Prediction Method for Straightness Defects after Cutting and Slitting of Hot-Rolled Tempered Strip Steel

Abstract

The present invention discloses a method for predicting the straightness defect of a hot-rolled and skin-passed strip after cutting and slitting, which includes the following steps: S1. Based on the thickness distribution h0(y) in the width direction of the strip before skin passing and the thickness distribution h1(y) in the width direction of the strip after skin passing, obtain the thickness distribution h(y) of the rolled piece in the deformation zone; S2. Represent the three-dimensional plastic deformation of the rolled piece by the energy method, and use the Powell algorithm to find the thickness deformation distribution u(y) in the width direction of the strip at the exit of the deformation zone corresponding to the minimum energy and the skin-pass force distribution P1(y) of the strip in the current width direction; S3. Compare the maximum difference between the current skin-pass distribution P1(y) of the strip in the width direction and the previous skin-pass force distribution P0(y) with a set threshold value; S4. If the difference is less than the set threshold value, execute step S5. If the difference is greater than the set threshold value, adjust the skin-pass force; S5. Calculate the extension difference ΔX(y) of each point in the width direction of the strip relative to the center position of the strip width, and further predict the magnitude of the strip side bending amount. The prediction of the side bending amount of strips with different specifications and different incoming materials after skin passing and cutting is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of sintering, and more specifically, the present invention relates to a method for predicting the straightness defect after cutting and slitting hot-rolled skin pass strip steel. Background Art

[0002] At present, in the hot-rolled skin pass production of steel mills, the flat strip steel warps after being cut and slit along the rolling direction, that is, the side bending straightness defect caused by the shape defect is generated, and at the same time, the longitudinal bending straightness defect is occasionally generated. The maximum side bending amount after cutting and slitting the flat strip steel can reach 12 mm, while the maximum straightness defect acceptable to customers is 4 mm. The straightness of the slit strip steel cannot meet the use requirements of customers. If this problem is not solved in time, it will seriously hinder the improvement of the strip steel product grade and cannot meet the increasingly stringent user requirements. Summary of the Invention

[0003] The present invention provides a method for predicting the straightness defect after cutting and slitting hot-rolled skin pass strip steel, aiming to predict the size of the side bending amount of the strip steel after skin pass cutting.

[0004] The present invention is implemented as follows. A method for predicting the straightness defect after cutting and slitting hot-rolled skin pass strip steel, the method specifically includes the following steps:

[0005] S1. Based on the thickness distribution h 0 (y) in the width direction of the strip steel before skin pass and the thickness distribution h 1 (y) in the width direction of the strip steel after skin pass, obtain the thickness distribution h(x, y) of the rolled piece in the deformation zone;

[0006] S2. Represent the three-dimensional plastic deformation of the rolled piece by the energy method, and use the Powell algorithm to find the thickness deformation distribution u(y) in the width direction of the strip steel at the outlet of the deformation zone corresponding to the minimum energy and the skin pass force distribution P 1 (y) of the strip steel in the current width direction;

[0007] S3. Compare the maximum difference between the current skin pass force distribution P 1 (y) of the strip steel in the width direction and the previous skin pass force distribution P 0 (y) with a set threshold;

[0008] S4. If the difference is less than the set threshold, execute step S5; if the difference is greater than the set threshold, adjust the skin pass force;

[0009] S5. Calculate the extension difference ΔX(y) of each point in the width direction of the strip steel relative to the center position of the strip width, and then predict the size of the side bending amount of the strip steel.

[0010] Further, the method for obtaining the extension difference ΔX(y) is specifically as follows:

[0011] (11) Calculate the stress distribution σ of the flattened strip along the width direction 1 (y);

[0012] (12) Since the tensile stress distribution near the strip outlet is in one-to-one correspondence with the outlet strip shape, calculate the elongation difference ΔX(y) of each point on the strip width direction relative to the center position of the strip width. The specific calculation formula is as follows:

[0013] ΔX(y) = (σ 1o - σ 1 (y)) / E

[0014] Among them, σ 1o is the pre-tensile stress at the center of the outlet strip width, and E is the elastic modulus of the strip.

