A prediction method for residual stress during the roller straightening process of metal sheets

Abstract

The present invention belongs to the technical field of sheet metal straightening, and particularly relates to a method for predicting residual stress during the roller straightening process of metal sheets. 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, and the obtained residual stress values are basically close to the actual values, 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 stress 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 sheet metal straightening, and particularly relates to a method for predicting residual stress during the roller straightening of metal sheets. Background Art

[0002] With the development of the economic society and the improvement of the level of urban modernization, as an important material for social infrastructure construction, sheets are widely used in bridges, intelligent factories, shipbuilding, oil platforms, oil and gas transportation pipelines, and high-rise building construction. At the present stage in China, the competition faced by steel is no longer about production volume and low price, but rather higher-level requirements in terms of shape quality and performance quality. Therefore, how to achieve breakthroughs in steel production efficiency and quality is the focus of attention. In actual production, the surface flatness and the distribution of residual stress of the sheet are important indicators determining the product quality. In particular, residual stress plays a crucial role in the use of the sheet. When a bridge collapses or a mechanical device fails, in addition to being related to the strength of the material itself, most of the cases are due to the influence of residual stress. The roller straightening machine is an important device on the production line to ensure the flatness of the product and reduce the residual stress.

[0003] The main purpose of the straightening process is to improve the sheet shape and quality. At present, the research on straightening theory mainly focuses on aspects such as the roll system structure, reduction amount, curvature, and residual stress. Among them, the research on residual stress is of great significance to actual production. How to effectively reduce residual stress is directly related to the final quality of the sheet.

[0004] At present, the main research methods for residual stress in the traditional roller straightening process include the experimental method, the beam bending method, and the finite element method, etc. The experimental method can only target specific processes each time and cannot meet the actual production needs; the beam bending method simplifies the straightening process but is not suitable for precisely calculating the residual stress quantitatively; the finite element method, which is time-consuming in calculation, is also limited by time, with a large amount of calculation and is not convenient for practical engineering applications. Therefore, it is necessary to develop a method for predicting roller straightening residual stress that is time-consuming, convenient to calculate, and has more 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 residual stress during the roller straightening of metal sheets.

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

[0007] A method for predicting residual stress during the roller straightening of metal sheets, 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 sheet;

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

[0010] Step 3: Initialize the residual stress in the width direction;

[0011] Step 4: Initialize the reverse bending rate in the width direction and calculate the curvature increment in the length direction;

[0012] Step 5: 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;

[0013] Step 6: 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 and the th unit in the width direction until all units in the width direction are all calculated, and then enter the th unit in the length direction and the th unit in the width direction. Finally, all units in the length direction and units in the width direction are all calculated; if they are not equal, reset the strain increment of the center line of the plate thickness in Step 5 and repeat the operation in Step 5 until they are equal;

[0014] Step 7: Enter the next straightening interval and repeat the operations in Steps 2 to 6 to obtain the stress distribution of the metal sheet in all straightening intervals;

[0015] Step 8: Solve the linear equations according to the stress distribution of the metal sheet in all straightening intervals and correct the strain increment of the center line of the plate thickness of each unit in each straightening interval;

[0016] Step 9: According to the corrected strain increment of the center line of the plate thickness of each unit in each straightening interval, recalculate the stress distributions of all straightening intervals;

[0017] Step 10: According to the convergence condition, determine whether the stress satisfies the principle of residual stress self - balance. If it does, output the calculation result of the residual stress; if not, re - initialize the reverse curvature in the width direction, calculate the curvature increment in the length direction, repeat the operation in Step 9 to calculate the stress until it is satisfied, and then output the calculation result of the residual stress.

[0018] Step 11: Solve the standard deviation of the residual stress to complete the prediction.

[0019] Further, the process parameters of the straightening analysis in Step 1 include the number of straightening rolls , the diameter of the straightening rolls , the roll pitch of the straightening rolls , the reduction at the entrance of the straightening rolls , the reduction at the exit 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 width of the metal sheet and the initial curvature .

[0020] Further, the specific method for initializing the residual stress in the width direction in Step 3 is:

[0021] ;

[0022] where is the residual stress in the width direction, is the coordinate in the width direction, and in ±: + represents edge wave, - represents middle wave.

[0023] Further, the specific method for initializing the reverse curvature in the width direction in Step 4 is:

[0024] ;

[0025] where is the distribution of the reverse curvature of the th roll along the width direction, is the distribution of the reduction of the th roll along the width direction;

[0026] The specific method for calculating the curvature increment in the length direction in Step 4 is:

[0027] ;

[0028] where is the curvature increment in the length direction, is the curvature change between two straightening intervals, For the The reverse curvature distribution of the roller along the width direction.

