Method, system and device for analyzing dynamic rolling force in cold continuous rolling elastoplastic deformation process

Abstract

The application belongs to the technical field of cold continuous rolling and provides a method, system and device for analyzing dynamic rolling force in the process of cold continuous elastic-plastic deformation, which comprises the following steps: collecting process parameters, rolling piece parameters and roller parameters; obtaining roller motion state and deformation zone dynamic parameters by using the above parameters; discretizing the deformation zone into a plurality of micro elements and obtaining micro element dynamic parameters by using the deformation zone dynamic parameters; analyzing deformation zone friction stress distribution by using the process parameters and the deformation zone dynamic parameters; analyzing rolling pressure of each micro element by using the micro element dynamic parameters and the deformation zone friction stress distribution, and obtaining dynamic rolling force by integrating the deformation zone; correcting the roller flattening radius according to the dynamic rolling force; judging whether the corrected roller flattening radius meets the convergence condition; if not, setting the corrected roller flattening radius as the initial value, reanalyzing the roller gap change speed and the deformation zone dynamic parameters. The application provides a reliable basis for realizing accurate control of product thickness and improving production stability and product quality.

Description

Technical Field

[0001] This invention relates to the field of cold rolling technology, and in particular to a method, system and apparatus for dynamic rolling force analysis during the elastoplastic deformation process of cold rolling. Background Technology

[0002] Rolling force is one of the most critical process parameters in cold rolling production. The accuracy of its prediction and control directly affects the formulation of rolling schedules and the control accuracy of plate thickness and shape. It also has a decisive impact on the stability of equipment operation, vibration suppression, and product quality consistency. As cold-rolled strip products develop towards higher strength and thinner specifications, the problems of "difficult rolling and difficult control" in the production process are becoming increasingly prominent, placing higher demands on the calculation accuracy and dynamic adaptability of rolling force.

[0003] Currently, the main methods for predicting rolling force include mechanistic models, data-driven models, and mechanistic-data combined models.

[0004] Traditional mechanistic models (such as Hill's formula and Stone's formula) often introduce assumptions and simplifications in their theoretical derivation, ignoring the coupling and dynamic interaction of multiple factors. This leads to significant calculation errors when the reduction rate is large, lubrication conditions change, or the rolling process is unsteady, thus limiting their reference value.

[0005] While data-driven methods can improve fitting accuracy through historical data, their "black box" nature leads to a lack of clear physical meaning and interpretability in the model, making it difficult to promote in actual production.

[0006] In addition, existing methods generally treat the rolling process as a steady state, failing to fully consider the dynamic changes in the shape of the deformation zone caused by the movement of the rolls and the time-varying characteristics of the lubrication state of the rolling interface. In particular, the friction coefficient is mostly selected based on experience, which cannot accurately reflect the unsteady lubrication behavior. This leads to a decrease in prediction accuracy and a lag in control response under dynamic conditions such as speed increase / decrease and vibration, which can easily cause plate thickness fluctuations, poor plate shape, or even equipment vibration.

[0007] Chinese patent application CN114722516B discloses a method for setting the rolling force and rolling torque in the full deformation zone of cold rolling of strip steel, and proposes a method for calculating the rolling force and rolling torque considering the elastic deformation zones at the inlet and outlet. However, it has the following technical drawbacks: During unsteady rolling stages such as acceleration / deceleration and vibration, the shape of the deformation zone and the metal flow in the roll gap will change, and the friction coefficient of the rolling interface will also change continuously. This leads to a large error in the rolling force calculation value obtained based on traditional rolling theory and Coulomb's friction law. Therefore, this method can only improve the accuracy of rolling force calculation in the steady rolling stage and cannot meet the accuracy requirements of the unsteady rolling stage.

[0008] Therefore, existing methods for calculating rolling force still have significant shortcomings in terms of accuracy, dynamic adaptability, mechanism interpretability, and multi-objective coordination.

[0009] There is an urgent need for a high-precision dynamic rolling force prediction method that can integrate the elastic-plastic deformation mechanism of the rolling process and accurately reflect the unsteady lubrication characteristics and roll motion state, so as to provide a reliable basis for achieving precise control of product thickness and improving the stability and product quality of cold continuous rolling production. Summary of the Invention

[0010] To overcome the problems of low accuracy in rolling force calculation and poor dynamic adaptability in existing technologies, this invention provides a method, system, and apparatus for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling.

[0011] According to one aspect of the present invention, a method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling is provided, comprising: Data acquisition steps: Collect process parameters, workpiece parameters, and roll parameters of the cold continuous rolling production line. The process parameters are parameters that characterize the dynamic operating state and boundary load conditions of the rolling process. The workpiece parameters are parameters used to characterize the initial geometric shape and intrinsic mechanical properties of the rolled material. The roll parameters are parameters used to establish the contact geometry characteristics of the deformation zone and the basis of the elastic response of the roll system. The analysis steps for the dynamic parameters of the roll motion state and deformation zone are as follows: First, determine the roll motion state based on whether the roll gap changes and the direction of change. Second, based on the initial value of the roll flattening radius, use process parameters, workpiece parameters, and roll parameters to obtain the dynamic parameters of the deformation zone corresponding to the roll motion state according to the geometric kinematic relationship between the roll and the workpiece, the amount of elastic deformation, and the geometric properties of the roll. The roll motion states include ordinary rolling, thickening rolling, and thinning rolling. The deformation zone includes the inlet elastic compression zone, the plastic deformation zone, and the outlet elastic recovery zone. The dynamic parameters of the deformation zone include the outlet thickness and inlet thickness, contact arc length, and contact angle of each region within the deformation zone. Steps for analyzing the dynamic parameters of micro-element: Discretize the deformation zone into multiple micro-elements along the rolling direction. Based on the parabolic geometric approximation of the workpiece thickness along the roll gap, the law of constant volume, and the kinematic coordination condition that the workpiece speed and the roll linear speed are equal at the neutral point, obtain the dynamic parameters of each micro-element using the dynamic parameters of the deformation zone. The dynamic parameters of the micro-element include average thickness, deformation resistance, horizontal motion speed, and neutral angle. Steps for analyzing the frictional stress distribution in the deformation zone: Based on the mixed lubrication theory, analyze the frictional stress distribution in the deformation zone using process parameters and dynamic parameters of the deformation zone; Rolling pressure analysis steps: Using the dynamic parameters of the micro-element and the frictional stress distribution in the deformation zone, establish static equilibrium equations for the discrete micro-element in the deformation zone along the rolling direction. Combine the constitutive relations of materials in different regions and analyze the rolling pressure of the micro-element in each region of the deformation zone using the roll motion state and neutral angle. Dynamic rolling force analysis steps: Integrate the rolling pressure within the deformation zone to obtain the dynamic rolling force; The roll flattening radius correction steps are as follows: Based on the coupling relationship between dynamic rolling force and roll flattening radius, the roll flattening radius is corrected to obtain the corrected roll flattening radius; Convergence judgment steps: Determine whether the flattening radius of the corrected roll meets the convergence condition; If the convergence condition is not met, set the initial value of the roll flattening radius to the corrected roll flattening radius, return to the roll motion state and deformation zone dynamic parameter analysis step, and re-analyze the roll gap change rate and deformation zone dynamic parameters.

[0012] Existing technologies typically assume that rolling is a steady-state process, neglecting the dynamic motion of the rolls in the vertical direction (such as vibration or roll gap adjustment). This invention, by determining whether the roll gap changes and the direction of change, subdivides the rolling state into ordinary rolling, thickening rolling (roll gap widening), and thinning rolling (roll gap narrowing). This allows the model to correct the geometric parameters of the deformation zone (such as contact arc length, contact angle, and thickness of each zone) in real time based on the actual dynamic motion of the rolls. Thus, even in unsteady-state stages such as acceleration / deceleration or vibration, it can still accurately describe the geometry of the deformation zone, rather than using steady-state formulas.

[0013] This invention abandons the traditional Coulomb's law of friction (constant friction coefficient) and instead adopts the hybrid lubrication theory to analyze the frictional stress distribution in the deformation zone. The hybrid lubrication theory can more realistically reflect the complex interaction between oil film thickness, surface roughness, and contact pressure during cold rolling, and accurately calculate the dynamically changing frictional stress under unsteady conditions, thereby significantly improving the physical accuracy of rolling force calculation.

[0014] This invention strictly divides the deformation zone into an inlet elastic compression zone, a plastic deformation zone, and an outlet elastic recovery zone, and establishes corresponding static equilibrium equations and constitutive relations for different regions (Hooke's law for the elastic zone and Tresca's criterion for the plastic zone). A "rolling force" is also established. Roll flattening radius Geometric parameters of the deformation zone The closed-loop feedback of "rolling force" ensures the self-consistency of the calculation results by continuously adjusting the roll flattening radius until the convergence condition is met. This refined partitioning and iterative algorithm eliminates the errors caused by traditional simplified formulas, accurately captures the transition details of elastic-plastic deformation during rolling, and significantly improves the prediction accuracy of the final dynamic rolling force.

[0015] In one possible implementation, the analysis steps for the roll motion state and dynamic parameters of the deformation zone include: Calculate the rate of change of the roll gap; The motion state of the rolls is determined by whether the speed of change of the roll gap changes and the direction of change. The dynamic parameters of the deformation zone corresponding to the roll motion state are obtained based on process parameters, workpiece parameters, and roll parameters.

[0016] This invention introduces the dynamic variable of the roll gap change rate to accurately capture the unsteady characteristics of the rolling process, thereby solving the problem of large calculation errors in the geometric parameters of the deformation zone under dynamic conditions such as acceleration / deceleration and vibration in existing technologies. By calculating the roll gap change rate and determining the roll motion state (ordinary rolling, thickening rolling, or thinning rolling), the geometric parameter calculation model of each region of the deformation zone (entry elastic compression zone, plastic deformation zone, and exit elastic recovery zone) can be dynamically adjusted. This allows the dynamic parameters of the deformation zone (such as contact arc length, contact angle, and thickness of each region) to reflect the influence of roll motion on metal flow and contact geometry in real time. As a result, a high-precision geometric description of the deformation zone can be obtained even in the unsteady rolling stage, laying the foundation for subsequent accurate calculation of rolling force. Ultimately, this achieves the beneficial effects of improving the accuracy of rolling force prediction in the unsteady rolling stage and enhancing the dynamic adaptability of the model.

[0017] In one possible implementation, the step of determining the roll motion state based on whether the roll gap change speed changes and the direction of change includes: The roll gap change rate is analyzed using a backward differential method based on the actual roll gap value.

[0018] This invention solves the problems of delayed judgment or complex calculation of roll motion state in existing technologies by using the backward difference method to process the actual roll gap value. It estimates the roll gap change rate in real time by using the difference between the roll gap data at the current moment and historical moments. This method is simple to calculate, responds quickly, and can accurately capture the minute vibrations or adjustment movements of the rolls during rolling, thereby accurately determining whether the rolls are in normal rolling, thickening rolling, or thinning rolling state. This provides a reliable kinematic basis for the accurate calculation of subsequent dynamic parameters of the deformation zone, ensuring that the model maintains high accuracy and real-time performance under dynamic unsteady conditions, and effectively improving the accuracy and stability of rolling force prediction.

[0019] In one possible implementation, the step of determining the roll motion state based on whether the roll gap change speed changes and the direction of change includes: The rolling motion state is determined by the magnitude of the change rate of the roll gap relative to 0.

[0020] This invention solves the problem in existing technologies where the dynamic motion trend of rolls cannot be accurately distinguished through quantitative indicators by establishing a logical comparison relationship between the roll gap change rate and zero. The positive or negative sign of the roll gap change rate directly maps the roll's motion direction: a speed of 0 indicates steady-state ordinary rolling, a speed greater than 0 indicates thickening rolling with increasing roll gap, and a speed less than 0 indicates thinning rolling with decreasing roll gap. This invention provides a clear and explicit physical criterion for identifying rolling conditions, enabling the model to automatically switch the corresponding geometric deformation zone calculation logic according to different motion states. This accurately eliminates geometric parameter calculation errors caused by neglecting the vertical motion component of the roll at the algorithm level, significantly improving the accuracy of the deformation zone parameter description in the unsteady rolling stage.

