CN103761370A - Method for predicting strip surface coefficients of heat transfer in hot rolling procedures - Google Patents

Abstract

The invention discloses a method for predicting strip surface coefficients of heat transfer in hot rolling procedures. The method includes predicting strip surface coefficients of heat transfer by the aid of a finite-element model and heat transfer modifier formulas; determining the strip surface coefficients of heat transfer according to comparison values of measured temperatures and computed temperatures of strips. The method has the advantages that the method is specially used for predicting the strip surface coefficients of heat transfer in the strip hot rolling procedures, change of the strip surface coefficients of heat transfer in the integral rolling procedures can be acquired, information is detailed and accurate, the strip surface coefficients of heat transfer are high in prediction precision, and setting and optimizing parameters can be provided for the rolling procedures; the method is high in applicability and computational efficiency and is applicable to roughing mills and finishing mills in hot continuous rolling procedures.

Description

A kind of Forecasting Methodology of process of plate belt hot rolling surface film thermal conductance

Technical field

The invention belongs to rolling technical field, particularly a kind of Forecasting Methodology of process of plate belt hot rolling surface film thermal conductance.

Background technology

Process of plate belt hot rolling strip surface film thermal conductance prediction is to realize the important parameter that process parameter optimizing, cooling device characteristic research, temperature field are accurately controlled and improved the quality of products.Hot rolling process plate belt experience process air cooler, Cooling Process and rolling contact process, thereby surface film thermal conductance and environment temperature, heat eliminating medium characteristic, the type of cooling, steel plate state and technological parameter etc. all closely related, increased surface film thermal conductance prediction and measured difficulty.

The acquisition of the course of hot rolling coefficient of heat transfer at present mainly relies on in-site measurement and reverse radiant heat method.Although in-site measurement is convenient, acceptor, objective factor affect larger, can not obtain comprehensive and accurate coefficient of heat transfer information; Oppositely radiant heat method mainly relies on scene temperature measurement data, utilizes heat transfer principle to carry out coefficient regression, and the method depends on site test condition and experimental data, computing method underaction, and computational accuracy is often lower.In addition, oppositely radiant heat method is mainly used in the roller surface coefficient of heat transfer and rolls the convection transfer rate prediction of rear laminar cooling process strip surface at present.

Summary of the invention

(1) technical matters that will solve

The object of the invention is and the professional shortcoming such as not strong low for the whole bag of tricks precision of predicting hot rolling process plate belt surface film thermal conductance in prior art, a kind of method of predicting hot rolling process plate belt surface film thermal conductance is provided.

(2) technical scheme

In order to solve the problems of the technologies described above, the invention provides a kind of Forecasting Methodology of process of plate belt hot rolling surface film thermal conductance, comprising:

Step 1: carry out dividing elements on hot rolled strip Width and thickness direction, set up finite element analysis model;

Step 2: gather the parameter of process of plate belt hot rolling, comprising:

Control parameter, comprise number of stages, every one-phase maximum iteration time, specification error;

Material thermal physical property parameter, comprises heat-conduction coefficient, specific heat, density;

Dividing elements information, comprises plate width unit number and thickness unit number;

Strip initial information, comprises width, thickness and surface temperature;

The rolling parameter of the operation of rolling, comprises initial slab thickness, the exit thickness of passage rolling, draught pressure, dephosphorization discharge;

Temperature and time information, comprises roller temperature, de-scaling coolant-temperature gage, environment temperature, strip surface phase temperature, every one-phase elapsed-time standards;

Step 3: determine initial coefficient of heat transfer h

Course of hot rolling comprises air cooling stage, dephosphorization or water cooling stage and rolling sequence, and the coefficient of heat transfer initial value of operation of rolling different phase is as follows:

(1) hot rolled strip is in the air cooling stage, and coefficient of heat transfer initial value through type (1) calculates:

HC _A，0＝1.1×[(T-T _air)/b] ^0.25+σ·ε·(T+T _air)(T ²+T _air ²)(W/m ²K) (1)

Wherein: σ=5.67 × 10 ^-8w/ (m ²k ⁴); ε is coefficient of blackness, and T is strip surface temperature, T _airfor environment temperature, b is plate width;

(2) hot rolled strip is in dephosphorization or water cooling stage, and coefficient of heat transfer initial value through type (2) calculates:

HC _W，0＝124.7×w ^0.663×10 ^{-0.00147(T-273.16)}(W/m ²K) (2)

Wherein, w is jet density, and T is strip surface temperature;

(3) hot rolled strip is at rolling sequence, and coefficient of heat transfer initial value through type (3) calculates:

HC _R，0＝695p _m-34400(W/m ²K) (3)

In formula: p _mfor draught pressure;

Step 4:

Utilize FEM (finite element) calculation ultimate principle, calculate the type function of the ginseng unit such as quadrilateral;

Step 5: the system of linear equations of setting up temperature field finite element solving

(1) set up thermal conduction differential equation, the fundamental equation of Two-Dimensional Heat Conduction is:

$k(\frac{{\∂}^{2}T}{\∂x^2}+\frac{{\∂}^{2}T}{\∂y^2})-\mathrm{\ρc}\frac{\∂T}{\∂t}=0---\left(4\right)$

Wherein: T transient temperature; ρ density of material; C material specific heat; The t time; K heat-conduction coefficient;

(2) utilize Eulerian equation two-dimensional heat equation to be become to equivalent general culvert expression formula under the given boundary condition of step 1 and starting condition:

The equivalent Functional expression formula of each unit is expressed as:

$I^{\left(e\right)}=\frac{1}{2}{\∫\∫}_{S^e}\left[k\right[{\left(\frac{\∂T^{\left(e\right)}}{\∂x}\right)}^2+{\left(\frac{\∂T^{\left(e\right)}}{\∂y}\right)}^2]+2\mathrm{\ρc}\frac{\∂T^{\left(e\right)}}{\∂t}{T}^{\left(e\right)}]\mathrm{dS}+\frac{1}{2}{\∫}_{l^e}h(T^{\left(e\right)}-T_{\∞})\mathrm{dl}---\left(5\right)$

S is Heat transfer boundary area, and l is Heat transfer boundary length, and h is the coefficient of heat transfer, and e represents each unit;

According to the variational principle of heat conduction problem, functional formula (5) is asked to single order partial derivative zero setting, discrete unit is assembled, the stiffness matrix of unit is assembled into integral rigidity matrix, obtain two-dimensional finite element method and solve the system equation in temperature field:

$\left[K_T\right]\left\{T\right\}+\left[K_3\right]\left\{\frac{\∂T}{\∂t}\right\}=\left\{p\right\}---\left(6\right)$

Wherein: [K _t]-temperature stiffness matrix,

[K ₃]-alternating temperature matrix,

p}-constant term row formula,

{ T}-temperature row formula; E-unit sum; Subscript e represents each unit;

Concerning each unit, stiffness matrix, alternating temperature matrix and constant term can solve by through type (7):

${\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HSA0000099815560000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{1\mathrm{ij}}^{\left(e\right)}={\&Integral;\&Integral;}_{S^e}k(\frac{{\&PartialD;N}_i}{\&PartialD;x}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;x}+\frac{{\&PartialD;N}_i}{\&PartialD;y}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;y})\mathrm{dS}---\left(7a\right)$

$K_{2\mathrm{ij}}^{\left(e\right)}={\&Integral;}_{L^e}h{N}_i{N}_j\mathrm{dL}---\left(7b\right)$

${\mathrm{<figure-callout\; id="3"\; label="K"\; filenames="HSA0000099815560000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{3\mathrm{ij}}^{\left(e\right)}={\&Integral;\&Integral;}_{S^e}\mathrm{\&rho;c}{N}_i{N}_j\mathrm{dS}---\left(7c\right)$

${\left\{p_i\right\}}^{\left(e\right)}={\&Integral;}_{L^e}h{T}_{\&infin;}{N}_i\mathrm{dL}---\left(7d\right)$

Wherein: N-type function; I, j node serial number;

(3) utilize 2 backward difference forms, system equation be converted into the system of linear equations that transient state temperature field solves, the temperature in system equation (6) is expressed as to 2 backward difference forms to time partial derivative:

$\frac{\&PartialD;T}{\&PartialD;t}=\frac{1}{\mathrm{\&Delta;t}}(T_t-T_{t-\mathrm{\&Delta;t}})---\left(8\right)$

Time backward difference form (8) and system equation formula (6) connection in temperature field are separated, are obtained the system of linear equations of solution of Temperature:

$\left(\right[K_T]+\frac{1}{\mathrm{\&Delta;t}}[K_3\left]\right){\left\{T\right\}}_t=\frac{1}{\mathrm{\&Delta;t}}\left[K_3\right]{\left\{T\right\}}_{t-\mathrm{\&Delta;t}}+\left\{p\right\}---\left(9\right)$

Step 6: the system of linear equations (9) forming is solved, obtain n time period strip surface temperature, will calculate and obtain n time period strip surface temperature and this moment strip surface temperature measured value T _{m, t}compare, if error is less than specification error value, the output board belt surface coefficient of heat transfer; If do not meet setting value and iterations is less than maximum iteration time, according to the temperature error correction coefficient of heat transfer, recalculate temperature;

