Rolling edge crack forecasting method suitable for cold rolling mill

Abstract

The invention discloses a rolling edge crack forecasting method suitable for a cold rolling mill, and the method comprises the following steps: calculating and solving a front tension distribution array through a plate shape model based on the equipment characteristic parameters of the cold rolling mill and the rolling process parameters of the cold rolling mill; calculating a critical stress intensity factor of the crack tip according to the front tension distribution array and the current crack length based on a linear elastic fracture mechanics theory; calculating a correction stress intensity factor of the current unit after shape correction; calculating the crack propagation energy release rate of the current unit based on the corrected stress intensity factor, thereby calculating the propagation displacement of the crack tip under the plane strain condition; and whether the correction stress intensity factor # imgabs0 # of the current unit subjected to shape correction is true or not is judged, then the final solution of the crack propagation displacement is obtained, namely, the strip steel edge crack length is obtained, and the method has important practical significance for improving the rolling quality and efficiency. The edge crack forecasting method is accurate and easy to implement.

Description

Technical Field

[0001] The invention belongs to the technical field of cold rolling and relates to a rolling edge crack prediction method suitable for a cold rolling mill. Background Art

[0002] Edge cracking is a common and challenging problem in steel rolling, particularly in cold rolling mills. These cracks not only affect product quality but can also reduce production efficiency. Therefore, predicting and controlling edge cracking is a key research topic in rolling technology.

[0003] Traditional crack prediction methods rely primarily on empirical formulas and simplified mechanical models, which often fail to accurately predict crack initiation and propagation. For example, empirical formulas are often based on extensive experimental data, but this data can be affected by numerous factors, such as the material's microstructure and rolling conditions. Consequently, the predictions from these formulas often deviate from actual conditions. Simplified mechanical models often overlook the many complex factors that influence crack initiation and propagation, such as the material's nonlinear behavior and stress concentration at the crack tip. Consequently, these models also offer limited predictive accuracy.

[0004] Although some new crack prediction methods have been proposed in recent years, such as those based on the finite element method (FEM), these methods are computationally complex, require extensive computing resources, and are very sensitive to the choice of model parameters, limiting their practical application. For example, the FEM requires a detailed description of the material's mechanical behavior, which necessitates a large number of material parameters that are often difficult to obtain. Furthermore, the FEM calculation process typically requires extensive computing resources, making it impractical in practical production. Summary of the Invention

[0005] In order to solve the above problems, the technical solution adopted by the present invention is: a rolling edge crack prediction method suitable for a cold rolling mill, comprising the following steps:

[0006] S1: Obtain equipment characteristic parameters of the cold rolling mill;

[0007] S2: Obtain rolling process parameters of the cold rolling mill;

[0008] S3: Based on the equipment characteristic parameters and rolling process parameters of the cold rolling mill, the discrete element method is used to solve the front tension distribution array σ1(i) in the width direction of the rolled strip through coupling with the plate shape model; where: i = 0, 1...n...; i is the serial number of the strip unit;

[0009] S4: Set the iteration variable a to the crack length and give the initial crack length a0;

[0010] S5: Based on the theory of linear elastic fracture mechanics, the critical stress intensity factor at the crack tip is calculated from the previous tension distribution array σ1(i) and the current crack length a

[0011] S6: Calculate the corrected stress intensity factor K of the current unit of the rolled strip after shape correction Ι (i);

[0012] S7: Based on modified stress intensity factor K Ι (i) Calculate the energy release rate of the crack propagation of the current unit of the rolled strip, and calculate the propagation displacement δ of the crack tip under plane strain conditions;

[0013] S8: Determine the corrected stress intensity factor of the current unit of the rolled strip after shape correction Is it true? If it is true, it means that the crack continues to grow. Let the crack length a = a + δ, i = i + 1, and go to step S5. Otherwise, the final solution a of the crack extension displacement is obtained, that is, the crack length at the edge of the strip.

[0014] Furthermore, the characteristic parameters of the rolling mill mainly include: the diameter D of the working roll S , the diameter D of the first intermediate roller P , diameter D of the second intermediate roller JK , diameter of support roller D CD ; The roller body lengths of the working rolls are L S , the first intermediate roller's roller length L P , the roller length L of the second intermediate roller JK , the roller body length of the support roller is L CD ; Coordinates of the plum blossom hole of the support roller (X C ,Z C ),(X D ,Z D ); the upper working roll shifting amount δc1, the lower working roll shifting amount δc2.

