Mechanism-data-based prediction method for rolling force and forward slip in cold rolling elastic-plastic deformation

Abstract

The present invention provides a method for predicting cold rolling elastic-plastic deformation rolling force and forward slip based on mechanism data, which relates to the field of metallurgical rolling technology and includes the following steps: S1, collecting actual production data of equipment, specifications and process parameters in cold rolling production; S2, constructing a mechanism model of contact arc length in each zone of non-circular arc flattening of the roll; S3, constructing a rolling pressure mechanism model of the rolled piece elastic-plastic deformation and non-circular arc flattening of the roll; S4, constructing a new forward slip mechanism model based on the non-circular flattening curve of the roll; S5, correcting the middle-thickness ratio and the proportion of the forward neutral zone in the mechanism model through the industrial data in step S1; S6, calculating the rolling force, forward slip and plate and strip exit speed. It uses the collected measured data of the process parameters of the cold rolling process to continuously correct the parameters of the mechanism model using a cyclic traversal and iterative method to obtain an accurate rolling pressure distribution curve, thereby improving the prediction accuracy of the rolling force and forward slip.

Description

Technical Field

[0001] The present invention relates to the technical field of metallurgical rolling, and in particular to a cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data. Background Art

[0002] As cold-rolled sheet and strip production develops towards high strength and thinning, the problems of difficult rolling and difficult control become increasingly prominent, leading to abnormal equipment operating conditions and degradation of product functional accuracy. The accuracy of the mathematical model in the control system of the cold rolling mill is a core factor in ensuring the control of the rolling process, the setting of key parameters and the stable operation of the equipment. Among them, the rolling force and forward slip models are particularly critical. The calculation accuracy of the rolling force model directly affects the formulation of the rolling schedule, the adjustment of the reduction amount and the setting of the roll gap, which in turn affects the control accuracy of the plate thickness and plate shape; while the calculation accuracy of the forward slip model affects the speed and tension setting of each stand, which is related to the stability of the rolling process and the quality of the final product. Therefore, improving the calculation accuracy of the rolling force model and the forward slip model is crucial for the efficient and high-quality production of high-strength thin plates.

[0003] Currently, the main research methods for mathematical models of cold rolling include mechanism prediction, data prediction, and mechanism-data collaborative prediction. The mechanism prediction method usually simplifies the theoretical derivation process to a certain extent and introduces some assumptions, resulting in reduced model prediction accuracy. When the data is sufficient and of good quality, the data prediction method can improve prediction accuracy. However, this "black box" prediction process often lacks clear physical meaning and mathematical relationships, making the prediction results difficult to intuitively understand and interpret, which limits the application of the data prediction method in actual production. The mechanism-data collaborative prediction method uses industrial data to compensate and correct the mechanism prediction model, which can construct a prediction model that is both highly accurate and well-interpreted.

[0004] Domestic researchers have done a lot of work on the rolling force and forward slip prediction model during the rolling process. A Chinese invention patent (publication number CN114722516A) discloses a mechanism prediction method for the rolling force and rolling torque in the cold rolling deformation zone. The rolling force model is established by considering the elastic-plastic deformation of the rolled piece. The rolling force and the Hitchcock flattening radius are iteratively calculated to continuously optimize the calculation results until the iterative convergence accuracy is met. This method comprehensively considers the deformation behavior of the rolled piece and its influence on the rolling force. A Chinese invention patent (publication number CN112487700A) discloses a rolling force data prediction method based on a neural network and a genetic algorithm. With pre-processed production data as input, a fast non-dominated genetic sorting algorithm is used to optimize the neural network model parameters, and a rolling force network model is established, thereby improving the rolling force prediction accuracy during the specification change process. A Chinese invention patent (publication number CN117983661A) discloses a rolling force model update method driven by mechanism and data. This method takes into account the impact of the use of equipment such as rollers on the rolling force, and by continuously comparing the deviation between the calculated rolling force and the actual rolling force, it self-learns and saves the new self-learning coefficients into the model. This method has both the accuracy of data-driven and the interpretability of mechanism analysis, which helps to improve the control accuracy and production efficiency of the rolling process. A Chinese invention patent (publication number CN112711867A) discloses a rolling force prediction method that combines a mechanism model and a data model. This method is based on the rolling force mechanism model and uses the BP neural network data prediction model to correct and supplement the mechanism model, thereby improving the prediction accuracy of the rolling force. In addition to data methods, methods based on mechanisms and mechanism-data collaboration have also been used in the study of forward slip models. A Chinese invention patent (publication number CN107433288B) discloses a rolling stability determination method based on forward slip. This method modifies the Dresden forward slip formula and neutral angle, deriving a new forward slip model that can calculate the "negative forward slip" phenomenon. It also links forward slip with mill slip and vibration, establishing a mill stability determination equation and clarifying the quantitative relationship between forward slip and mill instability. A Chinese invention patent (publication number CN108655176A) discloses a mechanism-data-driven forward slip calculation method. After introducing a forward slip compensation factor, this method derives an adaptive coefficient for the current strip from the measured forward slip value and the model-calculated value, and applies it to subsequent coils, improving the setting accuracy of the roll speeds of each stand.