Wherein, the concrete correction formula of the different phase coefficient of heat transfer is shown in (10), (11) and (12):

(1) the air cooling stage plate belt surface coefficient of heat transfer calculates by formula (10) and calculates:

${\mathrm{HC}}_{A,n}=(1+\frac{T_{A,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{A,n-1}---\left(10\right)$

Wherein: T _{a, n}for the n time period in air cooling stage finishes chronothermometer calculation value, T _{m, n}measured temperature when the air cooling stage, the n time period finished;

(2) water-cooled or the de-scaling stage plate belt surface coefficient of heat transfer calculate by formula (11) and calculate:

${\mathrm{HC}}_{W,n}=(1+\frac{T_{W,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{W,n-1}---\left(11\right)$

Wherein: T _{w, n}for water-cooled or n time period in de-scaling stage finish chronothermometer calculation value, T _{m, n}measured temperature while finishing for water-cooled or de-scaling process n time period;

(3) operation of rolling strip surface film thermal conductance calculates by formula (12) and calculates:

${\mathrm{HC}}_{R,n}=(1+\frac{T_{R,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{R,n-1}---\left(12\right)$

Wherein: T _{r, n}for the operation of rolling n time period finishes chronothermometer calculation value, T _{m, n}measured temperature while finishing for the operation of rolling n time period.

(3) beneficial effect

Maximum efficiency of the present invention is: the present invention is directed to process of plate belt hot rolling prediction hot rolled strip surface film thermal conductance, based on iterative and finite element technique, predict that plate strip rolling process is at each stage surface film thermal conductance, can obtain whole operation of rolling strip surface film thermal conductance changes, information is detailed accurately, can obtain very high strip surface film thermal conductance precision of prediction, for the operation of rolling provides, set and Optimal Parameters; Exploitation specific program, application is strong, and counting yield is high; The present invention is applicable to roughing mill and the finishing mill of during Hot Strip Rolling, thereby optimizes rolling mill practice and improve cooling control accuracy, rolling efficiency and product quality.

Accompanying drawing explanation

Fig. 1 is the finite element model figure of an embodiment of the present invention;

Fig. 2 is the process flow diagram of the process of plate belt hot rolling surface film thermal conductance Forecasting Methodology of an embodiment of the present invention;

Fig. 3 is the coefficient of heat transfer predicted value variation diagram of each stage of Hot Strip in Rough Rolling process;

Fig. 4 is strip finishing stands coefficient of heat transfer predicted value variation diagram.

In Fig. 1: i is element number, j is node serial number, and H is thickness, and W is width, AB and the thermal insulation of AD border, BC and CD heat transfer boundary.

In Fig. 3 and Fig. 4: R1-1, R1-2, R1-3 are rough rolling process the first frame rolling, one, two, three passages; R2-1, R2-2, R2-3, R2-4, R2-5 be respectively rough rolling process the second frame rolling first, second, third and fourth, five passages; F1, F2, F3, F4, F5, F6, F7 are respectively seven frame operations of rolling of finishing stands.

Embodiment

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.Following examples are used for illustrating the present invention, but are not used for limiting the scope of the invention.Below in conjunction with drawings and Examples, the present invention is further described.

The invention provides a kind of process of plate belt hot rolling surface film thermal conductance Forecasting Methodology, as described in Figure 1, concrete steps are as follows:

1. according to hot rolled strip width and gauge, division unit data, set up finite element analysis model:

While 1. solving hot rolled strip surface film thermal conductance, suppose as follows:

roll to size and be far longer than width and thickness direction size, therefore ignore the conduction of rolling direction heat;

width coboundary heat transfer boundary condition and symmetrical geometry, consider 1/2nd sections;

operation of rolling tabularium side is identical with the upper and lower surface coefficient of heat transfer;

plastic yield and friction are ignored on operation of rolling temperature rise impact;

2. according to plate width and gauge, horizontal end face is carried out to dividing elements, on Width and thickness direction, unit is evenly divided, and sets up finite element analysis model, and cell node is numbered, computing node coordinate; Unit and node serial number through-thickness and Width increase gradually, and wherein i is element number, and j is node serial number, and H is thickness, and W is width, AB and the thermal insulation of AD border, BC and CD heat transfer boundary; Take A point coordinate as zero, calculate each node coordinate;

2. the parameter that gathers process of plate belt hot rolling, comprises control parameter, material thermal physical property parameter, dividing elements information, temperature and time information, the rolling parameter of initial information and the different operations of rolling;

Control parameter and comprise number of stages, every one-phase maximum iteration time, specification error;

Material thermal physical property parameter comprises heat-conduction coefficient, specific heat, density;

Dividing elements packets of information rubbing board bandwidth unit number and thickness unit number;

Strip initial information comprises width, thickness and surface temperature;

The rolling parameter of the operation of rolling comprises initial slab thickness, the exit thickness of passage rolling, draught pressure, dephosphorization discharge;

Temperature and time information comprises roller temperature, de-scaling coolant-temperature gage, environment temperature, strip surface phase temperature, every one-phase elapsed-time standards.

