CN115846423A - Method for calculating roller temperature in plate and strip rolling process - Google Patents
Method for calculating roller temperature in plate and strip rolling process Download PDFInfo
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Abstract
The invention discloses a method for calculating the temperature of a roller in the process of rolling a plate strip, which comprises the following steps: acquiring various parameters of a working roll; establishing a finite element model of the working roll according to various parameters of the working roll; dividing the working roll into a plurality of heat exchange areas according to the hot rolling working condition; calculating the heat exchange coefficient of each heat exchange area; establishing a temperature field model of the working roll according to the hot rolling working condition and the related parameters of each heat exchange area; the temperature of the working roll is calculated according to the temperature field model of the working roll, the technical problem that the prediction precision of the temperature of the roll is low due to the fact that the circumferential temperature change cannot be accurately predicted in the prior art is solved, the prediction precision of the temperature of the roll can be improved, and the yield of strip steel is further improved.
Description
Technical Field
The invention relates to the technical field of hot-rolled strips, in particular to a method for calculating the temperature of a roller in the strip rolling process.
Background
The roll temperature is one of important process parameters in the strip rolling process, and the roll temperature distribution directly influences the on-load roll gap appearance in the rolling process, so that the control precision of the strip shape of a product is influenced; the distribution of the temperature field of the working roll not only determines the working period and the service life of the working roll, but also the temperature is one of the most main factors influencing the metal deformation resistance in the hot rolling process, so that the quality of a rolled piece is influenced to a great extent by the temperature field of the working roll, and the yield of the strip steel can be effectively improved by predicting the temperature field of the working roll.
In the current research on the temperature field of the roller, a Chinese patent CN 108052757A, a finite element method for determining the temperature field of the working roller in the hot rolling process of the plate and strip steel, provides a rapid and effective finite element method for determining the temperature field of the working roller in the hot rolling process of the plate and strip steel, and omits the calling of subprograms. Bin (machine manufacturing, 2018 (05): 87-91.) using ANSYS to create a work roll two-dimensional transient temperature field, the effect of different factors on work roll temperature was studied; chinese patent CN 110765671A a hot rolling work roll temperature distribution acquisition method and device establishes a two-dimensional work roll temperature field difference equation, the method is clear and definite, few in assumed and simplified conditions, and can accurately forecast the temperature field change of a work roll in the hot rolling process.
The research on the temperature field and the influence factors of the roller is to perform two-dimensional modeling on the roller, neglects the influence of circumferential rotation of the roller on temperature distribution, and cannot accurately predict circumferential temperature change, so that the prediction precision of the roller temperature is low, and further the yield of strip steel is influenced.
Disclosure of Invention
The invention aims to provide a method for calculating the roller temperature in the plate and strip rolling process, which can improve the prediction precision of the roller temperature and further improve the yield of strip steel.
In order to achieve the above object, the present invention provides a method for calculating a roll temperature in a strip rolling process, comprising:
acquiring various parameters of a working roll;
establishing a finite element model of the working roll according to various parameters of the working roll;
dividing the working roll into a plurality of heat exchange areas according to the hot rolling working condition;
calculating the heat exchange coefficient of each heat exchange area;
establishing a temperature field model of the working roll according to the hot rolling working condition and the related parameters of each heat exchange area;
and calculating the temperature of the working roll according to the temperature field model of the working roll.
Preferably, the parameters of the working roll include: the roll comprises a working roll radius, a working roll body length, a working roll rotating speed, a working roll specific heat capacity, a working roll heat conductivity coefficient, a working roll initial temperature, a working roll density, a cooling water temperature and an air temperature.
Preferably, the establishing a finite element model of the work roll according to each parameter of the work roll specifically includes:
according to various parameters of the working roll, carrying out axial, radial and circumferential grid division on the working roll by adopting a thermal unit SOLID 70;
carrying out grid division on the outermost layer of the working roll;
and meshing the interior of the working roll to establish a finite element model of the working roll.
Preferably, according to the hot rolling working condition, the working roll is divided into a plurality of heat exchange areas, which specifically includes:
dividing the axial area of the working roll into three areas, taking the center of the working roll as a starting point, taking the axial direction as an x axis, and dividing the surface of the working roll into three areas by taking the 1/2 width L of a rolled piece as a range, wherein the three areas comprise:
rolling the inner area: x is more than or equal to 0 and less than 1/2L;
rolled edge region: x =1/2L;
rolling the outer area: x is more than 1/2L;
and dividing the surface of the working roll in the rolling internal area into an outlet air cooling area, an outlet water cooling area, a supporting roll contact area, an inlet water cooling area, an inlet air cooling area and a rolling contact area according to the hot rolling working condition of the working roll.
Preferably, the calculating the heat exchange coefficient of each heat exchange region specifically includes:
comprehensive heat exchange coefficient h of supporting roller contact area j Calculated according to the following formula:
h j ＝1.465ΔT 1/3
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air;
the comprehensive heat exchange coefficient h of the rolling contact zone s Calculated according to the following formula:
S＝α 1 +α 2 exp(α 3 T s )
h s ＝α 4 +α 5 S
in the formula (I), the compound is shown in the specification,
T s -strip temperature, deg.c;
α 1 ＝4.168；
α 2 ＝1.712×10 -6 ；
α 3 ＝0.0146；
α 4 、α 5 is a constant whose value is related to the rolling lubrication conditions;
the heat exchange coefficient h of the water cooling area at the inlet or the water cooling area at the outlet cw Calculated according to the following formula:
Q≤10000L/(s·m 2 )
Q≥10000L/(s·m 2 )
in the formula (I), the compound is shown in the specification,
γ 1 -a heat transfer correction factor of the cooling water;
q-water flow density of cooling water, and Q = V sp /A sp ；
P sp -injection pressure, mpa;
T cw -temperature of the cooling water, K;
V sp -amount of cooling water, L/s;
A sp area of ejection, m 2 ；
The heat exchange coefficient h of the inlet air cooling area or the outlet air cooling area α Calculated according to the following formula:
h α ＝1.465ΔT 1/3 ；
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air.
