Roll shape design method based on curvature change and springback amount

Abstract

The application provides a roll type design method based on curvature change and rebound amount, and relates to the technical field of roll pressing design.The application provides a design scheme for reversely determining the curvature of each pass roll type by establishing a deformation-rebound response relationship, first obtains basic data of a pipe blank and target parameters after roll pressing forming, and establishes a response relationship between the deformation amount and the rebound amount of the pipe blank on this basis, which reflects the rebound amount change rule of the pipe blank under different deformation degrees; then, the target parameters are taken as constraints, the required deformation amount of each pass is reversely calculated based on the response relationship, and then the curvature of each pass roll is determined according to the deformation amount. The curvature of each pass roll determined by the application is relatively feasible and has relatively great reference significance, and finally the precision of the product is improved.

Description

Technical Field

[0001] This invention relates to the field of roll forming design technology, and in particular to a roll design method based on curvature variation and springback. Background Technology

[0002] Roll forming is a plastic forming process that uses sequentially arranged multi-pass rolls to continuously bend a tube blank into a profile with a specific cross-section at room temperature. It is widely used in the manufacturing of irregularly shaped tubes in the automotive, construction, and aerospace industries. As a typical irregularly shaped tube, the forming quality of elliptical cross-section tubes mainly depends on the rationality of the design of the curvature of each roll pass.

[0003] In traditional multi-pass roll forming processes, the bending angle distribution and roll pass dimensions for each pass are typically predetermined during the design phase, relying primarily on the designer's engineering experience or simplified empirical formulas. This lacks a quantitative consideration of the inherent relationship between deformation and springback during the material's transformation process. Regarding springback control, current technologies often employ over-bending or reverse-bending methods for single-pass springback compensation in the final pass. These practices result in a lack of clear theoretical basis for determining the roll curvature for each pass, making it difficult to meet high-quality product requirements and leading to poor final product accuracy. Summary of the Invention

[0004] This invention provides a roller design method based on curvature variation and springback, which solves the problem of poor final product forming accuracy caused by unreasonable roller curvature design.

[0005] This invention provides a roller design method based on curvature variation and springback, the method comprising: Obtain basic data of the tube blank, including the material parameters and structural dimensions of the tube blank; Determine the target parameters of the tube blank after roll forming; Based on the basic data and the target parameters, a response relationship is established between the deformation and springback of the tube blank; the response relationship characterizes the variation law of the springback generated by the tube blank under different deformation degrees. Based on the response relationship, and with the target parameters as the target constraints, the required deformation amount for each pass is determined by reverse calculation. Based on the deformation amount, the roll curvature of each pass is determined, and finally the roll shape scheme design is completed.

[0006] In one possible implementation, establishing the response relationship between the deformation and springback of the tube blank based on the basic data and the target parameters specifically includes: The work hardening index and Bauschinger effect parameters of the tube blank are obtained during the successive deformation process, and the work hardening index and Bauschinger effect parameters are used as material state variables. Based on the basic data, the target parameters, and the material state variables, a nonlinear response relationship between deformation and springback is constructed.

[0007] In one possible implementation, constructing the nonlinear response relationship between deformation and springback based on the basic data, the target parameters, and the material state variables specifically includes: Obtain the cross-sectional data of the tube blank; Based on the cross-sectional data, the orientation distribution information and deformation path information during the forming process are obtained; Based on the orientation distribution information and the deformation path information, the differential distribution of the work hardening index in each region of the tube blank in the circumferential direction is determined; Based on the aforementioned differential distribution, a nonlinear response relationship between deformation and springback is constructed.

[0008] In one possible implementation, constructing the nonlinear response relationship between deformation and springback based on the basic data, the target parameters, and the material state variables specifically includes: Obtain the cumulative deformation information of the billet before the current pass, and determine the actual value of the Bauschinger effect parameter in the current pass based on the cumulative deformation information; Using the actual values ​​of the Bauschinger effect parameter in each pass as dynamic variables, a response relationship containing the Bauschinger effect is constructed based on the dynamic variables; the response relationship includes a dynamic response correction factor used to characterize the change in yield stress of the material under reverse loading or directional loading.

[0009] In one possible implementation, the step of determining the required deformation for each pass based on the response relationship and using the target parameter as the target constraint specifically includes: Obtain the response relationship of the tube blank in each region of the circumferential direction; Starting from the final pass, using the response relationship of each region as the mapping function, the deformation amount required for the previous pass in each region is calculated backwards for each pass. Based on the required deformation amount in each region of the previous pass, the final output is the sequence of required deformation amounts in each region of each pass.

[0010] In one possible implementation, after the final output of the required deformation sequence for each pass in each region, the method further includes: Obtain preset optimization constraints, which include at least one or more of the following: the maximum allowable single-pass deformation of the equipment, the minimum allowable single-pass deformation of the equipment, the balance requirement of deformation load in each pass, the upper limit of springback of the tube blank after each pass forming, the upper limit of wall thickness reduction rate of the tube blank in each pass forming process, and the cracking risk judgment threshold of the tube blank in each pass forming process. The deformation sequence is optimized and adjusted using the response relationship and the target parameters as the main constraints and the optimization constraints as the additional constraints. Output the optimized deformation sequence for each pass.