[0005] Although the above patents have improved the calculation accuracy of the rolling force and forward slip models from multiple methods and angles, the non-circular flattening phenomenon of the roll caused by the elastic-plastic deformation of the rolled piece in cold rolling production and its impact on the rolling force and forward slip still need to be further studied. Moreover, with the development of newer materials, higher strength and thinner specifications of plate and strip products, the accuracy of traditional rolling force models is low, and the forward slip correction model that can effectively predict "negative forward slip" has not yet been popularized, which seriously restricts the improvement of production efficiency and product quality. Therefore, based on the mechanism-data collaborative drive method, constructing a rolling force model and forward slip model for the elastic-plastic deformation of the rolled piece and the non-circular flattening phenomenon of the roll is a new way to improve the model accuracy. Summary of the Invention

[0006] The purpose of the present invention is to provide a cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data. On the basis of the rolling pressure and forward slip mechanism model of the elastic-plastic deformation of the rolled piece and the non-circular arc flattening of the roller, the measured data of the process parameters of the cold rolling process are collected, and the mechanism model parameters are continuously corrected by using a cyclic traversal and iterative method to obtain an accurate rolling pressure distribution curve, thereby improving the prediction accuracy of the rolling force and forward slip.

[0007] Specifically, the present invention provides a mechanism-data-based cold rolling elastic-plastic deformation rolling force and forward slip prediction method, which includes the following steps:

[0008] S1. Collecting actual production data in cold rolling production;

[0009] S2. Construct a contact arc length model for each zone of the roller with non-circular flattening to calculate the distance x0 from the center line of the roller before flattening to the exit of the plastic zone, the distance x1 from the center line of the roller before flattening to the entrance of the plastic zone, the total contact arc length l in the plastic zone, the contact arc length Δx0 in the elastic recovery zone at the exit, and the contact arc length Δx1 in the elastic compression zone at the entrance;

[0010] S3. Construct a rolling pressure mechanism model of the elastic-plastic deformation of the rolled piece and the non-circular flattening of the roller. The rolling pressure mechanism model is as follows:

[0011]

[0012] Among them, P is the total rolling force, b is the width of the rolled piece, and p rx is the unit pressure of the elastic compression zone at the inlet, p hx is the unit pressure in the backslip zone, p hnx is the unit pressure in the post-neutral zone, p cx is the unit pressure of the outlet elastic recovery zone; p qnx is the unit pressure in the front neutral zone, p qx is the unit pressure in the front sliding area, x n is the coordinate of the neutral point, l nis the arc length of the neutral zone, which includes the front neutral zone and the back neutral zone, k l is the ratio of the anterior neutral zone to the entire neutral zone;

[0013] S4. A new forward slip mechanism model is constructed based on the non-circular flattening curve of the roller. The forward slip mechanism model is as follows:

[0014]

[0015] Among them, h qn is the thickness of the rolled piece at the intersection of the neutral zone and the front sliding zone, y qn is the coordinate of the roller at the intersection of the neutral zone and the front slip zone, h p is the thickness of the rolled piece at the junction of the front sliding zone and the outlet elastic recovery zone, ε x is the elastic deformation of the workpiece in the rolling direction, and R is the radius of the working roll;

[0016] S5, correcting the mid-thickness ratio and the proportion of the front neutral zone using the actual production data in step S1, specifically including the following sub-steps:

[0017] S51, based on the current thickness ratio a n and actual production data to determine the initial contact arc length;

[0018] Among them, l n / h y is the arc length l in the neutral zone n and the average thickness of the rolled piece h y The ratio of n ;

[0019] S52, at the current initial contact arc length and the proportion of the front neutral zone k l Next, the rolling force and contact arc length are iteratively calculated using the actual production data of step S1. Starting from the second iteration step, it is determined whether the rolling force meets the convergence accuracy, and the rolling force, forward slip, and roller non-circular coordinate points that meet the requirements are saved:

[0020]

[0021] Where kl = l n1 / l n , l n1 is the arc length of the anterior neutral zone, P j is the rolling force calculated in step j, ε is the convergence accuracy;

[0022] S53, loop through the thickness ratio a in sequence n and the proportion of the front neutral zone k l , repeat steps S51-S52 in each layer cycle until the two layers are traversed, minimize the relative errors between the rolling force and the front slip and the measured values, and obtain the corrected values ​​of the mid-to-thickness ratio and the proportion of the front neutral zone;

[0023] S6. Substitute the mid-to-thickness ratio and the front neutral zone ratio obtained in step S53 into the models of step S3 and step S4 to calculate the rolling force, forward slip and strip exit speed during the stable rolling process.

[0024] Preferably, in step S53, a weight coefficient is added during minimization, and the weight coefficient calculation formula is as follows:

[0025]

[0026] Among them, α1 is the weight coefficient of the relative error of rolling force, α2 is the weight coefficient of the relative error of forward slip; P cal(i,m) The calculated rolling force value returned under the current iteration parameters, P act is the actual value of rolling force, f slip,cal(i,m) The forward sliding calculation value returned under the current iteration parameter, f slip,act is the actual value of forward slip;

[0027] S21. After the arc of the roller before flattening undergoes elastic deformation, the coordinates of the roller profile curve are as follows:

[0028]

[0029] Where R is the working roll radius of the roll, x0 is the distance from the center line of the roll before flattening to the exit of the plastic zone, and v is the elastic displacement of the roll surface, which is calculated from the unit pressure in the deformation zone according to the elastic half-plane formula.

