A method for controlling bending radius of tube spinning bending incremental forming

Abstract

This application relates to the field of metal bending component manufacturing technology, and discloses a method for controlling the bending radius in progressive forming of tubular materials by spinning and bending. The method includes the following steps: S1, obtaining an optimal combination of loading parameters affecting the forming quality indicators of the tubular material through orthogonal experiments; S2, establishing a regression function between the bending radius and the spinning and bending deformation parameters based on the optimal combination and the Maximin Latin square test results through stepwise regression analysis; S3, testing the regression function; if the test passes, obtaining the regression model of the bending radius; if the test fails, returning to step S2; S4, controlling the bending radius under the optimal loading parameter conditions using the regression model. This application incorporates a diameter reduction parameter into the control method, significantly improving the accuracy of bending radius control compared to existing geometric control models. It reduces the average error between tubular bending radius prediction and control from 10.28% to 5.2%, offering advantages such as high forming accuracy, wide applicability, and higher reliability.

Description

Technical Field

[0001] This application relates to the field of metal bending component manufacturing technology, specifically to a method for controlling the bending radius of a tube in a progressive forming process of spinning and bending. Background Technology

[0002] Currently, the aerospace, automotive, and other fields have an increasing demand for precise and highly reliable pipeline transportation systems, which in turn have a significant need for curved pipe fittings with varying diameters and wall thicknesses. Spin bending progressive forming technology, combining spinning and bending steps, is a primary method for manufacturing complex curved pipe fittings with varying diameters, wall thicknesses, and multiple bending radii. In spin bending progressive forming technology, the bending radius is the most important forming dimension for complex curved pipe fittings and a crucial indicator of final forming accuracy; therefore, precise control of the bending radius is extremely important.

[0003] However, spin bending progressive forming differs from simple flexible tube bending. It involves the combined action of a spinning wheel and a bending die, and the forming process is influenced by numerous parameters, including the bending die displacement, step spacing, diameter reduction, spinning wheel feed ratio, spinning wheel fillet radius, spinning wheel forming angle, spinning speed, and bending die speed. This makes precise control of the bending radius difficult. To address the problem of bending radius control in spin bending progressive forming, Staupendahl et al. derived a bending radius control formula considering the bending die displacement and step spacing based on the geometric relationship theory in bending processes.

[0004]

[0005] Where R is the bending radius of the pipe, A is the step spacing, and U is the bending die displacement.

[0006] In actual production, the above formula provides some convenience for controlling the bending radius. However, its shortcomings are that it only considers geometric relationships and ignores the influence of spinning bending deformation parameters such as pipe diameter reduction on the bending radius. This results in insufficient accuracy in predicting and controlling the bending radius, and it can only be applied to conditions with large bending radii and small diameter reduction. Summary of the Invention

[0007] To address the problems existing in the prior art, the purpose of this application is to provide a method for controlling the bending radius of tubes in progressive spinning bending. This method establishes a quantitative relationship between the bending die displacement, step spacing, diameter reduction, and bending radius. Based on this quantitative relationship, the bending radius of the tubes in progressive spinning bending is controlled, effectively solving the problem that existing geometric methods cannot be applied to predicting and controlling the bending radius of tubes under conditions of small bending radius and large diameter reduction. This method achieves high-precision overall forming of complex bent tubes with variable diameter, variable wall thickness, and multiple bending radii.

[0008] To achieve the above objectives, the present application adopts the following technical solution.

[0009] This application provides a method for adjusting the bending radius in progressive forming of tubular spinning and bending, comprising the following steps:

[0010] S1, the optimal combination of loading parameters affecting the quality index of pipe forming is obtained through orthogonal experiments;

[0011] S2, Based on the preferred combination and the results of the Maximin Latin square test, a regression function between the bending radius and the spinning bending deformation parameter is established through stepwise regression analysis;

[0012] S3, Test the regression function. If the test passes, the regression model of the bending radius is obtained; if the test fails, return to step S2.

[0013] S4, under the preferred loading parameters, the bending radius is adjusted by the regression model.

