CN103920859A - Continuous casting sheet billet internal crack online prediction method - Google Patents

Continuous casting sheet billet internal crack online prediction method Download PDF

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CN103920859A
CN103920859A CN201310012646.7A CN201310012646A CN103920859A CN 103920859 A CN103920859 A CN 103920859A CN 201310012646 A CN201310012646 A CN 201310012646A CN 103920859 A CN103920859 A CN 103920859A
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strand
heat
temperature
crystallizer
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CN103920859B (en
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幸伟
范小刚
马春武
徐永斌
徐海伦
陈洪智
邵远敬
叶理德
袁德玉
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Wisdri Engineering and Research Incorporation Ltd
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Abstract

The invention relates to a continuous casting sheet billet internal crack online prediction method which is characterized in that a casting billet is divided into a plurality of slices from a crystallizer meniscus to the tail end of a control area, a slice heat tracking model of two-dimensional solidification heat transfer of each slice is built based on ignoring heat transfer along the withdrawal direction, the casting billet solidification process is dynamically tracked through the slice heat tracking models, all slices are connected together to dynamically describe temperature field distribution of the whole strand, bulging strain generated by the casting billet is computed online in real time through a bulging strain model according to temperature field distribution or solidification parameters of the casting billet, a critical strain value of the casting billet is set and serves as a standard for generating an internal crack, and the casting billet generates the internal crack when the bulging strain exceeds the critical strain value of the casting billet. The internal crack of the sheet billet can be predicted online in real time, so that a lot of detection cost is saved.

Description

A kind of continuous casting steel billet underbead crack on-line prediction method
Technical field
The present invention relates to a kind of continuous casting steel billet underbead crack on-line prediction method, belong to steel-making continuous casting field.
Background technology
Along with country advocates and develops a circular economy energetically, smelter is also more and more higher to energy-saving and cost-reducing requirement.The obvious characteristic such as hot charging and hot rolling of continuous casting slab and continuous casting billet continuous rolling technology have that energy consumption is low, reduced investment, lumber recovery are high, with short production cycle, thereby become the most active research field in continuous casting field.Past, the slab quality that conticaster is produced is mainly evaluated with the quality of strand under cold conditions, in process of production, continuous casting billet underbead crack degree and distribute and need detect to obtain by sufur printing or hot acid erosion low power, this cold conditions sampling and the traditional slab quality control method checking obviously can not meet that heat is sent, the requirement of hot charging and direct rolling process.Therefore the online forecasting system of, setting up slab quality is subject to extensive concern.
The rolling of the combination property of the underbead crack of continuous casting billet to steel and strand is become a useful person and is had a strong impact on.The domestic research about on-line prediction continuous casting billet underbead crack at present also rarely has report.
Summary of the invention
The technical problem to be solved in the present invention is: propose a kind of continuous casting billet underbead crack on-line prediction method, can predict slab underbead crack in real time online, thereby save a large amount of testing costs.
For solving the problems of the technologies described above, the technical solution used in the present invention is:
A kind of continuous casting steel billet underbead crack on-line prediction method, it is characterized in that: strand is divided into several sections from crystallizer meniscus to control zone end, ignoring on the basis of conducting heat along throwing direction, setting up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section; By section heat-tracking model, casting blank solidification process is dynamically followed the tracks of, all sections are connected together and dynamically describe the temperature field distribution of whole casting stream; Distribute or casting blank solidification parameter according to temperature field, by the online bulgs stress that calculates in real time strand generation of bulgs stress model, set the critical strain values of strand as the standard that produces underbead crack, in the time that bulgs stress exceedes strand critical strain values, there is underbead crack in strand simultaneously.