[0029] Furthermore, the specific process of step 5 is as follows:

[0030] Step 5.1: According to the curvature increment in the length direction Set the strain increment at the center line of the plate thickness , specifically:

[0031] ;

[0032] in, Indicates the thickness direction Unit in The stress distribution in the direction, Indicates the thickness direction Unit in The plate thickness centerline offset in the direction, Indicates the thickness direction The distance from the element to the center line of the plate thickness;

[0033] Step 5.2: Calculate the thickness direction Unit in Strain increment in the direction , specifically:

[0034] ;

[0035] Step 5.3: Calculate the thickness direction Unit in direction, Stress increment in the direction , , specifically:

[0036] Within the elastic range:

[0037] like : ;

[0038] ;

[0039] like : ;

[0040] ;

[0041] In the plastic range:

[0042] like : ;

[0043] ;

[0044] ;

[0045] If : ;

[0046] ;

[0047] ;

[0048] Step 5.4: Calculate the stress distributions of the element in the direction and direction, specifically: , :

[0049] ;

[0050] ;

[0051] Step 5.5: Repeat Steps 5.2 to 5.4 until the stress distributions of all elements in the thickness direction are all calculated.

[0052] Furthermore, the convergence condition in Step 6 is:

[0053] ;

[0054] where represents the tensile stress in the cross-section.

[0055] Furthermore, the linear equations in Step 8 are:

[0056] ;

[0057] where represents the stress increment of the th element in the width direction, represents the offset of the centerline of the plate thickness of the th element in the width direction, represents the curvature increment of the th element in the width direction, represents the strain increment of the centerline of the plate thickness of the th element in the width direction.

[0058] Furthermore, the convergence condition in Step 10 is:

[0059] The resultant forces on the cross-sections in the direction and direction are zero:

[0060] ;

[0061] ;

[0062] The bending moment about the central plane is zero:

[0063] ;

[0064] .

[0065] Furthermore, the specific method for solving the standard deviation of the residual stress in step 11 is as follows:

[0066] ;

[0067] wherein, is the standard deviation of the residual stress.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] The present invention predicts the straightening residual stress of metal sheets during the roller straightening process, and the obtained residual stress value is basically close to the actual value. During 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, with accurate calculation, and is simple and convenient. It can accurately predict the straightening residual stress of metal sheets under different straightening process specifications, enabling the product to be better applied to actual production. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is the schematic diagram of eleven-roll straightening provided by the present invention;

[0071] Figure 2 is the schematic diagram of the plate division unit of the present invention;

[0072] Figure 3 is the comparison diagram of the predicted value of the straightening residual stress of the present invention and the actual value at a certain site. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0073] 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

[0074] The straightening equipment adopted in this embodiment is an eleven-roll straightening machine, as Figure 1As shown, the upper row of rolls on the straightening machine is inclined and pressed down, while the lower row of rolls remains stationary. Once the pressing amounts of the first and last rolls are set for the upper row of rolls, the pressing amounts of the entire roll system can be determined according to a 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.

[0075] 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 for straightening analysis 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 yield stress of the metal sheet , the elastic modulus , the Poisson's ratio , the thickness of the metal sheet , the width of the metal sheet and the initial curvature .

[0076] Step 2: Conduct three-dimensional mesh division on the metal sheet in the length, width, and thickness directions within a straightening interval. As Figure 2 shown, the length direction is divided into units, the width direction is divided into units, and the thickness direction is divided into units, and the calculation starts from the th unit in the length direction and the th unit in the width direction.

[0077] Step 3: Initialize the residual stress in the width direction. Specifically:

[0078] ;

[0079] Among them, is the residual stress in the width direction, is the coordinate in the width direction, ± in: + represents edge wave, - represents middle wave;

[0080] In this embodiment, the calculated is:

[0081] .

[0082] Step 4: Initialize the anti-curvature in the width direction and calculate the curvature increment in the length direction;

[0083] The specific method for initializing the anti-curvature in the width direction is:

[0084] ;

[0085] Among them, is the anti-bending rate distribution of the roll along the width direction, is the reduction distribution of the roll along the width direction;

[0086] The specific method for calculating the curvature increment in the calculation length direction is:

[0087] ;

[0088] Among them, is the curvature increment in the length direction, is the curvature change between two straightening intervals, is the anti-bending rate distribution of the roll along the width direction.

[0089] Taking the first unit of the first straightening interval and the first unit of the second straightening interval in this embodiment as an example, the calculation process is as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] Among them, is the anti-bending rate of the first unit in the width direction of the first roll, is the anti-bending rate of the first unit in the width direction of the second roll, is the reduction of the first unit in the width direction of the entrance roll.