[0021] In one possible implementation, the step of obtaining the dynamic parameters of the deformation zone corresponding to the roll motion state based on process parameters, workpiece parameters, and roll parameters includes: The bite angle increment is obtained based on the geometric relationship of the deformation zone; Based on the exit thickness, inlet thickness, front tension, back tension, workpiece grade, and bite angle increment, and combined with Hooke's law, the exit thickness and inlet thickness of the plastic deformation zone are obtained. The contact arc length of each region is obtained based on the outlet thickness of the rolled piece, the inlet thickness of the rolled piece, the outlet thickness of the plastic deformation zone, and the inlet thickness of the plastic deformation zone. The contact angles of each region are obtained based on the thickness of the rolled piece exit, the thickness of the rolled piece inlet, the thickness of the plastic deformation zone exit, and the thickness of the plastic deformation zone inlet.

[0022] This invention addresses the problem in existing technologies that treat the deformation zone as a single plastic zone or ignore the dynamic changes in the geometric boundaries of the elastic deformation zone by constructing a calculation logic based on Hooke's law for elastoplastic deformation. By utilizing the bite angle increment combined with material mechanical parameters (tension, grade) and Hooke's law, this invention accurately calculates the thickness boundaries at the inlet and outlet of the plastic deformation zone, thereby deriving the contact arc length and contact angle of the inlet elastic compression zone, the plastic deformation zone, and the outlet elastic recovery zone. This invention achieves a refined partitioning description of the deformation zone's geometry, accurately reflecting the dynamic migration law of the boundaries between the elastic and plastic deformation zones under unsteady conditions. This provides a precise geometric basis for subsequent micro-element stress analysis, significantly improving the calculation accuracy of the rolling force model under complex conditions.

[0023] In one possible implementation, the frictional stress distribution analysis step in the deformation zone includes: Analyze the real-time roughness of the work roll based on the parameters of the rolled piece and the roll parameters; Dynamic inlet oil film thickness analysis based on process parameters; Based on the assumptions of real-time roughness, dynamic inlet oil film thickness, and roughness distribution, the frictional stress distribution in the deformation zone is calculated.

[0024] This invention solves the problem that existing technologies, which use constant friction coefficients or Coulomb's friction law, cannot accurately reflect unsteady lubrication characteristics by introducing a coupled calculation of real-time roughness and dynamic oil film thickness. Based on real-time analysis of roll surface roughness using workpiece and roll parameters, this invention calculates the dynamic inlet oil film thickness using process parameters, and accurately solves the frictional stress distribution within the deformation zone using hybrid lubrication theory based on roughness distribution assumptions, rather than relying on empirical values. This invention can realistically reproduce the time-varying characteristics of lubrication under dynamic operating conditions such as acceleration / deceleration and vibration, eliminating rolling force calculation errors caused by deviations in friction coefficient selection, and significantly improving the prediction accuracy and physical realism of the model under complex lubrication environments.

[0025] In one possible implementation, the rolling pressure analysis step includes: Discretization step: The deformation zone is discretized into multiple parts along the rolling direction to form multiple micro-elements; Micro-element analysis steps: Analyze the average thickness, deformation resistance, and horizontal movement speed of each micro-element based on the dynamic parameters and process parameters of the deformation zone; Steps for analyzing the horizontal velocity of the rolled piece: Based on the entry thickness of the rolled piece, the entry velocity of the rolled piece, the length of the deformation zone, the position of the cross section, and the thickness of the rolled piece at the cross section, and in conjunction with the law of constant volume, analyze the horizontal velocity of the rolled piece at any cross section; Neutral angle analysis steps: Determine the position of the neutral plane based on the horizontal movement speed of the rolled piece, and obtain the neutral angle.

[0026] This invention solves the problem of neutral angle calculation errors caused by the assumption of constant velocity or simplified kinematic relationships in existing technologies during unsteady rolling stages by introducing a metal flow law based on the law of volume invariance. This invention utilizes discretization to divide the deformation zone into infinitesimal elements. Based on the inlet parameters and real-time cross-sectional thickness, it accurately derives the horizontal velocity of any cross-section using the law of volume invariance, thereby precisely locating the neutral plane and neutral angle where the velocity equals the roll linear velocity. Therefore, this invention can accurately capture the nonlinear changes in metal flow velocity under dynamic conditions, providing a reliable kinematic basis for establishing accurate frictional stress distribution and static equilibrium equations, thus significantly improving the accuracy of rolling pressure integral calculation.

[0027] In one possible implementation, the infinitesimal element analysis step includes: Based on the parabolic form of the workpiece thickness in the roll gap, the inlet and outlet thicknesses of each micro-element are obtained. The average thickness of each micro-element is obtained based on the inlet and outlet thicknesses of the micro-element. Based on the average thickness of each micro-element, the average deformation resistance of each micro-element is obtained by combining the strip material with the deformation resistance model.

[0028] This invention addresses the problem in existing technologies that treat the deformation zone as a whole or use simplified geometries (such as linear approximations), leading to an inability to accurately describe the nonlinear changes in thickness and the distribution of local deformation resistance. It employs a method combining parabolic geometric approximation and infinitesimal element discretization. This invention uses a parabolic equation to fit the nonlinear distribution of the workpiece thickness in the roll gap, accurately calculating the inlet, outlet, and average thickness of each infinitesimal element. Then, it combines this with the material constitutive relation (deformation resistance model) to obtain the corresponding local average deformation resistance for each infinitesimal element, rather than using the average parameters of the entire deformation zone. Therefore, this invention can accurately capture the gradient variation characteristics of deformation resistance within the deformation zone, significantly improving the accuracy of rolling force integral calculations. Especially when dealing with high reduction rates or thin-gauge rolling, it can more realistically reflect the material's actual ability to resist plastic deformation.

[0029] In one possible implementation, the rolling pressure analysis step includes: Static equilibrium equations are constructed for the micro-elements in each region of the deformation zone along the rolling direction. Based on Hooke's law, the rolling pressure distribution in the inlet elastic compression zone and the outlet elastic recovery zone is obtained by using the static equilibrium relationship equation between the inlet elastic compression zone and the outlet elastic recovery zone. The rolling pressure distribution in the plastic deformation zone is obtained by using the static equilibrium equation of the plastic deformation zone based on the Tresca yield criterion.

[0030] This invention solves the problem that existing technologies, which use a single yield criterion or simplified formulas, cannot accurately describe the stress state of the entire deformation zone by matching corresponding mechanical constitutive equations to deformation zones with different physical properties. Based on the static equilibrium relationship of the micro-element, this invention applies Hooke's law to describe the linear relationship between stress and strain in the elastic deformation zone (inlet compression, outlet recovery), while applying Tresca's yield criterion to describe the material's plastic flow limit in the plastic deformation zone. This constructs a differentiated pressure calculation model that conforms to the physical nature of each region. Therefore, this invention can accurately solve the rolling pressure distribution of each micro-element within the deformation zone, eliminating theoretical errors caused by the mixing or simplification of mechanical models, and significantly improving the physical realism and calculation accuracy of the rolling force prediction model.

[0031] In one possible implementation, the convergence condition is that the error rate of the corrected roll flattening radius relative to the initial value of the roll flattening radius is not greater than a set error threshold.

[0032] This invention addresses the problem of divergent calculation results or insufficient accuracy caused by neglecting the strong coupling between roll elastic deformation and rolling force in existing technologies by establishing an iterative convergence criterion based on the roll flattening radius error rate. This invention uses the relative error rate between the corrected roll flattening radius and the initial value as an indicator of computational stability. When this error rate decreases to within a set threshold, it is determined that the roll flattening radius and dynamic rolling force have reached a state of mechanical equilibrium, thereby ensuring numerical self-consistency between geometric parameters and stress state. Therefore, this invention, while ensuring high accuracy of calculation results, avoids invalid calculations caused by excessive pursuit of convergence, achieving an optimal balance between computational accuracy and solution efficiency, and ensuring the reliability and stability of dynamic rolling force analysis results.

[0033] According to a second aspect of the present invention, a dynamic rolling force analysis system for the elastoplastic deformation process of cold continuous rolling is provided, comprising: The data acquisition unit is configured to collect process parameters, workpiece parameters, and roll parameters of the cold continuous rolling production line. The first analysis unit is configured to analyze the roll motion state and deformation zone dynamic parameters. Using process parameters, workpiece parameters, and roll parameters acquired by the acquisition unit, it obtains the roll running state and deformation zone dynamic parameters based on the geometric kinematic relationship between the roll and the workpiece, the amount of elastic deformation, and the geometric properties of the roll. The roll motion state includes ordinary rolling, thickening rolling, and thinning rolling. The deformation zone includes an inlet elastic compression zone, a plastic deformation zone, and an outlet elastic recovery zone. The deformation zone dynamic parameters include the outlet thickness and inlet thickness of each region of the deformation zone, the contact arc length, and the contact angle. The second analysis unit is configured to analyze the dynamic parameters of the micro-element. It discretizes the deformation zone into multiple micro-elements along the rolling direction and obtains the dynamic parameters of each micro-element using the dynamic parameters of the deformation zone obtained by the first analysis unit. The dynamic parameters of the micro-element include average thickness, deformation resistance, horizontal movement speed and neutral angle. The third analysis unit is configured to analyze the frictional stress distribution in the deformation zone. Based on the mixed lubrication theory, it analyzes the frictional stress distribution in the deformation zone by using the process parameters collected by the acquisition unit and the dynamic parameters of the deformation zone obtained by the first analysis unit. The fourth analysis unit is configured to analyze rolling pressure. It uses the roll motion state obtained from the first analysis unit, the neutral angle obtained from the second analysis unit, and the friction stress distribution in the deformation zone obtained from the third analysis unit to analyze the rolling pressure of the micro-elements in each region of the deformation zone. The fifth analysis section is configured to analyze the dynamic rolling force by integrating the rolling pressure obtained from the fourth analysis section within the deformation zone to obtain the dynamic rolling force. The correction unit is configured to correct the roll flattening radius of the first analysis unit based on the coupling relationship between the dynamic rolling force and the roll flattening radius obtained by the fifth analysis unit, thereby obtaining a corrected roll flattening radius. The judgment unit is configured to determine whether the corrected roll flattening radius obtained by the correction unit meets the convergence condition; if the convergence condition is met, the dynamic rolling force that meets the convergence condition is output; if the convergence condition is not met, the roll flattening radius adjustment signal is sent to the first analysis unit to set the initial value of the roll flattening radius to the corrected roll flattening radius obtained by the correction unit.

[0034] According to a third aspect of the present invention, a dynamic rolling force analysis device-computing equipment for the elastoplastic deformation process of cold continuous rolling is provided, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the dynamic rolling force analysis method for the above-mentioned cold continuous rolling elastic-plastic deformation process.

[0035] According to a fourth aspect of the present invention, a dynamic rolling force analysis device for a cold continuous rolling elastic-plastic deformation process is provided - a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of the above-described dynamic rolling force analysis method for a cold continuous rolling elastic-plastic deformation process.

[0036] According to a fifth aspect of the present invention, a computer program is provided, wherein when the computer program is executed in a computer, the computer is instructed to perform the steps of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described above.

[0037] The dynamic rolling force analysis method for the elastoplastic deformation process in cold continuous rolling described in this invention is based on the theories of elastic and plastic deformation and unsteady lubrication. It constructs a dynamic rolling force calculation model that comprehensively considers the elastic deformation zone, the unsteady lubrication characteristics of the rolling interface, and the motion state of the rolls. By calculating the influence of the inlet and outlet elastic deformation zones and the vertical movement of the rolls on the shape of the deformation zone, the accuracy of rolling force prediction is further improved, ultimately achieving precise control of product thickness.

