field as the boundary condition in the secondary cooling area, wherein the formula (6) is as follows:

hⁱ＝αⁱwⁱ _(x) ^0.55(1-0.0075T_w) (6)

in the formula (6), hⁱIs the equivalent heat exchange coefficient of the ith secondary cooling zone, W/(m)²·℃)；w_(x)The density L/(m) of the water flow at the position X of the width surface of the ith secondary cooling area is measured²S) density of the water stream according to the nozzles and water in the respective secondary cooling zoneThe flow is obtained through actual measurement; alpha is alpha_iThe correction coefficient in the ith secondary cooling area;

and (III) taking the radiation heat dissipation in the air cooling area as the boundary condition of the air cooling area, wherein the radiation heat dissipation in the air cooling area is as shown in the formula (7):

q_B＝σε((T+273)⁴-(T_amb+273)⁴) (7)

in the formula (7), q_BIs the heat radiation heat flow density of W/m on the surface of the casting blank in an air cooling area²；σ＝5.67×10^-8W/(m²·K⁴) The constant is Stefan-Boltzmann constant, and the radiation coefficient is epsilon 0.8; t is_surfThe surface temperature of the casting blank is DEG C; t is_ambIs at ambient temperature, DEG C.

Further, in the solving process of the solidification heat transfer model in the step S2, the distance from each integral point to the meniscus is calculated in real time by taking each integral point on the outer surfaces of the wide-surface and narrow-surface units of the casting blank as a unit, and a cooling boundary condition at a corresponding casting position is applied to each integral point according to the distance and the partition parameters of the second cooling zone of the continuous casting machine.

The step S3 includes the steps of:

s31, determining the minimum theoretical reduction required by each unit for feeding based on the density change of each unit in the two-phase region calculated by the two-dimensional solidification heat transfer model in the reduction interval; in the pressing process, the calculation formula of the minimum theoretical pressing amount required by each unit is as follows:

in the formula (8), Δ h_iAnd h_iRespectively representing the minimum theoretical pressing amount and the height of the unit i in the feeding two-phase region; rho_i ⁰And rho_iRespectively representing the cell density at the pressing start position and the pressing end position; the density of each unit element in the formula (8) is determined based on the corresponding unit temperature and steel grade components calculated in the two-dimensional solidification heat transfer model and the formula (9):

in the formula (9), ρ_s、ρ_lAnd rho (T) is the density of steel grades under solidus line, liquidus line temperature strip and other temperature T pieces respectively; wt% C is the percentage of carbon content in steel; t is_s、T_lThe solidus temperature and the liquidus temperature of the steel are respectively; f. of_sThe solid phase ratio of each unit; in the formula (9), f_s、ρ_s、ρ_lAnd ρ (T) and may be determined by equations (10) to (13), respectively,

ρ_l＝7100-73(wt％C)-(0.8-0.09(wt％C))(T_l-1550) (11)

ρ(T)＝ρ_sf_s+(1-f_s)f_L (12)

s32, determining the minimum theoretical reduction required by different positions in the width direction of the casting blank based on the minimum theoretical reduction required by each unit in the two-phase region; in the reduction interval, the minimum theoretical reduction required at different positions in the width direction of the casting blank can be determined by accumulating the minimum theoretical reduction of each unit in a two-phase area at the corresponding position in the width direction,

in the formula (14), Δ H is the minimum theoretical reduction, mm, required at a certain position in the width direction of the casting blank; and N is the number of units in the two-phase region of the casting blank at the corresponding wide position, and the shape of the two-phase region of the casting blank is determined by calculation of a two-dimensional solidification heat transfer model.

The method is suitable for a slab caster with a solidification tail end mechanical pressing function, and the width of the produced slab is 1600-2500 mm, and the thickness of the produced slab is 220-280 mm.

The invention discloses the non-uniform solidification heat transfer rule of a wide and thick slab by establishing a slab two-dimensional solidification heat transfer finite element model in the casting process by combining the actual casting working condition parameters of a field slab caster and taking large commercial finite element software MSC. And finally determining the minimum theoretical reduction required by different positions in the width direction according to the shape of the two-phase region of the wide and thick plate blank in the reduction interval and the solidification heat transfer rules such as the temperature field change and the like.

Compared with the prior art, the invention has the following positive effects: 1. the method determines the minimum theoretical reduction at the corresponding position based on the solidification shrinkage rules of the two-phase region and different positions of the wide and thick plate continuous casting blank in the width direction, and can fully consider the influence of the wide and thick plate continuous casting blank in the width direction non-uniform cooling solidification characteristic on the minimum theoretical reduction, thereby formulating more reasonable reduction, and comprehensively and effectively improving the internal quality defects of the wide and thick plate continuous casting blank, such as center segregation, shrinkage cavity, porosity and the like. 2. The method of the invention ensures that the proportion of the center segregation rating of the continuous casting slab of the wide and thick plate which is less than or equal to 1.0 is improved from 67.2 percent of the prior art to 95 percent of the prior art; the proportion of the center porosity is less than or equal to 1.0 is increased from 87.5 percent of the prior art to 100 percent of the prior art.

