CN115952720A

CN115952720A - Continuous casting billet temperature field and stress field coupling calculation method in casting process

Info

Publication number: CN115952720A
Application number: CN202310015373.5A
Authority: CN
Inventors: 王卫领; 吴磊; 罗森; 朱苗勇
Original assignee: Northeastern University China
Current assignee: Northeastern University China
Priority date: 2023-01-05
Filing date: 2023-01-05
Publication date: 2023-04-11

Abstract

The invention provides a method for calculating the coupling of a temperature field and a stress field of a continuous casting billet in a casting process, and relates to the technical field of continuous casting production. The invention refers to the actual continuous casting pouring process, and divides the calculation process into two parts, namely a seedling emergence stage and a starting stage by taking the starting of drawing as a boundary. In the emergence stage, liquid level positions are judged in real time to continuously activate casting blank units, different cooling boundaries are selected according to the positions of the casting blank units in the crystallizer, rollers are set to be rigid bodies according to collected roller column distribution diagrams, advancing in the casting flow direction is realized by controlling the displacement boundaries of casting blanks, new casting blank units are continuously activated at meniscus positions, the positions of the casting blank units in the casting flow are judged after each model updating, corresponding cooling conditions are applied, the process is repeated until the models reach the outlet of the continuous casting machine, and the casting starting process is completely finished. And extracting the temperature and the stress strain state of the characteristic points of the continuous casting billet in real time in the calculation process, tracking the position of the solidification tail end, and obtaining the distribution of the liquid-solid phase line along the casting flow.

Description

Continuous casting billet temperature field and stress field coupling calculation method in casting process

Technical Field

The invention relates to the technical field of continuous casting production, in particular to a method for calculating the coupling of a temperature field and a stress field of a continuous casting billet in a casting process.

Background

The continuous casting process is that molten steel in a steel ladle is injected into a crystallizer through a tundish, cooling is carried out for a period of time to ensure that a primary blank shell in the crystallizer has certain thickness and can be safely subjected to blank drawing, then a continuous casting machine is started, the blank drawing speed is gradually increased to the period of time when the production drawing speed is stable, and the period is an unavoidable unsteady state casting period in the continuous casting production process. The casting blank produced in the continuous casting and casting process is generally called a head blank, and the temperature of the head blank is lower than that of the casting blank under the steady-state production condition, so that the tension straightening resistance is large in the bending straightening process, the blank stagnation risk exists, equipment can be seriously damaged, and the safety accident is caused to influence the production progress. In addition, the molten steel level fluctuation of the crystallizer is large, the pulling speed is increased along with the time after the continuous casting is started, and the like, so that the casting blank is more prone to defects such as inclusion, segregation, cracks and the like in the casting starting process compared with the casting blank under the steady-state production condition. The problems are closely related to the complex temperature field and stress field change of the casting blank in the casting starting process, and the research on the temperature field and stress field change rule of the casting blank in the stage can provide a basis for selecting proper process parameters in the casting starting process, such as the determination of seedling emergence time, a secondary cooling scheme, a pulling speed change curve, the selection of a roller arrangement mode and the like, so that the method has important significance for improving the stability of the continuous casting process.

At present, the calculation of the temperature field and the stress field of the continuous casting billet is mostly assumed that the influence of the change of the drawing speed is not considered under the condition of steady-state casting. For example, patent "CN106001478a" discloses a method for making a basic roll gap process of a slab caster, which first calculates a temperature field result of a two-dimensional solidification heat transfer model, and then performs a thermal contraction calculation according to a thermal state of the model, wherein the model has insufficient consideration on heat transfer in a billet drawing direction, and accuracy of a result of a thermal calculation method is difficult to ensure. The patent CN105033214B discloses a method for making a basic roll gap of a wide and thick slab continuous casting machine, natural shrinkage behaviors of the basic roll gap are researched by solving a temperature field of a three-dimensional casting blank model, a basis is provided for roll gap design, the method decomposes the solution of the temperature field and the analysis of a stress field, a calculation method of weak thermal coupling is adopted, and large errors can be generated in the analysis. Part of the research also considers the temperature field change of the continuous casting billet in the unsteady state. For example, patent "CN111199119a" discloses a continuous casting beam blank head temperature simulation method, which establishes a three-dimensional continuous casting blank model, and divides the simulation process into three time periods according to the characteristics of the continuous casting process: and (4) seedling emergence time, starting a continuous casting stage, and growing the model to a set length stage. In the calculation process, a finite volume method is adopted to control the generation of a casting blank unit and the movement of a model, but the method ignores the characteristics of a straight arc-shaped continuous casting machine, does not consider the influence of the deformation of a casting blank on a temperature field in the continuous casting process, and lacks the analysis of the stress strain of the continuous casting blank in the casting process.

In summary, the current methods for calculating the temperature field and the stress field in the continuous casting starting process are less, and the complex situations of continuous casting in the starting process, such as the control of the emergence time after molten steel is injected into a crystallizer, the change of the rising speed curve after a casting machine is started, and the complex situations of contact between a casting blank and rollers in the processes of vertical bending and straightening, are not considered sufficiently. Therefore, an effective and reliable method for calculating the temperature field and the stress field of the head billet of the continuous casting billet in the casting process needs to be provided, and a theoretical basis is provided for the continuous casting process with reasonable design

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a method for calculating the coupling of a temperature field and a stress field of a continuous casting billet in the casting process.

A method for calculating the coupling of a temperature field and a stress field of a continuous casting blank in the casting process specifically comprises the following steps:

step 1: obtaining relevant parameters of the casting condition of a continuous casting machine: the method specifically comprises the steps of total length of a casting machine, a roller array diagram, casting temperature, components of cast steel and size specifications of casting blanks, a casting speed increasing curve diagram, effective height of a crystallizer, water quantity of the crystallizer, the number of secondary cooling zones, dividing parameters of the secondary cooling zones and water distribution of each zone of the secondary cooling zones;

step 2: obtaining physical property parameters required by calculation: specifically comprises heat-related physical parameters such as density rho, specific heat c, heat conductivity coefficient lambda and force-related physical parametersNumber, poisson's ratio v, elastic modulus E, yield strength σ _s ；

And step 3: the control equation used in the calculation process comprises a solidification heat transfer differential equation and a thermal elastic plastic constitutive equation;

the solidification heat transfer differential equation is as follows:

in the formula, the unit is K; rho is the density in kg/m ³ ；c _eff Is the heat capacity, in units of J/(kg. DEG C); k is the thermal conductivity, given in W/(m. DEG C); t represents time in units of s; c. C _s 、c _l The specific heat of the solid phase region and the specific heat of the liquid phase region are respectively, L is latent heat of solidification, and the unit is J/kg; f. of _s T, T for solid fraction _L And T _S Respectively representing the current temperature, the liquidus temperature and the solidus temperature in the solidification heat transfer process, wherein x and y represent two directions of a two-dimensional finite element model of a casting blank;

the thermal elastic-plastic constitutive equation is as follows:

1) And (3) elastic deformation stage: the total strain in the elastic deformation phase includes the elastic strain and the thermal strain generated by the temperature, and the formula is as follows:

in the formula, d { epsilon _ij Is the increment of the total strain tensor of the elastic deformation phase,

for the increment of the elastic strain tensor in the elastically deforming phase>

D { sigma ] being the increment of the thermal strain tensor in the elastic deformation phase _ij Is the increment of the total stress tensor in the elastically deforming phase, is>

Is a matrix of elastic stiffness, alpha is the coefficient of linear thermal expansion, delta _ij 、δ _kl 、δ _ik 、δ _jl 、δ _jk 、δ _il Is a kronecker symbol, if i = j, δ _ij =1; if i ≠ j, δ _ij =0,i, j, k, l for representing the directions of coordinate axes in a rectangular coordinate system in space; e is the elastic modulus of the material, upsilon is the Poisson ratio of the material, sigma _ij Is a stress component of epsilon _kl Is a strain component; />

2) The plastic deformation phase formula is as follows:

in the formula, d { epsilon _ij Is the increment of the total strain tensor in the plastic deformation phase,

is the increment of the elastic strain tensor in the plastic deformation phase>

Is the increment of the plastic strain tensor in the plastic deformation phase>

Increment of thermal strain tensor d { sigma } of plastic deformation phase _ij Is the increment of the total stress tensor in the plastic deformation phase, is>

Is a matrix of elastic stiffness, alpha is the coefficient of linear thermal expansion, delta _ij 、δ _kl Is a Cronck symbol, Q is a plastic potential function, F is a yield function, σ _kl For the stress component, a is the plastic multiplier correlation coefficient.

