CN104298884B - The finite element and finite difference coupling process of a kind of quick calculating rolled piece section temperature - Google Patents

Abstract

The invention discloses the finite element and finite difference coupling process of a kind of quick calculating rolled piece section temperature, first, Finite Difference Meshes before finite element grid before each passes and rolling are mapped, according to position relationship, Finite Difference Meshes node temperature before rolling is passed into the preceding finite element grid of rolling.Secondly, finite element node temperature before rolling is passed to finite element node after rolling, and plus rolling temperature rise.Then, the finite element grid data according to rolled piece after each passes carry out Finite Difference Meshes division to rolled piece after rolling, and judge that face inner face is outer and position of boundary point.Then, the finite element grid node temperature after rolling is mapped to finite difference node according to position relationship.Finally, using Finite Difference Meshes roll the temperature computation of post gap.The present invention can quickly calculate the transient state temperature field of the rolled piece operation of rolling any time of various sections, and calculating speed improves very big, it is not necessary to manual intervention, high degree of automation.

Description

The finite element and finite difference coupling process of a kind of quick calculating rolled piece section temperature

Technical field

It is quick more particularly in course of hot rolling to calculate having for special-shaped rolled piece section temperature the invention belongs to rolling technical field Limit unit and finite difference coupling process.

Background technology

Temperature is one of most important parameter in the operation of rolling.Because temperature directly influences roll-force and rolls rear rolled piece Bending, therefore the temperature in each stage is the key of controlled rolling and control cooling in Exact Forecast production process.Past is in production It is long while being only applicable to the strip and the online temperature computation of rod line of simple section that the middle finite element method for using calculates the time, it is difficult to It is adapted to the temperature computation of the complicated shaped steel of various sections.Using finite element when the temperature field of compound section rolled piece is calculated, consumption When too many, rolled piece nip difficulty, this causes quickly to calculate the temperature in the compound section rolled piece operation of rolling using FInite Element receives To limitation.And finite difference calculus is mainly used in the constant tool and mould of grid or the simple strip of deformation rule and Bar Wire Product in the past Temperature computation in.Law of metal flow before and after the unpredictable operation of rolling of rolled piece of compound section, and cannot apply.It is limited Calculus of finite differences can quickly calculate temperature, and FInite Element can accurately reflect operation of rolling law of metal flow, by two methods The temperature of the online rapid calculation that is coupled compound section rolled piece is possibly realized, but there is presently no by finite element and limited Two methods of difference are coupled and are applied in the compound section operation of rolling.

The Chinese patent of Publication No. CN 100495411C discloses a kind of the limited of prediction hot rolling process plate belt temperature field First method, it includes collection operation of rolling data；Quadrilateral finite dividing elements are carried out to strip section；Determine heat transfer boundary system Number and endogenous pyrogen intensity；Determine shape function, B matrixes and the Jacobian matrix J of quadrilateral units；Determine that the temperature of finite elements is firm The assembling of degree matrix and alternating temperature matrix；One-dimensional variant-banded storage method solves equation group.The method can faster obtain hot rolled plate Transient state temperature field with operation of rolling rolled piece section.It is complicated but the method is only applied in the simple strip of rolled piece section configuration The temperature computation of the course of hot rolling of section rolled piece cannot carry out effectively quick calculating.

The Chinese patent of Publication No. CN101046682 A discloses a kind of predicting hot-rolled Nb-contained and mechanical property The method of energy, it sets up rolled piece temperature model on temperature model, including roller-way, roughing section rolled piece temperature mould with finite difference calculus Type, finish rolling section rolled piece temperature model, section cooling section rolled piece temperature model.The rolled piece section temperature computation model is also suitable only for The simple Strip of rolled piece section configuration, the course of hot rolling temperature computation of compound section rolled piece cannot also carry out effectively quick meter Calculate.

The content of the invention

The purpose of the present invention be exactly overcome calculate compound section rolled piece temperature computation finite element method overlong time, it is difficult from The shortcoming of dynamicization, overcomes the shortcoming of law of metal flow before and after the unpredictable rolled piece rolling of finite difference calculus, improves rolled piece section The speed and automaticity of temperature computation, propose finite element and the finite difference coupling side of a kind of quick calculating rolled piece section Method.

The technical solution adopted in the present invention is：The finite element and finite difference coupling of a kind of quick calculating rolled piece section temperature Conjunction method, it is characterised in that comprise the following steps：

Step 1：Finite Difference Meshes division is carried out to blank cross section, Finite Difference Analysis model is set up；

Step 2：Section temperature of the rolled piece from coming out of the stove, before de-scaling and the first passes is calculated using finite difference simulator；

Step 3：FEM meshing is carried out to the rolled piece before the first passes, three-dimensional finite element model is set up and is gone forward side by side Row is calculated, the finite element unit and node data of rolled piece before and after the first passes of acquisition；

Step 4：Finite element and finite difference coupling model are set up, it is implemented including following sub-step：

Step 4.1：By rolled piece before rolled piece Finite Difference Meshes temperature map before the first passes to the first passes On finite element grid；

Step 4.2：Rolled piece finite element node temperature before first passes is delivered to rolled piece after the first passes On finite element node, and rolled piece temperature caused by plastic deformation heat is raised into △ T it is added to all of rolled piece after the first passes On finite element node；

Step 4.3：Rolled piece section after advance the first passes for using finite element method to calculate is carried out limited Difference gridding is divided, and the finite element node temperature of rolled piece after the first passes is mapped into having for rolled piece after the first passes On limit difference gridding；

Step 5：Using the Finite Difference Meshes of rolled piece after the first passes roll the temperature computation in gap；

Step 6：Later each passes process all carries out Finite Difference Meshes division using step 1 to rolled piece cross section Coupling model with step 4 is calculated, and the temperature of rolling gap and water smoke cooling is had using step 5 to rolled piece cross section Limit differential temperature is calculated, the final section temperature for obtaining each moment of rolled piece.

