A method for predicting springback in metal pipe bending considering non-isothermal thermal field loading

Abstract

The present invention discloses a method for predicting the bending springback of metal pipes taking into account non-isothermal thermal field loading. For the bending modes of half-circle heating of the outer arch of the bending section, half-circle heating of the inner arch, and full-circle heating, the temperature field of the bending process is regarded as a thermal equilibrium state, and the temperature distribution of the pipe cross section under different heating methods is evaluated; according to the material constitutive properties of the metal pipe at high temperature, based on the force balance conditions of the bending outer arch and the bending inner arch, the offset of the neutral layer on the pipe cross section and the asymmetry of the yield surface distribution in the elastic-plastic zone are taken into account, so as to accurately calculate the elastic-plastic bending moment and improve the prediction accuracy of the springback angle. The present invention can be used for the preliminary and rapid calculation of the springback angle after hot bending of pipes under different position mold heating conditions, and has a guiding role in the design of the temperature field of hot bending of pipes and the selection of forming parameters.

Description

Technical Field

[0001] The invention belongs to the field of metal plastic forming, and in particular relates to a metal pipe bending springback prediction method considering non-isothermal thermal field loading. Background Art

[0002] Precision CNC bending of metal pipes is a typical metal plastic forming process that can easily meet the needs of high-end fields such as aerospace, nuclear power, and shipbuilding for lightweight equipment and low consumption and high efficiency. At present, there are many mature cold bending processing methods for pipes, such as stretch bending, press bending, rotary traction bending and push bending under multi-mode constraints. However, these cold bending processing methods still face serious springback problems after bending unloading, resulting in shape accuracy that does not meet installation and performance requirements. Therefore, based on the cold bending equipment, heat-assisted CNC bending forming equipment has been developed. By adding a heating device to the bending mold and taking advantage of the temperature softening properties of the material, the springback defect can be reduced, thereby achieving high-precision processing of difficult-to-form metal pipes.

[0003] Compared with finite element evaluation and bending test methods, the pipe bending springback prediction theory can realize the rapid evaluation of springback defects under the corresponding forming requirements and save costs. Existing pipe springback prediction theories are mostly developed based on cold bending forming processes, which are difficult to apply to hot bending forming processes. The springback defects of pipe hot bending need to consider the mechanical response of the material under different temperature conditions, as well as the asymmetry of the inner and outer arch deformations of the bend caused by the uneven temperature field. Since the hot bending forming process is affected by the multi-mode constraints of the bending equipment and the thermal-solid coupling factors of the material, it is difficult to clearly describe the springback law of the hot bending forming of metal pipes. At the same time, the heating mold and heating position are very different under different hot bending strategies, resulting in an uneven temperature field for the bent pipe, which complicates the springback analysis. Summary of the Invention

[0004] In order to solve the problem in the background technology that it is difficult to accurately predict the springback defects of metal tube hot bending forming, the present invention proposes a metal tube bending springback prediction method considering non-isothermal thermal field loading, which improves the bending springback prediction accuracy under full-circumference heating and half-circumference heating conditions.

[0005] The technical solution adopted in the present invention is as follows:

[0006] 1) Based on the geometric center of the pipe section, the cross-sectional plane coordinate system under the strain neutral layer offset condition is established.

[0007] The pipe is bent and deformed to a certain angle under the constraint of the bending die. After the die is unloaded, the pipe is in a state of rebound. The heat source during hot bending of metal pipes is generally located on the bending and tightening dies that are in direct contact with the pipe. Therefore, the heating position is the outer arch half circle, inner arch half circle or the entire circle of the bending section. For the thin-walled metal pipe with a wall thickness of t involved in the present invention, the temperature change in the wall thickness direction is small and can be ignored.

[0008] 2) Considering the thermal field of the pipe to have reached thermal equilibrium, the distance e of the neutral layer offset and the position of the yield surface of the deformation zone on the cross section are solved according to the force balance equation. The solution equation is:

[0009]

[0010] Where r D Indicates the outer wall radius of the tube section, h o represents the location of the yield surface of the curved outer camber, h i represents the position of the yield surface of the curved inner arch, ζ eo represents the stress in the elastic region of the curved outer arch, ζ po represents the stress in the plastic zone of the curved outer arch, ζ ei represents the plastic zone of the inner arch of the bend, ζ pi represents the stress in the plastic zone of the inner arch of the bend s represents the yield limit, T(y) represents the temperature function, r m represents the median diameter of the tube section, ρ represents the curvature radius of the strain neutral layer, q ij represents the polynomial coefficient, h(r m ,T(y)) represents h o and h i About r m and T(y), dS represents the infinitesimal area of ​​the pipe wall cross section, and the calculation formula is as follows:

[0011]

[0012] The process of step 2) is:

[0013] Ⅰ The stress-strain relationship in the elastic and plastic zones is temperature sensitive. The calculation formula of the constitutive model is:

[0014]

[0015] Where, ε y represents the equivalent plastic strain, A represents the yield stress at the reference temperature, B represents the plastic strengthening parameter, n represents the strain hardening exponent, T a Indicates the ambient temperature, T m represents the melting temperature, and m represents the temperature softening coefficient. These parameters can be determined by consulting data or conducting high-temperature tensile tests.

