CN114472551B - High-precision prediction method for average temperature of intermediate blank of wide and thick plate - Google Patents
High-precision prediction method for average temperature of intermediate blank of wide and thick plate Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
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- B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
- B21B37/74—Temperature control, e.g. by cooling or heating the rolls or the product
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- B21B1/00—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations
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Abstract
The invention discloses a high-precision prediction method for average temperature of a wide and thick plate intermediate blank, which relates to the technical field of steel production, and is characterized in that a wide and thick plate temperature solving equation set is established by adopting an implicit finite difference method based on a temperature partial differential equation, temperature fields of intermediate blanks with different thicknesses in the temperature waiting process are calculated, temperature distribution in the thickness direction under the condition of stable temperature is obtained, and then the difference value between the surface temperature and the average temperature is obtained; the temperature field is calculated by adopting the mechanism model, so that the temperature calculation precision can be ensured, and meanwhile, the average temperature of the billet surface temperature value can be quickly calculated by carrying out regression processing on the calculation result, thereby meeting the engineering application requirements.
Description
Technical Field
The invention relates to the technical field of steel production, in particular to a high-precision prediction method for average temperature of a wide and thick plate intermediate blank.
Background
The temperature of the rolled piece in the hot rolling process of the wide and thick plate determines the deformation resistance of metal, is a sensitive influence factor of mechanical parameters such as rolling force, moment, power and the like, and the temperature control precision of the intermediate blank is critical to the distribution of regulations and the performance of products. The traditional temperature model considers boundary conditions of air cooling, rolling and high-pressure water descaling in the temperature prediction process, but the prediction result of the temperature model gradually changes the actual value of the temperature of a rolled piece along with the increase of calculation time due to the influence of factors such as roller way cooling conditions, environment temperature and the like in the production process, so that the prediction of the force energy model also deviates from the actual value.
The secondary start rolling temperature of the wide and thick plate intermediate billet is a key for determining a subsequent rolling schedule, and if the temperature deviation is too large, the preset roll gap deviates from the thickness control standard, and even the rolling force is over-limited, so that finished product rolling cannot be finished. In order to improve the control precision of the secondary start rolling temperature of the intermediate billet of the wide and thick plate, a thermometer near a rolling mill can be used for temperature measurement and fed back to a temperature model for correcting a temperature predicted value, but as the force energy model uses the average temperature of the billet to calculate, the temperature measured value is the surface temperature of the billet, the surface temperature of the billets with different thicknesses is greatly different from the average temperature, and how to quickly obtain the average temperature which can meet the production precision requirement according to the surface temperature of the billet is provided for the force energy model has very important significance for high-precision presetting and stable rolling of a rolling procedure.
Disclosure of Invention
Aiming at the technical problems and overcoming the defects of the prior art, the invention provides a high-precision prediction method for the average temperature of a wide and thick plate intermediate blank, which comprises the following steps:
(1) Implicit finite difference method for solving temperature field
For the temperature drop process of the intermediate blank of the wide and thick plate, neglecting heat dissipation in the length and width directions, regarding the heat transfer process as a one-dimensional heat transfer process along the thickness direction of the steel blank, and expressing a heat conduction differential equation of an internal heat source by a formula (1) without considering
Wherein α=k/(ρc) is a thermal conductivity, ρ is a material density, c is a specific heat, and k is a thermal conductivity;
the temperature boundary conditions for a given heat exchange coefficient and surrounding medium are in the form of:
wherein h is the heat exchange coefficient between the surface of the steel billet and the outside, T W The temperature is the ambient temperature, and y is the thickness direction;
for the formula (1) and the formula (2), a finite difference quotient is adopted to replace a differential quotient to carry out numerical solution, and the formats of the first-order and second-order difference quotient are as follows:
replacing the temperature heat conduction differential equation and the boundary condition by using a finite difference implicit form, and listing a temperature solving equation set; before calculating the temperature, dividing nodes of the blank in the thickness direction;
the implicit finite difference format for the internal nodes derived from the heat conduction differential equation is:
wherein f=αΔt/(Δy) 2 ,Represents the temperature of node j-1 at time k+1, < >>Represents the temperature of node j at time k+1, < >>Represents the temperature of node j+1 at time k+1, < >>The temperature of the node j at the moment k is represented;
the implicit finite difference format of the boundary conditions is:
wherein B is i =hΔy/k,Represents the temperature of node M-1 at time k+1, ">Represents the temperature of boundary node M at time k+1, < >>The temperature of boundary node M at time k is represented;
knowing the initial temperature of the steel plate at the moment k, and listing a temperature solving equation set according to formulas (5) and (6) to obtain the temperature change condition of the blank at a given calculation time;
