Method and device for calculating the contact arc length of the deformation zone suitable for the rolling of very thin strips

Abstract

The application discloses a method and device for calculating a contact arc length of a deformation zone suitable for rolling of an ultrathin strip, and comprises the following steps: establishing a coordinate system in a lateral section of a work roll and an ultrathin strip; drawing an ultrathin strip rolling deformation zone in the coordinate system, wherein the ultrathin strip rolling deformation zone comprises an outlet elastic deformation zone, an inlet elastic deformation zone and a plastic deformation zone; obtaining parameters of the ultrathin strip, parameters of a rolling mill and process parameters; and calculating the length of the outlet elastic deformation zone, the length of the inlet elastic deformation zone, the length of the plastic deformation zone and the contact arc length of the ultrathin strip rolling deformation zone according to the parameters of the ultrathin strip, the parameters of the rolling mill and the process parameters. The technical scheme of the application avoids the problem of non-convergence of iteration in the process of calculating the contact arc length of the ultrathin strip rolling deformation zone, and improves the calculation precision.

Description

Technical Field

[0001] This invention belongs to the field of rolling technology, and in particular relates to a method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling. Background Technology

[0002] Precision ultra-thin strip, a high-end product in the cold-rolled steel strip industry, is generally less than 0.1 mm thick, with the thinnest currently rolled to 0.01 mm. It is a primary raw material for manufacturing micro-components in sophisticated microelectromechanical systems (MEMS) and is widely used in industries such as instrumentation, aerospace, electronics and communications, and medical devices. The rolling production of precision ultra-thin strip typically employs a 20-roll mill with small work roll diameters and a complex roll system. Compared to ordinary cold-rolled steel strip, the contact arc morphology of the deformation zone differs during the rolling process. In ordinary cold-rolled steel strip, due to its relatively thicker thickness, the contact arc in the deformation zone can be considered as an arc with an increased work roll radius; however, for ultra-thin strip, the contact arc in the deformation zone is compressed very flat, even approaching a straight line. As is well known, the contact arc length in the deformation zone directly affects the calculation of rolling force. Representative formulas used in the past for calculating the rolling force of cold-rolled strip include the MDStone formula, the Hill formula, and the Fleck formula. The Stone and Hill formulas both treat the contact arc in the deformation zone as a circular arc with an increasing work roll radius, and fail to consider the influence of the elastic zones at the inlet and outlet. This leads to calculated rolling force values ​​that are larger than the actual values, making them unsuitable for ultra-thin strips. Furthermore, when the reduction in ultra-thin strips increases to a certain value, convergence issues arise, making it impossible to solve for the contact arc length in the deformation zone and the rolling force. For example, using the Stone formula, given an inlet thickness of 0.1 mm and a strip strength of 510 MPa, the contact arc length in the deformation zone can be obtained using graphical or iterative methods when the reduction is within the range of 0–0.025 mm. However, when the reduction exceeds 0.025 mm, the graphical method exceeds the range of the curve in the graph, and the iterative method fails to converge. In reality, such materials can be rolled normally with a reduction greater than 0.025 mm. Meanwhile, the Freck formula divides rolling conditions into three types based on the characteristics of the rolling deformation zone. To calculate the contact arc length of the deformation zone under a specific rolling condition, it is necessary to first determine which type of rolling condition it belongs to. This requires certain experience, making the solution process cumbersome. It also has the problem that the iterative process may diverge. Summary of the Invention

[0003] The technical problem this invention aims to solve is to provide a method and apparatus suitable for calculating the contact arc length of the deformation zone in ultra-thin strip rolling. During ultra-thin strip rolling, the contact arc in the deformation zone is flattened, not forming a circular arc, and may even approach a straight line. Under these rolling conditions, previous methods for calculating the contact arc length suffer from low accuracy and non-convergence in the iterative process. This invention fully considers the characteristics of the contact arc in the deformation zone during ultra-thin strip rolling, and takes into account the influence of the elastic deformation zones at the entrance and exit. By establishing a coordinate system, selecting key points, and drawing key auxiliary lines, it organically combines the geometric relationships within the coordinate system with the elastoplastic deformation within the rolling deformation zone. A quadratic function curve is used to characterize the contact arc form, thus achieving the calculation of the contact arc length in each region of the ultra-thin strip rolling deformation zone. This invention avoids the drawback of non-convergence in the iterative calculation process of the contact arc length in the ultra-thin strip rolling deformation zone and improves the calculation accuracy. It is of great significance for accurately calculating the rolling force required for ultra-thin strip rolling and for formulating rolling procedures.