[0015] Further, the calculation formula of the stress distribution σ 1 (y) of the flattened strip is as follows:

[0016]

[0017] Among them, ΔB is the spread amount at the strip outlet, B is the strip width, E and ν are the elastic modulus and Poisson coefficient respectively, h 0 (y) is the thickness distribution of the strip in the width direction before leveling, h 1 (y) is the thickness distribution of the strip in the width direction after leveling, l 0 (y) is the thickness distribution of the strip in the length direction before leveling, is the average thickness of the strip in the width direction before leveling, is the average thickness of the strip in the width direction after leveling, is the average thickness of the strip in the length direction before leveling, T 1 is the total tensile force.

[0018] Further, the calculation formula of the side bending amount d of the slit strip is as follows:

[0019]

[0020] Among them, L is the longitudinal length of the slit strip; Δε is the elongation difference of the endpoints of the slit strip in the width direction relative to the center position of the strip width, Δy is the width of the slit strip, and a is the error coefficient.

[0021] The present invention can realize the prediction of the side bending amount of different specifications and different incoming strips after leveling and cutting. Brief Description of the Drawings

[0022] Figure 1 It is a flowchart of the prediction method for the straightness defect after hot rolling and leveling the strip and cutting it into strips provided by the embodiment of the present invention.

[0023] Figure 2 Schematic diagram of strip element segmentation in the deformation zone provided by an embodiment of the present invention;

[0024] Figure 3 Analytical model diagram of longitudinal cutting and posterior bending provided by an embodiment of the present invention. Specific embodiments

[0025] The following describes the specific embodiments of the present invention in further detail with reference to the accompanying drawings through the description of the embodiments, so as to help those skilled in the art have a more complete, accurate and in-depth understanding of the inventive concept and technical solution of the present invention.

[0026] Figure 1 Flowchart of the prediction method for the straightness defect after hot rolling and leveling strip steel cutting and slitting, combined with Figure 1 The prediction method for the straightness defect after strip steel cutting and slitting is described as follows:

[0027] (1) Roll system deformation during the leveling process

[0028] During the leveling process, the rolls will undergo elastic deformation under the influence of roll shape, bending roll force, and leveling force distribution. Only by fully considering the roll system deformation during the leveling process can the shape of the bearing roll gap, that is, the transverse distribution of the rolled piece outlet thickness, be determined more accurately.

[0029] When studying the roll system elastic deformation model, the rolls are generally simplified into beams, and are calculated using the influence function method based on various process parameters such as leveling force, bending roll force, roll shifting, and roll shape during leveling. Its basic idea is to discretize the rolls into several units, and also discretize the loads on the rolls and the elastic deformation of the rolls according to the same units. First, use the concept of influence function in mathematical physics to determine the deformation of each point on the roll body when a unit force is applied to each unit, and then superimpose the deformations of each unit when all loads act, to obtain the deformation values of each unit, thereby determining the thickness and tension distribution at the outlet, etc. Since the influence function method discretizes the roll body, loads, and deformations of the rolls, the roll shape, loads, etc. of the rolls can be arbitrarily input, and the unknowns in the solution process, such as the roll gap contact pressure distribution. In the joint solution process of roll system deformation and rolled piece deformation, it can be assumed that the leveling force p(y) is uniformly distributed during the initial calculation, then the initial leveling force vector P m It can be known. Using the concept of influence function, if the deformation generated at unit i when a unit force acts on unit j is g(i,j), then when a concentrated force φ j acts on unit j, the deformation y 0 (i,j) at unit i is g(i,j)φ j . For all distributed forces, the deformation y i generated at unit i is:

[0030]

[0031] If y w (x) and y b (x) represent the bending deformations of the work roll and the backup roll respectively. From the discretization of the roll, load, and deformation, it can be seen that since a local coordinate system with the rolling center line as the origin is adopted, the calculated deformation values are only the deformations of each element relative to the origin, rather than the absolute deformations. Since the flatness is concerned with the shape of the roll gap, that is, the relative deformation, this treatment method is completely feasible. The above deformations and the roll loads are discretized and represented by matrices as follows:

[0032]

[0033] In the formula, Y w is the work roll deflection vector; Y b is the backup roll deflection vector; Q m is the inter-roll pressure vector; P m is the temper rolling force vector.