By technique scheme, said method specifically comprises the steps:
The first step: data initialization process: the model calculating parameter that reads steel grade information, steel grade physical parameter, technological parameter, device parameter and setting from one-level computer, second computer and three-level computer;
Second step: strand is divided into several sections from crystallizer meniscus to control zone end, for each section, taking width of plate slab direction as X-axis, thickness direction is Y-axis, the direction of motion is that Z axis is set up coordinate system, and then ignoring on the basis of conducting heat along throwing direction, set up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section;
The 3rd step: dynamically follow the tracks of each section, the independent information unit by each section is in the same time along with the real-time change of technological parameter, determines each section at the solidification and heat transfer differential equation boundary condition under in the same time not; The differential equation is carried out to periodicity and solves, dynamically describe each section not in the same time, the temperature field at diverse location place, all sections are connected together, the temperature field of dynamically describing whole casting stream distributes; Described independent information comprises life-span, surface temperature, shell thickness, the position of section; Middle bag temperature, temperature field, solid-liquid phase line position and pulling rate.
Heat-tracking model is followed the tracks of storage to the important information of all sections.Calculation procedure is inner has set up special data storage cell for these information;
The 4th step: carry out casting blank bulging and answer deformation analysis: in the strand temperature field that the heat-tracking model of cutting into slices in step 3 is calculated and shell thickness information substitution bulgs stress model, calculate the bulgs stress that current slice produces;
The 5th step: in the time that bulgs stress exceedes strand critical strain values, system sends the advance notice of strand generation underbead crack; , all sections are stringed together meanwhile, dynamically represent the bulgs stress situation of whole casting stream.
By technique scheme, described section heat-tracking model, represents by the following solidification and heat transfer differential equation:
ρc ∂ T ∂ t = λ ∂ 2 T ∂ x 2 + λ ∂ 2 T ∂ y 2 - - - ( 1 )
In formula: the density of ρ-steel, kg/m 3;
C-equivalent specific heat holds, J/kg.K;
λ-thermal conductivity factor, W/m. DEG C;
T-temperature, K;
In this model required input initial condition parameters is comprised to four kinds are respectively: steel grade and steel grade parameter; The technological parameter that comprises pouring temperature, pulling rate, casting blank cross-section size, the each subregion cooling water inflow of secondary, environment temperature; The casting machine structural parameters that comprise the cold subregion of casting machine two, roller row layout, arrangement of nozzles; The calculating parameter that comprises time step, space step-length, slice length, computing cycle;
The uniform temperature fields of whole section of steel billet of early solidification is consistent, all identical with cast temperature;
In casting blank solidification process, pass through successively crystallizer, two cold-zones, air cooling zone, all heats spread out of by surface, the cooling condition difference in each district, boundary condition is also different;
Crystallizer internal boundary condition:
The expression formula of crystallizer transient heat flow density is:
q = A - B t ( W / m 2 ) - - - ( 2 )
In formula, A, B are constant, conventionally get A=2 × 10 6~ 3 × 10 6w/m 2; B has characterized air gap impact on heat flow density q in crystallizer short transverse;
By above formula, can obtain the mean heat flux of crystallizer:
q ‾ = ∫ 0 t m ( A - B t ) dt t m = A - 2 3 B t m - - - ( 3 )
Wherein: t m = L m V × 60 - - - ( 4 )
In formula, t mfor strand exports required time, s from meniscus to crystallizer; L mfor the length of crystallizer, m; V is pulling rate, m/min;
The heat that cooling water is taken away calculates by following formula:
q w = ρ w · C w · ΔT · Q w F - - - ( 5 )
In formula, ρ wfor the density of water, 1.0 × 10 3kg/m 3; C wfor specific heat of water, 4.2 × 10 3j/ (kg DEG C); Δ T is crystallizer cooling range, DEG C; Q wfor crystallizer cooling water flow, m 3/ s; F is that strand contacts area with crystallizer, m 2;
By just can calculate B, and then the expression formula that obtains crystallizer transient heat flow density is as differential equation boundary condition in crystallizer;
Two cold-zones, adopt third boundary condition to calculate its heat flow density, are shown below:
q 2=h(T s-T w) (6)
In formula, h is water spray cooling heat transfer coefficient, W/ (m 2dEG C); T sfor casting blank surface temperature, DEG C; T wfor spraying cooling coolant-temperature gage, DEG C;
h=A+BW n (7)
In formula, A, B, n are empirical, test by experiment and are drawn by field measurement correction, and w is jet density, L/ (m 2s);
Air cooling zone, surface heat flux is pressed following formula and is determined:
q k=εσ[(T b+273) 4-(T a+273) 4] (8)
In formula, ε-casting billet surface blackness, generally gets 0.8;
σ-Boltzmann constant, W/m 2.k 4, get 5.67 × 10 -8;
T a-environment temperature, DEG C;
T b-casting blank surface temperature, DEG C;
The solidification and heat transfer differential equation (1) that primary condition and boundary condition substitution are set up based on casting machine structural parameters and process conditions carries out the time, space step-length is divided simultaneously, and solidification and heat transfer equation is solved, and can obtain the Solidification Parameters of strand.