[0016] ⅠⅠDetermine the temperature distribution function of the pipe bending section according to the heating method:

[0017] Before bending, the tube is generally preheated to keep the section to be bent in a predetermined temperature field. The thermal field during bending does not fluctuate significantly and can be considered to have reached a steady state. When the full-circle heating method is used, the cross-sectional temperature of the bending section is consistent under the thermal equilibrium state, T(y) = T0. When the outer arch half or inner arch half of the bending section is heated, the temperature of the half section directly heated is T0. The temperature of the half section heated by heat conduction is calculated by the following equilibrium formula at a position y from the geometric center of the section: y (y):

[0018]

[0019] Where T0 represents the heating temperature of the heat source, H represents the arc length of 1 / 4 of the pipe wall mid-diameter circle, Δδ T represents the temperature equilibrium coefficient, p i represents the linear coefficient and can be solved by the following heat balance equation:

[0020]

[0021] Where P represents the perimeter of the longitudinal section of the curved section, k represents the composite heat transfer coefficient, λ represents the heat conduction coefficient, and A c Represents 1 / 2 area of ​​the pipe cross section.

[0022] ⅠⅠⅠBased on the principle of axial force balance between the inner and outer arches of the bend, the equilibrium equation is established as follows:

[0023]

[0024] Where, F out Indicates the axial force of the curved outer arch, F in Indicates the axial force of the inner arch, and the boundary line between the tensile part of the outer arch and the compression part of the inner arch on the cross section of the pipe is not the geometric center, but the strain neutral layer. At this time, the position of the yield surface of the outer arch and the inner arch is h o and h i is unknown.

[0025] IV solves the distance e of the neutral layer offset and the position of the yield surface of the deformation zone on the cross section:

[0026] According to the yield criterion, the following equilibrium equation can be written:

[0027]

[0028] In the formula, ± represents the two cases of curved inward arch and curved outward arch, the curved inward arch is +, and the curved outward arch is -.

[0029] Combine the above formula with the axial force balance formula in ⅠⅠⅠ to solve the distance e of the neutral layer offset and the position h of the yield surface of the deformation zone on the cross section. o and h i .

[0030] 3) According to the forming radius parameter R of the tube blank and the heating position (half-circle or full-circle heating), the bending moment M in the elastic zone of the cross section is calculated. e , plastic zone bending moment M p And the total bending moment M T :

[0031] Total bending moment M T =M e +M p , bending moment M in the elastic region of the cross section e and the plastic zone bending moment M p The calculation formula is:

[0032]

[0033]

[0034] 4) Calculate the springback angle Δθ of the metal tube bending considering non-isothermal thermal field loading:

[0035] First, calculate the residual stress Δζ after bending unloading θ :

[0036]

[0037] Where, I D represents the section moment of inertia, the residual strain Δε after bending unloading θ It can be expressed as:

[0038]

[0039] The movement of the strain neutral layer during bending unloading can be ignored. The relationship between the neutral layer bending angle, springback angle, bending radius and springback radius is:

[0040]

[0041] The residual stress-strain relationship after bending unloading (residual strain Δε θ Substituting the above expression into the above formula can determine the bending springback angle Δθ:

[0042]

[0043] Where θ represents the bending angle.

[0044] The beneficial effects of the present invention are:

[0045] This invention considers the temperature sensitivity of the tube material during hot bending, as well as the offset behavior of the strain neutral layer and deformation yield surface under the corresponding thermal field. On the one hand, this invention accurately describes the material's temperature-softening properties through a temperature-dependent constitutive model to accommodate the thermal field conditions under non-isothermal field loading. On the other hand, this invention describes the thermal field distribution caused by different heating strategies on the tube cross-section and calculates the neutral layer offset and asymmetrically distributed yield surface position under the influence of the thermal field based on force balance conditions. This is then incorporated into the springback modeling of tube bending, thereby improving the springback prediction accuracy of tube thermal-mechanical coupling bending.

