A multi-step stress relief method and system for tube end forming

Abstract

This invention discloses a multi-step stress relief method and system for pipe end forming, specifically relating to the field of non-cutting machining of metal pipes. It addresses the problems of uneven stress release and unstable forming quality and consistency caused by rough planning in existing multi-step forming processes. By acquiring the pipe material and geometric parameters, the method determines whether the preset forming path meets the stress relaxation conditions. If the conditions are met, simulation is used to obtain the residual stress field distribution characteristics of each step and calculate the degree of difference between steps. Based on the evolution of the degree of difference, the mode transfer characteristics of stress redistribution are identified to assess the damage risk level. When the risk level is high, the energy conversion efficiency parameter of the path in the verification stage is measured. Combining the risk level and efficiency parameter, the process parameters of subsequent steps of the path are adjusted to generate and execute an optimized forming path. This achieves scientific evaluation and dynamic optimization of the forming process, promotes the orderly and full release of stress, and improves forming accuracy.

Description

Technical Field

[0001] This invention relates to the field of non-cutting machining technology for metal pipes, and more specifically, to a multi-step stress relief method and system for pipe end forming. Background Technology

[0002] In the field of non-cutting machining of metal pipes, especially in the pipe end forming process of high-requirement components such as automotive intake and exhaust systems, a multi-step forming process can be adopted to improve the problems of large material springback and easy cracking caused by single-stage, intense forming. In existing technologies, this type of process decomposes the forming process into multiple sequentially executed steps, aiming to gradually accumulate deformation and release some stress between steps. Its implementation typically relies on a pre-set fixed program to control the feed rate of each step, and the determination of the step sequence and process parameters is mostly based on experience or a simple geometric decomposition of the final target shape.

[0003] However, due to the lack of precise consideration of the complex interaction between the internal stress relaxation dynamics and subsequent plastic deformation of the material during multiple intermittent loading and unloading cycles, existing methods have inherent defects in planning multi-step forming paths. This extensive step planning method makes it difficult to achieve orderly and full release of internal stress in the material during the forming process, resulting in uneven stress release effects. Consequently, it is impossible to reliably coordinate the contradiction between high-precision forming and suppressing material damage, thus restricting further improvement in the forming quality and consistency of the tube end. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a multi-step stress relief method and system for pipe end forming to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A multi-step stress relief method for pipe end forming includes the following steps:

[0007] S1. Obtain the material parameters and initial geometric dimensions of the pipe to be formed;

[0008] S2. Based on the material parameters and initial geometric dimensions, determine whether the pipe meets the stress relaxation condition under the preset initial multi-step forming path.

[0009] S3. When the stress relaxation condition is met, the initial multi-step forming path is simulated to obtain the residual stress field distribution characteristics of the pipe after each forming step, and the degree of difference in the residual stress field distribution characteristics between adjacent steps is calculated.

[0010] S4. Identify the mode transfer characteristics of residual stress redistribution in the initial multi-step molding path based on the evolution of the degree of difference in the molding step sequence, and assess the risk level of material damage based on the mode transfer characteristics.

[0011] S5. When the risk level is high, measure the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage.

[0012] S6. Combining the risk level and energy conversion efficiency parameters, adjust the process parameters of subsequent steps in the initial multi-step molding path to generate and execute an optimized multi-step molding path.

[0013] Furthermore, S1 includes:

[0014] The yield strength and elastic modulus of the pipe are obtained as material parameters through standard tensile testing.

[0015] The outer diameter, wall thickness, and straight segment length of the pipe are obtained by laser 3D scanning as the initial geometric dimensions.

[0016] Furthermore, the pipe to be formed is a stainless steel pipe used in automotive exhaust systems.

[0017] Furthermore, S2 includes:

[0018] Based on the obtained yield strength, elastic modulus, outer diameter and wall thickness, the estimated mechanical energy of the maximum deformation in a single step in the initial multi-step forming path is calculated.

[0019] The estimated mechanical energy of the maximum deformation in a single step is compared with the material's single-step deformation energy threshold determined based on yield strength and elastic modulus.

[0020] At the same time, the total step length of the initial multi-step forming path is compared with the material characteristic relaxation length determined based on yield strength and elastic modulus;

[0021] When the estimated mechanical energy of the maximum deformation in a single step is less than the material's single-step deformation energy threshold, and the total step length is greater than the material's characteristic relaxation length, the stress relaxation condition is deemed to be met.

[0022] Furthermore, S3 includes:

[0023] Based on the obtained yield strength, elastic modulus, outer diameter and wall thickness, a finite element model of the pipe is established.

[0024] Following the sequence of steps in the initial multi-step forming path, displacement boundary conditions corresponding to each step are applied sequentially to the finite element model to simulate forming. After each step of forming simulation, the displacement boundary conditions are removed to simulate unloading, thereby obtaining the residual stress field after each step of unloading simulation.

[0025] For the residual stress field after each simulated unloading step, the equivalent stress in the deformation zone of the pipe is extracted, and the average value and variance of the equivalent stress are calculated as the distribution characteristics of the residual stress field.

[0026] For two adjacent steps, calculate the absolute value of the difference between the average equivalent stress of the previous step and the average equivalent stress of the next step, and calculate the absolute value of the difference between the variance of the equivalent stress of the previous step and the variance of the equivalent stress of the next step. The weighted sum of the two absolute values ​​is used as the degree of difference in the residual stress field distribution characteristics between adjacent steps.

[0027] Furthermore, S4 includes:

[0028] The degree of difference in the residual stress field distribution characteristics between each adjacent step is calculated and arranged according to the corresponding molding step sequence to form a sequence of the degree of difference evolution.

[0029] Calculate the ratio of each subsequent degree of difference to the previous degree of difference in the evolution sequence of degree of difference to obtain the sequence of rate of change of degree of difference;

[0030] Identify points in the sequence of rate of change of difference where the ratio is greater than a preset rate of change threshold, and mark the positions of the molding steps corresponding to these points as pattern transfer features;

[0031] The number of molding step locations marked as mode transfer features in the initial multi-step molding path is counted. When the number exceeds a preset threshold, the risk level of material damage is assessed as high risk.

[0032] Furthermore, the preset change rate threshold is determined based on the ratio of yield strength to elastic modulus, and the preset quantity threshold is determined based on the total number of steps in the initial multi-step molding path.

[0033] Furthermore, S5 includes:

[0034] When the risk level of material damage is high, multiple consecutive molding steps are selected in the initial multi-step molding path as the molding verification stage.

[0035] Based on the finite element model, each molding step in the molding verification stage is simulated, and the total mechanical work done by the mold on the pipe is recorded during the application of displacement boundary conditions in each step.

[0036] Based on the simulation results of the finite element model, the plastic strain energy density field after each step of the forming verification stage of the pipe is extracted, and the effective plastic deformation work of each step is obtained by integrating the plastic strain energy density field within the volume of the pipe.

[0037] The ratio of the sum of effective plastic deformation work in all steps of the molding verification stage to the sum of total input mechanical work is calculated, and this ratio is used as an energy conversion efficiency parameter.