By technique scheme, receive after " open and water " signal at section heat-tracking model, first calculate temperature field and the solid-liquid phase line position of playing first section in crystallizer from meniscus; In the time entering next computing cycle, upgrade tundish temperature, and the pulling rate of all sections, upgrade crystallizer width face and two cold each subregion water yields simultaneously, and crystallizer cooling water temperature rise data; In the time of a newly-generated section, set up a data storage cell for newly-generated section, the data storage cell that has gone out control zone section is discharged simultaneously, a time step Δ t is often walked in section, the current residing boundary condition of cutting into slices is once judged, and then the solidification and heat transfer differential equation of section is solved to the section temperature field and the solid-liquid phase line position that obtain now, repeat this process, until section moves to next slice position, next section repeats this process again, last until the control zone of cutting into slices out;
Following the tracks of mould in section heat receives after " going out tail base " signal, next computing cycle is by the not new section of regeneration, old section continues toward casting machine outlet mobile, calculate in real time its temperature field and solid-liquid phase line position simultaneously, and upgrade slice number, the section to the last producing has gone out control zone, just finishes whole hot tracing process;
Follow the tracks of mould in section heat and receive after " stopping watering " signal, empty the trace information to all sections, all slice information reset.
By technique scheme, in bulgs stress model, the bulgs stress computing formula of i roller place strand is:
ϵ i = 1600 S i δ i l i 2 - - - ( 9 )
The bulge amount of i roller place strand is:
δ i = ηaP l i 4 32 E e S i 3 t - - - ( 10 )
In formula (9) and (10), each parameter-definition is:
δ ithe bulge amount (mm) of the-the i roller place strand;
The form factor of a-consideration strand width;
The correction factor (for slab, η=1) of η-form factor a;
P ferrostatic pressure (kg/mm 2);
L ithe-the i roller spacing (mm);
E e-equivalent elastic modelling quantity, E e = T sol - T m T sol - 100 × 10 6 N / cm 2
T solthe setting temperature of-molten steel (DEG C);
T mthe mean temperature of-base shell, T m=(T sol+ T s)/2;
T sthe surface temperature of-base shell (DEG C);
S ithe shell thickness (mm) of-i roller place strand:
T-strand is by the time of a roll spacing;
Calculate for bulgs stress between i-1 roller and i roller, first determine from i two sections that roller is nearest, then obtain casting blank surface temperature and the shell thickness at i pair of rollers place with the surface temperature of these two sections and shell thickness interpolation; And then calculating equivalent elastic modulus E ewith bulgs stress ε i.
By technique scheme, described strand critical strain values is tested by experiment and is drawn by field measurement correction.
Principle of the present invention is:
The generation of continuous casting steel billet underbead crack is the result of various stress resultant effects, is the result that this steel grade high-temperature mechanics intensity can not be resisted combined stress.Stress source in casting blank solidification process mainly contains frictional force, ferrostatic pressure between crystallizer and base shell and acts on additional mechanical stress that the even thermal stress causing of bulge power, temperature distributing disproportionation that base shell causes, aligning stress that aligning process produces and deflector roll distortion, die misalignment etc. cause etc.
The present invention found through experiments, when near critical intensity combined stress exceedes the solidus temperature of this steel grade, the base shell at solid liquid interface place can not have been resisted the effect of stress and produced cracking and expand to solid phase, due to the own one-tenth of molten steel partly solidify state or when solid-state molten steel cannot supplement, therefore crackle is able to form strand is inner.Thermal strain and elongation strain on the strain producing due to stress in casting blank solidification process and total, casting blank solidification interface are all less than 0.1%, negligible; Casting machine radius is larger on aligning strain impact, and this is taken into full account in the time of design casting machine; And that bulgs stress accounts for the impact of overall strain is quite large, thereby it is also the principal element that produces underbead crack.
