A prediction method for the residual curvature of a metal sheet straightened by a roller straightening machine

Abstract

The present invention belongs to the technical field of sheet metal straightening, and particularly relates to a method for predicting the residual curvature of a metal sheet straightened by a roller straightening machine. In the calculation process of the present invention, various influences of process parameters on the straightening process during the roller straightening process are comprehensively considered. By predicting the straightening residual curvature of the metal sheet during the roller straightening process, the obtained residual curvature value is basically close to the actual value, improving the calculation accuracy. The method of the present invention is safe and reliable, accurate in calculation, and simple and convenient. It can accurately predict the straightening residual curvature of metal sheets under different straightening process specifications, enabling the product to be better applied to actual production.

Description

Technical Field

[0001] The present invention belongs to the technical field of plate straightening, and particularly relates to a method for predicting the residual curvature of a metal plate straightened by a roller straightening machine. Background Art

[0002] During the rolling production process of plates, various defects such as waviness, bending, and camber often occur due to uneven plate thickness, temperature changes, improper transportation, and improper storage. With the continuous development of science and technology and the continuous saturation of the steel industry, the steel market has higher and higher requirements for the performance and quality of products. Steel with a large output but insufficient additional performance has become difficult to meet the increasingly high living and production needs. Therefore, how to control the plate shape has become a more prominent problem, and good flatness and extremely small internal stress have received extensive attention. In actual production, the straightening process is an effective means to improve the flatness of plates and control residual stress. Plates that meet engineering standards after straightening are widely used in many fields such as aerospace, petrochemical, shipbuilding, water conservancy, and power construction.

[0003] The main purpose of the straightening process is to improve the plate shape and quality. At present, the research on straightening theory mainly focuses on aspects such as roll system structure, reduction, curvature, and residual stress. Among them, the analysis of curvature is the most basic and important in the straightening process. The analysis of other parameters such as straightening force and residual stress must be based on the analysis of curvature. Therefore, in the research of straightening theory, the distribution law of curvature has always been the focus of attention.

[0004] At present, the research on the curvature of the traditional roller straightening process mainly includes experimental methods, beam bending methods, and finite element methods. The experimental method can only be targeted at specific processes each time, with great limitations; the beam bending method simplifies the straightening process and is easy to calculate, but there is a certain deviation from the actual straightening process; the finite element method has a large amount of calculation and a long time consumption, which cannot meet the actual production needs and is not convenient for engineering applications. Therefore, it is necessary to develop a method for predicting the curvature of roller straightening that takes a short time, is convenient to calculate, and has relatively accurate calculation results. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method for predicting the residual curvature of a metal plate straightened by a roller straightening machine.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A method for predicting the residual curvature of a metal plate straightened by a roller straightening machine, comprising the following steps:

[0008] Step 1: Determine the process parameters for straightening analysis according to the equipment conditions of a certain pass straightening process and the material properties of the metal plate;

[0009] Step 2: In a straightening interval, perform two-dimensional meshing on the metal sheet in the length and thickness directions. The length direction is divided into units, and the thickness direction is divided into units, and start the calculation from the th unit in the length direction;

[0010] Step 3: Initialize the reverse bending rate and calculate the curvature increment in the length direction;

[0011] Step 4: Set the strain increment of the center line of the plate thickness and calculate the stress distribution of the th unit in the thickness direction until the stress distributions of all units in the thickness direction are all calculated;

[0012] Step 5: According to the convergence condition, judge whether the stress and tensile stress in the cross-section are equal. If they are equal, enter the th unit in the length direction until all units in the length direction are all calculated; if they are not equal, reset the strain increment of the center line of the plate thickness in Step 4 and repeat Step 4 until they are equal;

[0013] Step 6: Enter the next straightening interval and repeat Steps 2 to 5 until all straightening intervals are calculated to obtain the stress distribution of the metal sheet in all straightening intervals;

