Optimization method and system for profiled steel bar drawing forming parameters

Abstract

The application relates to the technical field of metal plastic working, and discloses a special-shaped steel rod drawing forming parameter optimization method and system. The method comprises the following steps: extracting special-shaped section geometric features and performing flow field simulation to generate a flow velocity distribution map; potential vortex area is identified and its influence range is determined through velocity gradient analysis; the material flow path is tracked in the influence range to generate a vortex intensity distribution map; the vortex intensity distribution map is correlated and analyzed with wall thickness deviation data, lubrication process parameters are adjusted to generate a lubrication condition distribution map; the lubrication condition distribution map is superimposed and mapped with the flow velocity distribution map, the influence of shearing extrusion stress on wall thickness evolution is analyzed, and a drawing speed compensation field is determined; the simulation parameters are updated according to the drawing speed compensation field, and a wall thickness prediction distribution map is generated; the wall thickness uniformity is taken as a target function, the drawing speed compensation field is iteratively calculated through an optimization algorithm, and drawing forming control parameters are generated. The application improves the wall thickness uniformity and machining precision of the special-shaped steel rod.

Description

Technical Field

[0001] This application relates to the field of metal plastic processing technology, and in particular to a method and system for optimizing the drawing parameters of irregularly shaped steel bars. Background Technology

[0002] Shaped steel bars, due to their asymmetric, multi-curvature transitions, and abrupt changes in local dimensions, can meet the requirements of lightweight mechanical structures, functional integration, and specific assembly fits, and have been widely used in the automotive, construction machinery, rail transportation, and high-end equipment industries. Compared to round bars or regular profiles, shaped steel bars are more prone to uneven material flow, local thinning, or accumulation during the drawing process, leading to uneven wall thickness (or equivalent thickness) distribution, dimensional accuracy fluctuations, and uncontrollable subsequent machining allowances, thus affecting product consistency and service reliability.

[0003] Regarding the quality control of drawing forming of irregularly shaped steel bars, related technologies have generally evolved from "empirical parameter setting" to "process mechanism analysis and simulation-assisted optimization" and then to "data-driven iterative optimization and closed-loop control." In the early stages, process engineers relied on experience to set drawing speed, lubricant type, and supply method based on material grade, die structure, and drawing passes, obtaining usable parameters through trial drawing and correction. However, this method had limited adaptability to different cross-sectional shapes and die conditions. Subsequently, to improve process repeatability, the industry gradually introduced finite element simulation and other methods to analyze stress, strain, and metal flow during the drawing process, and optimized parameters such as die angle, reduction ratio, and speed accordingly. Furthermore, to address local flow anomalies in complex irregular cross-sections at corners and curvature abrupt changes, research and engineering practice began to focus on the coupling effects between friction boundaries, lubrication conditions, and material flow, and attempted to use multi-parameter optimization methods to correct the process window.

[0004] However, existing solutions still have the following shortcomings when dealing with complex irregular cross-sections: On the one hand, uneven wall thickness is often related to excessive local velocity gradients, flow separation, and turbulent flow phenomena such as eddies / backflows. However, traditional optimization is mainly based on macroscopic process parameters, which makes it difficult to reliably identify and quantify turbulent regions. On the other hand, parameters such as lubrication conditions and drawing speed are usually set globally uniformly, lacking spatial compensation and collaborative control mechanisms for local areas of different cross-sections. This results in low parameter adjustment efficiency, sensitivity to changes in working conditions, and difficulty in obtaining stable molding results with high wall thickness uniformity.

[0005] Therefore, how to effectively identify and quantify the material flow velocity distribution and flow turbulence such as eddies during the drawing process of irregular steel bars, and thereby achieve synergistic optimization and iterative compensation of lubrication parameters and drawing speed to improve wall thickness uniformity and forming stability, has become a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] To address the problems of uneven material flow velocity distribution, difficulty in identifying and quantifying local flow disturbances (such as eddies / backflows), and lack of regional coordinated control of process parameters such as lubrication and drawing speed during the existing shaped steel bar drawing process, which lead to uneven wall thickness (or equivalent thickness) and insufficient forming stability, this application provides a method and system for optimizing shaped steel bar drawing parameters to achieve effective control of wall thickness uniformity.

[0007] In a first aspect, this application provides a method for optimizing the drawing parameters of irregularly shaped steel bars, the method comprising:

[0008] S1. Extract the geometric features of the irregular cross-section data, perform flow field simulation based on the geometric features, and generate a preliminary flow velocity distribution map;

[0009] S2. Based on the flow velocity distribution map, perform velocity gradient analysis to identify potential vortex regions with abnormal velocity gradients and determine the influence range of the potential vortex regions.

[0010] S3. Track the flow path of the material within the influence range and generate an eddy current intensity distribution map based on the tracking results;

[0011] S4. Perform correlation analysis between the eddy current intensity distribution map and the preset wall thickness deviation data, adjust the lubrication process parameters based on the analysis results, and generate a lubrication condition distribution map.

[0012] S5. Spatially overlay and map the lubrication condition distribution map with the flow velocity distribution map, analyze the influence of shear extrusion stress on wall thickness evolution, and determine the drawing speed compensation field used to correct uneven flow.

[0013] S6. Update the flow field simulation parameters based on the drawing speed compensation field, recalculate the material flow path, and generate the corresponding wall thickness prediction distribution map.

[0014] S7. Using the uniformity of the predicted wall thickness distribution map as the objective function, the drawing speed compensation field is iteratively calculated through an optimization algorithm to generate the final control parameters for drawing and forming of irregular steel bars.

[0015] Secondly, this application provides a parameter optimization system for drawing and forming irregularly shaped steel bars, the system comprising:

[0016] The geometric simulation module is used to extract the geometric features of irregular cross-section data, perform flow field simulation based on the geometric features, and generate a preliminary flow velocity distribution map.

[0017] The eddy current identification module is used to perform velocity gradient analysis based on the flow velocity distribution map, identify potential eddy current regions with abnormal velocity gradients, and determine the influence range of the potential eddy current regions.

[0018] The path tracing module is used to track the flow path of the material within the influence area and generate an eddy current intensity distribution map based on the tracking results.

[0019] The lubrication optimization module is used to perform correlation analysis between the eddy current intensity distribution map and the preset wall thickness deviation data, adjust the lubrication process parameters based on the analysis results, and generate a lubrication condition distribution map.

[0020] The speed compensation module is used to spatially overlay and map the lubrication condition distribution map with the flow velocity distribution map, analyze the influence of shear and extrusion stress on wall thickness evolution, and determine the drawing speed compensation field used to correct flow unevenness.

[0021] The wall thickness prediction module is used to update the flow field simulation parameters based on the drawing speed compensation field, recalculate the material flow path, and generate the corresponding wall thickness prediction distribution map.

[0022] The parameter optimization module is used to generate the final control parameters for drawing and forming of irregular steel bars by iteratively calculating the drawing speed compensation field through an optimization algorithm, with the uniformity of the wall thickness prediction distribution map as the objective function.

[0023] Compared with the prior art, the beneficial effects of the technical solution of this application are at least as follows:

[0024] 1. The "flow velocity distribution - velocity gradient diagnosis - flow path tracing - eddy current intensity quantification" link enables the location and intensity characterization of the turbulent flow region during the drawing process of irregular cross sections, making the key abnormal flow factors that cause uneven wall thickness identifiable and quantifiable, thereby improving the pertinence of process analysis and parameter tuning.

[0025] 2. By correlating the eddy current intensity distribution with the wall thickness deviation data, and using this as a basis to regionally adjust the lubrication process parameters, a lubrication condition distribution map is formed. This transforms the lubrication boundary from "globally uniform setting" to "differentiated control according to key areas," which helps to suppress local flow turbulence and reduce the amplification effect of wall thickness deviation.

[0026] 3. By spatially superimposing and mapping lubrication conditions and velocity fields, a drawing speed compensation field is constructed. Closed-loop iteration and optimization are performed using the wall thickness prediction distribution map. This upgrades the drawing speed control from a single constant parameter to a spatial compensation strategy that takes into account the equipment's execution capabilities. This improves wall thickness uniformity, forming stability, and product consistency, while reducing the cost of repeated trial drawing and debugging based on experience.

[0027] 4. A complete closed-loop control system of "perception-diagnosis-optimization-verification" has been constructed, which has transformed the determination of process parameters for drawing and forming irregular steel bars from a trial-and-error mode based on experience to a scientific calculation mode based on simulation. This has significantly shortened the process development cycle of new products, reduced debugging costs, and provided key technical support for the intelligent manufacturing of precision profiles with complex cross-sections. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of the method for optimizing the drawing forming parameters of irregularly shaped steel bars in this application;

[0030] Figure 2 This is a schematic diagram of the eddy current intensity distribution cloud map of the irregular steel bar cross section in the embodiments of this application;

[0031] Figure 3 This is a schematic diagram comparing the predicted wall thickness distribution before and after optimization in an embodiment of this application;

[0032] Figure 4 This is a schematic diagram of the structure of the shaped steel bar drawing forming parameter optimization system of this application. Detailed Implementation

[0033] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms “comprising” or “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0034] For ease of understanding, the specific process of the embodiments of this application is described below. Figure 1 The diagram shows a flowchart of the method for optimizing the drawing and forming parameters of irregularly shaped steel bars provided by the present invention. The flowchart specifically includes the following steps:

[0035] S1. Extract the geometric features of the irregular cross-section data, perform flow field simulation based on the geometric features, and generate a preliminary flow velocity distribution map.

[0036] In one specific embodiment, the process of performing step S1 may specifically include the following steps:

[0037] Obtain the global model space corresponding to the irregular cross-section data, and perform initial mesh generation of the global model space based on the basic density;

[0038] Geometric rotation features and curvature abrupt change features were extracted from irregular cross-section data using finite element simulation tools.

[0039] For local regions containing geometric corner features and curvature abrupt change features, a high-density mesh is generated based on the basic density. If the curvature abrupt change value of any local region exceeds the preset abrupt change threshold, the mesh density of any local region is further adaptively refined and adjusted.

[0040] Obtain initial distribution data of lubricant on the surface of the irregular steel bar. The initial distribution data shall include at least the lubricant coating thickness and the lubricant viscosity grade.

[0041] Based on the mesh generation results and initial distribution data, a flow velocity distribution map is generated through finite element simulation calculation.

