CN112474823A - Method for acquiring asymmetric rolling roll gap outlet thickness distribution of four-roll mill - Google Patents

Abstract

The invention discloses a method for acquiring asymmetric rolling roll gap outlet thickness distribution of a four-high mill, which comprises the following steps: acquiring roll system parameters, process parameters and setting parameters; discretizing the roll system and the rolled piece along the width direction to obtain the number of discrete sections of the upper working roll, the lower working roll, the upper support roll, the lower support roll and the rolled piece, the middle abscissa of each discrete section and the width of each discrete section; calculating to obtain elastic bending influence functions of the upper working roll, the lower working roll, the upper supporting roll and the lower supporting roll; assuming that the thickness distribution of the roll gap outlet is the thickness distribution of the idle roll gap; calculating to obtain the transverse distribution of rolling pressure, the total rolling pressure and the relevant parameters of elastic deformation of the upper and lower roller systems; obtaining the thickness distribution of the roll gap outlet meeting the asymmetric rolling condition; and judging whether the thickness distribution of the roll gap outlet is converged. The invention has the beneficial effects that: the method disclosed by the invention is clear and definite in principle and few in simplified conditions, and compared with the traditional analytical method, the method can be used for more accurately simulating the elastic deformation behavior of the roller system and is higher in calculation precision.

Description

Method for acquiring asymmetric rolling roll gap outlet thickness distribution of four-roll mill

Technical Field

The invention belongs to the technical field of rolling, and particularly relates to a method for acquiring asymmetric rolling roll gap outlet thickness distribution of a four-roll rolling mill.

Background

In the strip rolling process, the outlet thickness distribution of the rolled piece is directly determined by the outlet thickness distribution of the on-load roll gap, so that the calculation of the outlet thickness distribution of the roll gap in the rolling process is one of important contents of the setting calculation of the shape of the rolled piece and is also the basis of the shape control of the rolled piece, and the high-efficiency high-precision outlet thickness distribution calculation method of the roll gap has important significance for improving the shape control precision of the rolled piece.

The existing method for calculating the outlet thickness distribution of the roll gap simplifies and processes a rolling mill roll system and a rolled piece into a symmetrical model, and because asymmetric factors such as asymmetric roll shapes of an upper working roll, a lower working roll, an upper supporting roll and a lower supporting roll, uneven distribution of shapes of incoming material sections and the like caused by deviation of the rolled piece, uneven wear of the rolls and uneven thermal expansion exist in the rolling process, the adoption of the symmetrical model for calculation inevitably brings large errors and is inconsistent with the actual situation on site. Therefore, there is still a need to further develop a roll gap outlet thickness distribution calculation method considering asymmetric rolling conditions.

Disclosure of Invention

The invention aims to provide a method for acquiring asymmetric rolling roll gap outlet thickness distribution of a four-high rolling mill aiming at the defects of the prior art, so as to solve the problem that the calculation result is inconsistent with the actual field situation because the influence of asymmetric factors on the rolling roll gap outlet thickness distribution is not considered in the conventional calculation method.

The technical scheme adopted by the invention is as follows: a method for acquiring the asymmetric rolling roll gap outlet thickness distribution of a four-high rolling mill comprises the following steps:

s1, acquiring roll system parameters, process parameters and setting parameters;

s2, discretizing the roll system and the rolled piece along the width direction to obtain the number of discrete sections of the upper working roll, the lower working roll, the upper supporting roll, the lower supporting roll and the rolled piece, the middle abscissa of each discrete section and the width of each discrete section;

s3, calculating elastic bending influence functions of the upper working roll, the lower working roll, the upper supporting roll and the lower supporting roll;

s4, assuming that the thickness distribution of the roll gap outlet is idle roll gap thickness distribution;

s5, calculating to obtain transverse distribution of rolling pressure and total rolling pressure;

s6, calculating and obtaining relevant parameters of the elastic deformation of the upper roll system, including the elastic deflection distribution of the upper working roll and the upper supporting roll, the distribution of the elastic flattening amount between the rolls and the distribution of the elastic flattening amount of the upper working roll caused by rolling pressure;

s7, calculating and obtaining the related parameters of the elastic deformation of the lower roll system, including the elastic deflection distribution of the lower working roll and the lower supporting roll, the distribution of the elastic flattening amount between the rolls and the distribution of the elastic flattening amount of the lower working roll caused by rolling pressure;

s8, calculating to obtain the roll gap outlet thickness distribution meeting the asymmetric rolling condition;

s9, judging whether the thickness distribution of the roll gap outlet is converged: if the convergence is achieved, the calculation is completed and the result is output; if not, the roll gap outlet thickness distribution is corrected, and the corrected roll gap outlet thickness distribution is switched to S5 to be recalculated until the roll gap outlet thickness distribution converges.

According to the scheme, in S3, the calculation method of the elastic bending influence function of each roller is as follows:

(1) elastic bending influence function g of working roll_{B_yw_x}(z_yw(i),z_yw(j) ) is:

when z is_yw(i)×z_yw(j) Not less than 0, and | z_yw(j)|≤|z_yw(i) In the case of l, the number of the terminal,

when z is_yw(i)×z_yw(j) Not less than 0, and | z_yw(j)|＞|z_yw(i) In the case of l, the number of the terminal,

elastic bending influence function g of working roll generated in i-th section by unit roll bending force of working roll_{B_ywF_x}(z_yw(i) ) is:

in the formulae (1) to (3), when it is the aboveWhen working on a roll, subscript y is u; when the lower working roll is used, the subscript y is b; when operating the side part for the working roll, the subscript x is o, 1. ltoreq. i, j. ltoreq. n_ywo(ii) a When driving the side sections for the working rolls, the subscripts x are d, n_ywo+1≤i,j≤n_yw；n_ywo-the number of discrete segments of the operative side portion of the work roll; n is_yw-number of discrete segments of work rolls;