[0011] In one possible implementation, after determining the roll profile curvature of each pass roll based on the deformation amount and finally completing the roll profile design, the method further includes: Obtain the actual springback value of the tube blank after the previous forming pass, compare the actual springback value with the springback amount predicted by the response relationship, and calculate the prediction deviation; The parameters in the response relationship are corrected based on the prediction deviation, and the corrected response relationship is output. The deformation and corresponding roll curvature of all subsequent passes are recalculated based on the corrected response relationship, and the corrected scheme design is output.

[0012] In one possible implementation, the step of correcting the parameters in the response relationship based on the prediction deviation and outputting the corrected response relationship specifically includes: The causes of the prediction deviation are classified and analyzed to determine the type of deviation to which the prediction deviation belongs; Based on the deviation type, a correction strategy corresponding to the deviation type is selected to make targeted corrections to the corresponding parameters in the response relationship; Output the corrected response relationship.

[0013] In one possible implementation, the method further includes: By establishing different response relationships, multiple scheme designs are obtained based on these different response relationships; The various proposed design schemes were verified separately, and the corresponding quality evaluation indicators were obtained. Based on the aforementioned quality evaluation indicators, the schemes that meet the requirements are selected as the final roll type design.

[0014] In one possible implementation, the step of verifying the various design schemes and obtaining corresponding quality evaluation indicators includes: Finite element simulations were performed on various design schemes to verify the accuracy of the cross-sectional profile and the uniformity of the wall thickness after the final forming of each design scheme. The cross-sectional profile accuracy data and the wall thickness uniformity data are used as the quality evaluation indicators.

[0015] This invention provides a roll profile design method based on curvature variation and springback. It offers a design scheme that reverse-engineers the roll profile curvature for each pass by establishing a deformation-springback response relationship. First, the invention obtains the basic data of the tube blank and the target parameters after roll forming. Based on this, it establishes a response relationship between the deformation and springback of the tube blank, reflecting the variation of springback under different deformation degrees. Then, using the target parameters as constraints, it reverse-engineers the required deformation for each pass based on this response relationship, and finally determines the roll profile curvature for each pass based on the deformation. The roll profile curvature determined by this invention is highly feasible and has significant reference value, ultimately improving product accuracy. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic flowchart of the roller design method based on curvature change and springback provided in an embodiment of the present invention. Detailed Implementation

[0018] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0020] like Figure 1 As shown, this embodiment of the invention provides a roller design method based on curvature variation and springback. The method includes steps S101-S104.

[0021] S101. Obtain the basic data of the tube blank, including the material parameters and structural dimensions of the tube blank.

[0022] Specifically, the material parameters include at least the yield strength, tensile strength, elastic modulus, Poisson's ratio, and work hardening index of the tube blank. These parameters can be obtained through standard tensile tests or material reports provided by material suppliers. The structural dimensions include at least the outer diameter, wall thickness, and length of the tube blank, which can be obtained using measuring tools such as vernier calipers and ultrasonic thickness gauges. The above basic data are the foundational input parameters for establishing the response relationship and determining the roll profile curvature. Their accuracy directly affects the reliability of the response relationship and the design accuracy of the final roll profile scheme. In this embodiment, the tube blank material can be Q355B low-carbon steel, aluminum alloy, or other metal materials with significant springback characteristics. This embodiment does not specifically limit this.

[0023] Specifically, the change in cross-sectional curvature is used as a unified quantitative index for deformation, and the difference in curvature before and after unloading is used as a quantitative index for springback. For any position in the circumferential direction of the tube blank cross-section, the bending curvature under loading is... The bending curvature after unloading and springback is The curvature after the previous rebound is Then the deformation per pass ; Characterizing the degree of bending deformation applied in this pass, the springback amount per pass. The response relationship is essentially a nonlinear mapping, representing the reduction in curvature caused by elastic recovery after unloading. ; in To accumulate equivalent plastic strain, For yield strength, For elastic modulus, The thickness is the wall thickness of the tube blank.

[0024] Based on the elastic-plastic beam bending springback theory, a power-law nonlinear function considering work hardening is adopted as the fundamental form of the response relationship, specifically expressed as follows: ; in The work hardening index of the material. The equivalent plastic strain for this pass is... The initial yield strain is given by the formula, which covers the entire deformation range from small curvature to large curvature and can reflect the nonlinear growth characteristic of springback as the deformation increases.

[0025] The response relationship can be calibrated through experimental or simulation methods. Taking the three-point bending test as an example, firstly, a standard strip specimen of the same material and wall thickness as the tube blank is cut, and five sets of gradient compression displacements are set to correspond to five levels of bending deformation. Each set of specimens is loaded to a set deflection, and the mid-span curvature under loading conditions is collected by displacement sensors and strain gauges. After complete unloading, the rebound curvature of the sample in its free state was measured. Calculate the rebound amount for each group. Then, based on the amount of deformation The horizontal axis represents the springback amount. Using the vertical axis as the ordinate, the power function expression above is fitted using the nonlinear least squares method to calibrate the corresponding material model parameters. The finite element simulation calibration process is consistent with the above logic. By establishing a single-pass bending finite element model, multiple sets of loading / unloading curvatures corresponding to the reduction are extracted to complete the parameter fitting. When converting the billet loading curvature to the roll pass curvature, the influence of the tube wall thickness on the neutral layer position is considered. The conversion formula is: in The working curvature of the roll pass is given by the corresponding roll profile radius of curvature. The roll profile dimensions can be directly obtained from the target loading curvature of the pass.