Detailed Description

The present invention will be described in further detail with reference to specific examples.

Example 1, the casting steel type is peritectic steel, and the chemical components of the steel type in percentage by weight are as follows: c: 0.17%, Si: 0.15%, Mn: 0.6%, P: 0.015%, S: 0.01 percent; the cross section of the cast steel plate blank is 2000mm multiplied by 280 mm; the pulling speed of the field work is 0.8 m/min; the specific water amount of the secondary cooling zone is 0.86L/Kg.

Parameters of the slab caster: the casting temperature is 1540 ℃, the crystallizer height is 900mm, the effective height is 800mm, the wide-side water flow of the crystallizer is 5632L/min, the return water temperature difference is 6.7 ℃, the narrow-side water flow of the crystallizer is 598L/min, the return water temperature difference is 7.2 ℃, and the casting machine comprises 8 secondary cooling zones and 2 air cooling zones, wherein the length of the secondary cooling zone is 20.57m, and the total cooling length is 34.725 m.

The secondary cooling zone division parameters and the water amount in each secondary cooling zone are shown in a table 1; the equivalent heat transfer coefficient of the secondary cooling zone is shown in Table 2.

A method for determining the minimum theoretical reduction in a soft reduction process of a wide and thick plate continuous casting slab comprises the following steps:

s1, collecting casting condition parameters of the slab caster, wherein the casting condition parameters comprise: the section size of the casting steel grade, the components of the casting steel grade, the casting temperature, the working pulling speed, the water flow and the backwater temperature difference of the crystallizer, the dividing parameters of the secondary cooling zones and the water amount in each secondary cooling zone; measuring the density distribution characteristics of cooling water flow in the casting blank width direction in the secondary cooling area by a nozzle cold state experimental method;

s2, establishing a two-dimensional solidification heat transfer finite element model of the slab, and calculating according to the casting condition parameters of the continuous casting machine to obtain the solidification heat transfer law of the wide and thick slab in the casting process;

s21, taking a slab cross section 1/4 as a calculation domain in the casting process, and establishing a two-dimensional solidification heat transfer finite element model; the solidification heat transfer control equation of the two-dimensional solidification heat transfer finite element model is shown as the formula (1):

in the formula (1), T is temperature, DEG C; rho is the density of steel, kg/m³(ii) a H is enthalpy, J/kg; k is the thermal conductivity, W/(m.DEG C); x and y are coordinates of the casting blank; t is the casting time, s;

s22, determining the cooling boundary condition of the two-dimensional solidification heat transfer finite element model according to the casting condition parameters of the continuous casting machine, and solving the two-dimensional solidification heat transfer finite element model to obtain a two-dimensional temperature field of the wide and thick plate blank in the casting process;

boundary conditions at different casting positions of the two-dimensional solidification heat transfer finite element model are respectively as follows:

taking the heat flow density of the casting blank in the crystallizer as a boundary condition of the crystallizer, and taking the heat flow density of the casting blank in the crystallizer measured by a method of Savage and Pritcard as a boundary condition, wherein the formula (2) is as follows:

in the formula (2), q_(z)The heat flow density of the crystallizer is the distance between a two-dimensional solidification heat transfer finite element model and the meniscus in the crystallizer is z, MW/m²(ii) a l is the distance between each unit of the two-dimensional solidification heat transfer finite element model and a meniscus, m and v are working pulling speeds, m/s, A generally takes an empirical value of 2.64, and B is determined according to water flow and return water temperature difference of a crystallizer during on-site casting by the following formula (3) and formula (4):

in the formulae (3) and (4),is the uniform heat flux density in the crystallizer, MW/m²，ρ_wFor the density of cooling water, kg/m³，V_wFor cooling water flow, m³/s；C_wCooling water heat capacity is 4200J/(kg. DEG C.), delta t is return water temperature difference in the crystallizer, A_sIs the area of the heat transfer surface of the crystallizer, m²，t_moldThe cooling time in the crystallizer can be calculated according to the effective height h and the working pulling speed v of the crystallizer, and t_mold＝h/v，q_(t)The heat flux density, MW/m, of the casting blank entering the crystallizer at different moments²(ii) a By combining the two formulas, the expression of B is finally obtained as shown in formula (5):

a, B finally formulated by combining the relevant working condition parameters of the crystallizer and the formula (5) is as follows: wide surface of the crystallizer: a is 2.688; b-0.2346, narrow face of crystallizer: a is 2.688; b-0.2402;