[0042] Specifically, the data for irregular cross-sections can be derived from 2D engineering drawings of the product, cross-sectional slices of 3D models, or cross-sectional profile point sets output by online measuring equipment. Before importing into the simulation environment, the data needs to be geometrically consistent to ensure that the cross-sectional profile is closed, without self-intersections or break points, and the dimensions of the inlet and outlet designed according to the drawing pass are checked. Based on the processed cross-sectional profile, a 3D solid model is constructed in finite element simulation software (such as ABAQUS) through stretching operations. This model should fully contain the geometry of the irregular steel bar, such as the cross-sectional profile, length, and geometric constraints of the die inlet section, working zone, and outlet section. If the cross-section has significant asymmetric characteristics and there is a 3D flow effect, a 3D solid model should be used; if the cross-section is approximately symmetrical and the deformation is mainly plane strain, a 2D plane strain model can be used to reduce the computational load. The output is a 3D geometric model in the global model space, which defines the coordinate system of the simulation calculation domain, the initial material occupation domain, and the die wall boundary, and defines the drawing direction as the main motion direction.

[0043] The base mesh size must be set in relation to the minimum feature size of the cross-section to avoid element distortion caused by the mesh crossing sharp corners. For example, when the minimum fillet radius of an irregular cross-section is in the range of 1mm to 3mm, the base mesh size can be set to 1mm to 2mm. Tetrahedral or hexahedral elements are used to mesh the 3D geometric model to generate the initial mesh model. The element quality must meet the solver requirements; for example, the element twist and aspect ratio must not exceed the solver's recommended thresholds. To ensure that subsequent local refinement does not cause numerical reflection due to abrupt mesh changes, a transition zone needs to be set between the base mesh and the refined mesh. The element size variation in the transition zone is limited to no more than twice that of adjacent levels.

[0044] The purpose of extracting geometric features using finite element simulation tools is not to identify the shape, but to locate regions where the flow boundary conditions change rapidly. Geometric corner features are located by the angle change of the contour lines; for example, corners with an interior angle less than 130° are marked as corner feature points. Curvature abrupt change features are located by the rate of curvature change along the contour arc length. Curvature can be calculated as the reciprocal of the radius obtained by fitting a local circular arc, and the rate of curvature change is characterized by the ratio of the curvature difference between adjacent sampling points to the arc length distance. For example, when the cross-sectional contour points are sampled at 0.2 mm, if the curvature of a certain contour segment jumps from 0.1 mm to 0.3 mm within a 1 mm arc length, the rate of curvature change is 0.2 mm / s², and this area should be marked as a curvature abrupt change feature region. Feature points are extended to both sides along the contour by a preset arc length (e.g., 1 mm to 3 mm) to form feature regions to avoid insufficient resolution of surrounding areas due to only refining at single points.

[0045] The size of the high-density mesh must support the spatial resolution required for velocity gradient calculation. For example, with a base mesh size of 1 mm, the mesh size for feature regions can be set to 0.25 mm to 0.5 mm, and further refined to 0.25 mm in the feature region near the mold working zone to better resolve velocity redistribution. A curvature abrupt change threshold is set to trigger adaptive refinement adjustment. This threshold can be determined empirically based on material properties, reduction ratio, and mold angle, and corrected through a small amount of verification simulation, such as 0.15 per square millimeter. When the rate of curvature change in a local region exceeds this threshold, the mesh size in that region is further reduced by a preset refinement ratio, and the refinement range is simultaneously expanded to the area surrounding the feature points (e.g., 1 to 3 mm) to ensure the velocity field gradient is continuously solvable in the feature region. Adaptive refinement can be automatically completed through error estimation and mesh refinement algorithms provided by the software, and must be combined with element quality constraints. When refinement leads to a decrease in local element quality, the refinement strategy needs to be adjusted (e.g., switching to local reconstruction or changing the mesh growth direction) until the accuracy requirements are met.

[0046] The initial distribution data of the lubricant on the surface of the shaped steel bar needs to correspond to the frictional boundary conditions of the drawing process. This is because the contact pressure and relative sliding velocity differ in different local areas, and the thickness and viscosity grade of the lubricant film directly affect the interfacial friction coefficient and thus the velocity boundary of the material surface. The initial distribution data should include at least the lubricant coating thickness and the lubricant viscosity grade, which can be obtained through coating process settings, average film thickness converted from weighing, or online film thickness detection results. For example, when using a phosphating saponification or polymer lubrication system, the coating thickness can be set in the range of 5 μm to 30 μm, and the viscosity grade can be the kinematic viscosity at 40 degrees Celsius as input (e.g., 100 mm² / s to 300 mm² / s). When mapping the lubricant distribution data to the model surface, the circumferential or surface partitions of the cross section need to correspond to the lubricant data partitions. For example, the outer perimeter of the cross section can be divided into several surface segments according to geometric features, and each surface segment can be assigned a corresponding film thickness and viscosity grade. In finite element simulation, these data need to be converted into frictional boundary parameters, and the conversion relationship can be achieved using an empirical model or experimental calibration curve that matches the lubrication system. When segmented lubrication data is lacking, the average film thickness and viscosity grade can be entered as global initial values ​​and the assumptions recorded.

[0047] In the finite element simulation software, a material constitutive model is set up. For example, the steel bar material is defined as an elasto-plastic or rigid-plastic body, and strain hardening is considered. If the drawing speed is high and shear heat generation is significant, a thermo-mechanical coupling model needs to be introduced to consider the effect of temperature rise on flow stress and lubricant viscosity; otherwise, an isothermal assumption can be used to improve computational stability. Boundary conditions are set: material feed or drawing traction conditions are defined at the steel bar inlet end, and drawing speed boundaries are applied at the outlet end or traction end (e.g., the drawing speed is set to an initial value within the range of 20 to 60 meters per minute); contact and friction boundaries are applied to the die wall, and the friction parameters are obtained by lubrication distribution mapping and vary with surface segments. For example, a hybrid form of Coulomb friction and shear friction is used between the die working zone and the material, with the friction coefficient obtained by lubrication mapping as the input. Implicit integration is used for solution control, and convergence criteria are set (e.g., residual norm threshold and maximum number of iterations). When non-convergence occurs, incremental step size control or contact parameter relaxation is used. The simulation output includes the velocity vector, velocity magnitude, and velocity components related to the drawing direction for each mesh node or integration point. The velocity field results are projected onto an observation plane consistent with the cross section to generate a flow velocity distribution map displayed in the form of a cloud map. This map should contain the correspondence between spatial coordinates and velocity quantities, and maintain sufficient resolution in the characteristic region to support subsequent velocity gradient analysis.

[0048] This technical solution improves the numerical analysis capability of feature regions by driving mesh refinement through geometric rotation and curvature abrupt change features, and avoids local velocity field smoothing errors or velocity abrupt changes being misjudged as numerical artifacts due to excessively coarse meshes. By using the thickness and viscosity grade of the lubricant coating as input friction boundary conditions and establishing a partition mapping with the model surface, the velocity field can reflect the changes in slip conditions caused by lubrication differences in various local areas of the irregular cross section, providing a reliable velocity gradient basis for subsequent eddy current region identification.

[0049] S2. Based on the flow velocity distribution map, perform velocity gradient analysis to identify potential vortex regions with abnormal velocity gradients and determine the influence range of the potential vortex regions.

[0050] In one specific embodiment, the process of performing step S2 may specifically include the following steps:

[0051] Extract velocity gradient data for each local region from the flow velocity distribution map;

[0052] The velocity gradient data is compared with the preset velocity gradient threshold range. If the velocity gradient data of any local area exceeds the velocity gradient threshold range, the local area is identified as a potential vortex region, and the spatial coordinates of the potential vortex region are extracted.

[0053] A local addressing space is established based on the spatial coordinates of the potential eddy region. The distribution uniformity index of the lubricant and the local accumulation characteristic data within the local addressing space are obtained, and then the disturbance effect of the potential eddy region on the flow of surrounding materials is analyzed.

[0054] Based on the analysis results of the disturbance impact, the influence range of the potential eddy region is determined by using the spatial coordinates of the potential eddy region as a reference and the boundary expansion algorithm.

[0055] Specifically, the flow velocity distribution map corresponds to the velocity vector field of the mesh nodes or integration points output by the finite element solver and its interpolation results. Before entering the velocity gradient analysis, the velocity data and mesh topology relationship need to be exported together. Local regions can be analyzed using finite element mesh elements as the smallest computational unit, or by dividing the cross-sectional area into blocks. When there are sharp corners and narrow ribs in irregular cross-sections, using the mesh element level makes it easier to ensure the resolution of gradient calculations. The nodal velocities of each mesh element are read, and the velocities within the element are spatially interpolated based on the element shape function, and the spatial derivative is calculated to obtain the velocity gradient data corresponding to that element. In the drawing forming scenario, the focus is on the velocity changes along the circumferential direction of the cross-section and along the drawing direction. Within the plane of the cross-section, the rate of change of velocity magnitude along the arc length is calculated for adjacent nodes to obtain the tangential velocity gradient; the rate of change of velocity along the axial direction is calculated along the drawing direction to obtain the axial velocity gradient. To avoid gradient spikes introduced by element distortion or velocity discrete noise, the gradient data undergoes consistency verification and filtering. Filtering can employ neighborhood weighted averaging or median filtering. The filtering window is limited to the set of adjacent cells sharing a surface or edge to ensure that the filtering does not cross geometric abrupt boundaries, thus smoothing out the true abrupt changes. The output is a velocity gradient dataset for each local region, stored as a local region identifier, spatial location, gradient magnitude, or gradient level, reflecting the drastic spatial changes in velocity.

[0056] The velocity gradient threshold range is used to distinguish between normal flow regions and regions with abnormal velocity changes. It can be obtained statistically from historical simulation results of similar cross-sections, or calibrated using benchmark simulations under the same material grade, the same pass reduction rate, and the same die angle. If the velocity gradient data of any local region exceeds the corresponding threshold range, that local region is identified as a potential vortex region. The judgment logic uses a unit-by-unit comparison method. When the velocity gradient value of a unit is greater than the upper threshold or less than the lower threshold, that unit is marked as a member of a potential vortex region. To avoid fragmented vortex regions caused by a single unit triggering the process, adjacent abnormal units are clustered and merged. The clustering rule is limited to adjacent shared surfaces or adjacent shared edges, which merge them into the same potential vortex cluster. For each cluster, the cluster center coordinates and the cluster boundary unit set are output, forming the spatial coordinate set of the potential vortex region and its initial region boundary.

[0057] The local addressing space is a spatial region centered on the potential eddy region and extending outwards within a certain range. It is used to define the scope of subsequent lubricant data acquisition and analysis. The local addressing space can be a circular neighborhood, elliptical neighborhood, or rectangular window centered on the spatial coordinates. The window radius or side length must match the length of the mold working zone, the local feature size, and the mesh density. The local addressing space is determined based on the spatial distribution of the anomaly cluster: when the anomaly cluster is a single, compact region, the circumscribed rectangle or circle of that region can be taken and extended outwards by a preset distance as the local addressing space; when the anomaly cluster contains multiple fragmented regions, the smallest envelope polygon of all fragmented regions is taken and extended outwards by a preset distance. The extension distance can be set according to the length of the mold working zone, the local feature size, and the mesh density.

