A billet rough rolling and spreading method and system

Abstract

The present application relates to the technical field of steel metallurgy and metal rolling, in particular to a billet rough rolling and spreading method and system, comprising: a step of constructing a non-uniform deformation zone geometry: configuring a special-shaped pass based on a flow resistance gradient, and establishing a non-uniform hydrostatic pressure field; a step of executing forced transverse flow deformation induced rolling: forcing the metal to actively migrate in transverse mass from the center to both sides; a step of collecting lateral pressure rheological response data: monitoring width and resistance fluctuations and calculating lateral pressure rheological response lag time; a step of implementing dynamic lateral pressure adaptive control: applying dynamic lateral pressure to the intermediate billet based on the lag time, suppressing overturning instability and correcting the spread; the present application changes the direction of the minimum resistance of metal flow, solves the problem of time and space asynchronization between the system and flow deformation, and ensures the rolling stability of the non-steady state section.

Description

Technical Field

[0001] This invention relates to the field of iron and steel metallurgy and metal rolling technology, specifically to a method and system for widening steel billet rough rolling. Background Technology

[0002] With the increasing demand for wide steel plates in modern manufacturing, the billet widening efficiency in the roughing stage has become a key indicator for measuring production line capacity. How to overcome the natural limitations of metal flow within a limited number of rolling passes to achieve a large-scale width expansion is a technical problem that the metallurgical industry urgently needs to solve.

[0003] Traditional billet roughing and widening processes currently rely mainly on the following methods: flat roll high-reduction rolling, vertical roll side pressing combined with flat roll leveling, and standard box pass rolling. However, flat roll high-reduction, vertical roll side pressing, and standard box pass rolling all have certain drawbacks. For example, flat roll rolling is limited by the law of least resistance, and metal particles tend to extend longitudinally rather than flow laterally, resulting in low widening efficiency. Vertical roll side pressing is prone to forming an unsteady dog-bone cross-section at the end, requiring additional passes for shaping. Standard box pass rolling is difficult to provide sufficient active transverse hydrostatic pressure gradient, which can easily cause billet overturning, instability, or torsion under high-reduction conditions, and it is difficult to solve the problem of time-space asynchrony between the hydraulic system action and the plastic rheology of the metal in high-speed rolling. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention discloses a method and system for widening steel billet rough rolling. Specifically, the technical solution of this invention is as follows: On the one hand, the present invention provides a method for widening steel billet rough rolling, comprising the following steps: A non-uniform deformation zone geometry is constructed. Based on the law of minimum resistance and the rheological resistance gradient, an irregularly shaped die with a differentiated reduction rate distribution is configured. The irregularly shaped die is used to establish a non-uniform hydrostatic pressure field within the rolling gap. Forced transverse rheological induced rolling is performed by feeding the billet into the special-shaped roll pass for pressing and rolling. The non-uniform hydrostatic pressure field forces the metal to undergo active transverse mass migration from the center to both sides, generating an intermediate billet with an unsteady cross section. Side pressure rheological response data are collected, and the width change and deformation resistance fluctuation of the intermediate billet are monitored in real time during the rolling process. The action feedback of the hydraulic system is obtained, and the side pressure rheological response hysteresis time is calculated. Dynamic lateral pressure adaptive control is implemented. Based on the lateral pressure rheological response data and the preset cross-sectional profile filling target, dynamic lateral pressure is applied to the intermediate billet to suppress overturning instability and correct insufficient or excessive width.

[0005] Preferably, the construction of the non-uniform deformation zone geometry, based on the law of minimum resistance and the rheological resistance gradient, involves configuring an irregularly shaped aperture with a differentiated reduction rate distribution, including: The difference in reduction rate between the center and the edge of the deformation zone is determined, and the difference in reduction rate determines the magnitude of the driving force for the central metal to flow to both sides; The butterfly-shaped hole is designed as the irregular hole type, wherein a high-pressure lowering zone is set at the center of the hole type and a low-pressure lowering zone is set on both sides of the hole type, forming a deformable channel that is thin in the middle and thick on both sides. The trapezoidal sidewalls and butterfly protrusions are configured to provide boundary guidance when the metal flows laterally, preventing the metal from twisting or collapsing during forced widening.

[0006] Preferably, the forced transverse rheology-induced rolling process, which involves feeding the billet into the shaped roll pass for reduction rolling, includes: A lateral expansion efficiency coefficient is set, which is the ratio of the actual expansion amount to the theoretical maximum expansion amount under the principle of constant pure volume. The roll speed and reduction are adjusted according to the transverse width efficiency coefficient so that the transverse logarithmic strain of the metal in the die is greater than the longitudinal logarithmic strain. Through continuous extrusion of the irregular hole pattern, the metal is induced to overcome the natural tendency of longitudinal extension, achieving a high width expansion ratio in the lateral direction.

[0007] Preferably, the acquisition of lateral pressure rheological response data, and the real-time monitoring of the width change and deformation resistance fluctuation of the intermediate billet during the rolling process, includes: The real-time width data of the exit section of the intermediate billet is obtained using a laser profiler or a width gauge; By monitoring rolling force and lateral pressure torque using rolling mill sensors, the dynamic distribution of deformation resistance can be identified; The time difference between receiving a command and actually applying pressure in the hydraulic actuator of the hydraulic system is recorded as the mechanical response delay, and the time difference between the moment the pressure is actually applied and the moment when the width data of the intermediate billet changes is measured as the material rheological response delay. The mechanical response delay and the material rheological response delay are added together to obtain the side pressure rheological response hysteresis time.

[0008] Preferably, the implementation of dynamic lateral pressure adaptive control, based on the lateral pressure rheological response data and a preset cross-sectional profile filling target, applies dynamic lateral pressure to the intermediate billet, including: Compare the real-time width data with the preset target width to calculate the width deviation value; The control command used to adjust the lateral pressure is feedforward compensated based on the lateral pressure rheological response hysteresis time to eliminate the impact of system delay on control accuracy; If the width deviation value is greater than the preset positive threshold, the vertical roller or side pressure mechanism is controlled to increase the lateral constraint force to correct the excessive width; If the width deviation value is less than the preset negative threshold, the vertical roller or side pressure mechanism is controlled to reduce the lateral constraint force in order to correct the insufficient width. If the width deviation value is between the negative threshold and the positive threshold, the lateral constraint force remains unchanged.