(2) the elastic bending influence function of the supporting roller is as follows:

when z is_yb(i)×z_yb(j) Not less than 0, and | z_yb(j)|≤|z_yb(i) In the case of l, the number of the terminal,

when z is_yb(i)×z_yb(j) Not less than 0, and | z_yb(j)|＞|z_yb(i) In the case of l, the number of the terminal,

the bending influence function of the supporting roller generated by the unit bearing reaction force of the supporting roller bearing at the ith section is as follows:

in formulas (4) to (6), when it is the upper support roller, the subscript y is u; when the lower support roller is used, subscript y is b; when the operation side part of the support roller is used, the subscript x is o, i is more than or equal to 1, and n is more than or equal to j_ybo(ii) a When the side part is driven by the supporting roller, the subscript x is d, n_ybo+1≤i,j≤n_yb；n_ybo-the number of discrete segments of the operative side portion of the support roll; n is_yb-number of discrete segments of support rolls;

in the formulae (1) to (6), E_yw、E_yb-the modulus of elasticity, in MPa, of the work and support rolls; i is_yw、I_ybMoment of inertia in mm for the working and backup rolls⁴；z_yw(i)、z_yw(j) -workerTaking the transverse coordinates of the ith section and the jth section in the axial direction of the roller in unit mm; z is a radical of_yb(i)、z_yb(j) -axial i-th and j-th section abscissa of the support roller in mm; k-cross-sectional shape coefficient, taking

G_yw、G_yb-working and backup roll shear modulus in MPa; a. the_yw、A_ybCross-sectional area of the working and supporting rolls in mm²；l_ywrx-the distance of the working roll bending force action point to the center of the frame in mm; l_ybrxThe distance between the bearing reaction point of the support roller and the center of the frame is unit mm.

According to the scheme, in S8, the calculation formula of the outlet thickness of the i-th section of the roll gap under the asymmetric condition is as follows:

in the formula (7), h is the target outlet thickness of the rolled piece in mm; delta_u、Δ_b-the overall vertical movement, delta, of the upper and lower work rolls at the centre of the stand with the roll gap exit thickness at the target exit thickness h of the rolled piece_u＝-y_{B_uw_m}+y_{F_uwp_m}，Δ_b＝-y_{B_bw_m}+y_{F_bwp_m}，y_{B_uw_m}、y_{B_bw_m}Elastic deflection of the upper and lower work rolls in mm, y at the center of the frame_{F_uwp_m}、y_{F_bwp_m}The amount of elastic flattening in mm of the upper and lower working rolls at the center of the stand caused by the rolling pressure; y is_{B_uw}(i)、y_{B_bw}(i) Elastic deflection of the upper working roll and the lower working roll corresponding to the ith section of the roll gap in unit mm; y is_{F_uwp}(i)、y_{F_bwp}(i) The elastic deflection of the upper working roll and the lower working roll corresponding to the ith section of the roll gap caused by the rolling pressure is unit mm.

According to the scheme, the method for calculating the elastic deformation of the upper roller system and the elastic deformation of the lower roller system comprises the following steps:

s601, calculating the support roller support reaction force, wherein the calculation formula is as follows:

the support roll operating side reaction force is:

the supporting roll transmission side reaction force is as follows:

in formulas (8) and (9), when it is the upper support roller, the subscript y is u; when the lower support roller is used, subscript y is b; p_n-total rolling pressure, in KN; f_yo、F_ydThe work roll operating side roll bending force and the drive side roll bending force, unit KN; l_ybrd、l_ybroThe distance between the bearing reaction point on the operating side and the transmission side of the supporting roller and the center of the frame is measured in mm; l_ywrd、l_ywroThe distance in mm between the operating side and the drive side of the working rolls and the center of the frame; p (j) -rolling pressure of the jth section of the width of the rolled stock, in KN; z is a radical of_s(j) -transverse coordinates of the jth section of the width of the rolled stock in mm; n is_so-number of discrete segments on the operative side of the product; n is_s-number of discrete segments of product;

s602, assuming the rigid rotation angle theta of the working roll relative to the supporting roll _y0 and flag 0;

s603, judging whether the identifier flag is 0: if the value is 0, the step (4) is carried out; if not, go to step S605;

s604, assuming that the contact pressure distribution between the rollers is uniformly distributed, and the flag is 1, calculating the contact pressure distribution between the rollers under the uniform distribution condition by static balance of the working rollers as follows:

i＝1、2、3…n_yb，n_yb-number of discrete segments of support rolls;

s605, supposing that the flattening amount y between the middle rollers of the supporting roller_{F_ywb_m}＝0；

S605, calculating the deflection distribution of the working roll and the supporting roll by an influence function method,

(1) and for the working roll:

when the ith section is the operating side of the working roll, the elastic deflection of the ith section of the working roll is as follows:

when the ith section is the transmission side of the working roll, the elastic deflection of the ith section of the working roll is as follows:

(2) for the support roller:

when the ith section is the operating side of the supporting roller, the elastic deflection of the ith section of the supporting roller is as follows:

when the ith section is the transmission side of the supporting roller, the elastic deflection of the ith section of the supporting roller is as follows:

in the formulas (10) to (14), when the roll system is the upper roll system, the subscript y is u; when the roll is a lower roll system, the subscript y is b; q. q.s_y(j) -contact pressure between the j-th section of rolls, in KN; p (j) -jth rolling pressure, unit KN; theta_y-the rigid angle of rotation of the work roll relative to the support roll, in degrees; p_yo、P_yd-operating and driving side counter forces of the support rolls, in KN;

s607, calculating the distribution of the elastic flattening amount between the rollers by the deformation coordination equation between the working roller and the supporting roller, wherein the elastic flattening amount between the i-th section of rollers can be expressed as:

in the formula (14), D_yb(i) -the diameter of the support roll for the ith contact section in mm; d_yw(i) -the working roll diameter for the ith contact section in mm; d_{yb_m}-the diameter of the support rolls at the centre of the frame in mm; d_{yw_m}-work roll diameter at the centre of the frame in mm; y is_{F_ywb_m}-the amount of resilient flattening between the rolls in the centre of the frame, in mm;

s608, calculating the contact pressure distribution between the rollers according to the elastic flattening amount distribution between the rollers, specifically solving by adopting an iterative method, wherein an iterative calculation equation is as follows:

in the formula (15), Δ z_y(i) -the width of the ith segment in mm; k is a radical of_yw、k_ybCoefficient of material of work and backup rolls in MPa^-1，

v_yw、v_yb-the poisson's ratio of the work and support rolls; d_yw、D_ybNominal diameters of the working and support rolls in mm;

s609, judging whether the contact pressure distribution between the rollers is converged: if the convergence is achieved, the next step of calculation is carried out; if not, correcting the contact pressure distribution between the rollers, and transferring the corrected contact pressure distribution between the rollers to the step S606 for recalculation until the contact pressure distribution between the rollers is converged;

s610, calculating total inter-roller contact pressure according to inter-roller contact pressure distribution