[0004] To achieve the above objectives, the present invention adopts the following solution:

[0005] A method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling includes the following steps:

[0006] Step S1: Establish a coordinate system within the lateral cross-section of the working roll and the ultra-thin strip;

[0007] Step S2: Draw the ultra-thin strip rolling deformation zone in the coordinate system. The ultra-thin strip rolling deformation zone includes the exit elastic deformation zone, the inlet elastic deformation zone, and the plastic deformation zone.

[0008] Step S3: Obtain the parameters of the ultra-thin strip, the rolling mill parameters, and the process parameters;

[0009] Step S4: Calculate the length of the exit elastic deformation zone, the length of the entrance elastic deformation zone, the length of the plastic deformation zone, and the contact arc length of the ultra-thin strip rolling deformation zone based on the ultra-thin strip parameters, mill parameters, and process parameters.

[0010] Preferably, the ultrathin strip parameters include: inlet thickness, outlet thickness, reduction amount, Young's modulus of the ultrathin strip, Poisson's ratio of the ultrathin strip, inlet deformation resistance, and outlet deformation resistance.

[0011] Preferably, the mill parameters include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

[0012] Preferably, the process parameters include: inlet tensile stress, outlet tensile stress, and friction coefficient.

[0013] The present invention also provides a device for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, comprising:

[0014] A module is established to create a coordinate system within the lateral cross-section of the work roll and the ultra-thin strip;

[0015] A drawing module is used to draw the ultra-thin strip rolling deformation zone in the coordinate system, wherein the ultra-thin strip rolling deformation zone includes an exit elastic deformation zone, an inlet elastic deformation zone, and a plastic deformation zone;

[0016] The acquisition module is used to acquire parameters of ultra-thin strip, rolling mill parameters, and process parameters;

[0017] The calculation module is used to calculate the length of the exit elastic deformation zone, the length of the entrance elastic deformation zone, the length of the plastic deformation zone, and the contact arc length of the ultra-thin strip rolling deformation zone based on the ultra-thin strip parameters, mill parameters, and process parameters.

[0018] Preferably, the ultrathin strip parameters include: inlet thickness, outlet thickness, reduction amount, Young's modulus of the ultrathin strip, Poisson's ratio of the ultrathin strip, inlet deformation resistance, and outlet deformation resistance.

[0019] Preferably, the mill parameters include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

[0020] Preferably, the process parameters include: inlet tensile stress, outlet tensile stress, and friction coefficient.

[0021] The present invention has the following technical effects:

[0022] This invention organically combines the geometric relationships within the deformation zone during ultra-thin strip rolling with the elastic-plastic deformation within that zone. Taking the length of the exit elastic deformation zone as a starting point, and based on the contact arc curve form with quadratic function characteristics, it sequentially calculates the contact arc lengths of the exit elastic deformation zone, the entrance elastic deformation zone, the plastic deformation zone, and the entire deformation zone. This method offers high calculation accuracy and speed, and solves the problem of iterative non-convergence in the calculation of the contact arc length in the deformation zone of ultra-thin strip rolling. It provides a theoretical basis for subsequent calculation of rolling force and formulation of rolling specifications for ultra-thin strip products, reduces the number of trial rolling operations for ultra-thin strip, and ensures stable production of the unit. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the overall process for calculating the contact arc length of the deformation zone during ultra-thin strip rolling.

[0024] Figure 2 This is a schematic diagram illustrating the formation principle of the contact arc in the deformation zone during the rolling process of ultra-thin strip.

[0025] Figure 3 Flowchart for calculating the length of the elastic deformation zone at the outlet;

[0026] Figure 4 Flowchart for calculating the length of the elastic deformation zone at the entrance. Detailed Implementation

[0027] The technical solutions in the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0028] Example 1:

[0029] like Figure 1 As shown, the present invention provides a method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, comprising the following steps:

[0030] Step S1: Establish a coordinate system within the lateral cross-section of the working roll and the ultra-thin strip;

[0031] Step S2: Draw the ultra-thin strip rolling deformation zone in the coordinate system. The ultra-thin strip rolling deformation zone includes the exit elastic deformation zone, the inlet elastic deformation zone, and the plastic deformation zone.

