A method for predicting rolling force in the process of cold tandem rolling of strip steel

Abstract

The present invention discloses a method for predicting rolling force during the production process of cold continuous rolling strip, belonging to the field of rolling technology. Aiming at the problem of predicting the actual rolling force during cold continuous rolling under different production conditions, the present invention first determines parameters such as the inlet and outlet thicknesses of the slab, the original radius of the rolling roll, and the friction factor between the rolling roll and the slab according to the process specification data of a certain pass in cold continuous rolling. Considering the influence of the front and back tensions on the length of the deformation zone and the rolling force, it calculates the rolling force in the elastic deformation zone. By minimizing the total power functional of the plastic deformation zone in the cold continuous rolling strip process, it predicts the rolling force in the plastic deformation zone, and then obtains the total rolling force. Then, according to the mutual coupling between the rolling force and the flattened radius of the rolling roll, through iterative calculation, it calculates the rolling force that meets the convergence condition. The present invention is safe and reliable, with accurate calculation, and can calculate the rolling force in the continuous rolling process online in real time, saving the production investment cost while improving the control accuracy of the product thickness.

Description

Technical Field

[0001] The present invention belongs to the technical field of rolling, and particularly relates to a method for predicting rolling force in the production process of cold tandem rolling strip. Background Art

[0002] Cold-rolled strip belongs to high-value-added steel products and is widely used in related fields such as automobiles, electrical appliances, aviation, precision instruments, and food. With the development of China's economy and the progress of technology, the industrial structure has been gradually upgraded, and the manufacturing industries such as automobiles, household appliances, and aviation have expanded rapidly. The domestic market demand for cold-rolled strip has been continuously increasing, and the output of cold-rolled strip has been continuously increasing. With the increase in the output of cold-rolled strip, the downstream industries have also raised the requirements for the quality of cold-rolled strip. The plate thickness accuracy and shape quality have become important indicators of the product.

[0003] Rolling force is an important equipment parameter and process parameter of the rolling mill. It is mainly used to set the parameters of the rolling mill, and the prediction accuracy of the rolling force directly affects the thickness accuracy and shape quality of the rolled plate. To obtain strip with high plate thickness accuracy and shape quality, it is necessary to improve the prediction accuracy of the rolling force. Therefore, the research on rolling force has important significance.

[0004] At present, the research on cold tandem rolling force mainly adopts the engineering method and the finite element method. Although the engineering method is simple and convenient to calculate, it uses an approximate calculation method to simplify the mathematical model, and the prediction accuracy needs to be improved; although the finite element method has high accuracy, the calculation time is long, and each calculation can only display the results of a specific process. Therefore, it is necessary to propose a method with short calculation time and high accuracy in the cold tandem rolling process. Summary of the Invention

[0005] Aiming at the problem of predicting the actual rolling force in the cold tandem rolling process under different production conditions, the present invention provides a method for predicting the rolling force in the production process of cold tandem rolling strip.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for predicting rolling force in the cold tandem rolling process of strip steel, comprising the following steps:

[0008] Step 1: Determine the inlet thickness 2h in and the outlet thickness 2h out of the slab, the inlet width 2b, the front tension σ f and the back tension σ b according to the process specification data of a certain pass in the cold tandem rolling;

[0009] Step 2: Detect the inlet speed v0, the outlet speed v1 and the roll speed v R of the slab, and obtain the original roll radius R0 and the friction factor m between the roll and the slab;

[0010] Step 3: Consider the influence of the front and back tensions on the length of the deformation zone and the rolling force, and calculate the rolling force in the elastic deformation zone;

[0011] Step 3.1: Consider the influence of the front and back tensions on the length of the deformation zone, and calculate the reduction in half thickness Δh of the entrance elastic deformation zone and the exit elastic recovery zone in and Δh out ;

[0012] Step 3.2: According to the roll radius, the reduction in half thickness of the entrance and exit elastic deformation zones, calculate the projected lengths l in and l out ;

[0013] Step 3.3: Consider the influence of the front and back tensions on the rolling force in the elastic deformation zone, and calculate the rolling forces in the entrance and exit elastic deformation zones and