[0030] S22. The boundary condition of the lowest point of the contour curve after elastic flattening of the roller is used to obtain x0:

[0031]

[0032] in, is the surface displacement derivative of the roll, θ is a composite parameter variable, p(ξ) is the pressure of the workpiece on the roll, ξ is the abscissa of the rolling unit pressure diagram, x is the distance of the displacement point to be determined, and dξ is the infinitesimal element of the unit pressure abscissa ξ;

[0033] S23, x1 is obtained from the thickness difference of the rolled piece at the entrance and exit of the plastic zone:

[0034]

[0035] Wherein, Δh′ is the thickness difference of the rolled product between the entrance and exit of the plastic zone, x1 is the distance from the center line of the roll to the entrance of the plastic zone before flattening, and Δv is the displacement difference of the roll surface at the entrance and exit of the plastic zone.

[0036] S24. The total contact arc length l in the plastic zone is:

[0037] l=x0+x1;

[0038] S25. Obtain Δx0 from the thickness difference of the rolled piece in the exit elastic recovery zone:

[0039]

[0040] Among them, Δr1 is the elastic deformation of the outlet elastic recovery zone, and Δv′ is the roller surface displacement difference at the outlet and outlet of the outlet elastic recovery zone;

[0041] S26, Δx1 is obtained from the thickness difference of the rolled piece in the elastic compression zone at the entrance:

[0042]

[0043] Wherein, Δr0 is the elastic deformation of the inlet elastic compression zone, and Δv″ is the roller surface displacement difference between the inlet and outlet of the inlet elastic compression zone.

[0044] Preferably, step S3 specifically includes the following sub-steps:

[0045] S31, dividing the rolling deformation zone and establishing a coordinate system, from the rolling entrance to the exit, the zone is divided into an entrance elastic compression zone, a rear sliding zone, a neutral zone, a front sliding zone, and an exit elastic recovery zone;

[0046] S32. The unit pressure distribution curves of the elastic recovery zone at the outlet and the elastic compression zone at the inlet of the rolled piece are respectively established based on the geometric equation, physical equation and equilibrium equation of the rolled piece:

[0047]

[0048] Among them, p rx is the unit pressure of the inlet elastic compression zone, p0 is the unit pressure at the junction of the inlet elastic compression zone and the back-slip zone, Δx1 is the contact arc length of the inlet elastic compression zone, l is the contact arc length of the plastic zone, B0 is the composite parameter variable of the inlet elastic compression zone, p cx is the unit pressure of the outlet elastic recovery zone, p1 is the unit pressure at the junction of the front sliding zone and the outlet elastic recovery zone, Δx0 is the contact arc length of the outlet elastic recovery zone, and B is the composite parameter variable of the outlet elastic recovery zone;

[0049] S33. Based on the equilibrium equation, plastic deformation conditions and friction model, the unit pressure distribution curves of the rear sliding zone, rear neutral zone, front neutral zone and front sliding zone of the rolled piece are respectively established:

[0050]

[0051] Among them, p hx is the unit pressure in the sliding area, μ is the friction coefficient, h y is the average thickness of the rolled piece, x is the horizontal coordinate of any point in the deformation zone, p hnxis the unit pressure in the post-neutral zone, p c ′ is the unit pressure at the junction of the rear sliding zone and the rear neutral zone, l n is the neutral zone length, k l is the proportion of the front neutral zone, x n is the neutral point position, p c ″ is the unit pressure at the junction of the front neutral zone and the front sliding zone;

[0052] S34. According to the unit pressure distribution, the unit pressure of each part is integrated along the contact arc length to obtain the rolling pressure mechanism model.

[0053] Preferably, step S4 specifically includes the following sub-steps:

[0054] S41, substituting the unit pressure distribution curve and the contact arc length of each zone into the coordinates of the roll profile curve to obtain the coordinates of the roll at the boundary points of each zone;

[0055] S42. Assuming that the speed of the rolled piece in the outlet elastic recovery zone satisfies a linear relationship, the speed relationship between the two end points of the outlet elastic recovery zone is:

[0056] v d =(1+2ε x )v p

[0057] Among them, v d is the exit speed of rolled product, v p is the speed of the rolled piece at the junction of the front sliding zone and the outlet elastic recovery zone, ε x The elastic deformation of the rolled piece in the rolling direction is calculated according to Hooke's law;

[0058] S43. Based on the definition of forward slip, the metal flow rate equation and the velocity relationship between the two end points of the outlet elastic recovery zone, a forward slip mechanism model of elastic-plastic deformation of the rolled piece and non-circular flattening of the roll is constructed.

[0059] Preferably, step S1 collects actual production data in cold rolling production, specifically including equipment parameters, specification parameters and process parameters:

[0060] Among them, the equipment parameter is the roller working radius R;

[0061] Specification parameters are workpiece width b, workpiece entry thickness h0, workpiece exit thickness h1, Poisson's ratio ν, and elastic modulus E;

[0062] The process parameters are inlet deformation resistance kf0, outlet deformation resistance kf1, front tension σ1, rear tension σ0, friction coefficient μ, actual rolling force P act And the actual forward slip value f slip,act .

[0063] Preferably, the friction model in step S33 is:

[0064]

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] (1) The present invention provides a method for predicting the rolling force and forward slip of the elastic-plastic deformation in the cold rolling process based on mechanism-data collaborative driving. The mechanism model of this method takes into account the elastic-plastic deformation of the rolled piece and the non-circular flattening of the roller, and refines the friction state in the neutral zone. Compared with the existing rolling force and forward slip prediction methods, the physical factors considered are more comprehensive, ensuring that the method has higher prediction accuracy and wider applicability.