(2) Calculating the average temperature and the surface temperature of blanks with different thicknesses when the blanks are heated
In the process of heating the intermediate billet, the surface exchanges heat with air through heat radiation and convection, the surface temperature is gradually reduced, heat in the billet is transferred to the surface through heat transfer, so that the overall temperature of the billet is continuously reduced, when the heating time is long enough, the temperature difference between the surface and the core is stable near a certain value, namely a stable state is achieved, the core and the surface temperature of the billet are calculated after the heating time is longer based on the temperature model, the temperature change condition is obtained, and the average temperature can be calculated by using the average value of the surface and the core temperature;
according to the analysis, selecting intermediate blanks with different thicknesses to perform temperature drop calculation in the temperature waiting process so as to obtain the temperature difference between the core and the surface respectively;
(3) Predicting average temperature based on intermediate surface temperature measurements
The temperature difference between the core and the surface during stable temperature drop is obtained by calculating the temperature drop process of the temperature waiting process of intermediate billets with different thicknesses, and the temperature difference between the core and the surface gradually increases along with the increase of the thickness of the intermediate billets, but the increasing trend of the temperature difference gradually becomes gentle;
to describe the relationship between the thickness of the intermediate blank and the temperature difference of the heart table, regression processing is performed on the temperature calculation result as in formula (7)
y=A 0 +A 1 x 0.5 +A 2 x+A 3 x 1.5 +A 4 x 2 ⑦
Wherein x is the width of the intermediate blank, and y is the temperature difference between the core and the surface after the temperature is stabilized;
carrying out regression processing on the formula (7) by using the data obtained in the step (2) to obtain regression coefficients;
before the intermediate blank is heated and rolled, the surface temperature T of the blank is measured by a thermometer near the rolling mill surface Calculating the difference T between the core and the surface temperature of the blank by the formula (7) diff Obtaining the core temperature T of the intermediate blank core Is that
T core =T surface +T diff ⑧
The average temperature of the intermediate billet is:
T avg =(T core +T surface )/2 ⑨
the calculated average temperature T of the intermediate blank avg The rolling start temperature of the secondary model is replaced, and the accuracy can be ensured because the rolling start temperature is calculated according to the actual measured value, so that the calculation accuracy of the rolling model for the preset regulation of the rolling mill can be greatly improved.
The technical scheme of the invention is as follows:
in the foregoing method for predicting the average temperature of the intermediate blank of the wide and thick plate with high precision, the thickness of the intermediate blank selected in the step (2) is 40, 60, 80, 100, 120, 140, 160mm, the initial temperature is set to 1000 ℃, and the core, the surface temperature and the average value data in the steady state are obtained based on the temperature model calculation.
The high-precision prediction method for the average temperature of the intermediate blank of the wide and thick plate is characterized in that the obtained regression coefficient is as follows: a is that 0 =-8.40528,A 1 =5.60183,A 2 =-0.93327,A 3 =0.13985,A 4 =-0.00586。
The beneficial effects of the invention are as follows:
(1) Based on a temperature partial differential equation, an implicit finite difference method is adopted to establish a wide and thick plate temperature solving equation set, the temperature field of intermediate blanks with different thicknesses in the temperature waiting process is calculated, the temperature distribution in the thickness direction under the condition of stable temperature is obtained, and then the difference value between the surface temperature and the average temperature is obtained; the temperature field is calculated by adopting the mechanism model, so that the temperature calculation precision can be ensured, and meanwhile, the average temperature of the billet surface temperature value can be quickly calculated by carrying out regression processing on the calculation result, thereby meeting the engineering application requirements;
(2) According to the method, the temperature distribution values from inside to outside of the intermediate blanks with different thicknesses when the intermediate blanks are heated can be obtained, the intermediate blanks are heated for a long time, the difference value between the surface temperature and the core temperature tends to be stable, the temperature difference value between the surface temperature and the average temperature is obtained after a temperature field with a certain time length is calculated for the intermediate blanks with different thicknesses, the curves of the difference values between the thickness of the intermediate blanks and the temperature are obtained through nonlinear regression, the average temperature value of the intermediate blanks can be rapidly calculated through measuring the surface temperature of the intermediate blanks, and the feedback energy model is fed back, so that the accumulated deviation of the temperature model in the long-time calculation process is eliminated, and the preset precision of a regulation is greatly improved;
(3) According to the invention, the final rolling hit rate of the wide and thick plate rolling mill is improved by improving the average temperature prediction precision of the intermediate billet, and the hit rate is improved from 94.5% to 98.3%; the structural performance of the steel plate is improved, the quality objection is reduced, the improvement rate of the steel plate performance is reduced from 0.56% to 0.35% by improving the finishing temperature hit of the wide and thick plate, the annual yield is calculated according to 160 ten thousand tons, and the annual benefit is 268.8 ten thousand yuan.
