Method and system for obtaining the maximum bending radius of free bending of a pipe

Abstract

This invention relates to the field of intelligent processing and manufacturing technology, specifically a method and system for obtaining the maximum bending radius of a pipe under free bending. The method includes the following steps: obtaining the basic mechanical performance parameters of the metal pipe; determining the stress distribution function of different deformation zones inside and outside the strain neutral layer of the section of the metal pipe to be bent; determining a first relation; determining a second relation; determining a third relation; calculating the ratio of the springback prediction angle to the bending angle under a series of bending radii based on the first, second, and third relations; plotting a dot-line graph; and obtaining the maximum bending radius of the metal pipe under free bending through the point with a vertical coordinate of 1 on the dot-line graph. This invention can easily and quickly obtain the maximum bending radius of a metal pipe under free bending, providing an effective means to clarify the free bending forming range of metal pipes of different specifications and materials, and providing technical support for the design of large bending radius spatial conduit components and high-performance rapid response manufacturing.

Description

Technical Field

[0001] This invention relates to the field of intelligent processing and manufacturing technology, specifically a method and system for obtaining the maximum bending radius of a pipe under free bending. Background Technology

[0002] Space metal conduit components are primarily used in the piping systems of aircraft, including fuel, hydraulic, lubricating oil, compressed air, and ejector water, serving as the "arteries and lifelines" of the aircraft. These conduit components typically feature complex spatial axes, continuous variable curvature, or complex mixed curvature, and often need to operate under extreme conditions such as ultra-high / ultra-low temperatures, high stress, and strong corrosion. Some are also limited by weight, requiring minimal mass to achieve equivalent performance under normal conditions. With the booming development of the aerospace manufacturing industry, the design of various high-end aircraft increasingly demands lightweight, high-efficiency, and highly reliable precision manufacturing of these components. Conventional metal conduit bending forming methods (such as CNC bending, roll bending, push bending, and pressure bending) present certain limitations in forming these components. As an emerging cutting-edge technology in the field of tubing processing, three-dimensional free bending forming technology can achieve the integral forming of tubing components with complex three-dimensional axes and continuous bending without straight sections simply by controlling the mold's movement trajectory. It has significant advantages and great development potential in the integral forming of a series of high-performance space metal conduit components.

[0003] Currently, researchers both domestically and internationally have conducted systematic research on the minimum forming limit (i.e., minimum relative bending radius) of free bending of pipes. For example, invention patent CN106903194B proposes a method for optimizing the combination of the eccentricity of the bending die movement and the distance between the center of the bending die and the front end of the guide mechanism, thereby achieving high-quality free bending forming of pipes with a smaller relative bending radius. Invention patent CN111545608B proposes a device and method for reducing the relative bending radius of free bending of pipes based on the optimized design of the mold structure and connection method, which promotes the popularization and engineering application of free bending technology of pipes. However, due to the widespread neglect of the influence of the elastic deformation stage of metal tubing during the forming process, methods for determining the maximum forming limit of free bending of tubing are rarely reported. This makes it impossible for engineers to determine whether tubing with a large bending radius can be processed and formed. Furthermore, during free bending of tubing, the bending deformation zone is only constrained at the center of the bending die and the front end of the guide die; other areas are in a state of no die constraint. The stress state and radius of curvature of the tubing change constantly during the eccentricity of the bending die and the return stroke. Simultaneously, the axial thrust applied by the propulsion mechanism continuously acts on the tail end of the tubing. These factors result in the stress-strain state of the tubing during free bending differing from conventional metal conduit bending forming processes such as CNC bending. Therefore, methods for determining the maximum forming limit under conventional tubing processes have limited reference value for free bending processes. How to simply, quickly, and effectively determine the maximum forming limit of free bending of tubing is of great significance for clarifying the applicable scope of free bending processes and realizing the design and high-performance rapid response manufacturing of large bending radius spatial conduit components. Summary of the Invention

[0004] To address the aforementioned deficiencies in the existing technology, this invention proposes a method and system for obtaining the maximum bending radius of a pipe under free bending. This application can simply, quickly, and effectively determine the maximum forming limit of a metal pipe under free bending, clarify the free bending forming range of metal pipes of different specifications and materials, and provide support for the design of large bending radius spatial conduit components and high-performance rapid response manufacturing.

[0005] To achieve the above-mentioned technical effects, the technical solution of this application is as follows:

[0006] A method for obtaining the maximum bending radius of a pipe under free bending includes the following steps:

[0007] Step 101: Obtain the basic mechanical property parameters of the metal pipe and determine the stress distribution function of different deformation zones inside and outside the strain neutral layer of the section of the metal pipe to be bent.

