CN113505482A - Method and device for solving taper curve of copper pipe of square billet crystallizer and storage medium - Google Patents
Method and device for solving taper curve of copper pipe of square billet crystallizer and storage medium Download PDFInfo
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- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 title claims abstract description 101
- 229910052802 copper Inorganic materials 0.000 title claims abstract description 101
- 239000010949 copper Substances 0.000 title claims abstract description 101
- 238000000034 method Methods 0.000 title claims abstract description 34
- 238000003860 storage Methods 0.000 title claims abstract description 14
- 238000005266 casting Methods 0.000 claims abstract description 106
- 239000007790 solid phase Substances 0.000 claims abstract description 91
- 239000007788 liquid Substances 0.000 claims abstract description 46
- 238000007711 solidification Methods 0.000 claims abstract description 31
- 230000008023 solidification Effects 0.000 claims abstract description 31
- 238000012546 transfer Methods 0.000 claims abstract description 18
- 239000007791 liquid phase Substances 0.000 claims abstract description 13
- 238000013178 mathematical model Methods 0.000 claims description 46
- 238000004590 computer program Methods 0.000 claims description 22
- 239000007787 solid Substances 0.000 claims description 22
- 239000000498 cooling water Substances 0.000 claims description 13
- 238000001816 cooling Methods 0.000 claims description 9
- 239000012071 phase Substances 0.000 claims description 8
- 238000004364 calculation method Methods 0.000 claims description 6
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 6
- 238000009749 continuous casting Methods 0.000 claims description 5
- 230000005499 meniscus Effects 0.000 claims description 3
- 230000000694 effects Effects 0.000 abstract description 6
- 230000015572 biosynthetic process Effects 0.000 abstract description 3
- 238000004519 manufacturing process Methods 0.000 abstract description 3
- 238000005457 optimization Methods 0.000 abstract description 3
- 229910000831 Steel Inorganic materials 0.000 description 7
- 230000006870 function Effects 0.000 description 7
- 239000010959 steel Substances 0.000 description 7
- 238000012545 processing Methods 0.000 description 6
- 239000002184 metal Substances 0.000 description 4
- 229910052751 metal Inorganic materials 0.000 description 4
- 230000002093 peripheral effect Effects 0.000 description 4
- 238000013461 design Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 238000005299 abrasion Methods 0.000 description 2
- 238000013473 artificial intelligence Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000001413 cellular effect Effects 0.000 description 1
- 230000008602 contraction Effects 0.000 description 1
- 230000017525 heat dissipation Effects 0.000 description 1
- 238000010801 machine learning Methods 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
Abstract
The application relates to a method, a device and a storage medium for solving a copper pipe taper curve of a square billet crystallizer, wherein the method comprises the following steps: determining a temperature field of a casting blank based on the solidification heat transfer characteristics of the casting liquid, and solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank; determining the total width of an air gap in the preset height according to the solid phase rate of the casting blank in the preset height; determining the width of the copper tube of the square billet crystallizer in each height according to the total width of the air gap of each preset height in turn; and determining the taper curve of the copper pipe of the square billet crystallizer according to the width of the copper pipe of the square billet crystallizer in each height. According to the scheme, the air gap width formed by solidification of the casting liquid can be effectively obtained, the width of the square billet crystallizer copper pipe is adjusted according to the air gap width, the optimization of the taper curve of the crystallizer copper pipe is effectively realized, the shape of the inner cavity of the crystallizer and the shape of the formed billet shell are as close as possible, the formation of the air gap is reduced, the heat transfer effect of the crystallizer is better improved, and the production requirement is met.
Description
Technical Field
The application relates to a method and a device for solving a taper curve of a copper pipe of a square billet crystallizer and a storage medium, belonging to the technical field of design of taper curves of copper pipes of crystallizers.
Background
The crystallizer is a key device in the continuous casting process, is a forced water-cooling bottomless ingot mould, promotes the molten steel to be rapidly solidified and ensures that a blank shell after a copper pipe of the crystallizer can bear the static pressure of the unset molten steel in the blank shell by uniformly and rapidly cooling the molten steel. The cooling performance of the mould directly affects the quality of the cast strand, known as the "heart" of the casting machine.
The casting liquid generates thermal contraction when being solidified in the crystallizer, an air gap is formed between the blank shell and the crystallizer, the heat transfer is greatly hindered, the cooling effect of the crystallizer is reduced, the blank shell is thinned, and the grain size of the primary blank shell is also influenced. The higher the continuous casting drawing speed, the higher the cooling and heat transfer effect of the crystallizer.
In order to improve the cooling effect, the inner cavity of the crystallizer is designed to be in an inverted cone shape, so that the blank shell and the copper pipe of the crystallizer have good contact. The taper is too small, so that a larger air gap can be generated between the inner cavity of the crystallizer and the solidified blank shell, the heat transfer of a casting blank is influenced, and the blank drawing speed is limited; the excessive taper can cause the abrasion of the solidified blank shell to the inner cavity of the crystallizer, influence the service life of the crystallizer copper pipe, and even cause the blank shell to be broken after the blank shell is taken out of the crystallizer, thereby causing the breakout accident.