Drawings
FIG. 1 is a schematic view of a node division of a blank in a half thickness direction;
FIG. 2 is a graph showing the change of core and surface temperature when an intermediate billet with a thickness of 50mm is heated;
FIG. 3 shows the temperature difference of the core table after a blank of different thickness is heated for a period of time.
Detailed Description
The high-precision prediction method for the average temperature of the intermediate blank of the wide and thick plate provided by the embodiment comprises the following steps:
(1) Implicit finite difference method for solving temperature field
For the temperature drop process of the intermediate blank of the wide and thick plate, neglecting heat dissipation in the length and width directions, regarding the heat transfer process as a one-dimensional heat transfer process along the thickness direction of the steel blank, and expressing a heat conduction differential equation of an internal heat source by a formula (1) without considering
Wherein α=k/(ρc) is a thermal conductivity, ρ is a material density, c is a specific heat, and k is a thermal conductivity;
the temperature boundary conditions for a given heat exchange coefficient and surrounding medium are in the form of:
wherein h is the heat exchange coefficient between the surface of the steel billet and the outside, T W The temperature is the ambient temperature, and y is the thickness direction;
for the formula (1) and the formula (2), a finite difference quotient is adopted to replace a differential quotient to carry out numerical solution, and the formats of the first-order and second-order difference quotient are as follows:
replacing the temperature heat conduction differential equation and the boundary condition by using a finite difference implicit form, and listing a temperature solving equation set; before calculating the temperature, nodes are required to be divided into the thickness direction of the blank, and FIG. 1 is a schematic diagram of node division in the half thickness direction of the blank, wherein M nodes are divided into the half thickness direction;
the implicit finite difference format for the internal nodes derived from the heat conduction differential equation is:
wherein f=αΔt/(Δy) 2 ,Represents the temperature of node j-1 at time k+1, < >>Represents the temperature of node j at time k+1, < >>Represents the temperature of node j+1 at time k+1, < >>The temperature of the node j at the moment k is represented;
the implicit finite difference format of the boundary conditions is:
wherein B is i =hΔy/k,Represents the temperature of node M-1 at time k+1, ">Represents the temperature of boundary node M at time k+1, < >>The temperature of boundary node M at time k is represented;
knowing the initial temperature of the steel plate at the moment k, and listing a temperature solving equation set according to formulas (5) and (6) to obtain the temperature change condition of the blank at a given calculation time;
(2) Calculating the average temperature and the surface temperature of blanks with different thicknesses when the blanks are heated
In the process of heating the intermediate billet, the surface exchanges heat with air through heat radiation and convection, the surface temperature is gradually reduced, the heat in the billet is transferred to the surface through heat transfer, the whole temperature of the billet is continuously reduced, and when the heating time is long enough, the temperature difference between the surface and the core is stable near a certain value, namely a stable state is achieved;
as shown in fig. 2, the thickness of the intermediate billet is 30mm, the initial temperature is 1000 ℃, the core and surface temperatures of the billet are calculated after a period of time to be warmed based on the above temperature model, so as to obtain the temperature change condition, and as can be seen from the graph, when the period of time to be warmed is about 25s, the difference between the core and the surface temperatures reaches a stable state, the difference is about 11.8 ℃, namely, if the surface temperature of the billet is measured at the moment, the core temperature of the billet can be estimated, and the average temperature can be calculated by using the average value of the surface and the core temperature;
according to the analysis, intermediate blanks with different thicknesses are selected for temperature drop calculation in the temperature waiting process to respectively obtain the temperature difference between the core and the surface, the thickness of the selected intermediate blank is 40, 60, 80, 100, 120, 140 and 160mm, the initial temperature is set to be 1000 ℃, and the core, the surface temperature and the average value data in the steady state are obtained based on temperature model calculation are shown in table 1:
TABLE 1 temperature variation of intermediate billets of different thickness at stand-by temperature
(3) Predicting average temperature based on intermediate surface temperature measurements
By calculating the temperature drop process of the temperature waiting process of intermediate billets with different thicknesses, the temperature difference between the core and the surface during stable temperature drop is obtained, as shown in fig. 3, it can be seen that as the thickness of the intermediate billets is increased, the temperature difference between the core and the surface is gradually increased, but the increasing trend of the temperature difference is gradually gentle;
to describe the relationship between the thickness of the intermediate blank and the temperature difference of the heart table, regression processing is performed on the temperature calculation result as in formula (7)
y=A 0 +A 1 x 0.5 +A 2 x+A 3 x 1.5 +A 4 x 2 ⑦
Wherein x is the width of the intermediate blank, and y is the temperature difference between the core and the surface after the temperature is stabilized;
regression processing is carried out on the formula (7) by using the data in the table 1, and regression coefficients are obtained as follows: a is that 0 =-8.40528,A 1 =5.60183,A 2 =-0.93327,A 3 =0.13985,A 4 =-0.00586;
Before the intermediate blank is heated and rolled, the surface temperature T of the blank is measured by a thermometer near the rolling mill surface Calculating the difference T between the core and the surface temperature of the blank by the formula (7) diff Obtaining the core temperature T of the intermediate blank core Is that
T core =T surface +T diff ⑧
The average temperature of the intermediate billet is:
T avg =(T core +T surface )/2 ⑨
the calculated average temperature T of the intermediate blank avg The rolling start temperature of the secondary model is replaced, and the accuracy can be ensured because the rolling start temperature is calculated according to the actual measured value, so that the calculation accuracy of the rolling model for the preset regulation of the rolling mill can be greatly improved.
Calculating the temperature of an intermediate blank in the rolling process of the wide and thick plate, wherein the process parameters of a rolled product are as follows:
steel grade: Q345B; blank dimensions (thickness x width x length, mm): 180.0× 2260.0 × 2850.0; finished size (thickness x width, mm): 20.0X 3200.0; tapping temperature: 1150 ℃; thickness of intermediate blank: 54.5mm.
According to the steps, the thickness of an intermediate blank after rough rolling of a wide-thick plate rolling mill is 54.5mm, a roller way between rough rolling and finish rolling is heated, the temperature is reduced to a set temperature for secondary start rolling, the surface temperature of a billet measured by a thermometer before a finishing mill is started to be 920 ℃, the thickness of the blank is brought in according to a regression formula (7), and the temperature difference is calculated to be: t (T) diff =20.95; from this, the core temperature of the intermediate billet at this time is: t (T) diff = 940.95 ℃, so its average temperature is: t (T) avg =(T core +T surface )/2=930.475℃。
At this time, the initial temperature at which the rolling model performs the protocol preset calculation should use the average temperature calculated by the above method. For thicker intermediate blanks, the temperature difference between the surface and the core is larger, and the temperature iterative calculation value in the model gradually deviates from the actual temperature due to longer temperature waiting time; if the measured temperature is directly used, the difference between the surface temperature and the average temperature is larger, and the learning speed and the accuracy between model passes in the subsequent rolling process are affected. The method is simple, suitable for engineering application, and capable of ensuring the required initial temperature calculated by the force energy model, and has important practical significance for improving the preset precision of the rolling procedure.
In addition to the embodiments described above, other embodiments of the invention are possible. All technical schemes formed by equivalent substitution or equivalent transformation fall within the protection scope of the invention.