Preferably, the establishing a temperature field model of the work roll according to the hot rolling condition and the related parameters of each heat exchange area specifically includes: and setting the initial temperature of a storage unit, giving physical property parameters to the geometric model and setting boundary conditions according to the hot rolling working condition, the contact area between the working roll and the strip steel, the air cooling area and the water cooling area.
Preferably, the calculating the temperature of the working roll according to the temperature field model of the working roll specifically includes:
arranging influence factors by using an orthogonal test method, substituting specific numerical values of each group of influence factors into the temperature field model of the working roll, and implementing numerical simulation experiments of finite element modeling, solving and extracting roll surface temperature parameters in the rolling process; wherein the influencing factors comprise product specification parameters and process parameters; the product specification parameters comprise initial temperature T1 of rolled pieces, width L of the rolled pieces and initial temperature T2 of cooling water; the process parameters include the roll running speed v.
Taking points in each region of the working roll along the rolling direction, extracting surface temperature change data of the working roll, and fitting by using the surface temperature change data of the working roll to obtain a temperature function of each region of the working roll;
and calculating the temperature of any point on the working roll according to the temperature function of each area of the working roll.
Preferably, the fitting by using the surface temperature change data of the working roll to obtain the temperature function of each region of the working roll specifically includes:
the temperature function of each zone of the roll is fitted using a quadratic polynomial function of the form:
air cooling zone T at outlet 1 (θ)：θ k1 ；
Water cooling zone T at outlet 2 (θ)：θ w1 ；
Contact zone T of the support roller 3 (θ)：θ j ；
Water cooling zone T at inlet 4 (θ)：θ w2 ；
Air cooling zone T at inlet 5 (θ)：θ k2 ；
Rolling contact zone T 6 (θ)：θ z (ii) a (unit: degree)
T(θ)＝A+a 1 t+b 1 t 2 +a 2 T 1 +a 3 T 2 +a 4 t`+b 2 t` 2
t＝2πr/v
Obtaining undetermined coefficients of all the areas to obtain a temperature function T (theta) of the rolling inner and edge rollers; the temperature of the edge area of the roller and the temperature change relationship of the inner area and the outer area can be determined by the following steps:
therefore, compared with the prior art, the method increases the prediction of the circumferential temperature change of the working roll, can specifically analyze the temperature change of the working roll in a three-dimensional state, and provides a formula for predicting the temperature field model of the working roll, so that the prediction precision of the roll temperature can be improved, and the yield of the strip steel can be improved.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a finite element simulation of a work roll according to the present invention;
FIG. 2 is a sectional view of the axial region of a work roll provided by the present invention;
FIG. 3 is a sectional view of a cooling water temperature drop zone provided by the present invention;
FIG. 4 is a detailed calculation chart of the cooling temperature drop range of a single nozzle provided by the present invention;
FIG. 5 is a sectional view of different heat exchange areas on the surface of the roller provided by the invention;
FIG. 6 is a diagram of the temperature field change of the working roll caused by the temperature of the rolled piece provided by the invention;
FIG. 7 is a diagram of the temperature field change of the work roll caused by the temperature of the cooling water provided by the present invention;
FIG. 8 is a comparison example diagram of the simulation data of the surface temperature of the roll according to the present embodiment and the measured data of the surface temperature of the roll in situ.
Detailed Description
The technical solution of the present invention is further illustrated by the accompanying drawings and examples.
As shown in fig. 1 to 8, a method for calculating the roller temperature in the rolling process of a strip comprises the following steps:
step 1, obtaining various parameters of the working roll, namely, obtaining the size of the working roll and various parameters thereof:
the method takes a first frame of working rolls of hot continuous rolling as a calculation prototype, and obtains various parameters of the rolls and value ranges of various factors influencing the temperature of the rolls in detail.
Establishing a finite element model of the working roll according to various parameters of the working roll:
and (3) establishing a 1/2 geometric model of the roller through finite element analysis software according to the relevant parameters determined in the step 1, and carrying out axial, radial and circumferential meshing on the roller model by adopting a thermal unit SOLID 70.
And step 3: the heat exchange area of the working roll is divided according to the arrangement form around the working roll, namely, the working roll is divided into a plurality of heat exchange areas according to the hot rolling working condition.
Divided into three zones in the axial region of the roll, with the roll centre
Is positioned as a starting point and is taken as an x-axis along the axial direction so as to press a rolled piece>
The width L is the range that divides the roll surface into three regions, wherein:
rolling the inner area: x is more than or equal to 0 and less than 1/2L;
rolled edge region: x =1/2L;
rolling the outer area: x is more than 1/2L.