[0015] Furthermore, the rolling process parameters of the cold rolling mill include the thickness lateral distribution value H of the incoming strip material. i , the front tension of the strip T0, the back tension of the strip T1, the inlet thickness H, the outlet thickness h, the strip width B, the yield limit K of the strip m , total rolling pressure P, elastic modulus E and Poisson's ratio v.

[0016] Furthermore: the expression of the plate shape model is as follows:

[0017]

[0018] Where: h(y) is the outlet thickness distribution, h is the outlet average thickness; H(y) is the inlet thickness distribution, H is the inlet average thickness;

[0019] L(y) is the inlet length distribution, L is the average inlet length; u`(y) is the lateral displacement increment distribution; T1 is the total front tension of the strip, Δb is the absolute width expansion;

[0020] is the deflection of the upper working roll, is the deflection of the lower working roll; is the crown of the upper working roll, is the crown of the lower working roll; K' is the flattening coefficient of the working roll and the strip; q BS is the distribution value of rolling pressure.

[0021] Furthermore: the critical stress intensity factor The calculation formula is as follows:

[0022]

[0023] Where: σ1(i) is the front tension distribution, a is the crack length of the strip.

[0024] Furthermore, the calculation formula of the modified stress intensity factor is as follows:

[0025]

[0026] in: is the crack shape correction factor; B is the strip width;

[0027]

[0028] Furthermore, the calculation formula of the crack growth energy release rate G is as follows:

[0029]

[0030] Where: E is the elastic modulus.

[0031] Furthermore, the formula used for the expansion displacement δ of the crack tip is as follows:

[0032]

[0033] Among them: K m The meaning is the yield resistance of the strip.

[0034] The present invention provides a method for predicting rolling edge cracks suitable for a cold rolling mill, which has the following advantages:

[0035] (1) The present invention ideally models the crack propagation process at the edge of the strip during rolling, using an infinite plate subjected to a non-uniform uniaxial tensile load as an approximation. This changes the previous research methods that overly relied on experimental observations and finite element simulations, and can achieve macroscopic calculation of crack length.

[0036] (2) The strip front tension calculated by coupling the flatness model is used as the load in the crack model. On the one hand, the direction of the front tension and the crack propagation direction conform to the requirements of a mode I crack, making the relevant theories of fracture mechanics applicable. On the other hand, because the calculation parameters of the flatness model basically cover the characteristic parameters of the rolling process, the obtained front tension distribution array can better reflect the operating characteristics of the rolling mill.

[0037] (3) Using crack length as a variable, the stress intensity factor, ultimate stress intensity factor, and tip displacement are calculated element by element, combined with the continuous accumulation of crack length. This method simplifies the complex crack propagation problem and has engineering practicality.

[0038] (4) The control results obtained by adopting the scheme described in the present invention are consistent with the product control scheme of industrial batch production. The proposed theoretical calculation model can be directly applied to industrial production lines to achieve the purpose of simplifying production processes and reducing production costs.

[0039] The invention is an accurate and easy-to-implement edge crack prediction method, has important practical significance for improving the quality and efficiency of rolling, and provides a novel edge crack prediction method.

[0040] The rolling edge crack prediction method suitable for cold rolling mills described in the present invention is different from previous edge crack control methods. Its implementation idea is to take the cold rolling mill as the research object, establish an edge stress state model based on the unit characteristics and rolling parameters, and calculate based on the linear elastic fracture mechanics theory to realize the prediction of crack initiation and crack propagation status. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0042] Figure 1 This is the overall flow chart of the method;

[0043] Figure 2 It is a schematic diagram of unit division;

[0044] Figure 3is the calculation result of the front tension distribution curve in Example 1;

[0045] Figure 4 is the calculation result of the front tension distribution curve in Example 2;

[0046] Figure 5 It is a schematic diagram of the ideal model of the crack texture of the strip edge in the present invention. DETAILED DESCRIPTION

[0047] It should be noted that, unless there is any conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0049] Figure 1 This is the overall flow chart of the method;

[0050] A method for predicting rolling edge cracks suitable for a cold rolling mill comprises the following steps:

[0051] S1: Obtain equipment characteristic parameters of the cold rolling mill;

[0052] S2: Obtain rolling process parameters of the cold rolling mill;