[0046] For r D For a 12.7mm×t2mm TA18 material tube blank, when the bending angle is 90° and the heat source temperature is 100°C to 300°C, the prediction error between the theoretical model of the present invention and the experimental value is less than 6%. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a method for predicting springback during metal tube bending considering non-isothermal thermal field loading.

[0048] Figure 2 Heat-assisted forming equipment for rotary stretch bending of pipes;

[0049] Figure 3 Schematic diagram of the bending springback before and after the outer arch of the pipe is heated;

[0050] Figure 4 For r D Comparison of theoretically predicted springback values ​​with finite element simulation and experimental values ​​for a 12.7mm×t2mm TA18 tube at a 90° bending angle and a heat source temperature of 100°C to 300°C.

[0051] In the figure: 1. Pressing die, 2. Pipe, 3. Anti-wrinkle die, 4. Bending die, 5. Clamping die, 6. Heating rod. DETAILED DESCRIPTION

[0052] The present invention will be further described below with reference to the accompanying drawings and examples.

[0053] This embodiment is a method for predicting the bending springback of metal pipes considering non-isothermal thermal field loading. In this embodiment, the heating mold is Figure 2 The die in the bending section heats half of the outer arch. The heat source temperature is 300℃. The material of the pipe to be bent is TA18 and the outer radius of the pipe is r. D The wall thickness t is 12.7 mm, the bending radius R is 76.2 mm, and the bending angle before springback is 90°.

[0054] 1) The pipe is bent and deformed to a certain angle under the constraint of the bending die. After the die is unloaded, the pipe is in a state of rebound. Based on the geometric center of the pipe section, a cross-sectional plane coordinate system under the condition of strain neutral layer offset is established. The dimensional parameters and forming parameters are as follows: Figure 3 As shown;

[0055] 2) Considering the thermal field of the pipe to have reached thermal equilibrium, the distance e of the neutral layer offset and the position of the yield surface of the deformation zone on the cross section (including the position h of the yield surface of the bending outer arch) are solved according to the force balance equation. o and the position h of the yield surface of the curved inner arch i ), the solution equation is:

[0056]

[0057] Where r D Indicates the outer wall radius of the tube section, h o represents the location of the yield surface of the curved outer camber, h i represents the position of the yield surface of the curved inner arch, ζ eo represents the stress in the elastic region of the curved outer arch, ζ po represents the stress in the plastic zone of the curved outer arch, ζ ei represents the stress in the elastic region of the inner arch, ζ pi represents the stress in the plastic zone of the inner arch of the bend, ζ s represents the yield limit, y represents the ordinate on the cross-section plane coordinate system, t represents the wall thickness, T(y) represents the temperature function, r m represents the median diameter of the tube section, ρ represents the radius of curvature of the strain neutral layer and ρ=Re,q ij represents the polynomial coefficient, h(r m ,T(y)) represents h o and h i About r m and T(y), dS represents the infinitesimal area of ​​the pipe wall cross section, and the calculation formula is as follows:

[0058]

[0059] The process of step 2) is:

[0060] Ⅰ Determine the parameters in the constitutive relationship model of the pipe fitting material. The constitutive model formula is as follows:

[0061]

[0062] Where σ represents the elastic-plastic stress in different regions;

[0063] Where, ε y represents the equivalent plastic strain, ε srepresents yield strain, A represents yield stress at reference temperature, B represents plastic strengthening parameter, n represents strain hardening exponent, T a Indicates the ambient temperature, T m Indicates melting temperature, m indicates temperature softening coefficient. Determine T by consulting the data m =1625℃, and assuming T a =25℃;

[0064] The material parameters are determined by high temperature tensile test data of TA18 pipe sheet specimens at 25-500℃ as follows:

[0065]

[0066] ⅠⅠ Determine the temperature distribution function of the cross section under the outer arch heating method of the curved section

[0067] When the full-circle heating method is adopted in step 2), the cross-sectional temperature of the curved section is T(y)=T0 under the thermal equilibrium state. When the outer arch half circumference or the inner arch half circumference of the curved section is heated, the temperature of the half circumference directly heated on the cross section is T0, and the temperature T at the position y from the geometric center layer of the cross section of the half circumference heated by heat conduction is calculated by the following equilibrium formula: y (y):

[0068] Before bending, the tube is generally preheated to keep the section to be bent in a predetermined temperature field. The thermal field during bending does not fluctuate significantly and can be considered to have reached a steady state. When the outer half of the bending section is heated, the temperature of the half of the section directly heated is T0 = 300 ° C. The temperature T at the position y from the geometric center of the section is calculated by the following equilibrium formula for the half of the section heated by heat conduction: y (y):

