CN114722516A - Method for setting rolling force and rolling moment of steel strip cold rolling full deformation area - Google Patents

Method for setting rolling force and rolling moment of steel strip cold rolling full deformation area Download PDF

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CN114722516A
CN114722516A CN202210207221.0A CN202210207221A CN114722516A CN 114722516 A CN114722516 A CN 114722516A CN 202210207221 A CN202210207221 A CN 202210207221A CN 114722516 A CN114722516 A CN 114722516A
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steel strip
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李长生
王煜
冯平杰
彭良贵
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Northeastern University China
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Abstract

The invention belongs to the technical field of rolling production, and particularly relates to a method for setting rolling force and rolling moment in a steel strip cold rolling full deformation area. The method mainly comprises the following steps: s1: determining rolling parameters; s2: dividing a deformation area; s3: calculating the thickness of an inlet of the plastic deformation area and the thickness of an outlet of the plastic deformation area; s4: calculating a neutral angle parameter; s5: calculating the total unit width rolling force of the rolling deformation area; s6: calculating unit width torque; s7: and setting the rolling force and the rolling moment in the rolling process according to the finally obtained calculated value of the total unit width rolling force and the calculated value of the unit width torque of the rolling deformation zone. In the method, the difference of the plastic deformation zone and the elastic deformation zone in the rolling pressure is considered and distinguished in the calculation process, the influence of the rolling plastic zone and the elastic deformation zone is comprehensively considered, and the rolling force setting calculation error value is within 8 percent.

Description

Method for setting rolling force and rolling moment of steel strip cold rolling full deformation area
Technical Field
The invention belongs to the technical field of rolling production, and particularly relates to a method for setting rolling force and rolling moment of a steel strip cold rolling full deformation area.
Background
The rolling force is an important parameter for setting a rolling process in the steel strip rolling process, the rolling force is particularly important in the steel strip rolling process in a rapid and accurate forecasting mode, and an automatic system in the rolling process realizes setting and control of a roller gap and a rolling speed in the rolling process according to a set value of the rolling force. With the development of the plate and strip production technology, the requirements of the thickness precision and the plate shape quality of products are improved, which serve as key and fundamental requirements for producing qualified steel strips, and the reasonable rolling force calculation model and the high-precision model directly influence the thickness control and the plate shape quality of the steel strips and are the basis for the automatic control of the steel strips.
The Chinese patent with application number 201510423680.2 discloses a "calculation method for mutual iteration of rolling force and rolling temperature". The invention comprehensively considers the coupling influence among the rolling force, the rolling temperature and the flattening radius, and achieves the purpose of simultaneously improving the predictive performance of the rolling force and rolling temperature models by a numerical iteration method. The Chinese patent with the application number of 201911045319.5 discloses a method for calculating the rolling force of a cold-rolled sheet strip. Parameters of the deformation resistance model and the friction model are optimized by using a least square method through field actual data, and the purposes of improving the prediction effect of the rolling force model and accurately guiding production are achieved. The Chinese patent with application number 202011284055.1 discloses a method for predicting the rolling force and the thickness of each layer of a cold-rolled metal composite plate. And calculating the rolling force of the bimetal composite plate and the thickness of each layer by calculating the rolling force of the soft metal plate blank and the hard metal plate blank during the rolling of respective equivalent single plates.
The Chinese patent with application number 201811435556.8 discloses a rolling force optimization method and a device. Aiming at the problem that the deviation of the set value of the rolling force is large due to the fact that the rolling sample size of a part of gauge steel strips is small, the expected correction coefficients and the neural network coefficients of the actual value and the set value of the rolling force are corrected again, and the final target rolling force setting is obtained. The Chinese patent with application number 201911331771.8 discloses a control method for optimizing a rolling force model based on offline self-adaptation. According to the method, the self-adaptive coefficient Zp of the rolling force is kept near 1.0 by adjusting the relevant parameters of the deformation resistance, the rolling force compensation coefficient and the like, and a new thought is provided for the optimization of the rolling force model. The invention discloses a rolling force prediction method fusing a theoretical model and a big data model in Chinese invention patent with the application number of 202110070446.1. The method establishes a BP neural network model based on actual production data, is used for compensating the prediction error of the rolling force theoretical model, inherits the structure of the theoretical model and exerts the precision of the neural network model.
The rolling force setting in the patent is based on the traditional Hill model and the adaptive correction model, neglects the influence of the elastic zone, or adopts the Ford model to simplify the elastic zone. At present, no method for setting the rolling force and the rolling moment of a steel strip in a plastic zone and a full deformation zone of an elastic zone is available.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for setting the rolling force and the rolling moment in a steel strip cold rolling full deformation area. The rolling force and rolling moment model of the cold rolling full deformation area established by the invention adopts the following basic assumptions:
(1) the width of the steel strip is much greater than the contact arc length and can be considered essentially as a planar deformation problem except for the narrow regions near the two side edges.
(2) The roll remained circular after elastic deformation, and the flattening radius was designated as R'.
(3) The coefficient of friction, μ, is constant throughout the arc of contact and conforms to coulomb's law of friction.