[0014] Step 7: Calculate the first integral value and the second integral value of the curvature change amount of each straightening interval;

[0015] Step 8: Calculate the inclination angle and curvature at the contact points of each straightening roll;

[0016] Step 9: Calculate the curvature increment in the corresponding length direction according to the curvature at the contact points of each straightening roll, and repeat Steps 4 to 8 to obtain the first integral value and the second integral value of the iterated curvature change amount;

[0017] Step 10: Judge whether the first integral value and the second integral value of the iterated curvature change amount satisfy the convergence condition , . If they are satisfied, directly output the curvature calculation result; if not, readjust the first integral value and the second integral value , repeat Steps 8 to 9 until the convergence condition is satisfied, output the curvature calculation result, and complete the prediction.

[0018] Further, the process parameters in Step 1 include the number of straightening rolls , the diameter of the straightening rolls , the roll pitch of the straightening rolls , the reduction of the straightening rolls , the yield stress of the metal sheet , the elastic modulus , the Poisson's ratio , the thickness of the metal sheet , the initial curvature and the initial residual stress , where the initial residual stress .

[0019] Further, the specific process of Step 3 is as follows:

[0020] Step 3.1: Initialize the reverse curvature of the roll, specifically: :

[0021] ;

[0022] Step 3.2: Calculate the curvature increment in the length direction according to the reverse curvature of the roll, specifically: :

[0023] ;

[0024] where is the curvature change between two rolls, and is the reverse curvature of the roll.

[0025] Further, the specific process of Step 4 is as follows:

[0026] Step 4.1: Set the strain increment of the center line of the plate thickness according to the curvature increment in the length direction, specifically: :

[0027] ;

[0028] where represents the stress distribution of the th element in the direction in the thickness direction, represents the offset of the center line of the plate thickness of the th element in the direction in the thickness direction, and represents the distance from the th element in the thickness direction to the center line of the plate thickness;

[0029] Step 4.2: Calculate the strain increment of the element in the direction, specifically: ;

[0030] ;

[0031] Step 4.3: Calculate the stress increments of the element in the direction and direction, specifically: , , specifically:

[0032] , within the elastic range:

[0033] ;

[0034] ;

[0035] , within the plastic range:

[0036] ;

[0037] ;

[0038] ;

[0039] Step 4.4: Calculate the stress distributions of the element in the direction and direction, specifically: , , specifically:

[0040] ;

[0041] ;

[0042] Step 4.5: Repeat Steps 4.2 to 4.4 until the stress distributions of all elements in the thickness direction are calculated.

[0043] Furthermore, the convergence condition in Step 5 is:

[0044] ;

[0045] where represents the tensile stress in the cross-section.

[0046] Furthermore, the specific process of Step 7 is as follows:

[0047] Step 7.1: Calculate the bending moment per unit width of each straightening section based on the obtained stress distribution, specifically as follows:

[0048] ;

[0049] where, represents the bending moment per unit width of the th unit in the length direction within the straightening section;

[0050] Step 7.2: Calculate the first integral value and the second integral value of the curvature change amount of each straightening section, specifically as follows:

[0051] ;

[0052] ;

[0053] where, , respectively represent the values of the bending moment per unit width at the contact point of the th roll and the contact point of the th roll, , , , , , , , respectively represent the values of the bending moment per unit width of the 1st, , , , , 、 , th units in the length direction within the straightening section.

[0054] Furthermore, the specific process of Step 8 is as follows:

[0055] Step 8.1: Calculate the initial inclination angle of the first roll contact point in the first straightening section, specifically as follows:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] wherein, represents the reduction of the first roll, represents the reverse bending rate of the first roll;

[0064] Step 8.2: Calculate the inclination angles at the contact points of each straightening roll, specifically:

[0065] When the first roll in the straightening section is the upper roll:

[0066] ;

[0067] wherein, , represents the contact inclination angle of the th roll, represents the contact inclination angle of the th roll;

[0068] When the first roll in the straightening section is the lower roll:

[0069] ;

[0070] Step 8.3: Calculate the curvature at the contact points of each straightening roll , specifically:

[0071] When the first roll in the straightening section is the upper roll:

[0072] ;

[0073] When the first roll in the straightening section is the lower roll:

[0074] .