[0014] In some implementations, the tube forming quality indicators include:

[0015] Maximum cross-sectional deformation rate Q max Maximum wall thickness reduction rate TN 0max Maximum wall thickness increase rate TK 0max Wrinkling trend I 0w Springback angle Δθ, deflection angle β, and bending radius R;

[0016] In some implementations, the loading parameters include:

[0017] The radius of the spinning wheel fillet, the forming angle of the spinning wheel, the feed rate, the spinning speed, and the speed of the bending die.

[0018] In some implementation schemes, the preferred combination of loading parameters affecting the quality indicators of pipe forming is obtained as follows:

[0019] Orthogonal experiments were conducted to analyze the effects of the spool radius, spool forming angle, feed rate, spinning speed, and bending die speed on the maximum cross-sectional deformation rate Q. max Maximum wall thickness reduction rate TN 0max Maximum wall thickness increase rate TK 0max Wrinkling trend I 0w The significant influence of springback angle Δθ, deflection angle β, and bending radius R was considered to obtain an optimal combination.

[0020] In some implementations, in step S2, the spinning bending deformation parameters include the diameter reduction, the step spacing, and the bending die displacement.

[0021] In some implementations, establishing the regression function between the bending radius and the spinning bending deformation parameters includes the following steps:

[0022] S21, based on the results of the Maximin Latin square test, a mathematical expression combining geometric relations and quadratic polynomials is used as the mathematical expression for the bending radius and the spinning bending deformation parameter, as shown in formula (1):

[0023]

[0024] Where y is the response value of the bending radius, x i and x j Let x be the spin bending deformation parameter, where x i x is any one of the following: diameter reduction, step spacing, or bending die displacement; j β0, β... ij β i β ii ε is the regression coefficient; ε is a random variable that follows a normal distribution.

[0025] S22, through stepwise regression analysis, the regression function of bending radius and spinning bending deformation parameter is obtained, as shown in formula (2):

[0026]

[0027] Where R is the bending radius, A is the step spacing, U is the bending die displacement, and x is the diameter reduction.

[0028] In some implementations, step S3, which tests the regression function, specifically involves:

[0029] Perform an F-test on the regression function of the bending radius. If the calculated F-value is greater than the F-value of the F-distribution table under the corresponding degrees of freedom, the model is significant and the test passes; otherwise, it is not significant and the test fails.

[0030] In some implementations, the adjustment of the bending radius includes:

[0031] The predicted bending radius is obtained by substituting the pipe diameter reduction, the step spacing, and the bending die displacement into the regression model of the bending radius.

[0032] Compared with the prior art, the beneficial effects of this application are as follows:

[0033] The method for adjusting the bending radius of the tube spinning and bending progressive forming method of this application has the advantages of high forming accuracy, wide applicability and higher reliability.

[0034] 1) The reduction in diameter parameter is incorporated into the control method, which greatly improves the accuracy of bending radius prediction and control compared with the existing geometric control model, reducing the average error of pipe bending radius prediction and control from 10.28% to 5.2%;

[0035] 2) The influence of loading parameters on the forming results and the distribution of their significance were analyzed through virtual orthogonal experiments. The optimal parameter combination was obtained to optimize the forming results. A regression model was established based on the optimal parameter combination, which has the advantages of high reliability and wide applicability.

[0036] 3) The regression model is easy to apply. The bending radius regression prediction model only requires inputting the bending modulus displacement U, the step spacing A, and the diameter reduction x into the model. The prediction result can be obtained through simple calculation, which is easy to apply. Attached Figure Description

[0037] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a schematic diagram of the spin bending progressive forming apparatus of this application;

[0039] The attached figures are labeled as follows:

[0040] 1. Bending die; 2. Bending die support rod; 3. Support; 4. Rotating wheel; 5. Rotating wheel base; 6. Pipe; 11. Bending roller frame; 12. Bending roller. Detailed Implementation

[0041] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0042] In the following description of this embodiment, the terms "including", "comprising", "having", and "containing" are all open-ended terms, meaning that they include but are not limited to.