(4) The normal compressive stress is approximately equal to the compressive stress in the vertical direction.
(5) For a point on the arc of contact between the strip and the roll, the arc between the arc of contact and the center line of the roll (arc of contact) is defined as
Figure BDA0003529640570000021
Because of the fact that
Figure BDA0003529640570000022
The value is usually small, so there are
Figure BDA0003529640570000023
As shown in fig. 1, R' is the flattening radius of the roll, the central connecting line of the two rolls is used as the y-axis, the rolling direction is the x-axis to establish a coordinate system, and the rolling inlet direction is the positive direction of the x-axis; the strip deformation zone is divided into three zones along the x-axis, from x to loX 0 to x l is the outlet elastic recovery zonepIs a plastic deformation zone, from x to lpTo x ═ lp+liIs an inlet elastic compression zone. The plastic deformation area is divided into a front sliding area on the near outlet side and a back sliding area on the near inlet side by taking the position of the neutral angle gamma as a boundary line. The inlet elastic compression zone and the outlet elastic recovery zone are collectively referred to as the elastic deformation zone.
x＝lp+liWhere, i.e. at the rolling entry, the thickness of the strip is the strip entry thickness hi；x＝lpThe thickness of the steel strip is the inlet thickness of the plastic deformation zone at the junction of the inlet elastic compression zone and the plastic deformation zone
Figure BDA0003529640570000024
x is 0, namely the junction of the elastic recovery area and the plastic deformation area of the outlet, and the thickness of the steel strip is the thickness of the outlet of the plastic deformation area
Figure BDA0003529640570000025
x＝-loWhere, i.e. at the rolling outlet, the thickness of the strip is the thickness h of the strip outleto；
As shown by the dashed shaded portion in fig. 1, taking a microcell in the deformation region and analyzing the force in the horizontal direction, the general form of the Karman unit rolling pressure differential equation can be obtained:
Figure BDA0003529640570000026
in the formula, pxThe unit rolling pressure at any point x (corresponding to the specific coordinate of the x axis) in the deformation zone, i.e. the rolling pressure per unit area, can be in units of MPa; sigmaxIs the water at point xThe flat stress has the unit of MPa; h is the thickness of the steel strip corresponding to the point x in mm; for the last term of the equation, the forward sliding region takes "+" and the backward sliding region takes "-".
Elastic deformation zone unit rolling pressure calculation
From hooke's theory of elasticity, the stress-strain relationship of the steel strip in the inlet and outlet elastic deformation zones can be expressed as:
Figure BDA0003529640570000031
(3) in the formula (I), the compound is shown in the specification,
Figure BDA0003529640570000032
true strain for the inlet (outlet) elastically deformed region; upsilon issThe Poisson ratio of the steel belt can be generally 0.3; esThe elastic modulus of the steel strip is MPa; sigmai(o)Inlet (outlet) tensile stress, MPa. It is obvious that in the inlet elastic compression zone, equation (4) takes σiAnd hiAt the outlet elastic recovery zone, take σoAnd ho。
The left side and the right side of the formula (2) are simultaneously subjected to derivation on x, and the derivation is obtained by combining the formula (1):
Figure BDA0003529640570000033
due to px+σx＜＜EsAnd the thickness of the steel strip in the elastic zone has little change compared with the whole, so the last term of the equation can be neglected, and the unit rolling pressure differential equation in the elastic zone is expressed as:
Figure BDA0003529640570000034
the relationship between the variables h and x in the differential equation of equation (6) can be expressed in terms of the radian measure between the contact arc of point x and the center line of the roll
Figure BDA0003529640570000035
(arc of contact arc). Since the contact arc in actual rolling is much smaller than the roll radius (the contact angle in cold rolling is usually not more than 4-8 °), replacing the contact curve with the following parabola has sufficient accuracy:
Figure BDA0003529640570000036
the thickness h of the steel strip corresponding to each point x in the deformation area on the x axis of the established coordinate system can be calculated by the formula (7), and the formula (7) is substituted into the formula (6):
Figure BDA0003529640570000037
for convenience of writing and calculation, new variables u and m are introduced:
Figure BDA0003529640570000041
by substituting u and m in formula (9) into formula (8), it is possible to obtain:
Figure BDA0003529640570000042
the boundary conditions at the inlet side and the outlet side of the elastic deformation zone can be expressed as:
when x is ═ loValue of time, variable u
Figure BDA0003529640570000043
When x is equal to lp+liValue of time, variable u
Figure BDA0003529640570000044
Wherein
Figure BDA0003529640570000045
Each is x ═ lo、x＝lp+li、x＝lpRelative reduction values at several critical locations.