[0008] Step 102, determine the first relationship; the first relationship represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the pipe section to be bent and the bending radius;

[0009] Step 103, determine the second relationship; the second relationship represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe section to be bent.

[0010] Step 104, determine the third relationship; the third relationship is the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent.

[0011] Step 105: Calculate the ratio of the predicted springback angle to the bending angle under a series of bending radii based on the first, second, and third relational formulas, and draw a dot-line graph. Obtain the maximum bending radius of the metal pipe under free bending through the point with the vertical coordinate of 1 on the dot-line graph.

[0012] Furthermore, the types of basic mechanical property parameters obtained in step 101 include: Young's modulus, yield strength, strength coefficient, and strain hardening index.

[0013] Furthermore, the acquisition of basic mechanical property parameters of the metal pipe in step 101 specifically includes: obtaining the Young's modulus, yield strength, strength coefficient, and strain hardening index of the metal pipe through axial tensile tests on standard longitudinal arc-shaped specimens of the metal pipe.

[0014] Furthermore, the standard longitudinal arc-shaped specimen is cut parallel to the pipe axis.

[0015] Furthermore, in step 101, the stress distribution function of different deformation zones inside and outside the strain neutral layer of the segment to be bent under free bending forming stress is obtained by introducing the axial stress generated by the propulsion mechanism in free bending forming, thus obtaining the axial stress at each point in different deformation zones inside and outside the strain neutral layer of the segment to be bent:

[0016]

[0017]

[0018] In equation (1), σ1(R) y ,ρ) represents the axial stress at a point in the plastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equation (2), σ2(R y ,ρ) represents the axial stress at a point in the elastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equations (1) and (2), R y ρ represents the distance from a point on the pipe wall to the center of the bend, K represents the bending radius of the bend, and σ represents the strength coefficient of the metal pipe. s The value represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, n represents the strain hardening exponent of the metal pipe, and σ represents the strain hardening exponent of the metal pipe. Nα represents the axial stress applied by the propulsion mechanism during the free bending forming process of the metal pipe, α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer, and R represents the bending radius between the inner and outer boundaries of the section to be bent and the bending center in the bending plane.

[0019] Furthermore, determining the first relation in step 102 specifically includes:

[0020] Based on the formula for the axial stress in the elastic deformation zones inside and outside the strain neutral layer of the section to be bent and the yield critical condition σ=σ s Determine the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius:

[0021]

[0022]

[0023] In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This indicates the average radius of the metal pipe.

[0024] Furthermore, determining the second relation in step 103 specifically includes:

[0025] Based on relevant formulas in mechanics of materials, the relationship between the bending moment of the elastic / plastic deformation zone on the inner and outer sides of the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the metal pipe section to be bent is determined as follows:

[0026]

[0027]

[0028] In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m α represents the average radius of the metal pipe, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer.

[0029] Furthermore, determining the third relation in step 104 specifically includes:

[0030] The expression for the third relation is:

[0031]

[0032] In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the variable moment of inertia of the pipe section during the bending process (under small deformation conditions, the wall thickness change, distortion change and center layer offset of the bent pipe section are ignored, and the variable moment of inertia of the section can be calculated by the plane assumption of the bent pipe section and the moment of inertia rotation formula).

[0033] Further, step 105 specifically includes:

[0034] Based on the functional relationship between the ratio of the springback prediction angle to the bending angle and the bending radius, the ratio of the springback prediction angle to the bending angle is plotted on the ordinate, and the bending radius is plotted on the abscissa, with the bending radius ranging from α... e1 When the angle is 90°, the corresponding bending radius value starts to increase (each increment is determined by a certain precision). Draw a dot-line graph and obtain the point with the vertical coordinate of 1 on the dot-line graph. The value of its horizontal coordinate is the maximum free bending radius value of the metal pipe.

[0035] A system for obtaining the maximum bending radius of a pipe under free bending includes:

[0036] The acquisition module is used to acquire the Young's modulus, yield strength, strength coefficient, and strain hardening index of a standard longitudinal arc-shaped specimen of a metal pipe, wherein the standard longitudinal arc-shaped specimen is cut parallel to the pipe axis.

[0037] The first relation determination module is used to determine the first relation; the first relation represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius.

[0038] The second relation determination module is used to determine the second relation; the second relation represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent section and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe to be bent section.

[0039] The third relation determination module is used to determine the third relation; the third relation represents the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment on the inner and outer sides of the strain neutral layer of the pipe section to be bent.

[0040] The springback prediction angle to bending angle ratio calculation module is used to calculate the ratio of springback prediction angle to bending angle for a series of bending radius values ​​based on the first, second and third relational formulas.