[0014] Step 4: Minimize the total power functional of the rolling plastic deformation zone to predict the rolling force in the plastic deformation zone during the cold tandem rolling of strip;

[0015] Step 4.1: Based on the velocity boundary conditions, volume constancy condition, and geometric equations of the strip rolling deformation zone, establish the velocity field and strain rate field of the rolling deformation zone that satisfy the kinematically admissible conditions;

[0016] Step 4.2: Express the unit second flow U using the velocity at the neutral plane of the rolling deformation zone, the neutral angle, and the geometric dimensions of the slab and the rolls;

[0017] Step 4.3: According to the actual material and rolling schedule in on-site rolling, calculate the deformation resistance of the plastic deformation zone of the cold-rolled strip;

[0018] Step 4.4: According to the velocity field, strain rate field, and slab deformation resistance, calculate the internal deformation power, friction power, shear power, and tension power in the plastic deformation zone of the cold-rolled slab to obtain the total power functional;

[0019] Step 4.5: According to the total power functional corresponding to different neutral angles, obtain the minimum value of the total power functional, calculate the force arm coefficient χ, and calculate the rolling force in the plastic deformation zone according to the relationship between the total power functional and the rolling force

[0020] Step 5: Calculate the rolling force in the entrance elastic deformation zone from Steps 3 and 4 The rolling force in the exit elastic recovery zone The rolling force in the plastic deformation zone Thus, the total rolling force F is obtained. According to the mutual coupling between the rolling force and the roll flattening radius, through iterative calculation, the rolling force that meets the convergence condition is calculated.

[0021] Further, in step 3.1, the influence of the front and back tensions on the length of the deformation zone is considered, and the reduction in half-thickness Δh of the entrance elastic deformation zone and the exit elastic recovery zone is calculated. in and Δh out The specific method is as follows:

[0022]

[0023]

[0024]

[0025]

[0026] Among them, E s is the elastic modulus of the strip, v s is the Poisson's ratio of the strip, h in represents the entrance half-thickness, h out represents the exit half-thickness, σ sin and σ sout are the deformation resistances of the strip on the entrance side and the exit side respectively, σ b is the back tension, σ f is the front tension, H0 is the entrance half-thickness of the strip in the first pass, h0 is the entrance half-thickness of the plastic deformation zone, and h1 is the exit half-thickness of the plastic deformation zone.

[0027] Further, in step 3.2, according to the roll radius, the reduction in half-thickness of the entrance and exit elastic deformation zones, the projected lengths l in and l out ;

[0028]

[0029]

[0030] Among them, Δh = h0 - h1 is the unilateral reduction of the plastic deformation zone, h0 is the entrance half-thickness of the plastic deformation zone, h1 is the exit half-thickness of the plastic deformation zone, and R is the roll flattening radius; Δh in is the reduction in half-thickness of the entrance elastic deformation zone, and Δh out is the reduction in half-thickness of the exit elastic recovery zone.

[0031] Further, in step 3.3, the influence of the front and back tensions on the rolling force in the elastic deformation zone is considered, and the rolling forces and

[0032] A coordinate system is established with the midpoint of the cross-section at the entrance of the plastic deformation zone of the strip as the origin, and x, y, and z represent the length, width, and thickness directions of the strip respectively;

[0033]

[0034]

[0035] where b is half of the width of the slab, h in is the half-thickness at the entrance of the slab, h out is the half-thickness at the exit of the slab, R is the flattening radius of the roll, Δh = h0 - h1 is the single-side reduction in the plastic deformation zone, h0 is the half-thickness at the entrance of the plastic deformation zone, h1 is the half-thickness at the exit of the plastic deformation zone, σ sin and σ sout are the deformation resistances of the strip on the entrance side and the exit side respectively, l in is the projection length of the elastic deformation zone at the entrance of the slab in the rolling direction, l out is the projection length of the elastic recovery zone at the exit of the slab in the rolling direction, E s is the elastic modulus of the strip, v s is the Poisson's ratio of the strip.