[0032] Step S3: Obtain the parameters of the ultra-thin strip, the rolling mill parameters, and the process parameters;

[0033] Step S4: Calculate the length of the exit elastic deformation zone, the length of the entrance elastic deformation zone, the length of the plastic deformation zone, and the contact arc length of the ultra-thin strip rolling deformation zone based on the ultra-thin strip parameters, mill parameters, and process parameters.

[0034] As one embodiment of the present invention, in step S1, as follows: Figure 2 As shown, a coordinate system is established within the lateral section of the work roll and the ultra-thin strip, with the x-axis passing through the center of the ultra-thin strip thickness and parallel to the rolling direction, and the y-axis passing through the center of the work roll and perpendicular to the rolling direction. The intersection of the x-axis and the y-axis is denoted as O, and the coordinate system is denoted as xOy.

[0035] In one embodiment of the present invention, in step S2, key points of the coordinate system xOy are set, wherein: A is the intersection of the ultra-thin strip on the inlet side and the work roll; B is the intersection of the extension line of the upper boundary line of the ultra-thin strip inlet thickness with the y-axis; C is the center of the work roll cross-section; D is the intersection of the ultra-thin strip on the outlet side and the work roll; E is the intersection of the extension line of the upper boundary line of the ultra-thin strip outlet thickness with the y-axis; F is the intersection of the arc line of the work roll without considering flattening with the y-axis; and the intersection of the arc line of the work roll under actual rolling conditions with the y-axis is... G; A line parallel to the y-axis drawn through point D intersects the extension of the upper boundary line of the ultra-thin strip inlet thickness at point H; the boundary line between the inlet elastic deformation zone and the plastic deformation zone intersects the extension of the upper boundary line of the ultra-thin strip inlet thickness at point I; the arc line of the work roll under actual rolling conditions intersects at point J; the length of the inlet elastic deformation zone is set as L1, the length of the outlet elastic deformation zone is L2, the sum of the lengths of the inlet elastic deformation zone and the plastic deformation zone is L3, and the length of the plastic deformation zone is L4; the contact arc length of the ultra-thin strip rolling deformation zone is L;

[0036] In one embodiment of the present invention, the parameters of the ultrathin strip in step S3 include: inlet thickness h0, outlet thickness h1, reduction Δh = h0 - h1, and Young's modulus E of the ultrathin strip. s extremely thin band Poisson's ratio v s Inlet deformation resistance σ s0 Export deformation resistance σ s1 The mill parameters include: work roll radius R, work roll Young's modulus E. r Poisson's ratio v of the working roll r The process parameters include: inlet tensile stress σ0, outlet tensile stress σ1, and friction coefficient μ.

[0037] As one embodiment of the present invention, in step S4, the length L2 of the outlet elastic deformation zone DE is calculated, such as... Figure 3 As shown, it includes the following steps:

[0038] (e1) Calculate the characteristic parameters of the exit elastic deformation zone, including: the shear yield strength of the exit strip. Export elastic deformation zone length coefficient

[0039] (e2) Set the initial value of L2 to L 2，0 The step size ΔL = 0.0001 is calculated, and the step size coefficient is k1.

[0040] (e3) Let k1 = 1;

[0041] (e4)L2=L 2，0 +k1·ΔL;

[0042] (e5) Calculate the intermediate coefficients of the elastic strain model for export strip steel.

[0043] (e6) Calculate the difference in strip displacement between points B and H (BG-HD), i.e., EG.

[0044] (e7) The flattening amount of the work roll, i.e., FG, can be calculated using one of the following two methods: (1) If there is experimental or field data on the rolling force of this type of ultra-thin strip, the unit rolling force is set as but (2) There is no relevant data on the rolling force of this type of ultra-thin strip, but it can be calculated according to... The calculation is performed, where λ is the influence coefficient of the ultra-thin strip material on the flattening of the work roll, generally λ = 0.9 to 1.1;

[0045] (e8) In △CED, according to the Pythagorean theorem DE 2 +CE 2 =CD 2 Calculate the length L2' of DE under the current conditions. Where EF = EG + FG;

[0046] (e9) Determine if the inequality |L2-L2'|<ε is true. Where ε is the calculation precision. If true, let L2=L2' and go to step (e10); if false, let k1=k1+1 and go to step (e4).