The present invention adopts Numerical Analytic Method, dynamic tracking according to the Mathematical Modeling of freezing mechanism to casting blank solidification process, the online bulgs stress that calculates in real time strand generation is realized the on-line prediction of slab underbead crack, and Inner Quality of Billet control and saving testing cost are had to certain guidance and reference.
Brief description of the drawings
Schematic diagram is divided in Fig. 1, section;
Fig. 2, continuous casting steel billet underbead crack on-line prediction method parameter input schematic flow sheet;
Fig. 3, continuous casting steel billet underbead crack on-line prediction method control flow chart;
Fig. 4, heat-tracking model calculation flow chart;
Fig. 5, bulgs stress model calculation flow chart.
Detailed description of the invention
Below in conjunction with accompanying drawing 1-5 and below embodiment the invention will be further described, but do not limit the present invention.
Embodiment 1: the Q235 steel that the slab caster upper section that is 10m at casting machine radius is 1600 × 200mm, online forecasting crack of billet, as shown in Figure 3, in whole flow process, parameter input flow chart is as shown in Figure 2 for whole process.
1, model data initialization procedure:
First confirm steel grade Q235, input steel grade physical parameter; Next reads technological parameter, hot-fluid parameter.
2, real time dynamic tracing:
Strand is divided into several sections from crystallizer meniscus to control zone end, dynamically follow the tracks of each section in life-span and positional information in the same time not, by the each section of dynamic tracking in " life-span " under in the same time not, positional information the real-time change along with pulling rate, middle bag temperature, each cooling subregion water yield, can determine each section at the solidification and heat transfer differential equation boundary condition under in the same time not, the differential equation is carried out to periodicity and solves, just can describe dynamically each section not in the same time, the temperature field at diverse location place; Each section is to include independently information unit; Described independent information comprises life-span, surface temperature, shell thickness, the position of section; All sections are connected together, and the temperature field that just can dynamically describe whole casting stream distributes.Obtain temperature field data or casting blank solidification parameter to carry out casting blank bulging stress deformation analysis.
As shown in Figure 1, strand is divided into several sections from crystallizer meniscus to control zone end, for a section shown in the section of left side, taking width of plate slab direction as X-axis, thickness direction is Y-axis, the direction of motion is that Z axis is set up coordinate system, represents the specifying information of the each step-length of this section with stereoscopic grid in inner side; And then ignoring on the basis of conducting heat along throwing direction, set up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section according to the flow process of Fig. 4.
3, casting blank bulging strain is calculated
Roller row arrangement parameter and the roller spacing of input 10m radius casting machine, read in casting blank surface temperature that the section solidification and heat transfer differential equation calculates, shell thickness substitution bulgs stress model simultaneously, calculate according to the flow process of Fig. 5 the bulgs stress that current slice produces, and carry out strain analysis.
4, the result of calculation prediction of output
All sections are stringed together, just can dynamically describe out the bulgs stress situation of whole casting stream, be worth and judge that whether strand can produce underbead crack, obtains crack of billet forecast result according to the critical strain of setting.

Claims (7)

1. a continuous casting steel billet underbead crack on-line prediction method, it is characterized in that: strand is divided into several sections from crystallizer meniscus to control zone end, ignoring on the basis of conducting heat along throwing direction, setting up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section; By section heat-tracking model, casting blank solidification process is dynamically followed the tracks of, all sections are connected together and dynamically describe the temperature field distribution of whole casting stream; Distribute or casting blank solidification parameter according to temperature field, by the online bulgs stress that calculates in real time strand generation of bulgs stress model, set the critical strain values of strand as the standard that produces underbead crack, in the time that bulgs stress exceedes strand critical strain values, there is underbead crack in strand simultaneously.