[0094] Step 5: 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 calculated completely. The specific process is as follows:

[0095] Step 5.1: Set the strain increment of the center line of the plate thickness according to the curvature increment in the length direction, specifically:

[0096] ;

[0097] Among them, represents the stress distribution of the th unit in the thickness direction in the direction, Indicates the offset of the center line of the plate thickness in the direction of the th unit in the thickness direction, Indicates the distance from the th unit in the thickness direction to the center line of the plate thickness;

[0098] In this embodiment, it is set that ;

[0099] Step 5.2: Calculate the strain increment of the th unit in the thickness direction in the direction, specifically:

[0100] ;

[0101] Taking the first unit in the thickness direction (i.e., ) as an example in this embodiment, the strain increment of the first unit in the thickness direction is solved as ;

[0102] Step 5.3: Calculate the stress increments and of the th unit in the thickness direction in the , direction, specifically:

[0103] Within the elastic range:

[0104] If : ;

[0105] ;

[0106] If : ;

[0107] ;

[0108] Within the plastic range:

[0109] If : ;

[0110] ;

[0111] ;

[0112] If : ;

[0113] ;

[0114] ;

[0115] In this embodiment, taking the elastic range as an example, the stress increments of the first unit in the thickness direction in the direction and the direction are : , :

[0116] ;

[0117] ;

[0118] Step 5.4: Calculate the stress distributions of the th unit in the thickness direction in the direction and the , , specifically:

[0119] ;

[0120] ;

[0121] In this embodiment, taking the first unit in the thickness direction as an example, the stress distributions of the first unit in the thickness direction in the direction and the , are:

[0122] ;

[0123] ;

[0124] Step 5.5: Repeat Steps 5.2 to 5.4 until the stress distributions of all units in the thickness direction are calculated completely.

[0125] Step 6: 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 th unit in the length direction and the th unit in the width direction until all units in the width direction are calculated completely, then enter the th unit in the length direction and the th unit in the width direction. Finally, all units in the length direction and units in the width direction are calculated completely; if they are not equal, reset the strain increment of the plate thickness center line in Step 5 and repeat the operations in Step 5 until they are equal;

[0126] The convergence condition is as follows:

[0127] ;

[0128] Wherein, represents the tensile stress in the cross-section.

[0129] Step 7: Enter the next straightening section, and repeat the operations in Steps 2 to 6 to obtain the stress distribution of the metal sheet in all straightening sections;

[0130] Step 8: Solve the linear equations according to the stress distribution of the metal sheet in all straightening sections, and correct the strain increment of the center line of the plate thickness of each unit in each straightening section;

[0131] The linear equations are as follows:

[0132] ;

[0133] Wherein, represents the stress increment on the th unit in the width direction, represents the offset of the center line of the plate thickness on the th unit in the width direction, represents the curvature increment on the th unit in the width direction, represents the strain increment of the center line of the plate thickness on the th unit in the width direction.

[0134] Taking the strain increment of the center line of the plate thickness on the first unit in the width direction as an example, is solved.

[0135] Step 9: Recalculate the stress distribution of all straightening sections according to the corrected strain increment of the center line of the plate thickness of each unit in each straightening section;

[0136] Step 10: According to the convergence condition, judge whether the stress satisfies the principle of self-equilibrium of residual stress. If it satisfies, output the calculation result of the residual stress; if it does not satisfy, re-initialize the reverse curvature in the width direction, calculate the curvature increment in the length direction, and repeat the operation in Step 9 to calculate the stress until it is satisfied, and then output the calculation result of the residual stress;

[0137] The convergence condition is as follows:

[0138] The resultant force on the cross-sections in the direction and the

[0139] direction is zero:

[0140] ;

[0141] The bending moment about the central plane is zero:

[0142] ;

[0143] ;

[0144] Step 11: Solve the standard deviation of the residual stress , and complete the prediction;

[0145] The calculation formula for solving the standard deviation of the residual stress is as follows,

[0146] ;

[0147] where, is the standard deviation of the residual stress.

[0148] In this embodiment, taking the entrance reduction as an example, the solution is to be 4.497 MPa.

[0149] According to the method for predicting the residual stress during the roller straightening process of metal sheets proposed by the present invention above, the model prediction values of the metal sheets used are statistically analyzed and the actual values at a certain site are as shown in Figure 3 . Through the comparison results, it can be obtained that the predicted residual stress of the metal sheets by the present invention is in good agreement with the actual values, and the calculation error of the residual stress is within 10%. It can be seen that the accuracy of the residual stress predicted during the roller straightening process of the metal sheets by the present invention is relatively high and can be better applied to actual production.