[0034] For the work roll, r represents W, and for the backup roll, r represents B. It is represented by a matrix as:

[0035]

[0036] When r represents W, G W is the work roll bending influence function matrix; when r represents B, G B is the backup roll bending influence function matrix.

[0037] J r is the roll elastic bending influence coefficient matrix generated by the concentrated force acting at the roll diameter, and is represented by the matrix J r =[j r (1), …, j r (n)] T ; φ is the load vector. For the work roll, φ = P m -Q m , and for the backup roll, φ = Q m .

[0038] If the elements are evenly divided, the roll elastic bending influence coefficient generated by the distributed force on the roll body is:

[0039]

[0040] In the formula, E r is the roll elastic modulus; I r is the roll bending moment of inertia; ν r is the Poisson's ratio; D ris the roll diameter; Δx is the divided unit length.

[0041] The influence function of the work roll bending force can be solved by using Castigliano's theorem. After the unit is evenly divided, the coordinates of two units are x i and x j . Considering the lateral movement of the work roll, when x i < x j , the influence function of the work roll bending is:

[0042]

[0043] In the formula, L w is the center distance of the work roll bending hydraulic cylinder; shift is the shifting amount of the work roll; E w is the elastic modulus of the work roll; I w is the section modulus of the work roll against bending; ν w is the Poisson's ratio; D w is the roll diameter.

[0044] From the above derivation, the elastic bending equations of the work roll and the backup roll are respectively:

[0045]

[0046] Y B = G B Q m

[0047] In the formula, G w and G B are the bending influence function matrices of the work roll and the backup roll, is the bending force influence matrix, F W are the bending forces respectively. The bending force is another skin pass force, and the influence principle on the roll bending deformation is the same as that of the skin pass force. Q m is the roll pressure vector, and P m is the skin pass force vector.

[0048] (2) Metal plastic deformation in the skin pass process

[0049] The metal plastic deformation is studied by using the energy method. The basic idea is to first construct a displacement or velocity function that satisfies the displacement boundary conditions according to the characteristics of the skin pass process, then determine the undetermined parameters or functions in the displacement function according to the principle of minimum energy, and finally calculate and analyze the three-dimensional stress and deformation;

[0050] To determine the metal plastic deformation, it is necessary to determine the lateral deformation amount of the metal in the deformation zone. To determine the lateral deformation of the metal in the rolling piece deformation zone, the lateral deformation function is reduced in dimension and simplified.

[0051] U(x, y) = f(x)u(y)

[0052] In the formula, f(x) is the variation law of the strip steel U in the x direction; u(y) is the thickness deformation function of the strip steel in the width direction at the exit of the deformation zone. The strip steel with width B is equally divided into (n - 1) longitudinal strip elements, that is, (n - 1) divided strip steels, and y i is the transverse coordinate at the node line position, and the transverse deformation u i at the exit of the i-th divided strip steel is equal to u(y i ), where i = 1, 2,..., n. After uniform division, the width of the strip element is S, as shown in Figure 2 .

[0053] A corresponding model is established by assuming linear interpolation for calculation, and u(y) can be expressed by a piecewise linear interpolation function.

[0054]

[0055] According to the interpolation model of the transverse deformation at the exit, when the transverse deformation amounts u i (i = 1, 2,..., n) at the exit node line are known, the transverse deformation function u(y) of the entire plate width can be determined. Therefore, based on the principle of minimum energy, an optimization solution method is used to determine the transverse deformation amounts at the exit node line.

[0056] The transverse thickness distribution of the strip before and after tempering is considered. At the same time, considering that the elastic flattening of the work roll surface is approximately parabolic along the longitudinal direction, the thickness change of the rolled piece in the deformation zone can be expressed as:

[0057]

[0058] h(x, y) = h 1 (y) + (h 0 (y) - h 1 (y))(x / l - 1) 2

[0059] In the formula, h 0 (y) is the thickness distribution function of the strip in the width direction before tempering, h 1 (y) is the thickness distribution function of the strip in the width direction after tempering, h(x, y) is the thickness distribution of the rolled piece in the width direction (y direction) in the deformation zone (i.e., at the position with length x), B i , b i are regression coefficients respectively, B is the plate width, l is the length of the deformation zone, h 0 (y) and h 1 (y) are obtained by linear regression of the detected values of the thickness distribution in the width direction of the strip before and after tempering, and the deformation zone is the contact area of the roll.