[0026] S102. Determine the target parameters of the tube blank after roll forming.

[0027] Specifically, the target parameters include at least the major axis and minor axis dimensions of the target elliptical cross-section, the curvature distribution requirements along the cross-sectional profile, and the wall thickness uniformity requirements. These target parameters are determined based on the final product's usage requirements and design specifications, and represent the final constraints and process objectives of the entire roll design. For example, if the target product is an elliptical tube of a certain specification, the specific values ​​of its major and minor axes, the allowable tolerance range, and the upper limit of the allowable wall thickness deviation must be clearly defined. These parameters will serve as the final constraints for subsequently determining the deformation amounts in each pass.

[0028] S103. Based on basic data and target parameters, establish the response relationship between the deformation and springback of the corresponding tube blank; the response relationship characterizes the variation law of the springback generated by the tube blank under different deformation degrees.

[0029] Specifically, the response relationship is one of the core elements that distinguishes this invention from existing technologies. This response relationship is not a simple linear proportional relationship or a constant compensation coefficient, but rather a mapping function constructed based on the actual material properties of the tube blank and the target shape. Through this response relationship, the amount of springback generated after unloading when the tube blank undergoes different degrees of deformation (i.e., different curvature changes) can be quantitatively described, thus providing a scientific basis for the back-calculation of deformation amounts in subsequent passes. This response relationship can be established through any one of the following methods: finite element simulation data fitting, theoretical analytical model derivation, or experimental measurement and regression analysis, or through a combination of multiple methods. By introducing this response relationship, the determination of the roll curvature in each pass is transformed from an empirical dependence to a scientific design based on the actual deformation-springback law of the material.

[0030] As one possible implementation, step S103 can be specifically implemented as steps S1031-S1032.

[0031] S1031. Obtain the work hardening index and Bauschinger effect parameters of the tube blank during the successive deformation process, and use the work hardening index and Bauschinger effect parameters as material state variables.

[0032] One embodiment uses the Bauschinger softening coefficient. As a quantitative parameter of the Bauschinger effect, it is defined as the ratio of the yield strength under reverse loading to the yield strength under normal loading: The formula is: in The yield strength after positive pre-deformation is the same direction. This represents the yield strength under reverse loading.

[0033] The calibration relationship between the Bauschinger softening coefficient and the cumulative equivalent plastic strain adopts an exponential function, expressed as follows: ; in The cumulative equivalent plastic strain prior to the current pass is obtained by summing the plastic strains from each pass. is the saturation softening coefficient, representing the limiting softening degree of the Bauschinger effect under large deformation.

[0034] Parameter calibration was performed through a tensile-compression cyclic test. First, the specimen was uniaxially stretched to the set prestrain, and then unloaded and subjected to a reverse compression test to determine the reverse yield strength and calculate the corresponding prestrain. Five sets of gradient prestrain repeated tests were set up to obtain multiple sets of data points. The above exponential function was fitted by nonlinear least squares method to obtain material-specific values. , Parameters. Dynamic response correction factor. Defined as the ratio of rebound amount considering the Bauschinger effect to rebound amount not considering the Bauschinger effect, the mathematical expression is: ; The corrected actual rebound amount is When the direction of deformation does not change, No correction is produced when the deformation direction is reversed or changed. The rebound decreases accordingly, which conforms to the mechanical laws of the Bauschinger effect. The successive coupling calculation of the relationship between the Bauschinger effect and the response is performed according to the following logic: during the reverse calculation, the cumulative equivalent plastic strain of each region and each pass of the cross section is recorded. Regarding the deformation direction, if the deformation direction of the current pass is opposite to that of the previous pass, call... The formula calculates the Bauschinger softening coefficient for the current stage, and then substitutes it into the dynamic response correction factor formula to calculate... The rebound amount of the original response relationship is corrected to obtain the actual rebound amount considering the Bauschinger effect. Then, the reverse calculation of the previous pass is continued with the corrected rebound amount to achieve dynamic coupling of each pass.

[0035] Specifically, the work hardening index reflects the rate at which the flow stress of the tube blank increases with increasing strain during plastic deformation, and its value can be obtained by fitting the true stress-true strain curve of the material tensile test. The Bauschinger effect parameter reflects the degree of decrease in yield stress when the material is reverse-loaded after pre-deformation, and its value can be determined by tensile-compression cyclic testing. The work hardening index and Bauschinger effect parameter are introduced as material state variables into the response relationship because during the successive roll forming process, the tube blank undergoes complex loading-unloading-reloading cycles, and its internal dislocation structure and residual stress state continuously evolve, leading to dynamic changes in deformation resistance and springback behavior in different passes. Existing technologies typically use fixed material parameters when designing roll profiles without considering this successive evolution effect. This step, by introducing the aforementioned state variables, enables the response relationship to truly reflect the changes in the mechanical behavior of the tube blank material throughout the entire forming process.

[0036] S1032. Based on basic data, target parameters, and material state variables, a nonlinear response relationship between deformation and springback is constructed.

[0037] Specifically, material properties and structural dimensions from the basic data, target shape constraints from the target parameters, and material state variables (work hardening index and Bauschinger effect parameters) are used as inputs to construct a nonlinear mapping function as the response relationship. The nonlinearity of this response relationship is reflected in the fact that the ratio between the increase in deformation and the increase in springback changes non-constantly with the increase in cumulative deformation, rather than the constant springback compensation coefficient assumed in traditional methods. By introducing nonlinear characteristics, the response relationship can provide different springback prediction values ​​in the low-deformation and high-deformation stages, thus more accurately describing the deformation-springback behavior in the actual forming process and providing a more precise mapping basis for the back-calculation of deformation in subsequent passes.

