CN103920859B - A kind of continuous casting steel billet underbead crack on-line prediction method - Google Patents

Abstract

The present invention relates to 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 along on the basis of throwing direction heat transfer, set 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, the thermo parameters method of the whole casting stream of Dynamic profiling that all sections are connected together; According to thermo parameters method or casting blank solidification parameter, the bulgs stress of strand generation is calculated online in real time by bulgs stress model, set the critical strain values of strand as the standard producing underbead crack, when bulgs stress exceedes strand critical strain values, namely there is underbead crack in strand simultaneously.Real-time online slab underbead crack can be predicted, thus save a large amount of testing cost.

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

Develop a circular economy along with country advocates energetically, smelter is also more and more higher to energy-saving and cost-reducing requirement.Hot charging and hot rolling of continuous casting slab and continuous casting billet continuous rolling technology have the obvious characteristics such as energy consumption is low, reduced investment, lumber recovery are high, with short production cycle, thus become the most active research field of continuous-casting art.Past, the slab quality that conticaster is produced mainly is evaluated with the quality of strand under cold conditions, in process of production, continuous casting billet underbead crack degree and distribution need detect by sufur printing or hot acid erosion low power and obtain, and the sampling of this cold conditions and the traditional slab quality control method checked obviously can not meet that heat is sent, the requirement of hot charging and direct rolling process.Therefore, the online forecasting system setting up slab quality is subject to extensive concern.

The underbead crack of continuous casting billet is become a useful person to the combination property of steel and the rolling of strand 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, thus save a large amount of testing cost.

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 along on the basis of throwing direction heat transfer, set 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, the thermo parameters method of the whole casting stream of Dynamic profiling that all sections are connected together; According to thermo parameters method or casting blank solidification parameter, the bulgs stress of strand generation is calculated online in real time by bulgs stress model, set the critical strain values of strand as the standard producing underbead crack, when bulgs stress exceedes strand critical strain values, namely 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 reading steel grade information, steel grade physical parameter, technological parameter, device parameter and setting from primary 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, with width of plate slab direction for X-axis, thickness direction is Y-axis, the direction of motion is that Z axis sets up coordinate system, and then ignoring along on the basis of throwing direction heat transfer, set up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section;

3rd step: dynamically follow the tracks of each section, by the independent information element of each section not in the same time along with the real-time change of technological parameter, determine each section not in the same time under solidification and heat transfer differential equation boundary condition; Carry out periodicity to the differential equation to solve, each section of Dynamic profiling not in the same time, the temperature field at diverse location place, all sections are connected together, the thermo parameters method of the whole casting stream of Dynamic profiling; Described independent information comprises life-span of section, surface temperature, shell thickness, position; Tundish temperature, temperature field, solid-liquid phase line position and pulling rate.

Heat-tracking model carries out tracking to the important information of all sections and stores.Calculation procedure is inner establishes special data storage cell for these information;

4th step: carry out casting blank bulging and answer deformation analysis: the strand temperature field calculated by heat-tracking model of cutting into slices in step 3 and shell thickness information substitute in bulgs stress model, calculate the bulgs stress that current slice produces;

5th step: when bulgs stress exceedes strand critical strain values, namely system sends the advance notice that strand produces 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:

$\mathrm{\ρc}\frac{\∂T}{\∂t}=\mathrm{\λ}\frac{{\∂}^{2}T}{{\∂x}^2}+\mathrm{\λ}\frac{{\∂}^{2}T}{{\∂y}^2}---\left(1\right)$

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;

Initial condition parameters being comprised four kinds and is respectively of required input in this model: steel grade and steel grade parameter; Comprise the technological parameter of pouring temperature, pulling rate, casting blank cross-section size, each subregion cooling water inflow of secondary, environment temperature; Comprise the casting machine structural parameters of the cold subregion of casting machine two, roller row layout, arrangement of nozzles; Comprise the calculating parameter of time step, spatial mesh size, slice length, computing cycle;