According to the standard solution of the first-order linear differential equation, for any point x (corresponding to a relative u value) of the outlet elastic recovery zone, the unit rolling pressure of the outlet elastic recovery zone is solved
Figure BDA0003529640570000046
Comprises the following steps:
Figure BDA0003529640570000047
for any x point (corresponding to a u value) of the inlet elastic compression zone, the unit rolling pressure of the inlet elastic compression zone
Figure BDA0003529640570000048
Comprises the following steps:
Figure BDA0003529640570000049
the integral terms in equations (13) and (14) are approximated as follows:
Figure BDA00035296405700000410
the approximate expression (15) is substituted into the expressions (13) and (14) to obtain the expressions (16) and (17), which are functions with u as a single variable:
Figure BDA0003529640570000051
Figure BDA0003529640570000052
when x is 0, u is 0, the position is the boundary of the elastic recovery area from the outlet and the plastic deformation area,substitution formula (14), unit rolling pressure p of the positionoComprises the following steps:
Figure BDA0003529640570000053
when x is equal to lpWhen the corresponding variable u is equal to
Figure BDA0003529640570000054
The position is the boundary from the inlet elastic compression area to the plastic deformation area, and is substituted by a formula (15), and the unit rolling pressure p of the positioniComprises the following steps:
Figure BDA0003529640570000055
formulae (20) and (21) are substituted for formulae (18) and (19), respectively, to give:
Figure BDA0003529640570000056
Figure BDA0003529640570000057
(II) calculation of Unit Rolling pressure in Plastic deformation zone
In the region of plastic deformation, unit rolling pressure pxWith horizontal stress sigmaxMeets the Mises yield criterion, namely:
Figure BDA0003529640570000058
in the formula, k is yield shear stress, MPa; and 2k is deformation resistance.
Formula (24) is substituted for formula (1), and the Karman differential equation can be rewritten as:
Figure BDA0003529640570000059
continuing with the parabolic approximation of equation (7), and introducing variables u and m defined by equation (9), we conclude that:
Figure BDA00035296405700000510
the unit rolling pressure of a certain point x (corresponding to u) of the forward sliding region can be obtained by solving the differential equation (26) in place of the boundary conditions of the equations (20) and (21)
Figure BDA00035296405700000511
Comprises the following steps:
Figure BDA0003529640570000061
specific rolling pressure at a certain point x (corresponding to u) of the back-sliding zone
Figure BDA0003529640570000062
Comprises the following steps:
Figure BDA0003529640570000063
wherein 2k isoResistance to deformation of the elastic recovery zone of the outlet, 2kiFor the deformation resistance of the elastic compression region of the inlet, the plastic deformation region at the inlet (x ═ l)p) Horizontal stress σ 'of'i＝2ki-piHorizontal stress σ of 0 at outlet of plastic deformation zone x ═ x'o＝2ko-po(ii) a 2k is the deformation resistance of the plastic deformation zone.
Likewise, the following approximate conditions were introduced:
Figure BDA0003529640570000064
and substituted into formulae (27) and (28) to obtain:
Figure BDA0003529640570000065
Figure BDA0003529640570000066
from the above analysis, it is necessary to determine the entrance (x ═ l) of the plastic deformation region to calculate the unit pressure distribution of the elastic region and the plastic deformation regionp) And the thickness of the steel strip at the outlet (x ═ 0)
Figure BDA0003529640570000067
And
Figure BDA0003529640570000068
since the steel strip necessarily satisfies the plastic condition in the plastic deformation region, it can be known from equation (24):
Figure BDA0003529640570000069
the following relationship can be obtained by substituting formula (32) for formula (2):
Figure BDA00035296405700000610
combining the first formula of formula (29) with formula (16)
Figure BDA00035296405700000611
In combination, it is not difficult to find that the resistance to deformation is 2koOutlet tensile stress σoOutlet steel strip thickness hoAnd the modulus of elasticity and the Poisson ratio of the steel strip are known, only exist
Figure BDA0003529640570000071
An unknown quantity, whereby the unknown quantity can be obtained
Figure BDA0003529640570000072
Meter (2)And calculating a result.
In the same way, the second formula of formula (17) and formula (29) are combined and substituted into the obtained
Figure BDA0003529640570000073
Can calculate out
Figure BDA0003529640570000074
Neutral angle parameter (III)
The unit rolling pressure distribution curves of the front sliding area and the rear sliding area at the neutral point are intersected, namely the position of the maximum rolling pressure is also the boundary of the front sliding area and the rear sliding area, and the contact arc corresponding to the neutral point is a neutral angle gamma.
Let u be the value of u (neutral angle parameter) corresponding to the coordinate of the neutral point on the x-axisγThe unit rolling pressures calculated according to the unit rolling pressure formulas of the front sliding zone and the rear sliding zone at the neutral point should be equal, and the following formulas (30) and (31) show that:
Figure BDA0003529640570000075
equation (34) the neutral angle parameter u can be easily determined by the dichotomyγ。
(IV) calculation of Total Rolling force
The total rolling force per unit width of the entire rolling deformation zone is the sum of the total pressure of the plastic deformation zone and the elastic deformation zone, i.e.
Figure BDA0003529640570000076
Wherein F is the total unit width rolling force; fpThe rolling force is the unit width rolling force of the plastic deformation area;
Figure BDA0003529640570000077
the rolling force is the unit width rolling force of the outlet elastic recovery area;
Figure BDA0003529640570000078
is the unit width rolling force of the inlet elastic compression area.