3. according to operation of rolling physical condition and rolling sequence, determine initial coefficient of heat transfer h, course of hot rolling comprises air cooling stage, dephosphorization or water cooling stage and rolling sequence; The coefficient of heat transfer initial value that calculates whole operation of rolling different phase is as follows:

(1) hot rolled strip is in process air cooler, strip surface heat exchanging mode is mainly radiation and natural convection, radiation heat transfer coefficient is equivalent to convection transfer rate, thereby process air cooler strip surface equivalent heat transfer coefficient initial value through type (1) calculates:

HC _A，0＝1.1×[(T-T _air)/b] ^0.25+σ·ε·(T+T _air)(T ²+T _air ²)(W/m ²K) (1)

Wherein: σ is Stefan-Boltzman constant, σ=5.67 × 10 ^-8w/ (m ²k ⁴); ε is coefficient of blackness, and the relational expression of ε and temperature is ε=0.125 (T/1000) ²-0.38 (T/1000)+1.1, T (K) is strip surface temperature, T _air(K) be environment temperature, b display plate bandwidth, HC is the coefficient of heat transfer, and subscript A represents the coefficient of heat transfer cooling in air, and subscript 0 represents initial time.

(2) hot rolled strip is in dephosphorize by high pressure water or Cooling Process, endogenous pyrogen intensity

value is zero; Surface heat exchanging mode is forced convection, and Cooling Process convection transfer rate initial value through type (2) calculates:

HC _W，0＝124.7×w ^0.663×10 ^{-0.00147(T-273.16)}(W/m ²K) (2)

Wherein, w (L/minm ²) be jet density; T (K) strip surface temperature, subscript W represents the coefficient of heat transfer of water quench.

(3) in the operation of rolling, between strip and roll, contact heat-exchanging is main thermal loss mode, and contact heat exchange coefficient is relevant with draught pressure.Contact heat exchange coefficient initial value through type (3) calculates:

HC _R，0＝695p _m-34400(W/m ²K) (3)

In formula: p _m(MPa)-draught pressure, subscript R represents strip and the roll contact process coefficient of heat transfer.

4. utilize conventional FEM (finite element) calculation ultimate principle, calculate the type function of the ginseng unit such as quadrilateral.

5. utilize spatial domain finite element discretization and the time domain finite difference method of combining to set up the system of linear equations of temperature field finite element solving,

(1) take the first law of thermodynamics as according to setting up thermal conduction differential equation, suppose material heat conduction isotropy, ignoring under endogenous pyrogen condition, the fundamental equation of Two-Dimensional Heat Conduction is:

$k(\frac{{\&PartialD;}^{2}T}{\&PartialD;x^2}+\frac{{\&PartialD;}^{2}T}{\&PartialD;y^2})-\mathrm{\&rho;c}\frac{\&PartialD;T}{\&PartialD;t}=0---\left(4\right)$

Wherein: T is strip transient temperature (K); ρ density of material (kg/m ³); C material specific heat (J/ (kgK)); T is time (s); K heat-conduction coefficient (W/ (mK)); X, y is coordinate.

(2) utilize Eulerian equation Two-Dimensional Heat Conduction problem to be become to equivalent general culvert expression formula under the given boundary condition of step 1 and starting condition and ask extreme-value problem:

The equivalent Functional expression formula of each unit is expressed as:

$I^{\left(e\right)}=\frac{1}{2}{\&Integral;\&Integral;}_{S^e}\left[k\right[{\left(\frac{\&PartialD;T^{\left(e\right)}}{\&PartialD;x}\right)}^2+{\left(\frac{\&PartialD;T^{\left(e\right)}}{\&PartialD;y}\right)}^2]+2\mathrm{\&rho;c}\frac{\&PartialD;T^{\left(e\right)}}{\&PartialD;t}{T}^{\left(e\right)}]\mathrm{dS}+\frac{1}{2}{\&Integral;}_{l^e}h(T^{\left(e\right)}-T_{\&infin;})\mathrm{dl}---\left(5\right)$

According to the variational principle of heat conduction problem, functional formula (5) is asked to single order partial derivative zero setting, according to conventional Combination of finite elements method, discrete unit is assembled, the stiffness matrix of unit is assembled into integral rigidity matrix, obtains two-dimensional finite element method and solve the system equation in temperature field:

$\left[K_T\right]\left\{T\right\}+\left[K_3\right]\left\{\frac{\&PartialD;T}{\&PartialD;t}\right\}=\left\{p\right\}---\left(6\right)$

Wherein: [K _t]-temperature stiffness matrix,

[K ₃]-alternating temperature matrix,

p}-constant term row formula,

{ T}-temperature row formula; E-unit sum; Subscript e represents each unit.