[0060] The unit flattening pressure p(y) is solved by using the differential equation of longitudinal balance and the stress boundary conditions at the flattening inlet and outlet, and the finite difference method.

[0061]

[0062] In the formula, σ x is the normal stress in the x direction; τ xy is the shear stress in the xy direction, and τ x is the unit frictional force in the x direction on the contact surface.

[0063] Based on the variational principle of rigid-plastic materials, considering the contact relationship between the rolled piece and the roll during the plate flattening process, since the normal velocity of the roll surface is zero, the unit flattening force p(y) does no work. The total energy function during the flattening process can be obtained from the displacement or velocity function that satisfies the displacement boundary conditions.

[0064]

[0065] In the formula, N p is the plastic deformation power in the deformation zone; N f is the frictional power on the contact surface; N s is the power on the inlet velocity discontinuity surface; is the power of the back tension stress; N σ1 is the power of the back tension stress.

[0066] The powers of each item are summed to obtain the representation form of the total energy variational principle:

[0067]

[0068] In the formula, k s is the shear resistance; H is the shear strain rate strength; τ is the combined friction stress in the longitudinal and transverse directions; v s is the relative sliding velocity of the metal with respect to the roll surface; v z0 is the z-direction flow velocity at the inlet; σ 0 is the back tension stress; v 0 is the inlet velocity of the rolled piece; σ 1 is the front tension stress; v 1 is the outlet velocity of the rolled piece. Finally, the total power functional can be obtained:

[0069]

[0070] represents the relative sliding velocity of the metal with respect to the roll surface at the inlet, and μ x and μ y represent the friction coefficients in the length direction and width direction of the strip in the deformation zone, respectively.

[0071] The total power functional is the transverse displacement u iFunctions of (i = 1, 2, …, n), according to the minimum energy, when u 1 , u 2 , u 3 ,... u n satisfies minN = N(u 1 , u 2 , u 3 ,... u n ), it is the solution. Since the Powell algorithm has a relatively simple structure, is easy to program, and can use conjugate directions to make the convergence speed faster during the calculation process, the Powell method is used for optimization to solve u 1 , u 2 , u 3 ,... u n and its corresponding P 1 (1), P 1 (2),..., P 1 (n), that is, finally, the thickness deformation distribution u(y) and the flattening force distribution P 1 (y) in the width direction of the exit of the deformation zone can be determined.

[0072] If the maximum difference between the current flattening distribution P 1 (y) of the strip in the width direction and the previous flattening force distribution P 0 (y) is compared with the set threshold; if the difference is less than the set threshold, the elongation difference ΔX(y) of each point in the strip width direction relative to the center position of the strip width is calculated, and then the magnitude of the strip side bending amount is predicted. If the difference is greater than the set threshold, the flattening force is adjusted. The initial assignment of the flattening force is small. Therefore, each adjustment increases the flattening force according to the set step size;

[0073] (III) Shape Prediction

[0074] During the flattening process, the transverse distribution of the flattening force is easily affected by factors such as the plate thickness distribution on the exit side of the roll, the deformation resistance of the rolled piece, and the tensile stress distribution. The elastic deformation of the roll due to the roll shape, bending roll force, and flattening force distribution forms a load-bearing roll gap, which further affects the deformation of the rolled piece. Therefore, during the flattening process, the deformation of the strip must be combined with the roll system elastic deformation model and the metal plastic deformation model to calculate the accurate transverse distribution of the transverse deformation at the exit of the flattening deformation zone.

[0075] When the thickness deformation distribution u(y) in the exit width direction is known, the forward tensile stress distribution and the transverse distribution of the strip elongation after flattening can be solved using the shape prediction model.