[0009] Preferably, it also includes a dynamic hardening compensation step under thermo-coupling: Obtain the cross-sectional temperature field distribution of the steel billet and identify the low-temperature region at the corner and the high-temperature region at the center; Calculate the dynamic hardening difference under thermo-coupling and evaluate the limiting effect of the low-temperature corner on the lateral flow of metal in the high-temperature core. The distribution of the center and edge reduction rates of the irregular hole is corrected according to the dynamic hardening difference to prevent internal cracks caused by the mismatch of deformation resistance.

[0010] Preferably, the evaluation and control of the cross-sectional profile filling degree during the implementation of dynamic lateral pressure adaptive control specifically includes: The ratio of the actual metal cross-sectional area at the exit of each pass to the ideal aperture design area is used as the cross-sectional profile filling degree. When the cross-sectional profile fill is lower than the preset lower limit, it is determined to be insufficient width, and the center reduction rate of the next pass is increased; When the cross-sectional profile fills more than the preset upper limit, it is determined to be overfilled or produce ears, and the center reduction rate of the next pass is reduced or the lateral constraint force is increased. When the cross-sectional profile fill is between the preset lower limit and the preset upper limit, the current compression rate and lateral constraint force settings are maintained.

[0011] On the other hand, this aspect provides a billet roughing and widening system, comprising: The geometry configuration building module is used to construct the geometry configuration of non-uniform deformation regions. Based on the law of minimum resistance and rheological resistance gradient, it configures irregular orifice types with differentiated reduction rate distributions. The rolling execution module is used to perform forced transverse rheology-induced rolling, which feeds the billet into the special-shaped die for pressing and rolling, and forces the metal to undergo active transverse mass migration from the center to both sides through a non-uniform hydrostatic pressure field. The data acquisition module is used to collect side pressure rheological response data, monitor the width change and deformation resistance fluctuation of the intermediate billet in real time during the rolling process, and calculate the side pressure rheological response hysteresis time. An adaptive control module is used to implement dynamic lateral pressure adaptive control, which applies dynamic lateral pressure to the intermediate billet based on the lateral pressure rheological response data and a preset cross-sectional profile filling target.

[0012] Preferably, the adaptive control module includes: The deviation calculation unit is used to compare the real-time width data with the preset target width and calculate the width deviation value. The hysteresis compensation unit is used to feedforward compensation of the control command for adjusting the lateral pressure based on the hysteresis time of the lateral pressure rheological response. An adjustment unit is used to adjust the vertical roller or the side pressure mechanism, configured to: increase the lateral constraint force when the width deviation value is greater than a preset positive threshold, decrease the lateral constraint force when the width deviation value is less than a preset negative threshold, and keep the lateral constraint force unchanged when the width deviation value is between the negative threshold and the positive threshold.

[0013] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention establishes a non-uniform hydrostatic pressure field within the rolling gap by constructing a non-uniform deformation zone geometry and configuring irregularly shaped passes with differentiated reduction ratios. This forces the metal to undergo active lateral mass migration from the center to both sides, breaking through the limitation of the law of least resistance on the natural flow of metal and achieving a large proportion of lateral widening within a limited number of passes. At the same time, by performing forced lateral rheological induced rolling to generate intermediate billets with unsteady cross-sections, combined with the boundary guidance of trapezoidal sidewalls and butterfly protrusions, this invention effectively solves the technical problems of low efficiency in traditional rolling and the easy occurrence of overturning instability or torsion during the widening process. 2. This invention decouples the lateral pressure rheological response lag time into mechanical response delay and material rheological response delay by collecting lateral pressure rheological response data, thus clarifying the spatiotemporal relationship between the hydraulic system action feedback and the changes in intermediate billet width and deformation resistance fluctuations. By summing and calculating the mechanical response delay and the material rheological response delay, a reliable time-domain reference is provided for precise control, which can accurately reflect the comprehensive response characteristics including transmission delay and plastic deformation lag. 3. This invention implements dynamic lateral pressure adaptive control, feedforward compensation of the control command used to adjust the lateral pressure based on the lateral pressure rheological response lag time, and applies dynamic lateral pressure to the intermediate billet in combination with the preset cross-sectional profile fullness target; by calculating the width deviation value and performing graded adjustment based on positive and negative thresholds, the influence of system delay on control accuracy is eliminated, ensuring dynamic high-precision control of the width of the intermediate billet during rolling, and effectively correcting the phenomenon of insufficient or excessive width. Attached Figure Description

[0014] Figure 1 This is a flowchart of the method of the present invention.