Concerning each unit, stiffness matrix, alternating temperature matrix and constant term can solve by through type (7):

${\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HSA0000099815560000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{1\mathrm{ij}}^{\left(e\right)}={\&Integral;\&Integral;}_{S^e}k(\frac{{\&PartialD;N}_i}{\&PartialD;x}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;x}+\frac{{\&PartialD;N}_i}{\&PartialD;y}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;y})\mathrm{dS}---\left(7a\right)$

${\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA0000099815560000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{ij}}^{\left(e\right)}={\&Integral;}_{L^e}h{N}_i{N}_j\mathrm{dL}---\left(7b\right)$

${\mathrm{<figure-callout\; id="3"\; label="K"\; filenames="HSA0000099815560000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{3\mathrm{ij}}^{\left(e\right)}={\&Integral;\&Integral;}_{S^e}\mathrm{\&rho;c}{N}_i{N}_j\mathrm{dS}---\left(7c\right)$

${\left\{p_i\right\}}^{\left(e\right)}={\&Integral;}_{L^e}h{T}_{\&infin;}{N}_i\mathrm{dL}---\left(7d\right)$

Wherein: k heat-conduction coefficient (W/ (mK)); ρ density of material (kg/m ³); C material specific heat (J/ (kgK)); The h-coefficient of heat transfer, N-type function; I, j node serial number; S is Heat transfer boundary area; L is Heat transfer boundary length.

(3) utilize 2 backward difference forms, system equation be converted into the system of linear equations that transient state temperature field solves, the temperature in system equation (6) is expressed as to 2 backward difference forms to time partial derivative:

$\frac{\&PartialD;T}{\&PartialD;t}=\frac{1}{\mathrm{\&Delta;t}}(T_t-T_{t-\mathrm{\&Delta;t}})---\left(8\right)$

Time backward difference form (8) and system equation formula (6) connection in temperature field are separated, are obtained the system of linear equations of solution of Temperature:

$\left(\right[K_T]+\frac{1}{\mathrm{\&Delta;t}}[K_3\left]\right){\left\{T\right\}}_t=\frac{1}{\mathrm{\&Delta;t}}\left[K_3\right]{\left\{T\right\}}_{t-\mathrm{\&Delta;t}}+\left\{p\right\}---\left(9\right)$

6. initial coefficient of heat transfer different phase being calculated by formula (1), (2) and (3) is brought formula (7) into, then the system of linear equations (9) forming is solved to the strip surface temperature that obtains different rolling sequences, will calculate and obtain n time period strip surface temperature and this moment strip surface temperature measured value T _{m, t}compare (measured value can have on-the-spot equipment to obtain or obtain by temperature sensor), if error is less than specification error value, exporting this moment strip surface film thermal conductance before (can certainly be the strip surface film thermal conductance of this moment preset range, the coefficient of heat transfer in for example this moment, strip surface film thermal conductance now can calculate acquisition by initial formula); If do not meet setting value and iterations is less than maximum iteration time, the temperature comparison point when stage of returning finishes, according to the temperature computation error correction coefficient of heat transfer, recalculates this phase temperature, iterates and calculates until error meets the demands.Calculating finishes this stage coefficient of heat transfer calculated value of rear output.

The modification method Main Basis observed temperature of the coefficient of heat transfer and the fiducial value of accounting temperature, if accounting temperature, higher than observed temperature, is calculated with heat exchange efficiency low so, the coefficient of heat transfer is little, need to improve the coefficient of heat transfer, otherwise, reduce coefficient of heat transfer value, so that approach the actual coefficient of heat transfer.The concrete correction formula of the different phase coefficient of heat transfer is shown in (10), (11) and (12).

(1) process air cooler strip surface film thermal conductance calculates by formula (10) and calculates:

${\mathrm{HC}}_{A,n}=(1+\frac{T_{A,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{A,n-1}---\left(10\right)$

Wherein: T _{a, n}for the process air cooler n time period finishes chronothermometer calculation value, T _{m, n}measured temperature while finishing for the process air cooler n time period.