[0075] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0076] By predicting the straightening residual curvature of the metal sheet during the roller straightening process, the obtained residual curvature value is basically close to the actual value. In the calculation process, various influences of process parameters on the straightening process during the roller straightening process are comprehensively considered, improving the calculation accuracy. The method of the present invention is safe and reliable, accurate in calculation, simple and convenient, and time-consuming short, and can accurately predict the straightening residual curvature of the metal sheet under different straightening process specifications, enabling the product to be better applied to actual production. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Schematic diagram of nine-roll straightening provided by the present invention;

[0078] Figure 2 Schematic diagram of dividing the metal sheet into units by the present invention;

[0079] Figure 3 Comparison chart of the predicted value of straightening curvature and the actual value at a certain site of the present invention.

[0080] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, these embodiments are provided to make the understanding of the disclosure of the present invention more thorough and comprehensive. Embodiment

[0081] The straightening equipment adopted in this embodiment is a nine-roll straightening machine (see Figure 1 ). The upper row of rolls on the straightening machine is inclined and pressed down, and the lower row of rolls remains stationary. As long as the pressing amounts of the head and tail rolls are set for the upper row of rolls, the pressing amounts of the entire roll system can be determined according to linear decrease. In each straightening interval, the straightening movement direction is defined as positive, the vertical downward direction is positive, the deformation curvature of downward convexity is positive, and the bending moment is positive. The specific implementation method of this embodiment is described as follows.

[0082] Step 1: Determine the process parameters for straightening analysis according to the equipment conditions of a certain pass straightening process and the material properties of the metal sheet. Among them, the process parameters include the number of straightening rolls , the diameter of the straightening rolls , the roll pitch of the straightening rolls , the entry pressing amount of the straightening rolls , the exit pressing amount of the straightening rolls , the pressing amount of the first roll of the straightening rolls , the yield stress of the metal sheet , the elastic modulus , the Poisson's ratio , the thickness of the metal sheet , the initial curvature and the initial residual stress .

[0083] Step 2: In a straightening interval, divide the metal sheet into two-dimensional meshes in the length and thickness directions, as shown in Figure 2 . The length direction is divided into units, and the thickness direction is divided into units, and the calculation starts from the first unit in the length direction and the first unit in the thickness direction of the first straightening interval.

[0084] Step 3: Initialize the reverse curvature and calculate the curvature increment in the length direction , the specific process is as follows:

[0085] Step 3.1: Initialize the reverse bending rates of the first roll and the second roll , , specifically:

[0086] ;

[0087] ;

[0088] Step 3.2: Calculate the curvature increment in the length direction according to the reverse bending rates of the first roll and the second roll , , specifically:

[0089] .

[0090] Step 4: Set the strain increment of the center line of the plate thickness and calculate the stress distribution of the th unit in the thickness direction until the stress distributions of all units in the thickness direction are all calculated; the specific process is as follows:

[0091] Step 4.1: Set the strain increment of the center line of the plate thickness according to the curvature increment in the length direction , specifically:

[0092] ;

[0093] Among them, represents the stress distribution of the th unit in the thickness direction in the direction, represents the offset of the center line of the plate thickness of the th unit in the thickness direction in the direction, represents the distance from the th unit in the thickness direction to the center line of the plate thickness;

[0094] In this embodiment, is set;

[0095] Step 4.2: Calculate the strain increment of the th unit in the thickness direction in the direction, specifically:

[0096] ;

[0097] In this embodiment, the strain increment of the first unit in the thickness direction in the direction is calculated as For example, the solution is:

[0098] ;