2. continuous casting steel billet underbead crack on-line prediction method according to claim 1, is characterized in that: said method specifically comprises the steps:
The first step: data initialization process: the model calculating parameter that reads steel grade information, steel grade physical parameter, technological parameter, device parameter and setting from one-level computer, second computer and three-level computer;
Second step: strand is divided into several sections from crystallizer meniscus to control zone end, for each section, taking width of plate slab direction as X-axis, thickness direction is Y-axis, the direction of motion is that Z axis is set up coordinate system, and then ignoring on the basis of conducting heat along throwing direction, set up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section;
The 3rd step: dynamically follow the tracks of each section, the independent information unit by each section is in the same time along with the real-time change of technological parameter, determines each section at the solidification and heat transfer differential equation boundary condition under in the same time not; The differential equation is carried out to periodicity and solves, dynamically describe each section not in the same time, the temperature field at diverse location place, all sections are connected together, the temperature field of dynamically describing whole casting stream distributes; Described independent information comprises life-span, surface temperature, shell thickness, the position of section; Middle bag temperature, temperature field, solid-liquid phase line position and pulling rate.
Heat-tracking model is followed the tracks of storage to the important information of all sections.Calculation procedure is inner has set up special data storage cell for these information;
The 4th step: carry out casting blank bulging and answer deformation analysis: in the strand temperature field that the heat-tracking model of cutting into slices in step 3 is calculated and shell thickness information substitution bulgs stress model, calculate the bulgs stress that current slice produces;
The 5th step: in the time that bulgs stress exceedes strand critical strain values, system sends the advance notice of strand generation underbead crack; , all sections are stringed together meanwhile, dynamically represent the bulgs stress situation of whole casting stream.
3. continuous casting steel billet underbead crack on-line prediction method according to claim 1 and 2, is characterized in that: described section heat-tracking model, represents by the following solidification and heat transfer differential equation:
ρc ∂ T ∂ t = λ ∂ 2 T ∂ x 2 + λ ∂ 2 T ∂ y 2 - - - ( 1 )
In formula: the density of ρ-steel, kg/m 3;
C-equivalent specific heat holds, J/kg.K;
λ-thermal conductivity factor, W/m. DEG C;
T-temperature, K;
In this model required input initial condition parameters is comprised to four kinds are respectively: steel grade and steel grade parameter; The technological parameter that comprises pouring temperature, pulling rate, casting blank cross-section size, the each subregion cooling water inflow of secondary, environment temperature; The casting machine structural parameters that comprise the cold subregion of casting machine two, roller row layout, arrangement of nozzles; The calculating parameter that comprises time step, space step-length, slice length, computing cycle;
The uniform temperature fields of whole section of steel billet of early solidification is consistent, all identical with cast temperature;
In casting blank solidification process, pass through successively crystallizer, two cold-zones, air cooling zone, all heats spread out of by surface, the cooling condition difference in each district, boundary condition is also different;
Crystallizer internal boundary condition:
The expression formula of crystallizer transient heat flow density is:
q = A - B t ( W / m 2 ) - - - ( 2 )
In formula, A, B are constant, conventionally get A=2 × 10 6~ 3 × 10 6w/m 2; B is air gap impact on heat flow density q in crystallizer short transverse;
By above formula, obtain the mean heat flux of crystallizer:
q ‾ = ∫ 0 t m ( A - B t ) dt t m = A - 2 3 B t m - - - ( 3 )
Wherein: t m = L m V × 60 - - - ( 4 )
In formula, t mfor strand exports required time, s from meniscus to crystallizer; L mfor the length of crystallizer, m; V is pulling rate, m/min;
The heat that cooling water is taken away calculates by following formula:
q w = ρ w · C w · ΔT · Q w F - - - ( 5 )
In formula, ρ wfor the density of water, 1.0 × 10 3kg/m 3; C wfor specific heat of water, 4.2 × 10 3j/ (kg DEG C); Δ T is crystallizer cooling range, DEG C; Q wfor crystallizer cooling water flow, m 3/ s; F is that strand contacts area with crystallizer, m 2;
By calculate B, and then the expression formula that obtains crystallizer transient heat flow density is as differential equation boundary condition in crystallizer;
Two cold-zones, adopt third boundary condition to calculate its heat flow density, are shown below:
q 2=h(T s-T w) (6)
In formula, h is water spray cooling heat transfer coefficient, W/ (m 2dEG C); T sfor casting blank surface temperature, DEG C; T wfor spraying cooling coolant-temperature gage, DEG C;
h=A+BW n (7)
In formula, A, B, n are empirical, test by experiment and are drawn by field measurement correction, and w is jet density, L/ (m 2s);
Air cooling zone, surface heat flux is pressed following formula and is determined:
q k=εσ[(T b+273) 4-(T a+273) 4] (8)
In formula, ε-casting billet surface blackness, generally gets 0.8;
σ-Boltzmann constant, W/m 2.k 4, get 5.67 × 10 -8;
T a-environment temperature, DEG C;
T b-casting blank surface temperature, DEG C;
The solidification and heat transfer differential equation (1) that primary condition and boundary condition substitution are set up based on casting machine structural parameters and process conditions carries out the time, space step-length is divided simultaneously, and solidification and heat transfer equation is solved to the Solidification Parameters that obtains strand.