(2) de-scaling or Cooling Process strip surface film thermal conductance calculate by formula (11) and calculate:

${\mathrm{HC}}_{W,n}=(1+\frac{T_{W,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{W,n-1}---\left(11\right)$

Wherein: T _{w, n}for water-cooled or de-scaling process n time period finish chronothermometer calculation value, T _{m, n}measured temperature while finishing for water-cooled or de-scaling process n time period;

(3) operation of rolling strip surface film thermal conductance calculates by formula (12) and calculates:

${\mathrm{HC}}_{R,n}=(1+\frac{T_{R,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{R,n-1}---\left(12\right)$

Wherein: T _{r, n}for the operation of rolling n time period finishes chronothermometer calculation value, T _{m, n}measured temperature while finishing for the operation of rolling n time period.

The present invention is directed to process of plate belt hot rolling prediction hot rolled strip surface film thermal conductance, based on iterative and finite element technique, predict that plate strip rolling process is at each stage surface film thermal conductance, and utilize correction formula to revise the coefficient of heat transfer in each stage, can obtain whole operation of rolling strip surface film thermal conductance changes, information is detailed accurately, can obtain very high strip surface film thermal conductance precision of prediction, for the operation of rolling provides, set and Optimal Parameters.

After step 6, also comprise the steps:

7. according to the error of calculation, judge whether the coefficient of heat transfer calculating of certain one-phase in the operation of rolling finishes; If this stage coefficient of heat transfer calculates, do not finish, iterations increases, and continues to calculate; If this stage coefficient of heat transfer calculates, finish, according to judging whether the whole operation of rolling finishes computing time, if be more than or equal to actual rolling time computing time, the whole operation of rolling coefficient of heat transfer calculates and finishes, otherwise, enter next stage.

8. according to judging that the coefficient of heat transfer of each stage of whole during Hot Strip Rolling calculates the T.T. of the operation of rolling, whether finish; If the whole during Hot Strip Rolling coefficient of heat transfer calculates, do not finish, image data is proceeded next stage calculating so, if finished, program predicts that each stage coefficient of heat transfer process finishes.

Maximum efficiency of the present invention is: the present invention is directed to process of plate belt hot rolling, by formula translation, develop special iterative algorithm program prediction hot rolled strip surface film thermal conductance, can obtain whole operation of rolling strip surface film thermal conductance changes, information is detailed accurately, can obtain very high strip surface film thermal conductance precision of prediction, for the operation of rolling provides, set and Optimal Parameters; Exploitation specific program, application is strong, and counting yield is high; The present invention is applicable to roughing mill and the finishing mill of during Hot Strip Rolling.

Below in conjunction with embodiment, Forecasting Methodology of the present invention is described:

First according to hot rolled strip width and gauge, division unit data, set up finite element analysis model (as (the finite element model figure as shown in Fig. 1), utilize finite element ultimate principle (iterative algorithm software flow pattern as shown in Figure 2) to utilize formula translation exploitation hot rolled strip coefficient of heat transfer prediction iterative computation program, prediction strip is at each stage surface film thermal conductance, thus the precision of prediction of raising hot rolled strip surface temperature.

Selecting a steel grade course of hot rolling is calculating object, utilizes iterative algorithm analysis from going out heating furnace, to finish rolling, to finish the coefficient of heat transfer Changing Pattern of whole process, is exemplified below:

Example 1: a certain steel mill during Hot Strip Rolling.Rough rolling process has 4 frames, and the second frame is reversible frame; Finishing stands has 7 frames.Reversible frame rolling 5 passages, all the other frame rolling a time.

Example: design conditions are in Table 1.

Table 1 design conditions

Example 2: whole during Hot Strip Rolling, rolling 15 passages altogether, exit thickness and the draught pressure of every a time rolling are shown in Table 2.

Table 2 passage exit thickness

Employing table 1 design conditions and table 2 passage exit thickness and draught pressure are predicted a certain steel mill hot rolling process plate belt surface film thermal conductance Changing Pattern.Result of calculation is as Fig. 3 and Fig. 4, and wherein Fig. 3 is this process coefficient of heat transfer variation of roughing exit of coming out of the stove; Fig. 4 is that roughing exports to finish rolling and exports this process coefficient of heat transfer and change.Can find out, the process air cooler coefficient of heat transfer is substantially close, is about 80 (W/m ^2.k), the de-scaling process coefficient of heat transfer is about 1.25 × 10 ⁴(W/m ^2.k), the operation of rolling is because drafts is different with process conditions, coefficient of heat transfer difference, and finishing stands the 5th frame operation of rolling coefficient of heat transfer maximum is about 1.5 × 10 ⁵(W/m ^2.k), rough rolling process and the finishing stands thermo-contact coefficient of heat transfer are shown in Table 3.