S611, judging whether the static balance of the working roll is met: if the static balance of the working roller is met, the next step of calculation is carried out; if the static balance of the working roll is not met, correcting the flattening amount between the rolls in the middle of the supporting roll, and transferring the corrected flattening amount between the rolls in the middle of the supporting roll to the step S606 for recalculation until the static balance of the working roll is met;

s612, judging whether the working roll moment balance is met: if the working roll moment is balanced, the next step of calculation is carried out; if the working roll moment balance is not met, correcting the rigid rotation angle of the working roll relative to the supporting roll, and transferring the corrected rigid rotation angle of the working roll relative to the supporting roll into S603 for recalculation until the working roll moment balance is met;

s613, calculating the distribution of the elastic flattening amount of the working roll caused by the transverse distribution of the rolling pressure, specifically calculating the distribution of the elastic flattening amount of the working roll caused by the transverse distribution of the rolling pressure by adopting a method of repeated iteration of a unit rolling pressure differential equation and a deformation roll profile curve equation;

according to the scheme, in S609, the specific method for judging whether the contact pressure distribution between the rollers is converged is as follows: if for each discrete segment, the following equation is satisfied:

|q(i)-q^m(i)|≤ε₁ (16)，

if the calculation condition is satisfied, the convergence condition of the contact pressure distribution between the rolls is indicated, and the next step of calculation is carried out; if there is a discrete segment r segment, | q (r) -q^m(r)＞ε₁If the roll contact pressure distribution is not converged, the roll contact pressure distribution is corrected by adopting a smoothing coefficient method, and the corrected roll contact pressure distribution is transferred to the step S606 to be recalculated until the roll contact pressure distribution is converged;

in equation (16), q (i) -the contact pressure between the i-th segment of the roll calculated in this iteration, q^m(i) Contact pressure between the i-th section of the roll, epsilon, used in the m-th iteration₁-convergence accuracy.

According to the scheme, in S611, if the static balance of the working roll is not met, the flattening amount between the rolls in the middle of the supporting roll is corrected by adopting a cutting line method.

According to the scheme, in S612, if the moment balance of the working roll is not met, the rigid rotation angle of the working roll relative to the supporting roll is corrected by adopting a secant method.

According to the scheme, in S9, the specific method for judging whether the thickness distribution of the roll gap outlet is converged is as follows: if for each discrete segment, the following equation is satisfied:

|h(i)-h^m(i)|≤ε₂ (17)，

the convergence condition of the thickness distribution of the roll gap outlet is met, the calculation is completed, and the calculation result is output; if there is a discrete segment (e.g., the r-th segment), | h (r) -h^m(r)|＞ε₂If the thickness distribution of the roll gap outlet is not converged, correcting the thickness distribution of the roll gap outlet by adopting a smoothing coefficient method, and transferring the corrected thickness distribution of the roll gap outlet to the step five for recalculation until the thickness distribution of the roll gap outlet is converged;

in formula (17), i ═ 1, 2, 3.. n_rgH (i) -the calculated thickness of the section i of the roll gap outlet h of the iteration^m(i) The thickness of the exit of the section i of the roll gap, epsilon, used in the m-th iteration₂-convergence accuracy.

The invention has the beneficial effects that:

(1) solving the elastic deformation of the four-roller mill roll system by adopting inner and outer four-layer iteration: the innermost layer iteration is used for performing cyclic iteration calculation on the distribution of the contact pressure between the rollers, the distribution of the elastic deflection of the roller system and the distribution of the flattening amount between the rollers so as to meet the convergence condition of the distribution of the contact pressure between the rollers; the second iteration establishes the static balance relation of the working rolls by introducing the iterative adjustment quantity of the flattening quantity between the middle rolls of the supporting rolls; in the third layer of iteration, the moment balance relation of the working roll is established by introducing the iteration adjustment quantity of the rigid rotation angle of the working roll relative to the supporting roll; and the outermost layer iteration is used for repeated iterative calculation of the roll system elastic deformation model and the rolled piece plastic deformation model so as to meet the convergence condition of the thickness distribution at the roll gap outlet. And finally obtaining the thickness distribution of the roll gap outlet meeting various balance convergence conditions by repeated calculation of four layers of iteration. The method disclosed by the invention is clear and definite in principle and few in simplified conditions, compared with the traditional analytic method, the method can more accurately simulate the elastic deformation behavior of the roll system, is higher in calculation precision, and compared with a finite element method, the method is greatly reduced in calculation amount, higher in convergence speed and higher in calculation efficiency, so that the method can be used for off-line analysis and calculation of the rolled piece strip shape and can also be used for on-line setting and calculation of the rolled piece strip shape.

(2) The method fully considers the influence of asymmetric factors (such as deviation of rolled pieces, asymmetry of roll shapes of upper and lower working rolls and upper and lower supporting rolls, uneven distribution of shapes of incoming material sections and the like) on the thickness distribution of the outlet of the roll gap, and obtains the thickness distribution of the outlet of the roll gap meeting asymmetric conditions by respectively and independently calculating the upper roll system and the lower roll system, so that the calculation result is more in line with the actual situation on site.

Drawings

FIG. 1 is a flow chart of an embodiment of the present invention.

FIG. 2 is a schematic view of the roll system parameters of the present embodiment.

FIG. 3 is a flowchart illustrating the calculation of the elastic deformation parameters related to the upper roll system in this embodiment.

FIG. 4 is a schematic diagram of the calculated value of the roll gap outlet thickness distribution obtained by the method of the present invention and the measured value of the rolled piece outlet thickness distribution.

Detailed Description

For a better understanding of the present invention, the present invention is further described below in conjunction with specific examples.

The method for acquiring the asymmetric rolling gap outlet thickness distribution of the four-high rolling mill shown in figure 1 comprises the following steps:

s1, acquiring roll system parameters, process parameters and setting parameters.