4. continuous casting steel billet underbead crack on-line prediction method according to claim 3, it is characterized in that: receive after " open and water " signal at section heat-tracking model, first calculate temperature field and the solid-liquid phase line position of playing first section in crystallizer from meniscus; In the time entering next computing cycle, upgrade tundish temperature, and the pulling rate of all sections, upgrade crystallizer width face and two cold each subregion water yields simultaneously, and crystallizer cooling water temperature rise data; In the time of a newly-generated section, set up a data storage cell for newly-generated section, the data storage cell that has gone out control zone section is discharged simultaneously, a time step Δ t is often walked in section, the current residing boundary condition of cutting into slices is once judged, and then the solidification and heat transfer differential equation of section is solved to the section temperature field and the solid-liquid phase line position that obtain now, repeat this process, until section moves to next slice position, next section repeats this process again, last until the control zone of cutting into slices out;
Following the tracks of mould in section heat receives after " going out tail base " signal, next computing cycle is by the not new section of regeneration, old section continues toward casting machine outlet mobile, calculate in real time its temperature field and solid-liquid phase line position simultaneously, and upgrade slice number, the section to the last producing has gone out control zone, just finishes whole hot tracing process;
Follow the tracks of mould in section heat and receive after " stopping watering " signal, empty the trace information to all sections, all slice information reset.
5. according to the continuous casting steel billet underbead crack on-line prediction method described in claim 1 or 2 or 4, it is characterized in that bulgs stress model
In the bulgs stress computing formula of i roller place strand be:
ϵ i = 1600 S i δ i l i 2 - - - ( 9 )
The bulge amount of i roller place strand is:
δ i = ηaP l i 4 32 E e S i 3 t - - - ( 10 )
In formula (9) and (10), each parameter-definition is:
δ ithe bulge amount (mm) of the-the i roller place strand;
The form factor of a-consideration strand width;
The correction factor (for slab, η=1) of η-form factor a;
P-ferrostatic pressure (kg/mm 2);
L ithe-the i roller spacing (mm);
E e-equivalent elastic modelling quantity, E e = T sol - T m T sol - 100 × 10 6 N / cm 2
T solthe setting temperature of-molten steel (DEG C);
T mthe mean temperature of-base shell, T m=(T sol+ T s)/2;
T sthe surface temperature of-base shell (DEG C);
S ithe shell thickness (mm) of the-the i roller place strand:
T-strand is by the time of a roll spacing;
Calculate for bulgs stress between i-1 roller and i roller, first determine from i two sections that roller is nearest, then obtain casting blank surface temperature and the shell thickness at i pair of rollers place with the surface temperature of these two sections and shell thickness interpolation; And then calculating equivalent elastic modulus E ewith bulgs stress ε i.
6. according to the continuous casting steel billet underbead crack on-line prediction method described in claim 1 or 2 or 4, it is characterized in that: described strand critical strain values is tested by experiment and drawn by field measurement correction.
7. continuous casting steel billet underbead crack on-line prediction method according to claim 5, is characterized in that: described strand critical strain values is tested by experiment and drawn by field measurement correction.
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