If the taper design of the crystallizer takes the center solidification shrinkage as a standard, air gaps are formed at corners, so that the corners are overheated, cracks are easily formed at the corners, and breakout occurs; if the taper design is based on the solidification shrinkage of the corner part, the problem of overlarge taper at other positions is caused, the taper is extruded with a copper plate, the blank drawing resistance is increased, the abrasion of a crystallizer is serious, and even a blank shell can be broken.
Disclosure of Invention
The application provides a method, a device and a storage medium for solving the taper curve of a copper pipe of a square billet crystallizer, aiming at solving the problems that in the prior art, when the crystallizer is designed by taking central solidification shrinkage as a standard, air gaps are formed at corners, the temperature of the corners is overheated, and the corners are easy to form cracks and produce bleed-out; the taper of the crystallizer is designed by taking the solidification shrinkage of the corner part as a standard, so that the problem of overlarge taper of other positions is caused, the taper is extruded with a copper plate, the blank drawing resistance is increased, the copper plate is seriously abraded, and even a blank shell is broken.
In order to solve the technical problem, the application provides the following technical scheme:
in a first aspect, an embodiment according to the present application provides a method for obtaining a taper curve of a copper tube of a square billet crystallizer, including:
determining a temperature field of a casting blank based on the solidification heat transfer characteristics of the casting liquid, and solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
determining the total width of an air gap in the preset height according to the solid phase rate of the casting blank in the preset height;
determining the width of each height of the copper tube inner cavity of the square billet crystallizer according to the total width of the air gap in each preset height in turn;
the taper curve of the copper pipe of the square billet crystallizer is determined according to the width of the copper pipe of the square billet crystallizer in each height.
Preferably, the determining the total width of the air gap in the preset height according to the solid phase ratio of the casting blank in the preset height comprises:
calculating the width of an air gap formed in an area with the solid phase ratio more than or equal to 1 in the preset height by adopting a first mathematical model;
according to the width of an air gap formed in an area with the solid phase ratio of more than or equal to 1 in the preset height, a second mathematical model is adopted to obtain the width of the air gap corresponding to each solid phase ratio between 0 and 1;
and determining the total width of the air gap formed in the preset height of the square billet crystallizer by adopting a third mathematical model according to the width of the air gap formed in the area with the solid phase ratio of more than or equal to 1 in the preset height and the width of the air gap corresponding to each solid phase ratio with the solid phase ratio of 0-1.
Preferably, the first and second electrodes are formed of a metal,
the first mathematical model is:
σ0＝(ρav/ρ-1)*h0 (1-1)
the second mathematical model is:
σi+1＝(0+0.05*i)*(σ0/h0)*hi+1 (1-2)
the third mathematical model is as follows:
where ρ isavIs the average density of the solid shell; rho is the density of the casting liquid, h0The thickness of the solid blank shell (namely the solid phase ratio is more than or equal to 1); sigma0The air gap width caused by the solidification of the casting liquid into a solid blank shell (namely the solid phase ratio is more than or equal to 1); h isi+1The thickness of a two-phase region blank shell with a solid phase ratio of between i/10 and (i +1)/10 is sigmai+1The casting liquid is changed into an air gap width caused by solidification shrinkage when the solid phase ratio is in a two-phase region between i/10 and (i + 1)/10; sigma is the total width of an air gap caused by the solidification of the final casting liquid in the preset height of the square billet crystallizer; wherein i is an integer from 0 to 9.
Preferably, the first and second electrodes are formed of a metal,
the method for determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
determining the air gap width corresponding to the corner according to the solid phase ratio of the corner position;
determining the air gap width corresponding to the center of the wide surface according to the solid phase ratio of the center position of the wide surface;
the method for determining the width of the copper tube of the square billet crystallizer in each height sequentially according to the total width of the air gap in each preset height comprises the following steps:
determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner;
determining the width of the center of the wide surface of the square billet crystallizer according to the width of the air gap corresponding to the center of the wide surface;
and S153, performing linear calculation on the corner width and the width of the center of the broad surface of the square billet crystallizer, and determining the corresponding widths of the square billet crystallizer in the heights of other positions except the corner and the center of the broad surface.
Preferably, the determining a temperature field of the casting slab based on the solidification heat transfer characteristics of the casting liquid, and the obtaining a solid fraction of each point of the casting slab in the square billet mold according to the temperature field, the solidus temperature and the liquidus temperature of the casting slab includes:
determining the temperature field of the casting blank in the square billet crystallizer according to a preset fourth mathematical model and boundary conditions thereof;
and solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank.