[0015] Figure 2 This is a system structure diagram of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0017] Example 1: Please see Figure 1 A method for widening a steel billet during rough rolling includes the following steps: constructing a geometric configuration of a non-uniform deformation zone; configuring a special-shaped pass with a differentiated reduction rate distribution based on the law of minimum resistance and the rheological resistance gradient; the special-shaped pass is used to establish a non-uniform hydrostatic pressure field within the rolling gap. Forced transverse rheological induced rolling is performed by feeding the billet into a special-shaped die for roll pressing. The non-uniform hydrostatic pressure field forces the metal to undergo active transverse mass migration from the center to both sides, generating an intermediate billet with an unsteady cross section. Side pressure rheological response data are collected, and the width change and deformation resistance fluctuation of the intermediate billet are monitored in real time during the rolling process. The action feedback of the hydraulic system is obtained, and the side pressure rheological response hysteresis time is calculated. Dynamic lateral pressure adaptive control is implemented. Based on the lateral pressure rheological response data and the preset cross-sectional profile filling target, dynamic lateral pressure is applied to the intermediate billet to suppress overturning instability and correct insufficient or excessive width. This embodiment proposes a method for widening steel billet rough rolling. Its core lies in breaking through the natural limitation of the law of least resistance on the lateral flow of metal in traditional rolling. By constructing a non-uniform deformation field, the widening of metal is actively induced. The system executes the step of constructing the geometric configuration of the non-uniform deformation zone. The non-uniform deformation zone geometric configuration in this step refers to a special spatial geometric configuration that breaks the conventional symmetrical uniform pressing of flat rolls or box-type rolls. Its construction basis follows the principle of rheological resistance gradient. During this process, the system establishes a non-uniform hydrostatic pressure field within the rolling gap through the pass design. Let the hydrostatic pressure at the center of the pass be... The hydrostatic pressure at the edge is This embodiment uses physical geometric constraints to make... Greater than Furthermore, the difference between the two reaches the preset pressure gradient threshold. This pressure gradient constitutes the driving force for the lateral flow of metal, forcing metal particles to migrate laterally in the direction of pressure reduction, rather than the traditional longitudinal extension. The system performs forced lateral rheological induced rolling, feeding the billet into the aforementioned special-shaped die for roll pressing. During this process, the metal not only undergoes plastic deformation, but also undergoes active lateral mass migration from the center to both sides. This process generates an intermediate billet, the cross-section of which is called an unsteady cross-section. That is, the cross-section is in an unsteady transition state where the thickness in the middle is less than the thickness at the two edges, which is intended to provide a material basis for subsequent widening. The system collects lateral pressure rheological response data, which refers to a comprehensive dataset that reflects the temporal and spatial relationship between equipment action and material deformation. During the rolling process, the system monitors the width change of the intermediate billet in real time. With deformation resistance fluctuation Simultaneously, the system acquires feedback signals from the hydraulic system, such as servo valve voltage signals, and calculates the side pressure rheological response hysteresis time based on these data. This is a key parameter for achieving precise control; the system calculates the hysteresis time of the side pressure rheological response. This parameter is the sum of the mechanical system delay and the material's physical response delay: The system implements dynamic side pressure adaptive control, a control strategy that combines feedforward and feedback; based on the calculated lag time... and the preset cross-sectional profile fullness target The system applies dynamic lateral pressure to the intermediate billet. Its control logic focuses not only on the width but also on the shape stability of the cross section, thereby suppressing overturning instability such as collapse and correcting insufficient or excessive width. This embodiment establishes a non-uniform hydrostatic pressure field with a high center and low edges, thereby changing the direction of minimum resistance to metal flow and achieving a large-scale widening within a limited number of passes. At the same time, by introducing rheological response hysteresis calculation, the problem of spatiotemporal asynchrony between the hydraulic servo system and the plastic rheology of the metal under heavy rolling conditions is solved, ensuring the rolling stability of the unsteady section.

[0018] Constructing a non-uniform deformation region geometry, and based on the law of minimum resistance and rheological resistance gradient, configuring irregularly shaped apertures with differentiated reduction rate distributions, including: Determine the reduction rate difference between the center and the edge of the deformation zone. The reduction rate difference determines the magnitude of the driving force for the central metal to split to both sides. The butterfly-shaped hole is designed as an irregular hole type. The butterfly-shaped hole has a high-pressure lowering zone at the center and low-pressure lowering zones on both sides, forming a deformable channel that is thin in the middle and thick on both sides. The trapezoidal sidewalls and butterfly protrusions are configured to provide boundary guidance when the metal flows laterally, preventing the metal from twisting or collapsing during forced widening. This embodiment is a further specification of the geometric configuration of the non-uniform deformation zone; it should be noted that the non-uniform deformation zone geometric configuration mentioned in the title of this embodiment and the irregular hole geometry configuration are equivalent descriptions of the same technical feature. The difference in terminology aims to emphasize the continuous connection characteristics of the deformation zone in space. Both physically refer to the three-dimensional spatial morphology of the irregular hole. The system determines the reduction rate difference. This parameter is the core parameter driving the metal shunting; in this embodiment, the center pressure reduction rate is defined. With edge reduction rate The formula for calculating the difference is as follows: in, This represents the logarithmic strain at the center of the deformation zone; This represents the logarithmic strain at the edge of the deformation zone; The value of this reduction rate difference directly determines the driving force for the central metal to split to both sides. In this embodiment, the difference is set to be greater than 0.15 to ensure that the kinetic energy of the lateral flow is sufficient to overcome frictional resistance; the system is designed with a butterfly-shaped hole as an irregular hole type; in the butterfly-shaped hole structure, a high-pressure zone corresponding to the hole height is set at the center of the hole type. Low-pressure zones are set on both sides of the orifice, corresponding to the orifice height. This creates a deformable channel that is thin in the middle and thick on both sides; To achieve the composite geometric features of trapezoidal sidewalls and butterfly-shaped protrusions, this embodiment constructs a segmented roll gap profile function. A transition algorithm is introduced to ensure overall continuity: definition Using the coordinates of distance from the center along the roller body direction, the die reference profile is divided into a butterfly-shaped protrusion area and a trapezoidal sidewall area: when At that time, the ridge line with a smooth transition is constructed using a sine exponential function, which serves as the reference for the butterfly-shaped protrusion area. in, The center of the hole is The minimum roll gap height at that point represents the extreme value under high pressure in the deformation zone; The edge of the transition zone, i.e. The maximum roll gap height represents the extreme value of low reduction in the deformation zone. Both parameters are based on the preset difference in reduction rate. The dimensions of the inlet billet are calculated in reverse. To ensure that the above reverse calculation has a unique solution, the system pre-sets the central target compression rate. Construct a solution set consisting of two independent equations: First, the center roll gap height is determined based on the target reduction rate at the center: Second, the formula for the difference in reduction rate. Calculate the edge roll gap height: Through the above closed-loop logic, the system uniquely determines the two extreme height parameters required to describe the irregular hole type; The transition zone width is half the width of the billet, taken as 0.85 times the width of the billet. The shape index is taken in this embodiment. To construct an irregular convex shape with high-order curvature features, the profile is geometrically distinct from the standard parabola, aiming to enhance the guiding gradient on both sides of the convex shape, and this region is responsible for constraining the center of the billet; when At that time, the trapezoidal sidewall region reference is used to construct the forced guide wall using a linear function: in, The sidewall slope is set to... This linear segment provides a clear geometric boundary for the lateral flow of metal, preventing it from becoming too wide; Regarding the above piecewise reference function at the intersection point There exists a theoretical derivative discontinuity problem, namely, the slope of the tangent line to the sine function is 0 while the slope of the trapezoidal sidewall is . In order to meet the requirements of smooth metal flow during the rolling process and prevent stress concentration, this embodiment introduces a transition fillet treatment in the physical die construction. Specifically, in Nearby Within the region, a cubic spline curve is used to replace the original benchmark function for fitting and connection; to ensure code-level reproducibility, this embodiment specifies the construction method of the spline curve. The four required boundary condition equations are: The left boundary position is continuous: ; The first derivative is continuous at the left boundary: ; The right boundary position is continuous: ; The first derivative is continuous on the right boundary: ; The system obtains the coefficients by solving the above system of linear equations. This ensures that the final generated roll surface profile satisfies strict geometric first-order derivative continuity, forming a continuous first-order derivative smooth transition ridge; the design combining piecewise function and transition fitting ensures the hydrostatic pressure gradient within the deformation zone. By continuously varying the flow in the central region and forming a steep geometric barrier in the edge region to limit instability, the technology effectively solves the common problems of overturning instability and torsion in wide-width rolling.