[0099] Step 4.3: Calculate the thickness direction Unit in direction, Stress increment in the direction , , specifically:

[0100] , within the elastic range:

[0101] ;

[0102] ;

[0103] , within the plastic range:

[0104] ;

[0105] ;

[0106] ;

[0107] In this embodiment, the first unit in the thickness direction is calculated. direction, Stress increment in the direction , For example, the solution is:

[0108] ;

[0109] ;

[0110] Step 4.4: Calculate the thickness direction Unit in direction, Stress distribution in the direction , , specifically:

[0111] ;

[0112] ;

[0113] In this embodiment, the first unit in the thickness direction is calculated. direction, Stress distribution in the direction , For example, the solution is:

[0114] ;

[0115] ;

[0116] Step 4.5: Repeat steps 4.2 to 4.4 until the stress distributions of units in the thickness direction (i.e., ) are all calculated.

[0117] Step 5: According to the convergence condition, judge whether the stress and the tensile stress in the cross-section are equal. If they are equal, enter the second unit in the length direction until all units in the length direction are calculated; if they are not equal, reset the strain increment of the center line of the plate thickness in step 4 and repeat step 4 until they are equal; because the tension on the metal plate remains unchanged during the straightening process, the convergence condition for judging the stress and the tensile stress in the cross-section is:

[0118] ;

[0119] where represents the tensile stress in the cross-section.

[0120] Step 6: Enter the next straightening interval and repeat steps 2 to 5 until all straightening intervals are calculated to obtain the stress distributions of the metal plate in all straightening intervals.

[0121] Step 7: Calculate the first integral value and the second integral value of the curvature change amount of each straightening interval. The specific process is as follows:

[0122] Step 7.1: Calculate the bending moment per unit width of each straightening interval according to the obtained stress distribution, specifically:

[0123] ;

[0124] where represents the bending moment per unit width of the th unit in the length direction within the straightening interval;

[0125] In this embodiment, taking the first straightening interval as an example, the solution is: the bending moment per unit width of the first unit in the length direction within the first straightening interval ; the bending moment per unit width of the 18th unit in the length direction within the first straightening interval ;

[0126] Step 7.2: Calculate the first integral value and the second integral value of the curvature change amount of each straightening interval according to the bending moment per unit width of each straightening interval, specifically:

[0127] ;

[0128] ;

[0129] Among them, and respectively represent the values of the bending moment per unit width at the contact point of the th roll and the contact point of the th roll. and and and and and and and respectively represent the values of the bending moment per unit width of the 1st, and and and and 、 and th units in the longitudinal direction within the straightening section;

[0130] In this embodiment, taking the first straightening section as an example, it is solved that: the first integral value of the curvature change amount in the first straightening section is 1.0651, and the second integral value is 71253.

[0131] Step 8: Calculate the inclination angle and curvature at each straightening roll contact point. The specific process is as follows:

[0132] Step 8.1: Calculate the initial inclination angle of the first roll contact point in the first straightening section, specifically:

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] ;

[0139] ;

[0140] Among them, represents the reduction of the first roll, and represents the reverse curvature of the first roll;

[0141] In this embodiment, the simultaneous solution is obtained as follows ;

[0142] Step 8.2: Calculate the inclination angles at the contact points of each straightening roll, specifically:

[0143] When the first roll in the straightening section is the upper roll:

[0144] ;

[0145] wherein , represents the contact inclination angle of the rd roll, represents the contact inclination angle of the th roll;

[0146] When the first roll in the straightening section is the lower roll:

[0147] ;

[0148] Taking the first straightening section with the first roll being the lower roll as an example in this embodiment, the inclination angles are obtained as follows:

[0149] ; ; ; ;

[0150] ; ; ; ;

[0151] Step 8.3: Calculate the curvature at the contact points of each straightening roll , specifically:

[0152] When the first roll in the straightening section is the upper roll:

[0153] ;