And 4, step 4: setting a characteristic number for each cooling area in the casting flow according to the effective height of the crystallizer, the water quantity of the crystallizer, the number of the secondary cooling areas, the dividing parameters of the secondary cooling areas and the water quantity distribution of each area of the secondary cooling areas, which are obtained in the step 1, the position of the crystallizer and the dividing parameters of the secondary cooling areas, and selecting proper cooling boundary conditions according to different cooling modes of the crystallizer and each area of the secondary cooling areas;

step 4.1: dividing the crystallizer and each zone of the second cooling zone according to the distance between the outlet of the crystallizer and the outlet of each cooling zone and the meniscus, storing the distance between the outlet of the crystallizer and the outlet of each cooling zone and the meniscus in a Dist array, and assigning a cooling characteristic number;

and 4.2: according to the change of the cooling mode, selecting proper cooling boundary conditions for each cooling area:

1) In the crystallizer, the cooling mode of the continuous casting billet is heat exchange with the wall of the crystallizer, so that the heat flow density is selected to describe the heat transfer behavior of the surface of the continuous casting billet in the crystallizer; the following formula is a calculation formula of the local heat flux density q between the wall of the crystallizer and the interface of the casting blank:

wherein t is time in units of s; z is the distance from the meniscus of the crystallizer in m; v is the pull rate in m/min; q is the local heat flux density between the wall of the crystallizer and the casting blank interface, and the unit is MW/m ² A, B is the coefficient to be determined, A =2.688, B is calculated according to the water flow and inlet and outlet temperature difference of the crystallizer, and the concrete process is as follows:

in the formula, ρ _w The density of the cooling water of the crystallizer is in kg/m ³ ；c _w Taking the specific heat capacity of cooling water of the crystallizer, and taking 4.2 kJ/(kg DEG C); q _w Is the flow rate of cooling water of the crystallizer and has the unit of m ³ /min；ΔT _w The temperature difference of the cooling water inlet and the cooling water outlet of the crystallizer is measured in unit; a. The _mold Effective cooling area in m for cooling water distribution of crystallizer ² ；h _mold Is the effective height of the crystallizer and is expressed in m, v _cast The unit is m/s for the withdrawal speed of the continuous casting machine.

2) The cooling mode of the casting blank after leaving the crystallizer is changed into spray cooling, and the temperature change of the surface of the casting blank in the secondary cooling area is described by adopting an equivalent heat exchange coefficient in combination with the heat exchange condition of the secondary cooling area; the influence of different water flow densities in the secondary cooling area on the surface temperature of the continuous casting billet is measured to obtain the water flow density and the heat transfer coefficient h _w Is a relational expression of

h _w ＝1.57W ^0.55 (1-0.0075T _w )

In the formula h _w Is the heat transfer coefficient and has the unit of kW/(m) ² DEG C.); w is the water flow density and has the unit of L/(m) ² ·s)；T _w Is the temperature of the cooling water;

3) In the air cooling zone, radiation heat dissipation is used as a boundary condition:

q _B ＝σ·ε((T _sur +273) ⁴ -(T _amb +273) ⁴ )

in the formula, q _B Is the surface heat flux density of the casting blank in natural cooling, and takes the Stefan-Boltzmann constant as sigma and 5.67 multiplied by 10 ^-8 W/(m ² K ⁴ ) (ii) a Epsilon is the blackness coefficient; t is _sur The surface temperature of the casting blank is measured in unit; t is _amb Is the ambient temperature in degrees celsius.

And 5: after the seedling stage is finished, starting blank drawing by a continuous casting machine, and applying a displacement boundary condition on the head part of the blank; the whole continuous casting machine is divided into a vertical section, a vertical bending section, an arc section, a straightening section and a horizontal section, the x-axis direction is set to be the horizontal direction according to a roller array diagram, the y-axis direction is set to be the vertical direction, a two-dimensional finite element model of a casting blank is set to apply a displacement boundary condition along the coordinate axis direction when passing through the vertical section and the horizontal section, a rectangular coordinate system is converted into a polar coordinate system when the model passes through the vertical bending section, the arc section and the straightening section, and then the casting flow is advanced by controlling the change of the angle;

step 5.1: establishing a displacement boundary condition of the vertical segment region:

loc_bender＝inc_disp×Inc_number_B

loc_total＝loc_bender

Inc_number＝Inc_number_B

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

wherein loc _ render is the displacement of the model in the vertical section, inc _ disp is the displacement of the model in a single incremental step, inc _ number _ B is the incremental step number of the model in the vertical section, inc _ number is the total incremental step number, loc _ total is the total displacement, dist (x _ total is the displacement of the model in the vertical section), inc _ disp is the displacement of the model in a single incremental step, inc _ number _ B is the total incremental step number, inc _ total is the total displacement, and _i ，y _i ) Distance of the node at each position of the model from the meniscus in the initial state, dist _ men (x) _i ，y _i ) The distance from the node at each position of the model to the meniscus at different moments as the casting advances; and judging the sizes of the total displacement and the length of the vertical section after each step of calculation is finished, if the total displacement is less than or equal to the length of the vertical section, indicating that the model is still positioned in the vertical section, and if the total displacement is greater than or equal to the length of the vertical section, indicating that the model starts to enter a bent section.

In particular, the change of the pulling speed in the casting process is reflected by changing the size of inc _ disp in the vertical section:

1) When the pulling speed is not changed:

inc_disp＝inc_time×v ₀

where inc _ time is a predetermined time step, v ₀ Initial pull rate;

2) The acceleration phase inc _ disp is set as a function of incremental steps:

inc_disp＝Inc_number_V×(v ₁ -v ₀ )/number_1×inc_time+inc_disp ₀

Inc_number_V＝Inc_number-number_0

number_0＝t ₀ /inc_time

number_1＝t ₁ /inc_time

inc_disp ₀ ＝inc_time×v ₀

wherein, the Inc _ number _ V is the increment step number of the acceleration stage, V ₀ Is the final pull rate of the previous stage, t ₀ Number _0 is the total time step elapsed before the start of the acceleration phase, v ₁ For the final pull rate after the end of the acceleration phase, t ₁ For the total acceleration phase time, number _1 is the total number of time steps that have elapsed during the acceleration phase, inc _ disp ₀ The displacement of the model within a single incremental step prior to the start of the acceleration phase.