The uniform temperature fields of early solidification whole section of steel billet is consistent, all identical with cast temperature;

Successively through crystallizer in casting blank solidification process, two cold-zones, air cooling zone, all heats spread out of by surface, and the cooling condition in each district is different, and boundary condition is also different;

Crystallizer internal boundary condition:

The expression formula of crystallizer transient heat flow density is:

$q=A-B\sqrt{t}(W/m^2)---\left(2\right)$

In formula, A, B are constant, usually get A=2 × 10 ⁶~ 3 × 10 ⁶w/m ²; B then characterizes air gap impact on heat flow density q in crystallizer short transverse;

By above formula, the mean heat flux of crystallizer can be obtained:

$\stackrel{\‾}{q}=\frac{{\∫}_0^{t_m}(A-B\sqrt{t})\mathrm{dt}}{t_m}=A-\frac{2}{3}B\sqrt{t_m}---\left(3\right)$

Wherein: $t_m=\frac{L_m}{V}\×60---\left(4\right)$

In formula, t _mfor strand to export from meniscus to crystallizer needed for time, s; L _mfor the length of crystallizer, m; V is pulling rate, m/min;

The heat that cooling water is taken away is calculated by following formula:

$q_w=\frac{{\mathrm{\ρ}}_w\·C_w\·\mathrm{\ΔT}\·Q_w}{F}---\left(5\right)$

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 strand and crystallizer contact area, m ²;

By just B can be calculated, and then the expression formula obtaining 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-spraying control 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, and test by experiment and drawn by field measurement correction, w is jet density, L/ (m ²s);

Air cooling zone, surface heat flux is determined by following formula:

q _k=εσ[(T _b+273) ⁴-(T _a+273) ⁴]（8）

ε in formula-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;

Primary condition and boundary condition are substituted into the solidification and heat transfer differential equation (1) set up based on casting machine structural parameters and process conditions, carries out the time simultaneously, spatial mesh size divides, and solidification and heat transfer equation is solved, the Solidification Parameters of strand can be obtained.

By technique scheme, after section heat-tracking model receives " open and water " signal, first calculate temperature field and the solid-liquid phase line position of playing first section in crystallizer from meniscus; Whenever entering next computing cycle, then 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; Whenever a newly-generated section, then set up a data storage cell for newly-generated section, the data storage cell having gone out control zone section is discharged simultaneously, a time step Δ t is often walked in section, then the current residing boundary condition of section is once judged, and then the cutting temperature field and solid-liquid phase line position that obtain now are solved to the solidification and heat transfer differential equation of section, repeat this process, until section moves to next slice position, next section repeats this process again, last until control zone of cutting into slices out;

After section heat tracking mould receives " going out tail base " signal, next computing cycle is by section new for not regeneration, old section continues to move toward caster outlet, calculate its temperature field and solid-liquid phase line position in real time simultaneously, and upgrade slice number, the section to the last produced has gone out control zone, just terminates whole hot tracing process;

After section heat tracking mould receives " stopping watering " signal, then empty the trace information to all sections, namely reset all slice information.

By technique scheme, in bulgs stress model, the bulgs stress computing formula of i-th roller place strand is:

${\mathrm{\ϵ}}_i=\frac{1600S_i{\mathrm{\δ}}_i}{{l_i}^2}---\left(9\right)$

The bulge amount of i-th roller place strand is:

${\mathrm{\δ}}_i=\frac{\mathrm{\ηaP}{l_i}^4}{32E_e{S_i}^3}\sqrt{t}---\left(10\right)$

In formula (9) and (10), each parameter is defined as:

δ _ithe bulge amount (mm) of-the i-th 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 _i-the i-th roller spacing (mm);

E _e-equivalent elastic modelling quantity, $E_e=\frac{T_{\mathrm{sol}}-T_m}{T_{\mathrm{sol}}-100}\×{10}^{6}N/{\mathrm{cm}}^2$

T _solthe setting temperature (DEG C) of-molten steel;