[0047] (e10) Output outlet elastic deformation zone length L2;

[0048] In one embodiment of the present invention, in step S4, in △ABC, according to the Pythagorean theorem AB... 2 +BC 2 =AC 2 Calculate the length L3 of the elastic deformation zone and the plastic deformation zone AB at the entrance.

[0049] As one embodiment of the present invention, in step S4, the length L1 of the entrance elastic deformation zone AI is calculated, such as... Figure 4 As shown, it includes the following steps:

[0050] (g1) Treat the curve AG as a quadratic function with the function form y AG (x)=ax 2 +c, where a is the coefficient of the quadratic term of the quadratic function and c is the constant term of the quadratic function;

[0051] (g2) Select feature points from curve AG and Obtained by solving for feature points Right now

[0052] (g3) Calculate the characteristic parameters of the elastic deformation zone at the entrance, including: the shear yield strength of the strip at the entrance. Inlet elastic deformation zone length factor

[0053] (g4) Set the initial value of L1 to L 1，0 The step size ΔL = 0.0001 is calculated, and the step size coefficient is k0.

[0054] (g5) Let k0 = 1;

[0055] (g6)L1=L 1，0 +k0·ΔL;

[0056] (g7) Calculate the intermediate coefficients of the elastic strain model for the inlet strip.

[0057] (g8) Calculate the displacement of the strip at point I, i.e., IJ.

[0058] (g9) The quadratic function curve AG intersects IJ at point J, therefore it should satisfy... Thus, the inequality is determined. Is it true? If it is true, proceed to step (g10); if it is not true, let k0 = k0 + 1 and proceed to step (g6).

[0059] (g10) Output inlet elastic deformation zone length L1;

[0060] In one embodiment of the present invention, in step S4, the contact arc length of the ultra-thin strip rolling deformation zone is L = L2 + L3, the length of the exit elastic deformation zone is L2, the length of the inlet elastic deformation zone is L1, and the length of the plastic deformation zone is L4 = L3 - L1.

[0061] Example 2:

[0062] This invention provides a method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, comprising:

[0063] (a) Establish a coordinate system in the lateral section between the work roll and the ultra-thin strip with the x-axis passing through the center of the ultra-thin strip thickness and parallel to the rolling direction, and the y-axis passing through the center of the work roll and perpendicular to the rolling direction. The intersection of the x-axis and the y-axis is denoted as O, and the coordinate system is denoted as xOy.

[0064] (b) Set up a coordinate system xOy with key points, where A is the intersection of the ultra-thin strip on the inlet side and the work roll, B is the intersection of the extension of the upper boundary line of the ultra-thin strip inlet thickness and the y-axis, C is the center of the work roll cross-section, D is the intersection of the ultra-thin strip on the outlet side and the work roll, E is the intersection of the extension of the upper boundary line of the ultra-thin strip outlet thickness and the y-axis, F is the intersection of the arc of the work roll when flattening is not considered and the y-axis, G is the intersection of the arc of the work roll under actual rolling conditions and the y-axis, H is the intersection of the line parallel to the y-axis through point D and the extension of the upper boundary line of the ultra-thin strip inlet thickness, I is the intersection of the boundary line of the elastic deformation zone and the plastic deformation zone at the inlet and the extension of the upper boundary line of the ultra-thin strip inlet thickness, and J is the intersection of the arc of the work roll under actual rolling conditions.

[0065] (c) Set the length of the inlet elastic deformation zone to L1, the length of the outlet elastic deformation zone to L2, the sum of the lengths of the inlet elastic deformation zone and the plastic deformation zone to L3, and the length of the plastic deformation zone to L4; the contact arc length of the entire deformation zone is L.