[0067] (2) The method of the present invention is based on the characteristics of elastic-plastic deformation of the rolled piece and non-circular flattening of the rolling roller, and at the same time constructs a rolling force and forward slip prediction method, which can not only accurately display the rolling pressure distribution in the deformation zone, but also provide theoretical support for the "negative forward slip" phenomenon that frequently occurs in cold rolling production, and can better solve these problems.

[0068] (3) The method of the present invention corrects the parameters of the mechanism model by introducing industrial data from actual production, thereby improving the stability and reliability of the model prediction and laying a technical foundation for achieving stable and efficient rolling. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Schematic diagram of the overall process of the cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data of the present invention;

[0070] Figure 2a and Figure 2b It is a schematic diagram of the friction shear stress and flattening curve of the deformation zone of the present invention, wherein: Figure 2a This is a schematic diagram of the friction shear stress in the deformation zone of the present invention. Figure 2b It is a schematic diagram of the flattening curve of the present invention;

[0071] Figure 3 is a rolling force calculation error diagram of each stand of the present invention;

[0072] Figure 4a-4e Schematic diagrams of the compression stress in the deformation zone, friction shear stress, roll flattening curve and exit speed corresponding to the rolling force prediction results on the five stands in the embodiment of the present invention, wherein: Figure 4a Schematic diagram of compressive stress, friction shear stress, roller flattening curve and exit speed in the S1 deformation zone. Figure 4b Schematic diagram of compressive stress, friction shear stress, roller flattening curve and exit speed in the S2 deformation zone. Figure 4c Schematic diagram of compressive stress, friction shear stress, roller flattening curve and exit speed in the S3 deformation zone. Figure 4d Schematic diagram of compressive stress, friction shear stress, roller flattening curve and exit speed in the S4 deformation zone. Figure 4e Schematic diagram of compressive stress, friction shear stress, roller flattening curve and exit velocity in the S5 deformation zone;

[0073] Figure 5a-5c The figures are respectively a comparison of the calculated value and the actual value of the embodiment of the present invention during the S1 stable rolling process, and the results of different rolling force prediction methods, wherein: Figure 5a are the calculated and actual values ​​of rolling force, forward slip and strip exit speed during the S1 stable rolling process of this method, Figure 5b and Figure 5c are the calculated values ​​and calculation errors of this method and the classical rolling force prediction method in the S1 stable rolling process;

[0074] Figure 6a-6c The diagrams are respectively a comparison of the calculated and actual values ​​of this method in the stable rolling process of the S2 deformation zone and the results of different rolling force prediction methods, where: Figure 6a Figures 6b and 6c are the calculated and actual values ​​of rolling force, forward slip, and strip exit speed during the stable rolling process in the S2 deformation zone by this method, and the calculated values ​​and calculation errors of this method and the classical rolling force prediction method during the stable rolling process in the S2 deformation zone, respectively;

[0075] Figure 7a-7c The results of the calculation and actual values ​​of this method in the stable rolling process of the S3 deformation zone and the results of different rolling force prediction methods are compared respectively. Figure 7a are the calculated and actual values ​​of rolling force, forward slip and strip exit speed during the stable rolling process in the S3 deformation zone according to this method, Figure 7b and Figure 7c are the calculated values ​​and calculation errors of this method and the classical rolling force prediction method in the stable rolling process of S3 deformation zone;

[0076] Figure 8a-8c The results of the calculation and actual values ​​of the method in the stable rolling process of the S4 deformation zone and the results of different rolling force prediction methods are compared respectively. Figure 8a are the calculated and actual values ​​of rolling force, forward slip and strip exit speed during the stable rolling process in the S4 deformation zone of this method, Figure 8b and 8c are the calculated values ​​and calculation errors of this method and the classical rolling force prediction method in the stable rolling process of S4 deformation zone;

[0077] Figure 9a-9c The results of the calculation and actual values ​​of the method in the stable rolling process of the S5 deformation zone and the results of different rolling force prediction methods are compared respectively. Figure 9aare the calculated and actual values ​​of rolling force, forward slip and exit speed during the stable rolling process in the S5 deformation zone of this method, Figure 9b and Figure 9c These are the calculated values ​​and calculation errors of this method and the classical rolling force prediction method in the stable rolling process of S5 deformation zone, respectively. DETAILED DESCRIPTION

[0078] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0079] The present invention provides a cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data, such as Figure 1 As shown, it includes the following steps:

[0080] S1. Collect actual production data of equipment, specifications and process parameters in cold rolling production, including the following parameters:

[0081] Equipment parameters: R roller working radius; Specification parameters: b width of rolled piece, h0 thickness of rolled piece at entry, h1 thickness of rolled piece at exit, ν Poisson's ratio, E elastic modulus; Process parameters: kf0 deformation resistance at entry, kf1 deformation resistance at exit, σ1 front tension, σ0 rear tension, μ friction coefficient, P act Actual rolling force, f slip,act Actual forward slip value.

[0082] S2. Constructing a contact arc length model for each area of ​​the roller during non-arc flattening, specifically including the following sub-steps:

[0083] S21. After the arc of the roller before flattening undergoes elastic deformation, the coordinates of the contour curve of the roller after elastic flattening are:

[0084]

[0085] Where R is the working roll radius of the roll, x0 is the distance from the center line of the roll to the exit of the plastic zone before flattening, and v is the elastic displacement of the roll surface, which is calculated from the unit pressure in the deformation zone according to the elastic half-plane formula.