According to the geometrical relationship of the rolling deformation zone, the unit width rolling force acting on the roller can be expressed as:
Figure BDA0003529640570000079
in the formula
Figure BDA00035296405700000710
Alpha and gamma are respectively at the rolling outlet (x ═ l)oWhere), at the rolling inlet (x ═ l)p+liWhere), neutral point (u ═ u-γWhere) arc of contact (with the roller centerline at 0 degrees), and p is the unit rolling pressure corresponding to the arc of contact. The vertical component of the friction force in brackets in the above formula contributes very little to the total rolling force and is negligible. The rolling force per unit width of the plastic deformation zone is therefore the integral of equations (30) and (31) over the plastic deformation zone, the value of which is related to the ratio of r, m,
Figure BDA00035296405700000711
the four values are related:
Figure BDA0003529640570000081
it is understood that the upper limit α of integration in the formula (33)pIs x ═ lpThe arc of contact arc at the position, namely the intersection of the inlet elastic compression area and the plastic deformation area, represents the starting point of the plastic deformation area; the lower integration limit 0 is x equal to 0, namely the contact arc radian of the intersection of the outlet elastic recovery area and the plastic deformation area represents the end point of the plastic deformation area; the middle integration point gamma represents the neutral angle, which is the boundary between the forward and aft slip regions.
Similarly, the integration of equation (22) in the exit elastic recovery region yields the exit elastic recovery region with a rolling force per unit width of:
Figure BDA0003529640570000082
the integral of equation (23) yields the rolling force per unit width of the inlet elastic compression region as:
Figure BDA0003529640570000083
(V) calculation of Rolling Torque
According to the Bland-Ford theory, the torque per unit width T can be expressed as:
Figure BDA0003529640570000084
according to the formula (40), the rolling torque can be decomposed into the rolling torque reference term caused by the rolling force
Figure BDA0003529640570000085
And the tension-influencing term. Rolling torque reference term
Figure BDA0003529640570000086
Can be further expressed as:
Figure BDA0003529640570000087
in the formula (I), the compound is shown in the specification,
Figure BDA0003529640570000091
rolling torque reference items in a plastic deformation area;
Figure BDA0003529640570000092
rolling a torque reference item in an outlet elastic recovery area;
Figure BDA0003529640570000093
rolling a torque reference term for the inlet elastic compression area. The three items can be respectively expressed as:
Figure BDA0003529640570000094
Figure BDA0003529640570000095
Figure BDA0003529640570000096
therefore, the total unit width rolling force and the unit width torque in the rolling process are obtained, and the set values of the rolling force and the rolling torque in the rolling process can be obtained after multiplying the total unit width rolling force and the unit width torque by the width of the steel strip respectively.
Most of the parameters in the above calculation process (e.g. the inlet and outlet thickness h of the steel stripi、hoCoefficient of friction of work rolls, R, and unit tension or tensile stress of steel strip inlet and outleti、σ0Etc.) can be determined by the actual conditions of rolling.
For the cold rolling process of the steel strip, the deformation resistance 2k at a certain point x of a plastic deformation zonexThe following formula can be used for calculation:
Figure BDA0003529640570000097
in the formula hxThe thickness of the steel strip at the point x (equation (5)), hinitIs the thickness of the steel strip incoming material, kmIn order to consider the deformation resistance reference constant of the material characteristics, epsilon and n are deformation resistance model parameters, the formula is a mature formula in the prior art, the parameters can be obtained by means of regression experiments and the like, and the obtaining methods are all the prior art.
2kiResistance to deformation at the inlet, 2koFor the deformation resistance at the outlet, h is respectively adoptedi、hoSubstituted into h in the above formulaxAnd (4) calculating. In the elastically deformed region, the deformation resistance can be regarded asDoes not change, so 2kiAnd 2koAnd also the deformation resistance of the inlet elastically compressed region and the outlet elastically deformed region, respectively. In the plastic deformation region, the deformation resistance varies with the value of x and the value of u, and the average deformation resistance 2k in the plastic deformation region can be used in the calculation of the formula (33). Specifically, the average deformation resistance 2k may be a definite integral average of the deformation resistances of the plastic deformation regions.
The mutual coupling relation exists between the rolling force and the flattening radius of the roller, the rolling force can be numerically solved in an iteration mode, and the iteration can be stopped until the relative error of the two flattening radii at the front and the back meets a certain precision requirement. The iterative convergence condition herein is defined as:
Figure BDA0003529640570000101
in the formula (II), R'0Calculating the value of the flattening radius in mm; r' is a calculated value of the last flattening radius, namely the value of the flattening radius used in the calculation, namely mm; epsilonRFor iterative calculation accuracy, 10 is generally taken-3The requirements can be met. Meanwhile, in order to prevent the calculation from falling into an infinite iteration loop, a maximum iteration loop number, for example, 5 iteration loop numbers, may be given to ensure the model calculation time.
For the continuous rolling process, the method can be used for setting and calculating the rolling force and the rolling moment of a certain cold rolling pass.