Preferably, carrying out Finite Difference Meshes division to blank cross section described in step 1, finite difference point is set up Analysis model；It is implemented including following sub-step：

Step 1.1：Uniform grid is used in the height and width direction of the blank cross-section, and sizing grid is according to rolled piece section Complexity adjust；Finite Difference Meshes scope is rectangular area, and it is cross-section that whole Finite Difference Meshes cover whole blank Face, for the ease of judging boundary point, Finite Difference Meshes bigger than blank cross section two node width and height；

Step 1.2：Build the two-dimensional finite difference equation of internal node；

For two-dimentional normal physical characteristics control equation (without thermal source) (heat transfer equilibrium equation)

By to the first-order derivative of time, with single order, difference coefficient replaces forward in formula (1), in the second derivative second order of coordinate Heart difference coefficient replace obtain internal node explicit difference equation be：

Here,Δ τ is time step, if uniform discrete Δ x=Δ y, then have：

During what node (i, j) temperature of each time horizon k+1 had been expressed as upper time horizon k is with the node (i, j) 5 explicit functions of node temperature of the heart, the stability condition of the form is：Fo≤1/4；

Step 1.3：Build the two-dimensional finite difference equation of boundary node；

Different according to the location of boundary node, the two-dimensional finite difference equation of boundary node is divided into 12 kinds；Specifically such as Under：

(1) right margin of straight boundary：

When boundary node is located at right straight boundary, to border, using heat balance method of, (hot-fluid of i.e. incoming node is equal to should The change of internal energy rate of the representative control of node) derive two-dimensional finite difference boundary node T_m,nEquation of heat balance is：

Δ x=Δs y is taken to obtain

(2) left margin of straight boundary：

(3) coboundary of straight boundary：

(4) lower boundary of straight boundary：

(5) the upper right salient angle on salient angle border：

(6) the bottom right salient angle on salient angle border：

(7) the upper left salient angle on salient angle border：

(8) the lower-left salient angle on salient angle border：

(9) lower right corner on re-entrant angle border：

(10) upper right corner on re-entrant angle border：

(11) upper left corner on re-entrant angle border：

(12) lower left corner on re-entrant angle border：

Wherein, ρ is density, and unit is kg/m³；C is specific heat capacity, and unit is J/ (kg DEG C)；λ is thermal conductivity, and unit is W/(m·K)；T is temperature, and unit is K；X, y are transverse and longitudinal coordinate, and unit is m；Δ x, Δ y are Finite Difference Meshes x, y directions Step pitch, unit is m；τ is the time, and unit is s；Δ τ is time step, and unit is s；A is temperature diffusivity, and unit is m²/s； It is Finite Difference Meshes node (m, n) in the temperature at k+1 moment, unit is K；Fo is Fourier number；H is changing for rolled piece and environment Hot coefficient, unit is W/ (m²·K)；ε is blackness；c₀It is the radiation coefficient of black matrix；T_eIt is radiation environment temperature, unit is K； T_fluidConvection environment temperature or water temperature, unit are K.

Preferably, carrying out FEM meshing to the rolled piece before the first passes described in step 3, three are set up Dimension FEM model simultaneously carries out FEM calculation, uses elastoplastic finite metatheory.

Preferably, the section temperature of rolled piece described in step 2 from coming out of the stove, before de-scaling and the first passes is calculated, First passage FEM meshing and calculating in step 3, finite element and finite difference coupling model are set up described in step 4 Operation of rolling calculating is carried out, finite gap differential temperature is rolled described in step 5 and is calculated and follow-up rolling road described in step 6 Secondary, gap and water smoke chilling temperature are calculated, and data required for calculating include：Blank parameter, physical parameter, device parameter, rolling Technological parameter, combined influence parameter.

Preferably, described blank parameter includes blank initial length, blank original width, blank original depth, base Material tapping temperature, blank radiused corner radius；Described physical parameter includes the coefficient of heat conduction, specific heat, density, blackness；Described sets Standby parameter includes spacing, de-scaling and the water smoke cooling device parameter of each equipment；Described rolling technological parameter includes that rolling is each The rolling time in stage and off time；Described combined influence parameter includes unit step-length, time step, environment temperature, each The coefficient of heat transfer in stage.

Preferably, the determination of described blank parameter is given by operator, the determination of described physical parameter is by material Composition and temperature determine that described device parameter is arranged and determined that described rolling technological parameter is by specifically advising by specific workshop The rolling schedule of the rolled products of lattice determines.

Preferably, the coefficient of heat transfer in described each stage includes air cooling heat exchange models, the de-scaling coefficient of heat transfer, water smoke cooling The coefficient of heat transfer, rolling heat exchange models.

