CN100495411C - Method for forecasting finite element of hot rolling process plate belt temperature field - Google Patents

Abstract

A finite element method of forecasting slab band temperature field during a hot rolling process belongs to the rolling technique field, and comprises the following steps: (1) collecting rolling process data; (2) carrying out unit division to cross section, establishing finite element analysis model, coding a unit node, and calculating a node coordinate; (3) ensuring border heat transfer coefficient and internal heat source intensity according to different rolling processes; (4) calculating the type-function of quadrangle isoparametric unit, B matrix, Jacobian matrix J and Jacobian matrix determinant |J| by using the finite element basic principle; (5) assembling the temperature rigidity matrix and dynamic heating matrix of the finite unit; (6) solving linear system of equations by adopting unidimensional variable bandwidth storage to obtain transient temperature field. The invention has the advantages that: the invention can obtain very high temperature forecasting precision and detailed information of the entire hot rolling slab band temperature distribution, which provides set and optimized parameter for rolling process, moreover, the invention has strong adaptability, reduces calculating time and improving calculating efficiency.

Description

A kind of Finite Element Method of predicting hot rolling process plate belt temperature field

Technical field

The invention belongs to rolling technical field, particularly a kind of Finite Element Method of predicting hot rolling process plate belt temperature field.

Background technology

In process of plate belt hot rolling, the board temperature Forecasting Methodology mainly contains in-site measurement, mathematical model, method of finite difference and finite element software emulation at present.Though in-site measurement is convenient, be subjected to subjective factor bigger, and can only obtain the strip surface temperature mostly, can not obtain comprehensive and accurate temperature information; Mathematical model depends on the site test condition greatly, the computing method underaction, and computational accuracy is often lower; Method of finite difference is a kind of numerical approximation solution that directly the differential problem is become algebra problem, and its theoretic defective makes the raising of computational accuracy be subjected to certain limitation; Common finite element software has reduced counting yield owing to need take a large amount of internal memories, and because it is professional not strong, precision is not high when the solving rolling process temperature.These factors have influenced the accurate prediction of course of hot rolling tabularium temperature to a certain extent, and then can not accurately set operation of rolling parameter, the carrying out smoothly of influence of rolled process.

Summary of the invention

At the low and professional shortcoming such as not strong of the whole bag of tricks precision of prediction hot rolling process plate belt temperature field in the prior art, the invention provides a kind of course of hot rolling prediction plate belt temperature field finite element method, its objective is and improve the plate belt temperature field precision of prediction, improve counting yield.

Realize that the object of the invention technical solution is as follows:

Carry out following hypothesis when utilizing finite element model for solving hot rolled strip temperature field:

Roll to size and be far longer than width and thickness direction size, therefore ignore rolling direction heat conduction

Width coboundary heat transfer boundary condition and symmetrical geometry are considered 1/2nd sections

1. gather operation of rolling data, comprising: rolling parameter, material thermal physical property parameter, dividing elements information, initial information, controlled variable

Rolling parameter: the exit thickness that passage is rolling, draught pressure, roller temperature, dephosphorization discharge

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

Dividing elements information: width unit number and thickness unit number

Initial information: rolled piece temperature, rolled piece width, rolled piece thickness

Controlled variable: iterations

2. dividing elements is carried out in the transversal section, set up finite element analysis model as shown in Figure 1, cell node is numbered, the computing node coordinate.

Set up finite element analysis model according to dividing elements data, rolled piece width and gauge, unit and node serial number increase gradually along thickness direction and Width, and among Fig. 1, i is an element number, and j is a node serial number, and H is a thickness, and W is a width.The adiabatic border of AB and AD, BC and CD heat exchange border.With the A point coordinate is zero, calculates each node coordinate, and the unit is evenly divided on Width and thickness direction.

3. determine coefficient of heat transfer h and endogenous pyrogen intensity according to operation of rolling physical condition and rolling sequence Course of hot rolling comprises the air cooling stage, dephosphorization stage, rolling sequence.The coefficient of heat transfer of whole operation of rolling different phase and endogenous pyrogen intensity are calculated as follows:

(1) hot rolled strip is in process air cooler,

Value is zero; Its surface heat exchanging mode is mainly radiation and natural convection, and coefficient of heat transfer h through type (1) and formula (2) are calculated:

HR＝σ·ε·(T+T _air)(T ²+T _air ²) (1)

Wherein: HR is a radiation coefficient, and σ is the Stefan-Boltzman constant, σ=5.67 * 10 ^-8W/ (m ²K ⁴);

ε is a coefficient of blackness, and the relational expression of ε and temperature is ε=0.125 (T/1000) ²-0.38 (T/1000)+1.1.