T _mthe mean temperature of-base shell, T _m=(T _sol+ T _s)/2;

T _sthe surface temperature (DEG C) of-base shell;

S _ithe shell thickness (mm) of-the i-th roller place strand:

T-strand is by the time of a roll spacing;

Bulgs stress between the i-th-1 roller and i-th roller is calculated, first determines from two nearest sections of i-th roller, then obtain casting blank surface temperature and the shell thickness at i-th pair of roller place with the surface temperature of these two sections and shell thickness interpolation; And then calculate 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 effect, is the result that this steel grade high-temperature mechanics intensity can not resist combined stress.The aligning stress that stress source in casting blank solidification process mainly contains frictional force between crystallizer and base shell, ferrostatic pressure acts on bulge power that base shell causes, even thermal stress, the straightening process caused of temperature distributing disproportionation produces and the additional mechanical stress etc. that deflector roll is out of shape, die misalignment etc. causes.

The present invention found through experiments, during critical intensity near the solidus temperature that combined stress exceedes 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 solid-state time molten steel cannot supplement, therefore crackle be able to strand inside formed.Thermal strain on the strain produced due to the stress in casting blank solidification process and total, casting blank solidification interface and elongation strain are all less than 0.1%, negligible; Casting machine radius is comparatively large on aligning strain impact, and this is taken into full account when designing casting machine; And the impact that bulgs stress accounts for overall strain is quite large, it is thus also the principal element producing underbead crack.

The present invention adopts Numerical Analytic Method, according to the Mathematical Modeling of freezing mechanism to the dynamic tracking of casting blank solidification process, the online bulgs stress calculating strand generation in real time realizes the on-line prediction of slab underbead crack, controls and save testing cost to have certain guidance and reference to Inner Quality of Billet.

Accompanying drawing explanation

Fig. 1, section divide schematic diagram;

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 at the casting machine radius slab caster upper section that is 10m being 1600 × 200mm, online forecasting crack of billet, as shown in Figure 3, in whole flow process, parameters input flow chart as shown in Figure 2 for whole process.

1, model data initialization procedure:

First steel grade Q235 is confirmed, 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, the each section of dynamic tracking is in not life-span in the same time and positional information, by dynamically follow the tracks of each section not in the same time under " life-span ", positional information is along with the real-time change of pulling rate, tundish temperature, each cooling subregion water yield, can determine each section not in the same time under solidification and heat transfer differential equation boundary condition, carry out periodicity to the differential equation to solve, just can describe dynamically each section not in the same time, the temperature field at diverse location place; Each section includes independently information unit; Described independent information comprises life-span of section, surface temperature, shell thickness, position; All sections are connected together, just can the whole thermo parameters method casting stream of Dynamic profiling.Obtain temperature field data or casting blank solidification parameter to carry out casting blank bulging stress and 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, with width of plate slab direction for X-axis, thickness direction is Y-axis, the direction of motion is that Z axis sets up coordinate system, represents the specifying information of each step-length of this section with stereoscopic grid in inner side; And then ignoring along on the basis of throwing direction heat transfer, 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 calculation

The roller row arrangement parameter of input 10m radius casting machine and roller spacing, the casting blank surface temperature that the solidification and heat transfer of the reading section simultaneously differential equation calculates, shell thickness substitute in bulgs stress model, according to the bulgs stress that the workflow management current slice of Fig. 5 produces, and carry out strain analysis.

4, the result of calculation prediction of output

All sections are stringed together, just can go out whole bulgs stress situation of casting stream by Dynamic profiling, be worth according to the critical strain of setting and judge whether strand can produce underbead crack, obtains crack of billet forecast result.