Step 5.2: establishing displacement boundary conditions of the bend straightening area:

loc_segment＝inc_disp×Inc_number_S

inc_disp＝inc_angle×(π/180)×R

loc_total＝loc_bender+loc_segment

Inc_number＝Inc_number_B+Inc_number_S

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

wherein loc _ segment is the displacement of the model in the bending and straightening section, inc _ number _ S is the increment step number of the model in the bending and straightening section, inc _ angle is the angle of a single increment step of the bending and straightening area, and R is the radius of the curvature circle of the bending section and the straightening section. And judging the sizes of the total displacement, the bending straightening section and the vertical section after the calculation of each step is finished, if the sizes are smaller than the sizes, indicating that the model is still positioned in the bending straightening section, and if the sizes are larger than or equal to the sizes, indicating that the model finishes the bending straightening and starting to enter the horizontal section.

In particular, the change of the pulling speed in the casting process is reflected by changing the size of inc _ angle in the bending straightening section:

1) When the pulling speed is not changed:

inc_disp＝inc_angle×(π/180)×R

inc_angle＝(inc_time×v ₀ )/R×(180/π)

2) The acceleration phase inc _ angle is set as a function of the incremental steps:

inc_disp＝inc_angle×(π/180)×R

inc_angle＝(Inc_number_V×(v ₁ -v ₀ )/number_1×inc_time)/R×(180/π)+inc_angel

Inc_number_V＝Inc_number-number_0

number_0＝t ₀ /inc_time

number_1＝t ₁ /inc_time

inc_angel ₀ ＝(inc_time×v ₀ )/R×(180/π)

ins_angel ₀ the displacement of the model within a single incremental step prior to the start of the acceleration phase.

Step 5.3: establishing displacement boundary conditions of the displacement boundary of the horizontal area:

loc_hori＝inc_disp×Inc_number_B

loc_total＝loc_bender+loc_segment+loc_hori

Inc_number＝Inc_number_B+Inc_number_S+Inc_number_H

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

where loc _ hori is the displacement of the model in the horizontal segment, and Inc _ number _ H is the incremental step number of the model in the vertical segment. Judging the total displacement and the total length of the casting flow after the calculation of each step is finished, if the total displacement and the total length of the casting flow are smaller than the total displacement, indicating that the model is still positioned in the horizontal section, and if the total displacement and the total length of the casting flow are equal to the total displacement, indicating that the model reaches the outlet of the continuous casting machine, and finishing the calculation of the model;

particularly, the change of the pulling rate in the casting starting process is reflected by changing the size of inc _ disp in the horizontal section:

1) In the horizontal section, when the pulling speed is not changed:

inc_disp＝inc_time×v ₀

2) Set as a function of incremental steps in the acceleration phase inc _ disp:

inc_disp＝Inc_number_V×(v ₁ -v ₀ )/number_1×inc_time+inc_disp ₀

Inc_number_V＝Inc_number-number_0

number_0＝t ₀ /inc_time

number_1＝t ₁ /inc_time

inc_disp ₀ ＝inc_time×v ₀

step 6: constructing a casting blank two-dimensional finite element model, and dividing the thermodynamic coupling calculation process of the casting blank two-dimensional finite element model into two stages according to the characteristics of the casting starting stage: emergence stage and launch stage.

The casting blank two-dimensional finite element model is established by taking the center of the width surface of a casting blank as a reference according to the total length of the casting flow, and specifically comprises a two-dimensional solidification heat transfer model and a two-dimensional thermodynamic coupling finite element model

Step 6.1: establishing a two-dimensional solidification heat transfer model with the effective height of the crystallizer as the size in the seedling emergence stage, wherein the two-dimensional solidification heat transfer model is a two-dimensional rectangle established according to the effective height of the crystallizer, all model units are set as dead units before calculation is not started, and the position of the molten steel level is judged in real time according to the calculation time and the rising speed of the molten steel level after calculation is started:

level_liquid＝v_liquid×time

num_level＝level_liquid/y_div

max_eleid＝num_level×num_ele

wherein v _ liquid is the liquid level rising speed, time is the liquid level rising time, level _ liquid is the liquid level height at the current time, y _ div is the unit size, num _ level is the number of unit layers to be activated at the current time, num _ ele is the number of units of each unit layer, and max _ eleid is the maximum number of units to be activated.

After each step of calculation, all the unit numbers less than or equal to max _ eleid are positioned below the position of the molten steel surface, the unit number is converted from a dead unit state to be activated, the temperature is initialized to be the casting temperature, other units are kept in the dead unit state, the calculation process of the activated unit cannot be influenced until the molten steel surface reaches the position of the meniscus, all the units of the model are activated, the seedling stage is finished, and the temperature field result is extracted to be used as the initial value of the model crystallizer part of the next stage.

Step 6.2: in the starting stage, a two-dimensional thermal coupling finite element model with the length being the total length of the casting flow is established according to the total length of the casting flow and a roller distribution diagram, the two-dimensional thermal coupling finite element model is a two-dimensional rectangle established according to the total length of the casting flow and the roller distribution diagram, and rollers are set as rigid bodies; only activating a casting blank of a crystallizer part in an initial state, and initializing by taking a settlement result of a temperature field in an emergence stage as the temperature of the part of the model; the method comprises the following steps of simulating blank drawing by applying a displacement boundary to a model node, continuously activating a unit displaced below a meniscus to participate in thermal coupling calculation, and simulating a casting blank to sequentially pass through a vertical section, a vertical bending section, an arc section, a straightening section and a horizontal section:

num_level_1＝loc_tatal/y_div

max_eleid_1＝num_level_1×num_ele

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

and activating the units with the numbers less than or equal to the max _ eleid number after the model moves along the blank drawing direction each time. After each activation and update of the model, the cooling characteristic numbers of different positions of the boundary of the model are judged through the outlet position Dist [ Cool _ number ] of each cold zone, then the corresponding cooling boundary condition is applied, and the calculation is submitted, wherein Cool _ iflag is the cooling characteristic number in the step 4.

And 7: extracting the characteristic point temperature and stress strain state of the continuous casting billet in real time in the thermodynamic coupling calculation process of the finite element model, tracking the position of a solidification tail end, and calculating the distribution of a liquid-solid phase line along the casting flow;

step 7.1: extracting the temperature field and stress field results of the center of the wide surface of the casting blank:

all nodes from meniscus to the head of the blank are chosen, according to Dist _ men (x) _i ，y _i ) Obtaining the distance between each node and the meniscus, and then extracting the temperature and stress value of each node at the moment to further obtain the distribution condition of the temperature field and the stress field of the casting blank along the casting flow direction;

step 7.2: extracted liquidus and solidus results:

step 7.2.1: appointing any time from the position of a billet head to a meniscus, and calculating the central position temperature of each layer of node of the two-dimensional longitudinal casting blank model;

if the center has a node, extracting the temperature value of the node at the moment:

if no node exists in the center, performing interpolation calculation according to the temperatures of the left and right nodes:

wherein, the first and the second end of the pipe are connected with each other,

is the temperature, T, at the center of the i-th layer node ⁱ _{center_node} Is the temperature of the i-th layer center node, T ⁱ _{outer_node} The node temperature T of the ith layer at the center position close to the outer arc side ⁱ _{inner_node} The node temperature of the ith layer at the center position close to the inner arc side, i is the distanceThe number of node layers at the position away from the blank head;

step 7.2.2: comparing the central position temperature with the liquidus temperature;

comparison with liquidus position:

if T ⁱ _cen <＝T _l If so, indicating that the position of the liquid phase line of the layer reaches the central position, and setting the position of the output liquid phase line as slab _ click/2;

if T ⁱ _cen >T _l Then T will be ⁱ _cen Marked as T ⁱ ₁ The node temperature of the central position along the inner arc side direction is sequentially marked as T ⁱ ₂ ，T ⁱ ₃ ………T ⁱ _max And in turn compared to the liquidus temperature;

when T is ⁱ _j >T _l And T ⁱ _j+1 <＝T _l And then, calculating the position coordinates of the liquidus point according to linear interpolation, wherein the position coordinates of the liquidus point are calculated as follows:

wherein, node ⁱ _{liquid_x} Is the abscissa, X, of the liquidus temperature position of the i-th node ⁱ _j Abscissa of nearest node above liquidus temperature, T ⁱ _j Is the temperature value of the node at that location, X ⁱ _j+1 Abscissa, T, for nearest node below liquidus temperature ⁱ _j+1 Is the temperature value, T, of the node at that location _l Obtaining the ordinate Node of the solidus temperature position of the i-th layer Node by the same method as the liquidus temperature ⁱ _{liquid_y} After that, the liquidus position is calculated:

X ⁱ _max is the abscissa, Y, of a node of the layer located on the inner-arc side surface ⁱ _max The longitudinal coordinate of the node of the layer positioned on the side surface of the inner arc is shown;

comparison with solid phase line position:

if T ⁱ _cen <＝T _s If so, indicating that the position of the solid phase line of the layer reaches the central position, and setting the position of the output solid phase line to be slab _ click/2;

if T ⁱ _cen >T _s Then T is added ⁱ _cen Mark T ⁱ ₁ The node temperature of the central position along the inner arc side direction is sequentially marked as T ⁱ ₂ ，T ⁱ ₃ ………T ⁱ _max And sequentially comparing with the solidus temperature;

when T is ⁱ _j >T _s And T ⁱ _j+1 <＝T _s Then, the position coordinates of the solidus point are calculated according to the linear interpolation, and the position coordinates of the solidus point are calculated as follows:

wherein, the Node ⁱ _{solid_x} Is the abscissa, X, of the temperature position of the solidus of the i-th node _j Abscissa of nearest node higher than solidus temperature, X _j+1 The abscissa, T, is obtained for the nearest node at a temperature higher than the solidus temperature _s The solidus temperature is obtained by the same method as the ordinate Node of the solidus temperature position of the i-th layer Node ⁱ _{solid_y} Then, the solidus position is calculated:

X ⁱ _max is the abscissa, Y, of a node of the layer located on the inner-arc side surface ⁱ _max Is the ordinate of the node where the layer is located on the inner arc side surface.

Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:

the invention provides a method for calculating the coupling of a temperature field and a stress field of a continuous casting blank in the casting process, which is characterized in that a thermodynamic coupling finite element model is established in stages by combining the actual production condition of a continuous casting machine in the casting process, the simulation that a crystallizer is gradually filled with molten steel in a seedling emergence stage is completed through a life and death unit, the change of the temperature field and the stress field of the casting blank caused by blank drawing after the continuous casting machine is started is simulated by utilizing the idea of a Lagrange method, and different cooling boundary conditions are applied according to the position of the casting blank in the calculation process of the temperature field and the stress field. The method can lead the model to be close to reality, has more reliable calculation results of the temperature field and the stress field, and has important reference significance for improving the continuous casting process and improving the continuous casting production level.

Drawings

FIG. 1 is a flow chart of a continuous casting billet temperature field and stress field coupling calculation method in a casting process according to an embodiment of the invention;

FIG. 2 is a schematic diagram of a longitudinal two-dimensional model of continuous casting established in an embodiment of the present invention;

FIG. 3 is a schematic diagram of a calculation method of a continuous casting billet temperature field in the seedling emergence stage in the embodiment of the invention;

FIG. 4 is a schematic diagram of a method for calculating a temperature field and a stress field of a continuous casting billet in a starting stage in the embodiment of the invention;

FIG. 5 is a graph showing the variation of the casting rate of the continuous casting according to the embodiment of the present invention;

FIG. 6 is a cloud diagram of the shell thickness distribution of the continuous casting slab at each stage in the embodiment of the invention;

FIG. 7 is a temperature field distribution diagram of the wide surface center of the continuous casting billet at different times according to the embodiment of the invention;

FIG. 8 is a distribution diagram of liquidus of a continuous casting slab at different times according to an embodiment of the invention;

FIG. 9 is a distribution diagram of solidus lines of a continuous casting slab at different moments according to an embodiment of the invention;

FIG. 10 is a stress field distribution diagram of the inner arc side of a continuous casting billet at different moments according to an embodiment of the invention;

FIG. 11 is a stress field distribution diagram of the outer arc side of the continuous casting slab at different times according to the embodiment of the invention.

Detailed Description

The following detailed description of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.

The method combines the actual parameters of a slab continuous casting line of a certain steel mill in China, adopts a finite element method to establish a two-dimensional thermodynamic coupling finite element model in the continuous casting and casting process and completes calculation, and finally obtains the temperature field change rule of the casting blank.

A method for calculating the coupling of a temperature field and a stress field of a continuous casting billet in the casting process is shown in figure 1, and specifically comprises the following steps:

the casting condition parameters in this example are: the composition of the steel grade is based on Q235B actually produced by a certain steel plant, the casting temperature is 1533.7 ℃, the size of a plate blank is 2100mm x 230mm, the effective height of a crystallizer is 800mm, the total length of a casting flow is 34.85m, the steel grade comprises 8 secondary cooling zones and 2 air cooling zones, the total length of the secondary cooling zones is 19.77m, the length of the air cooling zones is 14.28m, the cooling conditions of the crystallizer and the secondary cooling zones are shown in the following tables 1 and 2, and a graph of the change of the casting speed increase is shown in an attached figure 5; inputting physical parameters required by calculation, including heat-related physical parameters such as density rho, specific heat c, thermal conductivity coefficient lambda, force-related physical parameters, poisson's ratio v, elastic modulus E and yield strength sigma _s 。

TABLE 1 crystallizer Cooling conditions

Step 2: obtaining physical property parameters required by calculation: the material comprises heat-related physical property parameters of density rho, specific heat c, heat conductivity coefficient lambda, force-related physical property parameters, poisson's ratio v, elastic modulus E and yield strength sigma _s ；

And 3, step 3: the control equation used in the calculation process comprises a solidification heat transfer differential equation and a thermal elastic plastic constitutive equation;

the solidification heat transfer differential equation is as follows:

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in the formula, the unit is K; rho is the density in kg/m ³ ；c _eff Is the heat capacity, expressed in J/(kg. DEG. C.); k is the thermal conductivity, given in W/(m. DEG C); t represents time in units of s; c. C _s 、c _l The specific heat of the solid phase region and the specific heat of the liquid phase region are respectively, L is latent heat of solidification, and the unit is J/kg; f. of _s T, T for solid fraction _L And T _S Respectively representing the current temperature, the liquidus temperature and the solidus temperature in the process of solidification and heat transfer, wherein x and y represent two directions of a two-dimensional finite element model of a casting blank;

the thermal elastic-plastic constitutive equation is as follows:

1) And (3) elastic deformation stage: the continuous casting billet is in a high-temperature state in the continuous casting process, so that the total strain in the elastic deformation stage comprises elastic strain and thermal strain generated by temperature, and the formula is as follows:

in increments of the elastic strain tensor for the elastic deformation phase>

Is a matrix of elastic stiffness, alpha is the coefficient of linear thermal expansion, delta _ij 、δ _kl 、δ _ik 、δ _jl 、δ _jk 、δ _il Is a kronecker symbol, if i = j, δ _ij =1; if i ≠ j, δ _ij =0,i, j, k, l for representing directions of coordinate axes in a rectangular coordinate system in space; e is the elastic modulus of the material, upsilon is the Poisson's ratio of the material, sigma _ij Is a stress component of epsilon _kl Is the strain component;