Preferably, described air cooling heat exchange models：

The heat exchange that rolled piece occurs when placing or being transported on rollgang is mainly produced in the form of radiation and convection current Raw, convection coefficient is：

H=η (T₀-T_fluid)^0.25(18)；

Rolled piece radiation heat transfer heat is：

Φ_r=ε c₀[(T₀)⁴-(T_e)⁴]A (19)；

The radiation blackness ε of rolled piece is the number less than 1,

The determination of the described de-scaling coefficient of heat transfer：

During high-pressure water descaling process, the influence of jet density, hydraulic pressure and rolled piece surface temperature heat exchanging coefficient is than larger, Wherein surface heat exchanging mode is mainly forced convection, and convection coefficient expression formula is：

The determination of described water smoke cooling heat transferring coefficient：

During rolled piece Local cooling, in order to prevent the sputtering of water to not needing the influence of cooling position, using cooling capacity compared with It is small while the water spray cooling mode not sputtered；Water smoke cooling coefficient of heat transfer expression formula be：

lgh_sw=6.615-0.563lg (H/D)+0.200lgP-0.865lgT₀(22)；Described rolling heat exchange models：

The operation of rolling causes temperature to raise Δ T as disposed of in its entirety, heat during rolling produced by rolled piece plastic deformation：

Δ T=0.183 σ ln μ (23)；

The temperature rise of whole each rolling pass of the operation of rolling can be calculated according to formula (23), the temperature is uniformly added to limited In difference program.

Wherein, T₀It is rolled piece surface temperature, unit is K；η is correction factor；Φ_rIt is radiation exchange heat, unit is W；A It is swept area, unit is m²；λ is correction factor；h_cIt is the de-scaling coefficient of heat transfer, unit is W/ (m²·K)；W is jet density, Unit is L/ (minm²)；γ is influence of hydraulic pressure coefficient；h_swIt is water smoke cooling heat transferring coefficient, unit is W/ (m²·K)；H is spray To steel plate distance, unit is mm to mouth；D is nozzle diameter, and unit is mm, and P is hydraulic pressure, and unit is MPa；σ is metal deformation resistance, Unit is MPa, and Δ T is plastically deformed the temperature rise for causing for rolled piece in pass, and unit is K；μ is lengthening coefficient.

Relative to prior art, the present invention has following good effect：

(1) transient state temperature field at the rolled piece operation of rolling any moment of various sections can quickly be calculated；

(2) conventional finite element method calculates the time in the temperature field of the rolled piece operation of rolling with day calculating, is counted using the present invention Evaluation time is calculated in minutes, and calculating speed improves very big；

(3) finite difference method cannot calculate compound section rolled piece temperature；And finite element method is difficult continuous quick calculating The rolled piece section temperature of compound section, calculates intermediate demand manual intervention, and automaticity is not high；Calculating process of the present invention is not required to Want manual intervention, high degree of automation.

Brief description of the drawings

Fig. 1：(Finite Difference Meshes scope is more horizontal than blank for the blank geometric coordinate and finite difference coordinate of the embodiment of the present invention Section geometry is big) schematic diagram；

Fig. 2：The internal node Finite Difference Meshes schematic diagram of the embodiment of the present invention；

Fig. 3：The right straight boundary node schematic diagram of the embodiment of the present invention；

Fig. 4：The upper right salient angle boundary node schematic diagram of the embodiment of the present invention；

Fig. 5：The bottom right re-entrant angle boundary node schematic diagram of the embodiment of the present invention；

Fig. 6：A certain rolling pass FEM and FDM the coupling temperature computation flow chart of the embodiment of the present invention；

Fig. 7：The process layout of the heavy-rail production of the embodiment of the present invention.

Specific embodiment

Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with the accompanying drawings and embodiment is to this hair It is bright to be described in further detail, it will be appreciated that implementation example described herein is merely to illustrate and explain the present invention, not For limiting the present invention.

It is the process layout of the heavy-rail production of embodiment see Fig. 7, its rolling process is as follows：Blank is in heating To tapping temperature, -- --- --- BD2 abnormity rolls --- water smoke cooling --- ten thousand to BD1 split rolling methods to stove heat for water under high pressure dephosphorization Roughing can be rolled, and --- --- universal rolling finish rolling --- cold bed cooling --- is aligned for water smoke cooling.

The operation of rolling can quickly calculate rolled piece section temperature under certain process conditions, can by adjusting water smoke cooling parameter To control the uniformity coefficient of rolled piece section temperature after finish rolling, prevent rolled piece from rolling rear section temperature uneven and produced on cold bed curved Song, so as to cannot be aligned.

Rolled piece section temperature is calculated in order to quick, the technical scheme that the present embodiment is used is comprised the following steps：

Step 1：Finite Difference Meshes division is carried out to blank cross section, Finite Difference Analysis model is set up；Set up limited Difference analysis model is implemented including following sub-step：

Step 1.1：Finite Difference Analysis model is set up as shown in figure 1, adopting in the height and width direction of the blank cross-section With uniform grid, sizing grid is adjusted according to the complexity of rolled piece section；Finite Difference Meshes scope is rectangular area, whole Individual Finite Difference Meshes cover whole blank cross section, and for the ease of judging boundary point, Finite Difference Meshes are than blank cross section Big two node width and height；

Step 1.2：Build the two-dimensional finite difference equation of internal node；

For two-dimentional normal physical characteristics control equation (without thermal source) (heat transfer equilibrium equation)