[0038] As one possible implementation, step S1032 can be specifically implemented as steps S10321-S10324.

[0039] S10321. Obtain the cross-sectional data of the tube blank.

[0040] Specifically, the cross-sectional data includes the geometric information of the annular cross-section of the billet in its initial state and the geometric information of the target elliptical cross-section, including the circumferential radius distribution of the cross-section, the cross-sectional perimeter, and the angles in each quadrant. The purpose of obtaining the cross-sectional data is that during the deformation of the billet from an annular cross-section to an elliptical cross-section, the deformation amount and deformation path in different regions of the cross-section circumferential direction (such as the region corresponding to the major axis, the region corresponding to the minor axis, and the transition region between the two) are significantly different. Subsequently, it is necessary to establish response relationships for each region separately. Therefore, it is necessary to obtain complete cross-sectional data as the basis for subsequent zoning processing.

[0041] S10322. Based on cross-sectional data, obtain orientation distribution information and deformation path information during the forming process.

[0042] Specifically, orientation distribution information describes the grain orientation or fiber flow distribution in each region of the billet material along the circumferential direction of the cross-section, reflecting the anisotropic characteristics of the material; deformation path information describes the displacement trajectory of each region on the cross-section from the initial position to the final position. This information can be obtained through crystal plasticity finite element simulation or microstructure characterization. The purpose of obtaining orientation distribution and deformation path information is that the hardening behavior and springback characteristics of materials under different orientations and deformation paths are fundamentally different, and understanding this information helps to accurately construct the differentiated response relationships of each region.

[0043] S10323. Based on the orientation distribution information and deformation path information, determine the differential distribution of the work hardening index in each region of the tube blank in the circumferential direction.

[0044] Specifically, due to the different orientation distributions and deformation paths in different regions of the tube blank cross-section, the work hardening index values ​​also vary in each region. For example, the deformation path in the region corresponding to the major axis may be predominantly tensile, while that in the region corresponding to the minor axis may be predominantly compressive, and that in the transition region may be predominantly shear. The hardening rate of the material differs under different deformation modes. By using orientation distribution and deformation path information as input, the differentiated distribution of the work hardening index in the circumferential direction of the tube blank cross-section is determined, enabling the subsequent construction of the response relationship in each region to reflect the influence of material anisotropy and deformation modes.

[0045] S10324. Based on the differential distribution, construct the nonlinear response relationship between deformation and springback.

[0046] Specifically, by incorporating the differentially distributed work hardening index into the construction of the response relationship, the final response relationship is expressed differently in different regions of the billet cross-section circumferentially; that is, the major axis region, minor axis region, and transition region each employ their own response relationship. Thus, when subsequently extrapolating the deformation amount for each pass, the deformation amount in each region is independently determined by its corresponding response relationship, rather than using a uniform springback compensation coefficient. This method of independently constructing regional responses effectively improves the accuracy of springback prediction and solves the problem of uneven circumferential springback leading to distortion of the final profile.

[0047] As one possible implementation, step S1032 can be specifically implemented as steps S20321-S20322.

[0048] S20321. Obtain the cumulative deformation information of the billet before the current pass, and determine the actual value of the Bauschinger effect parameter in the current pass based on the cumulative deformation information.

[0049] Specifically, the cumulative deformation information includes the total deformation of the billet before the current pass and the direction of each deformation. The Bauschinger effect parameter is not a fixed constant but changes with the increase of the cumulative deformation. Specifically, when the billet has undergone pre-deformation in a certain direction, if the deformation direction changes in subsequent passes (e.g., from compression to tension), its yield stress will decrease, and the magnitude of the decrease is directly related to the pre-deformation degree. This step determines the actual value of the Bauschinger effect parameter in the current pass by obtaining the cumulative deformation information, thereby enabling the response relationship to dynamically track the true mechanical state of the material in each pass.

[0050] S20322. Using the actual values ​​of the Bauschinger effect parameters in each pass as dynamic variables, construct a response relationship that includes the Bauschinger effect based on the dynamic variables; the response relationship includes a dynamic response correction factor used to characterize the change in yield stress of the material under reverse loading or directional loading.

[0051] Specifically, the actual values ​​of the Bauschinger effect parameter in each pass are introduced as dynamic variables into the response relation, thus including a dynamic response correction factor. This correction factor characterizes the change in yield stress relative to the original yield stress of the billet material when subjected to reverse or directional loading. For example, when a region undergoes compressive deformation in the first pass and tensile deformation in the second pass, the yield stress in that region will decrease due to the Bauschinger effect, resulting in reduced deformation resistance and a change in springback. By introducing this dynamic response correction factor, the response relation can automatically consider the changes in mechanical properties caused by the change in loading direction when back-calculating the deformation amount in each pass, overcoming the springback prediction bias caused by neglecting the Bauschinger effect in existing technologies.

[0052] S104. Based on the response relationship and with the target parameters as the target constraints, the required deformation amount for each pass is determined by reverse calculation. Based on the deformation amount, the roll curvature of each pass is determined, and finally the roll shape scheme design is completed.