[0053] S3: Based on the equipment characteristic parameters and rolling process parameters of the cold rolling mill, the discrete element method is used to solve the front tension distribution array σ1(i) in the width direction of the rolled strip through coupling with the plate shape model; where: i = 0, 1...n...; i is the serial number of the strip unit;

[0054] S4: Set the iteration variable a to the crack length and give the initial crack length a0;

[0055] S5: Based on the theory of linear elastic fracture mechanics, the critical stress intensity factor at the crack tip is calculated from the previous tension distribution array σ1(i) and the current crack length a

[0056] S6: Calculate the corrected stress intensity factor K of the current unit of the rolled strip after shape correction Ι(i) Shape correction refers to (a / B) in the calculation formula of this step, which is a shape-related function;

[0057] S7: Based on modified stress intensity factor K Ι (i) Calculate the energy release rate of the crack propagation of the current unit of the rolled strip, and calculate the propagation displacement δ of the crack tip under plane strain conditions;

[0058] S8: Determine the corrected stress intensity factor of the current unit of the rolled strip after shape correction Is it true? If it is true, it means that the crack continues to grow. Let the crack length a = a + δ, i = i + 1, and go to step S5. Otherwise, the final solution a of the crack extension displacement is obtained, that is, the crack length at the edge of the strip.

[0059] Furthermore, the characteristic parameters of the rolling mill mainly include: the diameter D of the working roll S , the diameter D of the first intermediate roller P , diameter D of the second intermediate roller JK , diameter of support roller D CD ; The roller body lengths of the working rolls are L S , the first intermediate roller's roller length L P , the roller length L of the second intermediate roller JK , the roller body length of the support roller is L CD ; Coordinates of the plum blossom hole of the support roller (X C ,Z C ),(X D ,Z D ); the upper working roll shifting amount δc1, the lower working roll shifting amount δc2.

[0060] Furthermore, the rolling process parameters of the cold rolling mill include the thickness lateral distribution value H of the incoming strip material. i , the front tension of the strip T0, the back tension of the strip T1, the inlet thickness H, the outlet thickness h, the strip width B, the yield limit K of the strip m , total rolling pressure P, elastic modulus E and Poisson's ratio v.

[0061] The rolls and strip are divided into discrete units of equal length. The corresponding inter-roll pressure, rolling pressure, and tension are also divided into discrete units. The purpose of dividing the discrete units is to separate the continuous force curve into individual calculable units, which can be analyzed and calculated unit by unit. The calculation of edge cracks starts from the edge unit of the strip and calculates each unit inward. Figure 2 It is a schematic diagram of unit division;

[0062] Including metal plastic deformation model, roller elastic deformation model, and loaded roller gap model. In fact, the calculation scheme for edge cracks starts from the front tension.

[0063] The expression of the plate shape model is as follows:

[0064]

[0065] Where: h(y) is the outlet thickness distribution, h is the outlet average thickness; H(y) is the inlet thickness distribution, H is the inlet average thickness;

[0066] L(y) is the inlet length distribution, L is the average inlet length; u`(y) is the lateral displacement increment distribution; T1 is the total front tension of the strip, Δb is the absolute width expansion;

[0067] is the deflection of the upper working roll, is the deflection of the lower working roll; is the crown of the upper working roll, is the crown of the lower working roll; K' is the flattening coefficient of the working roll and the strip; q BS is the distribution value of rolling pressure.

[0068] Furthermore: the critical stress intensity factor The calculation formula is as follows:

[0069]

[0070] Where: σ1(i) is the front tension distribution, a is the crack length of the strip.

[0071] Furthermore, the calculation formula of the modified stress intensity factor is as follows:

[0072]

[0073] in: is the crack shape correction factor; B is the strip width;

[0074]

[0075] Furthermore, the calculation formula of the crack growth energy release rate G is as follows:

[0076]

[0077] Where: E is the elastic modulus.

[0078] Furthermore, the formula used for the expansion displacement δ of the crack tip is as follows:

[0079]

[0080] Among them: K m The meaning is the yield resistance of the strip

[0081] Below, a cold rolling mill group is taken as an example to explain in detail the rolling edge crack prediction method suitable for a cold rolling mill according to the present invention.