[0036] Furthermore, in step 4.1, according to the velocity boundary conditions, volume invariance conditions, and geometric equations of the strip rolling deformation zone, a velocity field and a strain rate field of the rolling deformation zone that satisfy the kinematic admissibility conditions are established;

[0037] The velocity field of the cold rolling plastic deformation zone is:

[0038]

[0039] A coordinate system is established with the midpoint of the cross-section at the entrance of the plastic deformation zone of the strip as the origin, and x, y, and z represent the length, width, and thickness directions of the strip respectively, where v x , v y , v z are the velocity components in the length, width, and thickness directions of the cold rolling slab respectively, v0 is the slab entrance velocity, λ is a parameter to be determined, h x is half of the slab thickness at any position in the rolling deformation zone; h x ′ is the first derivative of h x h x ′ = dh x / dx, h0 is the half-thickness at the entrance of the plastic deformation zone, h1 is the half-thickness at the exit of the plastic deformation zone, and l is the projection of the contact arc between the slab and the roll in the rolling direction in the plastic deformation zone;

[0040]

[0041] The strain rate field in the cold rolling plastic deformation zone is as follows:

[0042]

[0043] where are the strain rate components in the length, width, and thickness directions of the slab, respectively.

[0044] Furthermore, in step 4.2, the unit second flow rate U is expressed by using the velocity at the neutral plane in the rolling deformation zone, the neutral angle, and the geometric dimensions of the slab and the roll, as follows:

[0045] U = v0h0b = v R cosα n b(R + h1 - Rcosα n ) = v1h1b

[0046] where v0 is the slab inlet velocity, h0 is the inlet half-thickness of the plastic deformation zone, b is the inlet half-width of the slab, v R is the roll velocity, α n is the neutral angle, R is the flattened radius of the roll, v1 is the slab outlet velocity, and h1 is the outlet half-thickness of the plastic deformation zone.

[0047] Furthermore, in step 4.3, according to the actual materials and rolling schedule in on-site rolling, the deformation resistance in the plastic deformation zone of the cold-rolled sheet is calculated, as follows:

[0048]

[0049] where σ s represents the deformation resistance considering the influence of front and back tensions, σ represents the slab deformation resistance, σ f is the front tension, σ b is the back tension, H0 is the inlet half-thickness of the strip in the first pass, h0 is the inlet half-thickness of the plastic deformation zone, and h1 is the outlet half-thickness of the plastic deformation zone.

[0050] Furthermore, in step 4.4, according to the velocity field, strain rate field, and slab deformation resistance, the internal deformation power in the plastic deformation zone of the cold-rolled slab is calculated friction power shearing power tension power to obtain the total power functional, as follows:

[0051] Total power functional

[0052] Internal deformation power

[0053] Friction power

[0054]

[0055] Shearing power

[0056] Tension power

[0057] where σ s is the deformation resistance considering the influence of front and back tensions, ε = (h0 - h1) / h0, h0 is the half thickness at the entrance of the plastic deformation zone, h1 is the half thickness at the exit of the plastic deformation zone, λ is a parameter to be determined, m is the friction factor between the roll and the slab, k is the yield shear stress, b is the half width at the entrance of the slab, R is the flattened radius of the roll, v R is the roll speed, θ is the angle between the line connecting the entrance contact point of the plastic deformation zone during rolling and the center of the roll and the center line of the rolls, α n is the neutral angle, g b and g f are the parameters of the back slip and front slip zones respectively, h mb and h mf are the average thicknesses of the back slip and front slip zones respectively, h αn is the half thickness of the slab corresponding to the neutral angle, σ f and σ b are the front and back tensions of the slab respectively.

[0058] Furthermore, in step 4.5, the total power functional corresponding to different neutral angles is calculated to obtain the minimum value Φ min of the total power functional, and then the force arm coefficient χ is calculated. According to the relationship between the total power functional and the rolling force, the rolling force is calculated Specifically as follows:

[0059]

[0060] where: α n is the neutral angle, Φ is the total power functional, is the internal deformation power of the plastic deformation zone of the cold-rolled slab, is the friction power of the plastic deformation zone of the cold-rolled slab, is the shearing power of the plastic deformation zone of the cold-rolled slab, is the tension power of the plastic deformation zone of the cold-rolled slab,

[0061]

[0062]

[0063]

[0064]