[0053] Specifically, after obtaining the response relationship, the target parameters (i.e., the major axis, minor axis, and curvature distribution of the target elliptical cross section) are used as the endpoint constraint. Starting from the final state of the forming process, the calculation is performed backwards step by step according to the response relationship. Specifically, the target parameters are first taken as the state to be achieved after the last forming and springback. Then, based on the deformation-springback mapping in the response relationship, the deformation required for the last forming is calculated in reverse. The state before the last forming is then taken as the target after the previous forming, and the calculation continues in reverse, and so on, until the deformation required for the first forming is calculated. After the deformation required for each forming is determined, the roll curvature of each forming is calculated based on the geometric relationship between the deformation and the roll curvature, ultimately forming a complete roll profile scheme. This method of backward calculation from the endpoint to the starting point ensures that the roll curvature of each forming step serves the final forming target, avoiding the loss of final accuracy control caused by the accumulation of errors step by step when designing forwards from the starting point to the endpoint.

[0054] One real-time example is as follows: Let the total number of forming passes be... The first region in the circumferential direction of the tube blank cross section The loading curvature of the track is , No. The curvature after the rebound is The initial tube blank curvature is ,in Let be the initial tube radius, and the final target curvature be . The forward equation for single-pass deformation-springback is: ; in This is the response relationship function corresponding to this region. For the first The cumulative plastic strain before each pass is used to solve for the curvature after springback in the known final pass. The loading curvature of all passes is solved by reverse recursion. .

[0055] The solution employs a combination of reverse recursion and single-pass Newton iteration. First, the final pass condition is initialized, letting... Set the initial value of the loading curvature. ,in To estimate the springback, a value of 0.2 times the target curvature difference can be used. The springback is then calculated forward, taking the current loading curvature as the reference value. Substitute the response relationship to calculate the rebound amount. After the springback curvature is obtained Then calculate the curvature deviation. If the convergence condition is not met, calculate the iteration increment: ; in Update the loading curvature in response to the first derivative of the relation function with respect to the deformation. Repeat the above forward calculation and iterative update process until the convergence condition is met, and obtain the first... Track loading curvature .

[0056] After completing the single-pass solution, let Solve the same method sequentially. , Until the first pass, the loading curvature of all passes is finally summarized, and the deformation sequence of each region in each pass is output. The solution process adopts a dual convergence criterion, and iterative convergence is determined when both criteria are met to avoid geometric inconsistencies. The first criterion is the curvature accuracy criterion, which requires that the relative deviation of the curvature after springback is less than a threshold, i.e.: ; in Pick First, to ensure the forming accuracy meets engineering requirements; second, there is the geometric compatibility criterion, which requires the relative deviation of the cross-sectional perimeter to be less than a threshold, i.e. ,in The initial tube blank cross-section perimeter, The perimeter of the cross section corresponding to the current curvature distribution. Pick This criterion ensures that the perimeter is approximately conserved during deformation, avoiding cross-sectional geometric distortion that may occur during reverse solution.

[0057] As one possible implementation, step S104 can be specifically implemented as steps S1041-S1043.

[0058] S1041. Obtain the response relationship of the tube blank in each region of the circumferential direction.

[0059] Specifically, as described in steps S10321-S10324 above, each region (major axis region, minor axis region, and transition region) of the tube blank cross-section is established with its own independent response relationship. Before starting the back calculation, these regional response relationships are first obtained as the mapping basis for the subsequent back calculation of each region.

[0060] S1042. Starting from the final pass, using the response relationship of each region as the mapping function, calculate the required deformation amount of the previous pass in each region in reverse order for each pass.

[0061] Specifically, for each pass and each circumferential region, the response relationship corresponding to that region is used as a mapping function. The target state of that region in the target parameters is taken as input, and the deformation amount that the region needs to achieve after the previous pass is calculated in reverse. Since the response relationships of each region are independent, the reverse calculation of each region is also performed independently without interference. This method of independent reverse calculation by region ensures that each region ultimately approximates the target shape on its own optimal deformation path.

[0062] S1043. Based on the deformation amount required in each region of the previous pass, the final output is the sequence of deformation amounts required in each region of each pass.

[0063] Specifically, the back-calculation results of all passes and all regions are summarized to form a deformation quantity sequence containing the complete pass sequence and deformation quantity information of each region. This deformation quantity sequence clearly shows the deformation target of each region of the billet cross-section at each stage from the first pass to the last pass, providing a direct input basis for determining the subsequent roll curvature.

[0064] The present invention also provides a method for outputting an optimized deformable sequence, including steps S201-S203.

[0065] S201. Obtain preset optimization constraints. The optimization constraints shall include at least one or more of the following: the maximum allowable single-pass deformation of the equipment, the minimum allowable single-pass deformation of the equipment, the balance requirement of deformation load in each pass, the upper limit of springback of the tube blank after each pass forming, the upper limit of wall thickness reduction rate of the tube blank during each pass forming process, and the cracking risk judgment threshold of the tube blank during each pass forming process.