[0058] The lubricant distribution data comes from the initial distribution data obtained in S1, which has been mapped onto the model surface. Within the local addressing space, the lubricant coating thickness value corresponding to each element is extracted. The distribution uniformity index is used to characterize the consistency of the lubricant thickness within this space. For example, the film thickness of each surface mesh node within the local addressing space is sampled, and the standard deviation of the thickness value is calculated. If the standard deviation is less than a preset threshold, the lubricant distribution is considered uniform; otherwise, uneven distribution exists. Local accumulation feature data refers to areas where the coating thickness is significantly higher than the average. By setting a thickness threshold (e.g., the average plus twice the standard deviation), elements with excessive thickness are identified, these elements are marked as accumulation locations, and their coordinates and thickness values ​​are recorded.

[0059] The fusion analysis of the severity of multiphysics coupling anomalies is based on the following understanding: In complex irregular cross-section drawing processes, local flow anomalies (potential eddies) and abnormal lubricant accumulation are essentially coupled co-occurring phenomena. This step does not presuppose a single causal relationship between the two, but instead uses the spatial overlap of kinematic distortion (velocity anomaly) and tribological anomaly (lubricant accumulation) as a characteristic fusion index to assess the comprehensive potential energy of the local anomaly spreading to the surrounding flow field. The analysis process includes: spatially superimposing and comparing the spatial coordinates of the potential eddy region with the local accumulation characteristic data; if the accumulation location is located within the eddy region, it indicates that the lubrication anomaly and velocity anomaly are highly overlapped in space, and the abnormal flow field is in a state of strong coupling intensification; if the accumulation location is only located outside the eddy region but close to the boundary, it indicates that the co-occurring anomaly is in a state of edge contact; simultaneously, the rate of change of velocity vector direction within the local addressing space is extracted, or the angle between the velocity vectors of adjacent units is extracted and the proportion exceeding a preset angle threshold is statistically analyzed, and the difference in lubricant uniformity index between the eddy region and the surrounding region is calculated. The above results are then used for comprehensive feature determination: if the accumulation location is within the eddy region, and the lubricant uniformity within the eddy region is significantly worse than the surrounding area, and the velocity vector direction abrupt change ratio exceeds a preset threshold, then the multiphysics coupling distortion at this location is determined to be the most severe, possessing strong outward diffusion potential energy, and the boundary expansion weight level is marked as high; if the accumulation location is only adjacent to the eddy region and the uniformity difference is not significant, but the velocity abrupt change ratio is still relatively high, then it is marked as medium weight; if the accumulation location is far from the eddy region and the uniformity difference is small and the velocity abrupt change ratio is low, then it is marked as weak weight. This boundary expansion weight level is directly used as the control parameter for subsequent boundary expansion algorithms.

[0060] The purpose of the boundary expansion algorithm is to extend the potential eddy region outward to the area where the flow state returns to normal, forming a complete eddy influence range. The expansion process must be limited to reproducible region growth rules and a stopping condition must be given. The boundary expansion algorithm adopts a region growth method, that is, using the boundary cells of the potential eddy cluster as the initial frontier and checking adjacent cells layer by layer outward. The expansion strategy is directly related to the boundary expansion weight level: at a high weight level, isotropic expansion is used with a large expansion step size / distance; at a medium weight level, anisotropic expansion is used, and the expansion direction is preferentially directed towards regions of abrupt velocity changes; at a weak weight level, the number of expansion layers is strictly limited to avoid erroneous expansion. After each expansion layer, the average velocity gradient within the newly covered area is calculated. When the average velocity gradient drops below the lower limit of the velocity gradient threshold, the expansion stops. To avoid holes in the influence range due to local isolated anomalies, morphological closing operations are performed after region growth to fill small-scale holes. The hole size is limited to no more than two mesh layers thick. The output format of the influence range must be able to be directly called by S3 as the computational domain input for path tracing. The output can be a set of mesh cells within the influence range or a polygonal region corresponding to the envelope boundary curve. For example, when using a set of mesh cells as output, the sequence of the outermost boundary nodes corresponding to that set is included for visual verification; when using a polygonal region as output, the coordinates of the polygon vertices are given in order and the polygons are guaranteed not to intersect themselves.

[0061] This technical solution identifies potential eddy regions by using a velocity gradient threshold, pinpointing flow anomalies to specific spatial locations. The local addressing space incorporates lubrication distribution uniformity indices and local accumulation characteristic data for disturbance impact analysis. This allows the determination of the impact range to no longer rely solely on the velocity gradient index, but to distinguish between geometrically inevitable velocity redistribution and turbulent propagation induced by friction boundary anomalies, thus avoiding both over-judgment and under-judgment. The boundary extension algorithm expands discrete eddy regions into continuous impact ranges, providing clear spatial boundaries for subsequent flow path tracing.

[0062] S3. Track the flow path of the material within the influence range and generate an eddy current intensity distribution map based on the tracking results.

[0063] In one specific embodiment, the process of performing step S3 may specifically include the following steps:

[0064] Within the influence range of the potential eddy region, virtual particle image velocimetry technology based on flow field simulation is used to track the equivalent flow path of the material within the potential eddy region and extract the corresponding path deviation vector data.

[0065] Obtain the nonlinear interface parameters corresponding to the equivalent flow path. The nonlinear interface parameters include at least the dynamic friction coefficient between the lubricant and the molding material, and the high-temperature stability parameters characterizing the lubricant under shear heating conditions.

[0066] By combining path deviation vector data and nonlinear interface parameters, the local energy dissipation rate caused by flow turbulence is calculated based on the energy dissipation model, and then an eddy intensity distribution map is generated. The location of the eddy core is located and marked in the eddy intensity distribution map.

[0067] Extract the peak intensity data at the core of the vortex. If the peak intensity data exceeds the preset vortex intensity threshold, perform a detailed tracking analysis of the flow path at the core of the vortex and its surrounding area, and iteratively generate an updated vortex intensity distribution map until the accuracy requirements are met.

[0068] Specifically, a virtual particle tracking method based on flow field simulation is adopted. The method involves placing virtual particles at the nodes or center of the finite element mesh within the influence range, with the initial position coordinates of each particle known. The placement of virtual particles must cover the interior of the potential vortex region and its boundary transition zone to avoid path deviation due to placement only at the vortex core, making comparison with the external reference path impossible. Particles can be uniformly sampled within the influence range by mesh nodes, by Gaussian integration points of elements, or by a regular grid, with finer sampling in characteristic regions. The finer sampling scale can be consistent with the mesh size of the characteristic regions in step S1. Based on the flow velocity distribution map obtained in S1, the particle trajectory is solved by numerical integration. The fourth-order Runge-Kutta method can be used for integration. The time step selection must match the maximum velocity and minimum mesh size to avoid trajectory distortion caused by particles advancing across multiple elements at once. The time step can be set according to the criterion that the single-step displacement does not exceed half of the minimum mesh size. For example, when the drawing speed is in the range of 20 m / min to 60 m / min and the minimum grid size is 0.25 mm, the time step can be on the order of 0.00001 s. For each particle, the spatial coordinates of each point on its trajectory and the velocity vector at the corresponding time are recorded. Particles must comply with constraints within the material domain and must not cross the mold wall boundary or the free surface boundary of the material. Therefore, boundary collision detection must be performed during the advancement process, and particles that cross the boundary must be projected back to the inside of the boundary or the particle trajectory must be terminated directly. The equivalent flow path refers to the streamline cluster formed by these particle trajectories. The output particle trajectory dataset includes particle identifiers, initial particle positions, position sequences at each time step, and velocity vector sequences at each time step.

[0069] Before extracting path deviation vector data, a reference path or reference direction needs to be defined; otherwise, the deviation amount cannot have a consistent physical meaning. The reference direction can be the average path direction of reference particles outside the boundary of the influence range, or the pull-out direction can be used as a global reference superimposed with a local geometric guidance direction. Near the corners of irregular cross-sections, using only the pull-out direction as a reference will misinterpret geometrically necessary turning as disorder; therefore, a local average flow direction outside the influence range is more suitable as the reference direction. For example, a set of reference particles with a radius of 2 mm to 5 mm is taken near each particle position, and their velocity directions are weighted by the inverse of the distance to serve as the local reference direction for that position. The path deviation vector is defined as the difference between the instantaneous particle velocity vector and the local reference velocity vector. This difference must reflect changes in both direction and velocity magnitude; otherwise, directional noise will be amplified in low-speed stagnation zones. When the particle velocity is below a certain lower limit, the deviation amount is marked as low confidence; the lower velocity limit can be selected based on process experience. The path deviation vector dataset includes spatial location, deviation vector, and deviation vector statistics, including the mean, mean square value, and deviation duration of the deviation vector.

[0070] The nonlinear interface parameters include at least the dynamic friction coefficient between the lubricant and the molding material, and parameters characterizing the high-temperature stability of the lubricant under shear heating conditions. The dynamic friction coefficient varies with contact pressure, relative sliding velocity, and lubricating film thickness, and can be obtained from the lubricating film thickness and viscosity grade in S1 through a preset mapping, or it can be obtained by real-time updates from the contact model. For example, for a certain phosphating saponification lubrication system, the dynamic friction coefficient can be taken as 0.08 when the contact pressure is 200 MPa and the sliding velocity is 0.5 m / s; when the sliding velocity increases to 2 m / s, the friction coefficient can decrease to 0.06. The high-temperature stability parameters are used to describe the effect of the lubricant's viscosity decrease or lubricating film rupture tendency on friction when the temperature rises due to shear heating. They can be recorded as the viscosity decay coefficient with temperature or the critical temperature threshold and degradation rate, and their values ​​can be derived from lubricant technical specifications or process verification data. To achieve spatial alignment and multiphysics boundary-driven analysis, nonlinear interface parameters need to be output on mesh nodes or surface contact elements and mapped to near-wall particle trajectory positions through interpolation. This characterizes the induced effect of boundary friction state on internal material shear distortion, so that each path point has a corresponding dynamic friction coefficient and high-temperature stability parameter value.