[0069]

[0070] Where H represents the arc length of 1 / 4 of the pipe wall mid-diameter circle, Δδ T Represents the temperature balance coefficient, expressed as H = πr m / 2, in this embodiment, H=19.9mm, Δδ T =91591;

[0071] p i represents the linear coefficient and can be solved by the following heat balance equation:

[0072]

[0073] Where P represents the perimeter of the longitudinal section of the curved section, k represents the composite heat transfer coefficient, λ represents the heat conduction coefficient, and A c Indicates 1 / 2 area of ​​the pipe cross section;

[0074] In this embodiment, P=243.4 mm, k=10 W / m 2 °C, λ = 15 W m -1 ℃ -1 , A c =239.39mm 2 . , solve T y (y) is expressed as follows:

[0075]

[0076] ⅠⅠⅠBased on the principle of axial force balance between the inner and outer arches of the bend, the equilibrium equation is established as follows:

[0077]

[0078] Where, F out Indicates the axial force of the curved outer arch, F in Indicates the axial force of the inner arch, and the boundary line between the tensile part of the outer arch and the compression part of the inner arch on the cross section of the pipe is not the geometric center, but the strain neutral layer. At this time, the position of the yield surface of the outer arch and the inner arch is h o and h i is unknown;

[0079] IV solves the distance e of the neutral layer offset and the position of the yield surface of the deformation zone on the cross section

[0080] According to the yield criterion, the following equilibrium equation can be written:

[0081]

[0082] In the formula, ± represents the two cases of bending inward and bending outward, and the yield limit ζ at different temperatures s The fitting formula is ζ s =-3.582T(y) 0.676 +302.7;

[0083] Combine the above formula with the axial force balance formula in ⅠⅠⅠ to solve the distance e of the neutral layer offset and the position h of the yield surface of the deformation zone on the cross section. o and h i ;

[0084] In this embodiment, the neutral layer offset distance e=-0.24mm, the yield surface position of the curved outer arch is 3.1mm, and the yield surface position of the curved inner arch is 3.7mm;

[0085] 3) According to the forming radius parameter R of the tube blank and the heating position (half-circle or full-circle heating), the bending moment M in the elastic zone of the cross section is calculated. e , plastic zone bending moment M p And the total bending moment M T :

[0086] Total bending moment M T =M e +M p , bending moment M in the elastic region of the cross section e and the plastic zone bending moment M p The calculation formula is:

[0087]

[0088]

[0089] In this embodiment, the bending moment M in the elastic region of the cross section e and the plastic zone bending moment M p The calculation formula is:

[0090]

[0091]

[0092] 4) Calculate the springback angle Δθ of the metal tube bending considering non-isothermal thermal field loading:

[0093] First, calculate the residual stress Δζ after bending unloading θ :

[0094]

[0095] Where, I D represents the section moment of inertia, the residual strain Δε after bending unloading θ It can be expressed as:

[0096]

[0097] Where ρ′ represents the curvature radius of the strain neutral layer after rebound;

[0098] The movement of the strain neutral layer during bending unloading can be ignored. The relationship between the neutral layer bending angle, springback angle, bending radius and springback radius is:

[0099]

[0100] Substituting the residual stress-strain relationship after bending unloading into the above formula can determine the bending springback angle Δθ:

[0101]

[0102] Where θ represents the bending angle, and ρ represents the bending radius of the strain neutral layer;

[0103] In this embodiment, the rebound angle of the bent pipe after bending unloading is 9.66°. Figure 4 As shown in the figure, the predicted value of this application is closer to the actual result than the finite element simulation result.