The strip steel bites and fills the roll gap in the rolling process, and the heat exchange boundary of the working roll is changed due to the rotation of the working roll. When the temperature field of the working roll is analyzed, the boundary condition of the working roll changes periodically, namely, the surface of the working roll is repeatedly heated and cooled along with the rotation of the working roll in the rolling process and mainly changes in the rolling internal area, wherein the heat conduction of the working roll to the supporting roll and the friction heat of the working roll and the supporting roll are mutually offset due to the direct contact of the working roll and the supporting roll, so that the heat behavior of the working roll and the supporting roll is not considered to be calculated according to an air cooling area. The surface of the working roll of the rolling inner area is divided into 6 boundary areas,
air cooling area at the outlet: theta k1 ；
Water cooling area at the outlet: theta.theta. w1 ；
Supporting roller contact area: theta j ；
Water cooling area at the inlet: theta w2 ；
Entrance air cooling area: theta k2 ；
Rolling a contact zone: theta z (ii) a (unit: degree)
And 4, step 4: calculating the heat exchange coefficient of each heat exchange area in the working roll manufacturing area:
comprehensive heat exchange coefficient h of contact area of working roll and supporting roll j Calculated according to the following formula:
h j ＝1.465ΔT 1/3
comprehensive heat exchange coefficient h of contact area of working roll and strip steel s Calculated according to the following formula:
S＝α 1 +α 2 exp(α 3 T s )
h s ＝α 4 +α 5 S
forced convection heat transfer coefficient h of cooling water cw Calculated according to the following formula:
Q≤10000L/(s·m 2 )
Q≥10000L/(s·m 2 )
air cooling heat exchange coefficient h of working roll α Calculated according to the following formula:
h α ＝1.465ΔT 1/3
and 5: establishing a working roll temperature field model to extract roll temperature field data, namely establishing the temperature field model of the working roll according to the hot rolling working condition and the related parameters of each heat exchange area;
according to the hot rolling working condition, different area units are respectively a contact area between a working roll and strip steel, an air cooling area and a water cooling area, the initial temperature of a storage unit is set, physical performance parameters are given to the geometric model, boundary conditions are set, and data of the change of the surface temperature of the roll along with time are extracted according to the calculation result of a temperature field.
According to the extracted data, the surface temperature of the roller is analyzed to be the same along the axial change rule, but the temperature in the rolled piece is higher, the temperature at the edge of the rolled piece is rapidly reduced, and the external range of the rolled piece is basically the same as the room temperature and the temperature of the cooling water without obvious change; the temperature along the circumferential direction changes along with the angle change of the roller and changes periodically along with temperature fields in different areas; the temperature change rule along the radial direction is the same as the surface change rule, but the farther the node is away from the surface of the roller, the smaller the temperature rise amplitude is; the closer the nodes are to the roll surface, the greater the magnitude of the temperature rise.
Calculating the temperature of the working roll according to the temperature field model of the working roll, and comprises the following steps of 6-7, wherein the step 6: numerical simulation experiment:
and (5) arranging the influence factors by using an orthogonal test method, substituting the specific numerical value of each group of influence factors into the step 5, and implementing numerical simulation experiments of finite element modeling, solving and extracting the surface temperature parameters of the roller in the rolling process.
And 7: and (3) fitting the roller temperature field data:
according to the partitioning of the temperature field in the step 3, rolling an inner area, a rolling edge area and a rolling outer area, taking points in each area along the rolling direction theta =12 degrees, thereby extracting the surface temperature change data of the roller, and fitting by using all the roller temperature data to obtain a roller temperature function T (theta) in the rolling area, wherein the temperature of the rolling outer area is basically the same as the room temperature and is unchanged, and the rolling edge area is in a linear relation with the inner area and the outer area, so that the roller temperature function T is further obtained General assembly 。
Further, according to the method for calculating the temperature of the roll in the strip rolling process, the modeling parameters comprise the radius of the working roll, the length of the roll body of the working roll, the rotating speed of the working roll, the specific heat capacity of the working roll, the heat conductivity coefficient of the working roll, the initial temperature of the working roll, the density of the working roll, the temperature of cooling water, the temperature of air and the like.
The influencing factors comprise product specification parameters and process parameters; the product specification parameters comprise initial temperature T1 of rolled pieces, width L of the rolled pieces and initial temperature T2 of cooling water; the process parameters include the roll running speed v.
Further, according to the method for calculating the temperature of the roller in the plate strip rolling process, in the step 2, the outermost layer of the working roller is in contact with the plate strip, the deformation is large due to large temperature gradient, so that the working roller is refined, and the internal division is thick. Half of the solid was used for analysis, taking into account the symmetry of the work roll boundary conditions. The generation method is that firstly, a 2-dimensional combined rectangle is built, and then the combined rectangle is rotated by 360 degrees along an axis to form a cylinder. In order to avoid the singularity of the unit from influencing the calculation convergence, a concentric circular hole with a small radius and penetrating through the whole model is dug in the model along the axis direction so as to avoid the singularity of the internal unit. In the analysis, a suitable simplification was made, with 30 equal portions in the radial direction of the work roll, each portion being 12 °, and the zone of the strip in contact with the work roll being one portion.
Further, according to the method for calculating the temperature of the roller in the strip rolling process, in the step 3, the heat exchange area of the working roller is divided, the roller in a temperature balance state is selected, and the center of the roller is used as the center of the roller
Is positioned as a starting point and is taken as an x-axis along the axial direction so as to press a rolled piece>
The width L is the range that divides the roll surface into three regions, wherein:
rolling the inner area: x is more than or equal to 0 and less than 1/2L;
rolled edge region: x =1/2L;
rolling the outer zone: x is more than 1/2L.
And divides the surface of the working roll in the rolling inner area into 6 boundary areas,
the heat exchange area of the water cooling area can be determined according to the injection angle of the nozzle, the distance between the nozzle and the working roll, and the geometric injection condition formula,
where D is the spray range (unit: mm), HD is the nozzle distance (unit: mm) from the work roll, and α is the spray angle (unit: degree). For the convenience of calculation, the heat exchange area theta of the water cooling area is assumed to be directly opposite to the center of the roller w Calculated according to the triangle similarity theory
In the contact area between the working roll and the supporting roll, because the working roll is in direct contact with the supporting roll, the heat conduction of the working roll to the supporting roll and the friction heat of the working roll and the supporting roll are mutually offset and have a small range, and the thermal behaviors of the working roll and the supporting roll are not considered. Is located between the outlet and inlet water cooling, so that when it is regarded as an air cooling model, the range of the contact zone can be obtained from the range of the water cooling zone, and is set as theta j 。
The range of the rolling contact zone is related to the thickness change of the rolled piece before and after rolling,
wherein H' is the initial thickness (unit: mm) of the rolled piece, H is the thickness (unit: mm) of the rolled piece after being rolled by the working roll, and r is the roll radius (unit: mm).