[0043] In the following description of this embodiment, the term "and / or" is used to describe the association relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, B existing alone, and A and B existing simultaneously. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0044] In the following description of this embodiment, the term "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items. For example, "at least one of a, b, or c", or "at least one of a, b, and c", can both mean: a, b, c, ab (i.e., a and b), ac, bc, or abc, where a, b, and c can be single or multiple.

[0045] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. The singular forms "a" and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0046] Those skilled in the art should understand that, in the following description of the embodiments of this application, the sequence of numbers does not imply the order of execution. Some or all steps may be executed in parallel or sequentially. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0047] Those skilled in the art will understand that the numerical ranges in the embodiments of this application should be understood to specifically disclose each intermediate value between the upper and lower limits of the range. Each smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included within the scope of this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0048] Unless otherwise stated, the technical / scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. While this application describes only preferred methods and materials, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this application. All references to this specification are incorporated by way of citation to disclose and describe methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0049] The method for adjusting the bending radius in the progressive forming of tubular spinning bending of this application is implemented by a progressive forming device for spinning bending. The progressive forming device for spinning bending has the following structure: Figure 1 As shown, it includes spinning units and bending units;

[0050] The spinning unit includes a spinning wheel base 5 and a spinning wheel 4. The spinning wheel base 5 has a through hole at its center, and the spinning wheel 4 is arranged circumferentially outside the through hole. The tube 6 enters the spinning unit through the through hole.

[0051] The bending unit includes a bending die 1, a bending die support 2, and a support 3. The bending die 1 includes a bending roller frame 11 and two bending rollers 12. The bending roller frame 11 is composed of a shaft hole at the upper part and the lower part of the bending roller frame with a clearance fit, so as to assemble the required bending rollers 12. The bending rollers 12 are rotating bodies with an arc-shaped profile, and the radius of each arc is the same as the radius of the pipe to be bent. Before bending, the bending roller with the corresponding arc radius is selected according to the radius of the pipe. An axial through hole with a clearance fit with the bending roller frame 11 is provided between the two bending rollers 12, which can rotate around its own axis under the action of friction of the formed pipe.

[0052] The lower middle part of the bending die is fitted with one end of the bending die support rod through a clearance hole; the support has a cylindrical hole at its center, and the other end of the bending die support rod is inserted into the cylindrical hole of the support and fitted with the cylindrical hole of the support through a clearance hole, so that the bending die can rotate around the axis of the bending die support rod. At the initial moment, the axis of the pipe, the axis of the spinning wheel base 5 and the axis of the hollow part of the bending unit are on the same axis, so that the pipe can be fed axially through the spinning step and then through the hollow part formed by the two bending rollers.

[0053] During the spinning and bending process, the tube axis, the axis of the spinning wheel base, and the axial through hole between the two bending rollers are always coaxial. The tube 6 enters the spinning unit at a set feed speed. The spinning wheel 4 in the spinning unit can simultaneously rotate circumferentially around the center of the spinning wheel base 5 and feed radially toward the tube. When the spinning wheel 4 reaches the predetermined diameter reduction position, it continues to rotate circumferentially around the axis of the tube 6. When the tube 6 reaches the spinning plane, the spinning process begins. The tube 6 is spun and reduced in diameter to the predetermined diameter, reaching the predetermined diameter. The spinning process continues as the tube is fed. When the front end of the spun tube reaches the center of the bending roller frame 11 and passes through the two bending rollers 12, the support 3 moves horizontally along the direction perpendicular to the initial feed of the tube 6, so that the bending die 1 reaches the predetermined position according to the predetermined bending die displacement U. The tube 5 is continuously fed forward to obtain a tube of the predetermined shape.

[0054] Based on the aforementioned spinning bending progressive forming apparatus, the method for adjusting the bending radius of tubular materials using this application for spinning bending progressive forming includes the following steps:

[0055] S1, the optimal combination of loading parameters affecting the quality index of pipe forming is obtained through orthogonal experiments;

[0056] In this application, the tubing forming quality index includes: maximum cross-sectional deformation rate Q. max Maximum wall thickness reduction rate TN 0max Maximum wall thickness increase rate TK 0max Wrinkling trend I 0w The springback angle Δθ, deflection angle β, and bending radius R are among the loading parameters that significantly affect the tube forming quality in the reduced diameter spinning and flexible bending process of this application.