Fig. 2 is internal node Finite Difference Meshes, and the temperature for calculating internal node (m, n) is related to 4 finite differences around Node (m, n+1), (m, n-1), (m-1, n), (m+1, n).By in formula (1) to the first-order derivative of time with single order difference coefficient generation forward Replace, replace the explicit difference equation for obtaining internal node to be with second-order central difference coefficient to the second derivative of coordinate：

Here,Δ τ is time step, if uniform discrete Δ x=Δ y, then have：

During what node (i, j) temperature of each time horizon k+1 had been expressed as upper time horizon k is with the node (i, j) 5 explicit functions of node temperature of the heart, the stability condition of the form is：Fo≤1/4；

Step 1.3：Build the two-dimensional finite difference equation of boundary node；

Different according to the location of boundary node, the two-dimensional finite difference equation of boundary node is divided into 12 kinds；Specifically such as Under：

(1) right margin of straight boundary：

When boundary node is located at right straight boundary, the node of temperature computation is participated in as shown in figure 3, calculating boundary node The temperature of (m, n) be related to around 3 finite difference nodes (m, n-1), (m-1, n), (m+1, n).Heat balance method of is used to border (hot-fluid of i.e. incoming node is equal to the change of internal energy rate of the representative control of the node) derives two-dimensional finite difference boundary node T_m,n Equation of heat balance is：

Δ x=Δs y is taken to obtain

(2) left margin of straight boundary：

(3) coboundary of straight boundary：

(4) lower boundary of straight boundary：

(5) the upper right salient angle on salient angle border：

When boundary node is located at upper right salient angle border, the node of temperature computation is participated in as shown in figure 4, calculating boundary node The temperature of (m, n) be related to around 2 finite difference nodes (m, n-1), (m-1, n).

(6) the bottom right salient angle on salient angle border：

(7) the upper left salient angle on salient angle border：

(8) the lower-left salient angle on salient angle border：

(9) lower right corner on re-entrant angle border：

When boundary node is located at bottom right re-entrant angle border, the node of temperature computation is participated in as shown in figure 5, calculating boundary node The temperature of (m, n) be related to around 4 finite difference nodes (m, n+1), (m, n-1), (m-1, n), (m+1, n).

(10) upper right corner on re-entrant angle border：

(11) upper left corner on re-entrant angle border：

(12) lower left corner on re-entrant angle border：

Wherein, ρ is density, and unit is kg/m³；C is specific heat capacity, and unit is J/ (kg DEG C)；λ is thermal conductivity, and unit is W/(m·K)；T is temperature, and unit is K；X, y are transverse and longitudinal coordinate, and unit is m；Δ x, Δ y are Finite Difference Meshes x, y directions Step pitch, unit is m；τ is the time, and unit is s；Δ τ is time step, and unit is s；A is temperature diffusivity, and unit is m²/s； It is Finite Difference Meshes node (m, n) in the temperature at k+1 moment, unit is K；Fo is Fourier number；H is changing for rolled piece and environment Hot coefficient, unit is W/ (m²·K)；ε is blackness；c₀It is the radiation coefficient of black matrix；T_eIt is radiation environment temperature, unit is K； T_fluidConvection environment temperature or water temperature, unit are K.

Step 2：Section temperature of the rolled piece from coming out of the stove, before de-scaling and the first passes is calculated using finite difference method；

Step 3：FEM meshing is carried out to the rolled piece before the first passes, is built using elastoplastic finite metatheory Vertical three-dimensional finite element model is simultaneously calculated, the finite element unit and node data of rolled piece before and after the first passes of acquisition；

The three-dimensional finite element model of each rolling pass is set up using elastoplastic finite metatheory, special-shaped passage rolled piece is difficult Next passage is nipped, substantially each passage is required for individually simulation.In the serious passage of mesh distortion, net is carried out to rolled piece Lattice are drawn again.Derived using ANSYS APDL language, updated geometry method, LS-PREPOST and VB softwares a certain section before and after rolling The cell data and node coordinate in face, and save as single file.

Step 4：Finite element and finite difference coupling model are set up, see Fig. 6, it is implemented including following sub-step：

Step 4.1：By rolled piece before rolled piece Finite Difference Meshes temperature map before the first passes to the first passes On finite element grid；

Step 4.2：Rolled piece finite element node temperature before first passes is delivered to rolled piece after the first passes On finite element node, and rolled piece temperature caused by plastic deformation heat is raised into △ T it is added to all of rolled piece after the first passes On finite element node；

Step 4.3：Rolled piece section after advance the first passes for using finite element method to calculate is carried out limited Difference gridding is divided, and the finite element node temperature of rolled piece after the first passes is mapped into having for rolled piece after the first passes On limit difference gridding；

Step 5：Using the Finite Difference Meshes of rolled piece after the first passes roll the temperature computation in gap；

Step 6：Later each passes process all carries out Finite Difference Meshes division using step 1 to rolled piece cross section Coupling model with step 4 is calculated, and the temperature of rolling gap and water smoke cooling is had using step 5 to rolled piece cross section Limit differential temperature is calculated, the final section temperature for obtaining each moment of rolled piece.

Section temperature of the rolled piece from coming out of the stove, before de-scaling and the first passes is calculated wherein in step 2, first in step 3 Passage FEM meshing and calculating, set up finite element and finite difference coupling model described in step 4 rolled Journey is calculated, and finite gap differential temperature is rolled described in step 5 and is calculated and follow-up rolling pass, gap and water described in step 6 Fog cooling temperature computation, data required for calculating include：It is blank parameter, physical parameter, device parameter, rolling technological parameter, comprehensive Close affecting parameters.