The range of the air cooling zone is the range except the water cooling zone and the contact zone, and is set as theta k 。
In summary, the temperature field is divided into the following regions, as shown in fig. 5:
air cooling area at the outlet: theta k1 ；B-C
Water cooling area at the outlet: theta w1 ；C-D
Supporting roller contact area: theta j ；D-G
Water cooling area at the inlet: theta w2 ；G-H
Entrance air cooling area: theta k2 ；H-A
Rolling a contact zone: theta.theta. z (ii) a A-B. (unit: degree)
Further, according to the method for calculating the temperature of the roller in the strip rolling process, in the step 4, the specific step of calculating the coefficient of each area,
comprehensive heat exchange coefficient h of contact area of working roll and supporting roll j Calculated according to the following formula:
h j ＝1.465ΔT 1/3
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air.
Comprehensive heat exchange coefficient h of contact area of working roll and strip steel s Calculated according to the following formula:
S＝α 1 +α 2 exp(α 3 T s )
h s ＝α 4 +α 5 S
in the formula
In the formula (I), the compound is shown in the specification,
T s -strip temperature, deg.c;
α 1 ＝4.168；
α 2 ＝1.712×10 -6 ；
α 3 ＝0.0146；
α 4 、α 5 is a constant whose value is related to the rolling lubrication conditions;
the values of 4 and 5 under the lubrication condition of no lubrication and water lubrication and the condition of containing 40 percent of CaCO3 hot rolling oil are shown in the table:
the greatest heat loss of the work rolls occurs in the forced convection zone of the cooling water. The geometrical spray conditions such as spray angle, distance of the spray nozzle from the work roll, geometrical position of the header and the like are of great importance. Forced convection heat transfer coefficient h of cooling water cw Calculated according to the following formula:
Q≤10000L/(s·m 2 )
Q≥10000L/(s·m 2 )
in the formula
γ 1 -a heat transfer correction factor of the cooling water;
q-the water flow density of the cooling water and has a value of QV sp /A sp ；
P sp -injection pressure, mpa;
T cw -temperature of the cooling water, K;
V sp -amount of cooling water, L/s;
A sp -ejection area, m2.
Air cooling heat exchange coefficient h of working roll α Calculated according to the following formula:
h α ＝1.465ΔT 1/3
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air.
Further, according to the method for calculating the roller temperature in the plate strip rolling process, in the step 5, a working roller temperature field model is established to extract roller temperature field data, and according to the fact that all factors influencing the working roller temperature field in the step 5 are known, the initial temperature T1 of a rolled piece and the cooling water temperature T2 are in a linear change relation. Due to the fact that the temperature of a rolled piece is changed, the temperature of the roller is changed differently under the comprehensive influence of mutual contradiction between different transmission energy and different heat exchange coefficients. As can be seen from FIG. 6, the temperature of the central surface of the roll rises by about 2.5 ℃ every time the temperature of the strip steel rises by 20 ℃; from FIG. 7, it can be seen that the temperature of the central surface of the roll increases 8 ℃ every time the temperature of the cooling water increases 10 ℃; the roller part which is not contacted with the strip steel is positioned between the temperature of the cooling water and the air, and the temperature of the roller is closer to the temperature of the cooling water; the temperature of the roller and the edge node of the strip steel is between the temperature of cooling water and the temperature of the strip steel in rolling.
Further, according to the method for calculating the roll temperature in the strip rolling process, in the step 6, according to the method for calculating the roll temperature in the strip rolling process, the method is characterized in that 3 factors and 3 levels are adopted to arrange the influencing factors by using an orthogonal test method, and an L9 (33) orthogonal test table is selected to arrange the influencing factors.
Further, according to the calculating method of the roller temperature in the plate strip rolling process, the temperature balance state of the roller in the rolling process can be obtained according to data, and the highest temperature and the lowest temperature are basically kept unchanged when the temperature is balanced.
Further, according to the method for calculating the temperature of the roller in the plate strip rolling process, the polynomial function is used for fitting the temperature function of each area of the roller, and according to the data analysis, the temperature change rule of the roller in each temperature area is different, so that the function is fitted in a segmented mode according to the temperature field.
Further, the method for calculating the roller temperature in the plate strip rolling process is characterized in that linear fitting is adopted in an air cooling area temperature field; fitting by using quadratic polynomial in a temperature field of the water cooling area; linear fitting is adopted in the temperature field in the contact area; the time of rolling is short, and the temperature rise is violent, and linear fitting is adopted.
Further, according to the calculation method of the roll temperature in the strip rolling process, fitting a roll temperature parameter function by using all the roll temperature data extracted in the step (5), and adopting linear fitting in an air cooling area temperature field; fitting by using quadratic polynomial in a temperature field of the water cooling area; linear fitting is adopted in the temperature field in the contact area; the rolling time is short, and the temperature rise is violent, and linear fitting is adopted.
Fitting the initial temperature of the roller during temperature balance: y = A + a 1 t+b 1 t 2 +a 2 T 1 +a 3 T 2 ；
t＝2πr/v
And converting y into T0 to obtain an expression of the initial value of the temperature in the temperature balance period. And (3) adopting a levenberg-Marquardt optimization algorithm in Origin software to perform fitting calculation on the roll temperature parameter function.