Hot rolled strip is natural convection at the convection type of process air cooler, and its expression formula is:

Wherein: T (K) is the strip surface temperature; T _AirBe environment temperature; B display plate bandwidth.

(2) hot rolled strip is in the dephosphorize by high pressure water process,

Value is zero; The surface heat exchanging mode is forced convection and side radiation, and coefficient of heat transfer h through type (1) and formula (3) are calculated:

HC _W＝124.7×w ^0.663×10 ^{-0.00147(T-273.16)} (3)

W (L/minm wherein ²) be jet density; T (K) strip surface temperature.

(3) in the operation of rolling, contact heat-exchanging is main thermal loss mode between strip and the roll, ignores plastic yield and friction acting, $\stackrel{.}{q}=0$ 。Contact heat exchange coefficient is relevant with draught pressure.Coefficient of heat transfer h through type (4) calculates:

IHTC＝695p _m-34400(W/m ²K) (4)

In the formula: p _m(MPa)-draught pressure

4. utilize the finite element ultimate principle, type function, B matrix and Jacobian matrix J and the Jacobian matrix determinant of ginseng unit such as calculating quadrilateral | J|.

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) be that foundation is set up the heat conduction differential equation with the first law of thermodynamics, suppose material heat conduction isotropy, two-dimentional heat conducting fundamental equation is:

$k(\frac{{\∂}^{2}T}{\∂x^2}+\frac{{\∂}^{2}T}{\∂y^2})+\stackrel{\·}{q}-\mathrm{\ρc}\frac{\∂T}{\∂t}=0---\left(5\right)$

Wherein: T transient temperature (K)

ρ density of material (kg/m ³)

C material specific heat (J/ (kgK))

The t time (s)

K heat-conduction coefficient (W/ (mK))

Endogenous pyrogen intensity (J/m ³)

(2) utilize Eulerian equation under given boundary condition and starting condition, two-dimentional heat conduction problem to be become equivalent functional expression formula and ask extreme-value problem:

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

$I^{\left(e\right)}=\frac{1}{2}\∫{\∫}_{S^e}[k[{\left(\frac{\∂T^{\left(e\right)}}{\∂x}\right)}^2+{\left(\frac{{\∂T}^{\left(e\right)}}{\∂y}\right)}^2]-2(\stackrel{\·}{q}-\mathrm{\ρc}\frac{{\∂T}^{\left(e\right)}}{\∂t})T^{\left(e\right)}]\mathrm{dS}+\frac{1}{2}{\∫}_{l^e}h(T^{\left(e\right)}-T_{\∞})\mathrm{dl}---\left(6\right)$

Variational principle according to heat conduction problem, functional formula (6) is asked single order partial derivative and zero setting,, discrete unit is assembled according to finite element combined method commonly used, the stiffness matrix of unit is assembled into the integral rigidity matrix, obtains the system equation that two-dimensional finite element method is found the solution the temperature field:

$\left[K_T\right]\left\{T\right\}+\left[K_3\right]\left\{\frac{\∂T}{\∂t}\right\}=\left\{p\right\}---\left(7\right)$

Wherein: [K _T]-temperature stiffness matrix, $\left[K_T\right]=\underset{e=1}{\overset{E}{\mathrm{\Σ}}}(\left[K_1^{\left(e\right)}\right]+\left[K_2^{\left(e\right)}\right]);$ [K ₃]-alternating temperature matrix, $\left[K_3\right]=\underset{e=1}{\overset{E}{\mathrm{\Σ}}}\left[K_3^{\left(e\right)}\right];$ P}-constant term row formula, $\left\{p\right\}=\underset{e=1}{\overset{E}{\mathrm{\Σ}}}\left\{p^{\left(e\right)}\right\};$ { T}-temperature row formula; E-unit sum; Subscript e represents each unit.