[0038] The dynamic rolling force analysis system for the elastoplastic deformation process in cold rolling, as described in this invention, solves the problems of fragmented calculation models, inability to adapt to unsteady conditions in real time, and lack of dynamic self-consistency in existing technologies by constructing a systematic architecture that integrates data acquisition, multi-physics field coupling analysis, and closed-loop iterative correction. This invention organically integrates roll motion state identification, elastoplastic partition modeling, hybrid lubrication friction analysis, and micro-element discretization calculation through the coordinated operation of various functional modules. It uses a feedback mechanism of "dynamic rolling force—roll flattening radius" for iterative correction until the convergence condition is met. Therefore, this invention achieves high-precision, real-time dynamic prediction of rolling force throughout the entire cold rolling process (especially during unsteady stages such as acceleration / deceleration and vibration), significantly improving the accuracy of strip shape and thickness control and production stability, and providing a reliable theoretical model and system support for intelligent manufacturing. Attached Figure Description

[0039] Figure 1 This is a schematic flowchart of an embodiment of the dynamic rolling force analysis method for the elastoplastic deformation process in cold continuous rolling described in this invention; Figure 2(a) is a schematic diagram of the shape of the deformation zone under the motion state of the roll in ordinary rolling according to the present invention; Figure 2(b) is a schematic diagram of the shape of the deformation zone under the motion state of the roll in the thinning rolling process described in this invention; Figure 2(c) is a schematic diagram of the shape of the deformation zone under the motion state of the roll in the thickening rolling process described in this invention; Figure 3(a) is a schematic diagram of the force analysis of the micro-element under the motion state of the roll in ordinary rolling according to the present invention; Figure 3(b) is a schematic diagram of the force analysis of the micro-element under the motion state of the roll in the thinning rolling process described in this invention; Figure 3(c) is a schematic diagram of the force analysis of the micro-element under the motion state of the roll in the thickening rolling process described in this invention. Figure 4 This is a schematic diagram of the structure of an embodiment of the dynamic rolling force analysis system for the elastoplastic deformation process in cold continuous rolling according to the present invention; Figure 5 This is a schematic diagram of an application scenario of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described in this invention. Figure 6 This is a schematic diagram illustrating another application scenario of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described in this invention. The system includes: 10. Dynamic rolling force analysis system; 1. Acquisition unit; 2. First analysis unit; 21. Roll motion state analysis module; 211. Roll gap change speed acquisition unit; 212. Judgment unit; 22. Deformation zone dynamic parameter analysis module; 221. Biting angle equal quantity acquisition unit; 222. Plastic deformation zone analysis unit; 223. Contact arc length analysis unit; 224. Contact intersection analysis unit; 3. Second analysis unit; 31. Discrete processing module; 32. Micro-element analysis module; 33. Section analysis module; 34. Neutral angle acquisition module; 4. Third analysis unit; 41. Roughness analysis module; 42. Oil film thickness... 43. Deformation Zone Friction Stress Distribution Module; 5. Fourth Analysis Unit; 51. Static Equilibrium Relationship Equation Construction Module; 52. Rolling Force Analysis Module; 6. Fifth Analysis Unit; 7. Correction Unit; 8. Judgment Unit; 100. Calculation Equipment; 101. Process Parameters; 102. Roll Parameters; 103. Roll Parameters; 104. Roll Motion State; 105. Deformation Zone Dynamic Parameters; 106. Micro-element Dynamic Parameters; 107. Friction Stress Distribution; 108. Dynamic Rolling Force; 110. Memory; 120. Processor; 130. Bus; 140. Access Device; 150. Database; 160. Network. Detailed Implementation

[0040] Numerous specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0041] The terminology used in one or more embodiments of the present invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of the invention. The singular forms “a” and “the” as used in one or more embodiments of the invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in one or more embodiments of the invention refers to and includes any or all possible combinations of one or more associated listed items.

[0042] It should be understood that although the terms first, second, etc., may be used to describe various information in one or more embodiments of the present invention, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first may also be referred to as second without departing from the scope of one or more embodiments of the present invention, and similarly, second may also be referred to as first. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to a determination."

[0043] Figure 1 This is a schematic flowchart of an embodiment of the dynamic rolling force analysis method for the elastoplastic deformation process in cold continuous rolling described in this invention, as shown below. Figure 1 As shown, the dynamic rolling force analysis method includes: Step S1: Collect process parameters, workpiece parameters, and roll parameters of the cold continuous rolling production line; Step S2: Set the initial value of the roll flattening radius to the roll radius, for example, let... R f1 = R 0, R f1 This is the initial value of the roll flattening radius. R 0 represents the roll radius. Based on the process parameters, workpiece parameters, and roll parameters collected in step S1, the roll gap change rate and deformation zone dynamic parameters are obtained, and the roll motion state is determined. The roll motion state includes ordinary rolling, thickening rolling, and thinning rolling. The deformation zone includes the inlet elastic compression zone, the plastic deformation zone, and the outlet elastic recovery zone. The deformation zone dynamic parameters include the outlet thickness and inlet thickness of each area of ​​the deformation zone, the contact arc length, and the contact angle. Step S3: Discretize the deformation zone into multiple micro-elements along the rolling direction. Based on the dynamic parameters of the deformation zone obtained in step S2, obtain the dynamic parameters of each micro-element. The dynamic parameters of the micro-element include average thickness, deformation resistance, horizontal movement speed and neutral angle. Step S4: Analyze the frictional stress distribution in the deformation zone based on the hybrid lubrication theory; Step S5: Based on the roll motion state determined in step S2 and the neutral angle in step S3, analyze the rolling pressure of the micro-elements in each region of the deformation zone in conjunction with the frictional stress distribution in step S4. Step S6: Integrate the rolling pressure within the deformation zone to obtain the dynamic rolling force; Step S7: Based on the coupling relationship between dynamic rolling force and roll flattening radius, correct the roll flattening radius to obtain the corrected roll flattening radius. R f2 ; Step S8: Determine whether the corrected roll flattening radius obtained in step S7 meets the convergence condition; If the convergence condition is not met, proceed to step S9, setting the initial value of the roll flattening radius to the corrected roll flattening radius obtained in step S7, i.e. R f1 = R f2 Return to step S2 and recalculate the roll gap change rate and dynamic parameters of the deformation zone; If the convergence condition is met, execute step S10 and output the corrected roll flattening radius and the corresponding dynamic rolling force that meet the convergence condition.

[0044] This invention, based on elastic deformation theory, incorporates the influence of the inlet elastic compression zone and the outlet elastic recovery zone into the rolling force model. By combining the roll motion state with unsteady lubrication theory, it characterizes the dynamic characteristics of the deformation zone shape parameters and the lubrication state of the rolling interface over time. This method significantly improves the calculation accuracy of dynamic rolling force, providing a reliable basis for precise control of product thickness, improvement of the stability of cold continuous rolling processes, and enhancement of product quality.

[0045] The following details each step of the above dynamic rolling force analysis method: Step S1: Data Acquisition Steps: In step S1, process parameters, workpiece parameters, and roll parameters can be collected from the primary control system and secondary control system on the continuous rolling production line.

[0046] In one feasible embodiment, the process parameters include one or more of the following: rolling speed for each pass, exit speed of the workpiece, inlet speed of the workpiece, inlet thickness of the workpiece, pre-tension stress of the workpiece, post-tension stress of the workpiece, actual roll gap value, lubricating oil viscosity and its viscosity-pressure coefficient.

[0047] In one feasible embodiment, the rolling parameters include one or more of the rolling grade, hot-rolled incoming material thickness, and width.

[0048] In one feasible embodiment, the roll parameters include one or more of roll radius, elastic modulus, surface roughness, and rolling length.

[0049] This invention solves the problem of distorted model input caused by scattered data sources and incomplete parameter dimensions in existing technologies by constructing a multi-source heterogeneous parameter acquisition system for dynamic rolling force analysis. This invention breaks down the data barriers between primary and secondary control systems, simultaneously acquiring parameters covering all dimensions of process dynamics (such as speed, tension, and roll gap), material properties (such as grade and incoming material size), and roll conditions (such as roughness and elastic modulus). This provides high-fidelity data support for subsequent accurate calculations of deformation zone geometry, friction state, and deformation resistance. Therefore, this invention significantly improves the completeness and real-time performance of the rolling force model input, ensuring that the model can accurately reflect the complex working conditions of the production site, and laying a solid data foundation for high-precision dynamic rolling force prediction.

[0050] Step S2: Obtaining dynamic parameters of the deformation zone and judging the motion state of the roll: In one feasible embodiment, step S2 includes: Step S21: Obtain the roll gap change rate based on process parameters; Step S22: Determine the roll motion state based on the roll gap change speed; Step S23: Obtain dynamic parameters of the deformation zone based on the roll gap change rate, process parameters, workpiece parameters, and roll parameters.

[0051] In one feasible embodiment, step S21 includes: Based on the actual roll gap value, the roll gap change rate is analyzed using a backward differential method.

[0052] Preferably, in step S21, the following formula (1) is used: (1) in: The sampling interval; for i The actual roll gap value at time -1; for i The actual roll gap value at any given time; for i The rate of change of the roll gap at any given moment.

[0053] This invention utilizes the discrete-time difference method to replace traditional continuous function differentiation or static assumptions, solving the problem of existing technologies' difficulty in accurately quantifying the instantaneous dynamic changes in roll gap during unsteady rolling. This invention directly acquires data from adjacent sampling times (…). and The actual roll gap value, using its difference and sampling interval The ratio is used to calculate the rate of change of the roll gap in real time. Therefore, this invention can accurately capture the dynamic response of the roll gap during transient processes such as strip threading, acceleration and deceleration, or vibration of the rolling mill, providing key real-time kinematic parameters for subsequent analysis of workpiece thickness fluctuations and dynamic rolling forces, and significantly improving the model's adaptability to unsteady conditions and calculation accuracy.

[0054] In one feasible embodiment, step S22 includes: The rolling motion state is determined by the magnitude of the change rate of the roll gap relative to 0.

[0055] Preferably, step S22 includes: like If the roll remains stationary in the vertical direction, this is the normal rolling state. like If the roller moves upward, it is in a thickening rolling state. like Then the rolls move downwards, which is the thinning rolling state.

[0056] This invention utilizes the varying speed of the roll gap. A rolling state discrimination logic is established, solving the problem of poor model adaptability caused by the inability of existing technologies to effectively distinguish between steady-state rolling and dynamic variable-thickness rolling (such as speed increase / decrease and thickness transition). This invention utilizes the changing speed of the roll gap. The positive, negative, and zero values ​​of the values ​​accurately map the complex rolling process to ordinary rolling. Thickening rolling () ) and thinning rolling ( The invention identifies three physical states, providing accurate boundary conditions for calculating the geometric parameters of the deformation zone under different working conditions. Therefore, this invention achieves real-time identification and classification of the dynamic characteristics of the rolling process, ensuring that the subsequent rolling force model can call the corresponding calculation logic according to the specific rolling state, significantly improving the robustness and prediction accuracy of the model throughout the entire process.

[0057] As shown in Figures 2(a)-2(c), the rolling deformation zone includes an inlet elastic compression zone I, a plastic deformation zone II, and an outlet elastic recovery zone III. However, the rolling deformation zone has different shapes under different roll motion states. The contact angle, deformation zone length, and outlet thickness all change with the roll motion state. In one feasible embodiment, step S23 includes: Step S231: Obtain the bite angle increment based on the geometric relationship of the deformation zone; Step S232: Based on the exit thickness, inlet thickness, front tension, back tension, grade of the rolled piece, and bite angle increment, and in conjunction with Hooke's law, obtain the exit thickness and inlet thickness of the plastic deformation zone. Step S233: Obtain the contact arc length of each region based on the workpiece exit thickness, workpiece inlet thickness, plastic deformation zone exit thickness, and plastic deformation zone inlet thickness; Step S234: Obtain the contact angle of each region based on the thickness of the rolled piece exit, the thickness of the rolled piece inlet, the thickness of the plastic deformation zone exit, and the thickness of the plastic deformation zone inlet.

[0058] In one feasible embodiment, step S231 includes: Since the bite angle increment is very small during the up-and-down movement of the roll, it can be approximated and obtained by the following formula (2): (2) in: This is the bite angle increment; This refers to the exit speed of the rolled product.