[0071] The energy dissipation model is based on the core physical understanding of viscoplastic mechanics in continuous media: a deviation of the flow path from the ideal state signifies additional internal shear deformation of the material during flow. This redundant plastic deformation work, undertaken to overcome internal viscoplastic resistance, is converted into heat dissipation, and the magnitude of its unit volume dissipation rate directly reflects the intensity of the eddies. In the plastic flow of drawn metals, local dissipation can be divided into two parts: internal plastic shear dissipation and interfacial friction dissipation. To accurately quantify the intensity of eddies in three-dimensional space, this step abandons the dimensionality-reducing approximation that forcibly converts surface friction work into volume dissipation, and instead adopts a rigorous physical model primarily based on internal redundant plastic shear dissipation. The calculation method is as follows: at the particle trajectory position, the spatial derivative of the path deviation vector (i.e., the turbulent velocity component) is taken to extract the "redundant equivalent plastic strain rate" reflecting the intensity of local shear distortion; simultaneously, the "dynamic rheological stress" of the forming material at that position is combined; the two are multiplied to directly calculate the unit volume dissipation rate for overcoming internal turbulence. The specific spatial differentiation and extraction methods include: First, constructing a local support domain centered on the target particle, extracting the deviation vector difference and spatial coordinate difference between adjacent particles within the support domain, and calculating the three-dimensional deviation velocity gradient tensor at that point using the moving least squares method or the Jacobian matrix based on the finite element shape function; Second, extracting the symmetric component of this gradient tensor to construct a redundant strain rate tensor, thereby filtering out rigid body rotation components that do not produce plastic dissipation; Finally, based on the Von Mises equivalence principle, calculating the second invariant of this redundant strain rate tensor to obtain the scalar form of the redundant equivalent plastic strain rate. For example, under typical steel bar drawing conditions, the local dynamic rheological stress of the material is in the range of 300 MPa to 800 MPa. Turbulent velocity components on the order of 0.1 m / s to 0.5 m / s, combined with the local mesh scale (e.g., minimum mesh size 0.25 mm), can be directly spatially differentiated to obtain the local velocity gradient extremum at 400 s⁻¹. -1 By the 2000s -1 The gradient data, to eliminate grid extremum noise and match the true macroscopic eddy current scale, undergoes orientation tensor decomposition (i.e., decomposition into strain rate tensor and rotation tensor) and local spatial averaging based on characteristic scales. This process extracts redundant equivalent plastic strain rates (e.g., using von Mises equivalent strain rate form) that truly reflect the core of internal shear distortion. The effective values ​​are within 5 s. -1 up to 75s -1The effective strain rate is multiplied by the dynamic rheological stress, resulting in a redundant plastic dissipation rate per unit volume ranging from 1.5 GW / m³ to 60 GW / m³. This calculation is performed on all elements within the entire influence range to obtain the energy dissipation rate value for each element. These values ​​are then plotted as contour maps on the 3D geometric model to generate an eddy current intensity distribution map. The eddy current core location refers to the local maximum point of the energy dissipation rate; the spatial continuity of the peak value must be considered to avoid mislabeling of single-point noise. Peak value detection can utilize local maxima and require the existence of a continuous high-intensity region within a certain radius. The radius can be correlated with the mesh scale of the characteristic region. For example, with a radius of 2 mm, the area within the radius exceeding the intensity threshold is required to account for more than 30%.

[0072] The eddy current intensity threshold can be preset based on the material's thermal damage sensitivity or process stability requirements, or it can be obtained statistically based on stable production conditions of similar products. The dissipation rate value at the core location is extracted. If it exceeds the eddy current intensity threshold, the current mesh resolution or particle density is considered insufficient to accurately resolve the flow details in that region, and refinement is required. Refinement strategies include: densifying the mesh size to half its original size within the core location and its surrounding layer; simultaneously rearranging virtual particles within this densified area, doubling the number of particles, and reducing the particle spacing within the core radius (e.g., 3 mm) (e.g., from 0.5 mm to 0.2 mm); halving the time step; and extending the path tracking time to cover the characteristic residence time of the material within the influence range. The flow path tracking and energy dissipation rate calculation in S3 are re-executed to obtain an updated eddy current intensity distribution map. The peak intensity at the new core location is extracted again. If it still exceeds the threshold, refinement continues until the core peak value change between two adjacent iterations is less than 5% and the core boundary position change is less than one layer of mesh thickness. The final eddy current intensity distribution map and eddy current core location coordinates that meet the accuracy requirements are output.

[0073] The above technical solution, based on virtual particle tracking of simulated flow fields, transforms the material motion within the potential eddy region into a calculable equivalent flow path and outputs the path deviation vector. This allows the degree of turbulence to no longer depend on a single velocity gradient but to reflect streamline bending, backflow tendency, and stagnation characteristics. Employing a rigorous volumetric dissipation model based on internal redundant plastic strain rates not only completely resolves the dimensional conflict between surface friction work and internal eddy dissipation but also, by correlating the dynamic friction coefficient and high-temperature stability parameters of near-wall particles, enables the system to incorporate the amplification effect of lubrication boundary degradation and shear heat generation on turbulence into the overall boundary-driven mechanism analysis, and spatially generates a comparative eddy intensity distribution map. The location of the eddy core and iterative verification of the peak intensity threshold ensure the reliability and resolution adaptability of the eddy quantification results, thereby solving the problems of difficulty in quantifying eddy hazard, locating the core, and defining subsequent lubrication and velocity parameter adjustment targets in the drawing process of irregularly shaped steel bars.

[0074] Figure 2 This paper presents a cloud map of eddy current intensity distribution for an irregularly shaped steel bar cross-section (example: a complex shape with grooves and flanges). In the map, colors from blue to red represent the change in local energy dissipation rate from low to high, in units of GW / m³. The highlighted red areas represent locations with high energy dissipation rates, i.e., regions of intense flow turbulence (eddies / backflow). Through velocity gradient analysis in step S2 and flow path tracing and energy dissipation modeling in step S3 of this application, two significant eddy current cores were successfully identified (marked with white asterisks in the map): one located at the root of the groove in the upper left corner (region A), with a peak energy dissipation rate exceeding 60 GW / m³; the other located at the transition of the flange in the lower right corner (region B), with a peak energy dissipation rate exceeding 70 GW / m³. White dashed circles indicate the influence range of each eddy current core, determined by a boundary expansion algorithm, covering the surrounding areas where the flow is disturbed. This map visually verifies the ability of the method in this application to locate and quantify turbulent flow regions, providing precise spatial basis for targeted adjustment of lubrication process parameters and construction of the drawing speed compensation field in subsequent steps.

[0075] S4. Perform correlation analysis between the eddy current intensity distribution map and the preset wall thickness deviation data, adjust the lubrication process parameters based on the analysis results, and generate a lubrication condition distribution map.

[0076] In one specific embodiment, the process of performing step S4 may specifically include the following steps:

[0077] By spatially superimposing and comparing the eddy current intensity distribution map with the wall thickness deviation data, key influencing areas where the eddy current intensity is higher than the preset intensity threshold and the wall thickness deviation exceeds the preset diagnostic deviation range are identified.

[0078] For key affected areas, a negative correlation response model between eddy current intensity and lubrication interface friction coefficient is established. Based on the negative correlation response model, the target friction coefficient distribution for suppressing eddy current intensity is calculated.

[0079] Based on the target friction coefficient distribution, the corresponding lubrication process parameters are solved in reverse by using a preset lubrication mechanism function. The lubrication process parameters include at least the range of lubricant pressure applied to the key affected area and the dynamic update frequency of lubricant supply.

[0080] Based on the lubrication process parameters, a lubrication condition distribution map is generated. At the same time, the changing trend data of the local accumulation state of lubricant in the key influence area under the adjustment of lubrication process parameters are recorded to quantitatively characterize the suppression effect of lubricant distribution state on eddy current intensity.

[0081] Specifically, when spatially overlaying and comparing the eddy current intensity distribution map with the wall thickness deviation data, it is necessary to clarify the source and resolution differences of the two types of data and complete the data registration process. The eddy current intensity distribution map is stored on the three-dimensional geometric model in the form of a cloud map, with each spatial location corresponding to an energy dissipation rate value. The sources of wall thickness deviation data can include the following: First, in the initial optimization stage, the wall thickness deviation data is the difference distribution between the target wall thickness distribution and the theoretical wall thickness specified in the design drawings. The allowable deviation range specified in the design drawings is used to determine whether the difference exceeds the diagnostic interval, but it is not used as the deviation data itself. Second, the wall thickness deviation data can be derived from the measured wall thickness statistics of the same cross-sectional structure, the same material grade, and the same reduction rate in historical production batches. The difference between the measured thickness and the corresponding target thickness is discretized into a spatial distribution form consistent with the coordinates of the current simulation model and used as the initial deviation reference field input. Third, in the closed-loop optimization iteration stage, after the wall thickness prediction distribution map is output in step S6, the difference between the wall thickness prediction distribution map and the target wall thickness distribution can be calculated. The calculated spatial difference distribution is used as the new wall thickness deviation data input in step S4 to realize the dynamic correlation analysis between eddy current intensity and wall thickness deviation. The registration process can employ a cross-sectional contour feature point alignment method, using cross-sectional corner points, maximum external width points, or curvature abrupt change points as alignment anchor points. The measured contour coordinates are aligned to the simulated contour coordinates through translation and rotation transformations, controlling the alignment error to not exceed twice the measurement resolution. After registration, the wall thickness deviation is regionalized, which can be achieved by averaging by grid cells, by surface segments, or by local addressing space, to ensure the same spatial partitioning scale as the eddy current intensity distribution map. The spatial overlay comparison method involves unifying the eddy current intensity distribution map and wall thickness deviation data into the same spatial coordinate system. Each grid node or cell is traversed, determining whether the eddy current intensity value at that location exceeds a preset intensity threshold, and simultaneously determining whether the wall thickness deviation exceeds a preset diagnostic deviation range. The preset intensity threshold can be set based on the material's thermal damage sensitivity or process stability requirements; the preset diagnostic deviation range is determined based on product specifications. When both conditions are met simultaneously, the node or cell is marked as a member of the critical influence region. Connectivity merging is performed on all marked nodes and their connected regions to form a continuous critical influence region. Output identification information for key affected areas, including area boundaries, area center coordinates, area or length scale, and statistics on eddy current intensity and wall thickness deviation within the area.

[0082] The negative correlation response model is used to describe the quantitative inverse compensation relationship between the friction coefficient of the target lubrication interface and the measured eddy current intensity. Its physical basis is that, in the forming mechanism, a higher friction coefficient intensifies shear concentration, leading to enhanced eddy currents, while a lower friction coefficient helps reduce the shear resistance between the material and the mold wall, thus suppressing eddy currents. Based on this physical positive correlation, inverse compensation must be adopted in the process control strategy; that is, the larger the measured eddy current intensity, the smaller the required target friction coefficient must be. The two are strictly negatively correlated in the control dimension. This model needs to be derived through experimental calibration or fitting historical process data, rather than purely mathematical construction, to ensure its physical feasibility. Two feasible paths can be used to establish the model: one is process calibration experiments, i.e., conducting multiple sets of lubrication condition experiments under the same operating conditions, measuring the mapping curve between the friction coefficient and eddy current intensity, and then mathematically inverting it to establish a negative feedback control law with eddy current intensity as input and the target friction coefficient as output; the other is historical data regression, combining simulation back-calculation to obtain the sensitivity of eddy current intensity to friction coefficient changes, and constructing a compensation formula accordingly. The fitting function can be a linear, power, or exponential function, depending on the data distribution. For example, for the drawing of a certain steel, the fitted negative correlation response model relationship is: Target friction coefficient = Base friction coefficient - 0.0015 × (Current measured eddy current intensity - Preset intensity threshold). That is, for every 10 MW / m³ that the current eddy current intensity exceeds the threshold, the target friction coefficient needs to be reduced by 0.015. After obtaining this response model, for each location within the critical influence area, the current measured eddy current intensity value is substituted into the model to directly obtain the target friction coefficient distribution required to eliminate flow turbulence. For example, if the reduced target friction coefficient is lower than the equipment lubrication limit, the target level can be set to 80% of the preset intensity threshold to ensure a safety margin. The final target friction coefficient distribution is the direct basis for guiding the process execution end to perform regional lubrication pressure adjustment.