The overall idea of the calculation of the present invention is described above, and the following describes the specific steps of the present invention, and the method of the present invention includes the following basic steps:
s1: determining rolling parameters:
the rolling parameters mainly comprise: thickness h of steel strip supplied materialinitThickness h of steel strip entranceiOutlet thickness h of steel stripoModulus of elasticity E of steel stripsModulus of elasticity E of work rollwrInlet unit tension σiOutlet unit tension σoThe friction coefficient mu of the roller and the steel strip and the radius R of the roller;
s2: establishing a coordinate system, and dividing a deformation area:
establishing a coordinate system by taking a central connecting line of the two rollers as a y axis and a rolling direction as an x axis, wherein a rolling inlet direction is the positive direction of the x axis; the strip deformation zone is divided into three zones along the x-axis, from x to loTo x-0 is the outlet elastic recovery zone, from x-0 to x-lpIs a plastic deformation zone, from x to lpTo x ═ lp+liAn inlet elastic compression zone;
x＝lp+lithe thickness of the steel strip at the position is the thickness h of the steel strip inleti，x＝lpThe thickness of the steel strip is the thickness of the inlet of the plastic deformation zone
Figure BDA0003529640570000102
The thickness of the steel strip at the position where x is 0 is the thickness of the outlet of the plastic deformation area
Figure BDA0003529640570000103
x＝-loThe thickness of the steel strip is the outlet thickness h of the steel stripo；
The thickness of the steel strip corresponding to any x value on the x axis in the deformation zone
Figure BDA0003529640570000104
R' is the flattening radius of the roller;
s3: calculating the inlet thickness of the plastic deformation zone
Figure BDA0003529640570000105
And outlet thickness of plastic deformation zone
Figure BDA0003529640570000106
Introducing variables u and m related to x:
Figure BDA0003529640570000111
outlet thickness of plastic deformation zone
Figure BDA0003529640570000112
Calculated using the formula:
Figure BDA0003529640570000113
wherein 2k isoResistance to deformation of the elastic recovery zone of the outlet, poFor the unit rolling pressure starting from the outlet elastic recovery zone into the plastic deformation zone, the calculation formula is as follows:
Figure BDA0003529640570000114
wherein x is-loRelative reduction of
Figure RE-GDA0003692248270000115
Is x ═ loThe value of the variable u;
Figure RE-GDA0003692248270000116
inlet thickness of plastic deformation zone
Figure BDA0003529640570000117
Calculated using the formula:
Figure BDA0003529640570000118
wherein 2k isiThe unit rolling pressure p at which the elastic compression zone of the inlet starts to enter the plastic deformation zone is the deformation resistance of the elastic compression zone of the inletiThe calculation formula is as follows:
Figure BDA0003529640570000119
wherein x is lp+liRelative reduction of
Figure BDA00035296405700001110
Is x ═ lp+liValue of the variable u, urIs x ═ lpThe value of the variable u:
Figure BDA00035296405700001111
wherein x is lpRelative reduction of
Figure BDA00035296405700001112
S4: calculating a neutral angle parameter:
neutral angle parameter uγThe corresponding variable u value at the neutral angle γ is calculated using the following formula:
Figure BDA0003529640570000121
s5: calculating the total unit width rolling force F of the rolling deformation zone:
the total rolling force per unit width F of the entire rolling deformation region is the sum of the rolling forces per unit width of the plastic deformation region and the elastic deformation region, i.e.
Figure BDA0003529640570000122
Wherein F is the total unit width rolling force, FpIs the rolling force per unit width of the plastic deformation zone,
Figure BDA0003529640570000123
for the rolling force per unit width of the elastic recovery zone of the outlet, Fi eThe unit width rolling force of an inlet elastic compression area;
wherein:
Figure BDA0003529640570000124
wherein 2k is the deformation resistance of the plastic deformation regionHorizontal stress σ 'at the inlet'i＝2ki-piHorizontal stress σ 'at exit of plastic deformation zone'o＝2ko-po；
Figure BDA0003529640570000125
Figure BDA0003529640570000126
S6: calculating the unit width torque T:
the unit width torque T is expressed as:
Figure BDA0003529640570000127
wherein the rolling torque reference term
Figure BDA0003529640570000128
Can be further expressed as:
Figure BDA0003529640570000129
in the formula (I), the compound is shown in the specification,
Figure BDA00035296405700001210
rolling torque reference items in a plastic deformation area;
Figure BDA00035296405700001211
rolling a torque reference item in an outlet elastic recovery area;
Figure BDA00035296405700001212
rolling a torque reference item in an elastic compression area of the inlet; the three items can be respectively expressed as:
Figure BDA0003529640570000131
Figure BDA0003529640570000132
Figure BDA0003529640570000133
s7: and setting the rolling force and the rolling moment in the rolling process according to the finally obtained calculated value F of the total unit width rolling force and the calculated value T of the unit width torque of the rolling deformation zone.