Claims

1. A method for predicting metal pipe bending springback considering non-isothermal thermal field loading, characterized by: Step 1) The pipe is bent and deformed under the constraint of a bending die. After the die is unloaded, the pipe is in a state of rebound. At this time, a cross-sectional plane coordinate system under the strain neutral layer offset condition is established based on the geometric center of the pipe cross section; Step 2) Considering the thermal field of the pipe to have reached thermal equilibrium, the distance e of the neutral layer offset and the position of the yield surface of the deformation zone on the cross section are solved according to the force balance equation, specifically: 2.1) Determine the parameters in the constitutive relationship model of the pipe material and construct a temperature-dependent constitutive model of the pipe material; 2.2) Determine the temperature distribution function T(y) of the pipe bending section; 2.3) Establish the axial force balance equation based on the principle of axial force balance between the inner and outer arches of the pipe; 2.4) Determine the distance e of the neutral layer offset and the position of the yield surface of the deformation zone on the cross section. The position of the yield surface of the deformation zone on the cross section includes the position h of the yield surface of the curved outer arch. o and the position h of the yield surface of the curved inner arch i ; Step 3) Calculate the bending moment M in the elastic zone of the cross section based on the forming radius parameter R and the heating position of the tube blank. e , plastic zone bending moment M p And the total bending moment M T ; Step 4) Calculate the bending springback angle Δθ of the metal tube considering non-isothermal thermal field loading; In step 2.1), the parameters in the constitutive relationship model of the pipe material are determined. The constitutive model formula is as follows: Where σ represents the elastic-plastic stress in different regions, and T(y) represents the temperature function; Where q ij represents the polynomial coefficient; ε y represents the equivalent plastic strain; ε s represents yield strain; A represents yield stress at reference temperature; B represents plastic strengthening parameter; n represents strain hardening exponent; T a Indicates ambient temperature; T m represents the melting temperature; m represents the temperature softening coefficient; the above parameters are obtained through high temperature tensile test; In the step 2.2): When the full-circle heating method is adopted, the cross-sectional temperature of the bending section is T(y)=T0 in the thermal equilibrium state; When the outer or inner half of the curved section is heated, the temperature of the half of the section directly heated is T0, and the temperature of the half heated by heat conduction at a position y from the geometric center of the section is calculated by the following equilibrium formula: y (y): Where T0 represents the heating temperature of the heat source; H represents the arc length of 1 / 4 of the pipe wall mid-diameter circle; r D Indicates the outer wall radius of the tube section; Δδ T represents the temperature equilibrium coefficient; y represents the ordinate on the cross-section plane coordinate system; Where p i represents the linear coefficient, which is solved by the following heat balance equation: Where P represents the perimeter of the longitudinal section of the curved section, r m represents the median diameter of the pipe section, k represents the composite heat transfer coefficient, λ represents the heat conduction coefficient, A c Indicates 1 / 2 area of ​​the pipe cross section; In step 2.3), the equilibrium equation is established based on the principle of axial force balance between the inner and outer arches of the pipe bending as follows: Where, F out Indicates the axial force of the curved outer arch, F in represents the axial force of the curved inner arch; r D Represents the outer wall radius of the tube section; σ eo , σ po , σ ei , σ pi are calculated through the constitutive model in step 2.1), σ eo represents the stress in the elastic region of the bending arch, σ po represents the stress in the plastic zone of the curved outer arch, σ ei represents the stress in the elastic region of the inner arch, σ pi represents the stress in the plastic zone of the inner arch of the bend; σ s represents the yield limit, r m represents the median diameter of the tube section, ρ represents the radius of curvature of the strain neutral layer and ρ = Re; h o represents the location of the yield surface of the curved outer camber, h i Indicates the location of the yield surface of the curved inner arch; Where dS represents the microelement area of ​​the pipe wall cross section, and the calculation formula is as follows: Where t represents the wall thickness; The step 2.4) is specifically as follows: First, according to the yield criterion, the following equilibrium equation is obtained: In the formula, ± represents the two cases of bending inward and bending outward, and the yield limit σ at different temperatures s The fitting formula is σ s =-3.582T(y) 0.676 +302.7;h(r m ,T(y)) represents h o and h i About r m and T(y); Then, the above balance equation is combined with the axial force balance equation in step 2.3) to solve the distance e of the neutral layer offset and the position h of the yield surface of the deformation zone on the cross section. o and h i , the solution equation is: In the step 3): Total bending moment M T =M e +M p , bending moment M in the elastic region of the cross section e and the plastic zone bending moment M p The calculation formula is: The step 4) is specifically as follows: 4.1) First, calculate the residual stress Δσ after bending unloading θ : Where, I D represents the section moment of inertia, the residual strain Δε after bending unloading θ Expressed as: Where ρ represents the bending radius of the strain neutral layer, and ρ′ represents the curvature radius of the strain neutral layer after rebound; 4.2) Ignoring the movement of the strain neutral layer during bending unloading, the relationship between the neutral layer bending angle, rebound angle, bending radius and rebound radius is: 4.3) Substitute the residual stress-strain relationship after bending unloading into the relationship in step 4.2) to determine the bending springback angle Δθ: Where θ represents the bending angle.

2. The method for predicting metal pipe bending springback considering non-isothermal thermal field loading according to claim 1, characterized in that: In the step 1), the tube is a thin-walled metal tube, the heating positions are the outer arch half circumference, the inner arch half circumference and the entire circumference of the curved section, and the temperature change in the wall thickness direction is ignored.

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