[0083] The lubrication mechanism function describes the mapping relationship between lubrication process parameters and the interfacial friction coefficient. This function also needs to be obtained through experimental calibration or fitting with historical process data to ensure its physical feasibility. The inputs to the lubrication mechanism function include the target friction coefficient, the contact pressure range of the key influence area, the drawing speed level, and the lubricant viscosity level. The outputs are the lubricant application pressure range and the supply dynamic update frequency. The application pressure range needs to meet the upper and lower pressure limits of the lubrication supply system, and the supply dynamic update frequency needs to meet the pump and valve response capabilities and the minimum pulse cycle of the spraying or supply device. For example, for a spray-type lubrication system, multiple sets of process parameter combinations are tested to measure the interfacial friction coefficient under different lubricant application pressures and dynamic update frequencies. The application pressure range can be set to 0.2 MPa to 0.8 MPa, and the dynamic update frequency can be set to 1 to 5 times per minute. The experimental data are tabulated or a functional relationship is fitted; for example, the friction coefficient decreases linearly with increasing application pressure and decays exponentially with increasing dynamic update frequency. After obtaining the lubrication mechanism function, it is inverted for reverse solving: each value in the target friction coefficient distribution is substituted into the inverted function to calculate the corresponding lubricant application pressure and dynamic update frequency. The feasible region of the process parameters must also be considered during the solution process; for example, the applied pressure cannot exceed the equipment upper limit of 0.8 MPa, and the dynamic update frequency cannot exceed 5 times per minute. If the calculation result exceeds the feasible region, the boundary value is taken, and that location is recorded as a point requiring special attention. The reverse solving method can employ table lookup interpolation or numerical search. Table lookup interpolation is suitable for pre-established two-dimensional or three-dimensional process parameter tables, while numerical search is suitable for continuous function fitting relationships and requires a search stopping condition, such as the target friction coefficient error being less than 0.005 and the parameter variation being less than the equipment resolution. For the lubrication process parameter set of the key influence area, at least the lubricant application pressure range and dynamic update frequency corresponding to each location should be included.

[0084] The lubrication condition distribution map is generated by mapping lubrication process parameters back to the surface of a 3D geometric model, assigning each surface region a corresponding applied pressure and dynamic update frequency value. For regions outside the critical influence area, the original lubrication parameters can be kept unchanged, or global default values ​​can be used. The distribution map needs to include segmented boundary coordinates or a set of mesh nodes consistent with the simulation coordinates, and the resolution and interpolation method of the distribution map should be clearly defined, for example, using 5 mm circumferential arc lengths as segments or using mesh surface nodes as the smallest unit. The lubrication condition distribution map displays the lubrication parameter settings for different regions in the form of cloud maps or zoned colors. Simultaneously, to verify the effectiveness of lubrication adjustments, the changing trend data of the local lubricant accumulation state within the critical influence area needs to be recorded. The accumulation state can be characterized by the spatial fluctuation of the lubricant film thickness within the critical influence area and the area proportion of high film thickness points. For example, a short-term simulation or a pull test is performed using the adjusted lubrication process parameters to extract the lubricant film thickness distribution within the critical influence area, calculate the average film thickness and the accumulation area proportion, and compare it with the data before adjustment. If the average film thickness decreases and the accumulation area proportion decreases, it indicates that the lubricant distribution state has improved. These trend data are linked to key impact area identifiers and correlated with eddy intensity distribution maps. For example, scatter plots can be drawn to show the correlation between the decrease in the percentage of accumulated area and the decrease in eddy intensity.

[0085] S5. Spatially overlay and map the lubrication condition distribution map with the flow velocity distribution map, analyze the influence of shear and extrusion stress on wall thickness evolution, and determine the drawing speed compensation field used to correct flow unevenness.

[0086] In one specific embodiment, the process of performing step S5 may specifically include the following steps:

[0087] By unifying the lubrication condition distribution map and the flow velocity distribution map into the same spatial coordinate system and performing spatial superposition mapping, a coupled physical model characterizing the relationship between the friction boundary and the internal kinematics is constructed.

[0088] Based on the coupled physical model, the shear and compressive stress distribution in each local region of the irregular cross section is calculated. Combined with the principle of material volume incompressibility, the influence of shear and compressive stress distribution on the plastic deformation of the material is quantitatively analyzed, and the evolution of wall thickness deviation in the local region is predicted and output.

[0089] If the wall thickness deviation of any local area exceeds the preset allowable forming tolerance range, the drawing speed local adjustment vector of the corresponding local area is calculated in reverse with the goal of offsetting the wall thickness deviation.

[0090] Extract the local adjustment vector of the drawing speed in each local area, and introduce a drawing speed distribution uniformity correction mechanism based on spatial smoothing filtering or spline interpolation to fit and reconstruct the discrete local adjustment vector of drawing speed into a continuous drawing speed compensation field.

[0091] Specifically, the flow velocity distribution map is used as the input for the material's internal kinematic state, and the lubrication condition distribution map is used as the input for the friction boundary conditions. A coupling relationship between the friction boundary and the internal flow is established under the same simulation geometry and coordinate system. Then, the shear and compressive stress distribution in each local region of the irregular cross-section is calculated. This stress distribution is transformed into a calculable influence on plastic deformation and wall thickness evolution. When the wall thickness deviation exceeds the allowable forming tolerance, this deviation is inversely mapped to the required local drawing speed adjustment. The discrete local adjustment is then fitted into a continuous drawing speed compensation field through spatial smoothing filtering or spline interpolation. The drawing speed compensation field is the spatial distribution of the drawing speed compensation amount defined in the local region of the irregular cross-section, used to replace or superimpose the drawing speed boundary conditions.

[0092] Flow velocity distribution maps are typically velocity vector fields on volumetric mesh nodes or elements, while lubrication condition distribution maps are segmented sets of lubrication parameters on material surfaces or mold contact surfaces. To couple these two types of data, the lubrication condition distribution map needs to be mapped onto the simulation model boundary objects consistent with the flow velocity field. The mapping process uses the global model space established by S1 as a reference. The boundary coordinates of each segment in the lubrication condition distribution map determine the set of surface mesh nodes covered by that segment. The lubricant application pressure range, supply dynamic update frequency, and corresponding target friction coefficient for that segment are then assigned to this set, thus forming a spatially continuous or segmentally continuous friction boundary parameter field. When the segment scale of the lubrication condition distribution map is larger than the surface mesh scale, direct assignment is used; when the segment scale is smaller than the surface mesh scale, the surface mesh resolution needs to be increased or interpolation assignment needs to be used to avoid high-frequency changes that cannot be represented. After boundary mapping is completed, the surface friction parameter field and the volume velocity field are coupled in the same coordinate system. That is, the surface friction parameter field is used as the contact boundary condition, and the volume velocity field is used as the internal kinematic state to construct a coupled physical model characterizing the relationship between the friction boundary and the internal kinematics. This coupled physical model includes at least the material constitutive relation, the contact and friction relationship, and the kinematic constraints that satisfy volume conservation. The friction relationship can be expressed in the form of Coulomb friction with the target friction coefficient as input. At the same time, the dynamic update frequency of the supply is converted into the friction coefficient update period that varies with the drawing length, so that the model can express the situation of friction increase and shear intensification caused by insufficient lubrication supply.

[0093] The shear and compressive stress distribution in various local regions of an irregular cross-section is calculated based on a coupled physical model. Local regions can be divided using a set of volumetric elements or by extrapolating the cross-section blocks along the drawing direction to form volumetric partitions. Finer partitions are set in areas with abrupt curvature changes and narrow ribs to avoid averaging stress concentration. Finite element simulation is run, and the stress tensor of each mesh element or integration point is extracted. The normal compressive stress and tangential frictional stress at the contact interface are decomposed to obtain the shear and compressive stress distribution in each local region, represented as a contour plot or element list. The stress output needs to include the principal compressive stress along the drawing direction, the shear stress along the tangential direction of the cross-section, and the interfacial frictional shear stress related to the contact boundary. These are then unified into representative or statistical values ​​for each local region. For example, the volume average of the Gaussian integration point stress within the local region is taken, and the peak value is recorded simultaneously to reflect the degree of concentration.

[0094] The principle of volume incompressibility states that the volume of a metal remains constant during plastic deformation, which can be used to correlate stress distribution with wall thickness changes. Based on a known stress distribution, the equivalent plastic strain increment in each local region is calculated using the plastic flow law. Then, according to the condition of constant volume, the strain increment is converted into a wall thickness change. For example, for a certain cross-sectional element, if the calculated strain along the pull-out direction is 0.02 and the strain along the width direction is -0.01, then according to the constant volume, the strain in the thickness direction should be -0.01, i.e., a 1% reduction in wall thickness. By summing or integrating the wall thickness changes of each element, the wall thickness deviation evolution variable for each local region is obtained, i.e., the expected change value relative to the target wall thickness. The distribution of the wall thickness deviation evolution variable for each local region is stored in the form of mesh nodes or an element list, with each value representing the expected wall thickness change at that location.

[0095] The allowable forming tolerance range is set according to the product specifications. It iterates through all local areas, comparing the wall thickness deviation evolution of each area with the tolerance range. If the absolute value of the evolution variable is greater than the allowable forming tolerance range, the area is marked as needing adjustment. The basic principle of reverse calculation is that wall thickness deviation is caused by uneven material flow velocity distribution. By locally adjusting the drawing speed, the strain in that area can be changed, thereby offsetting the deviation. The calculation method can use sensitivity analysis, that is, obtaining the sensitivity relationship between local velocity changes and local thickness evolution through small-disturbance simulation. For example, a boundary velocity disturbance of ±2% amplitude is applied to a key local area, a small steady-state process is recalculated, and the direction and magnitude of the increase or decrease of the wall thickness evolution variable with velocity change in that area are obtained, determining the sensitivity coefficient. Taking a certain local area as an example, assuming that the velocity-wall thickness sensitivity coefficient for that area is -0.5 obtained through sensitivity analysis, this coefficient indicates that for every 1% increase in drawing speed, the wall thickness in that area is relatively thinned by 0.5%. Let the current wall thickness of this area be H, then the absolute wall thickness reduction caused by a 1% increase in speed is 0.005H. If the wall thickness deviation in this area is positive (indicating excessive thickness) and exceeds the allowable tolerance range, let the deviation be ΔH. The percentage increase in speed required to offset this deviation can be calculated using the formula Δv=(ΔH / (0.005H))%. For example, when H=100 and ΔH=0.1, Δv=0.1 / (0.005×100)=0.2%, meaning the drawing speed in this area needs to be increased by 0.2% to offset the 0.1 mm wall thickness deviation. The speed adjustment is converted into a vector form, with the adjustment direction along the drawing direction. The magnitude is determined by the above calculation and expressed in m / s, while also meeting the speed variation limits achievable by the equipment, such as a single adjustment amplitude not exceeding 5% of the set drawing speed. The local adjustment vectors for the drawing speed of each local area are obtained. Each vector contains the adjustment direction and adjustment amplitude and is bound to the local area identifier.