[0019] Forced transverse rheological induced rolling is performed by feeding the steel billet into a special-shaped die for reduction rolling. This includes: setting a transverse width expansion efficiency coefficient, which is the ratio of the actual width expansion to the theoretical maximum width expansion under the principle of constant pure volume; adjusting the roll speed and reduction based on the transverse width expansion efficiency coefficient so that the transverse logarithmic strain of the metal in the die is greater than the longitudinal logarithmic strain; and inducing the metal to overcome the natural tendency of longitudinal extension through continuous extrusion in the special-shaped die, thereby achieving a high width expansion rate in the transverse direction. This embodiment is a further specification of the forced transverse rheology-induced rolling step; the system sets the transverse width expansion efficiency coefficient. As a core indicator for measuring flexibility, its definition formula is as follows: in, This refers to the width expansion obtained from actual measurement. This is the theoretical span calculated based on the principle of constant volume; Based on this, the system follows Dynamically adjust the roll speed and reduction to ensure the following strain relationship is met: To ensure the executability of this comparison logic, this embodiment clarifies the specific calculation paths for the two logarithmic strains mentioned above: Transverse logarithmic strain : Exit width based on real-time measurement With entrance width calculate: Longitudinal logarithmic strain Based on roll linear velocity With the speed of the inlet roller conveyor Speed ​​difference calculation, considering the forward slip coefficient : Where the forward sliding coefficient In this embodiment, the empirical constant is set to 0.05 under typical operating conditions. For steel billets of different materials, the forward slip coefficient can be corrected offline based on measured data. For other non-typical operating conditions, the system uses the Ekelund forward slip formula for real-time calculation to ensure the universality of the calculation. The formula is as follows: Here Defined as the equivalent average thickness of the intermediate billet exit section, the calculation formula is: in, The actual cross-sectional area obtained by integrating with the laser profilometer. The actual exit width is used; the equivalent average thickness is adopted to eliminate the ambiguity in thickness definition caused by unsteady cross-sectional shape. Indicates the coefficient of friction between the roll and the billet; inlet velocity. Data is collected in real time via roller encoder; An approximate value characterizing the contact arc length of the deformation zone; In specific control, in response to monitoring That is, longitudinal extension dominates deformation, and the system triggers an iterative adjustment mechanism; in order to clarify the specific control process for function implementation, this embodiment defines the discrete feedback adjustment loop of the following control algorithm: Initialize the iteration counter and maximum number of iterations ; Calculate the strain deviation index ;like and Execution parameter update: Reduce roll speed: Among them, step size gain Set as This increases the friction angle in the biting zone and restricts longitudinal slippage; Increase the amount of compression: Step gain Set as To force a change in strain tensor distribution; Check equipment safety constraints: If the calculated required torque If the motor's rated torque is reached, the adjustment will be forcibly terminated and the current maximum capacity value will be maintained; the counter will be updated. Return to step 2 for reassessment; this adjustment cycle continues until... Or, when the equipment reaches its load limit, a specific quantitative control strategy is used to ensure that lateral flow becomes the dominant deformation mode.

[0020] Acquire lateral pressure rheological response data and monitor the width change and deformation resistance fluctuation of the intermediate billet in real time during the rolling process, including: obtaining real-time width data of the exit section of the intermediate billet using a laser profiler or width gauge; and monitoring rolling force and lateral pressure torque through mill sensors to identify the dynamic distribution of deformation resistance. The time difference between receiving a command and actually applying pressure in the hydraulic actuator of the hydraulic system is recorded as the mechanical response delay, and the time difference between the actual application of pressure and the change in the width data of the intermediate billet is measured as the material rheological response delay. The mechanical response delay and the material rheological response delay are added together to obtain the lateral pressure rheological response hysteresis time.

[0021] This embodiment further specifies the steps for acquiring side-pressure rheological response data; the system uses a laser profilometer installed at the mill exit to scan the cross-section of the intermediate billet and extract real-time width data. The rolling force is monitored by pressure head sensors and main motor current sensors on the mill stand. and lateral pressure moment The dynamic distribution of these two parameters identifies fluctuations in the metal's resistance to deformation; the system calculates the hysteresis time of the lateral pressure rheological response. This parameter is the sum of the mechanical system delay and the material physical response delay, and its calculation model is as follows: in, The mechanical response delay originates from the difference in control log timestamps and is defined as the time from when the hydraulic command is issued by the control system. When the hydraulic cylinder pressure sensor detects a sudden pressure change The difference, in units of ; In the first steel billet after system startup or during a specific dynamic calibration phase, a step response test is performed to obtain characteristic parameters; in this test mode, for In this embodiment, gradient-based signal detection logic is used for the determination: real-time calculation of hydraulic pressure. The first derivative, when And the duration exceeds Mark that moment as This eliminates the inherent pressure pulsation noise interference of the hydraulic system; The material rheological response delay, derived from synchronous analysis of sensor data, is defined as the time from the moment the actual pressure is applied. The moment when the laser profilometer detects a substantial change in the width of the intermediate billet The difference, in units of ; To accurately define the criteria for determining a substantial change in width, this embodiment sets a specific threshold for signal discrimination: that is, it defines... For real-time width data Maintain before applying pressure The above steady-state reference values absolute value of deviation First time exceeding At that moment, among them In this embodiment, the standard deviation of the field sensor noise, which is determined in advance, is taken as... ; To ensure the sufficiency of the disclosure of this parameter definition, this embodiment clarifies that... Specific measurement method: With the rolling mill in idle standby mode, the hydraulic pump station and lubrication system are started to simulate the background vibration environment. A laser profilometer is used to continuously sample a stationary standard gauge block placed at the center of the roller conveyor. The sampling frequency is set to... Sampling time is , obtain Data from 10 measurement points; calculate the standard deviation of this data set. ; The threshold determined by this measurement procedure can effectively filter out environmental vibration interference; this difference objectively includes the time delay of the steel billet moving from the rolling deformation zone to the exit detection point. And the hysteresis of plastic deformation of the material itself, among which, This represents the physical distance from the center of the roll deformation zone exit to the measurement point of the laser profilometer. The billet exit speed is used as a comprehensive time constant to reflect the overall response characteristics of the system. This embodiment innovatively decouples the lag time into mechanical delay and material rheological delay. The former reflects the equipment performance, while the latter reflects the flow inertia and transport characteristics of the metal at specific temperatures and strain rates. Accurate measurement of the total lag time provides a time-domain reference for subsequent precise feedforward control, eliminating phase lag errors in high-speed rolling.