[0059] This invention utilizes the principle of small-angle approximation to increase the bite angle increment. The solution is transformed into the vertical motion speed of the roll and the exit speed of the rolled piece. The ratio calculation solves the problem in existing technologies where the contact geometry is complex and difficult to solve accurately in real time due to the dynamic movement of the rolls. This invention is based on the physical fact that the bite angle change caused by the roll movement in actual working conditions is extremely small, and employs... A mathematical approximation was established, creating a linear analytical relationship between the bite angle increment and the speed parameter. Therefore, while ensuring computational accuracy, this invention greatly simplifies the mathematical model of the dynamic bite angle, reduces computational complexity, and enables the system to respond to changes in the roll motion state in real time with extremely high efficiency, providing a fast and reliable geometric basis for the accurate calculation of dynamic deformation zone parameters.

[0060] In one feasible embodiment, step S232 includes: The outlet and inlet thicknesses of the plastic deformation zone are obtained by the following formulas (3)-(7): (3) (4) (5) (6) (7) in: The flattening radius of the roll; The elastic modulus of the rolled piece; Poisson's ratio of the rolled product; This represents the thickness at the entrance to the plastic deformation zone. This refers to the thickness at the exit of the plastic deformation zone. For the entry thickness of the rolled piece; For the exit thickness of the rolled product; The inlet yield strength of the rolled piece; The yield strength at the exit of the rolled piece; Tension before rolling; Tension after rolling; This refers to the thickness deformation of the inlet elastic compression zone. This represents the thickness deformation of the export elastic recovery zone.

[0061] This invention solves the problem of inaccurate calculation of the plastic deformation zone thickness caused by neglecting the elastic recovery and compression effects of the rolled piece in existing technologies by constructing a geometric-physical coupling model that includes elastic deformation correction. This invention is based on the generalized Hooke's law and utilizes the elastic modulus of the rolled piece. Poisson's ratio Based on yield strength and tensile stress, the inlet elastic compression and outlet elastic recovery are calculated respectively, and then the inlet thickness of the pure plastic deformation zone is extracted from the actual geometric thickness. and export thickness Therefore, this invention precisely defines the boundary conditions of the plastic deformation zone, restores the real deformation path of "elastic-plastic-elastic" during cold rolling, and provides accurate geometric and physical parameter support for the high-precision calculation of subsequent deformation resistance and rolling pressure.

[0062] In one feasible embodiment, step S233 includes: The contact arc length of each region is obtained by the following formulas (8)-(11): (8) (9) (10) (11) in, The contact arc length of the deformation zone; The length of the contact arc in the inlet elastic compression zone; This refers to the contact arc length in the plastic deformation zone. The length of the contact arc in the inlet elastic compression zone; This is the actual roll gap value.

[0063] This invention solves the problem of contact arc length calculation errors caused by neglecting the inlet / outlet elastic zone and dynamic roll gap changes in existing technologies by constructing a segmented calculation model for the contact arc length that integrates the elastic deformation zone and the dynamic roll gap motion effect. This invention calculates the total contact arc length... Decomposed into inlet elastic compression zone Plastic deformation zone and export flexibility response zone Three parts, and for the static roll gap ( ), tending to thicken ( ) and tending to thin ( Three operating conditions are introduced, and bite angle increments are introduced for each. The arc lengths of the plastic zone and the exit elastic zone are dynamically corrected. Therefore, this invention achieves a refined characterization of the contact geometry in the deformation zone, significantly improving the calculation accuracy of the contact arc length during dynamic rolling, and laying a solid geometric foundation for accurately solving friction and rolling forces.

[0064] In one feasible embodiment, step S234 includes: The contact angles of each region are obtained by the following formulas (12)-(15): (12) (13) (14) (15) in, Contact angle in the deformation zone; The contact angle of the inlet elastic compression zone; This refers to the contact angle in the plastic deformation zone. This refers to the contact angle in the plastic deformation zone during ordinary rolling. This refers to the contact angle of the export elastic recovery zone.

[0065] This invention solves the problem of existing technologies' inability to accurately describe the influence of roll gap dynamic motion on the angle distribution of each sub-region of the deformation zone by establishing a piecewise analytical model of dynamic contact angle based on geometric projection relationships. This invention utilizes the inverse cosine function to correlate the calculated thickness of each region with the roll flattening radius. Correlation, accurate solution of contact angle in the inlet elastic zone Contact angle in the plastic zone and the contact angle of the export elastic zone And according to the direction of the roller gap movement ( Introducing bite angle increment The contact angles of the plastic zone and the exit zone are dynamically superimposed or subtracted for correction, and finally synthesized into the total deformation zone contact angle. Therefore, this invention achieves a comprehensive and accurate reconstruction of the contact geometry of the deformation zone, ensuring the accuracy of the stress integral boundary during the dynamic adjustment of the rolls, thereby significantly improving the calculation accuracy of the rolling force model.

[0066] Step S3:

[0067] In one feasible embodiment, step S3 includes: Step S31: Discretize the deformation zone into multiple parts along the rolling direction to form multiple micro-elements; Step S32: Analyze the average thickness, deformation resistance, and horizontal movement speed of each micro-element based on the dynamic parameters and process parameters of the deformation zone; Step S33: Based on the entry thickness of the workpiece, the entry speed of the workpiece, the length of the deformation zone, the position of the cross section, and the thickness of the workpiece at the cross section, and in conjunction with the law of constant volume, analyze the horizontal movement speed of the workpiece at any cross section; Step S34: Determine the position of the neutral plane based on the horizontal movement speed of the rolled piece, and calculate the neutral angle.

[0068] In one feasible embodiment, step S32 includes: Step S321: Based on the parabolic form of the workpiece thickness in the roll gap, obtain the inlet thickness and outlet thickness of each micro-element; Step S322: Obtain the average thickness of each micro-element based on the inlet and outlet thicknesses of the micro-element; Step S323: Based on the average thickness of each micro-element, the average deformation resistance of each micro-element is obtained using the deformation resistance model in combination with the strip material.

[0069] In one feasible embodiment, step S321 includes: The thickness of the rolled piece at any cross section is obtained by the following formula (16), thereby obtaining the inlet and outlet thicknesses of each micro-element: (16) in: The distance from any cross section to the centerline of the roll; The thickness of the rolled piece at any cross-section.

[0070] This invention solves the problem that existing technologies, which typically only focus on the thickness along the rolling centerline, struggle to accurately describe the uneven thickness distribution along the rolling direction of strip by introducing a rolling thickness distribution model based on a parabolic approximation. This invention utilizes the roll flattening radius... As a curvature parameter, it is combined with the roll gap value at the roll centerline. Through formula Establish arbitrary rolling direction position Thickness of rolled piece at the location The analytical relationship.

[0071] In one feasible embodiment, step S322 includes: The average thickness of each infinitesimal element is obtained by the following formula (17): (17) in: The average thickness of the infinitesimal element; and These represent the inlet and outlet thicknesses of the micro-element, respectively.

[0072] This invention solves the problem that the simple arithmetic mean method in the prior art is difficult to accurately characterize the thickness variation law of the micro-element in the nonlinear deformation zone by adopting a weighted average algorithm. Considering that the thickness usually decreases nonlinearly along the deformation zone during rolling, and that the influence of the exit region on the rolling force is greater, this invention uses formula (17) to characterize the thickness at the inlet of the micro-element. and export thickness By applying weighted processing, a higher weighting coefficient is assigned to the exit thickness. Therefore, this invention can more accurately calculate the average geometric parameters of the micro-element, thereby improving the calculation accuracy of deformation resistance and stress state coefficient, and making the overall rolling force model more reflective of the actual physical deformation process.

[0073] In one feasible embodiment, step S33 includes: The horizontal speed of the rolled piece at any cross section can be obtained by the following formula (18): (18) in: The horizontal speed of the rolled piece at any cross section; This refers to the inlet speed of the rolled piece.

[0074] This invention solves the problem of inaccurate velocity distribution calculations caused by neglecting the influence of the vertical roll motion on the horizontal velocity field of the rolled piece in existing technologies by establishing the kinematic equations for the coupled roll gap motion velocity. Based on the principle of volume invariance and geometric relationships, this invention addresses the issue of inaccurate velocity distribution calculations at the inlet velocity. and entrance thickness Based on this, the vertical motion speed of the roll gap is introduced. With current location and the length of the deformation zone geometric correction terms This allows for the accurate calculation of the horizontal movement speed of the rolled piece at any cross-section. Therefore, this invention accurately describes the metal flow pattern during dynamic specification changes or roll gap adjustments, providing a reliable kinematic basis for subsequent accurate calculation of dynamic rolling forces.

[0075] In one feasible embodiment, step S34 includes: Combining the definition of the neutral plane and the horizontal movement speed of the rolled piece with arbitrary cross-section, the thickness of the rolled piece at the neutral plane, the position of the neutral plane, and the neutral angle are obtained by the following equations (19)-(21): (19) (20) (twenty one) in, The thickness of the rolled piece at the neutral plane; The location is the neutral plane; It is a neutral angle; The horizontal speed of the rolled piece at the neutral plane satisfies... In other words, the absolute value of the difference between the horizontal speed of the workpiece and the rolling speed reaches its minimum at the neutral plane. This refers to the rolling speed.

[0076] This invention solves the problem of accurately locating the neutral surface (i.e., the boundary between the forward and backward slip zones) under dynamic roll gap motion conditions by constructing a dynamic neutral surface analytical model based on velocity extremum conditions. This invention utilizes the physical definition of minimizing the difference between the workpiece velocity and the roll linear velocity at the neutral surface, combined with the aforementioned established horizontal velocity field model, to simultaneously solve for the workpiece thickness at the neutral surface. Horizontal position and the corresponding neutral angle Therefore, this invention achieves precise division of the frictional stress distribution state within the rolling deformation zone, providing key geometric and kinematic parameters for accurate calculation of dynamic rolling force.

[0077] Step S4:

[0078] In one feasible embodiment, step S4 includes: Step S41: Analyze the real-time roughness of the work roll based on the workpiece parameters and roll parameters; Step S42: Analyze the dynamic inlet oil film thickness based on process parameters; Step S43: Calculate the frictional stress distribution in the deformation zone based on the real-time roughness, dynamic inlet oil film thickness, and roughness distribution assumptions.

[0079] In one feasible embodiment, step S41 includes: The roughness of the work roll will continuously decrease during the rolling process, which will affect the distribution of frictional stress. The real-time roughness can be analyzed by the following formula (22): (twenty two) in: and These are the roughness of the working roll on the machine and the real-time roughness, respectively. L This refers to the rolling length; A 2. B 2 and C 2 represents the roll roughness model coefficient, which is determined based on actual production data.

[0080] This invention addresses the problem in existing technologies that typically assume a constant roll surface roughness, thus failing to reflect the dynamic changes in the friction coefficient caused by wear during actual rolling and its impact on rolling force. This invention utilizes formula (22) to represent the real-time roughness of the roll. Described as rolling length The function of initial roughness The rolling mileage decreases exponentially and then tends to stabilize. attenuation coefficient and amplitude coefficient The roughness evolution of the work roll surface is determined by fitting actual production data. Therefore, this invention can predict the roughness evolution of the work roll surface in real time and accurately, thus providing reliable physical parameter support for dynamically correcting the friction model and improving the prediction accuracy of the rolling force model in the cold continuous rolling process.

[0081] In one feasible embodiment, step S42 includes: Step S421: Obtain the oil film pressure according to the one-dimensional Reynolds equation; Step S442: At the junction of the inlet region and the deformation region, the boundary conditions are obtained based on the oil film pressure using the Tresca yield criterion. Step S423: Obtain the inlet oil film thickness change rate and dynamic inlet oil film thickness based on oil film pressure and boundary conditions.