[0096] Direct application of discrete adjustment vectors can lead to discontinuities in the velocity field, causing numerical instability or equipment malfunction. Spatial smoothing filtering can employ Gaussian filtering or moving average filtering. The filtering window must be limited to topological breakpoints that do not cross geometrical sharp corners to avoid incorrectly averaging compensation amounts that should be different on both sides of a corner. For example, using Gaussian filtering, a Gaussian kernel radius of 3 mm is defined centered on each adjustment vector point, with weights decreasing with distance. The magnitudes of all adjustment vectors in the neighborhood are weighted and averaged to obtain the smoothed magnitude. Spline interpolation can be performed by cubic spline fitting of the discrete velocity compensation amount on the circumferential arc length parameter. A first-order derivative continuity constraint is applied to the fitted curve to ensure the smoothness of the velocity compensation field. Simultaneously, an magnitude constraint is applied to the fitting result to ensure that the maximum compensation amount does not exceed the achievable range of the equipment. During the fitting process, it is necessary to ensure that the adjustment magnitude of the interpolated surface is close to the original calculated value in the critical influence region and approaches zero in the unadjusted region. The drawing speed compensation field is defined as the spatial distribution of the drawing speed compensation amount defined in the local region of the irregular cross-section, used to replace or superimpose the drawing speed boundary conditions. The compensation field is stored in the form of grid node data or analytical functions. Each node contains a velocity adjustment amplitude, and the pulling direction is a fixed direction.

[0097] The above technical solution associates lubrication conditions with velocity field through a coupled physical model, enabling shear and extrusion stress analysis to reflect boundary changes after lubrication optimization; it transforms stress distribution into wall thickness deviation prediction by combining the principle of volume incompressibility, giving velocity adjustment a clear physical objective; and it combines reverse calculation with smooth reconstruction, ensuring both the targeted nature of the adjustment and the continuous executability of the velocity field.

[0098] S6. Update the flow field simulation parameters based on the drawing speed compensation field, recalculate the material flow path, and generate the corresponding wall thickness prediction distribution map.

[0099] In one specific embodiment, the process of performing step S6 may specifically include the following steps:

[0100] The drawing speed compensation field is used as a new kinematic boundary condition to replace or superimpose on the initial drawing speed boundary of the flow field simulation, thereby updating the flow field simulation parameters.

[0101] The updated flow field simulation parameters are used to drive the finite element solver to recalculate the material flow path during the drawing process of irregular steel bars and output transient flow field data.

[0102] Based on the recalculated material flow path and transient flow field data, the corresponding wall thickness prediction distribution map is generated through volume integration or grid node displacement tracking algorithm.

[0103] The predicted wall thickness distribution map is compared with the preset target wall thickness distribution, and the wall thickness deviation of each local area is calculated.

[0104] If the wall thickness deviation in any local area exceeds the preset allowable deviation range, a correction command for the drawing speed compensation field is triggered, and the process proceeds to step S7.

[0105] Specifically, the drawing speed compensation field is used as an executable kinematic boundary input and written into the flow field simulation model. Thus, without changing the geometric model of the irregular cross-section, the material constitutive parameters, and the setting diameter of the lubrication boundary, the velocity field, streamlines, and nodal displacement evolution of the material during the drawing process are recalculated. Based on the recalculation results, the predicted distribution of wall thickness in each local area of ​​the cross-section is obtained. Then, the effectiveness of the speed compensation field is converted into a quantifiable wall thickness deviation. When the deviation exceeds the limit, it triggers the entry into S7 to recalculate the compensation field.

[0106] The drawing speed compensation field is the spatial distribution of drawing speed compensation amounts defined in local regions of irregular cross-sections. Its data format is mesh node data or surface segment data consistent with the global model space in S1. When the simulation uses a three-dimensional volume model, the drawing speed boundary is usually applied to the node set of the material exit section or the traction clamping section. Therefore, it is necessary to convert the distribution of the compensation field in the circumferential or section-specific direction of the cross-section into a speed assignment table for the nodes of the exit section, ensuring that the assignment direction is consistent with the drawing direction. The replacement method completely replaces the original boundary conditions with the speed distribution defined by the compensation field, suitable for situations where the compensation field already contains complete speed information. The superposition method adds the adjustment amount defined by the compensation field to the original boundary conditions, suitable for situations requiring only local correction. For example, if the initial drawing speed is 0.67 m / s and the compensation field provides +0.03 m / s in one local region and -0.02 m / s in another, then under the superposition method, the boundary speeds of these two local regions are 0.70 m / s and 0.65 m / s, respectively. The continuity of velocities between adjacent nodes needs to be checked. If the velocity jump between nodes exceeds a preset upper limit, such as 0.05 m / s, a boundary smoothing process should be performed before writing the boundary conditions to avoid numerical non-convergence of the solver. Simultaneously, the partition boundaries of the compensation field need to be bound and stored with the node set so that subsequent S7 can correct the compensation field according to the same partition structure without region drift. After writing the boundary conditions, the flow field simulation parameter file or solver input set should be updated synchronously. The updates should include at least the kinematic boundary condition table, the time function for applying the boundary conditions, and the solution step size setting. When the compensation field introduces spatially varying velocities, the solver needs to handle the redistribution of internal flow caused by the velocity differences between different boundary nodes. Therefore, the time integral needs to be set to a form that can achieve stable convergence. For example, a piecewise loading strategy can be adopted, loading the compensation boundary from 0 to the target value in a linear increment at the beginning of the simulation to reduce transient impacts. For example, the compensation boundary loading time can be set to 0.05 s to 0.2 s, and multi-step incremental loading can be used within this time period, while using a smaller time step during the loading phase to ensure contact iteration convergence. The updated finite element simulation input file includes information on the pull-out speed compensation field and the corresponding solution control parameters.

[0107] The updated simulation input file is submitted to the finite element solver for calculation. The solver uses the same numerical method as S1 (such as implicit static analysis or explicit dynamic analysis), keeping the material constitutive, friction boundary, mesh generation, and thermo-coupling options unchanged, only replacing or superimposing the kinematic boundaries. During the solution process, transient flow field data needs to be output, including at least three types of results: the volume velocity vector field, the volume nodal displacement field, and the contact pressure and friction shear stress distribution related to the contact boundary. This allows subsequent wall thickness prediction to be achieved either through geometric displacement tracking or volume integration. The time interval of the transient output needs to match the residence time of the material in the mold deformation zone. The residence time can be estimated from the deformation zone length and average flow velocity and used to determine the number of output steps, avoiding excessively sparse output that would prevent the wall thickness evolution process from being reconstructed. For example, when the equivalent length of the mold deformation zone is 50 mm and the average material velocity is 0.67 m / s, the residence time is approximately 0.075 s. Therefore, 7 to 10 frames of transient field data can be output at 0.01 s intervals, with an additional 1 to 2 frames output as a steady-state reference after the outlet stabilizes. The recalculation of the material flow path can follow the virtual particle tracking method of S3, that is, to advance virtual particles in the updated velocity field to obtain a new equivalent flow path, so that the wall thickness prediction can be combined with the path information to locate the local stretching and compression process of the material from the inlet to the outlet.

[0108] Two methods can be used to generate wall thickness predictions. The volume integration method is based on the principle of mass conservation. During drawing, the material volume remains constant, and the wall thickness change can be estimated by calculating the volumetric flow rate between adjacent sections. Specifically, several sections are taken along the drawing direction, and the material volumetric flow rate through each section is calculated. Combined with the known wall thickness at the inlet section, the wall thickness distribution of the downstream sections is calculated segment by segment, and the integration domain needs to be consistent with the local region partitioning. The mesh node displacement tracking algorithm is suitable for directly tracking the distance changes of inner and outer surface nodes in the normal direction. That is, several pairs of corresponding nodes or corresponding measuring points are defined at the inlet section, and corresponding node pairs are found at the outlet section. The distance between the two nodes is calculated as the local wall thickness prediction value. The correspondence can be established through material point tracking or through node label inheritance. For example, a measuring point is arranged every 5 mm circumferentially at the outlet section, and the corresponding surface node sequence is recorded at the inlet section. During the simulation, the deformation and migration of this node sequence are tracked along the flow path. New node positions are obtained at the outlet section to calculate the local thickness and form a thickness distribution curve along the circumferential direction. The curve is then mapped to the section coordinates to generate a wall thickness prediction distribution map. When using displacement tracking, it is necessary to prevent node misalignment or contact leading to node correspondence failure. Therefore, material point tracking needs to be enabled in the simulation model, or a Lagrange mesh should be used while maintaining mesh topology consistency. If an arbitrary Lagrange-Eulerian method is used, material point tracking information needs to be output simultaneously to establish the correspondence between the inlet and outlet. The predicted wall thickness distribution map is stored in the form of mesh node data or cross-sectional curves, with each location corresponding to a predicted wall thickness value.

[0109] The target wall thickness distribution is derived from product design drawings, such as the theoretical wall thickness values ​​at various cross-sectional positions of irregularly shaped steel bars. During comparison, the predicted and target distributions need to be sampled at the same scale. For example, both can be discretized into several sampling points using the circumferential arc length parameter, or the average thickness can be calculated using local region segments as units. The deviation is then calculated as the difference between the predicted and target thicknesses. The division of local regions can be consistent with the influence range of the potential eddy region in S2 or the key influence region in S4, in order to trace the source of the deviation. For example, if the target thickness is 3.0 mm and the predicted thickness of a certain local region is 2.86 mm, the deviation is -0.14 mm, representing a thinning trend; if the predicted thickness of another local region is 3.18 mm, the deviation is +0.18 mm, representing an accumulation trend. The absolute value and sign of the deviation need to be recorded simultaneously to ensure consistency in the correction direction of the compensation field in subsequent S7. After the deviation calculation is completed, the deviation is bound to the local region identifier, and a deviation table containing the local region boundary, deviation amount, and deviation statistics is output.