Claims (6)

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 along on the basis of throwing direction heat transfer, set 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, the thermo parameters method of the whole casting stream of Dynamic profiling that all sections are connected together; According to thermo parameters method or casting blank solidification parameter, the bulgs stress of strand generation is calculated online in real time by bulgs stress model, set the critical strain values of strand as the standard producing underbead crack, when bulgs stress exceedes strand critical strain values, namely there is underbead crack in strand simultaneously;

Said method specifically comprises the steps:

The first step: data initialization process: the model calculating parameter reading steel grade information, steel grade physical parameter, technological parameter, device parameter and setting from primary 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, with width of plate slab direction for X-axis, thickness direction is Y-axis, the direction of motion is that Z axis sets up coordinate system, and then ignoring along on the basis of throwing direction heat transfer, set up the section heat-tracking model of the two-dimentional solidification and heat transfer of each section;

3rd step: dynamically follow the tracks of each section, by the independent information element of each section not in the same time along with the real-time change of technological parameter, determine each section not in the same time under solidification and heat transfer differential equation boundary condition; Carry out periodicity to the differential equation to solve, each section of Dynamic profiling not in the same time, the temperature field at diverse location place, all sections are connected together, the thermo parameters method of the whole casting stream of Dynamic profiling; Described independent information comprises life-span of section, surface temperature, shell thickness, position, tundish temperature, temperature field, solid-liquid phase line position and pulling rate;

Heat-tracking model carries out tracking to the important information of all sections and stores; Calculation procedure is inner establishes special data storage cell for these information;

4th step: carry out casting blank bulging and answer deformation analysis: the strand temperature field calculated by heat-tracking model of cutting into slices in step 3 and shell thickness information substitute in bulgs stress model, calculate the bulgs stress that current slice produces;

5th step: when bulgs stress exceedes strand critical strain values, namely system sends the advance notice that strand produces underbead crack; , all sections are stringed together meanwhile, dynamically represent the bulgs stress situation of whole casting stream.

2. continuous casting steel billet underbead crack on-line prediction method according to claim 1, is characterized in that: described section heat-tracking model, represents by the following solidification and heat transfer differential equation:

$\mathrm{\ρ}c\frac{\∂T}{\∂t}=\mathrm{\λ}\frac{{\∂}^{2}T}{\∂x^2}+\mathrm{\λ}\frac{{\∂}^{2}T}{\∂y^2}---\left(1\right)$

In formula: the density of ρ-steel, kg/m ³;

C-equivalent specific heat holds, J/kgK;

λ-thermal conductivity factor, W/m DEG C;

T-temperature, K;

Initial condition parameters being comprised four kinds and is respectively of required input in this model: steel grade and steel grade parameter; Comprise the technological parameter of pouring temperature, pulling rate, casting blank cross-section size, each subregion cooling water inflow of secondary, environment temperature; Comprise the casting machine structural parameters of the cold subregion of casting machine two, roller row layout, arrangement of nozzles; Comprise the calculating parameter of time step, spatial mesh size, slice length, computing cycle;

The uniform temperature fields of early solidification whole section of steel billet is consistent, all identical with cast temperature;

Successively through crystallizer in casting blank solidification process, two cold-zones, air cooling zone, all heats spread out of by surface, and the cooling condition in each district is different, and boundary condition is also different;

Crystallizer internal boundary condition:

The expression formula of crystallizer transient heat flow density is:

$q=A-B\sqrt{t}(W/m^2)---\left(2\right)$

In formula, A, B are constant, usually 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:

$\stackrel{\‾}{q}=\frac{{\∫}_0^{t_m}(A-B\sqrt{t})dt}{t_m}=A-\frac{2}{3}B\sqrt{t_m}---\left(3\right)$

Wherein: $t_m=\frac{L_m}{V}\×60---\left(4\right)$

In formula, t _mfor strand to export from meniscus to crystallizer needed for time, s; L _mfor the length of crystallizer, m; V is pulling rate, m/min;

The heat that cooling water is taken away is calculated by following formula:

$q_w=\frac{{\mathrm{\ρ}}_w\·C_w\·\mathrm{\Δ}T\·Q_w}{F}---\left(5\right)$

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 strand and crystallizer contact area, m ²;