(II) taking the equivalent heat exchange coefficient determined by actually measured water flow density of the secondary cooling area as the boundary condition of the secondary cooling area, and taking the equivalent heat exchange coefficient of the secondary cooling area determined by Figelow and island field as the boundary condition in the secondary cooling area, wherein the formula (6) is as follows:

hⁱ＝αⁱwⁱ _(x) ^0.55(1-0.0075T_w) (6)

in the formula (6), hⁱIs the equivalent heat exchange coefficient of the ith secondary cooling zone, W/(m)²·℃)；w_(x)The density L/(m) of the water flow at the position X of the width surface of the ith secondary cooling area is measured²S) the density of the water flow is obtained through actual measurement according to the nozzles and the water flow in the corresponding secondary cooling area; alpha is alpha_iThe correction coefficient in the ith secondary cooling area;

and (III) taking the radiation heat dissipation in the air cooling area as the boundary condition of the air cooling area, wherein the radiation heat dissipation in the air cooling area is as shown in the formula (7):

q_B＝σε((T+273)⁴-(T_amb+273)⁴) (7)

in the formula (7), q_BIs the heat radiation heat flow density of W/m on the surface of the casting blank in an air cooling area²；σ＝5.67×10^-8W/(m²·K⁴) The constant is Stefan-Boltzmann constant, and the radiation coefficient is epsilon 0.8; t is_surfThe surface temperature of the casting blank is DEG C; t is_ambAmbient temperature, deg.C;

in the process of solving the solidification heat transfer model, corresponding cooling boundary conditions are applied to the two-dimensional solidification heat transfer model through secondary development subprograms Uflux and Ufilm in MSC. Calculating the distance from each integral point to a meniscus in real time by taking each integral point on the outer surfaces of the wide-surface unit and the narrow-surface unit of the casting blank as a unit, and applying a cooling boundary condition at the corresponding casting position to each integral point according to the distance and the partition parameters of the second cooling zone of the continuous casting machine;

s3, determining the theoretical reduction of the two-phase region solidification shrinkage of the feeding casting blank according to the two-dimensional solidification heat transfer model to calculate the two-phase region morphology of the casting blank and the temperature field change thereof in the reduction region;

s31, determining the minimum theoretical reduction required by each unit for feeding based on the density change of each unit in the two-phase region calculated by the two-dimensional solidification heat transfer model in the reduction interval; in the pressing process, the calculation formula of the minimum theoretical pressing amount required by each unit is as follows:

in the formula (8), Δ h_iAnd h_iRespectively representing the minimum theoretical pressing amount and the height of the unit i in the feeding two-phase region; rho_i ⁰And rho_iRespectively representing the cell density at the pressing start position and the pressing end position; the density of each unit element in the formula (8) is determined based on the corresponding unit temperature and steel grade components calculated in the two-dimensional solidification heat transfer model and the formula (9):

in the formula (9), ρ_s、ρ_lAnd rho (T) is the density of steel grades under solidus line, liquidus line temperature strip and other temperature T pieces respectively; wt% C is the percentage of carbon content in steel; t is_s、T_lThe solidus temperature and the liquidus temperature of the steel are respectively 1468 ℃ and 1518 ℃ in the implementation case; f. of_sThe solid phase ratio of each unit; in the formula (9), f_s、ρ_s、ρ_lAnd ρ (T) and may be determined by equations (10) to (13), respectively,

ρ_l＝7100-73(wt％C)-(0.8-0.09(wt％C))(T_l-1550) (11)

ρ(T)＝ρ_sf_s+(1-f_s)f_L (12)

the solid phase ratio of the central point of the casting blank corresponding to the reduction interval in the embodiment is 0.3-1.0, namely the solid phase ratio of the central point of the casting blank at the initial position and the end position of the reduction interval is 0.3 and 1.0 respectively;

s32, determining the minimum theoretical reduction required by different positions in the width direction of the casting blank based on the minimum theoretical reduction required by each unit in the two-phase region; in the reduction interval, the minimum theoretical reduction required by different positions of the casting blank in the width direction can be determined by accumulating the minimum theoretical reduction of each unit in a two-phase area at the corresponding width position:

in the formula (14), Δ H is the minimum theoretical reduction, mm, required at a certain position in the width direction of the casting blank; and N is the number of units in the two-phase region of the casting blank at the corresponding wide position, and the shape of the two-phase region of the casting blank is determined by calculation of a two-dimensional solidification heat transfer model.

Table 1 example 1 of the present invention second cold zone division parameter and water quantity parameter in each second cold zone

Table 2 equivalent heat transfer coefficient of the second cooling zone of example 1 of the present invention

The method has obvious effect of improving the quality of the cast blank on site, the center segregation of the cast blank is serious before the method is used, and particularly, the center segregation defect is obvious in the area near the position 1/4 in the width direction. In addition, by comparing production data within 1 year before and after the use of the invention, the casting blank center segregation rating is less than or equal to 1.0, and is improved from 67.2% to 95% at present, and the center porosity is less than or equal to 1.0, and is improved from 87.5% to 100% at present.

In addition to the above embodiments, the present invention may have other embodiments. All technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the claims of the present invention.