[0110] The allowable deviation range is set according to product specifications, such as ±0.05mm for the wall thickness of a certain irregular steel bar, or different thresholds are given for different wall sections. Trigger judgment is based on whether the absolute value of the deviation in a local area exceeds the threshold. In the presence of noise or local spikes, an area ratio condition can be introduced. That is, when the number of out-of-limit units or out-of-limit sampling points exceeds a preset proportion (e.g., 10%) of the number of sampling points in that local area, correction is triggered to avoid unnecessary iterations due to single-point errors. The wall thickness deviation of all local areas is traversed. If a region triggers correction, it is determined that the current drawing speed compensation field has not yet reached the optimization target. The correction command output includes an out-of-limit region identifier, the out-of-limit deviation amount, the deviation direction, and a suggested correction priority. The priority can be determined by the absolute value of the deviation or by whether it is within the potential eddy current influence range, thus allowing S7 to adjust the speed compensation amplitude of key areas with higher weight during optimization calculations. If the wall thickness deviation of all local areas is within the allowable range, the current drawing speed compensation field meets the requirements, iteration can be stopped, and the current compensation field is output as the final result.

[0111] S7. Using the uniformity of the predicted wall thickness distribution map as the objective function, the drawing speed compensation field is iteratively calculated through an optimization algorithm to generate the final control parameters for drawing and forming of irregular steel bars.

[0112] In one specific embodiment, the process of performing step S7 may specifically include the following steps:

[0113] With the goal of maximizing the uniformity of the predicted wall thickness distribution map, an objective function is constructed with the core objective of minimizing the variance or root mean square error of the wall thickness deviation in each local area.

[0114] For complex flow fields containing potential vortex regions, a drawing speed region segmentation strategy is applied to divide the drawing speed compensation field into several independent control sub-regions.

[0115] The speed compensation adjustment amplitude of the drawing speed compensation field in each independent control sub-region, and the transition time of the drawing speed command, which characterizes the smoothness of the speed change of the forming equipment, are jointly encoded as independent variables into decision variables of the genetic optimization algorithm.

[0116] A genetic optimization algorithm is used to perform crossover, mutation, and selection operations on decision variables based on the objective function to generate an updated drawing speed compensation field, which is then returned to S6 for flow field recalculation and wall thickness prediction evaluation.

[0117] Continue executing the iterative closed loop until the objective function converges and the wall thickness deviation in each local region is less than the preset allowable deviation range, then stop the iteration;

[0118] The lubrication condition distribution diagram and the drawing speed compensation field under the final convergence state are packaged to generate the final control parameters for drawing and forming of irregular steel bars.

[0119] Specifically, the wall thickness prediction distribution map includes the predicted wall thickness values ​​for each local region. The division of local regions follows the method used in S2 or S4, allowing the same partition to be used for both velocity compensation and thickness deviation evaluation. The objective function quantifies the uniformity of wall thickness under the current compensation field and can be expressed as the root mean square error (RMSE) of the deviation to avoid cancellation between positive and negative deviations. For example, the objective function can be defined as the RMSE, with the optimization objective being to minimize the RMSE. Simultaneously, higher weights can be assigned to local regions within the potential eddy current influence range, prioritizing the suppression of thickness anomalies related to flow turbulence during the optimization process. For instance, the weight of local regions within the potential eddy current influence range can be set to twice that of other regions, and the weight of regions where the absolute value of wall thickness deviation exceeds the diagnostic threshold can be set to three times that of other regions. Furthermore, an allowable deviation range should be introduced as a constraint. When the deviation of any local region exceeds the allowable deviation range, the candidate compensation field is deemed not to meet the constraint, and its fitness is reduced or it is directly eliminated during the optimization selection process.

[0120] Region segmentation needs to correspond to the speed adjustment granularity achievable by the forming equipment to avoid introducing new speed fluctuations due to excessively fine regions causing frequent speed changes. Region segmentation is jointly determined based on cross-sectional geometric features, the coordinates and influence range of potential eddy current regions output by S2, and the boundaries of key influence regions output by S4. Geometric features ensure that the segmentation boundary is consistent with structural boundaries such as corners, narrow ribs, and abrupt curvature changes. The eddy current influence range ensures that the turbulent propagation region is covered as an independent control object. The key influence region ensures that areas exceeding thickness limits are not fragmented during segmentation. Segmentation methods can include segmentation using circumferential arc length parameters with segmentation points added at feature locations, or clustering segmentation based on surface mesh connected domains with connected domains as control sub-regions. For example, the outer perimeter of the cross-section is divided into several segments according to arc length, ensuring that each segment is not less than 5 mm and not more than 30 mm in length. The segment containing the eddy current core is treated as a separate control sub-region, and a transition sub-region is set outside the eddy current influence range to avoid compensating for abrupt changes.

[0121] The speed compensation control amplitude is the compensation amount of each control sub-region relative to the reference drawing speed. Its initial value is extracted from the drawing speed compensation field, such as taking the average value or center point value of the compensation amplitude of all nodes in the sub-region as a representative. The upper and lower limits of the amplitude are determined by the speed adjustment range of the forming equipment and the allowable single speed change amplitude, such as using ±5% of the reference speed as the boundary. At the same time, the boundary continuity constraint caused by the speed difference between adjacent sub-regions must be considered to avoid numerical instability or equipment execution difficulties caused by abrupt amplitude changes. The drawing speed command transition time is used to characterize the smoothing processing parameter of the forming equipment when executing speed change commands, that is, the ramp time experienced from the current speed to the target speed. This parameter is a programmable control parameter, and its value range is determined by the settable range of the equipment controller (e.g., 0.01s to 0.5s). This command transition time is used to constrain the gradient of the compensation field in space and the switching frequency in time, so that the compensation field does not require the equipment to switch frequently on a scale shorter than the command transition time, while avoiding mechanical shocks caused by abrupt speed changes. The encoding method employs real-number encoding, arranging the speed compensation amplitude of each control sub-region in a fixed order to form a real-number sequence. The pull-out speed command transition time is written into the chromosome as an additional gene locus. To ensure feasibility, boundary truncation and quantization are applied to the real-number variables; for example, the speed compensation amplitude is quantized to the 0.001 m / s level according to the equipment's speed resolution, and the command transition time is quantized to the 0.01 s level. An initial population is output, with a population size that can be set to 50 individuals.

[0122] The iterative process of the genetic algorithm includes the following operations: Fitness evaluation: Each individual is decoded into a drawing speed compensation field. The S6 simulation process is called to calculate the predicted wall thickness distribution under this compensation field. The objective function value is calculated as the fitness. Individuals that violate the hard constraint of the allowable deviation range are penalized to reduce their fitness. Selection operation: A tournament selection method is used to select excellent individuals to enter the next generation based on their fitness. Crossover operation: Simulated binary crossover is used to perform fragment crossover in the control sub-region dimension, exchanging the speed compensation amplitude fragments of two individuals in several sub-regions. The crossover probability is set to 0.8. Mutation operation: Polynomial mutation is used to slightly increase or decrease the speed compensation amplitude of randomly selected sub-regions and slightly perturb the command transition time gene. The mutation probability is set to 0.1. At the same time, boundary continuity correction and command transition time constraint checks are performed after mutation (such as ensuring that the transition time does not exceed the settable range of the controller and that the compensation amplitude transition of adjacent sub-regions is smooth). After each genetic operation is completed, a new generation of population is generated, and the new generation of individuals is decoded into a new drawing speed compensation field. The compensation field serves as the input to S6, and the flow field simulation and wall thickness prediction are performed again, forming a two-layer loop structure of outer search by genetic algorithm and inner evaluation by finite element simulation.

[0123] The iteration termination conditions include two aspects: global convergence, where the improvement in optimal fitness of the population for five consecutive generations is less than a preset value, or the preset maximum number of iterations is reached; and local feasibility, where the absolute value of the wall thickness deviation in all local regions of the wall thickness prediction distribution map corresponding to the current best individual is less than a preset allowable deviation range. The iteration stops when both conditions are met simultaneously. The output is the optimal individual in the final convergent state, i.e., a set of optimal decision variable values, including the velocity compensation amplitude and the pull-out speed command transition time for each control sub-region.

[0124] Preferably, after the speed optimization converges, the optimal speed compensation field can be substituted back into S4 to check the lubrication conditions. If the eddy current intensity in the key influence area rises above a preset threshold (e.g., 10%), then an outer iteration is performed to fix the updated lubrication conditions again and restart speed optimization until the two converge together.

[0125] The lubrication condition distribution map, derived from the final output of S4, includes the lubricant application pressure range and supply dynamic update frequency for each surface segment or key influence area, along with corresponding coordinate boundary information. The drawing speed compensation field is the optimized individual decoded compensation field, containing the speed compensation amplitude distribution for each control sub-region and the corresponding drawing speed command transition time. Both are stored in the same parameter table file, clearly defining the lubrication parameters, drawing speed compensation amplitude, and command transition time for each local region, and specifying whether the compensation field is applied by replacing or superimposing it onto the baseline drawing speed boundary conditions. The packaged results include at least the section identifier, die identifier, material grade, baseline drawing speed, speed compensation amplitude for each sub-region, drawing speed command transition time, lubrication pressure range and update frequency for each zone, and allowable deviation range, ensuring parameter traceability and reusability under the same operating conditions during subsequent production calls.

[0126] The above process divides the compensation field into independent control sub-regions through a region segmentation strategy, ensuring that the number of optimization variables is controllable and matches the physical problem area. The transition time of the drawing speed command is introduced as a programmable control parameter into the optimization, ensuring that the optimization result considers both the spatial distribution of speed compensation and the smoothing capability of the equipment execution. A genetic algorithm is used for global optimization to avoid getting trapped in local optima. Closed-loop iteration continues until convergence and the deviation reaches the target, ensuring that the final control parameters meet the wall thickness uniformity requirements. This technical solution can automatically search for the drawing speed compensation field that optimizes wall thickness uniformity while considering the smoothing capability of the equipment commands, and together with lubrication conditions, form executable forming control parameters.

[0127] Figure 3The figure shows a comparison between the predicted wall thickness distribution before and after optimization and the target wall thickness. In the figure, the horizontal axis represents the distance (in mm) along the circumference of the irregular cross-section, and the vertical axis represents the corresponding wall thickness value (in mm). The black dashed line represents the target wall thickness required by the product design (a constant value of 3.0 mm); the red solid line represents the predicted wall thickness distribution before optimization, showing significant wall thickness accumulation (approximately 3.18 mm) and thinning (approximately 2.82 mm) around 30 mm and 70 mm in the circumferential direction, with a maximum deviation of ±0.18 mm, exceeding the allowable forming tolerance range; the blue solid line represents the predicted wall thickness distribution after iterative optimization through steps S1 to S7 of this application, where fluctuations are effectively suppressed, and the maximum deviation is controlled within ±0.05 mm, highly consistent with the target wall thickness. This comparison result intuitively verifies the significant technical effect of the proposed method for optimizing the drawing parameters of irregular steel bars in improving wall thickness uniformity and processing accuracy.