Preferably, the first and second electrodes are formed of a metal,
the fourth mathematical model is:
the boundary conditions are as follows:
T(x,y)|t＝0＝TC (1-7)
wherein T is temperature, DEG C; t is the residence time of the casting liquid in the crystallizer s; λ (T) is the effective thermal conductivity, W/(m ℃); rho (T) is the density of the casting liquid, kg/m3(ii) a C (T) is the specific heat of the casting liquid, J/(kg. DEG C); q is the instantaneous heat flow density in the height direction of the crystallizer, W/m2(ii) a L is the distance between the casting liquid and the meniscus at time tDistance, m; v is the drawing speed of the continuous casting machine, m/s; cwThe specific heat of cooling water is 4200J/(kg DEG C); qwFor cooling water flow, m3/s；ΔTwThe temperature difference of water at the inlet and the outlet of the cooling water is DEG C; rhowFor the density of cooling water, 1000kg/m3(ii) a S is the effective area of the crystallizer, m2For square billets, the value of A is 2680000, and the value of B is related to the water cooling parameter of the crystallizer.
Preferably, the first and second electrodes are formed of a metal,
the method for determining the corner width of the inner cavity of the square billet crystallizer according to the air gap width corresponding to the corner comprises the following steps:
adopting a fifth mathematical model based on the width alpha of the upper opening of the inner cavity of the copper pipe and the air gap width sigma corresponding to the corner part(0,h)Calculating the corner width of the square billet crystallizer as z(0,h)The fifth mathematical model is:
z(0,h)＝α-σ(0,h) (1-9)
adopting a sixth mathematical model based on the width alpha of the upper opening of the inner cavity of the copper pipe and the air gap width sigma corresponding to the center of the wide surface(α/2,h)Calculating the width of the center of the wide surface of the square billet crystallizer as z(α/2,h)The sixth mathematical model is:
z(α/2,h)＝α-σ(α/2,h) (1-10)
adopting a seventh mathematical model based on the corner width z of the square billet crystallizer(0,h)The width z of the center of the wide surface of the square billet crystallizer(α/2,h)And the width z of the inner cavity of the crystallizer at the position of x mm away from the corner part is obtained(x,h)The seventh mathematical model is:
z(x,h)＝z(0,h)+2(z(α/2,h)-z(0,h))/α*x (1-11)
wherein, the width of the upper opening of the inner cavity of the copper pipe is alpha mm, the coordinates of the corner part are set to be (0, h) at the position which is hmm away from the upper opening of the copper pipe, the central coordinates of the broad surface are (alpha/2, h), the coordinates between the corner part and the center of the broad surface and at the position which is xmm away from the corner part are (x, h), the width of the corner part is z(0,h)The width of the center position of the broad face is z(α/2,h)。
In a second aspect, an apparatus for determining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application includes:
the temperature field and solid phase rate calculating module is used for determining the temperature field of the casting blank based on the solidification heat transfer characteristics of the casting liquid and calculating the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
the air gap total width calculating module is used for determining the air gap total width in the preset height according to the solid phase ratio of the casting blank in the preset height;
the copper tube inner cavity width obtaining module is used for determining the width of the square billet crystallizer copper tube in each height according to the total width of the air gap of each preset height in sequence;
the taper curve of the square billet crystallizer copper pipe is determined according to the width of the crystallizer copper pipe in each height.
In a third aspect, according to an embodiment of the present application, there is provided an apparatus for obtaining a copper tube taper curve of a square billet crystallizer, the apparatus includes a processor, a memory, and a computer program stored in the memory and executable on the processor, where the computer program is loaded and executed by the processor to implement any one of the above steps of the method for obtaining a copper tube taper curve of a square billet crystallizer.
In a fourth aspect, according to an embodiment of the present application, there is provided a computer-readable storage medium, which stores a computer program, wherein the computer program is used for implementing the steps of the method for obtaining a copper tube taper curve of a billet crystallizer described in any one of the above paragraphs when the computer program is executed by a processor.
The beneficial effect of this application lies in: and solving the solid phase rate of each point of the square billet based on the obtained temperature field, the liquidus temperature and the solidus temperature, then determining the air gap width in each height of the square billet crystallizer copper pipe according to the solid phase rate of the casting blank in each preset height, and further determining the width of the square billet crystallizer copper pipe in each height according to the air gap width. According to the scheme, the air gap width formed by solidification of the casting liquid can be effectively obtained, the width of the square billet crystallizer is adjusted according to the air gap width, the optimization of the copper pipe taper curve of the crystallizer is effectively realized, the shape of the inner cavity of the crystallizer and the shape of a formed billet shell are as close as possible, the formation of air gaps is reduced, the heat transfer effect of the crystallizer is better improved, and the production requirement is met.
In addition, according to the scheme, the width of the corner part and the width of the air gap at the center of the wide surface are obtained through a mathematical model, the widths of the inner cavities of the crystallizer at the center positions of the corner part and the wide surface are obtained, and the widths of the inner cavities of the crystallizer at other positions are obtained through linear calculation, so that the taper curve of the square billet crystallizer copper pipe is designed.