Claims (3)
1. A high-precision prediction method for average temperature of a wide and thick plate intermediate blank is characterized by comprising the following steps of: the method comprises the following steps:
(1) Implicit finite difference method for solving temperature field
For the temperature drop process of the intermediate blank of the wide and thick plate, neglecting heat dissipation in the length and width directions, regarding the heat transfer process as a one-dimensional heat transfer process along the thickness direction of the steel blank, and expressing a heat conduction differential equation of an internal heat source by a formula (1) without considering
Wherein α=k/(ρc) is a thermal conductivity, ρ is a material density, c is a specific heat, and k is a thermal conductivity;
the temperature boundary conditions for a given heat exchange coefficient and surrounding medium are in the form of:
wherein h is the heat exchange coefficient between the surface of the steel billet and the outside, T W The temperature is the ambient temperature, and y is the thickness direction;
for the formula (1) and the formula (2), a finite difference quotient is adopted to replace a differential quotient to carry out numerical solution, and the formats of the first-order and second-order difference quotient are as follows:
replacing the temperature heat conduction differential equation and the boundary condition by using a finite difference implicit form, and listing a temperature solving equation set; before calculating the temperature, dividing nodes of the blank in the thickness direction;
the implicit finite difference format for the internal nodes derived from the heat conduction differential equation is:
wherein f=αΔt/(Δy) 2 ,Represents the temperature of node j-1 at time k+1, < >>Represents the temperature of node j at time k+1, < >>Represents the temperature of node j+1 at time k+1, < >>The temperature of the node j at the moment k is represented;
the implicit finite difference format of the boundary conditions is:
wherein B is i =hΔy/k,Represents the temperature of node M-1 at time k+1, ">Represents the temperature of boundary node M at time k+1, < >>The temperature of boundary node M at time k is represented;
knowing the initial temperature of the steel plate at the moment k, and listing a temperature solving equation set according to formulas (5) and (6) to obtain the temperature change condition of the blank at a given calculation time;
(2) Calculating the average temperature and the surface temperature of blanks with different thicknesses when the blanks are heated
In the process of heating the intermediate billet, the surface exchanges heat with air through heat radiation and convection, the surface temperature is gradually reduced, heat in the billet is transferred to the surface through heat transfer, so that the overall temperature of the billet is continuously reduced, when the heating time is long enough, the temperature difference between the surface and the core is stable near a certain value, namely a stable state is achieved, the core and the surface temperature of the billet are calculated after the heating time is longer based on the temperature model, the temperature change condition is obtained, and the average temperature can be calculated by using the average value of the surface and the core temperature;
according to the analysis, selecting intermediate blanks with different thicknesses to perform temperature drop calculation in the temperature waiting process so as to obtain the temperature difference between the core and the surface respectively;
(3) Predicting average temperature based on intermediate surface temperature measurements
The temperature difference between the core and the surface during stable temperature drop is obtained by calculating the temperature drop process of the temperature waiting process of intermediate billets with different thicknesses, and the temperature difference between the core and the surface gradually increases along with the increase of the thickness of the intermediate billets, but the increasing trend of the temperature difference gradually becomes gentle;
to describe the relationship between the thickness of the intermediate blank and the temperature difference of the heart table, regression processing is performed on the temperature calculation result as in formula (7)
y=A 0 +A 1 x 0.5 +A 2 x+A 3 x 1.5 +A 4 x 2 ⑦
Wherein x is the width of the intermediate blank, and y is the temperature difference between the core and the surface after the temperature is stabilized;
carrying out regression processing on the formula (7) by using the data obtained in the step (2) to obtain regression coefficients;
before the intermediate blank is heated and rolled, the surface temperature T of the blank is measured by a thermometer near the rolling mill surface Calculating the difference T between the core and the surface temperature of the blank by the formula (7) diff Obtaining the core temperature T of the intermediate blank core Is that
T core =T surface +T diff ⑧
The average temperature of the intermediate billet is:
T avg =(T core +T surface )/2 ⑨
the calculated average temperature T of the intermediate blank avg The rolling start temperature of the secondary model is replaced, and the accuracy can be ensured because the rolling start temperature is calculated according to the actual measured value, so that the calculation accuracy of the rolling model for the preset regulation of the rolling mill can be greatly improved.
2. The high-precision prediction method for average temperature of a wide and thick plate intermediate blank according to claim 1, wherein the method comprises the following steps: and (3) the thickness of the intermediate blank selected in the step (2) is 40, 60, 80, 100, 120, 140 and 160mm, the initial temperature is set to 1000 ℃, and the core, surface temperature and average value data in the steady state are obtained based on the temperature model calculation.
3. The high-precision prediction method for average temperature of wide and thick plate intermediate blanks according to claim 2, wherein the method comprises the following steps of: the regression coefficients were obtained as: a is that 0 =-8.40528,A 1 =5.60183,A 2 =-0.93327,A 3 =0.13985,A 4 =-0.00586。
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CN101045242A (en) * | 2006-03-29 | 2007-10-03 | 宝山钢铁股份有限公司 | Optimization control method for intermediate blanket heating device |
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