[0038] Furthermore, S6 includes:

[0039] If the assessed risk level of material damage is high and the energy conversion efficiency parameter is lower than the preset efficiency threshold, then increase the pause time of the steps after the molding step marked as mode transfer feature in the initial multi-step molding path, and reduce the feed amount of subsequent steps.

[0040] If the assessed risk level of material damage is high risk but the energy conversion efficiency parameter is not lower than the preset efficiency threshold, then only the pause time of the steps after the molding step marked as mode transfer feature in the initial multi-step molding path is increased.

[0041] The optimized multi-step forming path is generated by adjusting the pause duration and / or the feed rate, and the tube end forming is performed according to the optimized multi-step forming path.

[0042] On the other hand, the present invention provides a multi-step stress relief system for pipe end forming, comprising the following modules:

[0043] The parameter acquisition module is used to obtain the material parameters and initial geometric dimensions of the pipe to be formed;

[0044] The condition judgment module is used to determine whether the pipe meets the stress relaxation condition under the preset initial multi-step forming path based on the material parameters and initial geometric dimensions.

[0045] The difference calculation module is used to simulate the initial multi-step forming path when the stress relaxation condition is met to obtain the residual stress field distribution characteristics of the pipe after each forming step, and to calculate the degree of difference in the residual stress field distribution characteristics between adjacent steps.

[0046] The rating assessment module is used to identify mode transfer characteristics of residual stress redistribution in the initial multi-step molding path based on the evolution of the degree of difference in the molding step sequence, and to assess the risk level of material damage based on the mode transfer characteristics.

[0047] The parameter measurement module is used to measure the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage when the risk level is high.

[0048] The path generation module is used to combine risk level and energy conversion efficiency parameters to adjust the process parameters of subsequent steps in the initial multi-step forming path, so as to generate and execute an optimized multi-step forming path.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. By elevating the planning and evaluation of forming paths from reliance on static experience to dynamic scientific decision-making based on simulation and data-driven approaches, the control logic of multi-step forming is transformed. By acquiring precise material and geometric parameters and establishing physical stress relaxation conditions, an objective benchmark for path feasibility is provided, replacing subjective experience-based selection. Through systematic finite element simulation, the residual stress field distribution characteristics after each forming step and the evolutionary differences between step sequences are quantitatively extracted, making the previously invisible internal stress dynamics measurable and analyzable. This allows for the precise capture of the complex interaction between stress relaxation and subsequent deformation during intermittent loading, thereby identifying potential risk points that traditional methods cannot detect, leading to uneven stress release—namely, mode transition characteristics. Based on this, risk assessments are conducted, making the design of forming paths no longer a simple geometric decomposition of the final shape, but a precise control process based on a deep understanding of the internal mechanical behavior of materials.

[0051] 2. Improve the forming quality and process stability of the tube end. By comprehensively evaluating the stability of the stress field evolution and the energy conversion efficiency of the process, the initial path can be diagnosed from multiple angles. The adjustments to the process parameters of subsequent steps based on the diagnosis results are highly targeted. For example, after identifying risky steps, the pause time can be extended to promote stress relaxation, or the feed rate can be reduced in coordination when the energy efficiency is low to optimize the deformation process. This adjustment mechanism based on real-time analysis and feedback ensures that the internal stress of the material is released more orderly and fully during the forming process, effectively coordinating the contradiction between high-precision forming and suppressing material damage. The optimized path generated at the end can significantly improve the dimensional accuracy and contour consistency of the formed parts, reduce the cracking risk of high-strength materials under complex deformation, and thus stably meet the stringent standards of airtightness and reliability of high-requirement components such as automotive intake and exhaust systems. Attached Figure Description

[0052] Figure 1 This is a flowchart of a multi-step stress relief method for pipe end forming according to the present invention;

[0053] Figure 2 This is a schematic diagram of the structure of a multi-step stress relief system for pipe end forming according to the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0055] Example 1: Figure 1This invention provides a multi-step stress relief method for pipe end forming, which includes the following steps:

[0056] S1. Obtain the material parameters and initial geometric dimensions of the pipe to be formed;

[0057] S2. Based on the material parameters and initial geometric dimensions, determine whether the pipe meets the stress relaxation condition under the preset initial multi-step forming path.

[0058] S3. When the stress relaxation condition is met, the initial multi-step forming path is simulated to obtain the residual stress field distribution characteristics of the pipe after each forming step, and the degree of difference in the residual stress field distribution characteristics between adjacent steps is calculated.

[0059] S4. Identify the mode transfer characteristics of residual stress redistribution in the initial multi-step molding path based on the evolution of the degree of difference in the molding step sequence, and assess the risk level of material damage based on the mode transfer characteristics.

[0060] S5. When the risk level is high, measure the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage.

[0061] S6. Combining the risk level and energy conversion efficiency parameters, adjust the process parameters of subsequent steps in the initial multi-step molding path to generate and execute an optimized multi-step molding path.

[0062] S1. Obtain the material parameters and initial geometric dimensions of the pipe to be formed. The specific implementation is as follows:

[0063] The yield strength and elastic modulus of the pipe to be formed are obtained as material parameters according to the standard tensile test. The specific process of the standard tensile test includes: firstly, a ring-shaped section is cut from the straight section of the stainless steel pipe blank to be formed for the automotive exhaust system. The ring-shaped section is then cut and flattened along the generatrix to obtain a rectangular sheet. The rectangular sheet is then processed into a plate-shaped specimen that meets the general requirements for room temperature tensile testing of metallic materials using a wire cutting machine. The gauge length of the specimen is 12.5 mm wide, the parallel length is 50 mm, and the transition arc radius is not less than 12 mm. The plate-shaped specimen is mounted on a universal testing machine, and a uniaxial tensile load is applied at a constant beam displacement rate. This rate should ensure that the stress increase rate of the specimen in the elastic stage is between 1 and 10 MPa per minute. During the test, the axial deformation within the gauge length of the specimen is measured in real time using an extensometer, and the tensile load is recorded using a load sensor, thereby simultaneously obtaining the stress-strain curve of the tensile process. The yield strength of the material is determined from this stress-strain curve. For materials with a distinct yield plateau, the highest stress point before the first drop on the stress-strain curve is taken as the yield strength. For austenitic stainless steel with continuous yielding, the stress at a specified plastic elongation of 0.2% is measured as the conditional yield strength. The elastic modulus is obtained by selecting a data segment with stress values ​​between 70% and 90% of the proportional limit during the initial linear elastic stage of the stress-strain curve. A linear regression is performed on the stress and strain data in this segment, and the slope of the resulting fitted line is the elastic modulus of the material, expressed in gigapascals (GPa).