[0066] Specifically, the above-mentioned optimization constraints are preset by the user based on actual production conditions. The maximum / minimum allowable deformation per pass is limited by the mill's rigidity and motor power; exceeding this range may lead to equipment overload or ineffective biting. The deformation load balance requirement aims to ensure a relatively uniform distribution of deformation across passes, preventing excessive deformation in a single pass from causing increased equipment impact and wear. The upper limit for springback is used to control the springback after unloading in each pass to not exceed the material's tolerance. The upper limit for wall thickness reduction rate is used to prevent excessive wall thinning during the deformation process, which could lead to insufficient product strength or localized cracking. The cracking risk assessment threshold is used to avoid surface cracks in the billet caused by excessive deformation in a single pass. These constraints together constitute the boundary conditions for optimization adjustment, ensuring that the final output deformation sequence not only forms the target shape but is also feasible, safe, and economical in actual production.

[0067] S202. The deformation sequence is optimized and adjusted using the response relationship and target parameters as the main constraints and the optimization constraints as additional constraints.

[0068] Specifically, the primary constraint ensures that the optimized deformation sequence can ultimately reach the target parameters through the reverse mapping of the response relationship; the secondary constraint ensures that the optimized deformation sequence meets the requirements of equipment capacity, material limits, and process stability in actual production. The optimization adjustment method is as follows: while ensuring that the primary constraint is not breached, the deformation amounts in each pass and region of the deformation sequence are fine-tuned to ensure they fall within the feasible region defined by the secondary constraint. If a value in the deformation sequence exceeds the upper or lower limit of the secondary constraint, the value is adjusted to the corresponding boundary value, and the primary constraint is simultaneously checked to ensure it is still satisfied. If not, corresponding iterative adjustments are performed. The optimized deformation sequence balances forming quality, equipment safety, and production efficiency.

[0069] S203, Output the optimized deformation sequence for each pass.

[0070] Specifically, the optimized deformation sequence is output in rows by pass and columns by region, serving as input for determining the roll curvature of each pass. This optimized deformation sequence ensures both the final forming accuracy and meets the various constraints of actual production.

[0071] The present invention also provides an optimization method for scheme design, including steps S301-S303.

[0072] S301. Obtain the actual springback value of the billet after the previous forming pass, compare the actual springback value with the springback amount predicted by the response relationship, and calculate the prediction deviation.

[0073] Specifically, during trial production or actual production, after a specified forming pass is completed, the actual cross-sectional shape of the billet after forming and unloading is obtained using a contour scanning device (such as a laser contour analyzer or optical measurement system). This actual cross-sectional shape is compared with the cross-sectional shape immediately after forming (under loading), and the actual springback value is calculated. Then, this actual springback value is compared with the springback amount predicted for that pass by the response relationship, and the difference between the two is taken as the prediction deviation. The magnitude of this prediction deviation reflects the accuracy of the current response relationship in predicting the actual deformation-springback behavior of the billet.

[0074] S302. Correct the parameters in the response relationship based on the prediction deviation, and output the corrected response relationship.

[0075] Specifically, based on the specific value and direction of the prediction deviation, the relevant parameters in the response relationship are adjusted to make the predicted value of the corrected response relationship closer to the actual measured value. The correction can be achieved by using parameter estimation algorithms (such as least squares method, maximum likelihood estimation, or Kalman filtering) to optimize and update the model parameters in the response relationship. Through this correction, the response relationship can gradually approximate the true deformation-springback characteristics of the billet under current actual process conditions.

[0076] A specific implementation example is as follows: Taking the balanced deformation load across all passes as the core optimization objective, while ensuring the final forming accuracy, a constrained nonlinear optimization model is constructed. The optimization objective is to minimize the root mean square error of the deformation in each pass, thereby achieving uniform distribution of deformation load and reducing equipment impact and wear. The objective function is... ; in For the first Curvature deformation of the track. The average deformation across all passes. This represents the total number of passes.

[0077] The optimization model includes multiple types of constraints, one of which is the equipment capacity constraint, requiring the deformation in a single pass to be within the upper and lower limits. ,in Determined by the maximum rolling force of the rolling mill and the section modulus of the billet bending resistance. The first factor is determined by the roll bite conditions, and the second is the upper limit constraint on the springback amount. ,in For the first The rebound amount of each pass, The third constraint is the maximum allowable springback per pass, and the fourth constraint is the wall thickness reduction rate. The requirements are as follows: ; in This is the initial wall thickness. For the first Minimum wall thickness after each pass. The maximum allowable thinning rate is typically 8% to 15% in engineering. The fourth constraint is the cracking risk constraint, requiring the equivalent plastic strain to not exceed the material's fracture strain. ,in For the first The maximum equivalent plastic strain of the pass, The fracture strain of the material is used as a threshold for determining the risk of cracking.

[0078] The optimization solution employs a sequential quadratic programming algorithm, suitable for small- to medium-scale nonlinear constrained optimization problems. Its efficiency and accuracy meet engineering requirements. The solution begins by using the initial deformation sequence obtained through backpropagation as the initial optimization point. At each iteration point, a quadratic approximation is performed on the objective function, and a linear approximation is performed on the constraints, constructing a quadratic programming subproblem. Solving this subproblem yields the search direction. The step size is determined using an Armijo line search, and the design variables are updated. The constraint violation rate and the convergence accuracy of the objective function are then checked; if not satisfied, the iteration continues. The iteration adjustment process follows specific rules. Regarding step size control, the initial iteration step size is 10% of the current deformation. During iteration, the step size is dynamically adjusted based on the constraint violation rate; a large constraint violation decreases the step size, while sufficient constraint margin increases it. Regarding constraint priority, crack risk constraints and wall thickness reduction constraints are prioritized, followed by equipment capacity constraints, and finally, load balance objectives are adjusted. The termination condition is when the relative change in the objective function value is less than a certain threshold. And the degree of violation of all constraints is less than When the iteration terminates, the optimized deformation sequence is output.