Establishing a roller temperature function, taking the initial temperature T1 of a rolled piece, the temperature T2 of cooling water, the running speed v of a roller and the angle theta along the rotation direction of the roller (the initial state of the roller is that the rolled piece enters an outlet water cooling area after being occluded, and at the moment, theta = 0) as 4 input variables, taking an output variable as the temperature T of a corresponding position, and fitting the roller temperature function by using all roller temperature data to obtain the roller temperature function T (theta);
fitting the temperature function of each area of the roller by using a quadratic polynomial function, wherein the quadratic polynomial function has the following form:
air cooling zone T at outlet 1 (θ)：θ k1 ；
Water cooling zone T at outlet 2 (θ)：θ w1 ；
Contact zone T of the support roller 3 (θ)：θ j ；
Water cooling zone T at inlet 4 (θ)：θ w2 ；
Air cooling zone T at inlet 5 (θ)：θ k2 ；
Rolling contact zone T 6 (θ)：θ z . (unit: degree)
T(θ)＝A+a 1 t+b 1 t 2 +a 2 T 1 +a 3 T 2 +a 4 t`+b 2 t` 2
t＝2πr/v
And (4) obtaining the temperature function T (theta) of the rolling inner and edge rolls by calculating the undetermined coefficient of each area. The outer area of the roller is the same as the room temperature, and the temperature change relation between the edge area of the roller and the temperature change relation between the inner area and the outer area can be determined.
In summary,
therefore, the invention comprehensively considers the radial, axial and circumferential temperature changes of the working roll in the three-dimensional state for prediction, obtains the influence rule of each influence factor including product specification and process parameters on the roll temperature, reduces the field reality to the maximum extent, and establishes the three-dimensional solid simulation model of the working roll in the hot rolling process.
The invention axially partitions the roller, determines the range of each area according to the width L of a rolled piece, establishes the quasi-prediction of the temperature distribution of the working roller, solves the problem that the temperature of the roller is difficult to measure in the actual production process, and is beneficial to improving the prediction precision of the temperature of the roller so as to improve the yield of strip steel.
The following examples illustrate the processes provided by the present invention:
step 1: obtaining the size of the working roll and various parameters thereof: the method takes a first working roll of the hot continuous rolling as a calculation prototype, and obtains various parameters of the roll in detail, such as the radius of the working roll, the length of the roll body of the working roll, the rotating speed of the working roll, the specific heat capacity of the working roll, the heat conductivity coefficient of the working roll, the initial temperature of the working roll, the density of the working roll, the temperature of cooling water, the temperature of air and the like.
In this embodiment, the value ranges of the influencing factors include: the initial temperature T1 of the rolled piece ranges from 960 ℃ to 1000 ℃; the temperature T2 of the cooling water is 25-45 ℃; the width L of the rolled piece ranges from 1000mm to 1400mm; the roll running period t is in the range of 3 s-5 s, i.e. the roll speed v is in the range of 0.524 m/s-0.873 m/s.
Step 2: establishing a working roll finite element model: the whole working roll is subjected to axial, radial and circumferential grid division by adopting the thermal unit SOLID70, and the outermost layer of the working roll is in contact with the plate strip, so that the deformation is large due to large temperature gradient, the working roll is refined, and the internal division is thick. Half of the solid was used for analysis, taking into account the symmetry of the work roll boundary conditions. The generation method is to first create a 2-dimensional combined rectangle and then rotate the combined rectangle 360 degrees along the axis to form a cylinder as shown in fig. 1.
In order to avoid the singularity of the unit from influencing the calculation convergence, a concentric circular hole with a small radius and penetrating through the whole model is dug in the model along the axial direction so as to avoid the singularity of the internal unit, as shown in fig. 1. As the outermost layer of the working roll is in contact with the plate strip, the deformation is large due to large temperature gradient, the working roll is refined, and the internal division is thick. Half of the solid was used for analysis, taking into account the symmetry of the work roll boundary conditions. The generation method is that firstly, a 2-dimensional combined rectangle is built, and then the combined rectangle is rotated by 360 degrees along an axis to form a cylinder. In order to avoid the singularity of the unit from influencing the calculation convergence, a concentric circular hole with a small radius and penetrating through the whole model is dug in the model along the axis direction so as to avoid the singularity of the internal unit. In the analysis, a suitable simplification was made, with 30 equal portions in the radial direction of the work roll, each portion being 12 °, and the zone of the strip in contact with the work roll being one portion.
And step 3: divided into three zones in the axial region of the rolls, with the roll centre
Is positioned as a starting point and is taken as an x-axis along the axial direction so as to press a rolled piece>
The width L ranges the roll surface into three regions as shown in fig. 2, where:
rolling the inner area: x is more than or equal to 0 and less than 1/2L;
rolled edge region: x =1/2L;
rolling the outer zone: x is more than 1/2L.
The strip steel bites and fills the roll gap in the rolling process, and the heat exchange boundary of the working roll is changed due to the rotation of the working roll. When the temperature field of the working roll is analyzed, the boundary condition of the working roll changes periodically, namely, the surface of the working roll is repeatedly heated and cooled along with the rotation of the working roll in the rolling process and mainly changes in the rolling internal area, wherein the heat conduction of the working roll to the supporting roll and the friction heat of the working roll and the supporting roll are mutually offset due to the direct contact of the working roll and the supporting roll, so that the heat behavior of the working roll and the supporting roll is not considered to be calculated according to an air cooling area. The surface of the working roll of the rolling inner area is divided into 6 boundary areas.
The heat exchange area of the water cooling area can be determined according to the geometrical injection condition formulas such as the injection angle of the nozzle, the distance between the nozzle and the working roll, and the like, as shown in figure 3,
where D is the spray range (unit: mm), HD is the nozzle distance (unit: mm) from the work roll, and α is the spray angle (unit: degree). For the convenience of calculation, the heat exchange area theta of the water cooling area is assumed to be directly opposite to the center of the roller w Based on triangle similarity theory to calculate out->
Where x is one-half of the distance AB and r is the roll radius (in mm), and where the individual nozzle calculations are shown in FIG. 4.