2) The plastic deformation phase formula is as follows:

is the increment of the elastic strain tensor in the plastic deformation phase>

In increments of the plastic strain tensor for the plastic deformation phase>

D { sigma ] being the increment of the thermal strain tensor in the plastic deformation phase _ij Is the increment of the total stress tensor in the plastic deformation phase, is>

The total strain of the continuous casting blank in the continuous casting process consists of three parts, elastic strain, plastic strain and thermal strain generated by temperature;

step 4.1: the crystallizer and the second cooling zone are divided according to the distance between the outlet of the crystallizer and the outlet of each cooling zone and the meniscus, the distance between the outlet of the crystallizer and the outlet of each cooling zone and the meniscus is stored in a Dist array, and a cooling characteristic number is given;

the partial procedure in this example is as follows:

wherein cool _ number represents the total number of cooling zones, in this example the total length of the strand is 34.85m, comprising 8 secondary cooling zones, dist [8 ]]＝[0.8，1.04，1.6，2.71，4.27，6.19，10.03，13.87，20.57]，Dist[0]Is crystallizedThe distance of the outlet of the device from the meniscus, dist [1 ]]Distance of exit position from meniscus for two cold zones and one zone, and so on, dist _ men (x) _i ，y _i ) Representing the distance between the node at any position of the casting flow and the meniscus, cool _ iflag is a feature number for judging the cooling boundary condition, and particularly the cooling feature number of the air cooling zone part is set to 404.

1) In the crystallizer, the cooling mode of the continuous casting billet is heat exchange with the wall of the crystallizer, so that the heat flow density is selected to describe the heat transfer behavior of the surface of the continuous casting billet in the crystallizer; the following formula is shown in Savage (J.Savage, W.H.Pritcard, J.Iron Steel Inst.1954,178, 268.) A calculation formula for the local heat flow density q between the wall of the crystallizer and the interface of the casting blank is obtained by measuring the relationship between the heat flow in the stationary water-cooled crystallizer and the residence time of molten Steel when low-carbon Steel is cast at a pulling speed of 1.0 m/min:

wherein t is time in units of s; z is the distance from the meniscus of the crystallizer in m; v is the pull rate in m/min; q is the local heat flux density between the wall of the crystallizer and the casting blank interface, and the unit is MW/m ² A, B is a coefficient to be determined, A =2.688, B is calculated according to the water flow and inlet and outlet temperature difference of the crystallizer, and the specific process is as follows:

in the formula, ρ _w The density of cooling water of the crystallizer is kg/m ³ ；c _w Taking the specific heat capacity of cooling water of the crystallizer, and taking 4.2 kJ/(kg DEG C); q _w Is the flow rate of cooling water of the crystallizer, and has the unit of m ³ /min；ΔT _w The temperature difference of the cooling water inlet and the cooling water outlet of the crystallizer is measured in unit; a. The _mold Effective cooling area of cooling water distribution of crystallizer, and unit is m ² ；h _mold Is the effective height of the crystallizer and is expressed in m, v _cast The unit is m/s for the withdrawal speed of the continuous casting machine. Finally, the value of the parameter B is determined to be 0.285 under the working condition.

2) The cooling mode of the casting blank after leaving the crystallizer is changed into spray cooling, and the temperature change of the surface of the casting blank in the secondary cooling area is described by adopting an equivalent heat exchange coefficient in combination with the heat exchange condition of the secondary cooling area; the influence of different water flow densities of the secondary cooling zone on the surface temperature of the continuous casting billet is measured in a continuous casting billet surface defect experiment by adopting Nozaki (Transactions ISIJ,1978,18 (6): 330-338) _w Is a relational expression of

h _w ＝1.57W ^0.55 (1-0.0075T _w )

In the formula h _w Is the heat transfer coefficient and has the unit of kW/(m) ² DEG C.); w is the water flow density and has the unit of L/(m) ² ·s)；T _w Is the temperature of cooling water, which is taken to be 25 ℃ in the embodiment;

TABLE 3 Secondary Cooling zone Water flow Density

3) In the air cooling area, radiation heat dissipation is used as a boundary condition:

q _B ＝σ·ε((T _sur +273) ⁴ -(T _amb +273) ⁴ )

in the formula, q _B Is the surface heat flux density of the casting blank in natural cooling, and takes the Stefan-Boltzmann constant as sigma and 5.67 multiplied by 10 ^-8 W/(m ² K ⁴ ) (ii) a Epsilon is the blackness coefficient; t is _sur The surface temperature of the casting blank is measured in units of; t is _amb Is the ambient temperature in degrees celsius.

And 5: after the seedling stage is finished, starting blank drawing by a continuous casting machine, and applying a displacement boundary condition to the part of the blank head; the whole continuous casting machine is divided into a vertical section, a vertical bending section, an arc section, a straightening section and a horizontal section, the x-axis direction is set to be the horizontal direction according to a roller array diagram, the y-axis direction is set to be the vertical direction, a two-dimensional finite element model of a casting blank is set to apply a displacement boundary condition along the coordinate axis direction when passing through the vertical section and the horizontal section, a rectangular coordinate system is converted into a polar coordinate system when the model passes through the vertical bending section, the arc section and the straightening section, and then the casting flow is advanced by controlling the change of the angle;

in this embodiment, the pull rate variation in the casting start stage is shown in fig. 5. Initial pull rate v at the starting stage ₀ (0.4 m/min), duration 42s, after which the pull rate is increased to v in one minute ₁ (0.9 m/min) for 84s, after which the pull rate continues to increase to v in one minute ₂ (1.05 m/min) and the entire pull-up stage is about 246s, comprising essentially the entire vertical section.

loc_bender＝inc_disp×Inc_number_B

loc_total＝loc_bender

Inc_number＝Inc_number_B

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

in this embodiment, the time step inc _ time is set to 0.05s, and y _ disp is set according to the initial pull rate:

inc_disp＝3.33×10 ^-4 m

the first acceleration phase inc _ disp is set to:

inc_disp＝Inc_number_V×3.47×10 ^-7 +3.33×10 ^-4

Inc_number_V＝Inc_number_B-number_0

number_0＝840

after accelerating to 0.9m/min, keeping the pulling speed at 84s, and setting y _ disp as:

inc_disp＝7.5×10 ^-4 m

then, the speed is continuously accelerated to 1.05m/min:

inc_disp＝Inc_number_V×1.04×10 ^-7 +7.5×10 ^-4

Inc_number_V＝Inc_number_B-number_0

number_0＝3732

loc_segment＝inc_disp×Inc_number_S

inc_disp＝inc_angle×(π/180)×R

loc_total＝loc_bender+loc_segment

Inc_number＝Inc_number_B+Inc_number_S

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

the pulling speed of the stage is improved to the production pulling speed and is stable and unchanged, and the following steps are set in combination with the curvature radius:

inc_angle＝5.5×10 ^-3 °

loc_hori＝inc_disp×Inc_number_B

loc_total＝loc_bender+loc_segment+loc_hori

Inc_number＝Inc_number_B+Inc_number_S+Inc_number_H

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

the billet head passes through the bending and straightening section and begins to advance along the horizontal direction, and the setting is as follows:

inc_disp＝8.75×10 ^-4 m

and 6: constructing a casting blank two-dimensional finite element model, and dividing the thermodynamic coupling calculation process of the casting blank two-dimensional finite element model into two stages according to the characteristics of the casting starting stage as shown in figure 2: the emergence stage and the initial stage are shown in fig. 3, 4 and 6, respectively.