Blank parameter includes blank initial length, blank original width, blank original depth, blank tapping temperature, blank Radius of corner；Described physical parameter includes the coefficient of heat conduction, specific heat, density, blackness；Described device parameter sets including each Standby spacing, de-scaling and water smoke cooling device parameter；Described rolling technological parameter include the rolling time in rolling each stage and Off time；Described combined influence parameter includes unit step-length, time step, environment temperature, the coefficient of heat transfer in each stage.

The determination of blank parameter is given by operator, and the determination of physical parameter is determined by the composition and temperature of material, equipment Parameter is arranged and determined that rolling technological parameter is determined by the rolling schedule of the rolled products of The concrete specification by specific workshop.

The coefficient of heat transfer in each stage includes that air cooling heat exchange models, the de-scaling coefficient of heat transfer, water smoke cooling heat transferring coefficient, rolling are changed Thermal model.

Air cooling heat exchange models：The heat exchange that rolled piece occurs when placing or being transported on rollgang is main with radiation and right The form of stream and produce, convection coefficient is：

H=η (T₀-T_fluid)^0.25(18)；

Rolled piece radiation heat transfer heat is：

Φ_r=ε c₀[(T₀)⁴-(T_e)⁴]A (19)；

The radiation blackness ε of rolled piece is the number less than 1,

For hot-rolling stock, the degree of iron scale that be on its surface is different and value is also different, works as iron oxide 0.8 typically is taken when skin is more, and the smooth surface for just having shut out typically takes 0.55~0.65.

The determination of the de-scaling coefficient of heat transfer：

During high-pressure water descaling process, the influence of jet density, hydraulic pressure and rolled piece surface temperature heat exchanging coefficient is than larger, Wherein surface heat exchanging mode is mainly forced convection, and convection coefficient expression formula is：

The determination of water smoke cooling heat transferring coefficient：

During rolled piece Local cooling, in order to prevent the sputtering of water to not needing the influence of cooling position, using cooling capacity compared with It is small while the water spray cooling mode not sputtered；Water smoke cooling coefficient of heat transfer expression formula be：

lgh_sw=6.615-0.563lg (H/D)+0.200lgP-0.865lgT₀(22)；

Rolling heat exchange models：

In the operation of rolling, the contact surface of roll and rolled piece can produce frictional heat and the heat transfer, frictional heat to cause rolled piece temperature Raise, heat transfer causes the reduction of rolled piece temperature, because a certain section of rolled piece and roll contact time are very short, while contact surface is difficult It is determined that, it is believed that this two parts heat is cancelled out each other, and is not considered here.Here deformation heat is only considered.

The operation of rolling causes temperature to raise Δ T as disposed of in its entirety, heat during rolling produced by rolled piece plastic deformation：

Δ T=0.183 σ ln μ (23)；

The temperature rise of whole each rolling pass of the operation of rolling can be calculated according to formula (23), the temperature is uniformly added to limited In difference program.

Wherein, T₀It is rolled piece surface temperature, unit is K；η is correction factor；Φ_rIt is radiation exchange heat, unit is W；A It is swept area, unit is m²；λ is correction factor；h_cIt is the de-scaling coefficient of heat transfer, unit is W/ (m²·K)；W is jet density, Unit is L/ (minm²)；γ is influence of hydraulic pressure coefficient；h_swIt is water smoke cooling heat transferring coefficient, unit is W/ (m²·K)；H is spray To steel plate distance, unit is mm to mouth；D is nozzle diameter, and unit is mm, and P is hydraulic pressure, and unit is MPa；σ is metal deformation resistance, Unit is MPa, and Δ T is plastically deformed the temperature rise for causing for rolled piece in pass, and unit is K；μ is lengthening coefficient.

The operation of rolling can quickly calculate rolled piece section temperature under certain process conditions, can by adjusting water smoke cooling parameter To control the uniformity coefficient of rolled piece section temperature after finish rolling, prevent rolled piece from rolling rear section temperature uneven and produced on cold bed curved Song, so as to cannot be aligned.

The present embodiment by programming software VB will calculate institute's parameter as can input variable, by finite difference simulator and side Journey, each passes finite element section elements data and node coordinate, finite difference node and finite element node coupling algorithm Establishment in a program, realizes fast automatic calculating section rolled piece cross-section temperature.

It should be appreciated that the part that this specification is not elaborated belongs to prior art.

It should be appreciated that the above-mentioned description for preferred embodiment is more detailed, therefore can not be considered to this The limitation of invention patent protection scope, one of ordinary skill in the art is not departing from power of the present invention under enlightenment of the invention Profit requires under protected ambit, can also make replacement or deform, each falls within protection scope of the present invention, this hair It is bright scope is claimed to be determined by the appended claims.