[0086] S22. Based on the analysis of step S21, the boundary condition of the lowest point of the contour curve after elastic flattening by the roller can be obtained as x0:

[0087]

[0088] in, is the surface displacement derivative of the roll, θ is a composite parameter variable, p(ξ) is the pressure of the workpiece on the roll, ξ is the horizontal coordinate of the rolling unit pressure diagram, and x is the distance of the displacement point to be determined.

[0089] S23. Based on the analysis of step S21, x1 can be obtained from the thickness difference of the rolled piece at the entrance and exit of the plastic zone:

[0090]

[0091] Among them, Δh′ is the thickness difference of the rolled product between the entrance and exit of the plastic zone, x1 is the distance from the center line of the roll to the entrance of the plastic zone before flattening, and Δv is the surface displacement difference of the roll at the entrance and exit of the plastic zone.

[0092] S24. Based on the contact arc lengths of steps S32 and S33, the total contact arc length l of the plastic zone is:

[0093] l=x0+x1。

[0094] S25. Based on the analysis of step S21, Δx0 can be obtained from the thickness difference of the rolled piece in the outlet elastic recovery zone:

[0095]

[0096] Among them, Δr1 is the elastic deformation of the outlet elastic recovery zone, and Δv′ is the roller surface displacement difference at the outlet and outlet of the outlet elastic recovery zone.

[0097] S26. Based on the analysis of step S21, Δx1 can be obtained from the thickness difference of the rolled piece in the inlet elastic compression zone:

[0098]

[0099] Wherein, Δr0 is the elastic deformation of the inlet elastic compression zone, and Δv″ is the roller surface displacement difference between the inlet and outlet of the inlet elastic compression zone.

[0100] S3. Constructing a rolling pressure mechanism model of the rolled piece's elastic-plastic deformation and the roller's non-circular flattening, specifically including the following sub-steps:

[0101] S31. Divide the rolling deformation zone and establish a coordinate system. From the rolling entrance to the exit, it is divided into the entrance elastic compression zone, the plastic zone (backward sliding zone, neutral zone, forward sliding zone) and the exit elastic recovery zone.

[0102] S32. Based on the analysis of step S21, the unit pressure distribution curves of the elastic recovery zone at the outlet and the elastic compression zone at the inlet of the rolled piece are respectively established using the geometric equation, physical equation and equilibrium equation of the rolled piece:

[0103]

[0104] Among them, p rx is the unit pressure of the inlet elastic compression zone, p0 is the unit pressure at the junction of the inlet elastic compression zone and the back-slip zone, Δx1 is the contact arc length of the inlet elastic compression zone, l is the contact arc length of the plastic zone, B0 is the composite parameter variable of the inlet elastic compression zone, p cxis the unit pressure of the outlet elastic recovery zone, p1 is the unit pressure at the junction of the forward sliding zone and the outlet elastic recovery zone, Δx0 is the contact arc length of the outlet elastic recovery zone, and B is the composite parameter variable of the outlet elastic recovery zone.

[0105] S33. Based on the analysis of step S21, the unit pressure distribution curves of the rear sliding zone, rear neutral zone, front neutral zone and front sliding zone of the rolled piece are respectively established by the equilibrium equation, plastic deformation condition and friction model:

[0106]

[0107] Among them, p hx is the unit pressure in the sliding area, μ is the friction coefficient, h y is the average thickness of the rolled piece, x is the horizontal coordinate of any point in the deformation zone, p hnx is the unit pressure in the post-neutral zone, p c ′ is the unit pressure at the junction of the rear sliding zone and the rear neutral zone, l n is the neutral zone length, k l is the proportion of the front neutral zone, x n is the neutral point position, p c ″ is the unit pressure at the junction of the front neutral zone and the front sliding zone.

[0108] The friction model of step S33 is:

[0109]

[0110] S34. Based on the unit pressure distribution in steps S22 and S23, the unit pressure of each part is integrated along the contact arc length to obtain the total rolling force in the rolling deformation zone, i.e., the rolling pressure mechanism model is:

[0111]

[0112] Among them, P is the total rolling force and b is the width of the rolled piece.

[0113] S4. Constructing a new forward slip mechanism model based on the non-circular flattening curve of the roller, which specifically includes the following sub-steps:

[0114] S41. Substitute the unit pressure distribution curve of step S2 and the contact arc length of each zone obtained in steps S32-S36 into the coordinates of the roller profile curve of step S31 to obtain the coordinates of the roller at the boundary points of each zone.

[0115] S42. Since the rolled piece does not satisfy the metal flow rate equation in the outlet elastic recovery zone, assuming that the speed of the rolled piece in the outlet elastic recovery zone satisfies a linear relationship, the speed relationship between the two end points of the outlet elastic recovery zone is:

[0116] v d =(1+2ε x)v p

[0117] Among them, v d is the exit speed of rolled product, v p is the speed of the rolled piece at the junction of the front sliding zone and the outlet elastic recovery zone, ε x The elastic deformation of the rolled piece in the rolling direction is calculated according to Hooke's law in practical applications.

[0118] S43. Based on the definition of forward slip, the metal flow rate equation, and the speed relationship of step S42, the forward slip mechanism model considering the elastic-plastic deformation of the rolled piece and the non-circular flattening of the roll is:

[0119]

[0120] Among them, h qn is the thickness of the rolled piece at the intersection of the neutral zone and the front sliding zone, y qn is the coordinate of the roller at the intersection of the neutral zone and the front slip zone, h p It is the thickness of the rolled piece at the junction of the front sliding zone and the outlet elastic recovery zone.