[0076] The flatness prediction model is obtained based on the strip profile shape at the hot rolling exit and considering the influence of each hot rolling production line (mainly including laminar cooling, strip pinch roll process, strip coiling process) on the strip flatness. On the basis of considering the transverse flow of metal, the three-dimensional stress and deformation distribution of the metal in the deformation zone are analyzed and calculated using the flatness prediction model to obtain the transverse distribution of the front tension, and then the uneven component in the front tension distribution is extracted, and further the transverse distribution of the residual stress, that is, the on-line flatness, is obtained. The transverse distribution of the front tension is determined by the transverse distribution of the length after temper rolling. According to the condition of constant volume before and after temper rolling, the transverse distribution of the length after temper rolling can be determined.

[0077] Based on the law of constant volume in plastic mechanics and considering the transverse flow of metal during the temper rolling process, the stress distribution after temper rolling can be obtained as shown in the following formula:

[0078]

[0079] In the formula, ΔB is the spread at the strip exit, B is the strip width, E and ν are the elastic modulus and Poisson's coefficient respectively, h 0 (y) is the thickness distribution in the width direction of the strip before temper rolling, h 1 (y) is the thickness distribution in the width direction of the strip after temper rolling, l 0 (y) is the thickness distribution in the length direction of the strip before temper rolling, is the average thickness in the width direction of the strip before temper rolling, is the average thickness in the width direction of the strip after temper rolling, is the average thickness in the length direction of the strip before temper rolling, T 1 is the total tension.

[0080] Since the tensile stress distribution near the strip exit is in one-to-one correspondence with the exit flatness, the relationship is:

[0081] ΔX(y) = (σ 1o - σ 1 (y)) / E

[0082] In the formula, ΔX(y) is the elongation difference of the strip relative to the center position of the strip width, σ 1o is the front tensile stress at the center of the exit strip width.

[0083] (IV) Straightness prediction

[0084] Through the numerical calculation model of strip flatness during the rolling process of the rolled piece, the longitudinal plastic elongation difference distribution of the strip can be known. And ignoring the influence of the residual stress inside the narrow strip after slitting on the side bending amount, the side bending of the narrow strip after slitting is mainly caused by the uneven internal stress distribution induced by the uneven elongation of the initial strip. Combined with Figure 3 for explanation, when the total strain at the y position is ε, then there is

[0085] ε=ε 1 +(yy 1 ) / R

[0086] σ=E*ε

[0087] Where ε 1 is the strip cutting position y 1 The total strain at

[0088] The empirical formula obtained by combining the measurement results shows that the lateral bending amount is a function of the curvature radius.

[0089]

[0090] The analytical relationship between the relative extension difference of the strip and the lateral bending of the longitudinally cut strips can be obtained as follows:

[0091]

[0092] Wherein d is the amount of camber, mm; L is the longitudinal length of the strip, mm; Δε is the relative extension difference; Δy is the width of the strip, mm; a is the error coefficient; when y in Δx(y) is taken as the end value of the strip in the width direction, Δε=ΔX(y), assuming that the length of the strip is 10m and the width is 1.5m, and it is cut along the width direction into 10 strips, then ΔX(0), ΔX(0.15), ΔX(0.3), ΔX(0.45), …, ΔX(1.35) respectively represent the relative extension difference of the 10 strips, and then the amount of camber of the 10 strips is calculated.

[0093] By using finite element software to establish a finite element model, studying the relationship between the lateral bending amount and the extension difference, and comparing the finite element calculation results with the analytical model calculation results, it was determined that a is 0.212. The corrected straightness prediction analytical model ensures the accuracy of the calculation process.