[0082] This invention solves the problem of accurately calculating the dynamic oil film thickness and its impact on the friction coefficient during high-speed rolling by constructing a hybrid lubrication model based on the coupling of fluid mechanics and plasticity. First, the invention uses the one-dimensional Reynolds equation to solve for the oil film pressure distribution. Then, at the boundary between the inlet and deformation zones, the Tresca yield criterion is introduced to establish the boundary coupling condition between the oil film pressure and the plastic deformation of the rolled piece. Finally, the inlet oil film thickness change rate is solved and integrated to obtain the dynamic inlet oil film thickness. Therefore, this invention can accurately describe the evolution of the lubrication state at the rolling interface, providing key oil film parameter support for accurately calculating the friction factor and rolling force in the hybrid lubrication zone, significantly improving the applicability and accuracy of the model under high-speed rolling conditions.

[0083] In one feasible embodiment, step S421 includes: The oil film pressure is obtained by the following formulas (23)-(25): (twenty three) (twenty four) (25) In the formula: It is a dimensionless parameter; Oil film pressure; This refers to the viscosity-pressure coefficient of lubricating oil in the Barus equation; The viscosity of the emulsion at atmospheric pressure; The average speed of the strip and the rolls; The thickness of the inlet oil film; The rate of change of inlet oil film thickness; The thickness of the oil film in the inlet area; As an intermediate variable; For Derivative.

[0084] This invention solves the problem of calculation errors in oil film pressure and thickness caused by neglecting the nonlinear variation of lubricating oil viscosity with pressure in existing technologies by introducing a one-dimensional Reynolds equation modified by entrainment and compression effects. This invention utilizes the Barus equation to describe the viscosity-pressure characteristics (coefficients) of lubricating oil. By combining the inlet geometric parameters and motion parameters, a method is derived that includes dimensionless parameters. The analytical expression (Equations 23-25) is used to accurately solve for the inlet oil film thickness that takes into account viscosity-pressure characteristics. and its rate of change Therefore, this invention significantly improves the calculation accuracy of oil film pressure distribution in the inlet region, providing a reliable fluid dynamics basis for subsequent accurate determination of lubrication status and calculation of the mixed friction coefficient.

[0085] In one feasible embodiment, step S422 includes: The Tresca yield criterion corresponding to the oil film pressure is obtained by the following equation (26): (26); Based on the Tresca yield criterion, the boundary conditions are obtained through the following equations (27) and (28): (27) (28).

[0086] This invention solves the problem in existing technologies where oil film pressure calculation is disconnected from the plastic yielding behavior of rolled pieces, leading to ambiguous boundary condition definitions in the inlet region. This is achieved by establishing a physical coupling mechanism between fluid lubrication and plastic deformation. The invention utilizes the Tresca yield criterion to define the oil film pressure... Deformation resistance at the exit of the rolled piece and subsequent tension Establish an equation relationship and deduce the oil film thickness in the inlet region based on it. With initial thickness Continuity conditions and dimensionless parameters The boundary expression is thus obtained. Therefore, this invention achieves mathematical closure between the fluid dynamics model and the plastic deformation model of the rolled piece, ensuring the physical continuity and calculation accuracy of the oil film pressure at the entrance of the deformation zone, and laying a solid foundation for accurately solving the friction behavior under mixed lubrication conditions.

[0087] In one feasible embodiment, step S423 includes: The rate of change of inlet oil film thickness is obtained by the following formula (29): (29) in, The rate of change of inlet oil film thickness; The dynamic inlet oil film thickness is obtained by the following formula (30): (30) in, The dynamic inlet oil film thickness.

[0088] This invention addresses the problem that existing technologies typically treat the inlet oil film thickness as a static constant, failing to reflect transient fluctuations during the rolling process, by introducing a time dimension. This invention first utilizes formula (29) based on geometric curvature parameters... and intermediate variables Calculate the instantaneous rate of change of inlet oil film thickness Then, the time stepping method is adopted through formula (30). The oil film thickness is corrected in real time. Therefore, this invention realizes dynamic tracking and prediction of the inlet oil film thickness, which can more realistically simulate the fluctuation of lubricating film thickness caused by sudden changes in working conditions during rolling, and significantly improves the response speed and calculation accuracy of the rolling force model under dynamic working conditions.

[0089] In one feasible embodiment, step S43 includes: The frictional stress distribution under mixed lubrication conditions is obtained by the following equations (31) and (32): (31) (32) in: Frictional stress; This represents the actual contact area ratio; denoted as the average oil film thickness; z is the viscosity-pressure coefficient according to the Roelands equation. The viscosity of the emulsion; The viscosity of the emulsion at atmospheric pressure; This refers to the shear strength of the rolled piece.

[0090] This invention addresses the problem in existing technologies that often employ constant friction coefficients or consider only a single lubrication mechanism, failing to accurately describe the nonlinear changes in frictional stress under mixed lubrication conditions, by constructing a hybrid lubrication friction model based on the Roelands equation. This invention incorporates frictional stress... It is decomposed into two parts: boundary friction and fluid friction. The fluid part introduces the emulsion viscosity based on the Barus equation. (Equation 32) This viscosity model is precisely coupled with pressure. With viscosity coefficient The nonlinear relationship; combined with the shear strength of the rolled piece Ratio to actual contact area Constructing a system that includes speed difference With average oil film thickness The comprehensive frictional stress formula is (Formula 31). Therefore, this invention can accurately quantify the coupling effect of fluid dynamic pressure effect and boundary contact effect under mixed lubrication conditions, significantly improving the physical reality and accuracy of frictional stress distribution calculation.

[0091] Preferably, step S43 further includes: The actual contact area ratio is obtained by the following formula (33): (33) in, For dimensionless parameters, , The oil film thickness distribution within the deformation zone, ; The average oil film thickness is obtained by the following formula (34): (34).

[0092] This invention solves the problem in existing technologies of accurately quantifying the coupling relationship between the contact area of ​​micro-protrusions on rough surfaces and oil film thickness by constructing a micro-contact statistical model based on a dimensionless parameter Z. This invention introduces a method to characterize oil film thickness. With overall roughness dimensionless parameter of ratio The actual contact area ratio is accurately described using high-order polynomials (Formulas 33 and 34). and average oil film thickness Follow The nonlinear evolution law of the value, and the dynamic inlet oil film thickness This invention incorporates the calculation of oil film distribution in the deformation zone. Therefore, it can more accurately characterize the dynamic balance between the contact probability of micro-protrusions and the fluid carrying capacity under mixed lubrication conditions, providing crucial microscopic geometric parameters for the accurate calculation of frictional stress and rolling force.

[0093] Step S5:

[0094] In one feasible embodiment, step S5 includes: Step S51: Construct static equilibrium equations for the micro-elements in each region of the deformation zone along the rolling direction; Step S52: Based on Hooke's law, the rolling pressure distribution in the inlet elastic compression zone and the outlet elastic recovery zone is obtained using the static equilibrium equation of the inlet elastic compression zone and the outlet elastic recovery zone. Step S53: Based on the Tresca yield criterion, the rolling pressure distribution in the plastic deformation zone is obtained using the static equilibrium equation of the plastic deformation zone.

[0095] In one feasible embodiment, step S51 includes: like Figures 3(a)-3(c) As shown, the static equilibrium equations under different roll motion states are constructed using the following equations (35)-(37): , (35) (36) (37) in, For the rolled piece in Normal stress in the direction; This refers to the unit pressure exerted by the rolls on the workpiece. The bite angle at the contact point between the roll and the workpiece; This refers to the frictional shear stress at the contact surface between the roll and the workpiece; The equivalent bite angle after the change in the motion state of the rolled piece; For the rolled piece in Rolling speed in the direction.

[0096] This invention introduces the vertical movement speed of the rolled piece. The construction of a dynamic static equilibrium equation set solves the problem that existing technologies are based solely on quasi-static assumptions ( Establishing a force balance model cannot accurately describe the rolling force distribution when the workpiece vibrates. This invention utilizes geometric relationships to represent the vertical velocity of the workpiece. With rolling speed The ratio introduces the bite angle The revision defines the equivalent bite angle. ( Based on this, differentiated static equilibrium equations (Equations 35-37) covering three working conditions: static, thinning, and thickening. Therefore, this invention extends the rolling mechanics model from static to dynamic, enabling accurate calculation of unit pressure when the rolled workpiece vibrates. The distribution provides an accurate mechanical theoretical basis for analyzing thickness control.

[0097] In one feasible embodiment, step S52 includes: In the elastic deformation region, the material deformation is constructed to obey Hooke's law by the following equation (38): (38) in: The reduction rate in the thickness direction of the rolled piece; Hooke's law, combined with the static equilibrium equation, yields the rolling pressure in the inlet elastic compression zone and the outlet elastic recovery zone using equations (39) and (40): (39) (40) in: The rolling pressure is the rolling pressure of the micro-element within the elastic deformation zone; a positive sign indicates the forward slip zone, and a negative sign indicates the backward slip zone. Indicates the first The comprehensive relationship between the elastic strain and friction of a micro-element; For the first The reduction rate of an individual element in the thickness direction; For the first Frictional shear stress at a micro-element; Indicates the first The relationship between the elastic strain and contact angle of a micro-element.

[0098] This invention addresses the problem in existing technologies that often neglect the stress-strain relationship during the elastic deformation stage, leading to inaccurate calculations of rolling pressure in the inlet compression zone and outlet recovery zone. This is achieved by establishing a mechanical model of the elastic deformation zone based on Hooke's law. Firstly, this invention utilizes the generalized Hooke's law (Equation 38) to construct the thickness-direction reduction ratio. With unit pressure and normal stress Based on the physical relationship and combining it with the aforementioned static equilibrium relationship considering lateral velocity, a recursive formula for rolling pressure applicable to the elastic deformation zone is derived (Formulas 39 and 40). This invention innovatively introduces a factor incorporating frictional shear stress. With contact angle (and its correction value) The comprehensive coefficient of ) and This invention enables precise analysis of the stress state in the elastic zone. Therefore, it can accurately calculate the pressure distribution in the elastic deformation zones at the inlet and outlet of the rolling process, improve the mechanical model closure of the full deformation zone (elastic zone + plastic zone), and significantly enhance the overall accuracy of rolling force prediction.

[0099] In one feasible embodiment, step S53 includes: In the plastic deformation region, the material deformation conforms to the Tresca yield criterion by the following equation (41): (41) Where: K is the resistance to planar deformation; The Tresca yield criterion, combined with the static equilibrium equations, yields the rolling pressure distribution in the plastic deformation zone using equations (42) and (43): (42) (43) in: This represents the rolling pressure of the micro-element within the plastic deformation zone; a positive sign indicates the forward slip zone, and a negative sign indicates the backward slip zone. For the first Stress influence coefficient within a micro-element; For the first Deformation resistance of individual micro-elements.

[0100] This invention solves the problem that existing technologies struggle to accurately describe the stress state of materials during the plastic flow stage and the influence of mill vibration on rolling pressure by introducing the Tresca yield criterion to construct a stress calculation model for the plastic deformation zone. This invention utilizes the Tresca yield criterion (Equation 41) to establish a unit pressure... Resistance to planar deformation The plastic constitutive relationship between them, and taking into account vibration velocity. The static equilibrium equations affecting the stress are used to derive recursive calculation formulas for rolling pressure in the plastic deformation zone (Formulas 42 and 43). This invention introduces a stress influence coefficient... Deformation resistance Frictional shear stress With bite angle ( and equivalent bite angle By coupling the geometric relationship and friction state of the rolling force model, a precise analysis of the stress distribution in the plastic zone is achieved. Therefore, this invention can accurately calculate the rolling pressure distribution of the workpiece during the plastic deformation stage, and in particular, it can reflect the influence of mill vibration on the stress state in the plastic zone, thereby significantly improving the calculation accuracy and applicability of the rolling force model under complex working conditions.

[0101] Step S6:

[0102] In one feasible embodiment, step S6 includes: The rolling pressure of the micro-element in the inlet elastic compression zone, plastic deformation zone, and outlet elastic recovery zone is integrated respectively, and the dynamic rolling force in the deformation zone is obtained by the following formula (44). The calculation method is as follows: (44) in, It is a dynamic rolling force.