[0121] S5. Correcting the mid-to-thickness ratio and the proportion of the front neutral zone in the mechanism model using the industrial data in step S1, specifically including the following sub-steps:

[0122] S51, in the current thickness ratio a n And under the industrial data of step S1, determine the initial contact arc length.

[0123] Among them, the thickness ratio a n =l n / h y .

[0124] S52, at the current initial contact arc length and the proportion of the front neutral zone k l Next, the industrial data of step S1 is used to iteratively calculate the rolling force of steps S22-S24 and the contact arc length of each zone of steps S32-S36. Starting from the second iteration step, it is judged whether the rolling force meets the convergence accuracy, and the rolling force, forward slip and roller non-circular coordinate points that meet the requirements are saved:

[0125]

[0126] Among them, k l =l n1 / l n , l n1 is the arc length of the anterior neutral zone, P j is the rolling force calculated in step j, and ε is the convergence accuracy.

[0127] S53, loop through the thickness ratio an and the front neutral area ratio k in sequence lRepeat steps S51-S52 in each layer loop until the two layers are traversed, minimize the relative errors between the rolling force and the front slip and the measured values, and obtain the corrected values ​​of the thickness ratio and the proportion of the front neutral zone. Among them, due to the different magnitudes of the rolling force and the front slip, a weight coefficient is considered when minimizing:

[0128]

[0129] Among them, α1 is the weight coefficient of the relative error of rolling force, and α2 is the weight coefficient of the relative error of forward slip.

[0130] S6. Use the correction value of step S53 to calculate the rolling force, forward slip and strip exit speed during the stable rolling process of the re-coil.

[0131] The following is a further explanation in conjunction with a specific embodiment. In this embodiment, a cold rolling equipment of a certain factory is taken as an example. The above method is used to traverse and iteratively optimize the rolling force and contact arc length in sequence to obtain the thickness ratio a. n and the proportion of the front neutral zone k l The correction value is calculated and the correction result is used to predict the stable rolling process of the coil.

[0132] The present invention is based on the mechanism-data collaborative drive cold rolling process elastic-plastic deformation rolling force and forward slip prediction method, such as Figure 1 As shown, it includes the following steps:

[0133] S1. Collect process parameters in actual production and obtain actual production data of equipment, specifications and process parameters.

[0134] S2, by Figure 2a and Figure 2b The friction shear stress in the deformation zone and the roller flattening curve are shown, and the rolling pressure expressions of the elastic-plastic deformation of the rolled piece and the non-circular flattening of the roller are constructed. Figure 2a In the figure, a represents the elastic compression zone at the inlet, b represents the rear sliding zone, c represents the neutral zone, d represents the front sliding zone, e represents the elastic recovery zone at the outlet, f represents the rear neutral zone, and g represents the front neutral zone. Figure 2b In the figure, m represents the curve after roller flattening, and n represents the curve before roller flattening.

[0135] S3. Based on the roller flattening curve and corresponding boundary conditions shown in Figure 2, a contact arc length model for each zone of the roller non-circular flattening is constructed.

[0136] S4. Construct a new forward slip mechanism model based on the non-circular arc flattening curve of the roller.

[0137] S5. Use actual production data to correct the mid-to-thickness ratio and the proportion of the front neutral zone in the mechanism model to obtain the corresponding model parameter correction values ​​under this working condition.

[0138] S6. The correction value is used to calculate the rolling force, forward slip and strip exit speed during the stable rolling process of the coil.

[0139] In this embodiment, a certain oriented silicon steel coil is selected. Figure 1 Based on the prediction method shown in the figure, the correction values ​​of the model parameters on different stands were obtained respectively, and the rolling force, compressive stress, friction shear stress, roll flattening curve and outlet speed distribution in the deformation zone of different stands were calculated. Then the calculation ability of the method was compared with the classical rolling force prediction method. The results are shown in Table 1. The calculation error comparison results of each method and the actual rolling force value are shown in Table 1. Figure 3 As shown in the figure; the compressive stress, friction shear stress, roller flattening curve and outlet velocity distribution of each frame deformation zone are shown in the figure. Figure 4a-4e Table 1 shows the comparison of different rolling force models; Figure 3 The calculation error of rolling force on each stand for different prediction methods; Figure 4a The compressive stress, friction shear stress, roller flattening curve and outlet velocity distribution in the S1 deformation zone; Figure 4b The compressive stress, friction shear stress, roller flattening curve and outlet velocity distribution in the S2 deformation zone; Figure 4c The compressive stress, friction shear stress, roller flattening curve and outlet velocity distribution of the S3 deformation zone; Figure 4d The compressive stress, friction shear stress, roller flattening curve and outlet velocity distribution of the S4 deformation zone; Figure 4e The compressive stress, friction shear stress, roller flattening curve and outlet velocity distribution of the S5 deformation zone. Figure 3 It can be seen that compared with the classic rolling force mechanism model, the elastic-plastic rolling force model based on mechanism-data collaborative drive proposed in this invention has calculated values ​​on each stand that are closer to the measured values ​​of rolling force, showing better prediction effect; Figure 4a-4e As shown, the precise distribution of key parameters in the deformation zone is displayed, which also provides a basis for explaining the “negative forward slip” phenomenon.