[0057] This application uses orthogonal experimental analysis to examine the effects of the spool radius, spool forming angle, feed rate, spinning speed, and bending die speed on the maximum cross-sectional deformation rate Q. max Maximum wall thickness reduction rate TN 0max Maximum wall thickness increase rate TK 0max Wrinkling trend I 0w The significance of the effects of the springback angle Δθ, deflection angle β, and bending radius R was investigated to obtain the optimal combination of loading parameters, specifically:

[0058] Under four horizontal conditions, the following parameters were considered: rotary wheel fillet radius ρ, rotary wheel forming angle α, feed rate f, spinning speed ω, and bending die speed v. b Five factors were analyzed, and the levels were selected as shown in Table 1:

[0059] Table 1. Factor Level Table for Orthogonal Experiments

[0060]

[0061] Using orthogonal array L16(4) 5 An orthogonal experiment was conducted, and the experimental plan is shown in Table 2. The experimental conditions were: pipe diameter D... i The pipe is 40mm thick with a wall thickness of t. i The diameter was 2mm, the reduction in diameter x was 4mm, the step spacing A was 60mm, the bending die displacement U was 20mm, and the bending angle θ was 90°. The bent sections of the pipe were compared after the test.

[0062] Table 2 shows 16 experimental schemes using orthogonal experimental design.

[0063]

[0064] The results of the orthogonal experiment are shown in Table 3.

[0065] Table 3 Results of 16 orthogonal experiments

[0066]

[0067] The order of significance of the effects of each loading parameter on the quality indicators was analyzed. The results show that the spinning wheel forming angle α and the bending die motion speed v are the most significant. b For the maximum cross-sectional deformation rate Q max The impact is quite significant because the larger the forming angle α of the spinning die, the smaller the tangential contact area between the spinning die and the inner side of the bent tube during the spinning bending process, while the larger the circumferential contact area. This increases the resistance to tangential deformation of the material, causing the spinning process to bulge and increasing the degree of cross-sectional deformation. Furthermore, as the bending die moves at a speed v... b As the pressure increases, the compressive stress on the inner side of the bending section also increases during the bending process, thereby increasing the amount of cross-sectional deformation.

[0068] The spinning speed ω has a greater impact on the wall thickness reduction than the other four factors;

[0069] The forming angle α of the spinning wheel has a strong influence on the wall thickness increase, deflection angle and wrinkling tendency; the larger the forming angle of the spinning wheel, the greater the wrinkling tendency, and increasing the forming angle of the spinning wheel will also greatly aggravate the deflection and cross-sectional distortion of the pipe.

[0070] The bending die speed has the greatest impact on springback.

[0071] The forming angle α of the spinning wheel has a decisive influence on the bending radius.

[0072] Based on the above experimental results, the optimal combination of loading parameters was obtained: the final parameter combination is A2B1C3D2E1, namely, the spinning wheel forming angle α = 10°, the spinning wheel fillet radius ρ = 5mm, the spinning speed ω = 2r / s, the feed rate f = 1mm / r, and the bending roller speed v. b =0.5mm / s.

[0073] The optimal combination of loading parameters was used for finite element model calculations, and the results are shown in Table 4. Table 4 shows that the forming results of interest in this invention are all in a favorable state. The wrinkling tendency and deflection angle are close to the lowest values ​​among the 16 orthogonal experiments, and the cross-sectional deformation has been significantly optimized compared to the orthogonal experiments. Under the optimal combination of loading parameters, the cross-sectional quality can be further optimized, and all quality indicators can be ensured to be at a favorable level.

[0074] Table 4 Comparison of the results of the optimal combination and the orthogonal experiment.