The casting blank two-dimensional finite element model is established by taking the center of the wide surface of a casting blank as a reference according to the total length of a casting flow, and specifically comprises a two-dimensional solidification heat transfer model and a two-dimensional thermodynamic coupling finite element model

Step 6.1: establishing a two-dimensional solidification heat transfer model with the effective height of a crystallizer as the size in the seedling emergence stage, wherein the two-dimensional solidification heat transfer model is a two-dimensional rectangle established according to the effective height of the crystallizer, setting all model units as dead units before calculation is not started for simulating the physical process that molten steel is gradually filled into the crystallizer in the seedling emergence stage, and judging the position of the molten steel level in real time according to the calculation time and the rising speed of the molten steel level after the calculation is started:

level_liquid＝v_liquid×time

num_level＝level_liquid/y_div

max_eleid＝num_level×num_ele

wherein v _ liquid is a liquid level rising speed, time is a liquid level rising time, level _ liquid is a liquid level height at the current time, y _ div is a unit size, num _ level is the number of unit layers to be activated at the current time, num _ ele is the number of units of each unit layer, and max _ eleid is the maximum number of units to be activated.

Step 6.2: in the starting stage, a two-dimensional thermal coupling finite element model with the length being the total length of the casting flow is established according to the total length of the casting flow and a roller distribution diagram, the two-dimensional thermal coupling finite element model is a two-dimensional rectangle established according to the total length of the casting flow and the roller distribution diagram, and rollers are set as rigid bodies; only activating the casting blank of the crystallizer part in the initial state, and initializing by taking the settlement result of the temperature field in the emergence stage as the temperature of the part of the model; the method comprises the following steps of simulating blank drawing by applying a displacement boundary to a model node, continuously activating a unit displaced below a meniscus to participate in thermal coupling calculation, and simulating a casting blank to sequentially pass through a vertical section, a vertical bending section, an arc section, a straightening section and a horizontal section:

num_level_1＝loc_tatal/y_div

max_eleid_1＝num_level_1×num_ele

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

and the unit with the number less than or equal to the max _ eleid number is activated after the model moves along the drawing direction each time. After each activation and update of the model, the cooling characteristic numbers of different positions of the boundary of the model are judged through the outlet position Dist [ Cool _ number ] of each cold zone, then the corresponding cooling boundary condition is applied, and the calculation is submitted, wherein Cool _ iflag is the cooling characteristic number in the step 4.

all nodes from meniscus to head are chosen according to Dist _ men (x) _i ，y _i ) Obtaining the distance between each node and the meniscus, and then extracting the temperature and stress value of each node at the moment to further obtain the distribution condition of the temperature field and the stress field of the casting blank along the casting flow direction;

step 7.2: extracted liquidus and solidus results:

wherein the content of the first and second substances,

is the temperature, T, at the center of the i-th layer node ⁱ _{center_node} Is the temperature of the i-th layer center node, T ⁱ _{outer_node} The node temperature T of the ith layer at the center position close to the outer arc side ⁱ _{inner_node} The node temperature of the ith layer center position close to the inner arc side is shown, and i is the number of the node layers away from the blank head position;

comparison with liquidus position:

if T is ⁱ _cen >T _l Then T will be ⁱ _cen Marked as T ⁱ ₁ The node temperature of the central position along the inner arc side direction is marked with T in sequence ⁱ ₂ ，T ⁱ ₃ ………T ⁱ _max And in turn compared to the liquidus temperature;

wherein, node ⁱ _{liquid_x} Is the abscissa, X, of the liquidus temperature position of the i-th node ⁱ _j Is the nearest node above the liquidus temperatureAbscissa of (a), T ⁱ _j Is the temperature value of the node at that location, X ⁱ _j+1 Abscissa, T, for nearest node below liquidus temperature ⁱ _j+1 Is the temperature value, T, of the node at that location _l Obtaining the ordinate Node of the solidus temperature position of the i-th layer Node by the same method as the liquidus temperature ⁱ _{liquid_y} Then, the liquidus position is calculated:

X ⁱ _max is the abscissa, Y, of the node of the layer located on the inner-arc side surface ⁱ _max The longitudinal coordinate of the node of the layer positioned on the side surface of the inner arc is shown;

comparison with solid phase line position:

if T ⁱ _cen >T _s Then T will be ⁱ _cen Marked as T ⁱ ₁ The node temperature of the central position along the inner arc side direction is sequentially marked as T ⁱ ₂ ，T ⁱ ₃ ………T ⁱ _max And sequentially comparing with the solidus temperature;

wherein, node ⁱ _{solid_x} Is the abscissa, X, of the temperature position of the solidus of the i-th node _j Abscissa of nearest node higher than solidus temperature, X _j+1 The abscissa, T, is the closest node at a temperature higher than the solidus temperature _s The solidus temperature is obtained by the same method as the ordinate Node of the solidus temperature position of the i-th layer Node ⁱ _{solid_y} Then, the solidus position is calculated:

/>

In this example, the temperature field distribution at the center point of the wide surface of the 2100 x 230mm thick slab at the casting stage is shown in fig. 7, and the temperature is relatively lower since the head portion of the slab is first cooled at the stage of emergence. At t =186.8s, the billet head portion travels to the vertical section, the billet head temperature being around 825 ℃; when t =513.3s, the temperature of the head of the billet is about 839 ℃, and when t =960.3s, the temperature of the head of the billet is about 874 ℃ when the temperature of the head of the billet is in the straightening section; when the casting speed is stabilized, the temperature at the same position of the casting flow is respectively 131 ℃, 85 ℃ and 58 ℃ higher than that of the head part of the billet.

As shown in FIGS. 8 and 9, the solid phase line of the continuous casting material at the start-up stage changes, and when the head of the cast strand advances to a distance of 15.62m from the meniscus, the core portion of the cast strand starts to be completely solidified, and the position of the cast strand corresponding to the start of the leveling zone is located. Fig. 10 and 11 respectively show the equivalent stress analysis of the contact between the inner arc side surface and the outer arc side surface of the continuous casting billet and a roller in the continuous casting starting stage, and the equivalent stress of the contact between the billet head part and the roller is larger due to the fact that the complete cooling is faster, the plasticity is poor, the brittleness is high, and the equivalent stress is larger. The equivalent stress of the bending section billet head and the contact position of the inner arc roller and the outer arc roller is 75MPa. The equivalent stress of the inner arc side of the subsequent casting blank at the position does not exceed 20MPa, and the outer arc side is 8-10 MPa lower than the inner arc side, because the casting blank is subjected to compressive stress at the inner arc side of the bending section part, and the outer arc side is subjected to tensile stress. The temperature of the part of the billet head which moves to the straightening section is increased due to the reduction of cooling strength and the release of latent heat, the plasticity is improved, the equivalent stress contacting with the inner arc roller and the outer arc roller is reduced to 65MPa, and the equivalent stress of a subsequent casting billet in the straightening section fluctuates at 55 MPa.

The foregoing description is only exemplary of the preferred embodiments of the disclosure and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the invention in the embodiments of the present disclosure is not limited to the specific combinations of the above-mentioned features, and other embodiments in which the above-mentioned features or their equivalents are combined arbitrarily without departing from the spirit of the invention are also encompassed. For example, the above features and (but not limited to) technical features with similar functions disclosed in the embodiments of the present disclosure are mutually replaced to form the technical solution.