[0103] This invention solves the problem that existing technologies, which typically use simplified average stress methods or empirical formulas to calculate rolling force, often fail to accurately reflect the differences in stress distribution between the entry elastic compression zone, plastic deformation zone, and exit elastic recovery zone of the rolled piece. This invention subdivides the deformation zone into three regions with distinctly different physical properties (…). , , ), respectively, the rolling pressure distribution function of each region's micro-element obtained from the previous steps ( and The integral calculation along the contact arc length is performed (Formula 44). Therefore, this invention achieves accurate synthesis from local stress distribution to macroscopic total rolling force, fully considering the contribution of the elastic deformation zone to the total rolling force and the non-uniformity of stress state in each zone, significantly improving the physical accuracy and engineering application value of dynamic rolling force calculation.

[0104] Step S7:

[0105] In one feasible embodiment, step S7 includes: During the cold rolling process, the rolls will be elastically flattened due to the load. The corrected roll flattening radius is obtained by correcting the effective radius of the flattened roll according to the following formula (45): (45) in: The initial radius of the work roll, R f It is the radius of the roll when it is under load; B This refers to the width of the rolled piece.

[0106] This invention addresses the problem in existing technologies that, when calculating rolling force or setting roll gap, often assume the roll to be a rigid body or use simplified linear elastic formulas, thus neglecting the significant elastic deformation in the roll contact area under high loads that leads to changes in the contact arc length. Based on Hertz contact theory and approximate solutions from elasticity mechanics, this invention establishes the effective radius after roll flattening using formula (45). With initial radius Dynamic rolling force , width of rolled piece and the elastic modulus of the material and thickness variation The nonlinear functional relationship between them. Therefore, the present invention can accurately correct the changes in roll geometry (i.e., flattening radius) caused by high load, thereby more accurately determining the actual contact arc length and geometric parameters of the deformation zone, and thus feeding back to improve the accuracy of rolling force calculation and strip shape control model, especially under large reduction or high stiffness rolling conditions, it has a significant correction effect.

[0107] Step S8:

[0108] In one feasible embodiment, the convergence condition in step S8 is constructed by the following equation (46): (46) in, This is the initial value of the roll flattening radius; To correct the roll flattening radius; This is the error threshold.

[0109] This invention addresses the problem in existing technologies where the lack of a clear iteration stopping criterion leads to insufficient accuracy in calculating rolling force and roll gap, or divergence and low computational efficiency during iteration, by constructing a convergence criterion based on the relative error of the roll flattening radius. This invention utilizes formula (46) to monitor the corrected roll flattening radius calculated in the current iteration step. Compared to the initial value (or the value from the previous iteration) The relative deviation between them, when the absolute value of the deviation is less than the preset error threshold. When the system reaches a self-consistent equilibrium in terms of mechanical and geometric states, the calculation stops. Therefore, this invention ensures that the coupled solution between the roll elastic flattening calculation and the rolling force model has strict mathematical convergence, avoiding resource waste caused by excessive iteration and ensuring that the final output rolling parameters meet high-precision engineering requirements.

[0110] The dynamic rolling force analysis method for the elastoplastic deformation process of cold continuous rolling provided by this invention calculates the lengths of the inlet elastic compression zone and the outlet elastic recovery zone based on the elastic deformation theory, and solves the rolling force in the elastoplastic zone by combining the Kalman differential equation, which can effectively improve the accuracy of rolling force calculation.

[0111] This invention introduces the influence of the roll motion state on the dynamic parameters of the deformation zone based on the Kalman differential equation, and extends the original steady-state rolling force calculation formula into a dynamic rolling force calculation formula, making the calculation method more widely applicable.

[0112] Unlike traditional methods that use Coulomb's law of friction to calculate frictional stress at various points on the rolling interface, this invention combines unsteady lubrication theory, which can fully consider the physical and chemical properties of lubricating oil and the time-varying characteristics of lubrication state, and can more realistically reflect the frictional changes at the rolling interface.

[0113] This invention can not only improve the calculation accuracy of rolling force in the steady-state rolling stage, but also improve the calculation accuracy of rolling force in the unsteady-state rolling stage such as acceleration / deceleration and vibration, providing a strong guarantee for the control of product thickness accuracy.

[0114] In one specific embodiment, the dynamic rolling force analysis method described in this invention is used to predict the rolling force of each stand in a 1450mm UCM six-high five-stand cold continuous rolling mill in a certain factory. All the mill rolls are flat rolls. The process parameters collected in step S1 are shown in Table 1 below, the lubricating oil parameters are shown in Table 2 below, the workpiece parameters are shown in Table 3 below, and the roll parameters are shown in Table 4 below. Table 1

[0115] Table 2

[0116] Table 3

[0117] Table 4

[0118] Table 5 shows a comparison between the predicted rolling force of this invention, the predicted value of the existing Hill formula, the predicted value of the existing finite element model, and the measured value of the rolling force. Table 5

[0119] As can be seen from the table above, the predicted value of the cold rolling force of Q195 steel strip by the dynamic rolling force analysis method described in this invention has an error of less than ±3% compared with the measured rolling force, demonstrating high accuracy. Furthermore, while finite element model calculations can take several or even tens of hours to produce a single result, this invention only requires a few seconds, significantly saving time and enabling online processing.

[0120] Figure 4 This is a schematic block diagram of an embodiment of the dynamic rolling force analysis system for the elasto-plastic deformation process in cold continuous rolling described in this invention, as shown below. Figure 4 As shown, the dynamic rolling force analysis system 10 includes: The data acquisition unit 1 is configured to acquire process parameters, workpiece parameters, and roll parameters of the cold continuous rolling production line. The first analysis unit 2 is configured to analyze the roll motion state and deformation zone dynamic parameters. Using the process parameters, workpiece parameters, and roll parameters collected by the acquisition unit 1, it obtains the roll running state and deformation zone dynamic parameters based on the geometric kinematic relationship between the roll and the workpiece, the amount of elastic deformation, and the geometric properties of the roll. The roll motion state includes ordinary rolling, thickening rolling, and thinning rolling. The deformation zone includes an inlet elastic compression zone, a plastic deformation zone, and an outlet elastic recovery zone. The deformation zone dynamic parameters include the outlet thickness and inlet thickness of each region of the deformation zone, the contact arc length, and the contact angle. The second analysis unit 3 is configured to analyze the dynamic parameters of micro-elements. It discretizes the deformation zone into multiple micro-elements along the rolling direction and obtains the dynamic parameters of each micro-element using the dynamic parameters of the deformation zone obtained by the first analysis unit 2. The dynamic parameters of the micro-element include average thickness, deformation resistance, horizontal movement speed and neutral angle. The third analysis unit 4 is configured to analyze the frictional stress distribution in the deformation zone. Based on the mixed lubrication theory, it analyzes the frictional stress distribution in the deformation zone by using the process parameters collected by the acquisition unit 1 and the dynamic parameters of the deformation zone obtained by the first analysis unit. The fourth analysis unit 5 is configured to analyze rolling pressure. It uses the roll motion state obtained by the first analysis unit 2 and the neutral angle obtained by the second analysis unit 3, combined with the friction stress distribution in the deformation zone obtained by the third analysis unit 4, to analyze the rolling pressure of the micro-elements in each region of the deformation zone. The fifth analysis unit 6 is configured to analyze the dynamic rolling force by integrating the rolling pressure obtained from the fourth analysis unit 5 within the deformation zone to obtain the dynamic rolling force. The correction unit 7 is configured to correct the roll flattening radius of the first analysis unit 2 based on the coupling relationship between the dynamic rolling force and the roll flattening radius obtained by the fifth analysis unit 6, and obtain the corrected roll flattening radius. The judgment unit 8 is configured to determine whether the corrected roll flattening radius obtained by the correction unit 7 meets the convergence condition; if the convergence condition is met, the dynamic rolling force that meets the convergence condition is output; if the convergence condition is not met, the roll flattening radius adjustment signal is sent to the first analysis unit 2, and the initial value of the roll flattening radius is set to the corrected roll flattening radius obtained by the correction unit.

[0121] In one feasible embodiment, the first analysis unit 2 includes: The roll motion state analysis module 21 is configured to analyze the roll gap change speed and analyze the roll motion state based on the change speed and change direction. The deformation zone dynamic parameter analysis module 22 is configured to obtain the deformation zone dynamic parameters corresponding to the roll motion state obtained by the roll motion state analysis module 21 based on process parameters, workpiece parameters, and roll parameters.

[0122] This invention addresses the problem of existing technologies that rely solely on steady-state assumptions for deformation zone calculations, failing to effectively characterize the instantaneous impact of dynamic roll adjustments (such as rapid roll gap changes) on the physical field of the deformation zone. By constructing a coupled analysis architecture of "motion state - dynamic parameters," this invention first utilizes the roll motion state analysis module 21 to calculate the speed and direction of roll gap changes in real time, establishing the dynamic kinematic characteristics of the roll. Then, the deformation zone dynamic parameter analysis module 22 uses these kinematic characteristics as boundary conditions or input variables, combined with process, workpiece, and roll parameters, to dynamically derive and update key physical parameters within the deformation zone. Therefore, this invention achieves a leap from static geometric calculation to dynamic process simulation, accurately capturing the transient changes in deformation zone parameters caused by roll motion during rolling, significantly improving the system's control accuracy and response capability for dynamic rolling processes (such as acceleration / deceleration and variable specification transitions).

[0123] In one feasible embodiment, the roll motion state analysis module 21 includes: The roll gap change rate acquisition unit 211 is configured to acquire the roll gap change rate based on the change of the actual roll gap value over time. The judgment unit 212 is configured to compare the roll gap change rate obtained by the roll gap change rate acquisition unit 211 with 0; if the roll gap change rate is equal to 0, the roll motion state is judged to be ordinary rolling state; if the roll gap change rate is greater than 0, the roll motion state is judged to be thickening rolling state; if the roll gap change rate is less than 0, the roll motion state is judged to be thinning rolling state.

[0124] This invention solves the problem in existing technologies of difficulty in accurately distinguishing the operating modes of rolling mills in different dynamic adjustment stages (such as constant speed rolling and variable thickness rolling) by establishing a discretized state recognition mechanism based on the sign of roll gap change speed. This results in a single control strategy and poor adaptability. The invention utilizes a roll gap change speed acquisition unit 211 to perform time differentiation on the actual roll gap value to obtain a speed signal. A judgment unit 212 then logically compares this speed value with a zero threshold, mapping the continuous physical motion process into three distinct discrete states: speed equal to 0 corresponds to normal rolling (steady state), speed greater than 0 corresponds to thickening rolling (roll gap increasing), and speed less than 0 corresponds to thinning rolling (roll gap decreasing). Therefore, this invention provides a clear basis for subsequent dynamic parameter calculations, enabling the system to automatically switch calculation models or control logic according to the actual movement trend of the rolls, significantly improving the identification ability and control targeting of the variable working condition rolling process.

[0125] In one feasible embodiment, the dynamic parameter analysis module 22 of the deformation zone includes: The bite angle increment obtaining unit 221 is configured to obtain the bite angle increment based on the geometric relationship of the deformation zone; The plastic deformation zone analysis unit 222 is configured to obtain the bite angle increment obtained by unit 221 based on the workpiece exit thickness, inlet thickness, front tension, back tension, workpiece grade and bite angle increment, and to obtain the plastic deformation zone exit thickness and plastic deformation zone inlet thickness by combining Hooke's law. The contact arc length analysis unit 223 is configured to obtain the contact arc length of each region based on the roll radius, actual roll gap value, workpiece thickness and bite angle increment, combined with the roll motion state, through geometric relationships. The contact angle analysis unit 224 is configured to obtain the contact angle of each region based on the roll radius, actual roll gap value, workpiece thickness, exit elastic recovery amount, and bite angle increment, combined with the roll motion state, through geometric relationships.