[0065] In the formula, σ s is the deformation resistance considering the influence of front and back tensions, h0 is the half thickness at the entrance of the plastic deformation zone, ε = (h0 - h1) / h0, h1 is the half thickness at the exit of the plastic deformation zone, g b and g f are the parameters of the back slip and front slip zones respectively, h mb and h mf are the average thicknesses of the back slip and front slip zones respectively, is the half thickness corresponding to the slab at the neutral angle, k is the yield shear stress, b is the half width at the entrance of the slab, R is the flattened radius of the roll, λ is a parameter to be determined, m is the friction factor between the roll and the slab, v R is the roll speed, θ is the angle between the line connecting the entrance contact point of the plastic deformation zone during rolling and the roll center and the line connecting the roll centers, α n is the neutral angle;

[0066] The moment arm coefficient χ:

[0067] σ0 is the stress reference value after dimensionless treatment, and its value is 100 MPa.

[0068] Rolling force

[0069] where R0 is the original radius of the roll, R is the flattened radius of the roll, and Δh = h0 - h1.

[0070] Furthermore, in step 5, the rolling force that meets the convergence condition is calculated through iterative operation according to the coupling of the rolling force and the flattened radius of the roll, specifically as follows:

[0071] Total rolling force: where the rolling forces in the entrance and exit elastic deformation zones and the rolling force in the plastic deformation zone

[0072] Iterative operation:

[0073]

[0074]

[0075]

[0076] Convergence condition:

[0077] wherein, R is the flattened radius of the roll, R0 is the original radius of the roll, v r is the Poisson's ratio of the roll, E r is the elastic modulus of the roll, b is the half-width of the slab at the inlet, Δh = h0 - h1, h0 is the half-thickness at the inlet of the plastic deformation zone, h1 is the half-thickness at the outlet of the plastic deformation zone, Δh t is the influence of the tension on the elastic flattening of the roll, Δh out is the reduced half-thickness in the elastic recovery zone at the outlet, v s is the Poisson's ratio of the strip, E s is the elastic modulus of the strip, σ b is the back tension, σ f is the front tension, h in is the half-thickness of the slab at the inlet, h out is the half-thickness of the slab at the outlet, σ sout is the deformation resistance of the strip on the outlet side, H0 is the half-thickness of the strip at the inlet of the first pass, R i is the roll radius at the i-th iteration, R i-1 is the roll radius at the (i - 1)-th iteration.

[0078] Compared with the prior art, the present invention has the following advantages:

[0079] The present invention predicts the rolling force of cold continuous rolling strip steel, and the obtained real-time predicted rolling force is closer to the actual value on site. On the basis of comprehensively considering various process parameters in the rolling process, the rolling force in the cold continuous rolling process is accurately predicted, and the problem of predicting the actual rolling force in the cold continuous rolling process under different production conditions is solved. The present invention is safe and reliable, with accurate calculation, and can calculate the rolling force in the continuous rolling process online in real time, saving the production investment cost while improving the control accuracy of the product thickness. Brief description of the drawings

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0081] Figure 1 It is a schematic diagram of a quarter of the cold rolling deformation zone in the embodiment of the present invention.

[0082] Figure 2This is the flowchart of the cold rolling strip rolling force prediction method in the embodiments of the present invention. Detailed implementation manners

[0083] To make the objectives, technical solutions and advantages of the present invention clearer, the following will describe in detail the specific implementation manners of the present invention with reference to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments recorded in the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0084] The following will describe in detail the specific implementation manners of the present invention with reference to the accompanying drawings. The rolling force calculation process of tandem cold rolling is as Figure 2 shown. Taking the tandem cold rolling of MRT-2.5 steel with a width of 0.885 m as an example, the process of calculating rolling using the method of the present invention will be described. Table 1 shows the rolling data required for each pass calculation.