As shown in FIG. 2, the roll system parameters include the nominal diameters D of the upper and lower work rolls_uw、D_bwRoller type D_uw(x)、D_bw(x) Width L of roll body_uw、L_bwAnd the distance l from the roll bending force action point to the center of the frame_uwro、l_uwrd、l_bwro、l_bwrd(ii) a Nominal diameter D of the upper and lower support rolls_ub、D_bbRoller type D_ub(x)、D_bb(x) Width L of roll body_ub、L_bbAnd the distance l from the bearing support reaction force action point to the center of the frame_ubr0、l_ubrd、l_bbr0、l_bbrd. The process parameters comprise the width B of the rolled piece_sThe thickness distribution of the incoming material of the rolled piece, the target outlet thickness h of the rolled piece and the roll shifting quantity delta₁Deviation delta of rolled piece₂And the bending force F of the working roll_uo、F_ud、F_bo、F_bd. The set parameters comprise a roll contact pressure distribution smooth coefficient, a roll contact pressure distribution convergence precision, an upper working roll static force balance convergence coefficient, an upper working roll moment balance convergence coefficient, a roll gap outlet thickness distribution smooth coefficient and a roll gap outlet thickness distribution convergence precision.

And S2, discretizing the roll system and the rolled piece along the width direction to obtain the number of discrete sections of the upper working roll, the lower working roll, the upper supporting roll, the lower supporting roll and the rolled piece, the middle abscissa of each discrete section and the width of each discrete section.

(1) The roll body of the supporting roll is discretely divided into n_yb2n sections, namely, the transmission side part and the operation side part are respectively n sections, the sections from the operation side to the transmission side are numbered in sequence as 1-2 n, and the length of each section is

The abscissa of the middle part is

Wherein, when an upper support roll, the subscript y is u; when a lower support roll, subscript y is b.

(2) Respectively dispersing the operation side and the transmission side of the working roll into m₁+1、m₂+1 stage, each stage numbered 1-m in sequence from the operation side to the transmission side₁+m₂+2，

In the case of the upper work roll,

middle abscissa z_uw(i) Comprises the following steps:

in the formula,. DELTA.z_uwo-upper work roll operating side section width,

Δz_uwd-the width of the upper work roll drive side section,

in the case of the lower work roll,

middle abscissa z_bw(i) Comprises the following steps:

i＝m₁+m₂at the time of +2, the reaction solution,

in the formula,. DELTA.z_bwo-lower work roll operational side section width,

Δz_bwd-the width of the lower work roll drive side section,

(3) respectively dispersing the operation side and the transmission side of the rolled piece into s₁+1、s₂+1 stage, each stage numbered from the operating side to the transmission side in sequence from 1 to s₁+s₂+2, then

Middle abscissa z_s(i) Comprises the following steps:

wherein, Delta z is the width of the rolled piece middle section, and Delta z is equal to Delta z_u；Δz_so-the width of the operative side section of the rolling stock,

Δz_sd-the width of the product-conveying side section,

and S3, calculating elastic bending influence functions of the upper working roll, the lower working roll, the upper supporting roll and the lower supporting roll.

(1) Elastic bending influence function g of working roll_{B_yw_x}(z_yw(i),z_yw(j) ) is:

when z is_yw(i)×z_yw(j) Not less than 0, and | z_yw(j)|≤|z_yw(i) In the case of l, the number of the terminal,

when z is_yw(i)×z_yw(j) Not less than 0, and | z_yw(j)|＞|z_yw(i) In the case of l, the number of the terminal,

(2) the elastic bending influence function g of the working roll generated in the ith section by the unit bending force of the working roll_{B_ywF_x}(z_yw(i) ) is:

when the roll is an upper work roll, the subscript y is u; when the lower working roll is used, the subscript y is b; when operating the side part for the working roll, the subscript x is o, 1. ltoreq. i, j. ltoreq. n_ywo(ii) a When driving the side sections for the working rolls, the subscripts x are d, n_ywo+1≤i,j≤n_yw；n_ywo-the number of discrete segments of the operative side portion of the work roll; n is_yw-number of discrete segments of work rolls.

(3) Elastic bending influence function g of support roller_{B_yb_x}(z_yb(i),z_yb(j) ) is:

when z is_yb(i)×z_yb(j) Not less than 0, and | z_yb(j)|≤|z_yb(i) In the case of l, the number of the terminal,

when z is_yb(i)×z_yb(j)≥0, and | z_yb(j)|＞|z_yb(i) In the case of l, the number of the terminal,

(4) a support roller bending influence function g generated in the i-th section by the unit support reaction force of the support roller bearing_{B_ybP_x}(z_yb(i) ) is:

when an upper support roll, subscript y is u; when the lower support roller is used, subscript y is b; when the operation side part of the support roller is used, the subscript x is o, i is more than or equal to 1, and n is more than or equal to j_ybo(ii) a When the side part is driven by the supporting roller, the subscript x is d, n_ybo+1≤i,j≤n_yb；n_ybo-the number of discrete segments of the operative side portion of the support roll; n is_yb-number of discrete segments of support rolls.

In the above formulae, E_yw、E_yb-the modulus of elasticity, in MPa, of the work and support rolls; i is_yw、I_ybMoment of inertia in mm for the working and backup rolls⁴；z_yw(i)、z_yw(j) -the abscissa of the i-th section and the j-th section in the axial direction of the working roll in mm; z is a radical of_yb(i)、z_yb(j) -axial i-th and j-th section abscissa of the support roller in mm; k-cross-sectional shape coefficient, taking

G_yw、G_yb-working and backup roll shear modulus in MPa; a. the_yw、A_ybCross-sectional area of the working and supporting rolls in mm²；l_ywrx-the distance of the working roll bending force action point to the center of the frame in mm; l_ybrxThe distance between the bearing reaction point of the support roller and the center of the frame is unit mm.

S4, assuming that the thickness distribution of the roll gap outlet is the thickness distribution of the idle roll gap, the thickness of the ith section of the roll gap under the idle condition is as follows:

in the formula, D_{uw_m}、D_{bw_m}-the diameter of the upper and lower working rolls in mm at the centre of the frame; d_uw(i)、D_bw(i) The diameter of the upper and lower work rolls at the ith section of the roll gap in mm.