[0079] As one possible implementation, step S302 can be specifically implemented as steps S3021-S3023.

[0080] S3021. Classify and analyze the causes of prediction deviations to determine the type of deviation to which the prediction deviation belongs.

[0081] Specifically, prediction deviations arise from various causes, each requiring different correction strategies. For example, the causes of prediction deviations can be categorized into at least the following types: deviations caused by input discrepancies between basic material data and actual material properties; deviations caused by missing deformation mechanisms not covered by the functional structure of the response relationship; deviations caused by the concentrated manifestation of accumulated errors from previous forming passes in the current pass; and deviations caused by fluctuations in process parameters during forming (such as changes in friction coefficient and deformation temperature fluctuations). Determining the type of prediction deviation provides a basis for selecting appropriate correction strategies.

[0082] S3022. Based on the type of deviation, select the correction strategy corresponding to the type of deviation and make targeted corrections to the corresponding parameters in the response relationship.

[0083] Specifically, different types of deviations correspond to different correction strategies. If the deviation is a material input deviation, the material parameters are calibrated and the response relationship is reconstructed. If the deviation is a mechanism-missing deviation, the corresponding influencing factors are added to the response relationship to cover the missing deformation mechanism. If the deviation is a cumulative error deviation, the deformation amount in subsequent passes is progressively redistributed. If the deviation is a process fluctuation deviation, the measured values ​​of the process parameters are substituted into the response relationship for online correction. Through categorized correction, the problem of existing technologies using a uniform compensation coefficient for overall correction, which cannot accurately eliminate the source of deviation, is overcome.

[0084] S3023, Output the corrected response relationship.

[0085] Specifically, the output of the response relationship after targeted correction will be used as the basis for recalculating the deformation in subsequent passes.

[0086] S303. Recalculate the deformation and corresponding roll curvature of all subsequent passes based on the corrected response relationship, and output the corrected scheme design.

[0087] Specifically, after obtaining the corrected response relationship, starting from the next pass after the current pass and up to the final pass, the deformation of all subsequent passes is recalculated using the reverse calculation method described in step S104, and the roll curvature of the corresponding pass roll is determined accordingly. This method of full recalculation, rather than just correcting the next adjacent pass, effectively avoids the problem of local corrections causing the error to re-accumulate in subsequent passes, ensuring that the accuracy of the entire subsequent forming process is based on the corrected and accurate response relationship.

[0088] The present invention also provides a screening method for roller design, including steps S401-S403.

[0089] S401. Establish different response relationships and obtain multiple scheme designs based on different response relationships.

[0090] Specifically, the response relationship of this invention is influenced by multiple factors, including the selection method of material state variables, the structural form of the nonlinear function, the coarseness of the partitioning method, and the preset number of passes. By changing the above factors, for example, setting different pass numbers such as 4 passes, 6 passes, and 8 passes, or using different forms of nonlinear functions to construct the response relationship, multiple different response relationships can be established. Then, for each response relationship, the corresponding roll profile design is generated according to the back-calculation method in step S104, thereby obtaining multiple candidate roll profile designs.

[0091] S402. Verify the design of multiple schemes separately and obtain the corresponding quality evaluation indicators.

[0092] Specifically, for each candidate roll profile, the design is verified through simulation or actual trial production to obtain the quality evaluation index of the final formed part under that design. The quality evaluation index is used to quantitatively evaluate the forming effect of the design.

[0093] As one possible implementation, step S402 can be specifically implemented as steps S4021-S4022.

[0094] S4021. Perform finite element simulation verification on multiple design schemes to obtain cross-sectional profile accuracy data and wall thickness uniformity data after the final forming of multiple design schemes.

[0095] Specifically, for each candidate roll profile scheme, a corresponding finite element model is established, and the roll profile curvature of each pass is used as the boundary condition input to simulate the complete process from the initial state of the billet to the final forming. After the simulation, the cross-sectional profile data of the final formed part is extracted and compared with the theoretical profile of the target elliptical cross section. The profile deviation value of each point is calculated as the cross-sectional profile accuracy data. At the same time, the wall thickness values ​​of each measuring point in the circumferential direction of the cross section are extracted, and the deviation range and standard deviation of the maximum and minimum wall thickness values ​​are calculated as the wall thickness uniformity data.

[0096] S4022. Use cross-sectional profile accuracy data and wall thickness uniformity data as quality evaluation indicators.

[0097] Specifically, the cross-sectional profile accuracy data and wall thickness uniformity data obtained in step S4021 are used together as quality evaluation indicators to assess the merits of the candidate scheme. Profile accuracy reflects the degree to which the scheme reproduces the target shape, while wall thickness uniformity reflects the scheme's control over material flow during deformation. Together, they determine the quality of the final product.

[0098] S403. Based on the quality evaluation indicators, select the schemes that meet the requirements as the final roll type design.

[0099] Specifically, the quality evaluation indicators of each group of candidate schemes are compared one by one with the accuracy requirements set in the target parameters. Candidate schemes with cross-sectional profile deviations within the allowable tolerance range and wall thickness uniformity meeting the design requirements are selected. If multiple schemes meet the requirements simultaneously, the optimal scheme is determined as the final roll design based on the principle of fewer passes and more balanced deformation load distribution across passes. Through this screening step, a final scheme that balances forming accuracy and production efficiency is selected from multiple candidate schemes.