[0066] (d) Collect key rolling parameters for ultra-thin strip, rolling mill, and process. Among them, the ultra-thin strip parameters include: entry thickness h0 = 0.1 mm, exit thickness h1 = 0.075 mm, reduction Δh = h0 - h1 = 0.025 mm, and ultra-thin strip Young's modulus E. s =2.1×10 5 MPa, Poisson's ratio of the ultrathin band v s =0.34, Inlet Deformation Resistance σ s0 =510MPa, outlet deformation resistance σ s1 =560MPa; Mill parameters include: work roll radius R = 35mm, work roll Young's modulus E r =5.4×10 5 MPa, Poisson's ratio of the working roll v r =0.3; Process parameters include: inlet tensile stress σ0 = 94MPa, outlet tensile stress σ1 = 125MPa, friction coefficient μ = 0.1;

[0067] (e) Calculate the length L2 of the outlet elastic deformation zone DE. The calculation steps are as follows:

[0068] (e1) Calculate the characteristic parameters of the exit elastic deformation zone, including: the shear yield strength of the exit strip. Export elastic deformation zone length coefficient

[0069] (e2) Set the initial value L of L2 2，0 =0, calculate step size ΔL = 0.0001, step size coefficient is k1;

[0070] (e3) Let k1 = 1;

[0071] (e4)L2=L2，0 +k1·ΔL=0.0001;

[0072] (e5) Calculate the intermediate coefficients of the elastic strain model for export strip steel.

[0073] (e6) Calculate the difference in strip displacement between points B and H (BG-HD), i.e., EG.

[0074] (e7) Calculate the flattening amount FG of the work roll and the experimental data of the rolling force. but

[0075] (e8) In △CED, according to the Pythagorean theorem DE 2 +CE 2 =CD 2 Calculate the length L2' of DE under the current conditions. Where EF = EG + FG = 0.00374;

[0076] (e9) Set the calculation precision ε to 0.0001. The inequality |L2-L2'|=0.5076<ε does not hold. Let k1=k1+1 and proceed to step (e4).

[0077] (e10) After 5118 iterations of equal-step accumulation, EG = 1.430 × 10⁻⁶ is obtained. -4 mm, FG=0.00360mm, EF=0.00374mm, L2'=0.5118mm, inequality |L2-L2'|=2.700×10 -5 If ε is true, the final output outlet elastic deformation zone length L2 = 0.5118 mm;

[0078] (f) In △ABC, according to the Pythagorean theorem AB 2 +BC 2 =AC 2 Calculate the length L3 of the elastic deformation zone and the plastic deformation zone AB at the entrance.

[0079] (g) Calculate the length L1 of the inlet elastic deformation zone AI. The calculation steps are as follows:

[0080] (g1) Treat the curve AG as a quadratic function with the function form y AG (x)=ax 2 +c, where a is the coefficient of the quadratic term of the quadratic function and c is the constant term of the quadratic function;

[0081] (g2) Select feature points A(-1.4181, 0.05) and G(0, 0.0373) on curve AG to obtain... That is, y AG (x)=0.00629x 2 +0.0373;

[0082] (g3) Calculate the characteristic parameters of the elastic deformation zone at the entrance, including: the shear yield strength of the strip at the entrance. Inlet elastic deformation zone length factor

[0083] (g4) Set the initial value L1. 1，0 =0, calculate step size ΔL = 0.0001, step size coefficient is k0;

[0084] (g5) Let k0 = 1;

[0085] (g6)L1=L 1，0 +k0·ΔL=0.0001mm;

[0086] (g7) Calculate the intermediate coefficients of the elastic strain model for the inlet strip.

[0087] (g8) Calculate the displacement of the strip at point I, i.e., IJ.

[0088] (g9) The quadratic function curve AG intersects IJ at point J, therefore it should satisfy... inequality This is not true. Let k0 = k0 + 1 and proceed to step (g6).

[0089] (g10) After 69 iterations of equal-step accumulation, IJ = 1.231 × 10⁻⁶ -4 mm, inequality The condition is met, and the final output inlet elastic deformation zone length L1 = 0.0069 mm;

[0090] (h) During the rolling process of the ultra-thin strip, the contact arc length of the entire deformation zone is L = L2 + L3 = 1.9299 mm, the length of the exit elastic deformation zone is L2 = 0.5118 mm, the length of the inlet elastic deformation zone is L1 = 0.0069 mm, and the length of the plastic deformation zone is L4 = L3 - L1 = 1.4112 mm.