The foregoing description is only an overview of the technical solutions of the present application, and in order to make the technical solutions of the present application more clear and clear, and to implement the technical solutions according to the content of the description, the following detailed description is made with reference to the preferred embodiments of the present application and the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a method for determining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application;
FIG. 2 is a flowchart of sub-steps involved in step S14 according to one embodiment of the present application;
FIG. 3 is a flowchart illustrating a method for determining a taper curve of a copper tube of a square billet crystallizer according to still another embodiment of the present application;
FIG. 4 is a flowchart illustrating the sub-steps involved in step S12 according to an embodiment of the present invention;
FIGS. 5 and 6 are schematic thickness curves of a solid shell at different solid fractions at corners and at the center of a broad surface;
FIG. 7 is a schematic view of the taper curve of the copper tube at the corner and the center of the broad face designed according to the determined width;
FIG. 8 is a block diagram of an apparatus for determining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application;
fig. 9 is a block diagram of an apparatus for determining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application.
Detailed Description
The following examples are intended to illustrate the present application but are not intended to limit the scope of the present application.
Fig. 1 is a method for determining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application, including:
step S12, determining a temperature field of a casting blank based on the solidification heat transfer characteristics of the casting liquid, and solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
in the embodiment of the present application, the space formed by the casting liquid in the billet mold is regarded as a three-dimensional space, so that the temperature of each point of the casting liquid in the billet mold can be determined by a preset fourth mathematical model and boundary conditions thereof, and a temperature field of the casting blank is formed.
In the examples of the present application, the solid phase ratio is represented as fS，fS0 or less represents a liquid phase region of the cast slab, 0<fS<1 represents a two-phase region of a casting blank, and f is not less than 1SRepresenting the solid phase region of the cast slab.
In the examples of the present application, the solid phase ratio fSThe following formula is adopted for solving the following steps:
wherein f isSThe solid phase ratio; t isSAnd TLSolidus temperature and liquidus temperature, respectively, deg.C; f. ofS0 or less means that the solidification region is a liquid phase region, 0<fS<1 represents that the solidification region is a two-phase region, and f is more than or equal to 1SThe solidification region is represented as a solid phase region.
Step S14, determining the total width of an air gap in the preset height according to the solid phase ratio of the casting blank in the preset height;
in the embodiment of the application, for each height which is divided in advance, the total width of an air gap in each height is determined according to the solid phase ratio of a casting blank in the height;
when the total width of the air gap of each height is calculated, on the basis that the heat dissipation is faster in the area close to the crystallizer, the solid phase ratio is generally the largest, the solid phase ratio is lower and is likely to be liquid in the area close to the center of the casting blank, and the solid phase ratio is sequentially increased from the center area to the edge area of the square blank, therefore, when the total width of the square blank crystallizer is calculated, the air gap width corresponding to each solid phase ratio, namely the air gap width formed by the solid phase ratio from 0 to 1, is sequentially calculated for each divided height, then the air gap widths corresponding to the solid phase ratios are superposed, and the total air gap width corresponding to each height is further determined; as an alternative embodiment, the solid fraction is divided by 10 equally between 0 and 1, i.e. the corresponding air gap widths are calculated for 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1 respectively, and then summed up to form the total air gap width for each height.
Step S16, determining the air gap width in each height of the copper tube inner cavity of the square billet crystallizer according to the total air gap width of each preset height in turn; the taper curve of the inner cavity of the copper tube of the square billet crystallizer is determined according to the width of the copper tube of the square billet crystallizer in each height.
In the embodiment of the application, the width of the corner of the copper tube and the width of the center of the broad surface are preferably determined firstly, and then the width of the copper tube of the square billet crystallizer in each height at other positions is determined according to the width of the corner and the width of the center of the broad surface. And linear solving can be carried out on the widths in the heights at other positions according to the width of the corner part and the width of the center of the wide surface.
In an embodiment of the present application, referring to fig. 2, in step S14, the determining the total width of the air gap in the preset height according to the solid phase ratio of the casting slab in the preset height includes:
step S141, calculating the width of an air gap formed by an area with the solid fraction more than or equal to 1 in the preset height by adopting a first mathematical model;
step S142, according to the air gap width formed by the area with the solid phase ratio more than or equal to 1 in the preset height, adopting a second mathematical model to obtain the air gap width corresponding to each solid phase ratio with the solid phase ratio between 0 and 1;
and S143, determining the total width of the air gap formed in the preset height of the square billet crystallizer by adopting a third mathematical model according to the width of the air gap formed in the area with the solid phase ratio more than or equal to 1 in the preset height and the width of the air gap corresponding to each solid phase ratio between 0 and 1.