[0022] Dynamic lateral pressure adaptive control is implemented. Based on the lateral pressure rheological response data and the preset cross-sectional profile fullness target, dynamic lateral pressure is applied to the intermediate billet. This includes: comparing the real-time width data with the preset target width to calculate the width deviation value; performing feedforward compensation on the control command used to adjust the lateral pressure according to the lateral pressure rheological response lag time to eliminate the influence of system delay on control accuracy; if the width deviation value is greater than the preset positive threshold, controlling the vertical roller or lateral pressure mechanism to increase the lateral constraint force to correct excessive width; if the width deviation value is less than the preset negative threshold, controlling the vertical roller or lateral pressure mechanism to decrease the lateral constraint force to correct insufficient width; if the width deviation value is between the negative threshold and the positive threshold, keeping the lateral constraint force unchanged. This embodiment further specifies the dynamic side pressure adaptive control steps; the system compares real-time width data in real time. With the preset target width Calculate the width deviation value The formula is ; Based on the calculated lag time The control system implements predictive compensation based on first-order Taylor expansion: Calculate the prediction width: To ensure the causality and noise immunity of the real-time control system, The real-time rate of change of width is calculated using a five-point backward difference algorithm: in, Width at the current sampling time. For the past The width of each sampling time, The system sampling period is set to [period] in this embodiment. This algorithm, while ensuring that future data is not used, effectively smooths high-frequency quantization noise compared to the ordinary difference method, thus improving the signal-to-noise ratio of the predicted values; based on this, the predicted values... Replace real-time value It participates in subsequent deviation calculations, thereby mathematically offsetting the physical lag. The resulting phase delay; Based on this, the system executes three-state control logic: responding to the width deviation value. Greater than the preset positive threshold For example, positive 2 The system determines that the width is too wide and controls the vertical roller or side pressure mechanism to increase the lateral constraint force. This forces the metal to flow longitudinally; in response to the width deviation value Less than the preset negative threshold For example, negative 2 The system determines that the width is insufficient and controls the vertical roller or side pressure mechanism to reduce the lateral constraint force. This allows the metal to flow fully to both sides under the extrusion of the irregularly shaped aperture; in response to the width deviation value Between the negative and positive thresholds, the system maintains the current lateral constraint force unchanged to avoid frequent system oscillations; This embodiment effectively solves the over-adjustment and under-adjustment problems in high-reduction rolling by introducing hysteresis compensation and three-state threshold control, realizes dynamic high-precision control of intermediate billet width, and suppresses the head and tail width deviation caused by control response hysteresis. Regarding specific technical means to increase or decrease lateral constraint force, this embodiment embeds a mechanical adjustment algorithm based on deviation ratio into the hydraulic actuator of the hydraulic system: when adjustment is determined to be needed, the system calculates the force adjustment amount: in This is the absolute value of the current trigger threshold, which corresponds to the positive threshold. Or negative threshold absolute value Stiffness adjustment coefficient Based on the stiffness characteristics of the rolling mill, it is set as follows: ; When the correction is too broad, a proportional overlay strategy based on the baseline value is adopted to update the target pressure setpoint as follows: in, This is the initial side pressure setting value before this rolling pass. Rated thrust of the hydraulic cylinder; when the correction width is insufficient, update to: This variable gain adjustment mechanism based on the deviation amplitude essentially constitutes a proportional controller with a dead zone. As a feedforward bias As a real-time stiffness correction, it effectively avoids the problems caused by direct accumulation. This leads to integral saturation and system divergence risks.