[0126] This invention addresses the problem in existing technologies where the calculation of geometric and physical parameters of the deformation zone is often based on steady-state assumptions and cannot accurately reflect the instantaneous impact of dynamic changes in the roll gap on the geometric boundaries and thickness distribution of each sub-region (elastic compression zone, plastic deformation zone, and elastic recovery zone). This is achieved by introducing the bite angle increment as a core coupling variable and combining it with the laws of material mechanics and kinematic states. The invention establishes a dynamic geometric benchmark using the bite angle increment acquisition unit 221, accurately calculates the inlet and outlet thickness of the plastic zone using the plastic deformation zone analysis unit 222 in conjunction with Hooke's law and tension and material parameters, and then deeply couples the roll motion state with the geometric relationship using the contact arc length analysis unit 223 and the contact angle analysis unit 224 to dynamically derive the contact arc length and contact angle of each sub-region. Therefore, this invention achieves a refined reconstruction of the geometric morphology of the deformation zone during dynamic rolling, ensuring the physical accuracy of the calculation of contact arc length, deformation zone range, and thickness distribution under varying roll gap conditions (thickening or thinning), providing reliable geometric boundary conditions for subsequent high-precision rolling force models.

[0127] In one feasible embodiment, the second analysis unit 3 includes: Discretization module 31 is configured to discretize the deformation zone into multiple parts along the rolling direction to form multiple micro-elements; The micro-element analysis module 32 is configured to analyze the average thickness, deformation resistance and horizontal motion speed of each micro-element formed by the discrete processing module based on the dynamic parameters and process parameters of the deformation zone. The section analysis module 33 is configured to analyze the horizontal movement velocity of the workpiece at any section of each micro-element based on the workpiece inlet thickness, workpiece inlet velocity, deformation zone length, section position and workpiece thickness at the section obtained by the micro-element analysis module, combined with the law of volume invariance. The neutral angle acquisition module 34 is configured to determine the position of the neutral surface based on the horizontal movement speed of the rolled piece at any cross section of each micro-element obtained by the cross section analysis module, and to calculate the neutral angle.

[0128] This invention solves the problem that existing technologies, which typically use global averaging or empirical formulas to estimate the neutral angle, struggle to accurately describe the nonlinear distribution of metal flow velocity along the rolling direction and the dynamic drift of the neutral plane within the deformation zone. This is achieved by constructing a dynamic velocity field analysis model based on the discretization of micro-elements and the law of volume invariance. The invention utilizes a discretization module 31 to transform the continuous deformation zone into multiple micro-elements. A micro-element analysis module 32 obtains local deformation resistance and thickness parameters. A section analysis module 33 then establishes a functional relationship between position and horizontal velocity based on the law of volume invariance (the principle of constant flow rate), accurately calculating the velocity of any section. Finally, a neutral angle acquisition module 34 locks the neutral plane position and calculates the neutral angle based on velocity field characteristics (such as the velocity difference between the front and rear sliding zones). Therefore, this invention achieves a refined description of the plastic flow behavior of metal within the deformation zone, dynamically tracks real-time changes in the neutral angle, significantly improves the accuracy of frictional stress distribution and rolling torque calculation, and provides a solid physical model support for high-precision plate shape and thickness control.

[0129] In one feasible embodiment, the third analysis unit 4 includes: Roughness analysis module 41 is configured to analyze the real-time roughness of the work roll based on workpiece parameters and roll parameters; Oil film thickness analysis module 42 is configured to analyze dynamic inlet oil film thickness based on process parameters; The deformation zone friction stress distribution module 43 is configured to calculate the friction stress distribution in the deformation zone based on the real-time roughness obtained by the roughness analysis module, the dynamic inlet oil film thickness obtained by the oil film thickness analysis module, and the roughness distribution assumptions.

[0130] This invention addresses the problem of nonlinear frictional stress distribution caused by the evolution of surface roughness and dynamic changes in the lubricating oil film during rolling, which is often addressed by constructing a multi-physics coupled model of "surface morphology-lubrication state-friction behavior." This model, which often employs a constant friction coefficient or simplified friction model, fails to accurately reflect the nonlinear distribution of frictional stress caused by the evolution of surface roughness and dynamic changes in the lubricating oil film during rolling. The invention utilizes a roughness analysis module 41 to capture the microscopic morphological features of the contact surface between the roll and the workpiece in real time. Combined with the dynamic inlet oil film thickness calculated based on process parameters by the oil film thickness analysis module 42, and introducing a roughness distribution assumption in the deformation zone frictional stress distribution module 43, the invention integrates microscopic contact mechanics with fluid lubrication theory to dynamically calculate the local frictional stress distribution at various locations within the deformation zone. Therefore, this invention achieves a refined description of frictional behavior under mixed lubrication conditions, accurately characterizing the spatiotemporal variation of the friction coefficient during rolling. This significantly improves the calculation accuracy and applicability of rolling force prediction and strip shape control models under complex lubrication conditions such as high-speed, thin strip rolling.

[0131] In one feasible embodiment, the fourth analysis unit 5 includes: The static equilibrium equation construction module 51 is configured to construct static equilibrium equations for each micro-element in the deformation zone along the rolling direction. The rolling force analysis module 52 is configured to obtain the rolling pressure distribution in the inlet elastic compression zone and the outlet elastic recovery zone based on Hooke's law and the static equilibrium equation construction module; and to obtain the rolling pressure distribution in the plastic deformation zone based on the static equilibrium equation construction module and the static equilibrium equation construction module for the plastic deformation zone.

[0132] This invention solves the problem that existing technologies, which typically use simplified average unit pressure formulas or single plasticity models, cannot accurately describe the differences in stress state and local mechanical behavior of the rolled piece at each stage of elastic compression, plastic deformation, and elastic recovery at the inlet, by constructing a piecewise coupled calculation model based on the static equilibrium equation of a micro-element and the constitutive law of materials. The invention utilizes the static equilibrium equation construction module 51 to perform mechanical slice analysis on the micro-element in the deformation zone, establishing the force equilibrium differential equation along the rolling direction. Then, the rolling force analysis module 52 introduces Hooke's law (for the elastic compression zone at the inlet and elastic recovery zone at the outlet) and Tresca's yield criterion (for the plastic deformation zone) as constitutive relations according to the physical properties of different regions, solving the rolling pressure distribution function for each region. Therefore, this invention achieves refined analysis of the stress state of the entire deformation zone (elastic + plastic + elastic), eliminating the theoretical blind spot in the calculation of the elastic zone using traditional methods, and significantly improving the physical accuracy of rolling pressure distribution prediction and the overall accuracy of rolling force calculation.

[0133] Figure 5 This diagram illustrates an application scenario of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described in this invention.

[0134] exist Figure 5In the application scenario, the computing device 100 collects the process parameters 101, workpiece parameters 102, and roll parameters 103 of cold continuous rolling. Then, based on the process parameters, workpiece parameters, and roll parameters, the computing device 100 obtains the roll motion state 104 and the corresponding dynamic parameters 105 of the deformation zone according to the geometric kinematic relationship between the roll and the workpiece, the elastic deformation amount, and the geometric properties of the roll. Based on the deformation zone dynamics 105, the computing device 100 obtains the dynamic parameters 106 of each micro-element. Subsequently, based on the mixed lubrication theory, the computing device 100 analyzes the frictional stress distribution 107 of the deformation zone using the process parameters and the dynamic parameters of the deformation zone. It also establishes static equilibrium equations for the discrete micro-elements of the deformation zone along the rolling direction using the dynamic parameters of the micro-elements and the frictional stress distribution of the deformation zone. Combining the constitutive relations of materials in different regions, the computing device 100 analyzes the rolling pressure of the micro-elements in each region of the deformation zone using the roll motion state and the neutral angle. Through integration, the dynamic rolling force 108 is obtained. Finally, the calculation device 100 corrects the roll flattening radius based on the dynamic rolling force 108, and obtains the corrected roll flattening radius that meets the convergence condition through iteration by the convergence condition, thereby obtaining the dynamic rolling force that meets the convergence condition.

[0135] This invention addresses the problem in existing rolling force models that often isolate or simplify geometry, friction, and material mechanics, leading to insufficient calculation accuracy under dynamic and variable working conditions. It constructs a full-process, multi-physics coupled iterative calculation framework. Based on collected multi-source parameters, this invention first determines the roll motion state and dynamic parameters of the deformation zone through geometric kinematics and elasticity analysis, then discretizes the deformation zone into micro-elements. On this basis, it integrates hybrid lubrication theory to accurately calculate the frictional stress distribution, and combines neutral angle analysis to establish static equilibrium equations for micro-elements in different regions (elastic / plastic), using appropriate material constitutive relations (such as Hooke's law and Tresca yield criterion) to solve for the rolling pressure distribution. Finally, it obtains the dynamic rolling force through integration and uses this force to reverse-correct the roll flattening radius, forming a closed-loop iteration until the convergence condition is met. Therefore, this invention achieves high-fidelity simulation of the dynamic rolling process, deeply coupling and self-consistently solving multiple key physical processes such as geometric deformation, friction and lubrication, material nonlinearity and roll elastic deformation, thereby significantly improving the prediction accuracy of dynamic rolling force and the robustness of the model, and providing a reliable theoretical model and calculation basis for high-precision plate shape and thickness control.

[0136] It should be noted that the aforementioned computing device 100 can be either hardware or software. When the computing device 100 is hardware, it can be implemented as a distributed cluster consisting of multiple servers or terminal devices, or as a single server or a single terminal device. When the computing device 100 is software, it can be installed in the hardware devices listed above. It can be implemented as, for example, multiple software programs or software modules used to provide distributed services, or as a single software program or software module. No specific limitations are made here.

[0137] Figure 6 This diagram illustrates another application scenario of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described in this invention.

[0138] exist Figure 6 In the application scenario, the components of the computing device 100 include, but are not limited to, a memory 110 and a processor 120. The processor 120 is connected to the memory 110 via a bus 130, and may also include a database 150 for storing data.

[0139] The computing device 100 also includes an access device 140 that enables the computing device 100 to communicate via one or more networks 160. Examples of these networks include Public Switched Telephone Network (PSTN), Local Area Network (LAN), Wide Area Network (WAN), Personal Area Network (PAN), or combinations of communication networks such as the Internet. The access device may include one or more of any type of wired or wireless network interface (e.g., a network interface controller (NIC)), such as a Wireless Local Area Network (WLAN) interface, a Wi-MAX (Worldwide Interoperability for Microwave Access) interface, an Ethernet interface, a Universal Serial Bus (USB) interface, a cellular network interface, a Bluetooth interface, or a Near Field Communication (NFC) interface.

[0140] In one embodiment of the present invention, the above-mentioned components of the computing device 100 and Figure 6 Other components, not shown, can also be connected to each other, for example, via a bus. It should be understood that... Figure 6The structural block diagram of the computing device 100 shown is for illustrative purposes only and is not intended to limit the scope of the invention. Those skilled in the art can add or replace other components as needed.

[0141] The computing device 100 can be any type of stationary or mobile computing device 100, including mobile computers or mobile computing devices 100 (e.g., tablet computers, personal digital assistants, laptop computers, notebook computers, netbooks, etc.), mobile phones (e.g., smartphones), wearable computing devices 100 (e.g., smartwatches, smart glasses, etc.) or other types of mobile devices, or stationary computing devices 100 such as desktop computers or personal computers (PCs). The computing device 100 can also be a mobile or stationary server.

[0142] The processor executes computer-executable instructions, which, when executed by the processor, implement the steps of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described above. The above is a schematic representation of a computing device 100 according to this embodiment. It should be noted that the technical solution of this computing device 100 and the technical solution of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described above belong to the same concept. Details not described in detail in the technical solution of the computing device 100 can be found in the description of the technical solution of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process described above.

[0143] The present invention also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of the above-described dynamic rolling force analysis method for the elastoplastic deformation process of cold continuous rolling.

[0144] The above is an illustrative scheme of the computer-readable storage medium described in this invention. It should be noted that the technical solution of this storage medium belongs to the same concept as the technical solution of the above-described dynamic rolling force analysis method for the elasto-plastic deformation process of cold continuous rolling. Details not described in detail in the technical solution of the storage medium can be found in the description of the technical solution of the above-described dynamic rolling force analysis method for the elasto-plastic deformation process of cold continuous rolling.