[0085] Table 1 Rolling force calculation parameters

[0086]

[0087] Taking the process parameters of the first pass as an example, the following are the detailed calculation steps:

[0088] Step 1: Determine the entrance half-thickness h in = 1.15 mm, the exit half-thickness h out = 0.76 mm, the entrance half-width b = 0.4425 m, the front tension σ f = 122.30 MPa, and the back tension σ b = 55.00 MPa of the slab according to the process specification data of the first pass of cold rolling;

[0089] Step 2: Detect the entrance speed v0 = 2.74 m / s of the slab and the roll speed v R = 3.95 m / s, and obtain the roll radius R = 212.62 mm and the friction factor m = 0.15 between the roll and the slab;

[0090] Step 3: Consider the influence of the front and back tensions on the deformation zone length and the rolling force, and calculate the rolling force in the elastic deformation zone;

[0091] In this embodiment, the three-dimensional schematic diagram of a quarter of the cold rolling deformation zone is as Figure 1 shown. Let the x, y, and z axes be the length, width, and thickness directions of the cold rolling slab respectively, and the coordinate origin is selected at the midpoint of the cross-section at the entrance of the plastic deformation zone of the slab in the current pass. The original roll radius is R0, the flattened roll radius is R, the entrance thickness of the slab is 2h in , and the exit thickness is 2h out, in the plastic deformation zone, the slab thickness near the entrance side is 2h0, and the slab thickness near the exit side is 2h1. l is the projection length of the contact arc in the plastic deformation zone in the rolling direction. α is the angle between the line connecting any point in the deformation zone and the center of the roll and the center line of the rolls. θ is the angle between the line connecting the entrance contact point in the plastic deformation zone during rolling and the center of the roll and the center line of the rolls. θ in is the contact angle of the entrance elastic zone, θ out is the contact angle of the exit elastic recovery zone. σ f and σ b are the front and back tensions of the slab.

[0092] Step 3.1: Considering the influence of the front and back tensions on the length of the deformation zone, calculate the reduction in half thickness Δh in and Δh out ;

[0093]

[0094]

[0095] where σ sin and σ sout are the deformation resistances of the strip on the entrance side and the exit side respectively; E s is the elastic modulus of the strip, ν s is the Poisson's ratio of the strip;

[0096]

[0097]

[0098] where H0 is the entrance thickness of the strip in the first pass.

[0099] Step 3.2: According to the roll radius and the reduction in half thickness of the entrance and exit elastic deformation zones, calculate the projection lengths l in and l out ;

[0100]

[0101]

[0102] where Δh = h0 - h1 is the single-side reduction of the plastic deformation zone;

[0103] Step 3.3 Considering the influence of the front and back tensions on the rolling force in the elastic deformation zone, calculate the rolling forces in the entrance and exit elastic deformation zones and

[0104]

[0105]

[0106] Step 4: Minimize the total power functional of the rolling plastic deformation zone to predict the rolling force in the plastic deformation zone during the cold rolling of strip materials;

[0107] Step 4.1: Based on the velocity boundary conditions, volume invariance conditions, and geometric equations in the rolling deformation zone of the strip, establish the velocity field and strain rate field in the rolling deformation zone that satisfy the kinematically admissible conditions;

[0108] The velocity field in the cold rolling deformation zone is:

[0109]

[0110] where v x , v y , v z are the components in the length, width, and thickness directions of the cold-rolled slab respectively; h x is half of the slab thickness at any position in the rolling deformation zone; h' x is the first derivative of h x , h' x = dh x / dx, h0 is the entrance half-thickness, and λ is an undetermined parameter.

[0111]

[0112] The strain rate field in the cold rolling deformation zone is:

[0113]

[0114] Step 4.2: Express the unit second flow rate U using the velocity, neutral angle, and geometric dimensions of the slab and the roll at the neutral plane in the rolling deformation zone;

[0115] The unit second flow rate U is: U = v0h0b = v R cosα n b(R + h1 - Rcosα n ) = v1h1b

[0116] From this, the undetermined parameter λ = 2.88 can be obtained;

[0117] Step 4.3: Based on the actual materials and rolling schedules in on-site rolling, calculate the deformation resistance in the plastic deformation zone of the cold-rolled sheet;

[0118]

[0119] where H0 is the entrance thickness of the strip in the first pass.