Table 3 coefficient of heat transfer

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, do not departing under the prerequisite of the technology of the present invention principle; can also make some improvement and replacement, these improvement and replacement also should be considered as protection scope of the present invention.

Claims (2)

1. a Forecasting Methodology for process of plate belt hot rolling surface film thermal conductance, is characterized in that, comprising:

Step 1: carry out dividing elements on hot rolled strip Width and thickness direction, set up finite element analysis model;

Step 2: gather the parameter of process of plate belt hot rolling, comprising:

Control parameter, comprise number of stages, every one-phase maximum iteration time, specification error;

Material thermal physical property parameter, comprises heat-conduction coefficient, specific heat, density;

Dividing elements information, comprises plate width unit number and thickness unit number;

Strip initial information, comprises width, thickness and surface temperature;

The rolling parameter of the operation of rolling, comprises initial slab thickness, the exit thickness of passage rolling, draught pressure, dephosphorization discharge;

Temperature and time information, comprises roller temperature, de-scaling coolant-temperature gage, environment temperature, strip surface phase temperature, every one-phase elapsed-time standards;

Step 3: determine initial coefficient of heat transfer h

Course of hot rolling comprises air cooling stage, dephosphorization or water cooling stage and rolling sequence, and the coefficient of heat transfer initial value of operation of rolling different phase is as follows:

(1) hot rolled strip is in the air cooling stage, and coefficient of heat transfer initial value through type (1) calculates:

HC _A，0＝1.1×[(T-T _air)/b] ^0.25+σ·ε·(T+T _air)(T ²+T _air ²)(W/m ²K) (1)

Wherein: σ=5.67 × 10 ^-8w/ (m ²k ⁴); ε is coefficient of blackness, and T is strip surface temperature, T _airfor environment temperature, b is plate width;

(2) hot rolled strip is in dephosphorization or water cooling stage, and coefficient of heat transfer initial value through type (2) calculates:

HC _W，0＝124.7×w ^0.663×10 ^{-0.00147(T-273.16)}(W/m ²K) (2)

Wherein, w is jet density;

(3) hot rolled strip is at rolling sequence, and coefficient of heat transfer initial value through type (3) calculates:

HC _R，0＝695p _m-34400(W/m ²K) (3)

In formula: p _mfor draught pressure;

Step 4:

Utilize FEM (finite element) calculation ultimate principle, calculate the type function of the ginseng unit such as quadrilateral;

Step 5: the system of linear equations of setting up temperature field finite element solving

(1) set up thermal conduction differential equation, the fundamental equation of Two-Dimensional Heat Conduction is:

$k(\frac{{\&PartialD;}^{2}T}{\&PartialD;x^2}+\frac{{\&PartialD;}^{2}T}{\&PartialD;y^2})-\mathrm{\&rho;c}\frac{\&PartialD;T}{\&PartialD;t}=0---\left(4\right)$

Wherein: T transient temperature; ρ density of material; C material specific heat; The t time; K heat-conduction coefficient;

(2) utilize Eulerian equation two-dimensional heat equation to be become to equivalent general culvert expression formula under the given boundary condition of step 1 and starting condition:

The equivalent Functional expression formula of each unit is expressed as:

$I^{\left(e\right)}=\frac{1}{2}{\&Integral;\&Integral;}_{S^e}\left[k\right[{\left(\frac{\&PartialD;T^{\left(e\right)}}{\&PartialD;x}\right)}^2+{\left(\frac{\&PartialD;T^{\left(e\right)}}{\&PartialD;y}\right)}^2]+2\mathrm{\&rho;c}\frac{\&PartialD;T^{\left(e\right)}}{\&PartialD;t}{T}^{\left(e\right)}]\mathrm{dS}+\frac{1}{2}{\&Integral;}_{l^e}h(T^{\left(e\right)}-T_{\&infin;})\mathrm{dl}---\left(5\right)$

S is Heat transfer boundary area, and l is Heat transfer boundary length, and h is the coefficient of heat transfer, and e represents each unit;

According to the variational principle of heat conduction problem, functional formula (5) is asked to single order partial derivative zero setting, discrete unit is assembled, the stiffness matrix of unit is assembled into integral rigidity matrix, obtain two-dimensional finite element method and solve the system equation in temperature field:

$\left[K_T\right]\left\{T\right\}+\left[K_3\right]\left\{\frac{\&PartialD;T}{\&PartialD;t}\right\}=\left\{p\right\}---\left(6\right)$