[0091] Example 3:

[0092] This invention provides a method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, comprising:

[0093] (a) Establish a coordinate system in the lateral section between the work roll and the ultra-thin strip with the x-axis passing through the center of the ultra-thin strip thickness and parallel to the rolling direction, and the y-axis passing through the center of the work roll and perpendicular to the rolling direction. The intersection of the x-axis and the y-axis is denoted as O, and the coordinate system is denoted as xOy.

[0094] (b) Set up a coordinate system xOy with key points, where A is the intersection of the ultra-thin strip on the inlet side and the work roll, B is the intersection of the extension of the upper boundary line of the ultra-thin strip inlet thickness and the y-axis, C is the center of the work roll cross-section, D is the intersection of the ultra-thin strip on the outlet side and the work roll, E is the intersection of the extension of the upper boundary line of the ultra-thin strip outlet thickness and the y-axis, F is the intersection of the arc of the work roll when flattening is not considered and the y-axis, G is the intersection of the arc of the work roll under actual rolling conditions and the y-axis, H is the intersection of the line parallel to the y-axis through point D and the extension of the upper boundary line of the ultra-thin strip inlet thickness, I is the intersection of the boundary line of the elastic deformation zone and the plastic deformation zone at the inlet and the extension of the upper boundary line of the ultra-thin strip inlet thickness, and J is the intersection of the arc of the work roll under actual rolling conditions.

[0095] (c) Set the length of the inlet elastic deformation zone to L1, the length of the outlet elastic deformation zone to L2, the sum of the lengths of the inlet elastic deformation zone and the plastic deformation zone to L3, and the length of the plastic deformation zone to L4; the contact arc length of the entire deformation zone is L.

[0096] (d) Collect key rolling parameters for ultra-thin strip, rolling mill, and process. Among them, the ultra-thin strip parameters include: entry thickness h0 = 0.08 mm, exit thickness h1 = 0.055 mm, reduction Δh = h0 - h1 = 0.025 mm, and Young's modulus E of ultra-thin strip. s =2.1×10 5 MPa, Poisson's ratio of the ultrathin band v s =0.32, Inlet Deformation Resistance σ s0 =545MPa, outlet deformation resistance σ s1 =605MPa; Mill parameters include: work roll radius R = 35mm, work roll Young's modulus E r =5.4×10 5 MPa, Poisson's ratio of the working roll v r =0.3; Process parameters include: inlet tensile stress σ0 = 88MPa, outlet tensile stress σ1 = 128MPa, friction coefficient μ = 0.1;

[0097] (e) Calculate the length L2 of the outlet elastic deformation zone DE. The calculation steps are as follows:

[0098] (e1) Calculate the characteristic parameters of the exit elastic deformation zone, including: the shear yield strength of the exit strip. Export elastic deformation zone length coefficient

[0099] (e2) Set the initial value L of L2 2，0 =0, calculate step size ΔL = 0.0001, step size coefficient is k1;

[0100] (e3) Let k1 = 1;

[0101] (e4)L2=L 2，0 +k1·ΔL=0.0001;

[0102] (e5) Calculate the intermediate coefficients of the elastic strain model for export strip steel.

[0103] (e6) Calculate the difference in strip displacement between points B and H (BG-HD), i.e., EG.

[0104] (e7) Calculate the flattening amount FG of the work roll and the experimental data of the rolling force. but

[0105] (e8) In △CED, according to the Pythagorean theorem DE 2 +CE 2 =CD 2 Calculate the length L2' of DE under the current conditions. Where EF = EG + FG = 0.00455;

[0106] (e9) Set the calculation precision ε to 0.0001. The inequality |L2-L2'|=0.5499<ε does not hold. Let k1=k1+1 and proceed to step (e4).

[0107] (e10) After 5640 iterations of equal-step accumulation, EG = 2.908 × 10⁻⁶ is obtained. -4 mm, FG=0.00425mm, EF=0.00407mm, L2'=0.5640mm, inequality |L2-L2'|=2.996×10 -5 If ε is true, the final output outlet elastic deformation zone length L2 = 0.5640 mm;

[0108] (f) In △ABC, according to the Pythagorean theorem AB 2 +BC 2 =AC 2 Calculate the length L3 of the elastic deformation zone and the plastic deformation zone AB at the entrance.