[0064] The outer diameter, wall thickness, and straight segment length of the pipe to be formed are obtained as initial geometric dimensions through laser 3D scanning. The specific process of laser 3D scanning involves scanning the outer surface and end face of the pipe using a handheld or fixed laser 3D scanner. Before scanning, several non-coded positioning markers are attached to the pipe surface to assist in stitching together multi-view point cloud data during the scanning process. The relative position of the scanner and the pipe is adjusted to ensure that the laser line completely covers the entire circumference and end face of the pipe segment to be measured. The scanner or pipe is moved at a uniform speed along the pipe axis to complete the scanning of the entire area to be measured, obtaining high-density 3D point cloud data. For measuring the outer diameter, firstly, the outer surface point cloud near a cross-section of the pipe is extracted from the point cloud data. The least squares method is used to fit the point cloud of the outer edge of this cross-section into a circle, and the diameter of this fitted circle is taken as the measured outer diameter value of that cross-section. To obtain an accurate outer diameter, this fitting operation needs to be repeated on multiple equally spaced cross-sections of the pipe. Finally, the arithmetic mean of the outer diameter measurements of all cross-sections is taken as the outer diameter of the pipe. For wall thickness measurement, both the inner and outer surface point clouds of the same cross-section need to be acquired simultaneously. The inner and outer circles are then fitted using the least squares method. The distance between the centers of the inner and outer circles at the cross-section is calculated, and the inner and outer radii are subtracted from each to obtain the wall thickness. Measurements are taken at multiple locations along the pipe's axial direction, and the arithmetic mean of the wall thickness values ​​at all locations is taken as the pipe's wall thickness. The measurement of the straight segment length refers to the length of the straight portion of the pipe that is not bent. The point cloud of this straight segment is identified in the 3D point cloud. The central axis of this segment is determined by fitting the point cloud, and the 3D coordinates of the two endpoints of this central axis are determined. The straight-line distance between the two endpoints is calculated, and this distance is the straight-line segment length. Simultaneously, the straightness of the segment can be evaluated by calculating the standard deviation of the distances from all point clouds of this segment to its fitted central axis, ensuring that subsequent analysis is based on accurate geometric information.

[0065] The tubing to be formed is a stainless steel pipe for automotive exhaust systems. This type of stainless steel pipe is typically austenitic stainless steel. Such pipes need to possess good high-temperature oxidation resistance, corrosion resistance, and certain thermal fatigue performance to meet the long-term usage requirements of automotive exhaust systems in high-temperature exhaust gas environments. When obtaining its material parameters and initial geometric dimensions, the specific grade and supply status of the material must be fully considered, as different grades or heat-treated austenitic stainless steels may have different yield strengths and elastic moduli. Accurately obtaining these parameters is fundamental for subsequent forming path simulation and optimization. Through the aforementioned standard tensile test and laser three-dimensional scanning method, the basic physical and geometric parameters required for the multi-step stress relief method can be obtained accurately and repeatably.

[0066] S2. Based on material parameters and initial geometric dimensions, determine whether the pipe meets the stress relaxation condition under the preset initial multi-step forming path. The specific implementation is as follows:

[0067] Based on the obtained yield strength, elastic modulus, outer diameter, and wall thickness, the estimated mechanical energy of the maximum deformation in a single step of the initial multi-step forming path is calculated. This estimated mechanical energy characterizes the minimum energy theoretically required to induce plastic deformation of the tube in a single forming step. The calculation method is as follows: First, according to the initial multi-step forming path plan, the step with the largest preset deformation is identified from all steps. The deformation of this step is defined by its preset mold movement trajectory or the change in the target shape of the tube, usually expressed as the increment of the bending angle of the tube's centerline or the radial displacement of the cross-section. For this maximum deformation in a single step, it is simplified into a physical model of plastic bending of the material. In the calculation, the cross-section of the tube is considered as a ring, with an outer radius equal to half the outer diameter and an inner radius equal to half the outer diameter minus the wall thickness. Based on the bending theory of beams in mechanics of materials, it is assumed that the deformation in this step brings the tube cross-section to a fully plastic state, i.e., the stress on the entire cross-section reaches the yield strength. The plastic work done in this step is the estimated mechanical energy. In specific calculations, the plastic strain energy corresponding to the plastic bending step can be approximated as a multiple of the elastic energy stored in the plastic bending region of the pipe. This multiple is related to the hardening characteristics of the material. A specific implementation calculation method is to first calculate the plastic section modulus of the pipe cross-section. For a circular cross-section, the plastic section modulus is equal to the difference between the cube of the outer diameter and the cube of the inner diameter, multiplied by a constant factor. Then, multiply this plastic section modulus by the yield strength of the material, then by the change in curvature corresponding to the maximum deformation in this single step, and finally by the axial length of the pipe where the plastic bending occurs. This yields the estimated mechanical energy, measured in joules. The change in curvature can be derived from preset path geometry parameters, and the axial length where the plastic bending occurs is usually related to the bending radius and bending angle.

[0068] The estimated mechanical energy of the maximum deformation in a single step is compared with the material's single-step deformation energy threshold determined based on yield strength and elastic modulus. The material's single-step deformation energy threshold is a critical energy value used to assess the severity of deformation in a single step. It is set to ensure that the plastic deformation energy absorbed by the material in each deformation step is not excessive, thus leaving sufficient margin to allow stress relaxation during the intervals between steps and preventing excessive energy accumulation leading to instantaneous cracking. This threshold is not a fixed value but is directly related to the material's mechanical properties. Specifically, the material's single-step deformation energy threshold can be constructed by combining the material's yield strength with its elastic modulus. One feasible method is to calculate the square of the material's yield strength, divide it by the material's elastic modulus, and then multiply it by a characteristic volume related to the pipe's cross-sectional area, thus obtaining a threshold with energy dimensions. This characteristic volume can be the volume represented by the product of the pipe's wall thickness, outer diameter, and a unit length. The physical significance of this setting lies in the fact that it reflects the product of the maximum elastic strain energy density that a material can store before yielding and its characteristic volume. It is an energy scale characterizing the transition of a material from an elastic state to a plastic state during a single loading event. By comparing the estimated mechanical energy with this threshold, it can be determined whether the maximum deformation in a single step is within the acceptable energy input range for the material. If the estimated mechanical energy is less than the single-step deformation energy threshold of the material, the degree of deformation severity in this step is considered to be within a safe range, satisfying the basic premise of stress relaxation from an energy perspective.

[0069] The total step length of the initial multi-step forming path is compared with the material characteristic relaxation length determined based on yield strength and elastic modulus. The total step length refers to the total geometric length of the tube centerline covered by the initial multi-step forming path, i.e., the cumulative length of all straight and curved segments along the tube axis from the forming start point to the forming end point, typically measured in millimeters. The material characteristic relaxation length is a characteristic parameter reflecting the spatial scale of material stress relaxation behavior. It defines the approximate range within which stress disturbances can effectively propagate and redistribute along the tube axis after a forming step. The determination of this length depends on the inherent properties of the material, particularly yield strength and elastic modulus. Its calculation method can draw upon concepts such as stress wave propagation or elastoplastic boundary layers. One implementation expresses the material characteristic relaxation length as the product of the material's elastic wave velocity and a characteristic relaxation time. The elastic wave velocity is proportional to the square root of the material's elastic modulus and inversely proportional to the square root of the material's density. The characteristic relaxation time is related to the creep or relaxation properties of the material. For many metallic materials being formed at room temperature or medium temperature, this time can be correlated with the yield strength. The higher the strength, the more difficult it is for atomic diffusion or dislocation movement, and the longer the characteristic relaxation time may be. As a simplified engineering approximation, the characteristic relaxation length of the material can be directly set as the ratio of the elastic modulus to the yield strength multiplied by a constant factor with the dimension of length. This constant factor can be several times the outer diameter or wall thickness of the tube. For example, the characteristic relaxation length of the material can be equal to the outer diameter of the tube multiplied by the ratio of the elastic modulus to the yield strength, multiplied by an empirical coefficient between 0.01 and 0.1. The purpose of comparing the total step length with the characteristic relaxation length of the material is to determine, on a spatial scale, whether the forming path provides sufficient length to supply force for relaxation and homogenization along the tube axis. If the total step length is much larger than the characteristic relaxation length of the material, it means that the forming process is fully expanded in space, with sufficient tube length to absorb and dissipate the stress generated by local deformation, avoiding high stress concentration in extremely short areas.