Further, in the embodiments of the present application,
the first mathematical model is:
σ0＝(ρav/ρ-1)*h0 (1-1)
the second mathematical model is:
σi+1＝(0+0.05*i)*(σ0/h0)*hi+1 (1-2)
the third mathematical model is as follows:
where ρ isavIs the average density of the solid shell; rho is the density of the casting liquid, h0The thickness of the solid blank shell (namely the solid phase ratio is more than or equal to 1); sigma0The air gap width caused by the solidification of the casting liquid into a solid blank shell (namely the solid phase ratio is more than or equal to 1); h isi+1The thickness of a two-phase region blank shell with a solid phase ratio of between i/10 and (i +1)/10 is sigmai+1The casting liquid is changed into an air gap width caused by solidification shrinkage when the solid phase ratio is in a two-phase region between i/10 and (i + 1)/10; sigma is the total width of an air gap caused by the solidification of the final casting liquid in the preset height of the square billet crystallizer; wherein i is an integer from 0 to 9.
In the embodiment of the present application, as shown in figure 3,
in step S14, the determining the total width of the air gap in the preset height according to the solid phase ratio of the casting blank in the preset height includes:
step S144, determining the air gap width corresponding to the corner according to the solid phase ratio of the corner position;
step S145, determining the air gap width corresponding to the central position of the wide surface according to the solid phase ratio corresponding to the central position of the wide surface;
in step S15, the determining the width of the copper tube of the square billet crystallizer in each height according to the total width of the air gap in each preset height in turn includes:
s151, determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner;
s152, determining the width of the center of the wide surface of the square billet crystallizer according to the width of the air gap corresponding to the center of the wide surface;
and S153, performing linear calculation on the corner width and the width of the center of the broad surface of the square billet crystallizer, and determining the corresponding widths of the square billet crystallizer in the heights of other positions except the corner and the center of the broad surface.
Further, in the embodiment of the present application, referring to fig. 4, in step S12, the determining a temperature field of a casting slab based on a solidification heat transfer characteristic of a casting liquid, and determining a solid phase ratio of each point of the casting slab in a square billet mold according to the temperature field, a solidus temperature of the casting liquid, and a liquidus temperature of the casting liquid includes:
step S121, determining a temperature field of a casting blank in the square billet crystallizer according to a preset fourth mathematical model and boundary conditions thereof;
and S122, solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank.
In a still further aspect of the present invention,
the fourth mathematical model is:
the boundary conditions are as follows:
T(x,y)|t＝0＝TC (1-7)
wherein T is temperature, DEG C; t is the casting liquid stops in the crystallizerThe time left, s; λ (T) is the effective thermal conductivity, W/(m ℃); rho (T) is the density of the casting liquid, kg/m3(ii) a C (T) is the specific heat of the casting liquid, J/(kg. DEG C); q is the instantaneous heat flow density in the height direction of the crystallizer, W/m2(ii) a L is the distance between the casting liquid and the meniscus at the moment t, m; v is the drawing speed of the continuous casting machine, m/s; cwThe specific heat of cooling water is 4200J/(kg DEG C); qwFor cooling water flow, m3/s；ΔTwThe temperature difference of water at the inlet and the outlet of the cooling water is DEG C; rhowFor the density of cooling water, 1000kg/m3(ii) a S is the effective area of the crystallizer, m2For square billets, the value of A is 2680000, and the value of B is related to the water cooling parameter of the crystallizer.
In the embodiment of the present application,
the method for determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner comprises the following steps:
adopting a fifth mathematical model based on the width alpha of the upper opening of the inner cavity of the copper pipe and the air gap width sigma corresponding to the corner part(0,h)Calculating the corner width of the square billet crystallizer as z(0,h)The fifth mathematical model is:
z(0,h)＝α-σ(0，h) (1-9)
adopting a sixth mathematical model based on the width alpha of the upper opening of the inner cavity of the copper pipe and the air gap width sigma corresponding to the center of the wide surface(α/2,h)The width of the center of the wide surface of the square billet crystallizer is obtained as z(α/2,h)The sixth mathematical model is:
z(α/2,h)＝α-σ(α/2,h) (1-10)
adopts seven mathematical models and is based on the corner width z of the square billet crystallizer(0,h)The width z of the center of the wide surface of the square billet crystallizer(α/2,h)And the width z of the inner cavity of the crystallizer at the position of x mm away from the corner part is obtained(x,h)The seventh mathematical model is:
z(x,h)＝z(0,h)+2(z(α/2,h)-z(0,h))/α*x (1-11)
wherein the width of the upper opening of the inner cavity of the copper pipe is alpha mm, the coordinates of the corner part are set as (0, h) at the position which is h mm away from the upper opening of the copper pipe,the coordinates of the center of the broad face are (alpha/2, h), the coordinates of the corner part and the center of the broad face are (x, h) at a position which is x mm away from the corner part, and the width of the corner part is z(0,h)The width of the center position of the broad face is z(α/2,h)，σ(x，h)The total width of the air gap resulting from the solidification of the final casting liquid.