S5, calculating and obtaining the transverse distribution of the rolling pressure and the total rolling pressure P_n。

The method for calculating the rolling pressure belongs to the technology disclosed in the industry, and can be seen in document 1 (application number 201811444901.4) or document 2 (application number 201410202854.8), and the details are not described here. Total rolling pressure

In the formula, n_sNumber of widthwise discrete segments, n, of the rolling stock_s＝s₁+s₂+2, p (i) -rolling pressure in the ith segment of the width of the product, in KN.

S6, calculating to obtain the parameters related to the elastic deformation of the upper roll system, including the elastic deflection distribution y of the upper working roll and the upper supporting roll_{B_uw}(i)、y_{B_ub}(i) Distribution of amount of resilient flattening between rolls_{F_uwb}(i) And distribution y of elastic flattening amount of upper working roll caused by rolling pressure_{F_uwp}(i) (ii) a In this step y_{B_uw}(i)、y_{B_ub}(i)、y_{F_uwb}(i) And y_{F_uwp}(i) The units of (A) are all mm.

S7, calculating to obtain the parameters related to the elastic deformation of the lower roll system, including the elastic deflection distribution y of the lower working roll and the lower supporting roll_{B_bw}(i)、y_{B_bb}(i) Distribution of amount of resilient flattening between rolls_{F_bwb}(i) And distribution y of elastic flattening amount of upper working roll caused by rolling pressure_{F_bwp}(i) (ii) a In this step y_{B_bw}(i)、y_{B_bb}(i)、y_{F_bwb}(i) And y_{F_bwp}(i) The units of (A) are all mm.

S8, calculating to obtain the roll gap outlet thickness distribution meeting the asymmetric rolling condition, wherein the outlet thickness calculation formula of the i-th section of the roll gap under the asymmetric rolling condition is as follows:

in the formula,. DELTA._u、Δ_b-the overall vertical movement, delta, of the upper and lower work rolls at the centre of the stand with the roll gap exit thickness at the target exit thickness h of the rolled piece_u＝-y_{B_uw_m}+y_{F_uwp_m}，Δ_b＝-y_{B_bw_m}+y_{F_bwp_m}，y_{B_uw_m}、y_{B_bw_m}Elastic deflection of the upper and lower work rolls in mm, y at the center of the frame_{F_uwp_m}、y_{F_bwp_m}The amount of elastic flattening in mm of the upper and lower working rolls at the center of the stand caused by the rolling pressure; y is_{B_uw}(i)、y_{B_bw}(i) Elastic deflection of the upper working roll and the lower working roll corresponding to the ith section of the roll gap in unit mm; y is_{F_uwp}(i)、y_{F_bwp}(i) The elastic deflection of the upper working roll and the lower working roll corresponding to the ith section of the roll gap caused by the rolling pressure is unit mm.

S9, judging whether the thickness distribution of the roll gap outlet is converged, and if so, outputting a calculation result; if not, the roll gap outlet thickness distribution is corrected by adopting a smoothing coefficient method, and the step S5 is carried out again until the roll gap outlet thickness distribution is converged.

For each discrete segment, | h (i) -h^m(i)|≤ε₂(i＝1、2、3...n_rgH (i) -the calculated thickness of the section i of the roll gap outlet h of the iteration^m(i) The thickness of the exit of the section i of the roll gap, epsilon, used in the m-th iteration₂Precision of convergence, preferably ε₂0.001), the convergence condition of the thickness distribution of the roll gap outlet is met, the calculation is completed, and the calculation result is output; if there is a discrete segment (e.g., the r-th segment), | h (r) -h^m(r)|＞ε₂If the roll gap outlet thickness distribution is not converged, the roll gap outlet thickness distribution is corrected by adopting a smoothing coefficient method, and the corrected roll gap outlet thickness distribution is transferred to the step S5 to be recalculated until the roll gap outlet thickness distribution is converged.

In steps S6 and S7, the calculation methods of the parameters relating to the elastic deformation of the upper roller system and the elastic deformation of the lower roller system are completely the same, and for convenience of description, the elastic deformation of the upper roller system and the elastic deformation of the lower roller system will be described by way of example only. As shown in fig. 3, the method for calculating the parameters related to the elastic deformation of the upper roller system includes the following steps:

s601, calculating the support roller reaction force, wherein,

the operation side branch counter-force of the upper supporting roll is as follows:

the transmission side branch counter force of the upper supporting roller is as follows:

in the formula, P_n-total rolling pressure, in KN; f_uo、F_udUpper work roll operating side roll bending force and drive side roll bending force, unit KN; l_ubrd、l_ubro-the distance in mm from the operating and drive side bearing reaction points of the upper support roll to the centre of the frame; l_uwrd、l_uwroThe distance in mm from the operating side and the driving side of the upper work roll to the centre of the frame; p (j) -rolling pressure of the jth section of the width of the rolled stock, in KN; z is a radical of_s(j) -transverse coordinates of the jth section of the width of the rolled stock in mm; n is_so-number of discrete segments on the operative side of the product; n is_s-number of discrete segments of product.

S602, assuming the rigid rotation angle theta of the upper working roll relative to the upper supporting roll _u0 and flag 0;

s603, judging whether the identifier flag is 0: if 0, go to step S604; if not, go to step S605;

s604, assuming that the contact pressure distribution between the rollers is uniformly distributed, and the flag is 1, calculating the contact pressure distribution between the rollers under the uniform distribution condition by static balance of the upper working roller as follows:

i＝1、2、3…n_ub，n_ub-number of discrete segments of upper support roll.

S605, supposing that the flattening amount y between the middle rollers of the upper supporting roller_{F_uwb_m}＝0。

And S606, calculating the deflection distribution of the upper working roll and the upper supporting roll by an influence function method.