[0094] The present invention is described above by way of example in conjunction with the accompanying drawings. It is obvious that the specific implementation of the present invention is not limited to the above-mentioned method. As long as various non-substantial improvements are made using the method concept and technical solution of the present invention, or the concept and technical solution of the present invention are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A prediction method for the straightness defect after cutting and slitting hot-rolled skin-pass strip steel, characterized in that, the method specifically comprises the following steps: S1. Based on the thickness distribution h 0 (y) of the strip before temper rolling and the thickness distribution h 1 (y) of the strip after temper rolling, obtain the thickness distribution h(x, y) of the rolled piece in the deformation zone; S2. Represent the three-dimensional plastic deformation of the rolled piece using the energy method, and use the Powell algorithm to find the thickness deformation distribution u(y) in the width direction of the strip at the exit of the deformation zone corresponding to the minimum energy and the leveling force distribution P 1 (y); S3. Compare the maximum difference between the current leveler force distribution P 1 (y) of the strip in the width direction and the previous leveler force distribution P 0 (y) with the set threshold value; 1 (y) and the previous leveler force distribution P 0 (y) with the set threshold value; S4. If the difference is less than the set threshold, then execute step S5; if the difference is greater than the set threshold, then adjust the skin-pass force; S5. Calculate the elongation difference ΔX(y) of each point in the strip width direction relative to the center position of the strip width, and then predict the magnitude of the strip side bend; The calculation formula of the thickness distribution h(x, y) of the rolled piece in the deformation zone is specifically as follows: h(x,y) = h 1 (y) + (h 0 (y) - h 1 (y))(x / l - 1) 2 ; where h 0 (y) is the thickness distribution function in the width direction of the strip before tempering, and h 1 (y) is the thickness distribution function in the width direction of the strip after tempering, and l is the length of the deformation zone; The calculation formula of the total power functional N during the flattening process is specifically as follows: Among them, k s is the shear resistance; H is the shear strain rate strength; τ is the combined frictional stress in the longitudinal and transverse directions; v s is the relative sliding velocity of the metal with respect to the roll surface; v z0 is the z-direction flow velocity at the entrance; σ 0 is the back tension stress; v 0 is the workpiece entrance velocity; σ 1 is the front tension stress; v 1 is the workpiece exit velocity, represents the relative sliding velocity of the metal with respect to the roll surface at the entrance, μ x , μ y respectively represent the friction coefficients in the length direction and width direction of the strip in the deformation zone, h, h 0 , h 1 respectively represent the thickness distribution of the workpiece in the deformation zone, the thickness distribution in the width direction of the strip before leveling, and the thickness distribution in the width direction of the strip after leveling, and u′ represents the derivative of the transverse deformation function of the strip steel; Optimize using the Powell method to solve for u when N is minimized 1 , u 2 , u 3 ,... u n and its corresponding P 1 (1), P 1 (2),..., P 1 (n), and then determine the thickness deformation distribution u(y) and the flattening force distribution P 1 (y).

2. The prediction method for the straightness defect after cutting and slitting hot-rolled skin-pass strip steel according to claim 1, characterized in that, the method for obtaining the elongation difference ΔX(y) is specifically as follows: (11) Calculate the stress distribution σ 1 (y) along the width direction of the flattened strip steel; (12) Since the tensile stress distribution near the strip outlet is in one-to-one correspondence with the outlet strip shape, calculate the elongation difference ΔX(y) of each point in the strip width direction relative to the center position of the strip width, and its calculation formula is specifically as follows: ΔX(y) = (σ 1o -σ 1 (y)) / E Among them, σ 1o is the pre-tensile stress at the center of the outlet plate width, and E is the elastic modulus of the strip steel.

3. The prediction method for the straightness defect after cutting and slitting hot-rolled skin-pass strip steel according to claim 2, characterized in that, Stress distribution σ of the flattened strip steel 1 (y) is calculated as follows: Among them, ΔB is the spread amount at the strip exit, B is the strip width, E and ν are the elastic modulus and Poisson's coefficient respectively, h 0 (y) is the thickness distribution in the width direction of the strip before temper rolling, h 1 (y) is the thickness distribution in the width direction of the strip after temper rolling, l 0 (y) is the thickness distribution in the length direction of the strip before temper rolling, is the average thickness in the width direction of the strip before temper rolling, is the average thickness in the width direction of the strip after temper rolling, is the average thickness in the length direction of the strip before temper rolling, T 1 is the total tension, and u′(y) is the derivative of the function representing the transverse deformation of the slit strip.

4. The prediction method for the straightness defect after cutting and slitting hot-rolled skin-pass strip steel according to claim 2, characterized in that, the calculation formula of the side bend d of the slit strip is specifically as follows: wherein, L is the longitudinal length of the slit strip; Δε is the elongation difference of the end points in the strip width direction of the slit strip relative to the center position of the strip width, Δy is the width of the slit strip, and a is the error coefficient.

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