In summary, according to the technical scheme provided by the application, the solid phase rate of each point of the square billet is obtained based on the obtained temperature field, the obtained liquidus temperature and the obtained solidus temperature, then the air gap width in each height of the copper tube of the square billet crystallizer is determined according to the total air gap width in each preset height, and then the width in each height of the inner cavity of the copper tube of the square billet crystallizer is determined according to the air gap width. According to the scheme, the air gap width formed by solidification of the casting liquid can be effectively obtained, the width of the square billet crystallizer copper pipe is adjusted according to the air gap width, the optimization of the taper curve of the crystallizer copper pipe is effectively realized, the shape of the inner cavity of the crystallizer and the shape of the formed billet shell are as close as possible, the formation of the air gap is reduced, the heat transfer effect of the crystallizer is better improved, and the production requirement is met.
In addition, according to the scheme, the air gap width of the corner part and the center of the wide surface is obtained through a mathematical model, the width of the inner cavity of the crystallizer at the center of the corner part and the center of the wide surface is obtained, and the widths of the inner cavities of the crystallizers at other positions are obtained through linear calculation, so that the taper curve of the square billet crystallizer copper pipe is designed.
As follows, a specific example is illustrated:
for a small billet caster, the casting steel grade is C70DA, the section size is 140 multiplied by 140mm, the casting temperature is 1500 ℃, the cooling water quantity of the crystallizer is 1750L/min, and the drawing speed is 2.6 m/min. Adjusting initial and boundary conditions, solving a heat transfer control equation, and obtaining a temperature field of a casting blank in the crystallizer. Combining the compositions, the solidus and liquidus temperatures of the C70DA steel grade were 1387 ℃ and 1476 ℃ respectively, and it was possible to obtain thickness curves of the solid shell at different solidus ratios at the corner and the center of the broad face, as shown in FIGS. 5 and 6, respectively.
Counting the temperature field of the solid shell in the crystallizer to obtain the average temperature of the wide-face central shell of about 1200 ℃, the average temperature of the corner shell of about 1100 ℃, and combining the C70DA steelThe average density of the center of the broad face of the obtained solid blank shell is about 7480kg/m3The corner shell has an average density of about 7530kg/m3The density of the molten steel at the casting temperature is about 7020kg/m3. And (3) solving the width of an air gap caused by solidifying molten steel into a solid blank shell by combining thickness curves at different solid fractions in the crystallizer, and further designing taper curves of the copper pipe at the corner and the center of the broad surface, as shown in fig. 7, wherein the upper curve is the width of the center of the broad surface, and the lower curve is the width of the corner.
The method for obtaining the taper curve of the copper pipe of the square billet crystallizer provided by the embodiment of the application comprises the steps of calculating the corner width and the air gap width of the center of a wide surface of the square billet crystallizer based on a mathematical model, then obtaining the corner width and the air gap width of the center of the wide surface, and carrying out linear calculation on the widths of other positions based on the corner width and the center width of the wide surface, thereby achieving the purpose of designing the taper of the copper pipe of the square billet crystallizer.
Example 2
The embodiment of the present application further provides a device for obtaining a taper curve of a copper tube of a square billet crystallizer, as shown in fig. 8, including:
a temperature field and solid phase rate calculating module 81 for determining the temperature field of the casting blank based on the solidification heat transfer characteristics of the casting liquid and calculating the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
the air gap total width calculating module 82 is used for determining the air gap total width in the preset height according to the solid phase ratio of the casting liquid in the preset height;
the copper tube inner cavity width calculating module 83 is used for determining the width of the copper tube of the square billet crystallizer in each height according to the total width of the air gap of each preset height in sequence;
the taper curve of the square billet crystallizer copper pipe is determined according to the width of the crystallizer copper pipe in each height.
Fig. 9 is a block diagram of an apparatus for obtaining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present disclosure, where the apparatus for obtaining a taper curve of a copper tube of a square billet crystallizer according to the present disclosure may be a desktop computer, a notebook computer, a palm computer, a cloud server, and other computing devices, and the apparatus may include, but is not limited to, a processor and a memory. The device for obtaining the taper curve of the copper tube of the square billet crystallizer in this embodiment at least comprises a processor and a memory, wherein a computer program is stored in the memory, the computer program can run on the processor, and when the processor executes the computer program, the steps in the method embodiment for obtaining the taper curve of the copper tube of the square billet crystallizer, such as the steps of the method for obtaining the taper curve of the copper tube of the square billet crystallizer shown in fig. 1, are implemented. Or, when the processor executes the computer program, the processor realizes the functions of the modules in the device embodiment for obtaining the copper tube taper curve of the square billet crystallizer.
Illustratively, the computer program may be partitioned into one or more modules that are stored in the memory and executed by the processor to implement the invention. The one or more modules can be a series of instruction segments of a computer program capable of performing specific functions, and the instruction segments are used for describing the execution process of the computer program in the device for obtaining the copper tube taper curve of the billet crystallizer. For example, the computer program may be divided into a temperature field obtaining module, a solid fraction calculating module, an air gap width calculating module, and a width determining module, and the specific functions of each module are as follows:
the temperature field and solid phase rate calculating module is used for determining the temperature field of the casting blank based on the solidification heat transfer characteristics of the casting liquid and calculating the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
the air gap total width calculating module is used for determining the air gap total width in the preset height according to the solid phase ratio of the casting blank in the preset height;
the square billet width obtaining module is used for determining the width of the copper tube of the square billet crystallizer in each height according to the total width of the air gap in each preset height in turn;
the taper curve of the square billet crystallizer copper pipe is determined according to the width of the crystallizer copper pipe in each height.