[0109] (g) Calculate the length L1 of the inlet elastic deformation zone AI. The calculation steps are as follows:

[0110] (g1) Treat the curve AG as a quadratic function with the function form y AG (x)=ax 2 +c, where a is the coefficient of the quadratic term of the quadratic function and c is the constant term of the quadratic function;

[0111] (g2) Select feature points A(-1.4378, 0.04) and G(0, 0.0272) on curve AG to obtain... That is, y AG (x)=0.00619x 2 +0.0272;

[0112] (g3) Calculate the characteristic parameters of the elastic deformation zone at the entrance, including: the shear yield strength of the strip at the entrance. Inlet elastic deformation zone length factor

[0113] (g4) Set the initial value L1. 1，0 =0, calculate step size ΔL = 0.0001, step size coefficient is k0;

[0114] (g5) Let k0 = 1;

[0115] (g6)L1=L 1，0 +k0·ΔL=0.0001mm;

[0116] (g7) Calculate the intermediate coefficients of the elastic strain model for the inlet strip.

[0117] (g8) Calculate the displacement of the strip at point I, i.e., IJ.

[0118]

[0119] (g9) The quadratic function curve AG intersects IJ at point J, therefore it should satisfy... inequality This is not true. Let k0 = k0 + 1 and proceed to step (g6).

[0120] (g10) After 61 iterations of equal-step accumulation, IJ = 1.081 × 10⁻⁶ -4 mm, inequality The condition is met, and the final output inlet elastic deformation zone length L1 = 0.0061 mm;

[0121] (h) During the rolling process of the ultra-thin strip, the contact arc length of the entire deformation zone is L = L2 + L3 = 2.0018 mm, the length of the exit elastic deformation zone is L2 = 0.5640 mm, the length of the entrance elastic deformation zone is L1 = 0.0061 mm, and the length of the plastic deformation zone is L4 = L3 - L1 = 1.4317 mm.

[0122] Example 4:

[0123] The present invention also provides a device for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, comprising:

[0124] A module is established to create a coordinate system within the lateral cross-section of the work roll and the ultra-thin strip;

[0125] A drawing module is used to draw the ultra-thin strip rolling deformation zone in the coordinate system, wherein the ultra-thin strip rolling deformation zone includes an exit elastic deformation zone, an inlet elastic deformation zone, and a plastic deformation zone;

[0126] The acquisition module is used to acquire parameters of ultra-thin strip, rolling mill parameters, and process parameters;

[0127] The calculation module is used to calculate the contact arc length of the exit elastic deformation zone, the entrance elastic deformation zone, the plastic deformation zone, and the ultra-thin strip rolling deformation zone based on the ultra-thin strip parameters, mill parameters, and process parameters.

[0128] As one embodiment of the present invention, the ultra-thin strip parameters include: inlet thickness, outlet thickness, reduction amount, Young's modulus of the ultra-thin strip, Poisson's ratio of the ultra-thin strip, inlet deformation resistance, and outlet deformation resistance.

[0129] As one embodiment of the present invention, the mill parameters include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

[0130] As one embodiment of the present invention, the process parameters include: inlet tensile stress, outlet tensile stress, and friction coefficient.