Claims

1. A method for calculating the coupling of a temperature field and a stress field of a continuous casting blank in the casting process is characterized by comprising the following steps of:

step 2: obtaining physical property parameters required by calculation: the material specifically comprises heat-related physical property parameters of density rho, specific heat c, thermal conductivity coefficient lambda, force-related physical property parameters, poisson's ratio v, elastic modulus E and yield strength sigma _s ；

And step 3: control equations used in the calculation process specifically comprise a solidification heat transfer differential equation and a thermal elastic plastic constitutive equation;

and 4, step 4: setting a characteristic number for each cooling area in the casting flow according to the effective height of the crystallizer, the water quantity of the crystallizer, the number of the secondary cooling areas, the dividing parameters of the secondary cooling areas and the water quantity distribution of each area of the secondary cooling areas obtained in the step 1 by combining the position of the crystallizer and the dividing parameters of the secondary cooling areas, and selecting proper cooling boundary conditions according to different cooling modes of the crystallizer and each area of the secondary cooling areas;

step 6: constructing a casting blank two-dimensional finite element model, and dividing the thermodynamic coupling calculation process of the casting blank two-dimensional finite element model into two stages according to the characteristics of the casting starting stage: a seedling emergence stage and a starting stage;

the casting blank two-dimensional finite element model is established by taking the center of the casting blank wide surface as a reference according to the total length of the casting flow, and specifically comprises a two-dimensional solidification heat transfer model and a two-dimensional thermodynamic coupling finite element model;

and 7: and extracting the characteristic point temperature and stress strain state of the continuous casting billet in real time in the thermodynamic coupling calculation process of the finite element model, tracking the position of the solidification tail end, and calculating the distribution of the liquid-solid phase line along the casting flow.

2. The method for calculating the coupling of the temperature field and the stress field of the continuous casting slab in the casting process according to claim 1, wherein the solidification heat transfer differential equation in the step 3 is as follows:

in the formula, the unit is K; ρ is the density in kg/m ³ ；c _eff Is the heat capacity, expressed in J/(kg. DEG. C.); k is the thermal conductivity, given in W/(m. DEG C); t represents time in units of s; c. C _s 、c _l The specific heat of the solid phase region and the specific heat of the liquid phase region are respectively, L is latent heat of solidification, and the unit is J/kg; f. of _s T, T for solid fraction _L And T _S Respectively representing the current temperature, the liquidus temperature and the solidus temperature in the solidification heat transfer process, wherein x and y represent two directions of a two-dimensional finite element model of a casting blank;

the thermal elastic-plastic constitutive equation is as follows:

in increments of the elastic strain tensor for the elastic deformation phase>

Increment of thermal strain tensor d { sigma } of elastic deformation phase _ij Is the increment of the total stress tensor in the elastically deforming phase, is>

Is a matrix of elastic stiffness, alpha is the coefficient of linear thermal expansion, delta _ij 、δ _kl 、δ _ik 、δ _jl 、δ _jk 、δ _il Is a kronecker symbol, if i = j, δ _ij =1; if i ≠ j, δ _ij =0,i, j, k, l for representing the directions of coordinate axes in a rectangular coordinate system in space; e is the elastic modulus of the material, upsilon is the Poisson ratio of the material, sigma _ij Is a stress component of epsilon _kl Is the strain component;

2) The plastic deformation phase formula is as follows:

in the formula, d { epsilon _ij Is the increment of the total strain tensor of the plastic deformation phase,

is the increment of the elastic strain tensor in the plastic deformation phase>

Is the increment of the plastic strain tensor in the plastic deformation phase>

3. The method for calculating the coupling of the temperature field and the stress field of the continuously cast bloom in the casting process according to claim 1, wherein the step 4 specifically comprises the following steps:

1) In the crystallizer, the cooling mode of the continuous casting billet is heat exchange with the wall of the crystallizer, so that the heat flow density is selected to describe the heat transmission behavior of the surface of the continuous casting billet in the crystallizer; the following formula is a calculation formula of the local heat flux density q between the wall of the crystallizer and the interface of the casting blank:

in the formula, ρ _w The density of cooling water of the crystallizer is kg/m ³ ；c _w Taking the specific heat capacity of cooling water of the crystallizer, and taking 4.2 kJ/(kg DEG C); q _w Is the flow rate of cooling water of the crystallizer and has the unit of m ³ /min；ΔT _w The temperature difference of the cooling water inlet and the cooling water outlet of the crystallizer is measured in unit; a. The _mold Effective cooling area of cooling water distribution of crystallizer, and unit is m ² ；h _mold Is the effective height of the crystallizer and is expressed in m, v _cast The unit is the withdrawal speed of the continuous casting machine and is m/s;

h _w ＝1.57W ^0.55 (1-0.0075T _w )

q _B ＝σ·ε((T _sur +273) ⁴ -(T _amb +273) ⁴ )

in the formula, q _B Is the heat flux density of the surface of the casting blank during natural cooling, and takes the Stefan-Boltzmann constant as sigma, and takes 5.67 multiplied by 10 ^-8 W/(m ² K ⁴ ) (ii) a Epsilon is the blackness coefficient; t is _sur The surface temperature of the casting blank is measured in unit; t is a unit of _amb Is the ambient temperature in degrees celsius.

4. The method for calculating the coupling of the temperature field and the stress field of the continuous casting slab in the casting process according to claim 1, wherein the step 5 specifically comprises the following steps:

step 5.1: establishing a displacement boundary condition of a vertical segment area:

loc_bender＝inc_disp×Inc_number_B

loc_total＝loc_bender

Inc_number＝Inc_number_B

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

wherein loc _ render is the displacement of the model in the vertical section, inc _ disp is the displacement of the model in a single incremental step, inc _ number _ B is the incremental step number of the model in the vertical section, inc _ number is the total incremental step number, loc _ total is the total displacement, dist (x _ total is the displacement of the model in the vertical section), inc _ disp is the displacement of the model in a single incremental step, inc _ number _ B is the total incremental step number, inc _ total is the total displacement, and _i ，y _i ) Distance of the node at each position of the model from the meniscus in the initial state, dist _ men (x) _i ，y _i ) The distance from the meniscus at different times for the nodes at each position of the model to travel with the strand; judging the size of the total displacement and the length of the vertical section after each step of calculation is finished, if the total displacement is less than or equal to the length of the vertical section, indicating that the model is still positioned in the vertical section, and if the total displacement is greater than or equal to the length of the vertical section, indicating that the model starts to enter a bent section;

in particular, the change of the pulling rate in the casting process is reflected by changing the size of inc _ disp in the vertical section:

1) When the pulling speed is not changed:

inc_disp＝inc_time×v ₀

wherein inc _ time is a preset time step, v ₀ Initial pull rate;