In the contact area between the working roll and the supporting roll, because the working roll is in direct contact with the supporting roll, the heat conduction of the working roll to the supporting roll and the friction heat of the working roll and the supporting roll are mutually offset and have a small range, and the thermal behaviors of the working roll and the supporting roll are not considered. Is located between the outlet and inlet water cooling, so that when it is regarded as an air cooling model, the range of the contact zone can be obtained from the range of the water cooling zone, and is set as theta j 。
The range of the rolling contact zone is related to the thickness change of the rolled piece before and after rolling,
wherein H' is the initial thickness (unit: mm) of the rolled piece, H is the thickness (unit: mm) of the rolled piece after being rolled by the working roll, and r is the radius (unit: mm) of the roll.
The range of the air cooling zone is the range except the water cooling zone and the contact zone, and is set as theta k 。
In summary, as shown in figure 5 of the drawings,
air cooling area at the outlet: theta k1 ；B-C
Water cooling area at the outlet: theta w1 ；C-D
Supporting roller contact area: theta j ；D-G
Water cooling area at the inlet: theta w2 ；G-H
Entrance air cooling area: theta k2 ；H-A
Rolling a contact zone: theta z (ii) a A-B (unit: degree)
And 4, step 4: calculating the heat exchange coefficient of each heat exchange area in the working roll manufacturing area
Comprehensive heat exchange coefficient h of contact area of working roll and supporting roll j Calculated according to the following formula:
h j ＝1.465ΔT 1/3
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air.
Comprehensive heat exchange coefficient h of contact area of working roll and strip steel s Calculated according to the following formula:
S＝α 1 +α 2 exp(α 3 T s )
h s ＝α 4 +α 5 S
in the formula
T s -strip temperature, deg.c;
α 1 ＝4.168；
α 2 ＝1.712×10 -6 ；
α 3 ＝0.0146；
α 4 、α 5 is a constant whose value is related to the rolling lubrication conditions. No lubrication, water lubrication, 40% CaCO 3 The values of 4 and 5 under the condition of hot rolling oil lubrication are shown in the table:
| constant number | No lubrication | No lubrication | CaCO3 hot rolling oil lubrication |
| α 4 | 32×10 -3 | 52.35×10 -3 | 15.1×10 -3 |
| α 5 | -2.32×10 -3 | -4.175×10 -3 | 0.32×10 -3 |
Forced convection heat transfer coefficient h of cooling water cw Calculated according to the following formula:
Q≤10000L/(s·m 2 )
Q≥10000L/(s·m 2 )
in the formula
γ 1 -heat transfer correction factor of the cooling water;
q-water flow density of cooling water, and has Q = V sp /A sp ；
P sp -injection pressure, mpa;
T cw -temperature of the cooling water, K;
V sp -amount of cooling water, L/s;
A sp area of ejection, m 2 。
Air cooling heat exchange coefficient h of working roll α Calculated according to the following formula:
h α ＝1.465ΔT 1/3
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air.
And 5: establishing a working roll temperature field model to extract roll temperature field data:
according to the hot rolling working condition, different area units are respectively a contact area between a working roll and strip steel, an air cooling area and a water cooling area, the initial temperature of a storage unit is set, physical performance parameters are given to the geometric model, boundary conditions are set, and data of the change of the surface temperature of the roll along with time are extracted according to the calculation result of a temperature field.
According to the extracted data, the surface temperature of the roller is analyzed to be the same along the axial change rule, but the temperature in the rolled piece is higher, the temperature at the edge of the rolled piece is rapidly reduced, and the external range of the rolled piece is basically the same as the room temperature and the temperature of the cooling water without obvious change; the temperature along the circumferential direction changes along with the angle change of the roller and changes periodically along with temperature fields in different areas; the temperature change rule along the radial direction is the same as the surface change rule, but the farther the node is away from the surface of the roller, the smaller the temperature rise amplitude is; the closer the nodes are to the roll surface, the greater the magnitude of the temperature rise.
And (5) establishing a working roll temperature field model to extract roll temperature field data, and knowing that the initial temperature T1 of the rolled piece and the cooling water temperature T2 are in a linear change relationship according to the factors influencing the working roll temperature field in the step 5. Due to the fact that the temperature of a rolled piece is changed, the temperature of the roller is changed differently under the comprehensive influence of mutual contradiction between different transmission energy and different heat exchange coefficients. As can be seen from FIG. 6, the temperature of the central surface of the roll increases by about 2.5 ℃ for every 20 ℃ rise in the temperature of the strip steel.
From FIG. 7, the temperature of the cooling water increases by 8 ℃ for every 10 ℃ increase of the temperature of the central surface of the roller; the roller part which is not contacted with the strip steel is positioned between the temperature of the cooling water and the air, and the temperature of the roller is closer to the temperature of the cooling water; the node temperature of the roller and the edge of the strip steel is between the temperature of the cooling water and the temperature of the strip steel in the roller.
Step 6: numerical simulation experiment:
arranging influence factors by using an orthogonal test method, substituting specific numerical values of each group of influence factors into the step 5, and implementing numerical simulation experiments of finite element modeling, solving and extracting the surface temperature parameters of the roller in the rolling process;
in order to completely analyze the influence of each influence factor on the roller temperature, the influence factors are selected by an orthogonal test method, 3 factors and 3 levels are adopted, an L9 (33) orthogonal test table is selected as shown in table 3, the steps 2, 3 and 4 are repeated according to the values of the influence factors in the table 3, finite element models of 9 groups of rolled pieces in the edge induction heating process are established, each group of models are solved, and the roller temperature data are extracted.