[0041] The maximum bending radius determination module is used to draw a dot-line graph showing the ratio of the springback prediction angle to the bending angle as a function of the bending radius, based on the ratio of the springback prediction angle to the bending angle under the series of bending radius values. The point with the vertical coordinate of 1 on the dot-line graph is obtained, and the value of its horizontal coordinate is the maximum bending radius of the metal pipe under free bending.

[0042] Furthermore, the third relationship determination module and the springback prediction angle to bending angle ratio calculation module specifically include:

[0043] According to the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius:

[0044]

[0045]

[0046] In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This represents the average radius of the metal pipe. For a detailed diagram of the geometric parameters, please refer to [link / reference needed]. Figure 2 and Figure 3 ; and the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe section to be bent:

[0047]

[0048]

[0049] In equation (5), M1(α) e1 ,α e2Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2 Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m The radius of the metal pipe is represented by α, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer. See the diagram for specific geometric parameters. Figure 2 Based on this, the expression for the ratio of the springback prediction angle to the bending angle is determined:

[0050]

[0051] In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the variable moment of inertia of the section during the bending process of the pipe (under small deformation, the wall thickness change, distortion change and center layer offset of the bent pipe section are ignored, and the variable moment of inertia of the section can be calculated by the plane assumption of the bent pipe section and the moment of inertia rotation formula); further, through the springback prediction angle to bending angle ratio calculation module, the ratio of springback prediction angle to bending angle under a series of bending radius values ​​is calculated.

[0052] Furthermore, the maximum bending radius determination module specifically includes:

[0053] The springback prediction angle to bending angle ratio curve plotting unit is used to plot a dotted line graph based on the ratio of springback prediction angle to bending angle under a series of bending radius values, with the ratio of springback prediction angle to bending angle as the vertical axis and the bending radius as the horizontal axis. Finally, it displays the points on the dotted line graph with a vertical axis of 1 and marks the value of their horizontal axis.

[0054] The advantages of this invention are:

[0055] This invention first derives the stress distribution functions of different deformation zones inside and outside the strain neutral layer of the section to be bent by analyzing the basic mechanical properties and stress characteristics of the metal pipe under free bending. Then, it calculates the variation of the boundary angle between the elastic / plastic deformation zones on both sides of the cross-section with the bending radius using the stress distribution expressions for the inner and outer sides. Next, based on the boundary angle, it calculates the bending moment values ​​for the inner and outer sides, and plots a curve showing the ratio of the springback prediction angle to the bending angle as a function of the bending radius. The maximum bending radius of the metal pipe under free bending is obtained from the point on the curve with a vertical coordinate of 1. The method and system provided by this invention can easily and quickly obtain the maximum bending radius of metal pipes under free bending, providing an effective means to clarify the free bending forming range of metal pipes of different specifications and materials. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating the method for obtaining the maximum bending radius of a pipe under free bending in this technical solution.

[0057] Figures 2-3 This is a schematic diagram of the static stress balance of a curved pipe micro-element in this technical solution.

[0058] Figure 4 This is a schematic diagram of a longitudinal arc-shaped specimen for an axial tensile test of a metal pipe according to an embodiment of the present invention.

[0059] Figure 5 This is a line graph showing the ratio of springback prediction angle to bending angle and bending radius in an embodiment of the present invention.

[0060] Figure 6 This is a system structure diagram for obtaining the maximum bending radius of the pipe under free bending in this technical solution. Detailed Implementation

[0061] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0062] It should be noted that all directional indications in the embodiments of the present invention (such as sides, edges, top, bottom, left, right, front, back, middle, top, bottom, tail, axial, radial, etc.) are only used to explain the relative positional relationship and motion state between the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indications will also change accordingly.

[0063] Example 1

[0064] like Figure 1 As shown, a method for obtaining the maximum bending radius of a pipe under free bending includes the following steps:

[0065] Step 101: Obtain the basic mechanical property parameters of the metal pipe and determine the stress distribution function of different deformation zones inside and outside the strain neutral layer of the section of the metal pipe to be bent.

[0066] Step 102, determine the first relationship; the first relationship represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the pipe section to be bent and the bending radius;

[0067] Step 103, determine the second relationship; the second relationship represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe section to be bent.

[0068] Step 104, determine the third relationship; the third relationship is the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent.

[0069] Step 105: Calculate the ratio of the predicted springback angle to the bending angle under a series of bending radii based on the first, second, and third relational formulas, and draw a dot-line graph. Obtain the maximum bending radius of the metal pipe under free bending through the point with the vertical coordinate of 1 on the dot-line graph.