With respect to the upper work roll,

when the ith section is the operation side of the upper working roll, the elastic deflection of the ith section of the upper working roll is as follows:

when the ith section is the transmission side of the upper working roll, the elastic deflection of the ith section of the upper working roll is as follows:

with respect to the upper support roll,

when the ith section is the operation side of the upper supporting roller, the elastic deflection of the ith section of the upper supporting roller is as follows:

when the ith section is the transmission side of the upper supporting roller, the elastic deflection of the ith section of the upper supporting roller is as follows:

in the formula, q_u(j) -contact pressure between the j-th section of rolls, in KN; p (j) -jth rolling pressure, unit KN; theta_u-rigid angle of rotation of the upper work roll relative to the upper support roll, in degrees; p_uo、P_udOperating and driving side reaction forces of the upper support roll, in KN.

S607, calculating the distribution of the elastic flattening amount between the rollers by the deformation coordination equation between the working roller and the supporting roller, wherein the elastic flattening amount between the i-th section of rollers can be expressed as:

in the formula, D_ub(i) -upper support roll diameter, in mm, for the ith contact section; d_uw(i) -the upper work roll diameter, in mm, for the ith contact section; d_{ub_m}Upper support roll diameter at the centre of the frame in mm; d_{uw_m}-upper work roll diameter at the centre of the frame in mm; y is_{F_uwb_m}The amount of elastic flattening between the rolls in the centre of the frame, in mm.

S608, calculating the contact pressure distribution between the rollers according to the elastic flattening amount distribution between the rollers, specifically solving by adopting an iterative method, wherein an iterative calculation equation is as follows:

in the formula,. DELTA.z_u(i) -the width of the ith segment in mm; k is a radical of_uw、k_ubUpper work roll and upper backing roll material coefficients in MPa^-1，

v_uw、v_ub-the poisson's ratio of the upper work roll and the upper support roll; d_uw、D_ubNominal diameter of the upper work roll and the upper support roll in mm.

S609, judging whether the contact pressure distribution between the rollers is converged: if the convergence is achieved, the next step of calculation is carried out; if not, the contact pressure distribution between the rolls is corrected by adopting a smoothing coefficient method, and the corrected contact pressure distribution between the rolls is transferred to the step S606 to be recalculated until the contact pressure distribution between the rolls is converged.

Whether the contact pressure distribution between the rollers is converged is judged, and the specific method comprises the following steps: if for each discrete segment, | q (i) -q are satisfied^m(i)|≤ε₁(i＝1、2、3...n_bQ (i) -the contact pressure between the i-th section of the roll calculated in this iteration, q^m(i) -m-th iteration meterContact pressure between i-th section of roll, epsilon₁Precision of convergence, preferably ε₁1), the convergence condition of the contact pressure distribution between the rolls is described to satisfy the calculation condition, and the next calculation is carried out; if there is a discrete segment (e.g., the r-th segment), | q (r) -q^m(r)|＞ε₁If the roll contact pressure distribution is not converged, the roll contact pressure distribution is corrected by using a smoothing coefficient method, and the corrected roll contact pressure distribution is transferred to the step S606 to be recalculated until the roll contact pressure distribution is converged.

S610, calculating total inter-roller contact pressure according to inter-roller contact pressure distribution

S611, judging whether static balance of the upper working roll is met: if the static balance of the upper working roll is met, the next step of calculation is carried out; if the static balance of the upper working roll is not met, correcting the flattening amount between the rolls in the middle of the upper supporting roll by adopting a cutting line method, and transferring the corrected flattening amount between the rolls in the middle of the upper supporting roll to the step S606 for recalculation until the static balance of the upper working roll is met.

S612, judging whether the upper working roll moment balance is met: if the upper working roll moment is balanced, the next step of calculation is carried out; if the upper working roll moment balance is not met, correcting the rigid rotating angle of the upper working roll relative to the upper supporting roll by adopting a secant method, and transferring the corrected rigid rotating angle of the upper working roll relative to the upper supporting roll to the step S603 for recalculation until the upper working roll moment balance is met.

And S613, calculating the distribution of the elastic flattening amount of the working roll caused by the transverse distribution of the rolling pressure, and calculating the distribution of the elastic flattening amount of the working roll caused by the transverse distribution of the rolling pressure by adopting a method of repeated iteration of a unit rolling pressure differential equation and a deformation roll profile curve equation. The method belongs to the technology disclosed in the industry, and can be seen in Chinese patent with application number 201811444901.4 or 201410202854.8, and the details are not described here.

The accuracy of the roll gap outlet thickness distribution value calculated by the method of the embodiment is verified by actually measured strip steel outlet thickness distribution data of a hot rolling four-high mill in a certain steel mill. The roll system parameters, process parameters and set parameters are shown in tables 1, 2 and 3, respectively. The comparison between the roll gap outlet thickness distribution value calculated by the method and the actually measured strip steel thickness distribution value is shown in fig. 4, and it can be seen that the calculation result of the method is very close to the actually measured value, the error is within 10%, and the engineering calculation precision requirement can be completely met.

TABLE 1 roll series parameters

TABLE 2 Process parameters

TABLE 3 setting parameters

Item	Numerical value
		Coefficient of smoothness of contact pressure distribution between rolls	0.3
Convergence accuracy of contact pressure distribution between rollers	1
		Static balance convergence coefficient of upper working roll	0.01
Upper work roll moment balance convergence coefficient	0.01
		Smooth coefficient of thickness distribution at roll gap outlet	0.3
Convergence accuracy of thickness distribution at roll gap outlet	0.001

It should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and the present invention is not limited thereto, and although the present invention has been described in detail with reference to the embodiments, it will be apparent to those skilled in the art that modifications can be made to the technical solutions described in the above-mentioned embodiments, or equivalent substitutions of some technical features, but any modifications, equivalents, improvements and the like within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (8)