TABLE 3 influence of the orthogonal test method arrangement
| Serial number | Initial temperature T of roller 1 (℃) | Temperature T of cooling water 2 (℃) | Rolling speed v (m/s) |
| 1 | 960 | 25 | 0.524 |
| 2 | 960 | 35 | 0.873 |
| 3 | 960 | 45 | 0.655 |
| 4 | 980 | 25 | 0.873 |
| 5 | 980 | 35 | 0.655 |
| 6 | 980 | 45 | 0.524 |
| 7 | 1000 | 25 | 0.655 |
| 8 | 1000 | 35 | 0.873 |
| 9 | 1000 | 45 | 0.524 |
And (5) further fitting the roll temperature function according to the influence rule of the roll temperature field on the roll temperature field by each influence factor analyzed in the step 5.
Taking the initial temperature T1 of the rolled piece as an example, the temperature of cooling water is 25 ℃, the rolling speed is 0.873m/s, the initial temperature of the rolled piece is 960 ℃, 980 ℃ and 1000 ℃ respectively as an example, the influence rule of the initial temperature change of the rolled piece on the roller temperature is analyzed: with the increase of the initial temperature of the rolled piece, the maximum temperature of the roller rises at the initial moment in the temperature balance period, and the temperature of the central surface of the roller rises by about 2.5 ℃ every time the temperature of the strip steel rises by 20 ℃, as shown in figure 6.
Taking cooling water temperature T2 as an example, rolling temperature is 960 ℃, rolling speed is 0.873m/s, cooling water temperature is respectively 25 ℃, 35 ℃ and 45 ℃ as an example, the influence rule of the cooling water temperature change on the roll temperature is analyzed: as the temperature of the cooling water increases, the surface temperature of the roll decreases by 8 ℃ every time the temperature of the cooling water decreases by 10 ℃ in a temperature balance period, and the temperature changes linearly as shown in FIG. 6.
And 7: and (3) fitting the roller temperature field data:
and (3) partitioning the temperature field according to the width of a rolled piece, rolling an inner region, a rolling edge region and a rolling outer region, taking points in each region along the rolling direction theta =12 degrees, thereby extracting the surface temperature change data of the roller, and fitting by using all the roller temperature data to obtain a roller temperature function T (theta). Fitting the roll temperature parameter function by using all the roll temperature data extracted in the step 5, and adopting linear fitting in the air cooling area temperature field; fitting by using quadratic polynomial in a temperature field of the water cooling area; linear fitting is adopted in the temperature field in the contact area; the time of rolling is short, and the temperature rise is violent, and linear fitting is adopted.
Fitting the initial temperature of the roller during temperature balance: y = A + a 1 t+b 1 t 2 +a 2 T 1 +a 3 T 2 ；
t＝2πr/v
And converting y into T0 to obtain an expression of the initial value of the temperature in the temperature balance period. The Levenberg-Marquardt optimization algorithm in Origin software is adopted to carry out fitting calculation on the roll temperature parameter function
Establishing a roller temperature function, taking the initial temperature T1 of a rolled piece, the temperature T2 of cooling water, the running speed v of a roller and the angle theta along the rotation direction of the roller (the initial state of the roller is that the rolled piece enters an outlet water cooling area after being occluded, and at the moment, theta = 0) as 4 input variables, taking an output variable as the temperature T of a corresponding position, and fitting the roller temperature function by using all roller temperature data to obtain the roller temperature function T (theta);
the temperature function of each zone of the roll is fitted using a quadratic polynomial function of the form:
y＝A+a 1 t+b 1 t 2 +a 2 T 1 +a 3 T 2 +a 4 t`+b 2 t` 2
t＝2πr/v
the undetermined coefficients A, a1 to 4, and b1 to 2 of each region are obtained, and the roll temperature function T (theta) is obtained.
Air cooling zone T at outlet 1 (θ)：θ k1 ；
Water cooling zone T at outlet 2 (θ)：θ w1 ；
Contact area T of support roller 3 (θ)：θ j ；
Water cooling zone T at inlet 4 (θ)：θ w2 ；
Air cooling zone T at inlet 5 (θ)：θ k2 ；
Rolling contact zone T 6 (θ)：θ z . (unit: degree)
In conclusion, the roll temperature function T (theta) is obtained.
Selecting a model with the initial temperature of a rolled piece T1=960 ℃, the temperature of cooling water T2=25 ℃, the running speed of a roller v =0.873m/s, the number of nozzles being 4, the angle of an upper nozzle opening α 1=30 °, the distance from the surface of a work roll HD1=265mm, the height from the 90 ° horizontal line of the work roll H1=612mm, the angle of a lower nozzle opening α 2=50 °, the distance from the surface of the work roll HD2=265mm, the height from the 90 ° horizontal line of the work roll H2=70mm, and the symmetrical arrangement of an inlet and an outlet, respectively substituting the values of T1, T2, and v into the function of T0 obtained in the step 7, and further substituting the values of T1, T2, and v into the function of the temperature of the roller obtained in the step 7 to obtain an expression of the temperature of the roller under the model about the angle θ:
in summary,
and F1 rack is selected for temperature verification. The selected points x are 75.00mm apart and the angle theta =90 DEG
| Distance/mm | 675 | 750 | 825 | 900 | 975 | 1050 |
| Calculated value/. Degree.C | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 |
| found/deg.C | 26.84 | 25.35 | 24.18 | 26.83 | 25.95 | 25.94 |
| Deviation/. Degree.C | -1.84 | -0.35 | 0.82 | -1.83 | -0.95 | -0.94 |
The measured temperatures of the middle position area and the edge area of the working roll are compared with the simulation result as shown in fig. 8; the result shows that the maximum temperature deviation between the measured temperature and the temperature obtained by simulation is about 3.62 ℃, and the effectiveness of the established model is proved.
Finally, it should be noted that: the above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and although the present invention is described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.
Claims (8)
1. A method for calculating the roller temperature in the plate and strip rolling process is characterized by comprising the following steps:
acquiring various parameters of a working roll;
establishing a finite element model of the working roll according to various parameters of the working roll;
dividing the working roll into a plurality of heat exchange areas according to the hot rolling working condition;
calculating the heat exchange coefficient of each heat exchange area;
establishing a temperature field model of the working roll according to the hot rolling working condition and the related parameters of each heat exchange area;
and calculating the temperature of the working roll according to the temperature field model of the working roll.