Claims (8)

1. the finite element and finite difference coupling process of a kind of quick calculating rolled piece section temperature, it is characterised in that including following Step：

Step 1：Finite Difference Meshes division is carried out to blank cross section, Finite Difference Analysis model is set up；

Step 2：Section temperature of the rolled piece from coming out of the stove, before de-scaling and the first passes is calculated using Finite Difference Analysis model；

Step 3：FEM meshing is carried out to the rolled piece before the first passes, three-dimensional finite element model is set up and is counted Calculate, the finite element unit and node data of rolled piece before and after the first passes of acquisition；

Step 4：Finite element and finite difference coupling model are set up, it is implemented including following sub-step：

Step 4.1：Rolled piece before rolled piece Finite Difference Meshes temperature map before first passes to the first passes is limited On first grid；

Step 4.2：Rolled piece finite element node temperature before first passes is delivered to the limited of rolled piece after the first passes On first node, and rolled piece temperature caused by plastic deformation heat is raised into △ T it is added to all limited of rolled piece after the first passes On first node；

Step 4.3：Finite difference is carried out to the rolled piece section after advance the first passes for using finite element method to calculate Mesh generation, the finite element node temperature of rolled piece after the first passes is mapped to the finite difference of rolled piece after the first passes On subnetting lattice；

Step 5：Using the Finite Difference Meshes of rolled piece after the first passes roll the temperature computation in gap；

Step 6：Later each passes process all carries out Finite Difference Meshes division and step using step 1 to rolled piece cross section Rapid 4 coupling model is calculated, and the temperature of rolling gap and water smoke cooling carries out finite difference using step 5 to rolled piece cross section Divide temperature computation, the final section temperature for obtaining each moment of rolled piece.

2. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 1, it is special Levy and be：Finite Difference Meshes division is carried out to blank cross section described in step 1, Finite Difference Analysis model is set up；Its Implement including following sub-step：

Step 1.1：Uniform grid, sizing grid is used to be answered according to rolled piece section in the height and width direction of the blank cross-section Miscellaneous degree is adjusted；Finite Difference Meshes scope is rectangular area, and whole Finite Difference Meshes cover whole blank cross section, are It is easy to judge boundary point, Finite Difference Meshes bigger than blank cross section two node width and height；

Step 1.2：Build the two-dimensional finite difference equation of internal node；

For two-dimentional normal physical characteristics control equation：

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

By to the first-order derivative of time, with single order, difference coefficient replaces forward in formula (1), the second derivative to coordinate is poor with second-order central Shang dynasty for obtain internal node explicit difference equation be：

$T_{m,n}^{k+1}=\frac{a\mathrm{\Δ}\mathrm{\τ}}{{\left(\mathrm{\Δ}x\right)}^2}(T_{m+1,n}^k-2T_{m,n}^k+T_{m-1,n}^k)+\frac{a\mathrm{\Δ}\mathrm{\τ}}{{\left(\mathrm{\Δ}y\right)}^2}(T_{m,n+1}^k-2T_{m,n}^k+T_{m,n-1}^k)+T_{m,n}^k---\left(2\right);$

Here,△ τ are time step, if uniform discrete Δ x=Δ y, then have：

$T_{m,n}^{k+1}=Fo(T_{m+1,n}^k+T_{m-1,n}^k+T_{m,n+1}^k+T_{m,n-1}^k)+(1-4Fo)T_{m,n}^k---\left(3\right);$

$Fo=\frac{a\mathrm{\Δ}\mathrm{\τ}}{{\left(\mathrm{\Δ}x\right)}^2}=\frac{\mathrm{\λ}}{\mathrm{\ρ}c}\frac{\mathrm{\Δ}\mathrm{\τ}}{{\left(\mathrm{\Δ}x\right)}^2}---\left(4\right);$

Node (i, j) temperature of each time horizon k+1 has been expressed as centered on the node (i, j) the 5 of upper time horizon k The explicit function of individual node temperature, stability condition is：Fo≤1/4；

Step 1.3：Build the two-dimensional finite difference equation of boundary node；

Different according to the location of boundary node, the two-dimensional finite difference equation of boundary node is divided into 12 kinds；It is specific as follows：

(1) right margin of straight boundary：

When boundary node is located at right straight boundary, two-dimensional finite difference boundary node T is derived using heat balance method of to border_m,n Equation of heat balance is：

$\mathrm{\λ}\mathrm{\Δ}y\frac{T_{m,n-1}^{\left(k\right)}-T_{m,n}^{\left(k\right)}}{\mathrm{\Δ}x}+\mathrm{\λ}\frac{\mathrm{\Δ}x}{2}\frac{T_{m+1,n}^{\left(k\right)}-T_{m,n}^{\left(k\right)}}{\mathrm{\Δ}y}+\mathrm{\λ}\frac{\mathrm{\Δ}x}{2}\frac{T_{m-1,n}^{\left(k\right)}-T_{m,n}^{\left(k\right)}}{\mathrm{\Δ}y}-h\left(T_{m,n}^{\left(k\right)}-T_{fluid}\right)\mathrm{\Δ}y-{\mathrm{\ϵc}}_0\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-{\left(T_e\right)}^4\]\mathrm{\Δ}y=\mathrm{\ρ}c\frac{\mathrm{\Δ}x}{2}\mathrm{\Δ}y\frac{T_{m,n}^{\left(k+1\right)}-T_{m,n}^{\left(k\right)}}{\mathrm{\Δ}\mathrm{\τ}}---\left(5\right);$

△ x=△ y are taken to obtain

$T_{m,n}^{k+1}=F_0\left(2T_{m,.n-1}^k+T_{m+1,n}^k+T_{m-1,n}^k\right)+T_{m,n}^k\left(1-4F_0\right)-\frac{2h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^k-T_{fluid}\right)-\frac{2{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^4-T_e^4\right)---\left(6\right);$