[0145] The present invention also provides a computer program, wherein when the computer program is executed in a computer, the computer is instructed to perform the steps of the above-described dynamic rolling force analysis method for the elastoplastic deformation process of cold continuous rolling.

[0146] The above is an illustrative scheme of the computer program described in this invention. It should be noted that the technical solution of this computer program belongs to the same concept as the technical solution of the aforementioned dynamic rolling force analysis method for the elastoplastic deformation process of cold continuous rolling. Details not described in detail in the computer program's technical solution can be found in the description of the aforementioned technical solution for the dynamic rolling force analysis method for the elastoplastic deformation process of cold continuous rolling.

[0147] This invention solves the problem that existing high-precision physical models, due to their massive computational load and complex logic, are difficult to implement in real-time online applications and achieve rapid response in industrial settings by encapsulating the aforementioned complex dynamic rolling force analysis algorithm (covering micro-element discretization, multi-physics coupling, and iterative convergence mechanisms) into computer-executable instructions and embedding them in a computing device. This invention utilizes the collaborative work of the processor and memory, efficiently transmits data via a bus, and combines diverse access devices (such as network interfaces and wireless modules) to achieve real-time communication with the rolling mill control system or cloud database. It transforms the abstract mathematical model into a concrete hardware execution process, enabling automatic parameter acquisition, iterative calculation, and output of corrected dynamic rolling force. Therefore, this invention achieves automated, digital, and intelligent deployment of the dynamic rolling force analysis method for cold continuous rolling mills. It not only significantly improves computational efficiency and the engineering practicality of the model but also flexibly adapts to various hardware environments, from portable terminals to industrial servers, ensuring that high-precision rolling force prediction technology can truly be implemented to serve real-time quality control and process optimization on the production line.

[0148] The foregoing has described specific embodiments of the invention. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired results. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0149] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the embodiments of the present invention.

[0150] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0151] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. The optional embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the embodiments of the present invention. These embodiments are selected and specifically described to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention.

Claims

1. A method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling, characterized in that, include: Data acquisition steps: Collect process parameters, workpiece parameters, and roll parameters of the cold continuous rolling production line. The process parameters are parameters that characterize the dynamic operating state and boundary load conditions of the rolling process. The rolling parameters are parameters used to characterize the initial geometry and intrinsic mechanical properties of the rolled material; The roll parameters are parameters used to establish the contact geometry characteristics of the deformation zone and the basis of the elastic response of the roll system; Steps for analyzing the motion state and dynamic parameters of the deformation zone of the rolls: Determine the motion state of the rolls based on whether the roll gap changes and the direction of change; Based on the initial value of the roll flattening radius, dynamic parameters of the deformation zone corresponding to the roll motion state are obtained using process parameters, workpiece parameters, and roll parameters, according to the geometric kinematic relationship between the roll and the workpiece, the amount of elastic deformation, and the geometric properties of the roll. The roll motion states include ordinary rolling, thickening rolling, and thinning rolling. The deformation zone includes an inlet elastic compression zone, a plastic deformation zone, and an outlet elastic recovery zone. The dynamic parameters of the deformation zone include the outlet thickness and inlet thickness, contact arc length, and contact angle of each region of the deformation zone. Steps for analyzing the dynamic parameters of micro-element: Discretize the deformation zone into multiple micro-elements along the rolling direction. Based on the parabolic geometric approximation of the workpiece thickness along the roll gap, the law of constant volume, and the kinematic coordination condition that the workpiece speed and the roll linear speed are equal at the neutral point, obtain the dynamic parameters of each micro-element using the dynamic parameters of the deformation zone. The dynamic parameters of the micro-element include average thickness, deformation resistance, horizontal motion speed, and neutral angle. Steps for analyzing the frictional stress distribution in the deformation zone: Based on the mixed lubrication theory, analyze the frictional stress distribution in the deformation zone using process parameters and dynamic parameters of the deformation zone; Rolling pressure analysis steps: Using the dynamic parameters of the micro-element and the frictional stress distribution in the deformation zone, establish static equilibrium equations for the discrete micro-element in the deformation zone along the rolling direction. Combine the constitutive relations of materials in different regions and analyze the rolling pressure of the micro-element in each region of the deformation zone using the roll motion state and neutral angle. Dynamic rolling force analysis steps: Integrate the rolling pressure within the deformation zone to obtain the dynamic rolling force; The roll flattening radius correction steps are as follows: Based on the coupling relationship between dynamic rolling force and roll flattening radius, the roll flattening radius is corrected to obtain the corrected roll flattening radius; Convergence judgment steps: Determine whether the flattening radius of the corrected roll meets the convergence condition; If the convergence condition is not met, set the initial value of the roll flattening radius to the corrected roll flattening radius, return to the roll motion state and deformation zone dynamic parameter analysis step, and re-analyze the roll gap change rate and deformation zone dynamic parameters.

2. The method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling according to claim 1, characterized in that, The analysis steps for the roll motion state and dynamic parameters of the deformation zone include: Calculate the rate of change of the roll gap; The motion state of the rolls is determined by whether the speed of change of the roll gap changes and the direction of change. The dynamic parameters of the deformation zone corresponding to the roll motion state are obtained based on process parameters, workpiece parameters, and roll parameters.

3. The method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling according to claim 2, characterized in that, The steps for determining the roll motion state based on whether the roll gap change speed and the direction of change include: The roll gap change rate is analyzed using a backward difference method based on the actual roll gap value; Or / and, the step of determining the roll motion state based on whether the roll gap change speed changes and the direction of change includes: The motion state of the roll is determined based on the magnitude of the change rate of the roll gap relative to 0. Or / and, the step of obtaining the dynamic parameters of the deformation zone corresponding to the roll motion state based on process parameters, workpiece parameters, and roll parameters includes: The bite angle increment is obtained based on the geometric relationship of the deformation zone; Based on the exit thickness, inlet thickness, front tension, back tension, workpiece grade, and bite angle increment, and combined with Hooke's law, the exit thickness and inlet thickness of the plastic deformation zone are obtained. The contact arc length of each region is obtained based on the outlet thickness of the rolled piece, the inlet thickness of the rolled piece, the outlet thickness of the plastic deformation zone, and the inlet thickness of the plastic deformation zone. The contact angles of each region are obtained based on the thickness of the rolled piece exit, the thickness of the rolled piece inlet, the thickness of the plastic deformation zone exit, and the thickness of the plastic deformation zone inlet.

4. The method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling according to claim 1, characterized in that, The steps for analyzing the frictional stress distribution in the deformation zone include: Analyze the real-time roughness of the work roll based on the parameters of the rolled piece and the roll parameters; Dynamic inlet oil film thickness analysis based on process parameters; Based on the assumptions of real-time roughness, dynamic inlet oil film thickness, and roughness distribution, the frictional stress distribution in the deformation zone is calculated.

5. The method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling according to claim 1, characterized in that, The rolling pressure analysis step includes: Discretization step: The deformation zone is discretized into multiple parts along the rolling direction to form multiple micro-elements; Micro-element analysis steps: Analyze the average thickness, deformation resistance, and horizontal movement speed of each micro-element based on the dynamic parameters and process parameters of the deformation zone; Steps for analyzing the horizontal velocity of the rolled piece: Based on the entry thickness of the rolled piece, the entry velocity of the rolled piece, the length of the deformation zone, the position of the cross section, and the thickness of the rolled piece at the cross section, and in conjunction with the law of constant volume, analyze the horizontal velocity of the rolled piece at any cross section; Neutral angle analysis steps: Determine the position of the neutral plane based on the horizontal movement speed of the rolled piece, and obtain the neutral angle.

6. The method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling according to claim 5, characterized in that, The micro-element analysis steps include: Based on the parabolic form of the workpiece thickness in the roll gap, the inlet and outlet thicknesses of each micro-element are obtained. The average thickness of each micro-element is obtained based on the inlet and outlet thicknesses of the micro-element. Based on the average thickness of each micro-element, the average deformation resistance of each micro-element is obtained by combining the strip material with the deformation resistance model.

7. The method for dynamic rolling force analysis during the elastoplastic deformation process of cold continuous rolling according to claim 1, characterized in that, The rolling pressure analysis step includes: Static equilibrium equations are constructed for the micro-elements in each region of the deformation zone along the rolling direction. Based on Hooke's law, the rolling pressure distribution in the inlet elastic compression zone and the outlet elastic recovery zone is obtained by using the static equilibrium relationship equation between the inlet elastic compression zone and the outlet elastic recovery zone. The rolling pressure distribution in the plastic deformation zone is obtained by using the static equilibrium equation of the plastic deformation zone based on the Tresca yield criterion. Or / and, the convergence condition is that the error rate of the corrected roll flattening radius relative to the initial value of the roll flattening radius is not greater than a set error threshold.

8. A dynamic rolling force analysis system for the elastoplastic deformation process of cold continuous rolling, characterized in that, include: The data acquisition unit is configured to collect process parameters, workpiece parameters, and roll parameters of the cold continuous rolling production line. The first analysis unit is configured to analyze the roll motion state and deformation zone dynamic parameters. Using process parameters, workpiece parameters, and roll parameters acquired by the acquisition unit, it obtains the roll running state and deformation zone dynamic parameters based on the geometric kinematic relationship between the roll and the workpiece, the amount of elastic deformation, and the geometric properties of the roll. The roll motion state includes ordinary rolling, thickening rolling, and thinning rolling. The deformation zone includes an inlet elastic compression zone, a plastic deformation zone, and an outlet elastic recovery zone. The deformation zone dynamic parameters include the outlet thickness and inlet thickness of each region of the deformation zone, the contact arc length, and the contact angle. The second analysis unit is configured to analyze the dynamic parameters of the micro-element. It discretizes the deformation zone into multiple micro-elements along the rolling direction and obtains the dynamic parameters of each micro-element using the dynamic parameters of the deformation zone obtained by the first analysis unit. The dynamic parameters of the micro-element include average thickness, deformation resistance, horizontal movement speed and neutral angle. The third analysis unit is configured to analyze the frictional stress distribution in the deformation zone. Based on the mixed lubrication theory, it analyzes the frictional stress distribution in the deformation zone by using the process parameters collected by the acquisition unit and the dynamic parameters of the deformation zone obtained by the first analysis unit. The fourth analysis unit is configured to analyze rolling pressure. It uses the roll motion state obtained from the first analysis unit, the neutral angle obtained from the second analysis unit, and the friction stress distribution in the deformation zone obtained from the third analysis unit to analyze the rolling pressure of the micro-elements in each region of the deformation zone. The fifth analysis section is configured to analyze the dynamic rolling force by integrating the rolling pressure obtained from the fourth analysis section within the deformation zone to obtain the dynamic rolling force. The correction unit is configured to correct the roll flattening radius of the first analysis unit based on the coupling relationship between the dynamic rolling force and the roll flattening radius obtained by the fifth analysis unit, thereby obtaining a corrected roll flattening radius. The judgment unit is configured to determine whether the corrected roll flattening radius obtained by the correction unit meets the convergence condition; if the convergence condition is met, the dynamic rolling force that meets the convergence condition is output. If the convergence condition is not met, a roll flattening radius adjustment signal is sent to the first analysis unit, and the initial value of the roll flattening radius is set to the corrected roll flattening radius obtained by the correction unit.

9. A dynamic rolling force analysis device for the elastoplastic deformation process of cold continuous rolling, characterized in that, The dynamic rolling force analysis device for the cold continuous rolling elastic-plastic deformation process is a computing device, which includes: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the dynamic rolling force analysis method for the cold continuous rolling elastic-plastic deformation process according to any one of claims 1 to 7.

10. A dynamic rolling force analysis device for the elastoplastic deformation process of cold continuous rolling, characterized in that, The dynamic rolling force analysis device for the elasto-plastic deformation process of cold continuous rolling is a computer-readable storage medium. The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, implement the steps of the dynamic rolling force analysis method for the elasto-plastic deformation process of cold continuous rolling according to any one of claims 1 to 7.

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