[0070] When the estimated mechanical energy of the maximum deformation in a single step is less than the material's single-step deformation energy threshold, and the total step length is greater than the material's characteristic relaxation length, the stress relaxation condition is considered met. This judgment is a logical AND relationship; both conditions must be met simultaneously. The first condition focuses on ensuring, in terms of energy input intensity, that the deformation in each step is not too drastic, leaving sufficient energy margin for stress relaxation between steps. The second condition focuses on ensuring, in terms of spatial scale, that the entire forming process has sufficient geometric length to accommodate stress redistribution and attenuation. Only when both conditions are met can the theoretically pre-defined initial multi-step forming path be considered to possess the basic physical framework for effective stress relaxation. If the estimated mechanical energy of the maximum deformation in a single step is greater than or equal to the material's single-step deformation energy threshold, it indicates that at least one step has an excessively drastic deformation. Even with increased pause time, the stress may not have enough time to fully relax due to excessive initial accumulation, posing a risk of cracking. In this case, the stress relaxation condition should not be met, and the initial path's step division or single-step deformation amount needs to be replanned. If the total step length is less than or equal to the material characteristic relaxation length, it means that the forming process is completed within an excessively short timeframe, leaving insufficient space for stress diffusion and homogenization. This can easily lead to a high residual stress gradient in the final product, thus failing to meet the stress relaxation condition. This judgment step, located at the beginning of the entire method, serves as a preliminary screening and check, preventing obviously unreasonable paths from being sent to subsequent time-consuming detailed simulation analyses, thereby improving the overall efficiency of the method. All thresholds used for comparison, including the material single-step deformation energy threshold and the material characteristic relaxation length, can be calculated using specific formulas and multipliers. These can be obtained by correlating and calibrating historical experimental data with forming effects in a process database for a specific grade of stainless steel pipe, thus making them more closely reflect the actual material and process characteristics.

[0071] S3. When the stress relaxation condition is met, simulate the initial multi-step forming path to obtain the residual stress field distribution characteristics of the pipe after each forming step, and calculate the degree of difference in the residual stress field distribution characteristics between adjacent steps. The specific implementation is as follows:

[0072] Based on the obtained yield strength, elastic modulus, outer diameter, and wall thickness, a finite element model of the pipe is established. This finite element model is built using a general-purpose commercial finite element analysis software environment. First, based on the obtained outer diameter and wall thickness, a three-dimensional solid model of the pipe is created in the software's geometric modeling module. This model is a hollow cylinder, and its axial length should be greater than the total step length covered by the initial multi-step forming path, including necessary clamping sections to avoid boundary effects. Then, the three-dimensional solid is meshed using high-order three-dimensional solid elements, such as second-order tetrahedral or hexahedral elements. In the region where plastic deformation is expected, i.e., the pipe segment covered by the initial multi-step forming path and its adjacent area, mesh refinement is required to ensure the accuracy of stress and strain field calculations. The mesh size is typically controlled between one-half and one-quarter of the wall thickness. In the material property definition module, material properties are assigned to the finite element model. Elastic behavior is defined by the elastic modulus and Poisson's ratio; for stainless steel, the Poisson's ratio is typically around 0.3. Plastic behavior is characterized by defining a plastic constitutive model of the material, which requires at least the yield strength obtained from a standard tensile test. To more accurately simulate large deformation processes, a plastic hardening curve can be further defined. This curve can be input using real stress-strain data obtained from tensile tests, or approximated using a simplified bilinear or multilinear hardening model. After completing the mesh generation and defining the material properties, a finite element model of the pipe suitable for simulation calculations is established.

[0073] Following the sequence of steps in the initial multi-step forming path, displacement boundary conditions are applied sequentially to the finite element model for each step to simulate forming. After each step of the forming simulation, the displacement boundary conditions are removed to simulate unloading, obtaining the residual stress field after each step of the simulated unloading. The initial multi-step forming path is defined by a series of ordered steps, each step describing the relative motion between the mold and the tube or the staged change in the target shape of the tube. In the finite element simulation, the forming process of each step is simulated by applying displacement boundary conditions. Specifically, according to the process requirements of the current step, nodes on the outer or inner surface of the tube that are in contact with the mold are selected on the finite element model, and specified displacement constraints are applied to these nodes. This displacement constraint can be a translational displacement along a certain direction or a rotational displacement about a certain axis, the magnitude and direction of which are determined by the amount of deformation to be achieved in that step. For example, for the bending step, the displacement boundary condition is manifested as applying a rotational displacement about the bending axis to a section of the tube; for the flaring step, it is manifested as applying a radially outward displacement to the end nodes of the tube. The application of displacement boundary conditions is achieved by defining analysis steps, each representing a forming step. Within each step, the displacement boundary conditions linearly increase from zero to a preset maximum value to simulate the slow loading process of the mold. After completing the loading of an analysis step (i.e., simulating forming), the next step is not immediately initiated; instead, an unloading analysis step begins. In this step, the displacement boundary conditions applied in the previous step are completely removed, allowing previously constrained nodes to return to a free state, while keeping other boundary conditions unchanged to simulate the elastic recovery behavior of the material after the mold is released. After this unloading process, the model reaches a new self-equilibrium state. At this point, the stress tensor at all integration points of the entire pipe finite element model is extracted; this stress field represents the residual stress field after the unloading of the current step. Then, using the stress and deformation states at the end of the previous step as initial conditions, this process is repeated. New displacement boundary conditions are applied to the next step for loading and forming simulation, followed by unloading to obtain the residual stress field for the next step. This cycle continues until all steps of the initial multi-step forming path are simulated, thus obtaining the residual stress field after each forming step.