[0023] It also includes a dynamic hardening compensation step under thermo-coupling: obtaining the cross-sectional temperature field distribution of the billet and identifying the low-temperature zone at the corner and the high-temperature zone at the center; Calculate the dynamic hardening difference under thermo-coupling and evaluate the limiting effect of the low-temperature corner on the lateral flow of metal in the high-temperature core. The distribution of the center and edge reduction ratio of the irregular hole is modified according to the dynamic hardening difference to prevent internal cracks caused by the mismatch of deformation resistance. This embodiment adds a dynamic hardening compensation step under thermal coupling; the system uses a thermal imager to acquire the temperature field of the billet cross section. Identify the temperature of the low-temperature area in the corner. Temperature of the high-temperature zone of the heart To ensure data consistency and reproducibility during the identification process, this embodiment defines... The distance between the surface in the cross section The arithmetic mean temperature of all grid nodes within the range, defined as Geometric center of the cross section Arithmetic mean temperature of nodes within the area; dynamic hardening difference index calculated by the system under thermo-coupling. The calculation is as follows: in, , , The strain hardening index is... The strain rate sensitivity index; Temperature values ​​in Celsius, unit: ; Represents equivalent plastic strain, dimensionless, and corresponds to the power term in the formula. ; Represents the equivalent plastic strain rate, unit: In the formula, the corresponding power term ; For the low-temperature areas in the corners, symbols are used. The equivalent plastic strain is expressed using a geometric approximation formula: in, The shear strain constant is 0.15 in this embodiment; the constant 0.15 here is the dimensionless corner shear strain coefficient based on experimental calibration; the specific method for determining this coefficient is as follows: a standard cylindrical specimen of the same material as the billet to be rolled, such as Q345B in this embodiment, is selected, and a confined compression test is performed on a thermal simulation testing machine to simulate the shear condition of the butterfly hole sidewall, and the experimental temperature is set to cover... to Strain rate coverage to By comparing the rheological stress-strain curves obtained from the experiment with the theoretical curves under pure compression, the additional stress increment caused by shear deformation is separated and converted into a dimensionless strain increment. The specific conversion calculation logic is as follows: using the material hardening equation: Here and It is obtained by power-law fitting of the pure compressive stress-strain curves of the same batch of materials at corresponding temperatures. Compared with the aforementioned Hansel-Spittel model, this equation is only used for the equivalent conversion of local shear effects; taking Q345B steel in this embodiment as an example... For example, the measured calibration value is , The additional stress measured in the experiment Substituting into the formula and solving in reverse, the formula is: in, The stress is pure compressive stress; after calculating multiple sets of data, the average value of multiple experiments, 0.15, is taken as a correction factor; for different steel grades or different temperature ranges, a system containing specific... The value is retrieved from a database or lookup table; this coefficient is applicable to sidewall inclination angles within... For orifice designs within this range, if the orifice angle exceeds this range, it must be recalibrated according to the above method: that is, in the restricted compression stage of the thermal simulation experiment, the inclination angle with the sidewall of the new orifice must be changed. Geometrically consistent inclined head or die to physically simulate specific shear components; Repeat the stress separation and equivalent conversion steps described above to obtain the dimensionless coefficients corresponding to the new angle. The value 0.15 is replaced to ensure that the computational model accurately captures the shear rheological differences caused by angle variations; this dimensionless constant term is introduced to correct the underestimation of corner deformation in the conventional compression formula, ensuring the adequacy of the hardening assessment; for the high-temperature core region, the following is adopted: And to accurately reflect rolling dynamics, this embodiment uses a modified average strain rate formula for explicit calculation: in, Roll speed , The radius of the roll , , Thickness of entrance and exit ; The conversion factor is the unit of rotational speed; the formula is based on the contact arc length of the deformation zone. Normalizing the linear velocity ensures the calculated strain rate. With standard Physical units; Because the instantaneous strain rates at different local points in the deformation zone differ, and the sensitivity index of flow stress to strain rate is relatively small, this embodiment uniformly uses the macroscopic average strain rate for equivalent calculations. However, due to the small sensitivity index of flow stress to strain rate in the constitutive model... The value is 0.125, which is much smaller than the temperature sensitivity index. Furthermore, the aforementioned strain constant term of 0.15 has already compensated for the additional hardening at the corners due to high strain rates at the energy equivalence level. Therefore, the macroscopic average rate is used. Using uniform calculation parameters is a reasonable engineering approximation that can guarantee The deviation in the calculation results is within the allowable range and will not mislead subsequent reduction rate correction steps; according to Correcting the reduction ratio distribution of irregular orifice types; in response to That is, the safety threshold, the system performs linear compensation: maintaining the center pressure reduction rate. Keeping the edge compression rate unchanged, adjust it as follows: Regarding the parameter source: threshold Based on fracture mechanics criteria, Q345B is selected as... Lower critical shear fracture stress ;coefficient The stiffness-flexibility coefficient is determined through regression analysis, and the unit is... ; Simultaneously, the system executes real-time monitoring and reset logic for the hardened state: responding to the calculated... The system determines that the difference in rheological stress between the corner and the center has returned to a safe range; at this point, the system resets the edge compression rate to the initial set value. And cancel the geometric correction command for the hole profile; When calculated At this time, the system maintains the current reduction ratio and hole profile settings unchanged.

[0024] This logic ensures that dynamic hardening compensation only intervenes when there is an abnormal temperature difference in the material, thus avoiding a reduction in the system's spreadability due to overcompensation under normal operating conditions. Furthermore, when the edge reduction rate is corrected to When this happens, the system will immediately trigger a geometric reconstruction interrupt, call the aperture generation algorithm, and adjust the corresponding new edge height. Substitute into piecewise function The spline curve coefficients are recalculated to generate a new die profile that is physically adapted to hardening compensation, preventing abnormal roll wear caused by the disconnect between parameter correction and geometric execution.

[0025] In the process of implementing dynamic lateral pressure adaptive control, the evaluation and control of the cross-sectional profile filling degree specifically includes: calculating the ratio of the actual metal cross-sectional area at the exit of each pass to the ideal hole design area as the cross-sectional profile filling degree; when the cross-sectional profile filling degree is lower than the preset lower limit, it is judged as insufficient width expansion, and the center reduction rate of the next pass is increased; when the cross-sectional profile filling degree is higher than the preset upper limit, it is judged as overfilling or ear formation, and the center reduction rate of the next pass is reduced or the lateral constraint force is increased; when the cross-sectional profile filling degree is between the preset lower limit and the preset upper limit, the current reduction rate and lateral constraint force settings are maintained. This embodiment is a further specification of the assessment of cross-sectional profile fullness; the system calculates the cross-sectional profile fullness. Defined as: in, The actual measured cross-sectional area of ​​the metal at the exit of each pass, in square millimeters; specifically, the laser profilometer outputs a set of discrete coordinate points of the intermediate billet cross-section. ,in Characterizes the corresponding width position The thickness value at that location is calculated using the discrete trapezoidal integral method to determine the area of ​​the irregular dog-bone-shaped cross-section in this embodiment. This algorithm can accurately process non-convex polygonal cross sections, eliminating geometric errors caused by simply relying on width and thickness to estimate the area; The ideal aperture design area is the area when the aperture is completely filled, in square millimeters, and is sourced from the aperture design database. Based on this, the system executes decision logic based on fill degree: in response to Less than the preset lower limit For example, 0.92, this lower limit value With the upper limit value mentioned later The settings are all based on statistical analysis of historical production data: qualified intermediate billet samples of the same specification produced within a preset historical production cycle are selected, and their cross-sectional fill degree is fitted with a normal distribution, and the mean value is taken. As a control boundary, 0.92 corresponds to The value at that location, to ensure Based on the confidence level, the system determines that the metal has not filled the edge of the aperture, indicating insufficient width. In this case, the controller directly calculates the increment based on the deviation proportional control law. Calculate the reduction rate correction: Among them, strain proportional gain Set as And set the center reduction rate for the next pass to: The center reduction rate of the next pass is increased in a quantitative manner to enhance the lateral driving force; the control system uses inverse geometric relationships to convert the calculated target strain into the actual roll gap displacement command of the mill's hydraulic reduction system. : in, The preset entry thickness for the next pass ensures that the control strategy can be recognized by the physical actuator; In response to Greater than the preset upper limit For example, 0.98 corresponds to the statistical distribution mentioned above. Upon reaching the boundary, the system determines that metal may overflow and form a lug, classifying it as overfilled. It then executes a priority-based adjustment strategy based on device capabilities: detecting the current lateral restraint force. Has the equipment reached its limit? This limit value is determined by the rated parameters of the rolling mill equipment; in this embodiment, it is taken as... ; like The preferred approach is to increase the lateral constraint force, and the increment is calculated as follows: Among them, stiffness coefficient ; like If the lateral constraint is determined to be saturated, then the center reduction rate of the next pass is reduced. The calculation formula is as follows: This deterministic logic eliminates execution ambiguity in operations; in response to Between the preset lower and upper limits, the system maintains the current compression rate and lateral constraint force settings; This embodiment controls not only the width in a single dimension but also the shape quality of the two-dimensional section by monitoring the cross-sectional fullness. This effectively prevents surface defects such as folds and ears caused by excessive pursuit of width expansion in a single pass, ensuring that the geometric quality of the intermediate billet meets the requirements of finishing rolling.