The processor may include one or more processing cores, such as: 4 core processors, 6 core processors, etc. The processor may be implemented in at least one hardware form of a DSP (Digital Signal Processing), an FPGA (Field-Programmable Gate Array), and a PLA (Programmable Logic Array). The processor may also include a main processor and a coprocessor, where the main processor is a processor for Processing data in an awake state, and is also called a Central Processing Unit (CPU); a coprocessor is a low power processor for processing data in a standby state. In some embodiments, the processor may further include an AI (Artificial Intelligence) processor for processing computing operations related to machine learning. The processor is a control center of the device for solving the taper curve of the copper pipe of the square billet crystallizer, and various interfaces and lines are utilized to connect all parts of the device for solving the taper curve of the copper pipe of the whole square billet crystallizer.
The memory can be used for storing the computer program and/or the module, and the processor realizes various functions of the device for obtaining the copper tube taper curve of the square billet crystallizer by running or executing the computer program and/or the module stored in the memory and calling the data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a memory device, or other volatile solid state storage device.
It can be understood by those skilled in the art that the apparatus described in this embodiment is only an example of the apparatus for obtaining the taper curve of the copper tube of the square billet crystallizer, and does not constitute a limitation to the apparatus for obtaining the taper curve of the copper tube of the square billet crystallizer. The processor, memory and peripheral interface may be connected by bus or signal lines. Each peripheral may be connected to the peripheral interface via a bus, signal line, or circuit board. Illustratively, peripheral devices include, but are not limited to: radio frequency circuit, touch display screen, audio circuit, power supply, etc.
Of course, the device for determining the taper curve of the copper tube of the billet crystallizer may also comprise fewer or more components, which is not limited in this embodiment.
Optionally, the present application further provides a computer-readable storage medium, which stores a computer program, and the computer program is used for implementing the steps of the above method for obtaining the copper tube taper curve of the square billet crystallizer when being executed by a processor.
Optionally, the present application further provides a computer product, which includes a computer-readable storage medium, where a program is stored in the computer-readable storage medium, and the program is loaded into and executed by a processor to implement the steps of the above-mentioned method for obtaining a copper tube taper curve of a billet crystallizer.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method for solving a taper curve of a copper pipe of a square billet crystallizer is characterized by comprising the following steps:
determining a temperature field of a casting blank based on the solidification heat transfer characteristics of the casting liquid, and solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
determining the total width of an air gap in the preset height according to the solid phase rate of the casting blank in the preset height;
determining the width of each height of the copper tube inner cavity of the square billet crystallizer according to the total width of the air gap of each preset height in sequence;
the taper curve of the inner cavity of the copper tube of the square billet crystallizer is determined according to the width of the copper tube of the square billet crystallizer in each height.
2. The method according to claim 1, wherein the determining the total width of the air gap in the preset height according to the solid phase ratio of the cast slab in the preset height comprises:
calculating the width of an air gap formed in an area with the solid phase ratio more than or equal to 1 in the preset height by adopting a first mathematical model;
according to the width of an air gap formed in an area with the solid phase ratio of more than or equal to 1 in the preset height, a second mathematical model is adopted to obtain the width of the air gap corresponding to each solid phase ratio between 0 and 1;
and determining the total width of the air gap formed in the preset height of the square billet crystallizer by adopting a third mathematical model according to the width of the air gap formed in the area with the solid phase ratio of more than or equal to 1 in the preset height and the width of the air gap corresponding to each solid phase ratio with the solid phase ratio of 0-1.
3. The method according to claim 2,
the first mathematical model is:
σ0＝(ρav/ρ-1)*h0 (1-1)
the second mathematical model is:
σi+1＝(0+0.05*i)*(σ0/h0)*hi+1 (1-2)
the third mathematical model is as follows:
where ρ isavIs the average density of the solid shell; rho is the density of the casting liquid, h0The thickness of the solid blank shell (namely the solid phase ratio is more than or equal to 1); sigma0The air gap width caused by the solidification of the casting liquid into a solid blank shell (namely the solid phase ratio is more than or equal to 1); h isi+1The thickness of a two-phase region blank shell with a solid phase ratio of between i/10 and (i +1)/10 is sigmai+1The casting liquid is changed into an air gap width caused by solidification shrinkage when the solid phase ratio is in a two-phase region between i/10 and (i + 1)/10; sigma is the total width of an air gap caused by the solidification of the final casting liquid in the preset height of the square billet crystallizer; wherein i is an integer from 0 to 9.