In the above method, the deformation resistance 2k of the inlet elastic compression region for the cold rolling processiThe calculation method comprises the following steps:
Figure BDA0003529640570000134
deformation resistance 2k of the elastic recovery zone of the outletoThe calculation method comprises the following steps:
Figure BDA0003529640570000135
the deformation resistance 2k of a certain point with the abscissa of the plastic deformation area as xxThe calculation method comprises the following steps:
Figure BDA0003529640570000136
in the formula hxThickness of the strip at point x, hinitIs the thickness of the steel strip incoming material, kmAnd epsilon and n are deformation resistance model parameters for considering the deformation resistance reference constant of the material characteristics.
In the plastic deformation region, the deformation resistance 2k may be an average deformation resistance over the entire plastic deformation region, for example, an average deformation resistance calculated by a constant integral may be used.
Since the rolling force and the flattening radius have a coupled relationship with each other, in the above method, the flattening radius R' needs to correspond to a calculated value of the rolling force. For this purpose, the values of the flattening radius R', the total rolling force per unit width F and the torque per unit width T of the rolling deformation zone can be obtained in an iterative manner, as shown in fig. 2, and the specific method is as follows:
recalculating crush radius R 'from current F value after calculating current calculated values of F and T from the steps S2 to S6 using current crush radius R'oAnd judging whether the current iterative calculation process meets the iterative convergence condition: if the iteration convergence condition is met, the calculation is finished, and the calculated values F and T obtained in the steps S5 and S6 of the current iteration calculation process are final values, and are used in the step S7; if the iterative convergence condition is not met, recalculating the current obtained flattening radius R'oIterate back to step S2, and perform the next iterative calculation of steps S2 to S6 as a new crush radius R'.
The initial value of the flattening radius R', namely the flattening radius R, is the roll radius R in the first calculation.
The iterative convergence condition is
Figure BDA0003529640570000141
εRFor iterative calculation accuracy, take not more than 10-3The numerical value of (c).
Recalculating crush radius R 'from current F value'oOne method of (1) is as follows:
Figure BDA0003529640570000142
in the formula (I), the compound is shown in the specification,
Figure BDA0003529640570000143
Ewrthe modulus of elasticity of the roll.
The invention has the beneficial effects that: the invention provides a method for setting and calculating the rolling force and the rolling moment of a steel strip rolling total deformation area, which considers and distinguishes the difference of a plastic deformation area and an elastic deformation area in the rolling pressure in the calculation process, comprehensively considers the influence of the rolling plastic area and the elastic deformation area, and sets the calculation error value of the rolling force within 8 percent.
Drawings
FIG. 1: the rolling deformation zone of the present invention is divided into schematic diagrams.
FIG. 2: the invention provides a flow chart of iterative computation.
Detailed Description
Example 1
Taking 1740mm five-stand six-roller cold continuous rolling unit as an example, the diameter of a working roller of the unit is 430-480 mm, the diameter of a middle roller of the unit is 510-580 mm, the diameter of a supporting roller of the unit is 1315-1465 mm, and the maximum rolling force of the unit is 32000 kN. The pre-rolling thickness (i.e., rolled strip entry thickness/pre-rolling thickness), post-rolling thickness (rolled strip exit thickness/post-rolling thickness), front-to-back tension, and rolling force and measured rolling force calculated using the method of the present invention for each rolling pass of a DP590 strip having a width of 1358mm are shown in table 1.
Table 1 example 1 steel strip thickness, front and rear tension, calculated rolling force and measured rolling force
Figure BDA0003529640570000144
Figure BDA0003529640570000151
As can be seen from Table 1, the error between the cold rolling force and the actually measured rolling force of the DP590 steel strip calculated by the method is within 7.6%, the error between the calculated value and the actually measured value of the rolling moment is within 19.8%, and the precision is high.
Example 2
Taking 1740mm five-stand six-roller cold continuous rolling unit as an example, the diameter of a working roller of the unit is 430-480 mm, the diameter of a middle roller of the unit is 510-580 mm, the diameter of a supporting roller of the unit is 1315-1465 mm, and the maximum rolling force of the unit is 32000 kN. The thickness before rolling (i.e., rolled strip entrance thickness/thickness before rolling), the thickness after rolling (rolled strip exit thickness/thickness after rolling), the tension before and after rolling, and the rolling force and the measured rolling force calculated using the method of the present invention for each rolling pass of a W780QX steel strip having a width of 1223mm are shown in Table 2.
Table 2 example 2 thickness, front and rear tension, calculated rolling force and measured rolling force of steel strip
Figure BDA0003529640570000152
As can be seen from Table 2, the error between the cold rolling force and the actually measured rolling force of the W780QX steel strip calculated by the method is within 7.8%, the error between the calculated value and the actually measured value of the rolling moment is within 15.7%, and the precision is high.
Example 3
Taking a six-roller cold continuous rolling unit of 1340mm as an example, the diameter of a working roller of the unit is 420-460 mm, the diameter of a middle roller of the unit is 440-490 mm, the diameter of a supporting roller of the unit is 1000-1090 mm, and the maximum rolling force of the unit is 15000 kN. The thickness before rolling (rolled strip entrance thickness/thickness before rolling), the thickness after rolling (rolled strip exit thickness/thickness after rolling), the tension before and after rolling, and the rolling force and the measured rolling force calculated using the method of the present invention for each rolling pass of a 16Mn steel strip having a width of 919.0mm are shown in table 3.