[0075]

[0076] S2, Based on the preferred combination and the results of the Maximin Latin square test, a regression function between the bending radius and the spinning bending deformation parameter is established through stepwise regression analysis;

[0077] The loading parameters are determined as follows: spool forming angle α = 10°, spool fillet radius ρ = 5 mm, spinning speed ω = 2 r / s, feed rate f = 1 mm / r, and bending roller speed v. b =0.5 mm / s. Based on this, 11 uniform simulation experiments were designed using the Maximin Latin square experiment, and the conditions of the simulation experiments are shown in Table 5.

[0078] Table 5. Setting of spinning bending deformation parameters in the Maximin Latin square test method.

[0079]

[0080]

[0081] Incorporate the reduction in diameter x into the bending radius control formula based on geometric relationships. The bending radius R is the bending radius after springback. The test scheme and test results are shown in Table 6.

[0082]

[0083] Maximin Latin Square Experimental Design and Results

[0084] Based on the experimental results in Table 6, a prediction model for the bending radius was obtained by combining geometric relation terms with a quadratic polynomial. A regression model with a clear mathematical expression was constructed to establish the correlation between design parameters and the target response. Specifically, the following steps were taken:

[0085] S21, based on the results of the Maximin Latin square test, a mathematical expression combining geometric relations and quadratic polynomials is used as the mathematical expression for the bending radius and the spinning bending deformation parameter, as shown in formula (1):

[0086]

[0087] Where y is the response value of the bending radius, x i and x j Let x be the spin bending deformation parameter, where x i x is any one of the following: diameter reduction, step spacing, or bending die displacement; j β0, β... ij β i β ii ε is the regression coefficient; ε is a random variable that follows a normal distribution.

[0088] S22, Equation (1) uses stepwise regression analysis to fit the regression function of bending radius and spinning bending deformation parameter, as shown in Equation (2):

[0089]

[0090] Where R is the bending radius, A is the step spacing, U is the bending die displacement, and x is the diameter reduction.

[0091] S3, Test the regression function. If the test passes, the regression model of the bending radius is obtained; if the test fails, return to step S2.

[0092] The F-test was performed on the regression function of the bending radius R, and the results are shown in Table 7. F = 1372.97, and the corrected coefficient of determination R0 is... adj 2 The value is greater than 0.90, which is very close to 1. The test is passed, and the bending radius control model is obtained.

[0093] Table 7. F-test results of the regression model for bending radius R.

[0094]

[0095] If the regression equation is not significant, the test fails, and the process returns to step S2 to re-establish the regression function between the bending radius and the spinning bending deformation parameter, and then test the regression function.

[0096] S4, under the preferred loading parameters, the bending radius is adjusted by the regression model.

[0097] The adjustment of the bending radius includes:

[0098] The predicted bending radius is obtained by substituting the pipe diameter reduction, the step spacing, and the bending die displacement into the regression model of the bending radius.

[0099] Simulation experiment:

[0100] Based on the progressive forming process of spinning bending, the forming angle of the spinning wheel is set to α = 10°, the radius of the spinning wheel fillet ρ = 5mm, the spinning speed ω = 2r / s, the feed rate f = 1mm / r, and the bending roller speed v. b =0.5mm / s.

[0101] Based on this, five sets of data were randomly selected for simulation to obtain the bending radius values ​​under finite element simulation conditions. The simulation data are shown in Table 8.

[0102] Table 8 shows five sets of finite element simulation data from the examples.

[0103]

[0104]

[0105] Substituting the step spacing A, bending die displacement U, and diameter reduction x of each group into the bending radius control formula based on geometric relationships and the bending radius control model of this application, the predicted bending radius values ​​of the geometric model and the bending radius control model were calculated respectively. The bending radius values ​​from finite element simulation, the bending radius prediction values ​​from the bending radius control model, and the bending radius prediction values ​​from the geometric model were compared, and the results are shown in Table 9. Table 9 shows that the prediction errors of each group in the bending radius control model are smaller than those of the geometric model, and the maximum error in the bending radius control model does not exceed 10%. The average prediction error of the bending radius control model is 5.20%, indicating that the bending radius control model has high prediction accuracy, while the average prediction error of the geometric model is 10.28%, which is significantly greater than that of the bending radius control model.