Concerning each unit, stiffness matrix, alternating temperature matrix and constant term can be found the solution by through type (8):

${\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C200710158981E00101.png"\; state="\{\{state\}\}">K</figure-callout>}}_{1\mathrm{ij}}^{\left(e\right)}=\&Integral;{\&Integral;}_{S^e}k(\frac{{\&PartialD;N}_i}{\&PartialD;x}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;x}+\frac{{\&PartialD;N}_i}{\&PartialD;y}\&CenterDot;\frac{{\&PartialD;N}_j}{\&PartialD;y})\mathrm{dS}---\left(8a\right)$

$K_{2\mathrm{ij}}^{\left(e\right)}={\&Integral;}_{L^e}h{N}_i{N}_j\mathrm{dL}---\left(8b\right)$

${\mathrm{<figure-callout\; id="3"\; label="K"\; filenames="C200710158981E00101.png"\; state="\{\{state\}\}">K</figure-callout>}}_{3\mathrm{ij}}^{\left(e\right)}=\&Integral;{\&Integral;}_{S^e}\mathrm{\&rho;c}{N}_i{N}_j\mathrm{dS}---\left(8c\right)$

${\left\{p_i\right\}}^{\left(e\right)}=\&Integral;{\&Integral;}_{S^e}\stackrel{\&CenterDot;}{q}{N}_i\mathrm{dS}++{\&Integral;}_{L^e}h{T}_{\&infin;}{N}_i\mathrm{dL}---\left(8d\right)$

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, the N type function; I, the j node serial number.

(3) utilize 2 backward difference forms, system equation is converted into the system of linear equations that transient state temperature field is found the solution.Temperature in the system equation (7) is expressed as 2 backward difference forms to the time partial derivative:

$\frac{\&PartialD;T}{\&PartialD;t}=\frac{1}{\mathrm{\&Delta;t}}(T_t-T_{t-\mathrm{\&Delta;t}})---\left(9\right)$

Bring time backward difference form (9) into system of linear equations that system equation obtains solution of Temperature:

$(\left[K_T\right]+\frac{1}{\mathrm{\&Delta;t}}\left[K_3\right]){\left\{T\right\}}_t=\frac{1}{\mathrm{\&Delta;t}}\left[K_3\right]{\left\{T\right\}}_{t-\mathrm{\&Delta;t}}+\left\{p\right\}---\left(10\right)$

6. the system of linear equations (11) that forms is found the solution, obtain to separate to be Temperature Distribution.Adopt the one-dimension variable bandwidth storage method to find the solution large-scale system of linear equations, thereby conserve storage improve counting yield.The one-dimension variable bandwidth storage means can be described as follows:

To general linear system of equations AX=B, if coefficient matrices A is a symmetrical and sparse.Can store since the first row nonzero element, till diagonal entry

Being stored as the one dimension matrix is:

Wherein: a-is a matrix element, first expression of following table line number, second expression columns.

7. judge according to iterations whether the temperature computation of a certain rolling sequence in the operation of rolling finishes.Do not finish if this phase temperature is calculated, iterations increases, and continues to calculate; Finish if this phase temperature is calculated, carry out next step operation so, judge whether whole operation of rolling temperature computation finishes.

8. whether finish according to judging that whole hot continuous rolling process temperature calculates the T.T. of the operation of rolling.Do not finish if whole hot continuous rolling process temperature calculates, image data is proceeded next stage calculating so, if finish, program predicted temperature process finishes.

The calculation procedure process flow diagram in finite element solving temperature field is shown in 2.

Maximum efficiency of the present invention is: can obtain the details that very high temperature prediction precision and whole hot rolling process plate belt temperature field distribute, set and parameters optimization for the operation of rolling provides; This method application is strong, has shortened computing time, has improved counting yield.The present invention is applicable to the roughing mill and the finishing mill of hot continuous rolling process.

Description of drawings

The finite element model figure of Fig. 1 the inventive method,

The finite element method software flow pattern of Fig. 2 the inventive method,

Fig. 3 roughing process temperature of the present invention variation diagram,

Fig. 4 finish rolling process temperature of the present invention variation diagram,

Fig. 5 the present invention begins rolling preceding temperature profile,

Fig. 6 roughing end temp of the present invention distribution plan,

Fig. 7 finish rolling end temp of the present invention distribution plan,

Among Fig. 1: i is an element number, and j is a node serial number, and H is a thickness, and W is a width, 1 is the heat exchange border, and A is a measured temperature before the open rolling, and B is that roughing finishes the back measured temperature, and C is a medial temperature, D is the upper surface temperature, and E is a underlaying surface temperature, and F is the side temperature, and G is a heart portion temperature.

Embodiment

Selecting a steel grade course of hot rolling is calculating object, utilizes finite element method analysis from going out heating furnace finishes whole process to finish rolling temperature development law.

A certain steel mill hot continuous rolling process.The roughing process has 4 frames, and second frame is reversible frame; The finish rolling process has 7 frames.Rolling 5 passages of reversible frame, the rolling a time of all the other frames.