Table 3 example 3 steel strip thickness, front and rear tension, calculated rolling force and measured rolling force
Figure BDA0003529640570000161
As can be seen from Table 3, the error between the 16Mn steel strip cold rolling force calculated by the method and the actually measured rolling force is within 7.4%, the error between the calculated value of the rolling moment and the actually measured value is within 16.6%, and the precision is high.
Example 4
Taking a six-roller cold continuous rolling unit of 1340mm as an example, the diameter of a working roller of the unit is 420-460 mm, the diameter of a middle roller of the unit is 440-490 mm, the diameter of a supporting roller of the unit is 1000-1090 mm, and the maximum rolling force of the unit is 15000 kN. The pre-rolling thickness (rolled strip entrance thickness/pre-rolling thickness), the post-rolling thickness (rolled strip exit thickness/post-rolling thickness), the front-to-back tension, and the rolling force and measured rolling force calculated using the method of the present invention for each rolling pass of a Q215 steel strip having a width of 1044.0mm are shown in Table 4.
Table 4 example 4 thickness of steel strip, front and rear tension, calculated rolling force and measured rolling force
Figure BDA0003529640570000162
As can be seen from Table 4, the error between the cold rolling force and the actually measured rolling force of the Q215 steel strip calculated by the method is within 4%, the error between the calculated value and the actually measured value of the rolling moment is within 18.1%, and the precision is high.

Claims (9)

1. A method for setting rolling force and rolling moment in a steel strip cold rolling full deformation area is characterized by comprising the following steps:
s1: determining rolling parameters;
s2: dividing a deformation area;
s3: calculating the inlet thickness of the plastic deformation zone
Figure FDA0003529640560000011
And plastic deformation zone exit thickness
Figure FDA0003529640560000012
S4: calculating a neutral angle parameter;
s5: calculating the total unit width rolling force F of the rolling deformation area;
s6: calculating unit width torque T;
s7: and setting the rolling force and the rolling moment in the rolling process according to the finally obtained calculated value F of the total unit width rolling force and the calculated value T of the unit width torque of the rolling deformation zone.
2. The method for setting the rolling force and the rolling moment in the cold-rolled full-deformation zone of the steel strip according to claim 1, comprising the following steps:
s1: determining rolling parameters:
the rolling parameters mainly comprise: thickness h of steel strip supplied materialinitThickness h of steel strip entranceiOutlet thickness h of steel stripoModulus of elasticity E of steel stripsModulus of elasticity E of work rollwrInlet unit tension σiOutlet unit tension σoThe friction coefficient mu between the roller and the steel strip and the radius R of the roller;
s2: establishing a coordinate system, and dividing a deformation area:
establishing a coordinate system by taking a central connecting line of the two rollers as a y axis and a rolling direction as an x axis, wherein a rolling inlet direction is the positive direction of the x axis; the strip deformation zone is divided into three zones along the x-axis, from x to loX 0 to x l is the outlet elastic recovery zonepIs a plastic deformation zone, from x to lpTo x ═ lp+liAn inlet elastic compression zone;
x＝lp+lithe thickness of the steel strip at the position is the thickness h of the steel strip inleti，x＝lpThe thickness of the steel strip is the inlet thickness of the plastic deformation zone
Figure FDA0003529640560000013
The thickness of the steel strip at the position where x is 0 is the thickness of the outlet of the plastic deformation area
Figure FDA0003529640560000014
x＝-loThe thickness of the steel strip is the outlet thickness h of the steel stripo；
The thickness of the steel strip corresponding to any x value on the x axis in the deformation zone
Figure FDA0003529640560000015
R' is the flattening radius of the roller;
s3: calculating the inlet thickness of the plastic deformation zone
Figure FDA0003529640560000016
And plastic deformation zone exit thickness
Figure FDA0003529640560000017
Introducing variables u and m related to x:
Figure FDA0003529640560000018
outlet thickness of plastic deformation zone
Figure FDA0003529640560000019
Calculated using the formula:
Figure FDA0003529640560000021
wherein 2k isoResistance to deformation of the elastic recovery zone of the outlet, poFor the unit rolling pressure starting from the outlet elastic recovery zone into the plastic deformation zone, the calculation formula is as follows:
Figure FDA0003529640560000022
wherein x is-loRelative reduction of
Figure FDA0003529640560000023
Figure FDA0003529640560000024
Is x ═ loThe value of the variable u at the time of day,
Figure FDA0003529640560000025
inlet thickness of plastic deformation zone
Figure FDA0003529640560000026
Calculated using the formula:
Figure FDA0003529640560000027
wherein 2k isiFor the deformation resistance of the elastic compression zone of the entry, the specific rolling pressure p at which the elastic compression zone of the entry begins to enter the plastic deformation zoneiThe calculation formula is as follows:
Figure FDA0003529640560000028
wherein x is lp+liRelative reduction of
Figure FDA0003529640560000029
Figure FDA00035296405600000210
Is x ═ lp+liValue of the variable u, urIs x ═ lpThe value of the variable u:
Figure FDA00035296405600000211
wherein x ═ lpRelative reduction of
Figure FDA00035296405600000212
S4: calculating a neutral angle parameter:
neutral angle parameter uγFor the value of the variable u corresponding to the neutral angle γ, the following formula is used to calculate:
Figure FDA00035296405600000213
s5: calculating the total unit width rolling force F of the rolling deformation area:
the total rolling force per unit width F of the entire rolling deformation zone is the sum of the rolling forces per unit width of the plastic deformation zone and the elastic deformation zone, i.e.