[0074] For each step of the simulated unloading of the residual stress field, the equivalent stress within the deformation zone of the pipe is extracted, and the mean and variance of the equivalent stress are calculated as characteristics of the residual stress field distribution. Equivalent stress, also known as von Mises stress, is a scalar used to comprehensively characterize the yield tendency of a material under complex stress states; its value is calculated based on the components of the stress tensor. In the post-processing module of the finite element software, the equivalent stress values ​​at all nodes or integration points of the entire model can be directly output. The pipe deformation zone refers to the area of ​​the pipe that undergoes plastic deformation due to the forming process. Its range can be determined by analyzing the equivalent plastic strain field. Typically, all elements with an equivalent plastic strain greater than a certain small value (e.g., 0.001) are defined as the deformation zone. The equivalent stress values ​​at all integration points within the deformation zone are extracted to form an equivalent stress dataset. The arithmetic mean of this dataset is calculated, reflecting the overall level of residual stress within the deformation zone after this step. Simultaneously, the variance of this dataset is calculated, reflecting the dispersion of the equivalent stress values ​​within the deformation zone, i.e., the non-uniformity of stress distribution. The mean and variance together constitute two key statistical indicators describing the distribution characteristics of the residual stress field in this step. A large mean indicates a high overall residual stress level and a high risk of springback; a large variance indicates extremely uneven stress distribution, with localized stress concentrations that easily lead to damage. The calculation of these two statistics follows standard mathematical definitions: the mean equals the sum of all equivalent stress values ​​in the dataset divided by the number of data points; the variance equals the sum of the squares of the differences between each equivalent stress value and the mean, divided by the number of data points minus one.

[0075] For two adjacent steps, calculate the absolute value of the difference between the equivalent stress average value of the previous step and the equivalent stress average value of the next step, and calculate the absolute value of the difference between the equivalent stress variance of the previous step and the equivalent stress variance of the next step. The weighted sum of these two absolute values ​​is used as the degree of difference in the residual stress field distribution characteristics between adjacent steps. This step aims to quantify the magnitude of change in the statistical characteristics of the residual stress field between two adjacent forming steps. Let there be steps i and i+1, where i is the step number. First, obtain the equivalent stress average value of step i and the equivalent stress average value of step i+1, and calculate the absolute value of the difference between these two values, denoted as the absolute difference of the average value. Similarly, obtain the equivalent stress variance of step i and the equivalent stress variance of step i+1, and calculate the absolute value of the difference between these two values, denoted as the absolute difference of the variance. The degree of difference is not simply determined by adding these two absolute differences, but rather by a weighted sum. A weighted sum means assigning a weight coefficient to each of the absolute difference of the average value and the absolute difference of the variance, and then summing the weighted values. The weighting coefficients reflect the relative importance of changes in the mean and variance in assessing the severity of stress field evolution between steps. One method for assigning weights is empirical; for example, if changes in the mean are considered more representative of the overall stress state transition, a larger weight is assigned to the absolute difference in the mean, such as 0.7, while a smaller weight is assigned to the absolute difference in the variance, such as 0.3. A more systematic approach is based on historical data or physical understanding. By analyzing numerous simulation cases, the correlation strength between these two indicators and subsequent material damage risk is determined, and this correlation strength is used as the basis for setting the weighting coefficients. The sum of the weighting coefficients is typically 1. Finally, multiplying the absolute difference in the mean by its corresponding weighting coefficient and adding the absolute difference in the variance by its corresponding weighting coefficient yields the degree of difference in the residual stress field distribution characteristics between step i and step i+1. This degree of difference is a dimensionless or stress-dimensional value, whose magnitude directly characterizes the extent of abrupt changes in the overall level and uniformity of the residual stress field from step i to step i+1. A greater degree of difference indicates a more severe stress redistribution process between steps, poorer process sequence stability, and higher potential risk. Repeating this calculation for all adjacent step pairs yields a series of degree of difference values ​​for subsequent analysis.

[0076] S4. Identify the mode transfer characteristics of residual stress redistribution in the initial multi-step molding path based on the evolution of the degree of difference in the molding step sequence, and assess the risk level of material damage based on the mode transfer characteristics. Specifically, this is implemented as follows:

[0077] The calculated differences in residual stress field distribution characteristics between adjacent steps are arranged according to the corresponding molding step sequence to form a difference degree evolution sequence. The initial multi-step molding path contains a specific number of steps. The aforementioned calculations yield a set of difference degree values, each corresponding to the degree of abrupt change in stress field characteristics between two consecutive steps. This set of difference degree values ​​is organized according to the order of the associated steps; for example, the first value is associated with steps 1 and 2, the second with steps 2 and 3, and so on, until the values ​​of the last two steps are associated. These values ​​are stored in an ordered dataset, which is the difference degree evolution sequence. Mathematically, this sequence represents the trajectory of the residual stress field distribution characteristics along the molding step sequence, and its numerical fluctuations directly reflect changes in the stability of the process. The position index of each value in the sequence corresponds to the number of its associated subsequent step; for example, a value at a certain position in the sequence is associated with the stress field change caused by a step plus one in the sequence relative to a step.

[0078] The ratio of each subsequent degree of difference to the preceding degree of difference in the evolution sequence of degree of difference is calculated sequentially to obtain the sequence of rate of change of degree of difference. Specifically, for the evolution sequence of degree of difference, starting from the second element, the value of the current element is divided by the value of the previous element; the quotient is a rate of change of degree of difference. Assuming the evolution sequence of degree of difference contains multiple values ​​from the first to the last, the second value is divided by the first value to obtain the first rate of change, the third value is divided by the second value to obtain the second rate of change, and so on, until the last value is divided by the second-to-last value to obtain the final rate of change. Arranging all the calculated rates of change in sequence constitutes the sequence of rate of change of degree of difference. The significance of this ratio calculation lies in capturing the rate or acceleration of change in degree of difference itself. If a ratio is significantly greater than 1, it means that the degree of abrupt change in the stress field increases sharply after that point; if the ratio is significantly less than 1, it means that the degree of abrupt change decreases. Small fluctuations of the ratio around 1 indicate a relatively stable evolution. By analyzing the rate of change sequence, inflection points or transition points in the evolution of degree of difference can be identified.

[0079] Points in the sequence of rate of change with a difference greater than a preset rate of change threshold are identified, and the corresponding molding step positions are marked as mode transfer features. The preset rate of change threshold is a critical value used to determine whether the rate of change is abnormal. This preset rate of change threshold is determined based on the ratio of the material's yield strength to its elastic modulus. The ratio of yield strength to elastic modulus is a dimensionless quantity that reflects the maximum elastic deformation a material can withstand before yielding, and is related to the material's stiffness-strength ratio. For metal plastic forming, this ratio is also associated with the material's tendency to undergo plastic instability. Therefore, the setting of the preset rate of change threshold can be functionally related to this ratio. One implementation is that the preset rate of change threshold equals a basic threshold constant plus an adjustment term proportional to the ratio of yield strength to elastic modulus. The basic threshold constant can be set to 1.5, indicating that a rate of change of 150% is considered a significant change. The adjustment term can be designed as dividing the yield strength by the elastic modulus and then multiplying by an amplification factor, such as 100 or 200. In this way, the preset rate of change threshold will automatically adjust for different materials; materials with higher strength or lower stiffness may correspond to a slightly higher threshold. During the identification process, each ratio in the rate of change sequence of difference is traversed and compared with a preset rate of change threshold. If a ratio is greater than the preset rate of change threshold, the point is determined to be an abnormal change point. The index position of this point in the rate of change sequence is incremented by 1, and then mapped back to the original forming step number to determine the corresponding forming step position. For example, if the ratio at a certain position in the rate of change sequence is greater than the threshold, it corresponds to the value at the +1 position in the difference evolution sequence. This value is associated with the change of the +2 step relative to the +1 step in the step sequence. Therefore, the forming step position corresponding to the marked pattern transfer feature is the +2 step. Recording all such identified step positions constitutes the pattern transfer feature set.