4. The method according to claim 1,
the method for determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
determining the air gap width corresponding to the corner according to the solid phase ratio of the corner position;
determining the air gap width corresponding to the center of the wide surface according to the solid phase ratio of the center position of the wide surface;
the width in each height of square billet crystallizer copper pipe inner chamber is confirmed according to the total width of air gap in every preset height in proper order, include:
determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner;
determining the width of the center of the wide surface of the square billet crystallizer according to the width of the air gap corresponding to the center of the wide surface;
and S153, performing linear calculation on the corner width and the width of the center of the broad surface of the square billet crystallizer, and determining the corresponding widths of the square billet crystallizer in the heights of other positions except the corner and the center of the broad surface.
5. The method according to claim 4, wherein the determining a temperature field of the cast slab based on the solidification heat transfer characteristics of the casting liquid, and the obtaining a solid fraction of each point of the cast slab in the square billet mold from the temperature field, a solidus temperature and a liquidus temperature of the cast slab comprises:
determining the temperature field of the casting blank in the square billet crystallizer according to a preset fourth mathematical model and boundary conditions thereof;
and solving the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank.
6. The method according to claim 5,
the fourth mathematical model is:
the boundary conditions are as follows:
T(x,y)|t＝0＝TC (1-7)
wherein T is temperature, DEG C; t is the casting liquid stops in the crystallizerThe time left, s; λ (T) is the effective thermal conductivity, W/(m ℃); rho (T) is the density of the casting liquid, kg/m3(ii) a C (T) is the specific heat of the casting liquid, J/(kg. DEG C); q is the instantaneous heat flow density in the height direction of the crystallizer, W/m2(ii) a L is the distance between the casting liquid and the meniscus at the moment t, m; v is the drawing speed of the continuous casting machine, m/s; cwThe specific heat of cooling water is 4200J/(kg DEG C); qwFor cooling water flow, m3/s；ΔTwThe temperature difference of water at the inlet and the outlet of the cooling water is DEG C; rhowFor the density of cooling water, 1000kg/m3(ii) a S is the effective area of the crystallizer, m2For square billets, the value of A is 2680000, and the value of B is related to the water cooling parameter of the crystallizer.
7. The method according to claim 4,
the method for determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner comprises the following steps:
adopting a fifth mathematical model based on the width alpha of the upper opening of the inner cavity of the copper pipe and the air gap width sigma corresponding to the corner part(0,h)Calculating the corner width of the square billet crystallizer as z(0,h)The fifth mathematical model is:
z(0,h)＝α-σ(0,h) (1-9)
adopting a sixth mathematical model based on the width alpha of the upper opening of the inner cavity of the copper pipe and the air gap width sigma corresponding to the center of the wide surface(α/2,h)Calculating the width of the center of the wide surface of the square billet crystallizer as z(α/2,h)The sixth mathematical model is:
z(α/2,h)＝α-σ(α/2,h) (1-10)
adopting a seventh mathematical model based on the corner width z of the square billet crystallizer(0,h)The width z of the center of the wide surface of the square billet crystallizer(α/2,h)The width z of the inner cavity of the crystallizer at the position of x mm away from the corner part is obtained(x,h)The seventh mathematical model is:
z(x,h)＝z(0,h)+2(z(α/2,h)-z(0,h))/α*x (1-11)
wherein, the width of the upper opening of the inner cavity of the copper pipe isAlpha mm, the coordinates of a corner part are set to be (0, h), the coordinates of the center of a broad face are set to be (alpha/2, h), the coordinates of the position between the corner part and the center of the broad face and at the position x mm away from the corner part are set to be (x, h), the width of the corner part is set to be z(0,h)The width of the center position of the broad face is z(α/2,h)。
8. The utility model provides a device is asked to square billet crystallizer copper pipe tapering curve which characterized in that includes:
the temperature field and solid phase rate calculating module is used for determining the temperature field of the casting blank based on the solidification heat transfer characteristics of the casting liquid and calculating the solid phase rate of each point of the casting blank in the square billet crystallizer according to the temperature field, the solid phase line temperature and the liquid phase line temperature of the casting blank;
the air gap total width calculating module is used for determining the air gap total width in the preset height according to the solid phase ratio of the casting blank in the preset height;
the copper tube inner cavity width obtaining module is used for determining the width of the square billet crystallizer copper tube in each height according to the total width of the air gap of each preset height in sequence;
the taper curve of the square billet crystallizer copper pipe is determined according to the width of the crystallizer copper pipe in each height.
9. An apparatus for determining a copper tube taper curve of a billet crystallizer, the apparatus comprising a processor, a memory and a computer program stored in the memory and capable of running on the processor, wherein the computer program is loaded and executed by the processor to implement the steps of the method for determining a copper tube taper curve of a billet crystallizer according to any one of claims 1 to 7.
10. A computer-readable storage medium, which stores a computer program, wherein the computer program is used for implementing the steps of the method for determining a copper tube taper curve of a bloom crystallizer as claimed in any one of claims 1 to 7 when the computer program is executed by a processor.
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