2) The acceleration phase inc _ disp is set as a function of incremental steps:

inc_disp＝Inc_number_V×(v ₁ -v ₀ )/number_1×inc_time+inc_disp ₀

Inc_number_V＝Inc_number-number_0

number_0＝t ₀ /inc_time

number_1＝t ₁ /inc_time

inc_disp ₀ ＝inc_time×v ₀

wherein, the Inc _ number _ V is the increment step number of the acceleration stage, V ₀ Is the final pull rate of the previous stage, t ₀ Number _0 is the total time step elapsed before the start of the acceleration phase, v ₁ For the final pull rate after the end of the acceleration phase, t ₁ To accelerate the total time of the phase, number _1 is the total time elapsed during the acceleration phaseStep number, inc _ disp ₀ The displacement of the model within a single incremental step before the acceleration phase begins;

loc_segment＝inc_disp×Inc_number_S

inc_disp＝inc_angle×(π/180)×R

loc_total＝loc_bender+loc_segment

Inc_number＝Inc_number_B+Inc_number_S

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

the method comprises the following steps of obtaining a curve straightening area, wherein loc _ segment is the displacement of a model in the curve straightening area, inc _ number _ S is the increment step number of the model in the curve straightening area, inc _ angle is the angle of a single increment step of the curve straightening area, and R is the radius of a curvature circle of the curve section and the curvature circle of the straightening section; judging the sizes of the total displacement, the bending straightening section and the vertical section after the calculation of each step is finished, if the sizes are smaller than the sizes, indicating that the model is still positioned in the bending straightening section, and if the sizes are larger than or equal to the sizes, indicating that the model finishes the bending straightening and starting to enter a horizontal section;

in particular, the change of the pulling rate in the casting process is reflected by changing the size of inc _ angle in the bending and straightening section:

1) When the pulling speed is not changed:

inc_disp＝inc_angle×(π/180)×R

inc_angle＝(inc_time×v ₀ )/R×(180/π)

inc_disp＝inc_angle×(π/180)×R

Inc_number_V＝Inc_number-number_0

number_0＝t ₀ /inc_time

number_1＝t ₁ /inc_time

inc_angel ₀ ＝(inc_time×v ₀ )/R×(180/π)

ins_angel ₀ to accelerateDisplacement of the model within a single incremental step before the start of the phase;

loc_hori＝inc_disp×Inc_number_B

loc_total＝loc_bender+loc_segment+loc_hori

Inc_number＝Inc_number_B+Inc_number_S+Inc_number_H

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

wherein loc _ hori is the displacement of the model in the horizontal section, and Inc _ number _ H is the incremental step number of the model in the vertical section; judging the total displacement and the total length of the casting flow after the calculation of each step is finished, if the total displacement and the total length of the casting flow are smaller than the total displacement, indicating that the model is still positioned in the horizontal section, and if the total displacement and the total length of the casting flow are equal to the total displacement, indicating that the model reaches the outlet of the continuous casting machine, and finishing the calculation of the model;

particularly, the change of the pulling speed in the casting process is reflected by changing the size of inc _ disp in the horizontal section:

1) In the horizontal section, when the pulling speed is not changed:

inc_disp＝inc_time×v ₀

2) Set as a function of incremental steps in the acceleration phase inc _ disp:

inc_disp＝Inc_number_V×(v ₁ -v ₀ )/number_1×inc_time+inc_disp ₀

Inc_number_V＝Inc_number-number_0

number_0＝t ₀ /inc_time

number_1＝t ₁ /inc_time

inc_disp ₀ ＝inc_time×v ₀ 。

5. the method for calculating the coupling of the temperature field and the stress field of the continuous casting slab in the casting process according to claim 1, wherein the step 6 specifically comprises the following steps:

step 6.1: establishing a two-dimensional solidification heat transfer model with the effective height of the crystallizer as the size in an emergence stage, wherein the two-dimensional solidification heat transfer model is a two-dimensional rectangle established according to the effective height of the crystallizer, setting all model units as dead units before calculation is started, and judging the position of a molten steel level in real time according to calculation time and the rising speed of the molten steel level after the calculation is started:

level_liquid＝v_liquid×time

num_level＝level_liquid/y_div

max_eleid＝num_level×num_ele

wherein v _ liquid is the liquid level rising speed, time is the liquid level rising time, level _ liquid is the liquid level height at the current time, y _ div is the unit size, num _ level is the number of unit layers to be activated at the current time, num _ ele is the number of units of each unit layer, and max _ eleid is the maximum number of units to be activated;

after each step of calculation, all the unit numbers less than or equal to max _ eleid are positioned below the position of the molten steel surface, the unit number is converted from a dead unit state to activation, the temperature is initialized to the casting temperature, other units are kept in the dead unit state, the calculation process of the activated unit cannot be influenced until the molten steel surface reaches the position of a meniscus, all the units of the model are activated, the seedling stage is finished, and the temperature field result is extracted to serve as the initial value of the model crystallizer part of the next stage;

num_level_1＝loc_tatal/y_div

max_eleid_1＝num_level_1×num_ele

Dist_men(x _i ,y _i )＝dist(x _i ,y _i )+loc_total

wherein y _ div is the unit size, max _ eleid is the maximum number in each layer of unit, and the unit with the number less than or equal to the max _ eleid is activated after the model moves along the blank drawing direction each time; after the model is activated and updated every time, the cooling feature numbers of different positions of the boundary of the model are judged through the outlet position Dist [ Cool _ number ] of each secondary cooling zone, then corresponding cooling boundary conditions are applied, and calculation is submitted, wherein Cool _ iflag is the cooling feature number.

6. The method for calculating the coupling of the temperature field and the stress field of the continuously cast bloom in the casting process according to claim 1, wherein the step 7 specifically comprises the following steps:

step 7.2: the liquidus and solidus results were extracted.

7. The method for calculating the coupling of the temperature field and the stress field of the continuous casting slab in the casting process according to claim 6, wherein the step 7.2 specifically comprises the following steps:

is the temperature at the center of the node at the i-th level>

Is the temperature of the central node of the ith layer->

The temperature of a node at the center of the ith layer close to the outer arc side is->

The node temperature of the ith layer center position close to the inner arc side is shown, and i is the number of the node layers away from the blank head position;

comparison with liquidus position:

if it is

Indicating that the position of the liquid phase line of the layer reaches the central position, and setting the position of the output liquid phase line as slab _ click/2;

if it is

Will->

Is marked as->

The node temperatures in the direction of the inner arc side at the center position are marked as ^ in sequence>

And sequentially compared to the liquidus temperature;

when in use

And->

And then, calculating the position coordinates of the liquidus point according to linear interpolation, wherein the position coordinates of the liquidus point are calculated as follows:

is the abscissa of the liquidus temperature position of the i-th layer node>

Is the abscissa of the nearest node which is higher than the liquidus temperature, and>

for the temperature value of the node at that location,/>>

A nearest node below the liquidus temperature has a horizontal coordinate, and>

is the temperature value, T, of the node at that location _l The vertical coordinate of the i-th layer node solidus temperature position is obtained by taking the liquidus temperature as the temperature

The liquidus position was then calculated:

for the abscissa of the node of the layer located on the inner arc side surface, the value is greater than or equal to>

The longitudinal coordinate of the node of the layer positioned on the side surface of the inner arc is shown;

comparison with solid phase line position:

if it is

Then indicating that the position of the solid phase line of the layer reaches the central position, and setting the position of the output solid phase line as slab _ click/2; />

If it is

Will then >>

Is marked as->

The node temperatures in the direction of the inner arc at the center position are marked with>

And comparing with solidus temperature in turn;

when in use

And->

Then, the position coordinates of the solidus point are calculated according to the linear interpolation, and the position coordinates of the solidus point are calculated as follows:

wherein the content of the first and second substances,

is the abscissa, X, of the i-th layer node solidus temperature position _j Abscissa of nearest node higher than solidus temperature, X _j+1 The abscissa, T, is obtained for the nearest node at a temperature higher than the solidus temperature _s The solidus temperature is obtained by the same principle as the solidus temperature of the i-th layer node>

The solidus position is then calculated:

for the layer to lie on the abscissa of the node of the inner-arc side surface>

Is the ordinate of the node where the layer is located on the inner arc side surface. />