[0154] When the first roll in the straightening section is the lower roll:

[0155] ;

[0156] Taking the first straightening section with the first roll being the lower roll as an example in this embodiment, the curvatures are obtained as follows:

[0157] ; ; ; ;

[0158] ; ; ; 。

[0159] Step 9: Calculate the curvature increment in the corresponding length direction according to the curvature at each contact point of the straightening rolls, and repeat Steps 4 to 8 to obtain the first integral value of the iterated curvature change and the second integral value 。

[0160] Step 10: Determine whether the first integral value and the second integral value of the iterated curvature change satisfy the convergence condition , : If satisfied, directly output the curvature calculation result; if not satisfied, readjust the first integral value and the second integral value of the curvature change, and repeat Steps 8 to 9 until the convergence condition is satisfied, then output the curvature calculation result to complete the prediction.

[0161] According to the residual curvature prediction method for straightening metal sheets by the roller straightening machine proposed in the present invention above, the model prediction values of the metal sheets used are statistically analyzed and compared with the actual values at a certain site as Figure 3 shown. From the comparison results, it can be obtained that the residual curvature of the metal sheets predicted by the present invention is in good agreement with the actual values, and the curvature calculation error is within 10%. It can be seen that the accuracy of the residual curvature of the metal sheets straightened by the roller straightening machine predicted by the present invention is relatively high and can be better applied to actual production.

[0162] The above description is only an example for better explaining the present invention, and is not a limitation thereof. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall fall within the scope covered by the present invention.

Claims

1. A method for predicting the residual curvature of a metal sheet straightened by a roller straightening machine, characterized in that: The following steps are involved: Step 1: Determine the process parameters for straightening analysis according to the equipment conditions of a certain straightening process and the material properties of the metal sheet; Step 2: In a straightening interval, the metal sheet is divided into two-dimensional grids in the length and thickness directions. The length direction is divided into 2M units, and the thickness direction is divided into 2N units. The calculation starts from the jth unit in the length direction. Step 3: Initialize the inverse curvature and calculate the curvature increment in the length direction; Step 4: Set the strain increment of the center line of the plate thickness and calculate the stress distribution of the kth unit in the thickness direction until the stress distribution of 2N units in the thickness direction is calculated; Step 5: According to the convergence condition, determine whether the stress and tensile stress in the cross section are equal. If they are equal, enter the j+1th unit in the length direction until all 2M units in the length direction are calculated. If they are not equal, reset the strain increment of the center line of the plate thickness in step 4 and repeat step 4 until they are equal. Step 6: Enter the next straightening interval and repeat steps 2 to 5 until all straightening intervals are calculated to obtain the stress distribution of the metal sheet in all straightening intervals; Step 7: Calculate the single integral value G and double integral value H of the curvature change in each straightening interval; Step 8: Calculate the inclination angle and curvature at each straightening roller contact point; Step 9: Calculate the curvature increment in the corresponding length direction according to the curvature at each straightening roller contact point, repeat steps 4 to 8, and obtain the first integral value G' and the second integral value H' of the iterative curvature change; Step 10: Determine whether the first integral value G' and the second integral value H' of the curvature change after iteration meet the convergence conditions If it is satisfied, directly output the curvature calculation result; if it is not satisfied, readjust the first integral value G and the second integral value H of the curvature change, repeat steps 8 to 9 until the convergence condition is met, output the curvature calculation result, and complete the prediction; The process parameters in step 1 include the number of straightening rollers n, the diameter of the straightening rollers R, the distance between the straightening rollers l, the pressure reduction of the straightening rollers δ i , metal sheet yield stress σ s , elastic modulus E, Poisson's ratio μ, metal sheet thickness h, initial curvature k0 and initial residual stress σ0, where the initial residual stress σ0 = 0; The specific process of step 8 is as follows: Step 8.1: Calculate the initial inclination angle θ1 of the first roller contact point in the first straightening interval, specifically: bθ1 2 +cθ1+d=0; c=2N1N2R 2 A-RN1(2RA-1)+RN1+l(2RA-1)N2-2lRA+l; d=R 2 AN1 2 +l(2RA-1)N1+l 2 A-2δ1; A=G-2H; Among them, δ1 represents the pressing amount of the first roller, and k1 represents the reverse bending rate of the first roller; Step 8.2: Calculate the inclination angle at each straightening roller contact point, specifically: When the first roll in the straightening section is the upper roll: R 2 Ath i+1 2 +[(l-Rθ i )(2RA-1)+Rθ i ]θ i+1 +lθ i +(l-Rθ i ) 2 A-2d i =0; Where A = G-2H, θ i represents the contact inclination angle of the i-th roller, θ i+1 represents the contact inclination angle of the i+1th roller; When the first roll in the straightening section is the lower roll: -R 2 Ath i+1 2 +[Rθ i -(l-Rθ i )(2RA+1)]θ i+1 +lθ i -(l-Rθ i ) 2 A-2d i =0; Step 8.3: Calculate the curvature k at each straightening roller contact point i+1 * , specifically: When the first roll in the straightening section is the upper roll: When the first roll in the straightening section is the lower roll:

2. The method for predicting the residual curvature of a metal sheet straightened by a roller straightening machine according to claim 1, characterized in that: The specific process of step 3 is as follows: Step 3.1: Initialize the inverse curvature k of the i-th roller i , specifically: Step 3.2: According to the reverse curvature k of the i-th roller i Calculate the curvature increment dk in the length direction, specifically: Where Δk is the curvature change between the two rollers, k i+1 is the reverse curvature of the i+1th roller.

3. The method for predicting the residual curvature of a metal sheet straightened by a roller straightening machine according to claim 2, characterized in that: The specific process of step 4 is as follows: Step 4.1: Set the strain increment dε of the plate thickness centerline according to the curvature increment dk in the length direction c , specifically: Among them, σ x,k represents the stress distribution of the kth element in the x direction along the thickness direction, ε x,k represents the plate thickness centerline offset of the kth unit in the thickness direction in the x direction, and z represents the distance from the kth unit in the thickness direction to the plate thickness centerline; Step 4.2: Calculate the strain increment dε of the kth element in the x direction along the thickness direction x,k , specifically: dε x,k zdk+dε c 100. Step 4.3: Calculate the stress increment dσ in the x and y directions of the kth element in the thickness direction x,k , dσ y,k , specifically: Within the elastic range: In the plastic range: Step 4.4: Calculate the stress distribution σ of the kth element in the x and y directions along the thickness direction x,k , σ y,k , specifically: Step 4.5: Repeat steps 4.2 to 4.4 until the stress distribution of 2N units in the thickness direction is calculated.

4. The method for predicting the residual curvature of a metal sheet straightened by a roller straightening machine according to claim 3, characterized in that: The convergence condition in step 5 is: Among them, σ T Represents the tensile stress in the cross section.

5. The method for predicting the residual curvature of a metal sheet straightened by a roller straightening machine according to claim 4, characterized in that: The specific process of step 7 is as follows: Step 7.1: Calculate the unit width bending moment of each straightening interval according to the obtained stress distribution, specifically: Among them, M x It represents the bending moment per unit width of the x-th unit in the length direction within the straightening interval; Step 7.2: Calculate the single integral value G and double integral value H of the curvature change of each straightening interval according to the unit width bending moment of each straightening interval, specifically: Among them, M i+1 、M i M1 and M2 represent the unit width bending moment at the contact point of the i+1th roller and the contact point of the ith roller, respectively. 2M 、M j+1 、M j 、M m+1 、M m 、M s+1 、M s They respectively represent the values ​​of the unit width bending moment of the 1st, 2Mth, j+1, j, m+1, m, s+1, and sth units in the length direction within the straightening interval.

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