1. The method for acquiring the asymmetric rolling roll gap outlet thickness distribution of the four-roll rolling mill is characterized by comprising the following steps of:

s1, acquiring roll system parameters, process parameters and setting parameters;

s2, discretizing the roll system and the rolled piece along the width direction to obtain the number of discrete sections of the upper working roll, the lower working roll, the upper supporting roll, the lower supporting roll and the rolled piece, the middle abscissa of each discrete section and the width of each discrete section;

s3, calculating elastic bending influence functions of the upper working roll, the lower working roll, the upper supporting roll and the lower supporting roll;

s4, assuming that the thickness distribution of the roll gap outlet is idle roll gap thickness distribution;

s5, calculating to obtain transverse distribution of rolling pressure and total rolling pressure;

s6, calculating and obtaining relevant parameters of the elastic deformation of the upper roll system, including the elastic deflection distribution of the upper working roll and the upper supporting roll, the distribution of the elastic flattening amount between the rolls and the distribution of the elastic flattening amount of the upper working roll caused by rolling pressure;

s7, calculating and obtaining the related parameters of the elastic deformation of the lower roll system, including the elastic deflection distribution of the lower working roll and the lower supporting roll, the distribution of the elastic flattening amount between the rolls and the distribution of the elastic flattening amount of the lower working roll caused by rolling pressure;

s8, calculating to obtain the roll gap outlet thickness distribution meeting the asymmetric rolling condition;

s9, judging whether the thickness distribution of the roll gap outlet is converged: if the convergence is achieved, the calculation is completed and the result is output; if not, the roll gap outlet thickness distribution is corrected, and the corrected roll gap outlet thickness distribution is switched to S5 to be recalculated until the roll gap outlet thickness distribution converges.

2. The acquisition method according to claim 1, wherein in S3, the elastic bending influence function of each roller is calculated by:

(1) elastic bending influence function g of working roll_{B_yw_x}(z_yw(i),z_yw(j) ) is:

when z is_yw(i)×z_yw(j) Not less than 0, and | z_yw(j)|≤|z_yw(i) In the case of l, the number of the terminal,

when z is_yw(i)×z_yw(j) Not less than 0, and | z_yw(j)|＞|z_yw(i) In the case of l, the number of the terminal,

elastic bending influence function g of working roll generated in i-th section by unit roll bending force of working roll_{B_ywF_x}(z_yw(i) ) is:

in formulas (1) to (3), when it is the upper work roll, the subscript y is u; when the lower working roll is used, the subscript y is b; when operating the side part for the working roll, the subscript x is o, 1. ltoreq. i, j. ltoreq. n_ywo(ii) a When driving the side sections for the working rolls, the subscripts x are d, n_ywo+1≤i,j≤n_yw；n_ywo-the number of discrete segments of the operative side portion of the work roll; n is_yw-number of discrete segments of work rolls;

(2) the elastic bending influence function of the supporting roller is as follows:

when z is_yb(i)×z_yb(j) Not less than 0, and | z_yb(j)|≤|z_yb(i) In the case of l, the number of the terminal,

when z is_yb(i)×z_yb(j) Not less than 0, and | z_yb(j)|＞|z_yb(i) In the case of l, the number of the terminal,

the bending influence function of the supporting roller generated by the unit bearing reaction force of the supporting roller bearing at the ith section is as follows:

in formulas (4) to (6), when it is the upper support roller, the subscript y is u; when the lower support roller is used, subscript y is b; when the operation side part of the support roller is used, the subscript x is o, i is more than or equal to 1, and n is more than or equal to j_ybo(ii) a When the side part is driven by the supporting roller, the subscript x is d, n_ybo+1≤i,j≤n_yb；n_ybo-the number of discrete segments of the operative side portion of the support roll; n is_yb-number of discrete segments of support rolls;

in the formulae (1) to (6), E_yw、E_yb-the modulus of elasticity, in MPa, of the work and support rolls; i is_yw、I_ybMoment of inertia in mm for the working and backup rolls⁴；z_yw(i)、z_yw(j) -the abscissa of the i-th section and the j-th section in the axial direction of the working roll in mm; z is a radical of_yb(i)、z_yb(j) -axial i-th and j-th section abscissa of the support roller in mm; k-cross-sectional shape coefficient, taking

G_yw、G_yb-working and backup roll shear modulus in MPa; a. the_yw、A_ybCross-sectional area of the working and supporting rolls in mm²；l_ywrx-the distance of the working roll bending force action point to the center of the frame in mm; l_ybrxThe distance between the bearing reaction point of the support roller and the center of the frame is unit mm.

3. The obtaining method according to claim 1, wherein in S8, the exit thickness of the i-th section of the roll gap under the asymmetric condition is calculated by the formula:

in the formula (7), h is the target outlet thickness of the rolled piece in mm; delta_u、Δ_b-the overall vertical movement, delta, of the upper and lower work rolls at the centre of the stand with the roll gap exit thickness at the target exit thickness h of the rolled piece_u＝-y_{B_uw_m}+y_{F_uwp_m}，Δ_b＝-y_{B_bw_m}+y_{F_bwp_m}，y_{B_uw_m}、y_{B_bw_m}Elastic deflection of the upper and lower work rolls in mm, y at the center of the frame_{F_uwp_m}、y_{F_bwp_m}The amount of elastic flattening in mm of the upper and lower working rolls at the center of the stand caused by the rolling pressure; y is_{B_uw}(i)、y_{B_bw}(i) Elastic deflection of the upper working roll and the lower working roll corresponding to the ith section of the roll gap in unit mm; y is_{F_uwp}(i)、y_{F_bwp}(i) The elastic deflection of the upper working roll and the lower working roll corresponding to the ith section of the roll gap caused by the rolling pressure is unit mm.

4. The method of claim 1, wherein the upper roller system elastic deformation and the lower roller system elastic deformation are calculated by:

s601, calculating the support roller support reaction force, wherein the calculation formula is as follows:

the support roll operating side reaction force is:

the supporting roll transmission side reaction force is as follows:

in formulas (8) and (9), when it is the upper support roller, the subscript y is u; when the lower support roller is used, subscript y is b; p_n-total rolling pressure, in KN; f_yo、F_ydThe work roll operating side roll bending force and the drive side roll bending force, unit KN; l_ybrd、l_ybroThe distance between the bearing reaction point on the operating side and the transmission side of the supporting roller and the center of the frame is measured in mm; l_ywrd、l_ywroThe distance in mm between the operating side and the drive side of the working rolls and the center of the frame; p (j) -rolling pressure of the jth section of the width of the rolled stock, in KN; z is a radical of_s(j) -transverse coordinates of the jth section of the width of the rolled stock in mm; n is_so-number of discrete segments on the operative side of the product; n is_s-number of discrete segments of product;

s602, assuming the rigid rotation angle theta of the working roll relative to the supporting roll_y0 and flag 0;

s603, judging whether the identifier flag is 0: if the value is 0, the step (4) is carried out; if not, go to step S605;

s604, assuming that the contact pressure distribution between the rollers is uniform, and flag is 1, balancing by the static force of the working rollerThe contact pressure distribution between the rollers under the condition of uniform distribution calculated by the balance is as follows:

i＝1、2、3…n_yb，n_yb-number of discrete segments of support rolls;

s605, supposing that the flattening amount y between the middle rollers of the supporting roller_{F_ywb_m}＝0；