[0080] The number of molding step locations marked as mode transition features in the initial multi-step molding path is counted. When this number exceeds a preset threshold, the risk level of material damage is assessed as high risk. The preset threshold is determined based on the total number of steps in the initial multi-step molding path. The total number of steps directly reflects the path complexity. The principle for setting the preset threshold is to allow a small number of non-drastic mode transitions in the path, but when such transitions are too frequent, it means that the stability of the entire process sequence is very poor. A common setting method is to set the preset threshold as a percentage of the total number of steps, such as 10%, 15%, or 20%. The specific percentage can be determined based on experience or statistical analysis of paths with different complexities. For simple paths with fewer steps, the percentage can be slightly higher; for complex paths with many steps, the percentage should be relatively lower, because the probability of occasional anomalies increases with more steps, requiring stricter control. Another setting method is to preset a fixed minimum integer as a base plus an increment related to the total number of steps. For example, the preset threshold equals 1 plus the total number of steps divided by 10 and rounded down. The number of forming step locations marked as mode-transfer features is counted, which is equivalent to the number of elements in the statistical mode-transfer feature set. This number is compared to a preset threshold. If the count exceeds the preset threshold, the material damage risk level is assessed as high risk. A high risk level means that the initial multi-step forming path assessed based on the current analysis performs poorly in terms of stress evolution stability, with multiple risk points that could lead to abrupt stress redistribution or concentration. These risk points significantly increase the likelihood of cracking, excessive springback, or other forms of damage during the forming process. If the count does not exceed the preset threshold, it means that the stress evolution mode in the path is relatively stable with fewer abrupt changes, and it can be assessed as low or medium risk. This risk assessment based on the number of mode-transfer features provides an objective method for quantifying the overall risk level of a forming path.

[0081] S5. When the risk level is high, determine the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage. Specifically, the implementation is as follows:

[0082] When the risk level of material damage is high, several consecutive molding steps in the initial multi-step molding path are selected as molding verification stages. The purpose of selecting molding verification stages is to evaluate the energy utilization efficiency of the high-risk path segment. The selection principle is to cover the steps where the marked mode transfer feature is located and its adjacent subsequent steps to analyze the energy characteristics of the risk manifestation stage. In practice, firstly, the positions of all molding steps marked as mode transfer features are located in the step sequence of the initial multi-step molding path, and the earliest appearing step number is found from these positions. Then, starting from this step, a certain number of consecutive steps are selected to constitute the molding verification stage. The number of selected steps is usually no less than 3 steps to ensure that the evaluation is statistically significant; it should not be too many, generally not exceeding one-third of the total number of steps, to avoid including too many normal stable stages and diluting the characteristics of the risk stage. For example, if the earliest mode transfer feature appears in step 5, steps 5, 6, and 7 can be selected as molding verification stages. If multiple mode transfer features appear in a concentrated manner, the molding verification stage should cover all steps from the first to the last mode transfer feature, and may extend one step before and after it. This selection ensures that the analyzed stage truly includes the key processes of unstable stress evolution.

[0083] The molding verification stage is simulated using a finite element model, recording the total mechanical work input from the mold to the pipe during each step of applying displacement boundary conditions. This process continues using the finite element model already established and partially simulated in previous steps. The simulation starts from the initial multi-step molding path and progresses to the initial step of the molding verification stage. When entering the molding verification stage, precise recording of the energy input data for each step is necessary. In the finite element analysis software, historical output variables can be set to record the interaction force data on the contact surface between the mold and the pipe. Specifically, the software defines the nodes whose reaction forces are calculated by the software at the nodes where displacement boundary conditions are applied. Simultaneously, the software records the displacement increments of these constrained nodes. The principle for calculating the total mechanical work input is as follows: in each simulation increment step, the dot product of the mold node reaction force vector within the current increment step and the corresponding node displacement increment vector within that increment step is performed to obtain the incremental work done in that increment step. Then, the incremental work of all increment steps within the entire loading analysis step is accumulated to obtain the total mechanical work input for that molding step. This work is the total mechanical energy input to the pipe through the mold, measured in joules. For each step in the molding verification stage, this simulation and data recording process needs to be repeated to obtain the total mechanical energy input for each step. Software typically provides the function to automatically calculate and output this work, or it can be calculated manually through a post-processing script.

[0084] Based on the simulation results of the finite element model, the plastic strain energy density field after each step of the forming verification stage of the pipe is extracted, and the effective plastic deformation work of each step is obtained by integrating the plastic strain energy density field over the volume of the pipe. Plastic strain energy density is the energy density stored within the material after plastic deformation, and it is directly related to the energy consumed by the material due to microscopic mechanisms such as plastic slip. In finite element software, plastic strain energy density is one of the common state variable outputs. For each step of the forming verification stage, when the loading of that step is completed and the material enters the equilibrium state after unloading, the plastic strain energy density values ​​at all integration points of the entire pipe finite element model are extracted. The spatial distribution of these values ​​constitutes the plastic strain energy density field after that step. Effective plastic deformation work refers to the portion of energy actually used to drive irreversible plastic deformation of the material in that step. It is calculated by integrating the plastic strain energy density field over the entire volume domain of the pipe. The specific operation involves obtaining the plastic strain energy density values ​​at all integration points of each element in the finite element model, and calculating the average of these values ​​as the approximate average plastic strain energy density of the element. Then, the volume of the element is multiplied by this average density to obtain the plastic deformation energy stored in the element. Finally, the plastic deformation energies of all elements are summed, and the total is the effective plastic deformation work for this step. The element volume is automatically calculated by the software based on the nodal coordinates and element shape functions. The integration process can be completed by writing a post-processing script or using the software's built-in field variable integration function. The unit of the obtained effective plastic deformation work is also joules. This work value reflects how much of the input energy is permanently converted into plastic deformation of the material in this forming step, and is a core indicator for measuring the energy utilization efficiency of the forming process.

[0085] The ratio of the sum of effective plastic deformation work to the sum of total input mechanical work in all steps of the molding verification stage is calculated, and this ratio is used as the energy conversion efficiency parameter. After completing the simulation of all steps in the molding verification stage and the above data extraction, a set of data will be obtained, including the total input mechanical work and the effective plastic deformation work of each step. First, the total input mechanical work of all steps in the molding verification stage is arithmetically added to obtain the sum of the total input mechanical work for that stage. Second, the effective plastic deformation work of all steps in the molding verification stage is arithmetically added to obtain the sum of the effective plastic deformation work for that stage. The energy conversion efficiency parameter is the quotient obtained by dividing the sum of effective plastic deformation work by the sum of total input mechanical work. This ratio is a dimensionless number between 0 and 1. The closer the ratio is to 1, the higher the proportion of the total mechanical energy input in the molding verification stage that is converted into effective plastic deformation, the less energy is wasted, such as through frictional heat generation and elastic deformation storage, and the higher the energy efficiency of the process. Conversely, a low ratio indicates that a significant proportion of energy is not being used for plastic forming, and may be dissipated or stored as frictional heat, excessive elastic energy, etc. This usually signifies unreasonable process parameters or path design, possibly related to excessive mold friction, incoordination of deformation paths leading to unnecessary shearing within the material. This energy conversion efficiency parameter provides a crucial quantitative indicator for evaluating the quality of the initial multi-step forming path from an energy distribution perspective. Combined with the risk level assessed from the perspective of stress evolution stability, it provides a more comprehensive basis for subsequent path adjustment decisions. For example, a path assessed as high-risk, if its energy conversion efficiency parameter is also significantly low, indicates that the path is not only unstable in stress evolution but also inefficient in energy utilization, requiring more substantial adjustments.