[0070] The types of basic mechanical property parameters obtained in step 101 include: Young's modulus, yield strength, strength coefficient, and strain hardening index.

[0071] The specific steps for obtaining the basic mechanical properties of the metal pipe in step 101 include: obtaining the Young's modulus, yield strength, strength coefficient, and strain hardening index of the metal pipe through axial tensile tests on standard longitudinal arc-shaped specimens of the metal pipe.

[0072] The standard longitudinal arc-shaped specimen is cut parallel to the pipe axis.

[0073] In step 101, the stress distribution function of different deformation zones inside and outside the strain neutral layer of the segment to be bent under free bending forming stress is obtained by introducing the axial stress generated by the propulsion mechanism in free bending forming, thus obtaining the axial stress at each point in different deformation zones inside and outside the strain neutral layer of the segment to be bent:

[0074]

[0075]

[0076] In equation (1), σ1(R) y ,ρ) represents the axial stress at a point in the plastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equation (2), σ2(R y ,ρ) represents the axial stress at a point in the elastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equations (1) and (2), R y ρ represents the distance from a point on the pipe wall to the center of the bend, K represents the bending radius of the bend, and σ represents the strength coefficient of the metal pipe. s The value represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, n represents the strain hardening exponent of the metal pipe, and σ represents the strain hardening exponent of the metal pipe. N α represents the axial stress applied by the propulsion mechanism during the free bending forming process of the metal pipe, α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer, and R represents the bending radius between the inner and outer boundaries of the section to be bent and the bending center in the bending plane.

[0077] Step 102, determining the first relation specifically includes:

[0078] Based on the formula for the axial stress in the elastic deformation zones inside and outside the strain neutral layer of the section to be bent and the yield critical condition σ=σ s Determine the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius:

[0079]

[0080]

[0081] In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This indicates the average radius of the metal pipe.

[0082] Step 103, determining the second relation specifically includes:

[0083] Based on relevant formulas in mechanics of materials, the relationship between the bending moment of the elastic / plastic deformation zone on the inner and outer sides of the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the metal pipe section to be bent is determined as follows:

[0084]

[0085]

[0086] In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2 Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m α represents the average radius of the metal pipe, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer.

[0087] Step 104, determining the third relation specifically includes:

[0088] The expression for the third relation is:

[0089]

[0090] In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the variable moment of inertia of the pipe section during the bending process (under small deformation conditions, the wall thickness change, distortion change and center layer offset of the bent pipe section are ignored, and the variable moment of inertia of the section can be calculated by the plane assumption of the bent pipe section and the moment of inertia rotation formula).

[0091] Further, step 105 specifically includes:

[0092] Based on the functional relationship between the ratio of the springback prediction angle to the bending angle and the bending radius, the ratio of the springback prediction angle to the bending angle is plotted on the ordinate, and the bending radius is plotted on the abscissa, with the bending radius ranging from α... e1 When the angle is 90°, the corresponding bending radius value starts to increase (each increment is determined by a certain precision). Draw a dot-line graph and obtain the point with the vertical coordinate of 1 on the dot-line graph. The value of its horizontal coordinate is the maximum free bending radius value of the metal pipe.

[0093] Example 2

[0094] like Figure 6 As shown, a system for obtaining the maximum bending radius of a pipe under free bending includes:

[0095] The acquisition module is used to acquire the Young's modulus, yield strength, strength coefficient, and strain hardening index of a standard longitudinal arc-shaped specimen of a metal pipe, wherein the standard longitudinal arc-shaped specimen is cut parallel to the pipe axis.

[0096] The first relation determination module is used to determine the first relation; the first relation represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius.

[0097] The second relation determination module is used to determine the second relation; the second relation represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent section and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe to be bent section.

[0098] The third relation determination module is used to determine the third relation; the third relation represents the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment on the inner and outer sides of the strain neutral layer of the pipe section to be bent.

[0099] The springback prediction angle to bending angle ratio calculation module is used to calculate the ratio of springback prediction angle to bending angle for a series of bending radius values ​​based on the first, second and third relational formulas.

[0100] The maximum bending radius determination module is used to draw a dot-line graph showing the ratio of the springback prediction angle to the bending angle as a function of the bending radius, based on the ratio of the springback prediction angle to the bending angle under the series of bending radius values. The point with the vertical coordinate of 1 on the dot-line graph is obtained, and the value of its horizontal coordinate is the maximum bending radius of the metal pipe under free bending.