[0082] Example 1:

[0083] S1: Obtain the equipment characteristic parameters of the cold rolling mill, mainly including: working roll body length LS = 1677 mm, roll diameter length DS = 80 mm, first intermediate roll body length LP = 1500 mm, roll diameter length DP = 138 mm, second intermediate roll body length LJ = 1450 mm, roll diameter length DJ = 235 mm, backup roll body length LC = 1346 mm, roll diameter length DC = 406.4 mm.

[0084] S2: Obtain the process characteristic parameters of the cold rolling mill, including: strip width B = 1200 mm, rolled piece inlet h1 = 2.0 mm, outlet thickness h2 = 1.389 mm, metal deformation resistance k m =1003MPA, rolling pressure P = 570t, elastic modulus E = 2.1×10 5 MPA, Poisson's ratio v = 0.3, front tension T1 = 101 MPA, rear tension T0 = 25 MPA;

[0085] S3: Divide the rolls and strip into discrete units of the same length, and the corresponding inter-roller pressure, rolling pressure, tension, etc. are also divided into discrete arrays; based on the equipment characteristic parameters and rolling process parameters of the cold rolling mill, the discrete element method is used to solve the distribution array σ1(i) of the front tension in the width direction of the rolled strip through the plate shape model coupling; where: i = 0, 1...n...; i is the serial number of the strip unit; the calculation results are shown in Figure 3 ,σ1(0)=42.43MP;

[0086] S4: Set the iteration variable a to the crack length, and give the initial crack length a0 = 0.28 mm;

[0087] S5: Calculate the critical stress intensity factor of the current unit of the rolled strip. Based on the linear elastic fracture mechanics theory, the critical stress intensity factor of the crack tip is calculated from the front tension distribution array σ1(i) obtained in the above calculation step S3 and the current crack length a:

[0088]

[0089] S6: Calculate the corrected stress intensity factor of the current element of the rolled strip after shape correction:

[0090]

[0091] in: is the crack shape correction factor.

[0092]

[0093] S7: Calculate the energy release rate of the crack growth of the current unit of the rolled strip: The propagation displacement of the crack tip under plane strain conditions is calculated from this:

[0094] S8: Judgment Is it true? If so, the crack continues to grow. Let a = a + δ, i = i + 1, and go to step S5. Otherwise, end the above calculation and obtain the final solution of the crack extension displacement a = 0.301, which is the length of the crack at the edge of the strip.

[0095] Example 2:

[0096] S1: Obtain the equipment characteristic parameters of the single-stand cold rolling mill, mainly including: working roll body length LS = 1677 mm, roll diameter length DS = 80 mm, first intermediate roll body length LP = 1500 mm, roll diameter length DP = 138 mm, second intermediate roll body length LJ = 1450 mm, roll diameter length DJ = 235 mm, backup roll body length LC = 1346 mm, roll diameter length DC = 406.4 mm.

[0097] S2: Obtain the process characteristic parameters of the single-stand cold rolling mill, including: strip width B = 1230 mm, rolled piece entrance h1 = 2.2 mm, exit thickness h2 = 1.53 mm, metal deformation resistance k m =823MPA, rolling pressure P = 557t, elastic modulus E = 2.1×10 5 MPA, Poisson's ratio v = 0.3, front tension T1 = 136 MPA, rear tension T0 = 71 MPA;

[0098] S3: The rolls and strips are divided into discrete units of the same length, and the corresponding inter-roll pressure, rolling pressure, tension, etc. are also divided into discrete arrays; based on the equipment characteristic parameters and rolling process parameters of the cold rolling mill, after the plate shape model calculation (including the metal plastic deformation model, the roll system elastic deformation model, and the loaded roll gap model), the discrete element method is used to couple and solve the tension distribution array σ1(i). The calculation results are shown in Figure 4 , σ1(0)=79.46MP, where: i=0, 1…n…; i is the serial number of the strip unit;

[0099] S4: Set the iteration variable a to the crack length, and give the initial crack length a0 = 0.14 mm;

[0100] S5: Calculate the critical stress intensity factor of the current element. Based on the linear elastic fracture mechanics theory, the critical stress intensity factor of the crack tip is calculated from the pre-tension distribution array σ1(i) obtained in the above calculation step S3 and the current crack length a:

[0101]

[0102] S6: Calculate the corrected stress intensity factor of the current element after shape correction:

[0103]

[0104] in: is the crack shape correction factor.