By calculate B, and then the expression formula obtaining 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-spraying control 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, and test by experiment and drawn by field measurement correction, W is jet density, L/ (m ²s);

Air cooling zone, surface heat flux is determined by following formula:

Q _k=ε σ [(Τ _b+ 273) ⁴-(Τ _a+ 273) ⁴] ε-casting billet surface blackness in (8) formula, generally get 0.8;

σ-Boltzmann constant, W/m ²k ⁴, get 5.67 × 10 ^-8;

Τ _a-environment temperature, DEG C;

Τ _b-casting blank surface temperature, DEG C;

Primary condition and boundary condition are substituted into the solidification and heat transfer differential equation (1) set up based on casting machine structural parameters and process conditions, carries out the time simultaneously, spatial mesh size divides, and solidification and heat transfer equation is solved to the Solidification Parameters obtaining strand.

3. continuous casting steel billet underbead crack on-line prediction method according to claim 2, it is characterized in that: after section heat-tracking model receives " open and water " signal, first calculate temperature field and the solid-liquid phase line position of playing first section in crystallizer from meniscus; Whenever entering next computing cycle, then 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; Whenever a newly-generated section, then set up a data storage cell for newly-generated section, the data storage cell having gone out control zone section is discharged simultaneously, a time step Δ t is often walked in section, then the current residing boundary condition of section is once judged, and then the cutting temperature field and solid-liquid phase line position that obtain now are solved to the solidification and heat transfer differential equation of section, repeat this process, until section moves to next slice position, next section repeats this process again, last until control zone of cutting into slices out;

After section heat tracking mould receives " going out tail base " signal, next computing cycle is by section new for not regeneration, old section continues to move toward caster outlet, calculate its temperature field and solid-liquid phase line position in real time simultaneously, and upgrade slice number, the section to the last produced has gone out control zone, just terminates whole hot tracing process;

After section heat tracking mould receives " stopping watering " signal, then empty the trace information to all sections, namely reset all slice information.

4. the continuous casting steel billet underbead crack on-line prediction method according to claim 1 or 2 or 3, is characterized in that bulgs stress model

In the bulgs stress computing formula of i-th roller place strand be:

${\mathrm{\ϵ}}_i=\frac{1600S_i{\mathrm{\δ}}_i}{{l_i}^2}---\left(9\right)$

The bulge amount of i-th roller place strand is:

${\mathrm{\δ}}_i=\frac{{\mathrm{\ηaPl}}_i^4}{32E_e{S}_i^3}\sqrt{t}---\left(10\right)$

In formula (9) and (10), each parameter is defined as:

δ _ithe bulge amount of-the i-th roller place strand, unit mm;

The form factor of a-consideration strand width;

The correction factor of η-form factor a, for slab, η=1;

P-ferrostatic pressure, units/kg/mm ²;

L _i-the i-th roller spacing, unit mm;

E _e-equivalent elastic modelling quantity, $E_e=\frac{T_{sol}-T_m}{T_{sol}-100}\×{10}^{6}N/{\mathrm{cm}}^2$

T _solthe setting temperature DEG C of-molten steel;

T _mthe mean temperature of-base shell, T _m=(T _sol+ T _s)/2;

The surface temperature DEG C of Ts-base shell;

S _ithe shell thickness of-the i-th roller place strand, unit mm:

T-strand is by the time of a roll spacing;

Bulgs stress between the i-th-1 roller and i-th roller is calculated, first determines from two nearest sections of i-th roller, then obtain casting blank surface temperature and the shell thickness at i-th pair of roller place with the surface temperature of these two sections and shell thickness interpolation; And then calculate equivalent elastic modulus E _ewith bulgs stress ε _i.

5. the continuous casting steel billet underbead crack on-line prediction method according to claim 1 or 2 or 3, is characterized in that: described strand critical strain values is tested by experiment and drawn by field measurement correction.

6. continuous casting steel billet underbead crack on-line prediction method according to claim 4, is characterized in that: described strand critical strain values is tested by experiment and drawn by field measurement correction.