[0101] The third relationship determination module and the springback prediction angle to bending angle ratio calculation module specifically include:

[0102] According to the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius:

[0103]

[0104]

[0105] In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This represents the average radius of the metal pipe. For a detailed diagram of the geometric parameters, please refer to [link / reference needed]. Figure 2 and Figure 3 ; and the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe section to be bent:

[0106]

[0107]

[0108] In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m The radius of the metal pipe is represented by α, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer. See the diagram for specific geometric parameters. Figure 2 and Figure 3 Based on this, the expression for the ratio of the springback prediction angle to the bending angle is determined:

[0109]

[0110] In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the variable moment of inertia of the section during the bending process of the pipe (under small deformation, the wall thickness change, distortion change and center layer offset of the bent pipe section are ignored, and the variable moment of inertia of the section can be calculated by the plane assumption of the bent pipe section and the moment of inertia rotation formula); further, through the springback prediction angle to bending angle ratio calculation module, the ratio of springback prediction angle to bending angle under a series of bending radius values ​​is calculated.

[0111] The maximum bending radius determination module specifically includes:

[0112] The springback prediction angle to bending angle ratio curve plotting unit is used to plot a dotted line graph based on the ratio of springback prediction angle to bending angle under a series of bending radius values, with the ratio of springback prediction angle to bending angle as the vertical axis and the bending radius as the horizontal axis. Finally, it displays the points on the dotted line graph with a vertical axis of 1 and marks the value of their horizontal axis.

[0113] Example 3

[0114] Figure 1 This is a flowchart illustrating the method for obtaining the maximum bending radius of a pipe under free bending according to this technical solution. The method provided by this invention specifically includes the following steps:

[0115] Step 101: Obtain the basic mechanical property parameters of the metal pipe and determine the stress distribution function of different deformation zones inside and outside the strain neutral layer of the section of the metal pipe to be bent;

[0116] Step 102: Determine the first relationship; the first relationship represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the pipe section to be bent and the bending radius;

[0117] Step 103: Determine the second relationship; the second relationship represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent section and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe to be bent section.

[0118] Step 104: Determine the third relationship; the third relationship is the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent.

[0119] Step 105: Based on the first, second, and third relationships, calculate the ratio of the predicted springback angle to the bending angle under a series of bending radii, draw a dot-line graph, and obtain the maximum bending radius of the metal pipe under free bending through the point with the vertical coordinate of 1 on the dot-line graph.

[0120] Step 101 specifically includes:

[0121] According to GB / T 228 "Metallic Materials - Tensile Testing Standard", a standard longitudinal arc-shaped specimen for metal pipes was designed, and axial tensile tests were carried out on the metal pipes to obtain the Young's modulus, yield strength, strength coefficient, and strain hardening index of the metal pipes.

[0122] Considering the stress state of the metal tube during free bending forming, an axial thrust is introduced, and a piecewise nonlinear constitutive model is used to describe the elastoplastic deformation behavior of the tube: a classical linear elastic model is used in the elastic deformation stage, and a power-law hardening model with a constant is used in the plastic deformation stage. Based on the stress analysis of the metal tube micro-element, the axial stress at each point in different deformation zones inside and outside the strain neutral layer of the section to be bent is obtained:

[0123]

[0124]

[0125] In equation (1), σ1(R) y ,ρ) represents the axial stress at a point in the plastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equation (2), σ2(R y ,ρ) represents the axial stress at a point in the elastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equations (1) and (2), R y ρ represents the distance from a point on the pipe wall to the center of the bend, K represents the bending radius of the bend, and σ represents the strength coefficient of the metal pipe. s The value represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, n represents the strain hardening exponent of the metal pipe, and σ represents the strain hardening exponent of the metal pipe. N α represents the axial stress applied by the propulsion mechanism during the free bending forming process of the metal pipe, α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer, and R represents the bending radius between the inner and outer boundaries of the section to be bent and the bending center in the bending plane.

[0126] Step 102 specifically includes:

[0127] Based on the formula for the axial stress in the elastic deformation zones inside and outside the strain neutral layer of the section to be bent and the yield critical condition σ=σs Determine the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius:

[0128]

[0129]

[0130] In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This indicates the average radius of the metal pipe.

[0131] Step 103 specifically includes:

[0132] Based on relevant formulas in mechanics of materials, the relationship between the bending moment of the elastic / plastic deformation zone on the inner and outer sides of the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the metal pipe section to be bent is determined as follows:

[0133]

[0134]

[0135] In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2 Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m α represents the average radius of the metal pipe, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer.

[0136] Step 104 specifically includes:

[0137] Based on the principle of virtual work, applying the virtual work equation of the deformable system along the neutral layer, the expression for the ratio of the rebound prediction angle to the bending angle is obtained:

[0138]

[0139] In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the variable moment of inertia of the pipe section during the bending process (under small deformation conditions, the wall thickness change, distortion change and center layer offset of the bent pipe section are ignored, and the variable moment of inertia of the section can be calculated by the plane assumption of the bent pipe section and the moment of inertia rotation formula).