[0105]

[0106] S7: Calculate the energy release rate of the crack growth of the current element: The propagation displacement of the crack tip under plane strain conditions is calculated from this:

[0107] S8: Judgment Is it true? If so, it means the crack continues to grow. Let a = a + δ, i = i + 1, and go to step S5. Otherwise, end the above calculation and obtain the final solution of the crack extension displacement a = 0.155, which is the length of the crack at the edge of the strip.

[0108] Figure 5 It is a schematic diagram of the ideal model of the crack texture of the strip edge in the present invention.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting rolling edge cracks suitable for a cold rolling mill, characterized by: The following steps are involved: S1: Obtain equipment characteristic parameters of the cold rolling mill; S2: Obtain rolling process parameters of the cold rolling mill; S3: Based on the equipment characteristic parameters and rolling process parameters of the cold rolling mill, the discrete element method is used to solve the front tension distribution array σ1(i) in the width direction of the rolled strip through coupling with the plate shape model; where: i = 0, 1...n...; i is the serial number of the strip unit; S4: Set the iteration variable a to the crack length and give the initial crack length a0; S5: Based on the theory of linear elastic fracture mechanics, the critical stress intensity factor at the crack tip is calculated from the previous tension distribution array σ1(i) and the current crack length a S6: Calculate the shape-corrected stress intensity factor K of the current element of the rolled strip Ι (i); S7: Based on modified stress intensity factor K Ι (i) Calculate the energy release rate of the crack propagation of the current unit of the rolled strip, and calculate the propagation displacement δ of the crack tip under plane strain conditions; S8: Determine the corrected stress intensity factor of the current unit of the rolled strip after shape correction Is it true? If it is true, it means that the crack continues to grow. Let the crack length a = a + δ, i = i + 1, and go to step S5. Otherwise, the final solution a of the crack extension displacement is obtained, that is, the crack length at the edge of the strip.

2. A rolling edge crack prediction method suitable for a cold rolling mill according to claim 1, characterized in that: The equipment characteristic parameters of the rolling mill mainly include: the diameter D of the working roll S , the diameter D of the first intermediate roller P , diameter D of the second intermediate roller JK , diameter of support roller D CD ; The roller body lengths of the working rolls are L S , the first intermediate roller's roller length L P , the roller length L of the second intermediate roller JK , the roller body length of the support roller is L CD ; Coordinates of the plum blossom hole of the support roller (X C ,Z C ),(X D ,Z D ); the upper working roll shifting amount δc1, the lower working roll shifting amount δc2.

3. The method for predicting rolling edge cracks suitable for a cold rolling mill according to claim 1, characterized in that: The rolling process parameters of the cold rolling mill include the thickness lateral distribution value H of the incoming strip material. i , the front tension of the strip T0, the back tension of the strip T1, the inlet thickness H, the outlet thickness h, the strip width B, the yield limit K of the strip m , total rolling pressure P, elastic modulus E and Poisson's ratio v.

4. A rolling edge crack prediction method suitable for a cold rolling mill according to claim 1, characterized in that: The expression of the plate shape model is as follows: Where: h(y) is the outlet thickness distribution, h is the outlet average thickness; H(y) is the inlet thickness distribution, H is the inlet average thickness; L(y) is the inlet length distribution, L is the average inlet length; u`(y) is the lateral displacement increment distribution; T1 is the total front tension of the strip, Δb is the absolute width expansion; is the deflection of the upper working roll, is the deflection of the lower working roll; is the crown of the upper working roll, is the crown of the lower working roll; K' is the flattening coefficient of the working roll and the strip; q BS is the distribution value of rolling pressure.

5. The method for predicting rolling edge cracks suitable for a cold rolling mill according to claim 1, characterized in that: The critical stress intensity factor The calculation formula is as follows: Where: σ1(i) is the front tension distribution, a is the crack length of the strip.

6. The method for predicting rolling edge cracks suitable for a cold rolling mill according to claim 1, characterized in that: The calculation formula of the modified stress intensity factor is as follows: in: is the crack shape correction factor; B is the strip width; 7. The method for predicting rolling edge cracks suitable for a cold rolling mill according to claim 1, characterized in that: The calculation formula of the crack growth energy release rate G is as follows: Where: E is the elastic modulus.

8. The method for predicting rolling edge cracks suitable for a cold rolling mill according to claim 1, characterized in that: The crack tip extension displacement δ is calculated using the following formula: Among them: K m The meaning is the yield resistance of the strip.

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