Wherein: [K _t]-temperature stiffness matrix, [K ₃]-alternating temperature matrix,

p}-constant term row formula,

{ T}-temperature row formula; E-unit sum; Subscript e represents each unit;

Concerning each unit, stiffness matrix, alternating temperature matrix and constant term can solve by through type (7):

$K_{1\mathrm{ij}}^{\left(e\right)}={\&Integral;\&Integral;}_{S^e}k(\frac{{\&PartialD;N}_i}{\&PartialD;x}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;x}+\frac{{\&PartialD;N}_i}{\&PartialD;y}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;y})\mathrm{dS}---\left(7a\right)$

$K_{2\mathrm{ij}}^{\left(e\right)}={\&Integral;}_{L^e}h{N}_i{N}_j\mathrm{dL}---\left(7b\right)$

$K_{3\mathrm{ij}}^{\left(e\right)}={\&Integral;\&Integral;}_{S^e}\mathrm{\&rho;c}{N}_i{N}_j\mathrm{dS}---\left(7c\right)$

${\left\{p_i\right\}}^{\left(e\right)}={\&Integral;}_{L^e}h{T}_{\&infin;}{N}_i\mathrm{dL}---\left(7d\right)$

Wherein: N-type function; I, j node serial number;

(3) utilize 2 backward difference forms, system equation be converted into the system of linear equations that transient state temperature field solves, the temperature in system equation (6) is expressed as to 2 backward difference forms to time partial derivative:

$\frac{\&PartialD;T}{\&PartialD;t}=\frac{1}{\mathrm{\&Delta;t}}(T_t-T_{t-\mathrm{\&Delta;t}})---\left(8\right)$

Time backward difference form (8) and system equation formula (6) connection in temperature field are separated, are obtained the system of linear equations of solution of Temperature:

$\left(\right[K_T]+\frac{1}{\mathrm{\&Delta;t}}[K_3\left]\right){\left\{T\right\}}_t=\frac{1}{\mathrm{\&Delta;t}}\left[K_3\right]{\left\{T\right\}}_{t-\mathrm{\&Delta;t}}+\left\{p\right\}---\left(9\right)$

Step 6: the system of linear equations (9) forming is solved, obtain n time period strip surface temperature, will calculate and obtain n time period strip surface temperature and this moment strip surface temperature measured value T _{m, t}compare, if error is less than specification error value, the output board belt surface coefficient of heat transfer; If do not meet setting value and iterations is less than maximum iteration time, according to the temperature error correction coefficient of heat transfer, recalculate temperature;

Wherein, the concrete correction formula of the different phase coefficient of heat transfer is shown in (10), (11) and (12):

(1) the air cooling stage plate belt surface coefficient of heat transfer calculates by formula (10) and calculates:

${\mathrm{HC}}_{A,n}=(1+\frac{T_{A,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{A,n-1}---\left(10\right)$

Wherein: T _{a, n}for the n time period in air cooling stage finishes chronothermometer calculation value, T _{m, n}measured temperature when the air cooling stage, the n time period finished;

(2) water-cooled or the de-scaling stage plate belt surface coefficient of heat transfer calculate by formula (11) and calculate:

${\mathrm{HC}}_{W,n}=(1+\frac{T_{W,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{W,n-1}---\left(11\right)$

Wherein: T _{w, n}for water-cooled or n time period in de-scaling stage finish chronothermometer calculation value, T _{m, n}measured temperature while finishing for water-cooled or de-scaling process n time period;

(3) operation of rolling strip surface film thermal conductance calculates by formula (12) and calculates:

${\mathrm{HC}}_{R,n}=(1+\frac{T_{R,n}-T_{m,n}}{T_{m,n}}){\mathrm{HC}}_{R,n-1}---\left(12\right)$

Wherein: T _{r, n}for the operation of rolling n time period finishes chronothermometer calculation value, T _{m, n}measured temperature while finishing for the operation of rolling n time period.

2. the Forecasting Methodology of process of plate belt hot rolling surface film thermal conductance according to claim 1, is characterized in that, after step 6, also comprises:

Whether the coefficient of heat transfer calculating that judges certain one-phase in the operation of rolling according to iterations finishes; If this stage coefficient of heat transfer calculates, do not finish, iterations increases, and continues to calculate; If this stage coefficient of heat transfer calculates, finish, carry out next stage so, judge whether the whole operation of rolling finishes;

If the whole during Hot Strip Rolling coefficient of heat transfer calculates, do not finish, image data is proceeded next stage calculating so, if finished, predicts that each stage coefficient of heat transfer process finishes.

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