[0086] S6. Combining the risk level and energy conversion efficiency parameters, adjust the process parameters of subsequent steps in the initial multi-step molding path to generate and execute an optimized multi-step molding path. Specifically, the implementation is as follows:

[0087] If the assessed material damage risk level is high and the energy conversion efficiency parameter is lower than the preset efficiency threshold, then the pause time of steps after the forming step marked as a mode transition feature in the initial multi-step forming path is increased, and the feed rate of subsequent steps is reduced. The preset efficiency threshold is a critical value used to determine whether the energy conversion efficiency is sufficient. Its setting is mainly based on statistical analysis of typical energy conversion efficiencies achievable by similar materials under good forming processes. For example, for austenitic stainless steel pipes commonly used in automotive exhaust systems, simulation or measured data from historical successful forming cases are collected to calculate the energy conversion efficiency parameter during the forming verification stage, and its distribution range is statistically analyzed. The preset efficiency threshold can be set as the lower quartile or mean of this statistical distribution minus one standard deviation, ensuring that when the efficiency parameter is lower than this threshold, it is considered that the efficiency is significantly lower than the level of conventional good processes. Another setting method is to give an empirical range based on the material type; for example, the preset efficiency threshold can be set to 0.65 for carbon steel and 0.60 for stainless steel. In practice, the calculated energy conversion efficiency parameter is compared with this preset efficiency threshold. When the risk level is high and the energy conversion efficiency parameter is below the preset efficiency threshold, it indicates that the initial path not only has a risk point of unstable stress evolution but also low energy utilization efficiency, requiring a significant composite adjustment. The adjustment targets all subsequent steps after the mode transfer feature is marked. The pause duration refers to the time after a deformation step is completed, during which the mold remains stationary, allowing material stress relaxation. Increasing the pause duration means extending this interval. The increase can be determined by proportionally scaling up the material's characteristic relaxation time, for example, multiplying the original pause duration by a coefficient greater than 1, which can be between 1.5 and 2.5. The specific value can be fine-tuned based on the number of mode transfer features and the extent to which the energy conversion efficiency parameter is below the threshold; the larger the deviation, the larger the coefficient value. The feed rate refers to the speed at which the mold performs deformation motion in a single step or the amount of displacement per unit time. Reducing the feed rate means making the deformation process slower. The amount of reduction can be determined by scaling down proportionally, for example, by multiplying the original feed rate by a coefficient less than 1, which can be between 0.7 and 0.9, and adjusted according to the degree of low efficiency parameters.

[0088] If the assessed risk level of material damage is high, but the energy conversion efficiency parameter is not lower than the preset efficiency threshold, then only the pause time of steps after the molding step marked as a mode transfer feature in the initial multi-step molding path is increased. This judgment branch indicates that although the path is assessed as high-risk in terms of stress evolution stability and has multiple mode transfer features, its energy conversion efficiency is still at an acceptable level and not lower than the preset efficiency threshold. This means that the main problem of the process may be insufficient stress relaxation time between steps, leading to stress accumulation and abrupt changes, but the energy distribution mechanism of each deformation step itself is relatively reasonable, with no obvious energy waste. Therefore, the adjustment strategy is relatively mild, focusing only on extending the stress relaxation time. In this case, only the pause time of all subsequent steps after the molding step marked as a mode transfer feature is increased. The increase in pause time can also be determined based on a proportional coefficient, but since the energy efficiency is still acceptable, the increase can be slightly smaller than in the previous branch case, for example, multiplying the original pause time by a coefficient of 1.2 to 2.0. The goal of the adjustment is to provide a more adequate stress relaxation window for the identified high-risk step areas to smooth out the stress evolution trajectory without changing the deformation rate, thereby attempting to reduce the risk of damage while maintaining the existing energy utilization efficiency.

[0089] An optimized multi-step forming path is generated based on adjustments, featuring increased pause times and / or decreased feed rates. Tube end forming is then performed according to this optimized path. The adjustment operation involves numerically modifying the process parameters of the initial multi-step forming path. The path itself consists of a series of ordered step definition files or control instructions, each step containing parameters such as geometric targets, feed rates, and pause times. The process of generating the optimized multi-step forming path is as follows: First, a complete definition of the initial multi-step forming path is copied as a base. Then, based on the aforementioned judgment, the steps requiring adjustment are located in the path definition, i.e., all steps located after the forming steps marked as mode transition features. Next, the pause time parameter values ​​of these steps are updated to the increased pause times calculated according to the aforementioned rules. If feed rate adjustment is also required, the feed rate parameter values ​​of these steps are updated to the decreased feed rates calculated according to the aforementioned rules. If a step requires adjustment of both feed rate and pause time parameters, both parameters are updated simultaneously. After the parameters are updated, a new path definition file or instruction set with modified parameters is obtained. This new path is the optimized multi-step forming path. Finally, pipe end forming is performed. The generated optimized multi-step forming path is loaded into the control system of the CNC pipe bending machine, pipe end forming machine, or other corresponding automated processing equipment. According to each step instruction in the path, the control system drives the machine to move the mold according to the specified feed rate to deform the pipe. After each deformation step is completed, a specified pause time is waited before starting the next action. This process is repeated step by step until all forming steps defined by the optimized multi-step forming path are completed, thereby processing the target pipe end shape. Through this targeted parameter adjustment and execution based on risk assessment and efficiency assessment, the aim is to achieve smoother stress release, lower material damage risk, and more controllable forming quality in actual production.

[0090] Example 2: Figure 2 A schematic diagram of a multi-step stress relief system for pipe end forming according to the present invention is provided. The multi-step stress relief system for pipe end forming includes the following modules:

[0091] The parameter acquisition module is used to obtain the material parameters and initial geometric dimensions of the pipe to be formed;

[0092] The condition judgment module is used to determine whether the pipe meets the stress relaxation condition under the preset initial multi-step forming path based on the material parameters and initial geometric dimensions.

[0093] The difference calculation module is used to simulate the initial multi-step forming path when the stress relaxation condition is met to obtain the residual stress field distribution characteristics of the pipe after each forming step, and to calculate the degree of difference in the residual stress field distribution characteristics between adjacent steps.

[0094] The rating assessment module is used to identify mode transfer characteristics of residual stress redistribution in the initial multi-step molding path based on the evolution of the degree of difference in the molding step sequence, and to assess the risk level of material damage based on the mode transfer characteristics.