[0100] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to 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 the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A roller design method based on curvature variation and springback, characterized in that, include: Obtain the basic data of the tube blank, including the material parameters and structural dimensions of the tube blank; Determine the target parameters of the tube blank after roll forming; Based on the basic data and the target parameters, a response relationship is established between the deformation and springback of the tube blank. The response relationship characterizes the variation law of the springback amount generated by the tube blank under different degrees of deformation; Based on the response relationship, and with the target parameters as the target constraints, the required deformation amount for each pass is determined by reverse calculation. Based on the deformation amount, the roll curvature of each pass is determined, and finally the roll shape scheme design is completed.

2. The roller design method based on curvature variation and springback as described in claim 1, characterized in that, The step of establishing the response relationship between the deformation and springback of the tube blank based on the basic data and the target parameters specifically includes: The work hardening index and Bauschinger effect parameters of the tube blank are obtained during the successive deformation process, and the work hardening index and Bauschinger effect parameters are used as material state variables. Based on the basic data, the target parameters, and the material state variables, a nonlinear response relationship between deformation and springback is constructed.

3. The roller design method based on curvature variation and springback as described in claim 2, characterized in that, The construction of the nonlinear response relationship between deformation and springback based on the basic data, the target parameters, and the material state variables specifically includes: Obtain the cross-sectional data of the tube blank; Based on the cross-sectional data, the orientation distribution information and deformation path information during the forming process are obtained; Based on the orientation distribution information and the deformation path information, the differential distribution of the work hardening index in each region of the tube blank in the circumferential direction is determined; Based on the aforementioned differential distribution, a nonlinear response relationship between deformation and springback is constructed.

4. The roller design method based on curvature variation and springback as described in claim 2, characterized in that, The construction of the nonlinear response relationship between deformation and springback based on the basic data, the target parameters, and the material state variables specifically includes: Obtain the cumulative deformation information of the billet before the current pass, and determine the actual value of the Bauschinger effect parameter in the current pass based on the cumulative deformation information; Using the actual values ​​of the Bauschinger effect parameter in each pass as dynamic variables, a response relationship containing the Bauschinger effect is constructed based on the dynamic variables; the response relationship includes a dynamic response correction factor used to characterize the change in yield stress of the material under reverse loading or directional loading.

5. The roller design method based on curvature variation and springback as described in claim 1 or 3, characterized in that, The step of determining the required deformation for each pass based on the response relationship and using the target parameter as the target constraint specifically includes: Obtain the response relationship of the tube blank in each region of the circumferential direction; Starting from the final pass, using the response relationship of each region as the mapping function, the deformation amount required for the previous pass in each region is calculated backwards for each pass. Based on the required deformation amount in each region of the previous pass, the final output is the sequence of required deformation amounts in each region of each pass.

6. The roller design method based on curvature variation and springback as described in claim 5, characterized in that, After the final output of the required deformation sequence for each pass in each region, the following is also included: Obtain preset optimization constraints, which include at least one or more of the following: the maximum allowable single-pass deformation of the equipment, the minimum allowable single-pass deformation of the equipment, the balance requirement of deformation load in each pass, the upper limit of springback of the tube blank after each pass forming, the upper limit of wall thickness reduction rate of the tube blank in each pass forming process, and the cracking risk judgment threshold of the tube blank in each pass forming process. The deformation sequence is optimized and adjusted using the response relationship and the target parameters as the main constraints and the optimization constraints as the additional constraints. Output the optimized deformation sequence for each pass.

7. The roller design method based on curvature variation and springback as described in claim 1, characterized in that, After determining the roll profile curvature of each pass roll based on the deformation amount and finally completing the roll profile design, the process further includes: Obtain the actual springback value of the tube blank after the previous forming pass, compare the actual springback value with the springback amount predicted by the response relationship, and calculate the prediction deviation; The parameters in the response relationship are corrected based on the prediction deviation, and the corrected response relationship is output. The deformation and corresponding roll curvature of all subsequent passes are recalculated based on the corrected response relationship, and the corrected scheme design is output.

8. The roller design method based on curvature variation and springback as described in claim 7, characterized in that, The step of correcting the parameters in the response relationship based on the prediction deviation and outputting the corrected response relationship specifically includes: The causes of the prediction deviation are classified and analyzed to determine the type of deviation to which the prediction deviation belongs; Based on the deviation type, a correction strategy corresponding to the deviation type is selected to make targeted corrections to the corresponding parameters in the response relationship; Output the corrected response relationship.

9. The roller design method based on curvature variation and springback as described in claim 1, characterized in that, The method further includes: By establishing different response relationships, multiple scheme designs are obtained based on these different response relationships; The various proposed design schemes were verified separately, and the corresponding quality evaluation indicators were obtained. Based on the aforementioned quality evaluation indicators, the schemes that meet the requirements are selected as the final roll type design.

10. The roller design method based on curvature variation and springback as described in claim 9, characterized in that, The process of verifying various design schemes and obtaining corresponding quality evaluation indicators includes: Finite element simulations were performed on various design schemes to verify the accuracy of the cross-sectional profile and the uniformity of the wall thickness after the final forming of each design scheme. The cross-sectional profile accuracy data and the wall thickness uniformity data are used as the quality evaluation indicators.

Images