[0120] Step 4.4: Calculate the internal deformation power of the plastic deformation zone of the cold-rolled slab according to the velocity field, strain rate field, and deformation resistance of the slab. Friction power Shearing power Tension power Obtain the total power functional:

[0121]

[0122] Step 4.5: According to different neutral angles α n Obtain the minimum value Φ of the total power functional corresponding to it, and then calculate the lever arm coefficient χ. According to the relationship between the total power functional and the rolling force, calculate the rolling force in the plastic deformation zone as follows: min It can be obtained that α

[0123]

[0124] = 0.0243; n The lever arm coefficient χ:

[0125] Among them, ε = (h0 - h1) / h0, and σ0 is the stress reference value after dimensionless treatment, with a value of 100 MPa.

[0126]

[0127] Rolling force

[0128]

[0129]

[0130] Step 5: According to the mutual coupling of the rolling force and the flattening radius of the roll, through iterative calculation, calculate the rolling force that meets the convergence condition. The iterative flow chart is as Figure 2 shown:

[0131] Total rolling force:

[0132] Iterative calculation:

[0133] Convergence condition:

[0134] Thus, the total rolling force F = 7448.09 kN is obtained.

[0135] Similarly, the rolling forces of each pass in this embodiment can be calculated, and the comparison results of the rolling forces of each pass are shown in Table 2.

[0136] Table 2 Comparison of rolling force values

[0137] ​

[0138] In summary, the calculation process of the present invention is all completed. According to the on-site data, the rolling force calculated by the analytical solution of the present invention is compared with the rolling force calculated by the Hill formula and the measured value of the on-site rolling force as shown in the above table. The error between the present invention and the on-site measured value is within 4%. It can be seen that the rolling force prediction of the present invention is closer to the on-site measured value.

[0139] The content not described in detail in the specification of the present invention belongs to the prior art well-known to those skilled in the art. Although the illustrative specific embodiments of the present invention are described above for the understanding of those skilled in the art of the present technology, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

Claims

1. A method for predicting rolling force in the process of cold tandem rolling of strip steel, characterized in that: Including the following steps: Step 1: Determine the inlet thickness, outlet thickness, inlet width, front tension and rear tension of the slab according to the process specification data of a certain pass in cold tandem rolling , outlet thickness , inlet width , front tension and rear tension ; Step 2: Detect the slab inlet speed , the outlet speed and the roll speed , obtain the original radius of the roll and the friction factor between the roll and the slab ; Step 3: Considering the influence of the front and rear tensions on the length of the deformation zone and the rolling force, calculate the rolling forces in the entrance elastic deformation zone and the exit elastic recovery zone; Step 3.1: Considering the influence of the front and back tensions on the length of the deformation zone, calculate the reduced half thickness of the entrance elastic deformation zone and the exit elastic recovery zone and ; Step 3.2: Calculate the projected lengths in the rolling direction of the entrance elastic deformation zone and the exit elastic recovery zone according to the roll radius and the reduced thicknesses of the entrance elastic deformation zone and the exit elastic recovery zone and ; Step 3.3: Considering the influence of the front and back tensions on the rolling force in the deformation zone, calculate the rolling forces in the entrance elastic deformation zone and the exit elastic recovery zone and ; Step 4: Minimize the total power functional of the rolling plastic deformation zone to predict the rolling force in the plastic deformation zone during the cold tandem rolling of strip; Step 4.1: According to the velocity boundary conditions, volume invariance conditions and geometric equations of the strip rolling deformation zone, establish the velocity field and strain rate field of the rolling deformation zone that satisfy the kinematically admissible conditions; Step 4.2: Represent the unit second flow rate using the velocity at the neutral plane in the rolling deformation zone, the neutral angle, and the geometric dimensions of the slab and the roll ; Step 4.3: According to the actual materials and rolling schedules in on-site rolling, calculate the deformation resistance of the plastic deformation zone of the cold-rolled sheet; Step 4.4: According to the velocity field, strain rate field, and slab deformation resistance, calculate the internal deformation power, friction power, shear power, and tension power in the plastic deformation zone of the cold-rolled slab to obtain the total power functional; Step 4.5: Obtain the minimum value of the total power functional according to the total power functionals corresponding to different neutral angles, and calculate the arm coefficient , and calculate the rolling force in the plastic deformation zone according to the relationship between the total power functional and the rolling force ; Step 5: Calculate the rolling force in the entrance elastic deformation zone from Steps 3 and 4 , the rolling force in the exit elastic recovery zone , and the rolling force in the plastic deformation zone , so as to obtain the total rolling force . According to the mutual coupling between the rolling force and the flattened roll radius, through iterative calculation, calculate the rolling force that meets the convergence condition.