Example: design conditions see Table 1.

Table 1

Whole hot continuous rolling process is total to rolling 15 passages, and the rolling exit thickness of each passage is shown in Table 2.

Table 2

Rolling pass	1	2	3	4	5	6	7	8
									Exit thickness (mm)	170.7	146.5	118.3	95.2	72.3	55.3	43.1	30.9
Rolling pass	9	10	11	12	13	14	15
									Exit thickness (mm)	17.0	8.7	5.5	3.6	2.7	2.1	1.8

Employing table 1 design conditions and table 2 passage exit thickness carry out computational analysis to a certain steel mill hot rolling process plate belt temperature development law, result of calculation such as Fig. 3 and Fig. 4, wherein 3 are the variation of roughing process temperature, 4 are the variation of finish rolling process temperature, Fig. 5, Fig. 6 and Fig. 7 are the Temperature Distribution isoline of different measuring position.

This hot continuous rolling process is carried out scene temperature measures and follows the tracks of, the open rolling surface temperature is about 1150 ℃, roughing end temp value is about 990-1000 ℃, adopt the plate belt hot rolling temperature prediction computation model of finite element method exploitation, start rolling temperature that calculates and roughing end temp value and measured value coincide good, error has proved the accuracy and the reliability of the inventive method within 1%.

The inventive method can obtain the Temperature Distribution of any position of whole operation of rolling strip at process of plate belt hot rolling, and information is detailed accurately.The whole course of hot rolling of the inventive method calculates and consumes the about 384ms of CPU time.This method prediction hot rolled strip temperature has improved temperature prediction precision and efficient greatly, can better optimize course of hot rolling parameter.

Claims (1)

1, a kind of Finite Element Method of predicting hot rolling process plate belt temperature field, its feature may further comprise the steps:

(1) gathers operation of rolling data, comprising: rolling parameter, material thermal physical property parameter, dividing elements information, initial information, controlled variable;

Rolling parameter: the exit thickness that passage is rolling, draught pressure, roller temperature, dephosphorization discharge;

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

Dividing elements information: width unit number and thickness unit number;

Initial information: rolled piece temperature, rolled piece width, rolled piece thickness;

Controlled variable: iterations;

(2) dividing elements is carried out in the transversal section, set up finite element analysis model, cell node is numbered, the computing node coordinate;

(3), determine the border coefficient of heat transfer and endogenous pyrogen intensity according to the different operations of rolling;

Hot rolled strip is in process air cooler, and its surface heat exchanging mode is radiation and natural convection, and radiation coefficient is expressed as:

$\mathrm{HR}=\mathrm{\&sigma;}\&CenterDot;\mathrm{\&epsiv;}\&CenterDot;(T+T_{\mathrm{air}})(T^2+{T_{\mathrm{air}}}^2)$

In the formula: HR is a radiation coefficient;

σ＝5.67×10 ^-8W/(m ²·K ⁴)

ε＝0.125(T/1000) ²-0.38(T/1000)+1.1

ε is a coefficient of blackness, and σ is a Boltzmann constant;

Hot rolled strip is natural convection at the convection type of process air cooler, and its expression formula is:

In the formula:

T is the strip surface temperature;

T _AirBe environment temperature;

B display plate bandwidth; HC _ABe free-convection factor;

Hot rolled strip is in the dephosphorize by high pressure water process, and heat exchange mode is forced convection and side radiation, and the radiation computing method are the same, and the convection coefficient expression formula is:

HC _W＝124.7×w ^0.663×10 ^{-0.00147(T-273.16)}

In the formula:

W (L/minm ²) be jet density;

T is the strip surface temperature;

In the operation of rolling, contact heat-exchanging is the thermal loss mode between strip and the roll, and the contact heat exchange coefficient expression formula is:

IHTC＝695p _m-34400(W/m ²K)

In the formula: p _m(MPa)-draught pressure;

(4) utilize the finite element ultimate principle, type function, B matrix and Jacobian matrix J and the Jacobian matrix determinant of ginseng unit such as calculating quadrilateral | J|;

(5) the temperature stiffness matrix and the alternating temperature matrix of finite elements are assembled the system equation formula that formation temperature is found the solution

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

In the formula:

[K _T]-temperature stiffness matrix;

[K ₃]-alternating temperature matrix;

{ p}-constant term row formula; The t-time; { T}-temperature row formula;

(6) adopt the one-dimension variable bandwidth storage method to find the solution system of linear equations, obtain transient state temperature field.

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