[0140] The correction values ​​obtained on each stand are used to calculate the rolling force, forward slip and strip exit speed at other sampling points in the stable rolling process, and compared with the results calculated by the classic rolling force prediction method. The results are shown in Figures 5 to 9. Figure 5a 、 Figure 6a 、 Figure 7a 、 Figure 8a and Figure 9a The calculated and measured values ​​of rolling force, forward slip and strip exit speed of the five stands in this embodiment are shown in sequence; Figure 5b-5c 、 Figure 6b-6c 、 Figure 7b-7c 、 Figure 8b-8c and Figure 9b-9cThe comparison results of the present method and the classical rolling force prediction method in this embodiment are shown in turn; it can be seen from Figures 5 to 9 that, compared with the classical rolling force prediction method, the rolling force prediction error of the stable rolling process obtained by the method of the present invention is the smallest, and the plate and strip outlet speed calculated from the forward slip result is highly consistent with the actual plate and strip speed. This method can predict the "negative forward slip" phenomenon that occurs during the rolling process.

[0141] Table 1 Comparison of different rolling force models (MN)

[0142]

[0143]

[0144] It can be seen from the above embodiments that the method of the present invention is based on the correction of the mechanism model based on data, takes into account the elastic-plastic deformation of the rolled piece and the non-circular flattening of the roller, and constructs a rolling force and forward slip prediction method. The rolling force calculated during the stable rolling process is more accurate than the classic rolling force method, and the forward slip model can reflect the "negative forward slip" phenomenon in actual production, providing more accurate support for setting rolling procedures and stabilizing the rolling process.

[0145] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A mechanism-data-based method for predicting rolling force and forward slip during cold rolling elastic-plastic deformation, characterized by: It includes the following steps: S1. Collecting actual production data in cold rolling production; S2. Construct a contact arc length model for each zone of the roller with non-circular flattening to calculate the distance x0 from the center line of the roller before flattening to the exit of the plastic zone, the distance x1 from the center line of the roller before flattening to the entrance of the plastic zone, the total contact arc length l in the plastic zone, the contact arc length Δx0 in the elastic recovery zone at the exit, and the contact arc length Δx1 in the elastic compression zone at the entrance; S3. Construct a rolling pressure mechanism model of the elastic-plastic deformation of the rolled piece and the non-circular flattening of the roller. The rolling pressure mechanism model is as follows: Among them, P is the total rolling force, b is the width of the rolled piece, and p rx is the unit pressure of the elastic compression zone at the inlet, p hx is the unit pressure in the backslip zone, p hnx is the unit pressure in the post-neutral zone, p cx is the unit pressure of the outlet elastic recovery zone, p qnx is the unit pressure in the front neutral zone, p qx is the unit pressure in the front sliding area, x n is the coordinate of the neutral point, l n is the arc length of the neutral zone, which includes the front neutral zone and the back neutral zone, k l is the ratio of the anterior neutral zone to the entire neutral zone; S4. Based on the non-circular flattening curve of the roller, a forward slip mechanism model is constructed. The forward slip mechanism model is as follows: Among them, f slip For forward sliding, h qn is the thickness of the rolled piece at the intersection of the neutral zone and the front sliding zone, y qn is the coordinate of the roller at the intersection of the neutral zone and the front slip zone, h p is the thickness of the rolled piece at the junction of the front sliding zone and the outlet elastic recovery zone, ε x is the elastic deformation of the workpiece in the rolling direction, and R is the radius of the working roll; S5, correcting the mid-thickness ratio and the proportion of the front neutral zone using the actual production data in step S1, specifically including the following sub-steps: S51, based on the current thickness ratio a n and actual production data to determine the arc length of the neutral zone; The calculation formula of the mid-to-thickness ratio is as follows: n =l n / h y ; l n / h y is the arc length l in the neutral zone n and the average thickness of the rolled piece h y The ratio of n ; S52, at the current initial contact arc length and the proportion of the front neutral zone k l In this case, the rolling force and contact arc length are iteratively calculated using actual production data. Starting from the second iteration, it is determined whether the rolling force meets the convergence accuracy, and the rolling force, forward slip, and roller non-circular coordinate points that meet the requirements are saved: Among them, k l =l n1 / l n , l n1 is the arc length of the anterior neutral zone, P j is the rolling force calculated in step j, ε is the convergence accuracy; k l is the ratio of the anterior neutral zone to the neutral zone; S53, loop through the thickness ratio a in sequence n and the proportion of the front neutral zone k l , repeat steps S51-S52 in each layer cycle until the two layers are traversed, minimize the relative errors between the rolling force and the front slip and the measured values, and obtain the corrected values ​​of the mid-to-thickness ratio and the proportion of the front neutral zone; S6. Substitute the mid-to-thickness ratio and the front neutral zone ratio obtained in step S53 into the models of step S3 and step S4 to calculate the rolling force, forward slip and strip exit speed during the stable rolling process.

2. The cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data according to claim 1, characterized in that: In step S53, a weight coefficient is added during minimization. The weight coefficient calculation formula is as follows: Among them, α1 is the weight coefficient of the relative error of rolling force, α2 is the weight coefficient of the relative error of forward slip; P cal(i,m) The calculated rolling force value returned under the current iteration parameters, P act is the actual value of rolling force, f slip,cal(i,m) The forward sliding calculation value returned under the current iteration parameter, f slip,act is the actual value of the forward slip.