2. The rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, wherein: In step 3.1, considering the influence of the front and rear tensions on the length of the deformation zone, calculate the reduction of the half thickness in the entrance elastic deformation zone and the exit elastic recovery zone and The specific method is as follows: ； ； ； ； Among them, is the elastic modulus of the strip steel, is the Poisson's ratio of the strip steel, represents the entrance half-thickness, represents the exit half-thickness, and are respectively the deformation resistance of the strip steel on the entrance side and the exit side, is the back tension, is the front tension, is the entrance half-thickness of the strip steel in the first pass, is the entrance half-thickness of the plastic deformation zone, is the exit half-thickness of the plastic deformation zone.

3. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: Step 3.2 calculates the projected lengths in the rolling direction of the entrance elastic deformation zone and the exit elastic recovery zone according to the roll radius and the reduced thicknesses of the entrance elastic deformation zone and the exit elastic recovery zone. and ; ； ； Among them, is the single-side reduction amount in the plastic deformation zone, is the half-thickness at the entrance of the plastic deformation zone, is the half-thickness at the exit of the plastic deformation zone, is the flattening radius of the roll; is the half-thickness of reduction in the entrance elastic deformation zone, is the half-thickness of reduction in the exit elastic recovery zone.

4. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: Step 3.3 takes into account the influence of the front and back tensions on the rolling force in the deformation zone, and calculates the rolling forces in the entrance elastic deformation zone and the exit elastic recovery zone and ; Establish a coordinate system with the midpoint of the cross-section at the entrance of the strip plastic deformation zone as the origin, and x, y, and z represent the length, width, and thickness directions of the strip respectively; ； ； where b is half of the slab width, is the half-thickness at the slab entrance, is the half-thickness at the slab exit, is the flattening radius of the roll, is the reduction per side in the plastic deformation zone, is the half-thickness at the entrance of the plastic deformation zone, is the half-thickness at the exit of the plastic deformation zone, and are the deformation resistances of the strip on the entrance side and the exit side respectively, is the projected length in the rolling direction of the elastic deformation zone at the slab entrance, is the projected length in the rolling direction of the elastic recovery zone at the slab exit, is the elastic modulus of the strip, is the Poisson's ratio of the strip.

5. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: In Step 4.1, according to the velocity boundary conditions, volume invariance conditions and geometric equations of the strip rolling deformation zone, establish the velocity field and strain rate field of the rolling deformation zone that satisfy the kinematically admissible conditions; The velocity field of the cold rolling plastic deformation zone is: ; A coordinate system is established with the midpoint of the cross-section at the entrance of the plastic deformation zone of the strip as the origin, where x, y, and z represent the length, width, and thickness directions of the strip respectively. Among them , , are the velocity components in the length, width, and thickness directions of the cold-rolled slab respectively, is the slab entrance velocity, is a parameter to be determined, is half of the slab thickness at any position in the rolling deformation zone; is 's first derivative , is the half thickness at the entrance of the plastic deformation zone, is the half thickness at the exit of the plastic deformation zone, is the projection of the contact arc between the slab and the roll in the rolling direction in the plastic deformation zone; ； R is the flattened radius of the roll; The strain rate field of the cold rolling plastic deformation zone is: ； Among them , , are the strain rate components in the length, width, and thickness directions of the slab, respectively.

6. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: The unit second flow rate in step 4.2 is represented by using the velocity at the neutral plane in the rolling deformation zone, the neutral angle, and the geometric dimensions of the slab and the roll Specifically as follows: ； Among them is the slab inlet speed, is the half thickness at the inlet of the plastic deformation zone, and b is the half width of the slab inlet, is the roll speed, is the neutral angle, is the flattened radius of the roll, is the slab outlet speed, is the half thickness at the outlet of the plastic deformation zone.

7. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: In Step 4.3, according to the actual materials and rolling schedules in on-site rolling, calculate the deformation resistance of the plastic deformation zone of the cold-rolled sheet, specifically as follows: ； Among them, represents the deformation resistance considering the influence of front and back tensions, represents the slab deformation resistance, is the front tension, is the back tension, is the entrance half-thickness of the strip in the first pass, is the entrance half-thickness of the plastic deformation zone, is the exit half-thickness of the plastic deformation zone.

8. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: Step 4.4 calculates the internal deformation power of the plastic deformation zone of the cold-rolled slab according to the velocity field, strain rate field, and deformation resistance of the slab , frictional power , shearing power , and tension power to obtain the total power functional, which is specifically as follows: Total power functional: ; Internal deformation power : ; Frictional power : ； Shearing power : ; Tensile power : ; In the formula, is the deformation resistance considering the influence of front and back tensions, , is the half-thickness at the entrance of the plastic deformation zone, is the half-thickness at the exit of the plastic deformation zone, is a parameter to be determined, is the friction factor between the roll and the slab, k is the yield shear stress, b is the half-width at the entrance of the slab, is the flattened radius of the roll, is the roll speed, is the angle between the line connecting the entrance contact point of the plastic deformation zone and the center of the roll and the center line of the rolls during rolling, is the neutral angle, and are the parameters of the back slip and front slip zones respectively, , , and are the average thicknesses of the back slip and front slip zones respectively, , , is the half-thickness of the slab corresponding to the neutral angle, and are the front and back tensions of the slab respectively.

9. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: Step 4.5 obtains the minimum value of the total power functional according to the total power functionals corresponding to different neutral angles , calculates the arm coefficient , and calculates the rolling force according to the relationship between the total power functional and the rolling force , specifically as follows: ； Wherein: is the neutral angle, Φ is the total power functional, is the internal deformation power of the plastic deformation zone of the cold-rolled slab, is the friction power of the plastic deformation zone of the cold-rolled slab, is the shear power of the plastic deformation zone of the cold-rolled slab, is the tension power of the plastic deformation zone of the cold-rolled slab, ； ； ； ； In the formula, is the deformation resistance considering the influence of front and back tensions, is the half thickness at the entrance of the plastic deformation zone, , , is the half thickness at the exit of the plastic deformation zone, and are the parameters of the back slip and front slip zones respectively, , , and are the average thicknesses of the back slip and front slip zones respectively, , , is the half thickness corresponding to the slab at the neutral angle, k is the yield shear stress, b is the half width at the entrance of the slab, is the flattened radius of the roll, is a parameter to be determined, is the friction factor between the roll and the slab, is the roll speed, is the angle between the line connecting the entrance contact point of the plastic deformation zone and the center of the roll and the center line of the roll during rolling, is the neutral angle; Moment arm coefficient : ; is the stress reference value for dimensionless treatment, with a value of 100 MPa; and are the front and back tensions of the slab, respectively; Rolling force : ; wherein is the original radius of the roll, is the flattened radius of the roll, .

10. A rolling force prediction method for the cold tandem rolling process of strip steel according to claim 1, characterized in that: In Step 5, according to the mutual coupling of the rolling force and the roll flattened radius, through iterative calculation, calculate the rolling force that meets the convergence conditions, specifically as follows: Total rolling force , where the rolling forces in the entrance elastic deformation zone and the exit elastic recovery zone and , and the rolling force in the plastic deformation zone ; Iterative calculation: ； ； ； ； Convergence condition: , Among them, is the flattened radius of the roll, is the original radius of the roll, is the Poisson's ratio of the roll, is the elastic modulus of the roll, b is the half-width of the slab at the entrance, , is the half-thickness at the entrance of the plastic deformation zone, is the half-thickness at the exit of the plastic deformation zone, is the influence of the tension on the elastic flattening of the roll, The reduced half-thickness in the elastic recovery zone at the exit, is the Poisson's ratio of the strip, is the elastic modulus of the strip, is the back tension, is the front tension, is the half-thickness of the slab at the entrance, is the half-thickness of the slab at the exit, The deformation resistance of the strip on the exit side, is the half-thickness of the strip at the entrance of the first pass, is the roll radius at the i-th iteration, is the roll radius at the (i - 1)-th iteration.

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