[0095] The parameter measurement module is used to measure the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage when the risk level is high.

[0096] The path generation module is used to combine risk level and energy conversion efficiency parameters to adjust the process parameters of subsequent steps in the initial multi-step forming path, so as to generate and execute an optimized multi-step forming path.

[0097] All calculations involved in the embodiments are dimensionless numerical calculations, and the preset parameters and thresholds in the calculations are set by those skilled in the art according to the actual situation.

[0098] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0099] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and inventive constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0100] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0101] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0102] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0103] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-step stress relief method for pipe end forming, characterized in that, Includes the following steps: S1. Obtain the material parameters and initial geometric dimensions of the pipe to be formed; S2. Based on material parameters and initial geometric dimensions, determine whether the pipe meets the stress relaxation conditions under the preset initial multi-step forming path, including: Based on the obtained yield strength, elastic modulus, outer diameter and wall thickness, the estimated mechanical energy of the maximum deformation in a single step in the initial multi-step forming path is calculated. The estimated mechanical energy of the maximum deformation in a single step is compared with the material's single-step deformation energy threshold determined based on yield strength and elastic modulus. At the same time, the total step length of the initial multi-step forming path is compared with the material characteristic relaxation length determined based on yield strength and elastic modulus; When the estimated mechanical energy of the maximum deformation in a single step is less than the energy threshold of the material's single-step deformation, and the total step length is greater than the material's characteristic relaxation length, it is determined that the stress relaxation condition is met. S3. When the stress relaxation condition is met, simulate the initial multi-step forming path to obtain the residual stress field distribution characteristics of the pipe after each forming step, and calculate the degree of difference in the residual stress field distribution characteristics between adjacent steps, including: Based on the obtained yield strength, elastic modulus, outer diameter and wall thickness, a finite element model of the pipe is established. Following the sequence of steps in the initial multi-step forming path, displacement boundary conditions corresponding to each step are applied sequentially to the finite element model to simulate forming. After each step of forming simulation, the displacement boundary conditions are removed to simulate unloading, thereby obtaining the residual stress field after each step of unloading simulation. For the residual stress field after each simulated unloading step, the equivalent stress in the deformation zone of the pipe is extracted, and the average value and variance of the equivalent stress are calculated as the distribution characteristics of the residual stress field. For two adjacent steps, calculate the absolute value of the difference between the average equivalent stress of the previous step and the average equivalent stress of the next step, and calculate the absolute value of the difference between the variance of the equivalent stress of the previous step and the variance of the equivalent stress of the next step. The weighted sum of the two absolute values ​​is used as the degree of difference in the residual stress field distribution characteristics between adjacent steps. S4. Identify the mode transfer characteristics of residual stress redistribution in the initial multi-step forming path based on the evolution of the degree of difference in the forming step sequence, and assess the risk level of material damage based on the mode transfer characteristics, including: The degree of difference in the residual stress field distribution characteristics between each adjacent step is calculated and arranged according to the corresponding molding step sequence to form a sequence of the degree of difference evolution. Calculate the ratio of each subsequent degree of difference to the previous degree of difference in the evolution sequence of degree of difference to obtain the sequence of rate of change of degree of difference; Identify points in the sequence of rate of change of difference where the ratio is greater than a preset rate of change threshold, and mark the positions of the molding steps corresponding to these points as pattern transfer features; The number of molding step locations marked as mode transfer features in the initial multi-step molding path is counted. When the number exceeds a preset threshold, the risk level of material damage is assessed as high risk. S5. When the risk level is high, measure the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage. S6. Combining the risk level and energy conversion efficiency parameters, adjust the process parameters of subsequent steps in the initial multi-step molding path to generate and execute an optimized multi-step molding path.

2. The multi-step stress relief method for pipe end forming according to claim 1, characterized in that, S1 includes: The yield strength and elastic modulus of the pipe are obtained as material parameters through standard tensile testing. The outer diameter, wall thickness, and straight segment length of the pipe are obtained by laser 3D scanning as the initial geometric dimensions.

3. The multi-step stress relief method for pipe end forming according to claim 2, characterized in that, The pipe to be formed is a stainless steel pipe for automotive exhaust systems.

4. The multi-step stress relief method for pipe end forming according to claim 1, characterized in that, The preset rate of change threshold is determined based on the ratio of yield strength to elastic modulus, and the preset quantity threshold is determined based on the total number of steps in the initial multi-step forming path.

5. The multi-step stress relief method for pipe end forming according to claim 1, characterized in that, S5 include: When the risk level of material damage is high, multiple consecutive molding steps are selected in the initial multi-step molding path as the molding verification stage. Based on the finite element model, each molding step in the molding verification stage is simulated, and the total mechanical work done by the mold on the pipe is recorded during the application of displacement boundary conditions in each step. Based on the simulation results of the finite element model, the plastic strain energy density field after each step of the forming verification stage of the pipe is extracted, and the effective plastic deformation work of each step is obtained by integrating the plastic strain energy density field within the volume of the pipe. The ratio of the sum of effective plastic deformation work in all steps of the molding verification stage to the sum of total input mechanical work is calculated, and this ratio is used as an energy conversion efficiency parameter.

6. The multi-step stress relief method for pipe end forming according to claim 1, characterized in that, S6 include: If the assessed risk level of material damage is high and the energy conversion efficiency parameter is lower than the preset efficiency threshold, then increase the pause time of the steps after the molding step marked as mode transfer feature in the initial multi-step molding path, and reduce the feed amount of subsequent steps. If the assessed risk level of material damage is high risk but the energy conversion efficiency parameter is not lower than the preset efficiency threshold, then only the pause time of the steps after the molding step marked as mode transfer feature in the initial multi-step molding path is increased. The optimized multi-step forming path is generated by adjusting the pause duration and / or the feed rate, and the tube end forming is performed according to the optimized multi-step forming path.

7. A multi-step stress relief system for pipe end forming, used to implement the multi-step stress relief method for pipe end forming as described in any one of claims 1-6, characterized in that, Includes the following modules: The parameter acquisition module is used to obtain the material parameters and initial geometric dimensions of the pipe to be formed; The condition judgment module is used to determine whether the pipe meets the stress relaxation condition under the preset initial multi-step forming path based on the material parameters and initial geometric dimensions. The difference calculation module is used to simulate the initial multi-step forming path when the stress relaxation condition is met to obtain the residual stress field distribution characteristics of the pipe after each forming step, and to calculate the degree of difference in the residual stress field distribution characteristics between adjacent steps. The rating assessment module is used to identify mode transfer characteristics of residual stress redistribution in the initial multi-step molding path based on the evolution of the degree of difference in the molding step sequence, and to assess the risk level of material damage based on the mode transfer characteristics. The parameter measurement module is used to measure the energy conversion efficiency parameters of the initial multi-step molding path during the molding verification stage when the risk level is high. The path generation module is used to combine risk level and energy conversion efficiency parameters to adjust the process parameters of subsequent steps in the initial multi-step forming path, so as to generate and execute an optimized multi-step forming path.

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