2. The method of claim 1, wherein the parameters of the work rolls include: the roll comprises a working roll radius, a working roll body length, a working roll rotating speed, a working roll specific heat capacity, a working roll heat conductivity coefficient, a working roll initial temperature, a working roll density, a cooling water temperature and an air temperature.
3. The method for calculating the roll temperature in the strip rolling process according to claim 1, wherein the establishing of the finite element model of the working roll according to each parameter of the working roll specifically comprises:
according to various parameters of the working roll, carrying out axial, radial and circumferential grid division on the working roll by adopting a thermal unit SOLID 70;
carrying out grid division on the outermost layer of the working roll;
and meshing the interior of the working roll to establish a finite element model of the working roll.
4. The method for calculating the roller temperature in the strip rolling process according to claim 1, wherein the step of dividing the working roller into a plurality of heat exchange areas according to the hot rolling condition specifically comprises the following steps:
dividing the axial area of the working roll into three areas, taking the center of the working roll as a starting point, taking the axial direction as an x axis, and dividing the surface of the working roll into three areas by taking the 1/2 width L of a rolled piece as a range comprises the following steps:
rolling the inner area: x is more than or equal to 0 and less than 1/2L;
rolled edge region x =1/2L;
rolling the outer area with x greater than 1/2L;
and dividing the surface of the working roll in the rolling internal area into an outlet air cooling area, an outlet water cooling area, a supporting roll contact area, an inlet water cooling area, an inlet air cooling area and a rolling contact area according to the hot rolling working condition of the working roll.
5. The method for calculating the roll temperature in the strip rolling process according to claim 4, wherein the calculating the heat exchange coefficient of each heat exchange area specifically comprises:
comprehensive heat exchange coefficient h of supporting roller contact area j Calculated according to the following formula:
h j ＝1.465ΔT 1/3
wherein Δ T = T r -T a I.e. the temperature difference between the surface of the work roll and the ambient air;
the comprehensive heat exchange coefficient h of the rolling contact zone s Calculated according to the following formula:
S＝α 1 +α 2 exp(α 3 T s )
h s ＝α 4 +α 5 S
in the formula (I), the compound is shown in the specification,
T s -strip temperature, deg.c;
α 1 ＝4.168；
α 2 ＝1.712×10 -6 ；
α 3 ＝0.0146；
α 4 、α 5 is a constant whose value is related to the rolling lubrication conditions;
the heat exchange coefficient h of the water cooling area at the inlet or the water cooling area at the outlet cw Calculated according to the following formula:
Q≤10000L/(s·m 2 )
Q≥10000L/(s·m 2 )
in the formula (I), the compound is shown in the specification,
γ 1 -heat transfer correction factor of the cooling water;
q-water flow density of cooling water, and has Q = V sp /A sp ；
P sp -injection pressure, mpa;
T cw -temperature of the cooling water, K;
V sp -amount of cooling water, L/s;
A sp area of ejection, m 2 ；
The heat exchange coefficient h of the inlet air cooling area or the outlet air cooling area α Calculated according to the following formula:
h α ＝1.465ΔT 1/3 :
wherein Δ T = T r -T a I.e., the temperature difference between the work roll surface and the ambient air.
6. The method for calculating the roller temperature in the strip rolling process according to claim 5, wherein the establishing of the temperature field model of the working roller according to the hot rolling condition and the relevant parameters of each heat exchange area specifically comprises: and setting the initial temperature of a storage unit, giving physical property parameters to the geometric model and setting boundary conditions according to the hot rolling working condition, the contact area between the working roll and the strip steel, the air cooling area and the water cooling area.
7. The method for calculating the roll temperature in the strip rolling process according to claim 6, wherein calculating the temperature of the working roll according to the temperature field model of the working roll specifically comprises:
arranging influence factors by using an orthogonal test method, substituting specific numerical values of each group of influence factors into the temperature field model of the working roll, and performing numerical simulation experiments of finite element modeling, solving and extracting roll surface temperature parameters in the rolling process; wherein the influencing factors comprise product specification parameters and process parameters; the product specification parameters comprise initial temperature T1 of rolled pieces, width L of the rolled pieces and initial temperature T2 of cooling water; the process parameters include the roll running speed v.
Taking points in each region of the working roll along the rolling direction, extracting surface temperature change data of the working roll, and fitting by using the surface temperature change data of the working roll to obtain a temperature function of each region of the working roll;
and calculating the temperature of any point on the working roll according to the temperature function of each area of the working roll.
8. The method for calculating the roll temperature in the strip rolling process according to claim 7, wherein the fitting is performed by using the surface temperature change data of the working roll to obtain the temperature function of each region of the working roll, and specifically comprises:
fitting the temperature function of each area of the roller by using a quadratic polynomial function, wherein the quadratic polynomial function has the following form:
air cooling zone T at outlet 1 (θ)：θ k1 ；
Water cooling zone T at outlet 2 (θ)：θ w1 ；
Contact zone T of the support roller 3 (θ)：θ j ；
Water cooling zone T at inlet 4 (θ)：θ w2 ；
Air cooling zone T at inlet 5 (θ)：θ k2 ；
Rolling contact zone T 6 (θ)：θ z (ii) a (unit: degree)
T(θ)＝A+a 1 t+b 1 t 2 +a 2 T 1 +a 3 T 2 +a 4 t`+b 2 t` 2
t＝2πr/v
Obtaining undetermined coefficients of all the areas to obtain a temperature function T (theta) of the rolling inner and edge rollers; the temperature of the edge area of the roller and the temperature change relationship of the inner area and the outer area can be determined by the following steps:
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