S605, calculating the deflection distribution of the working roll and the supporting roll by an influence function method,

(1) and for the working roll:

when the ith section is the operating side of the working roll, the elastic deflection of the ith section of the working roll is as follows:

when the ith section is the transmission side of the working roll, the elastic deflection of the ith section of the working roll is as follows:

(2) for the support roller:

when the ith section is the operating side of the supporting roller, the elastic deflection of the ith section of the supporting roller is as follows:

when the ith section is the transmission side of the supporting roller, the elastic deflection of the ith section of the supporting roller is as follows:

in the formulas (10) to (14), the subscript y is u in the case of the upper roll system; when the roll is a lower roll system, the subscript y is b; q. q.s_y(j) -contact pressure between the j-th section of rolls, in KN; p (j) -j (th) rollingMaking pressure, unit KN; theta_y-the rigid angle of rotation of the work roll relative to the support roll, in degrees; p_yo、P_yd-operating and driving side counter forces of the support rolls, in KN;

s607, calculating the distribution of the elastic flattening amount between the rollers by the deformation coordination equation between the working roller and the supporting roller, wherein the elastic flattening amount between the i-th section of rollers can be expressed as:

in the formula (14), D_yb(i) -the diameter of the support roll for the ith contact section in mm; d_yw(i) -the working roll diameter for the ith contact section in mm; d_{yb_m}-the diameter of the support rolls at the centre of the frame in mm; d_{yw_m}-work roll diameter at the centre of the frame in mm; y is_{F_ywb_m}-the amount of resilient flattening between the rolls in the centre of the frame, in mm;

s608, calculating the contact pressure distribution between the rollers according to the elastic flattening amount distribution between the rollers, specifically solving by adopting an iterative method, wherein an iterative calculation equation is as follows:

in the formula (15), Δ z_y(i) -the width of the ith segment in mm; k is a radical of_yw、k_ybCoefficient of material of work and backup rolls in MPa^-1，

v_yw、v_yb-the poisson's ratio of the work and support rolls; d_yw、D_ybNominal diameters of the working and support rolls in mm;

s609, judging whether the contact pressure distribution between the rollers is converged: if the convergence is achieved, the next step of calculation is carried out; if not, correcting the contact pressure distribution between the rollers, and transferring the corrected contact pressure distribution between the rollers to the step S606 for recalculation until the contact pressure distribution between the rollers is converged;

s610, calculating total inter-roller contact pressure according to inter-roller contact pressure distribution

S611, judging whether the static balance of the working roll is met: if the static balance of the working roller is met, the next step of calculation is carried out; if the static balance of the working roll is not met, correcting the flattening amount between the rolls in the middle of the supporting roll, and transferring the corrected flattening amount between the rolls in the middle of the supporting roll to the step S606 for recalculation until the static balance of the working roll is met;

s612, judging whether the working roll moment balance is met: if the working roll moment is balanced, the next step of calculation is carried out; if the working roll moment balance is not met, correcting the rigid rotation angle of the working roll relative to the supporting roll, and transferring the corrected rigid rotation angle of the working roll relative to the supporting roll into S603 for recalculation until the working roll moment balance is met;

s613, calculating the distribution of the elastic flattening amount of the working roll caused by the transverse distribution of the rolling pressure, specifically calculating the distribution of the elastic flattening amount of the working roll caused by the transverse distribution of the rolling pressure by adopting a method of repeated iteration of a unit rolling pressure differential equation and a deformation roll profile curve equation;

5. the acquisition method according to claim 4, wherein in S609, the specific method of judging whether the contact pressure distribution between the rolls converges is: if for each discrete segment, the following equation is satisfied:

|q(i)-q^m(i)|≤ε₁ (16)，

if the calculation condition is satisfied, the convergence condition of the contact pressure distribution between the rolls is indicated, and the next step of calculation is carried out; if there is a discrete segment r segment, | q (r) -q^m(r)|＞ε₁If so, the contact pressure distribution between the rollers is not converged, the contact pressure distribution between the rollers is corrected by adopting a smoothing coefficient method, and the corrected contact pressure distribution between the rollers is transferred to the step S606 for recalculation until the contact pressure distribution between the rollers is not convergedUntil the pressure distribution converges;

in equation (16), q (i) -the contact pressure between the i-th segment of the roll calculated in this iteration, q^m(i) Contact pressure between the i-th section of the roll, epsilon, used in the m-th iteration₁-convergence accuracy.

6. The acquisition method as set forth in claim 4, wherein in S611, if the balance of the working roll static force is not satisfied, the amount of inter-roll flattening in the middle portion of the backup roll is corrected by a secant method.

7. The acquisition method as set forth in claim 4, wherein in S612, if the work roll moment balance is not satisfied, the rigid rotation angle of the work roll with respect to the backup roll is corrected by a secant method.

8. The acquisition method according to claim 1, wherein in S9, the specific method for judging whether the roll gap outlet thickness distribution converges is: if for each discrete segment, the following equation is satisfied:

|h(i)-h^m(i)|≤ε₂ (17)，

the convergence condition of the thickness distribution of the roll gap outlet is met, the calculation is completed, and the calculation result is output; if there is a discrete segment (e.g., the r-th segment), | h (r) -h^m(r)|＞ε₂If the thickness distribution of the roll gap outlet is not converged, correcting the thickness distribution of the roll gap outlet by adopting a smoothing coefficient method, and transferring the corrected thickness distribution of the roll gap outlet to the step five for recalculation until the thickness distribution of the roll gap outlet is converged;

in formula (17), i ═ 1, 2, 3.. n_rgH (i) -the calculated thickness of the section i of the roll gap outlet h of the iteration^m(i) The thickness of the exit of the section i of the roll gap, epsilon, used in the m-th iteration₂-convergence accuracy.

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