[0131] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, characterized in that, Includes the following steps: Step S1: Establish a coordinate system within the lateral cross-section of the working roll and the ultra-thin strip; Step S2: Draw the ultra-thin strip rolling deformation zone in the coordinate system. The ultra-thin strip rolling deformation zone includes the exit elastic deformation zone, the inlet elastic deformation zone, and the plastic deformation zone. Step S3: Obtain the parameters of the ultra-thin strip, the rolling mill parameters, and the process parameters; Step S4: Calculate the length of the exit elastic deformation zone, the length of the inlet elastic deformation zone, the length of the plastic deformation zone, and the contact arc length of the ultra-thin strip rolling deformation zone based on the ultra-thin strip parameters, mill parameters, and process parameters. The ultrathin strip parameters include: entrance thickness. Export thickness Pressure reduction Extremely thin band Young's modulus Poisson's ratio of extremely thin bands Inlet deformation resistance Export deformation resistance ; The mill parameters include: work roll radius. Young's modulus of the work roll Poisson's ratio of the working roll ; The process parameters include: inlet tensile stress. Export tension coefficient of friction ; In step S1, a coordinate system is established within the lateral section of the work roll and the ultra-thin strip, with the x-axis passing through the center of the ultra-thin strip thickness and parallel to the rolling direction, and the y-axis passing through the center of the work roll and perpendicular to the rolling direction. The intersection of the x-axis and the y-axis is denoted as O, and the coordinate system is denoted as xOy. In step S2, key points of the coordinate system xOy are set, where: A is the intersection of the ultra-thin strip on the inlet side and the work roll; B is the intersection of the extension line of the upper boundary line of the ultra-thin strip inlet thickness with the y-axis; C is the center of the work roll cross-section; D is the intersection of the ultra-thin strip on the outlet side and the work roll; E is the intersection of the extension line of the upper boundary line of the ultra-thin strip outlet thickness with the y-axis; F is the intersection of the arc line of the work roll (without considering flattening) with the y-axis; G is the intersection of the arc line of the work roll under actual rolling conditions with the y-axis; a line parallel to the y-axis is drawn through point D, intersecting the extension line of the upper boundary line of the ultra-thin strip inlet thickness at point H; the boundary line between the inlet elastic deformation zone and the plastic deformation zone intersects the extension line of the upper boundary line of the ultra-thin strip inlet thickness at point I; and J is the intersection of the arc line of the work roll under actual rolling conditions; the length of the inlet elastic deformation zone is set as... The length of the elastic deformation zone at the outlet is The sum of the lengths of the elastic deformation zone and the plastic deformation zone at the entrance is The length of the plastic deformation zone is The contact arc length of the deformation zone in the ultra-thin strip rolling process is... ; The calculation of the length of the outlet elastic deformation zone includes: (e1) Calculate the characteristic parameters of the elastic deformation zone at the exit, including: the shear yield strength of the strip at the exit. Export elastic deformation zone length coefficient ; (e2) setting The initial value is Calculate step size The step size coefficient is ; (e3) Let ; （e4） ； (e5) Calculate the intermediate coefficients of the elastic strain model for the exported strip. ; (e6) Calculate the difference in the amount of strip compression at point B and point H. That is, EG, EG = ; (e7) Calculate the flattening amount of the work roll, i.e., FG, using one of the following two calculation methods: (1) Use experimental data or field data of the rolling force of extremely thin strip, and set the unit rolling force as ,but (2) There is no relevant data on the rolling force of ultra-thin strips, so it is calculated according to FG= Calculations are performed, in which, The coefficient representing the influence of extremely thin strip material on the flattening of the work roll. ; (e8) In △CED, according to the Pythagorean theorem... Calculate the DE length under the current conditions. , ,in, ; (e9) Determine inequalities Whether it is true or not, among which, For the sake of calculation precision, if it holds true, then let... Proceed to step (e10); if not, then set Proceed to step (e4); (e10) Length of the elastic deformation zone at the output / exit ; Calculating the length of the elastic deformation zone at the inlet involves treating the curve AG as a quadratic function and selecting feature points on the curve AG.

2. A device for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling, used to implement the method for calculating the contact arc length of the deformation zone suitable for ultra-thin strip rolling as described in claim 1, characterized in that, include: A module is established to create a coordinate system within the lateral cross-section of the work roll and the ultra-thin strip; A drawing module is used to draw the ultra-thin strip rolling deformation zone in the coordinate system, wherein the ultra-thin strip rolling deformation zone includes an exit elastic deformation zone, an inlet elastic deformation zone, and a plastic deformation zone; The acquisition module is used to acquire parameters of ultra-thin strip, rolling mill parameters, and process parameters; The calculation module is used to calculate the length of the exit elastic deformation zone, the length of the entrance elastic deformation zone, the length of the plastic deformation zone, and the contact arc length of the ultra-thin strip rolling deformation zone based on the ultra-thin strip parameters, mill parameters, and process parameters. The parameters of the ultra-thin strip include: inlet thickness, outlet thickness, reduction, Young's modulus of the ultra-thin strip, Poisson's ratio of the ultra-thin strip, inlet deformation resistance, and outlet deformation resistance. The mill parameters include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio; The process parameters include: inlet tensile stress, outlet tensile stress, and friction coefficient.

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