[0106] Table 9 Comparison of prediction results between regression model and geometric model

[0107]

[0108] Simulation experiments show that the bending radius control model considering the diameter reduction of this application has higher prediction accuracy than the geometric model. It can effectively solve the problem that the existing geometric method cannot be applied to the prediction and control of the bending radius of pipes under the condition of small bending radius and large diameter reduction, thereby realizing the overall high-precision forming of complex bent pipes with variable diameter, variable wall thickness and multiple bending radii.

[0109] Although the present invention has been described in detail in this specification with general description and specific embodiments, some modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention are within the scope of protection claimed by the present invention.

Claims

1. A method for controlling the bending radius in progressive forming of tubular spinning and bending, characterized in that, Includes the following steps: S1, the optimal combination of loading parameters affecting the quality index of pipe forming is obtained through orthogonal experiments; S2, Based on the preferred combination and the results of the Maximin Latin square test, a regression function between the bending radius and the spinning bending deformation parameter is established through stepwise regression analysis; The spinning bending deformation parameters include the diameter reduction, the step spacing, and the bending die displacement. S3, Test the regression function. If the test passes, the regression model of the bending radius is obtained. If the test fails, return to step S2; S4, under the preferred combination of loading parameters, the bending radius is adjusted by the regression model; The adjustment of the bending radius includes: The predicted bending radius is obtained by substituting the pipe diameter reduction, the step spacing, and the bending die displacement into the regression model of the bending radius.

2. The method for adjusting the bending radius for progressive forming of tubular materials by spinning and bending according to claim 1, characterized in that: The tube forming quality indicators include: Maximum cross-sectional deformation rate Q max Maximum wall thickness reduction rate TN 0max Maximum wall thickness increase rate TK 0max Wrinkling trend I 0w Springback angle Δθ, deflection angle β, and bending radius R.

3. The method for adjusting the bending radius of tubular material in progressive spinning and bending according to claim 2, characterized in that, The loading parameters include: The radius of the spinning wheel fillet, the forming angle of the spinning wheel, the feed rate, the spinning speed, and the speed of the bending die.

4. The method for adjusting the bending radius for progressive forming of tubular materials by spinning and bending according to claim 3, characterized in that, The optimal combination of loading parameters affecting the quality indicators of pipe forming is obtained as follows: Orthogonal experiments were conducted to analyze the effects of the spool radius, spool forming angle, feed rate, spinning speed, and bending die speed on the maximum cross-sectional deformation rate Q. max Maximum wall thickness reduction rate TN 0max Maximum wall thickness increase rate TK 0max Wrinkling trend I 0w The significant influence of springback angle Δθ, deflection angle β, and bending radius R was considered to obtain an optimal combination.

5. The method for adjusting the bending radius of tubular material in progressive spinning and bending according to claim 1, characterized in that, The process of establishing the regression function between the bending radius and the spinning bending deformation parameters includes the following steps: S21, based on the results of the Maximin Latin square test, a mathematical expression combining geometric relations and quadratic polynomials is used as the mathematical expression for the bending radius and the spinning bending deformation parameter, as shown in formula (1): Formula (1) in, The response value is the bending radius. and Here are the parameters for spinning bending deformation, where It can be any one of the following: diameter reduction, step spacing, or bending die displacement; It can be either the step spacing or the bending die displacement; The number of parameters for spinning bending deformation; , ε is the regression coefficient; ε is a random variable that follows a normal distribution. S22, through stepwise regression analysis, the regression function of bending radius and spinning bending deformation parameter is obtained, as shown in formula (2): Formula (2) in, Where is the bending radius, For the distance between work steps, This is the displacement of the bending modulus. This is the amount of diameter reduction.

6. The method for adjusting the bending radius for progressive forming of tubular materials by spinning and bending according to claim 1, characterized in that, Step S3, which involves testing the regression function, specifically includes: Perform an F-test on the regression function of the bending radius. If the calculated F-value is greater than the F-value of the F-distribution table for the corresponding degrees of freedom, the model is significant and the test is passed. Otherwise, it is not significant and the test fails.

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