[0026] Example 2: Please see Figure 2 A billet roughing and widening system, comprising: The geometry configuration building module is used to construct the geometry configuration of non-uniform deformation regions. Based on the law of minimum resistance and rheological resistance gradient, it configures irregular orifice types with differentiated reduction rate distributions. The rolling execution module is used to perform forced transverse rheology-induced rolling, which feeds the billet into a special-shaped die for pressing and rolling, and forces the metal to undergo active transverse mass migration from the center to both sides through a non-uniform hydrostatic pressure field. The data acquisition module is used to collect side pressure rheological response data, monitor the width change and deformation resistance fluctuation of the intermediate billet in real time during the rolling process, and calculate the side pressure rheological response hysteresis time. The adaptive control module is used to implement dynamic lateral pressure adaptive control, which applies dynamic lateral pressure to the intermediate billet based on the lateral pressure rheological response data and the preset cross-sectional profile filling target. This embodiment discloses a billet roughing and widening system, which is a hardware and software combination for performing the above-described method. The system is equipped with a geometry configuration construction module, which corresponds to the mill design and roll changing strategy. It includes a database storing parameters of various irregular roll shapes such as butterfly and trapezoidal shapes. Before rolling, based on the law of minimum resistance and rheological resistance gradient calculation, the module automatically selects or configures roll combinations with specific center and edge reduction ratios to construct a non-uniform deformation zone. The system is equipped with a rolling execution module, which includes the main drive system and reduction device of the roughing mill. Its function is to perform forced transverse rheological induced rolling. It receives control commands and drives the shaped rolls to perform large reduction on the steel billet, using a non-uniform hydrostatic pressure field to force the metal to undergo active transverse mass migration from the center to both sides. At the same time, the system operates a data acquisition module, which integrates a laser width gauge, force sensor and hydraulic feedback sensor. Its core function is to collect lateral pressure rheological response data. It has an embedded real-time calculation unit for synchronously monitoring the width of the intermediate billet. Resistance to deformation And calculate the hysteresis time of the lateral pressure rheological response in real time. The system operates an adaptive control module, which is the core computing unit of the system and is used to implement dynamic lateral pressure adaptive control. It receives data from the acquisition module and combines it with a preset cross-sectional profile fullness target. It outputs control commands to the hydraulic actuator to apply precise dynamic lateral pressure to the intermediate billet; This embodiment achieves a closed-loop process from geometric construction, physical execution, data perception to intelligent control through modular design, ensuring the hardware feasibility and control stability of the forced widening process, and is particularly suitable for modern automated steel rolling production lines.

[0027] The adaptive control module includes: a deviation calculation unit, used to compare real-time width data with a preset target width and calculate the width deviation value; a hysteresis compensation unit, used to feedforward compensation of the control command used to adjust the lateral pressure based on the hysteresis time of the lateral pressure rheological response; and an execution adjustment unit, used to adjust the vertical roller or lateral pressure mechanism, configured to: increase the lateral constraint force when the width deviation value is greater than a preset positive threshold, decrease the lateral constraint force when the width deviation value is less than a preset negative threshold, and keep the lateral constraint force unchanged when the width deviation value is between the negative threshold and the positive threshold. This embodiment is a further specification of the adaptive control module; this module includes a deviation calculation unit for performing subtraction operations and comparing the width data acquired in real time. With preset target width Output width deviation value The signal is transmitted to the hysteresis compensation unit, which is a time-domain filter and predictor; it is based on the calculated hysteresis time of the lateral pressure rheological response. A predictive compensation model is constructed, and the control system implements predictive compensation based on first-order Taylor expansion, calculating the prediction width. : This virtual time advance is used to offset the lag of the physical system, replacing the physically impossible time axis shift of control commands, thereby eliminating the impact of system delay on control accuracy; The execution adjustment unit directly drives the vertical roller hydraulic cylinder or side pressure mechanism according to the compensated command. Its configuration logic is as follows: responsive to Greater than the positive threshold Output a boost command to increase lateral constraint force to limit the width; in response to Less than the negative threshold Output a pressure relief command to reduce lateral constraint forces and promote widening; in response to Between the negative and positive thresholds, a pressure holding command is output to maintain the lateral constraint force; This embodiment clarifies the signal flow processing path: from deviation calculation to time-domain compensation, and then to the mechanical adjustment of the actuator; this hierarchical architecture ensures the high response speed and robustness of the control system, and is particularly suitable for the high temperature and high vibration environment of the rolling mill.

[0028] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for widening steel billet during rough rolling, characterized in that, Includes the following steps: A non-uniform deformation zone geometry is constructed. Based on the law of minimum resistance and the rheological resistance gradient, an irregularly shaped die with a differentiated reduction rate distribution is configured. The irregularly shaped die is used to establish a non-uniform hydrostatic pressure field within the rolling gap. Forced transverse rheological induced rolling is performed by feeding the billet into the special-shaped roll pass for pressing and rolling. The non-uniform hydrostatic pressure field forces the metal to undergo active transverse mass migration from the center to both sides, generating an intermediate billet with an unsteady cross section. Side pressure rheological response data are collected, and the width change and deformation resistance fluctuation of the intermediate billet are monitored in real time during the rolling process. The action feedback of the hydraulic system is obtained, and the side pressure rheological response hysteresis time is calculated. Dynamic lateral pressure adaptive control is implemented. Based on the lateral pressure rheological response data and the preset cross-sectional profile filling target, dynamic lateral pressure is applied to the intermediate billet to suppress overturning instability and correct insufficient or excessive width.