[0140] Step 105 specifically includes:

[0141] Substituting equations (1), (2), (3), and (4) into equations (5) and (6), where R y ≈ρ+r m sinα, Then we can obtain M1(ρ) and M2(ρ) in equation (7);

[0142] From α e1 When the bend radius is 90°, the value of H(ρ) is calculated and incremented (each increment is determined by the accuracy). The ratio of the rebound prediction angle to the bend angle is used as the vertical axis and the bend radius is used as the horizontal axis to draw a dotted line graph.

[0143] The point with a vertical coordinate of 1 on the dot-line graph is obtained, and its horizontal coordinate value is the maximum free bending radius of the metal pipe.

[0144] The technical solutions disclosed in this invention will be illustrated below through specific embodiments.

[0145] In this embodiment, 1Cr18Ni10Ti stainless steel pipe with a specification of Φ32×1mm was selected, and wire cutting was used to make a sample in the axial direction of the pipe. Figure 4 The longitudinal arc-shaped specimen shown.

[0146] In this embodiment, the axial tensile test of the longitudinal arc-shaped specimen was conducted on a CMT5105 / 100KN microcomputer-controlled electronic universal testing machine, with the tensile rate maintained at a constant 1 mm / min during the tensile process. After data processing, the required basic mechanical property parameters of the 1Cr18Ni10Ti stainless steel pipe were obtained, as shown in Table 1.

[0147] Table 1 Basic Mechanical Properties of 1Cr18Ni10Ti Stainless Steel Pipes

[0148]

[0149] Substitute the parameters in Table 1 into equations (1), (2), (3), (4), (5), and (6), respectively, where R y Using ρ+r m sinα substitution The specific expression of equation (7) can be determined.

[0150] α was calculated numerically. e1 When the angle is 90°, the bending radius ρ = 1914 mm; then the bending radius ρ starts from 1914 mm and increases by 100 mm each time. H(ρ) is calculated numerically for each ρ value until H(ρ) > 1.

[0151] Draw a point-line graph of ρ to H(ρ), as follows: Figure 5 As shown, the point with a vertical coordinate of approximately 1 on the dot-line graph has a horizontal coordinate of 183900mm. Therefore, the maximum free bending radius of the Φ32×1mm 1Cr18Ni10Ti stainless steel pipe selected in this embodiment is 183900mm. Furthermore, the maximum free bending radius of the Φ32×1mm 1Cr18Ni10Ti stainless steel pipe obtained by this invention is basically consistent with the maximum bending radius obtained by the traditional trial-and-error method.

[0152] To achieve the above objectives, the present invention also provides a system for obtaining the maximum bending radius of a pipe under free bending. Figure 6 This is a system structure diagram for obtaining the maximum bending radius of a pipe under free bending, as described in this technical solution. The system includes:

[0153] The acquisition module 601 is used to acquire the Young's modulus, yield strength, strength coefficient and strain hardening index of a standard longitudinal arc-shaped specimen of a metal pipe, wherein the standard longitudinal arc-shaped specimen is cut parallel to the pipe axis.

[0154] The first relational expression determination module 602 is used to determine the first relational expression; the first relational expression represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius.

[0155] The second relation determination module 603 is used to determine the second relation; the second relation represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent section and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe to be bent section.

[0156] The third relation determination module 604 is used to determine the third relation; the third relation represents the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment on the inner and outer sides of the strain neutral layer of the pipe section to be bent.

[0157] The springback prediction angle to bending angle ratio calculation module 605 is used to calculate the ratio of springback prediction angle to bending angle for a series of bending radius values ​​based on the first, second and third relationship formulas.

[0158] The maximum bending radius determination module 606 is used to draw a dot-line graph showing the ratio of the springback prediction angle to the bending angle as a function of the bending radius, based on the ratio of the springback prediction angle to the bending angle under the series of bending radius values. The point with the vertical coordinate of 1 on the dot-line graph is obtained, and the value of its horizontal coordinate is the maximum bending radius of the metal pipe under free bending.