3. The cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data according to claim 1, characterized in that: Step S2 specifically includes the following sub-steps: S21. After the arc of the roller before flattening undergoes elastic deformation, the coordinates of the roller profile curve are as follows: Where R is the working roll radius of the roll, x0 is the distance from the center line of the roll before flattening to the exit of the plastic zone, and v is the elastic displacement of the roll surface, which is calculated from the unit pressure in the deformation zone according to the elastic half-plane formula. S22. The boundary condition of the lowest point of the contour curve after elastic flattening of the roller is used to obtain x0: in, is the surface displacement derivative of the roll, θ is a composite parameter variable, p(ξ) is the pressure of the workpiece on the roll, ξ is the abscissa of the rolling unit pressure diagram, x is the distance of the displacement point to be determined, and dξ is the infinitesimal element of the unit pressure abscissa ξ; S23, x1 is obtained from the thickness difference of the rolled piece at the entrance and exit of the plastic zone: Wherein, Δh′ is the thickness difference of the rolled product between the entrance and exit of the plastic zone, x1 is the distance from the center line of the roll to the entrance of the plastic zone before flattening, and Δv is the displacement difference of the roll surface at the entrance and exit of the plastic zone. S24. The total contact arc length l in the plastic zone is: l=x0+x1; S25. Obtain Δx0 from the thickness difference of the rolled piece in the exit elastic recovery zone: Among them, Δr1 is the elastic deformation of the outlet elastic recovery zone, and Δv′ is the roller surface displacement difference at the outlet and outlet of the outlet elastic recovery zone; S26, Δx1 is obtained from the thickness difference of the rolled piece in the elastic compression zone at the entrance: Wherein, Δr0 is the elastic deformation of the inlet elastic compression zone, and Δv″ is the roller surface displacement difference between the inlet and outlet of the inlet elastic compression zone.

4. The cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data according to claim 3, characterized in that: Step S3 specifically includes the following sub-steps: S31, dividing the rolling deformation zone and establishing a coordinate system, from the rolling entrance to the exit, the zone is divided into an entrance elastic compression zone, a rear sliding zone, a neutral zone, a front sliding zone, and an exit elastic recovery zone; S32. The unit pressure distribution curves of the elastic recovery zone at the outlet and the elastic compression zone at the inlet of the rolled piece are respectively established based on the geometric equation, physical equation and equilibrium equation of the rolled piece: Among them, p rx is the unit pressure of the inlet elastic compression zone, p0 is the unit pressure at the junction of the inlet elastic compression zone and the back-slip zone, Δx1 is the contact arc length of the inlet elastic compression zone, l is the contact arc length of the plastic zone, B0 is the composite parameter variable of the inlet elastic compression zone, p cx is the unit pressure of the outlet elastic recovery zone, p1 is the unit pressure at the junction of the front sliding zone and the outlet elastic recovery zone, Δx0 is the contact arc length of the outlet elastic recovery zone, and B is the composite parameter variable of the outlet elastic recovery zone; S33. Based on the equilibrium equation, plastic deformation conditions and friction model, the unit pressure distribution curves of the rear sliding zone, rear neutral zone, front neutral zone and front sliding zone of the rolled piece are respectively established: Among them, p hx is the unit pressure in the sliding area, μ is the friction coefficient, h y is the average thickness of the rolled piece, x is the horizontal coordinate of any point in the deformation zone, p hnx is the unit pressure in the post-neutral zone, p c ′ is the unit pressure at the junction of the rear sliding zone and the rear neutral zone, l n is the neutral zone length, k l is the proportion of the front neutral zone, x n is the neutral point position, p c ″ is the unit pressure at the junction of the front neutral zone and the front sliding zone; S34. According to the unit pressure distribution, the unit pressure of each part is integrated along the contact arc length to obtain the rolling pressure mechanism model.

5. The cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data according to claim 4, characterized in that: Step S4 specifically includes the following sub-steps: S41, substituting the unit pressure distribution curve and the contact arc length of each zone into the coordinates of the roll profile curve to obtain the coordinates of the roll at the boundary points of each zone; S42. Assuming that the speed of the rolled piece in the outlet elastic recovery zone satisfies a linear relationship, the speed relationship between the two end points of the outlet elastic recovery zone is: v d =(1+2ε x )v p Among them, v d is the exit speed of rolled product, v p is the speed of the rolled piece at the junction of the front sliding zone and the outlet elastic recovery zone, ε x The elastic deformation of the rolled piece in the rolling direction is calculated according to Hooke's law; S43. Based on the definition of forward slip, the metal flow rate equation and the velocity relationship between the two end points of the outlet elastic recovery zone, a forward slip mechanism model of elastic-plastic deformation of the rolled piece and non-circular flattening of the roll is constructed.

6. The cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data according to claim 1, characterized in that: Step S1 collects actual production data in cold rolling production, including equipment parameters, specification parameters and process parameters: Among them, the equipment parameter is the roller working radius R; Specification parameters are workpiece width b, workpiece entry thickness h0, workpiece exit thickness h1, Poisson's ratio ν, and elastic modulus E; The process parameters are inlet deformation resistance kf0, outlet deformation resistance kf1, front tension σ1, rear tension σ0, friction coefficient μ, actual rolling force P act And the actual forward slip value f slip,act .

7. The cold rolling elastic-plastic deformation rolling force and forward slip prediction method based on mechanism-data according to claim 1, characterized in that: The friction model in step S33 is:

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