2. The method for widening a steel billet during rough rolling according to claim 1, characterized in that, The construction of the non-uniform deformation region geometry, based on the law of minimum resistance and rheological resistance gradient, involves configuring irregularly shaped apertures with differentiated reduction rate distributions, including: The difference in reduction rate between the center and the edge of the deformation zone is determined, and the difference in reduction rate determines the magnitude of the driving force for the central metal to flow to both sides; The butterfly-shaped hole is designed as the irregular hole type, wherein a high-pressure lowering zone is set at the center of the hole type and a low-pressure lowering zone is set on both sides of the hole type, forming a deformable channel that is thin in the middle and thick on both sides. The trapezoidal sidewalls and butterfly protrusions are configured to provide boundary guidance when the metal flows laterally, preventing the metal from twisting or collapsing during forced widening.

3. The method for widening a steel billet during rough rolling according to claim 2, characterized in that, The forced transverse rheology-induced rolling process, which involves feeding the steel billet into the shaped roll pass for reduction rolling, includes: A lateral expansion efficiency coefficient is set, which is the ratio of the actual expansion amount to the theoretical maximum expansion amount under the principle of constant pure volume. The roll speed and reduction are adjusted according to the transverse width efficiency coefficient so that the transverse logarithmic strain of the metal in the die is greater than the longitudinal logarithmic strain. Through continuous extrusion of the irregular hole pattern, the metal is induced to overcome the natural tendency of longitudinal extension, achieving a high width expansion ratio in the lateral direction.

4. The method for widening a steel billet during rough rolling according to claim 3, characterized in that, The acquisition of lateral pressure rheological response data, and the real-time monitoring of the width change and deformation resistance fluctuation of the intermediate billet during the rolling process, includes: The real-time width data of the exit section of the intermediate billet is obtained using a laser profiler or a width gauge; By monitoring rolling force and lateral pressure torque using rolling mill sensors, the dynamic distribution of deformation resistance can be identified; The time difference between receiving a command and actually applying pressure in the hydraulic actuator of the hydraulic system is recorded as the mechanical response delay, and the time difference between the moment the pressure is actually applied and the moment when the width data of the intermediate billet changes is measured as the material rheological response delay. The mechanical response delay and the material rheological response delay are added together to obtain the side pressure rheological response hysteresis time.

5. The method for widening a steel billet during rough rolling according to claim 4, characterized in that, The implementation of dynamic lateral pressure adaptive control, based on the lateral pressure rheological response data and a preset cross-sectional profile filling target, applies dynamic lateral pressure to the intermediate billet, including: Compare the real-time width data with the preset target width to calculate the width deviation value; The control command used to adjust the lateral pressure is feedforward compensated based on the lateral pressure rheological response hysteresis time to eliminate the impact of system delay on control accuracy; If the width deviation value is greater than the preset positive threshold, the vertical roller or side pressure mechanism is controlled to increase the lateral constraint force to correct the excessive width; If the width deviation value is less than the preset negative threshold, the vertical roller or side pressure mechanism is controlled to reduce the lateral constraint force in order to correct the insufficient width. If the width deviation value is between the negative threshold and the positive threshold, the lateral constraint force remains unchanged.

6. The method for widening a steel billet during rough rolling according to claim 1, characterized in that, It also includes dynamic hardening compensation steps under thermo-coupling: Obtain the cross-sectional temperature field distribution of the steel billet and identify the low-temperature region at the corner and the high-temperature region at the center; Calculate the dynamic hardening difference under thermo-coupling and evaluate the limiting effect of the low-temperature corner on the lateral flow of metal in the high-temperature core. The distribution of the center and edge reduction rates of the irregular hole is corrected according to the dynamic hardening difference to prevent internal cracks caused by the mismatch of deformation resistance.

7. The method for widening a steel billet during rough rolling according to claim 1, characterized in that, The evaluation and control of the cross-sectional profile filling degree during the implementation of dynamic lateral pressure adaptive control specifically includes: The ratio of the actual metal cross-sectional area at the exit of each pass to the ideal aperture design area is used as the cross-sectional profile filling degree. When the cross-sectional profile fill is lower than the preset lower limit, it is determined to be insufficient width, and the center reduction rate of the next pass is increased; When the cross-sectional profile fills more than the preset upper limit, it is determined to be overfilled or produce ears, and the center reduction rate of the next pass is reduced or the lateral constraint force is increased. When the cross-sectional profile fill is between the preset lower limit and the preset upper limit, the current compression rate and lateral constraint force settings are maintained.

8. A billet roughing and widening system, applied to the method according to any one of claims 1-7, characterized in that, include: The geometry configuration building module is used to construct the geometry configuration of non-uniform deformation regions. Based on the law of minimum resistance and rheological resistance gradient, it configures irregular orifice types with differentiated reduction rate distributions. The rolling execution module is used to perform forced transverse rheology-induced rolling, which feeds the billet into the special-shaped die for pressing and rolling, and forces the metal to undergo active transverse mass migration from the center to both sides through a non-uniform hydrostatic pressure field. The data acquisition module is used to collect side pressure rheological response data, monitor the width change and deformation resistance fluctuation of the intermediate billet in real time during the rolling process, and calculate the side pressure rheological response hysteresis time. An adaptive control module is used to implement dynamic lateral pressure adaptive control, which applies dynamic lateral pressure to the intermediate billet based on the lateral pressure rheological response data and a preset cross-sectional profile filling target.

9. A billet roughing and widening system according to claim 8, characterized in that, The adaptive control module includes: The deviation calculation unit is used to compare the real-time width data with the preset target width and calculate the width deviation value. The hysteresis compensation unit is used to feedforward compensation of the control command for adjusting the lateral pressure based on the hysteresis time of the lateral pressure rheological response. An adjustment unit is used to adjust the vertical roller or the side pressure mechanism, configured to: increase the lateral constraint force when the width deviation value is greater than a preset positive threshold, decrease the lateral constraint force when the width deviation value is less than a preset negative threshold, and keep the lateral constraint force unchanged when the width deviation value is between the negative threshold and the positive threshold.

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