Figure FDA0003529640560000031
Wherein F is the total rolling force per unit width, FpIs the rolling force per unit width of the plastic deformation zone,
Figure FDA0003529640560000032
for the rolling force per unit width of the elastic recovery zone of the outlet, Fi eThe unit width rolling force of an inlet elastic compression area;
wherein:
Figure FDA0003529640560000033
wherein 2k is the average deformation resistance of the plastic deformation zone, and the horizontal stress sigma 'at the inlet of the plastic deformation zone'i＝2ki-piHorizontal stress σ 'at exit of plastic deformation zone'o＝2ko-po；
Figure FDA0003529640560000034
Figure FDA0003529640560000035
S6: calculating the unit width torque T:
the unit width torque T is expressed as:
Figure FDA0003529640560000036
wherein the rolling torque reference term
Figure FDA0003529640560000037
Can be further expressed as:
Figure FDA0003529640560000038
in the formula (I), the compound is shown in the specification,
Figure FDA0003529640560000039
rolling torque reference items in a plastic deformation area;
Figure FDA00035296405600000310
rolling a torque reference item in an outlet elastic recovery area;
Figure FDA00035296405600000311
rolling a torque reference term for an inlet elastic compression zone; the three items can be respectively expressed as:
Figure FDA00035296405600000312
Figure FDA0003529640560000041
Figure FDA0003529640560000042
s7: and setting the rolling force and the rolling moment in the rolling process according to the finally obtained calculated value F of the total unit width rolling force and the calculated value T of the unit width torque of the rolling deformation zone.
3. The method for setting the rolling force and the rolling moment in the full deformation zone for cold rolling of the steel strip according to claim 2, wherein the values of the flattening radius R', the total unit width rolling force F and the unit width torque T in the rolling deformation zone are obtained in an iterative manner, and the method comprises the following steps:
recalculating crush radius R 'from current F value after calculating current calculated values of F and T from the steps S2 to S6 using current crush radius R'oAnd judging whether the current iterative computation process meets the iterative convergence condition: if the iteration convergence condition is met, the calculation is finished, and the calculated values F and T obtained in the steps S5 and S6 of the current iteration calculation process are final values, and are used in the step S7; if the iterative convergence condition is not met, recalculating the current obtained flattening radius R'oIterate back to step S2 for the next iteration as the new crush radius R'.
4. The method for setting the rolling force and the rolling moment in the full deformation zone for cold rolling of steel strip according to claim 3, wherein the iterative convergence condition is
Figure FDA0003529640560000043
εRThe accuracy is calculated iteratively.
5. The method for setting the rolling force and the rolling moment in the full deformation zone for cold rolling of steel strip according to claim 4, wherein the iterative calculation precision εRNot more than 10-3。
6. The method for setting the rolling force and the rolling moment in the full deformation zone for cold rolling of steel strip according to claim 3, wherein the flattening radius R is recalculated based on the current F valueoThe method of' is:
Figure FDA0003529640560000044
in the formula (I), the compound is shown in the specification,
Figure FDA0003529640560000045
Ewrthe modulus of elasticity of the roll.
7. The method for setting the rolling force and the rolling moment in the cold-rolled full-deformation zone of the steel strip according to claim 3, wherein the roll radius R is used as the initial value of the flattening radius R'.
8. The method for setting the rolling force and the rolling moment in the full cold-rolled deformation zone of the steel strip according to claim 2, wherein the deformation resistance 2k of the entrance elastic compression zone isiThe calculation method comprises the following steps:
Figure FDA0003529640560000051
deformation resistance 2k of the elastic recovery zone of the outletoThe calculation method comprises the following steps:
Figure FDA0003529640560000052
the deformation resistance 2k of a certain point with the abscissa of the plastic deformation area as xxThe calculation method comprises the following steps:
Figure FDA0003529640560000053
in the formula hxIs the thickness of the steel strip at point x, hinitIs the thickness of the steel strip incoming material, kmAnd epsilon and n are deformation resistance model parameters for considering the deformation resistance reference constant of the material characteristics.
9. The method for setting the rolling force and the rolling moment in the full deformation zone for cold rolling of steel strip according to claim 8, wherein the average deformation resistance 2k in the plastic deformation zone is a definite integral average of the deformation resistance in the plastic deformation zone.
CN202210207221.0A 2022-03-03 2022-03-03 Method for setting rolling force and rolling moment of steel strip cold rolling full deformation area Pending CN114722516A (en)

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