(2) left margin of straight boundary：

$T_{m,n}^{k+1}=F_0(2T_{m,.n+1}^k+T_{m+1,n}^k+T_{m-1,n}^k)+T_{m,n}^k(1-4F_0)-\frac{2h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^k-T_{fluid})-\frac{2{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^4-T_e^4)---\left(7\right);$

(3) coboundary of straight boundary：

$T_{m,n}^{k+1}=F_0(2T_{m-1,n}^k+T_{m,n-1}^k+T_{m,n+1}^k)+T_{m,n}^k(1-4F_0)-\frac{2h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^k-T_{fluid})-\frac{2{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^4-T_e^4)---\left(8\right);$ (4) lower boundary of straight boundary：

$T_{m,n}^{k+1}=F_0\left(2T_{m+1,n}^k+T_{m,n-1}^k+T_{m,n+1}^k\right)+T_{m,n}^k\left(1-4F_0\right)-\frac{2h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^k-T_{fluid}\right)-\frac{2{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^4-T_e^4\right)---\left(9\right);$

(5) the upper right salient angle on salient angle border：

$T_{m,n}^{(k+1)}=\frac{F_0}{2}(T_{m,n-1}^{\left(k\right)}+T_{m-1,n}^{\left(k\right)})+T_{m,n}^{\left(k\right)}(1-F_0)-\frac{h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^{\left(k\right)}-T_{fluid})-\frac{{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-{\left(T_e\right)}^4\]---\left(10\right);$

(6) the bottom right salient angle on salient angle border：

$T_{m,n}^{\left(k+1\right)}=\frac{F_0}{2}\left(T_{m,n-1}^{\left(k\right)}+T_{m+1,n}^{\left(k\right)}\right)+T_{m,n}^{\left(k\right)}\left(1-F_0\right)-\frac{h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^{\left(k\right)}-T_{fluid}\right)-\frac{{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-{\left(T_e\right)}^4\]---\left(11\right);$

(7) the upper left salient angle on salient angle border：

$T_{m,n}^{\left(k+1\right)}=\frac{F_0}{2}\left(T_{m,n+1}^{\left(k\right)}+T_{m-1,n}^{\left(k\right)}\right)+T_{m,n}^{\left(k\right)}\left(1-F_0\right)-\frac{h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^{\left(k\right)}-T_{fluid}\right)-\frac{{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-{\left(T_e\right)}^4\]---\left(12\right);$

(8) the lower-left salient angle on salient angle border：

$T_{m,n}^{(k+1)}=\frac{F_0}{2}(T_{m,n+1}^{\left(k\right)}+T_{m+1,n}^{\left(k\right)})+T_{m,n}^{\left(k\right)}(1-F_0)-\frac{h\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^{\left(k\right)}-T_{fluid})-\frac{{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-{\left(T_e\right)}^4\]---\left(13\right);$

(9) lower right corner on re-entrant angle border：

$T_{m,n}^{\left(k+1\right)}=\frac{4}{3}{F}_0\left(T_{m,n-1}^{\left(k\right)}+T_{m+1,n}^{\left(k\right)}+\frac{T_{m-1,n}^{\left(k\right)}}{2}+\frac{T_{m,n+1}^{\left(k\right)}}{2}\right)+T_{m,n}^{\left(k\right)}\left(1-4F_0\right)-\frac{4h\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^{\left(k\right)}-T_{fluid}\right)-\frac{4{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-T_e^4\]---\left(14\right);$

(10) upper right corner on re-entrant angle border：

$T_{m,n}^{(k+1)}=\frac{4}{3}{F}_0(T_{m,n-1}^{\left(k\right)}+T_{m-1,n}^{\left(k\right)}+\frac{T_{m+1,n}^{\left(k\right)}}{2}+\frac{T_{m,n+1}^{\left(k\right)}}{2})+T_{m,n}^{\left(k\right)}(1-4F_0)-\frac{4h\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}(T_{m,n}^{\left(k\right)}-T_{fluid})-\frac{4{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-T_e^4\]---\left(15\right);$

(11) upper left corner on re-entrant angle border：

$T_{m,n}^{\left(k+1\right)}=\frac{4}{3}{F}_0\left(T_{m,n+1}^{\left(k\right)}+T_{m-1,n}^{\left(k\right)}+\frac{T_{m+1,n}^{\left(k\right)}}{2}+\frac{T_{m,n-1}^{\left(k\right)}}{2}\right)+T_{m,n}^{\left(k\right)}\left(1-4F_0\right)-\frac{4h\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^{\left(k\right)}-T_{fluid}\right)-\frac{4{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-T_e^4\]---16);$

(12) lower left corner on re-entrant angle border：

$T_{m,n}^{\left(k+1\right)}=\frac{4}{3}{F}_0\left(T_{m,n+1}^{\left(k\right)}+T_{m+1,n}^{\left(k\right)}+\frac{T_{m-1,n}^{\left(k\right)}}{2}+\frac{T_{m,n-1}^{\left(k\right)}}{2}\right)+T_{m,n}^{\left(k\right)}\left(1-4F_0\right)-\frac{4h\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\left(T_{m,n}^{\left(k\right)}-T_{fluid}\right)-\frac{4{\mathrm{\ϵc}}_0\mathrm{\Δ}\mathrm{\τ}}{3\mathrm{\ρ}c\mathrm{\Δ}x}\[{\left(T_{m,n}^{\left(k\right)}\right)}^4-T_e^4\]---\left(17\right);$

Wherein, ρ is density, and unit is kg/m³；C is specific heat capacity, and unit is J/ (kg DEG C)；λ is thermal conductivity, and unit is W/ (m K)；T is temperature, and unit is K；X, y are transverse and longitudinal coordinate, and unit is m；Δ x, Δ y are the step pitch in Finite Difference Meshes x, y directions, Unit is m；τ is the time, and unit is s；△ τ are time step, and unit is s；A is temperature diffusivity, and unit is m²/s；To have Temperature of limit difference gridding node (m, n) at the k+1 moment, unit is K；Fo is Fourier number；H is the heat exchange system of rolled piece and environment Number, unit is W/ (m²·K)；ε is blackness；c₀It is the radiation coefficient of black matrix；T_eIt is radiation environment temperature, unit is K；T_fluidIt is right Stream environment temperature or water temperature, unit is K.

3. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 1, it is special Levy and be：FEM meshing is carried out to the rolled piece before the first passes described in step 3, three-dimensional finite element mould is set up Type simultaneously carries out FEM calculation, uses elastoplastic finite metatheory.

4. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 1, it is special Levy and be：Rolled piece described in step 2 is from coming out of the stove, the section temperature before de-scaling and the first passes is calculated, the in step 3 A time FEM meshing and calculating, described in step 4 set up finite element and finite difference coupling model is rolled Process is calculated, and follow-up rolling pass, gap and water in the calculating of finite gap differential temperature and step 6 are rolled described in step 5 Fog cooling temperature computation, data required for calculating include：It is blank parameter, physical parameter, device parameter, rolling technological parameter, comprehensive Close affecting parameters.

5. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 4, it is special Levy and be：Described blank parameter include blank initial length, blank original width, blank original depth, blank tapping temperature, Blank radiused corner radius；Described physical parameter includes the coefficient of heat conduction, specific heat, density, blackness；Described device parameter includes each The spacing of individual equipment, de-scaling and water smoke cooling device parameter；When described rolling technological parameter includes the rolling in rolling each stage Between and off time；Described combined influence parameter includes unit step-length, time step, environment temperature, the heat exchange system in each stage Number.

6. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 5, it is special Levy and be：The determination of described blank parameter is given by operator, the determination of described physical parameter by material composition and temperature Degree determines that described device parameter is arranged by specific workshop and determined, described rolling technological parameter is produced by the rolling of The concrete specification The rolling schedule of product determines.

7. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 5, it is special Levy and be：The coefficient of heat transfer in described each stage include air cooling heat exchange models, the de-scaling coefficient of heat transfer, water smoke cooling heat transferring coefficient, Rolling heat exchange models.

8. the finite element and finite difference coupling process of quick calculating rolled piece section temperature according to claim 7, it is special Levy and be：

Described air cooling heat exchange models：

The heat exchange that rolled piece occurs when placing or being transported on rollgang is mainly produced in the form of radiation and convection current, Convection coefficient is：

H=η (T₀-T_fluid)^0.25(18)；Rolled piece radiation heat transfer heat is：

Φ_r=ε c₀[(T₀)⁴-(T_e)⁴]A (19)；

The radiation blackness ε of rolled piece is the number less than 1,

$\mathrm{\ϵ}=\mathrm{\λ}\[1.1+\frac{T_0}{1000}(0.125\frac{T_0}{1000}-0.38)\]---\left(20\right);$

The determination of the described de-scaling coefficient of heat transfer：

During high-pressure water descaling process, the influence of jet density, hydraulic pressure and rolled piece surface temperature heat exchanging coefficient is than larger, wherein Surface heat exchanging mode is mainly forced convection, and convection coefficient expression formula is：

$h_c=\mathrm{\γ}107.2w^{0.663}\×{10}^{-0.00147T_0}\×1.163---\left(21\right);$

The determination of described water smoke cooling heat transferring coefficient：

It is smaller same using cooling capacity in order to prevent the sputtering of water to not needing the influence of cooling position during rolled piece Local cooling When do not have sputtering water spray cooling mode；Water smoke cooling coefficient of heat transfer expression formula be：

lgh_sw=6.615-0.563lg (H/D)+0.200lgP-0.865lgT₀(22)；

Described rolling heat exchange models：

The operation of rolling causes temperature to raise △ T as disposed of in its entirety, heat during rolling produced by rolled piece plastic deformation：

Δ T=0.183 σ ln μ (23)；

The temperature rise of whole each rolling pass of the operation of rolling can be calculated according to formula (23), the temperature is uniformly added to finite difference In program；

Wherein, T₀It is rolled piece surface temperature, unit is K；η is correction factor；Φ_rIt is radiation exchange heat, unit is W；A is spoke Area is penetrated, unit is m²；λ is correction factor；h_cIt is the de-scaling coefficient of heat transfer, unit is W/ (m²·K)；W is jet density, unit It is L/ (minm²)；γ is influence of hydraulic pressure coefficient；h_swIt is water smoke cooling heat transferring coefficient, unit is W/ (m²·K)；H is arrived for nozzle Steel plate distance, unit is mm；D is nozzle diameter, and unit is mm, and P is hydraulic pressure, and unit is MPa；σ is metal deformation resistance, unit It is MPa, Δ T is plastically deformed the temperature rise for causing for rolled piece in pass, and unit is K；μ is lengthening coefficient；c₀It is the radiation of black matrix Coefficient；T_eIt is radiation environment temperature, unit is K；T_fluidConvection environment temperature or water temperature, unit are K.