[0128] The above describes the method for optimizing the drawing parameters of irregularly shaped steel bars in the embodiments of this application. The following describes the system for optimizing the drawing parameters of irregularly shaped steel bars in the embodiments of this application. Please refer to [link / reference]. Figure 4 The structural schematic diagram of the shaped steel bar drawing forming parameter optimization system provided in this application includes:

[0129] The geometric simulation module is used to extract the geometric features of irregular cross-section data, perform flow field simulation based on the geometric features, and generate a preliminary flow velocity distribution map.

[0130] The eddy current identification module is used to perform velocity gradient analysis based on the flow velocity distribution map, identify potential eddy current regions with abnormal velocity gradients, and determine the influence range of the potential eddy current regions.

[0131] The path tracing module is used to track the flow path of the material within the influence area and generate an eddy current intensity distribution map based on the tracking results.

[0132] The lubrication optimization module is used to perform correlation analysis between the eddy current intensity distribution map and the preset wall thickness deviation data, adjust the lubrication process parameters based on the analysis results, and generate a lubrication condition distribution map.

[0133] The speed compensation module is used to spatially overlay and map the lubrication condition distribution map with the flow velocity distribution map, analyze the influence of shear and extrusion stress on wall thickness evolution, and determine the drawing speed compensation field used to correct flow unevenness.

[0134] The wall thickness prediction module is used to update the flow field simulation parameters based on the drawing speed compensation field, recalculate the material flow path, and generate the corresponding wall thickness prediction distribution map.

[0135] The parameter optimization module is used to generate the final control parameters for drawing and forming of irregular steel bars by iteratively calculating the drawing speed compensation field through an optimization algorithm, with the uniformity of the wall thickness prediction distribution map as the objective function.

[0136] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for optimizing drawing parameters of irregularly shaped steel bars, characterized in that, The method includes: S1. Extract the geometric features of the irregular cross-section data, perform flow field simulation based on the geometric features, and generate a preliminary flow velocity distribution map; S2. Based on the flow velocity distribution map, perform velocity gradient analysis to identify potential vortex regions with abnormal velocity gradients and determine the influence range of the potential vortex regions. S3. Track the flow path of the material within the influence range and generate an eddy current intensity distribution map based on the tracking results; S4. Perform correlation analysis between the eddy current intensity distribution map and the preset wall thickness deviation data, adjust the lubrication process parameters based on the analysis results, and generate a lubrication condition distribution map; S5. Spatially superimpose and map the lubrication condition distribution map with the flow velocity distribution map, analyze the influence of shear extrusion stress on wall thickness evolution, and determine the drawing speed compensation field used to correct uneven flow. S6. Update the flow field simulation parameters according to the drawing speed compensation field, recalculate the material flow path, and generate the corresponding wall thickness prediction distribution map. S7. Using the uniformity of the predicted wall thickness distribution map as the objective function, the drawing speed compensation field is iteratively calculated using an optimization algorithm to generate the final drawing control parameters for the irregular steel bar.

2. The method according to claim 1, characterized in that, S1 includes: Obtain the global model space corresponding to the irregular cross-section data, and perform initial mesh generation of the global model space with basic density; Geometric rotation features and curvature abrupt change features were extracted from the irregular cross-section data using finite element simulation tools. For the local regions where the geometric corner features and curvature abrupt change features are located, a high-density mesh is divided based on the base density. If the curvature abrupt change value of any local region exceeds the preset abrupt change threshold, the mesh density of any local region is further adaptively refined and adjusted. Obtain initial distribution data of lubricant on the surface of the irregular steel bar, wherein the initial distribution data includes at least the lubricant coating thickness and the lubricant viscosity grade; Based on the mesh generation results and the initial distribution data, the flow velocity distribution map is generated through finite element simulation calculation.

3. The method according to claim 1, characterized in that, S2 include: Extract velocity gradient data for each local region from the flow velocity distribution map; The velocity gradient data is compared with a preset velocity gradient threshold range. If the velocity gradient data of any local area exceeds the velocity gradient threshold range, the local area is determined to be a potential vortex region, and the spatial coordinates of the potential vortex region are extracted. A local addressing space is established based on the spatial coordinates of the potential eddy region. The distribution uniformity index of the lubricant and the local accumulation characteristic data in the local addressing space are obtained, and then the disturbance effect of the potential eddy region on the flow of surrounding materials is analyzed. Based on the analysis results of the disturbance impact, the influence range of the potential eddy region is determined by using the spatial coordinates of the potential eddy region as a reference and the boundary expansion algorithm.

4. The method according to claim 1, characterized in that, S3 include: Within the influence range of the potential vortex region, virtual particle image velocimetry technology based on flow field simulation is used to track the equivalent flow path of the material within the potential vortex region and extract the corresponding path deviation vector data. Obtain the nonlinear interface parameters corresponding to the equivalent flow path. The nonlinear interface parameters include at least the dynamic friction coefficient between the lubricant and the molding material, and the high-temperature stability parameters characterizing the lubricant under shear heating conditions. Combining the path deviation vector data and the nonlinear interface parameters, the local energy dissipation rate caused by flow turbulence is calculated based on the energy dissipation model, thereby generating the eddy intensity distribution map, and locating and marking the eddy core position in the eddy intensity distribution map; Extract the peak intensity data at the core of the vortex. If the peak intensity data exceeds the preset vortex intensity threshold, perform a detailed tracking analysis of the flow path at the core of the vortex and its surrounding area, and iteratively generate an updated vortex intensity distribution map until the accuracy requirements are met.

5. The method according to claim 1, characterized in that, S4 include: By spatially superimposing and comparing the eddy current intensity distribution map with the wall thickness deviation data, key influencing areas where the eddy current intensity is higher than a preset intensity threshold and the wall thickness deviation exceeds a preset diagnostic deviation range are identified. For the key influencing region, a negative correlation response model between eddy current intensity and lubrication interface friction coefficient is established. Based on the negative correlation response model, the target friction coefficient distribution for suppressing eddy current intensity is calculated. Based on the target friction coefficient distribution, the corresponding lubrication process parameters are solved in reverse by using a preset lubrication mechanism function. The lubrication process parameters include at least the range of lubricant pressure applied to the key affected area and the dynamic update frequency of lubricant supply. Based on the lubrication process parameters, a lubrication condition distribution map is generated. At the same time, the changing trend data of the local accumulation state of lubricant in the key influence area under the adjustment of the lubrication process parameters are recorded to quantitatively characterize the suppression effect of the lubricant distribution state on the eddy current intensity.

6. The method according to claim 1, characterized in that, S5 include: The lubrication condition distribution map and the flow velocity distribution map are unified into the same spatial coordinate system and spatially superimposed and mapped to construct a coupled physical model characterizing the relationship between the friction boundary and the internal kinematics. Based on the coupled physical model, the shear and compressive stress distribution in each local region of the irregular cross section is calculated. Combined with the principle of material volume incompressibility, the influence of the shear and compressive stress distribution on the plastic deformation of the material is quantitatively analyzed, and the wall thickness deviation evolution of the local region is predicted and output. If the wall thickness deviation evolution variable of any local area exceeds the preset allowable forming tolerance range, then with the goal of offsetting the wall thickness deviation evolution variable, the local adjustment vector of the drawing speed of the corresponding local area is calculated in reverse. Extract the local adjustment vector of the pulling speed in each local region, introduce a pulling speed distribution uniformity correction mechanism based on spatial smoothing filtering or spline interpolation, and fit and reconstruct the discrete local adjustment vector of the pulling speed into a continuous pulling speed compensation field.

7. The method according to claim 1, characterized in that, S6 include: The drawing speed compensation field is used as a new kinematic boundary condition to replace or superimpose on the initial drawing speed boundary of the flow field simulation, thereby updating the flow field simulation parameters. The updated flow field simulation parameters are used to drive the finite element solver to recalculate the material flow path during the drawing process of irregular steel bars and output transient flow field data. Based on the recalculated material flow path and the transient flow field data, a corresponding wall thickness prediction distribution map is generated using volume integration or grid node displacement tracking algorithms. The predicted wall thickness distribution map is compared with the preset target wall thickness distribution, and the wall thickness deviation of each local area is calculated. If the wall thickness deviation in any local area exceeds the preset allowable deviation range, a correction command for the drawing speed compensation field is triggered, and the process proceeds to step S7.

8. The method according to claim 7, characterized in that, S7 includes: With maximizing the uniformity of the predicted wall thickness distribution map as the optimization objective, an objective function is constructed with minimizing the variance or root mean square error of the wall thickness deviation in each local area as the core objective. For complex flow fields containing potential vortex regions, a drawing speed region segmentation strategy is applied to divide the drawing speed compensation field into several independent control sub-regions. The speed compensation adjustment amplitude of the drawing speed compensation field in each independent control sub-region, and the drawing speed command transition time, which characterizes the smoothness of the speed change of the forming equipment, are jointly encoded as decision variables of the genetic optimization algorithm. A genetic optimization algorithm is used to perform crossover, mutation, and selection operations on the decision variables based on the objective function to generate an updated drawing speed compensation field, and then returns to S6 for flow field recalculation and wall thickness prediction evaluation. Continue executing the iterative closed loop until the objective function converges and the wall thickness deviation of each local region is less than the preset allowable deviation range, then stop the iteration; The lubrication condition distribution diagram and the drawing speed compensation field under the final convergence state are packaged together to generate the final drawing and forming control parameters for the irregular steel bar.

9. A parameter optimization system for drawing and forming irregularly shaped steel bars, used to implement the method as described in any one of claims 1 to 8, characterized in that, The system includes: The geometric simulation module is used to extract the geometric features of the irregular cross-section data, perform flow field simulation based on the geometric features, and generate a preliminary flow velocity distribution map. The eddy current identification module is used to perform velocity gradient analysis based on the flow velocity distribution map, identify potential eddy current regions with abnormal velocity gradients, and determine the influence range of the potential eddy current regions. The path tracing module is used to trace the flow path of the material within the influence range and generate an eddy current intensity distribution map based on the tracing results. The lubrication optimization module is used to perform correlation analysis between the eddy current intensity distribution map and the preset wall thickness deviation data, adjust the lubrication process parameters based on the analysis results, and generate a lubrication condition distribution map. The speed compensation module is used to spatially superimpose and map the lubrication condition distribution map and the flow velocity distribution map, analyze the influence of shear and extrusion stress on wall thickness evolution, and determine the drawing speed compensation field used to correct flow unevenness. The wall thickness prediction module is used to update the flow field simulation parameters based on the drawing speed compensation field, recalculate the material flow path, and generate the corresponding wall thickness prediction distribution map. The parameter optimization module is used to perform iterative calculations on the drawing speed compensation field using an optimization algorithm, with the uniformity of the predicted wall thickness distribution map as the objective function, to generate the final control parameters for drawing and forming of the irregular steel bar.

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