[0159] Optionally, the third relationship determination module 604 and the ratio calculation module 605 of the springback prediction angle and the bending angle specifically include:

[0160] According to the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius:

[0161]

[0162]

[0163] In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This represents the average radius of the metal pipe. For a detailed diagram of the geometric parameters, please refer to [link / reference needed]. Figure 2 and Figure 3 ; and the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe section to be bent:

[0164]

[0165]

[0166] In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2 Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent.m The radius of the metal pipe is represented by α, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer. See the diagram for specific geometric parameters. Figure 2 and Figure 3 Based on this, the expression for the ratio of the springback prediction angle to the bending angle is determined:

[0167]

[0168] In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the moment of inertia of the cross section during the bending process of the pipe; furthermore, after automatic calculation by the springback prediction angle to bending angle ratio calculation module 605, the moment of inertia of the cross section after bending the pipe is 0.7 times the original moment of inertia, that is:

[0169]

[0170] In formula (8), D represents the outer diameter of the metal pipe, and d represents the inner diameter of the metal pipe;

[0171] Optionally, the maximum bending radius determination module 606 specifically includes:

[0172] The springback prediction angle to bending angle ratio curve plotting unit is used to plot a dotted line graph based on the ratio of springback prediction angle to bending angle under a series of bending radius values, with the ratio of springback prediction angle to bending angle as the vertical axis and the bending radius as the horizontal axis. Finally, it displays the points on the dotted line graph with a vertical axis of 1 and marks the value of their horizontal axis.

[0173] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0174] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for obtaining the maximum bending radius of a pipe under free bending, characterized in that: Includes the following steps: Step 101: Obtain the basic mechanical property parameters of the metal pipe and determine the stress distribution function of different deformation zones inside and outside the strain neutral layer of the section of the metal pipe to be bent. Step 102, determine the first relationship; the first relationship represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the pipe section to be bent and the bending radius; Step 103, determine the second relationship; the second relationship represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe section to be bent. Step 104, determine the third relationship; the third relationship is the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent. Step 105: Calculate the ratio of the predicted springback angle to the bending angle under a series of bending radii based on the first, second, and third relational formulas, and draw a dot-line graph. Obtain the maximum bending radius of the metal pipe under free bending through the point with the vertical coordinate of 1 on the dot-line graph.

2. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 1, characterized in that: The types of basic mechanical property parameters obtained in step 101 include: Young's modulus, yield strength, strength coefficient, and strain hardening index.

3. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 2, characterized in that: The specific steps in step 101 for obtaining the basic mechanical properties of the metal pipe include: obtaining the Young's modulus, yield strength, strength coefficient, and strain hardening index of the metal pipe through axial tensile tests on standard longitudinal arc-shaped specimens of the metal pipe.

4. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 3, characterized in that: The standard longitudinal arc-shaped specimen is cut parallel to the pipe axis.

5. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 1, characterized in that: In step 101, the stress distribution function of different deformation zones inside and outside the strain neutral layer of the segment to be bent under free bending forming stress is obtained by introducing the axial stress generated by the propulsion mechanism in free bending forming, thus obtaining the axial stress at each point in different deformation zones inside and outside the strain neutral layer of the segment to be bent: In equation (1), σ1(R) y ,ρ) represents the axial stress at a point in the plastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equation (2), σ2(R y ,ρ) represents the axial stress at a point in the elastic deformation zone inside and outside the strain neutral layer of the section to be bent; in equations (1) and (2), R y ρ represents the distance from a point on the pipe wall to the center of the bend, K represents the bending radius of the bend, and σ represents the strength coefficient of the metal pipe. s The value represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, n represents the strain hardening exponent of the metal pipe, and σ represents the strain hardening exponent of the metal pipe. N α represents the axial stress applied by the propulsion mechanism during the free bending forming process of the metal pipe, α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer, and R represents the bending radius between the inner and outer boundaries of the section to be bent and the bending center in the bending plane.

6. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 1, characterized in that: Step 102, determining the first relation specifically includes: Based on the formula for the axial stress in the elastic deformation zones inside and outside the strain neutral layer of the section to be bent and the yield critical condition σ=σ s Determine the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius: In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m This indicates the average radius of the metal pipe.

7. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 1, characterized in that: Determining the second relation in step 103 specifically includes: The relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe section to be bent and the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe section to be bent is determined as follows: In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2 Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m α represents the average radius of the metal pipe, and α represents the angle between a point on the pipe wall of the section to be bent and the neutral layer.

8. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 1, characterized in that: Determining the third relation in step 104 specifically includes: The expression for the third relation is: In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the cross-sectional moment of inertia during the bending process of the pipe.

9. The method for obtaining the maximum bending radius of a pipe under free bending according to claim 1, characterized in that: Step 105 specifically includes: Based on the functional relationship between the ratio of the springback prediction angle to the bending angle and the bending radius, the ratio of the springback prediction angle to the bending angle is plotted on the ordinate, and the bending radius is plotted on the abscissa, with the bending radius ranging from α... e1 The bending radius value corresponding to 90° begins to increase. A dot-line graph is plotted, and the point with the vertical coordinate of 1 on the dot-line graph is obtained. The value of its horizontal coordinate is the maximum free bending radius value of the metal pipe.