[0150] The above are only embodiments for better explaining the present invention, and are not intended to limit it. 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 residual stress during roller straightening of metal sheets, 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 three-dimensional grids in the length, width and thickness directions. The length direction is divided into 2M units, the width direction is divided into L units, and the thickness direction is divided into 2N units. The calculation starts from the jth unit in the length direction and the sth unit in the width direction. Step 3: Initialize the residual stress in the width direction; Step 4: Initialize the inverse curvature in the width direction and calculate the curvature increment in the length direction; Step 5: 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. Specifically: Step 5.1: Set the strain increment dε of the plate thickness centerline according to the curvature increment dk in the length direction c ; Step 5.2: Calculate the strain increment dε of the kth element in the x direction along the thickness direction x,k ; Step 5.3: Calculate the stress increment dσ of the kth element in the thickness direction in the x and y directions x,k , dσ y,k ; Step 5.4: Calculate the stress distribution σ of the kth element in the x and y directions along the thickness direction x,k , σ y,k ; Step 5.5: Repeat steps 5.2 to 5.4 until the stress distribution of 2N units in the thickness direction is calculated; Step 6: According to the convergence condition, determine whether the stress and tensile stress in the cross section are equal. If they are equal, enter the jth unit in the length direction and the s+1th unit in the width direction until all L units in the width direction are calculated, then enter the j+1th unit in the length direction and the sth unit in the width direction, and finally all 2M units in the length direction and L units in the width direction are calculated. If they are not equal, reset the strain increment of the center line of the plate thickness in step 5 and repeat the operation of step 5 until they are equal. Step 7: Enter the next straightening interval and repeat the operations from step 2 to step 6 to obtain the stress distribution of the metal sheet in all straightening intervals; Step 8: Solve the linear equations according to the stress distribution of the metal sheet in all straightening intervals, and correct the strain increment of the center line of the plate thickness of each unit in each straightening interval; Step 9: Recalculate the stress distribution of all straightening intervals according to the corrected strain increment of the plate thickness centerline of each unit in each straightening interval; Step 10: According to the convergence condition, determine whether the stress satisfies the residual stress self-balance principle. If so, output the residual stress calculation result; if not, reinitialize the inverse curvature in the width direction, calculate the curvature increment in the length direction, repeat the operation in step 9 to calculate the stress, and output the residual stress calculation result; Step 11: Solve for the standard deviation of residual stress and complete the prediction.

2. The method for predicting residual stress during roller straightening of metal sheets according to claim 1, characterized in that: The process parameters of the straightening analysis 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 at the inlet δ in 、Straightening roller outlet pressure reduction δ out , metal sheet yield stress σ s , elastic modulus E, Poisson's ratio μ, metal sheet thickness h, metal sheet width b and initial curvature k0.

3. The method for predicting residual stress during roller straightening of metal sheets according to claim 2, characterized in that: The specific method for initializing the residual stress in the width direction in step 3 is: Among them, σ0 is the residual stress in the width direction, y is the coordinate in the width direction, and ±: + represents side wave, and - represents medium wave.

4. The method for predicting residual stress during roller straightening of metal sheets according to claim 3, characterized in that: The specific method for initializing the inverse curvature in the width direction in step 4 is: Among them, k i,L is the inverse curvature distribution of the i-th roller along the width direction, δ i,L is the distribution of the reduction of the i-th roller along the width direction; The specific method for calculating the curvature increment in the length direction in step 4 is: Where dk is the curvature increment in the length direction, Δk is the curvature change between two straightening intervals, and k i+1,L is the inverse curvature distribution of the i+1th roller along the width direction.

5. The method for predicting residual stress during roller straightening of metal sheets according to claim 4, characterized in that: The specific process of step 5 is as follows: Step 5.1: 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 5.2: 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 5.3: Calculate the stress increment dσ of the kth element in the thickness direction in the x and y directions x,k , dσ y,k , specifically: Within the elastic range: If k = 1: If k≠1: In the plastic range: If k = 1: If k≠1: Step 5.4: 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 5.5: Repeat steps 5.2 to 5.4 until the stress distribution of 2N units in the thickness direction is calculated.

6. The method for predicting residual stress during roller straightening of metal sheets according to claim 5, characterized in that: The convergence condition in step 6 is: Among them, σ T Represents the tensile stress in the cross section.

7. The method for predicting residual stress during roller straightening of metal sheets according to claim 6, characterized in that: The linear equation system in step 8 is: Among them, dσ x (s) represents the stress increment on the sth element in the width direction, dε x (s) Indicates the plate thickness centerline offset on the sth unit in the width direction, dk (s) represents the curvature increment of the sth unit in the width direction, dε c (s) It represents the plate thickness centerline strain increment on the sth element in the width direction.

8. The method for predicting residual stress during roller straightening of metal sheets according to claim 7, characterized in that: The convergence condition in step 10 is: The resultant force on the cross section in the x- and y-directions is zero: The bending moment about the center plane is zero:

9. The method for predicting residual stress during roller straightening of metal sheets according to claim 8, characterized in that: The specific method for solving the residual stress standard deviation in step 11 is: Among them, D σ is the standard deviation of residual stress.

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