10. A system for obtaining the maximum bending radius of a pipe under free bending, characterized in that: include The acquisition module is used to acquire the Young's modulus, yield strength, strength coefficient, and strain hardening index of a standard longitudinal arc-shaped specimen of a metal pipe, wherein the standard longitudinal arc-shaped specimen is cut parallel to the pipe axis. The first relation determination module is used to determine the first relation; the first relation represents the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius. The second relation determination module is used to determine the second relation; the second relation represents the relationship between the bending moment of the elastic / plastic deformation zone inside and outside the strain neutral layer of the metal pipe to be bent section and the boundary angle of the elastic / plastic deformation zone on the cross section inside and outside the metal pipe to be bent section. The third relation determination module is used to determine the third relation; the third relation represents the relationship between the ratio of the springback prediction angle to the bending angle and the bending moment on the inner and outer sides of the strain neutral layer of the pipe section to be bent. The springback prediction angle to bending angle ratio calculation module is used to calculate the ratio of springback prediction angle to bending angle for a series of bending radius values ​​based on the first, second and third relational formulas. The maximum bending radius determination module is used to draw a dot-line graph showing the ratio of the springback prediction angle to the bending angle as a function of the bending radius, based on the ratio of the springback prediction angle to the bending angle under the series of bending radius values. The point with the vertical coordinate of 1 on the dot-line graph is obtained, and the value of its horizontal coordinate is the maximum bending radius of the metal pipe under free bending.

11. The system for obtaining the maximum bending radius of a pipe under free bending according to claim 10, characterized in that: The third relationship determination module and the springback prediction angle to bending angle ratio calculation module specifically include: According to the relationship between the boundary angle of the elastic / plastic deformation zone on the inner and outer cross sections of the metal pipe to be bent and the bending radius: In equation (3), α e1 The angle represents the boundary between the elastic / plastic deformation zone on the outer cross-section of the section of the metal pipe to be bent; in equation (4), α e2 The angle represents the boundary between the elastic / plastic deformation zone on the inner cross-section of the section of the metal pipe to be bent; in equations (3) and (4), ρ represents the bending radius of the section to be bent, and σ represents the bending radius of the section to be bent. s σ represents the yield strength of the metal pipe, E represents the Young's modulus of the metal pipe, and σ represents the yield strength of the metal pipe. N The axial stress r represents the stress applied by the propulsion mechanism during the free bending and forming process of a metal tube. m The formulas represent the average radius of the metal pipe and the relationship between the bending moment of the elastic / plastic deformation zones on the inner and outer sides of the strain neutral layer of the metal pipe section to be bent and the boundary angles of the elastic / plastic deformation zones on the inner and outer cross sections of the metal pipe section to be bent. In equation (5), M1(α) e1 ,α e2 Equation (6) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the cross-section of the inner and outer sides of the section to be bent of the metal pipe; in equation (6), M2(α) represents the bending moment of the plastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer sides of the cross-section of the section to be bent of the metal pipe e1 ,α e2 Equation (5) and (6) represents the function of the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent and the boundary angle between the elastic / plastic deformation zone on the inner and outer cross sections of the section to be bent; in equations (5) and (6), t represents the wall thickness of the metal pipe, and r represents the bending moment of the elastic deformation zone inside and outside the strain neutral layer of the section to be bent. m Let represent the average radius of the metal pipe, and α represent the angle between a point on the pipe wall of the section to be bent and the neutral layer; based on this, determine the expression for the ratio of the springback prediction angle to the bending angle: In equation (7), E represents the Young's modulus of the metal pipe, ρ represents the bending radius of the section to be bent, and I represents the cross-sectional moment of inertia during the bending process of the pipe.

12. The system for obtaining the maximum bending radius of a pipe under free bending according to claim 10, characterized in that: The springback prediction angle to bending angle ratio calculation module calculates the ratio of springback prediction angle to bending angle for a series of bending radius values.

13. The system for obtaining the maximum bending radius of a pipe under free bending according to claim 10, characterized in that: The maximum bending radius determination module specifically includes: The springback prediction angle to bending angle ratio curve plotting unit is used to plot a dotted line graph based on the ratio of springback prediction angle to bending angle under a series of bending radius values, with the ratio of springback prediction angle to bending angle as the vertical axis and the bending radius as the horizontal axis. Finally, it displays the points on the dotted line graph with a vertical axis of 1 and marks the value of their horizontal axis.

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