CN112733360B - Rebound prediction theoretical calculation method for three-dimensional stretch-bending formed part - Google Patents
Rebound prediction theoretical calculation method for three-dimensional stretch-bending formed part Download PDFInfo
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Abstract
The invention discloses a rebound prediction theory calculation method of a three-dimensional stretch-bending formed part, which comprises the following steps: three-dimensional bending (horizontal-vertical step bending) of a rectangular section is equivalent to space plane bending of a rotary rectangular section; establishing a coordinate system with a centroid of a rotary rectangular section as an origin, and obtaining material parameters through a unidirectional tensile test; determining the stress-strain distribution relation of the whole profile by analyzing the elastic pre-stretching-bending process; judging the section stress strain plasticity and the elastic distribution state according to the elastic pre-stretching stress and the stretch bending radius; after the distribution state of the section elasticity and plasticity is determined, the bending radius and the total bending moment of the neutral layer are solved according to the stress-strain relation and the section stress-force balance and bending moment balance relation; establishing an elastic composite analytic equation, and determining the bending radius after rebound deformation according to the calculated geometric parameters such as the radius of a neutral layer, the total bending moment and the like and the technological parameters; comparing the calculated bending radius after rebound with an ideal bending radius, calculating rebound error of the bending radius, and comparing the calculated rebound error with an experimental value; the method can effectively predict the rebound result of three-dimensional bending.
Description
Technical Field
The invention belongs to the technical field of metal plastic forming, and particularly relates to a rebound prediction theory calculation method of a three-dimensional stretch-bending formed part.
Background
With the demands of assembly accuracy and service life, the forming quality of the profile plays a crucial role in manufacturing. However, in the actual bending forming process, the problem of rebound deformation is a main problem affecting the quality of formed parts, and how to accurately and effectively predict and restrain rebound is always a hot spot problem in the field of plastic bending forming. At present, the research on rebound is mainly divided into two aspects, namely, the rebound prediction and the rebound control, wherein the effective rebound deformation prediction is a precondition for realizing the rebound control. As the bending dimension increases, the construction of a three-dimensional bending resilience prediction model is a new difficulty. Therefore, the springback prediction theory calculation method of the three-dimensional stretch-bending forming piece is provided, and the rectangular section profile of the three-dimensional stretch-bending (respectively bending in the horizontal direction and the vertical direction) is equivalently abstracted into the space two-dimensional bending of the rotating rectangular section profile. And a rebound theory model is built, so that the calculation time is greatly reduced.
Disclosure of Invention
The invention aims to: in order to solve the problem of constructing a rebound prediction model of a three-dimensional stretch-bending structural member and realize the rapid prediction of rebound deformation of the structural member, the invention provides a rebound prediction theoretical calculation method of a three-dimensional stretch-bending forming part, which comprises the following steps:
step 1: the invention provides a new idea of three-dimensional stretch bending rebound theory calculation, namely that a rectangular section bar of three-dimensional stretch bending (respectively bending in horizontal and vertical directions) is equivalently abstracted into a space two-dimensional bending of a rotating rectangular section bar.
Step 2: taking the equivalent rotary rectangular section as a new stretch bending section, establishing a coordinate system ouvw, and determining an outermost fiber point A, an innermost fiber point B, a section height h, a distance c from the point A to a neutral layer, a section total length L, a section width B (u) at each position (changing along with the change of the coordinate u) and a section area A of the rotary rectangular section under the coordinate system; material parameters determined according to tensile test: stress sigma, strain epsilon, elastic modulus E, plastic modulus D, elastic limit strain epsilon s, yield stress sigma s.
Step 3: the pre-stretching makes the section bar reach the elastic stage, and then the section bar is subjected to stretch bending treatment, the pre-stretching stress is sigma T(σT≤σS), and the external load and deformation state of the section bar after stretch bending loading are shown in figure 3. In fig. 3, the axial tension T, R is the radius ρ of the bending die, the bending radius of the geometric neutral layer of the profile, and M is the total bending moment applied to the profile after stretch bending deformation. Where ρ=r+h-c, t=σ T a. In the stretching and bending process of the profile, the single loading stress-strain relation is:
Wherein σ S=εS E. The stretch bending deformation can be divided into 'complete elastic deformation', 'outer plastic inner layer elastic deformation', 'inner plastic compression outer layer elastic deformation', and 'outer plastic stretching inner layer plastic compression deformation'. The expression of strain and total stress in the strain neutral layer coordinate system xOz is
The strain and total stress expression under the geometrical neutral layer coordinate system wou is
Balance relation between internal force and external load after stretch bending deformation
T=∫AσdA (6)
M=∫AσudA (7)
Obtaining
The areas of the neutral layer plastic compression area, the elastic area and the outer layer stretching area of the profile are respectively A 1、A2 and A 3, the static moments on the v axis are respectively S 1、S2 and S 3, and the moments of inertia on the v axis are respectively I 1、I2 and I 3. According to the geometrical properties of the plane
Step 4: four different types of stretch bending deformation are possible when the pre-tension stress is equal to or less than the yield stress. Different stress strains of the inner layer fiber and the outer layer fiber can cause different results to occur, and the different conditions are divided into the following judging conditions:
P4-1 complete elasticity determination condition: when the fiber stress of the innermost layer and the fiber stress of the outermost layer simultaneously meet sigma T1(ρ)≤σT≤σT0 (rho), wherein
Elastic deformation of the P4-2 outer plastic inner layer: when the fiber stress of the innermost layer and the fiber stress of the outermost layer are simultaneously satisfied
max{σT0(ρ),σT2(ρ)}<σT≤σS (12)
Wherein σ T2 (ρ) solves the equation
Elastic deformation of the inner plastic layer and the outer plastic layer of the P4-3: when the fiber stress of the innermost layer and the fiber stress of the outermost layer are simultaneously satisfied
0<σT<min{σT1(ρ),σT3(ρ)} (14)
Wherein σ T3 (ρ) solves the equation
P4-4 outer layer plastic stretching inner layer plastic compression: when the fiber stress of the innermost layer and the fiber stress of the outermost layer are simultaneously satisfied
max{σT0(ρ),σT3(ρ)}<σT<min{σT1(ρ),σT2(ρ)} (16)
Step 5: based on the judgment condition of the step 4, the following expressions of the bending radius and the total bending moment of the four strain neutral layers are obtained: p5-1 is completely elastically deformed:
elastic deformation of the P5-2 outer plastic inner layer:
p5-3 elastic deformation of inner plastic layer:
p5-4 outer layer plastic stretching inner layer plastic compression:
step 6: based on the solved rho ε, M and geometric parameters and technological parameters, the method is based on a stretch bending rebound equation
And solving the bending radius rho p after rebound.
Step 7: and according to the comparison of the calculated bending radius rho p after rebound with the target bending radius rho, a corresponding rebound value is calculated, and compared with an experimental value, the relative error and the absolute error are calculated.
Drawings
FIG. 1 is a general flow chart of a theoretical calculation method for predicting rebound of a three-dimensional stretch-bent formed article according to the present invention.
Fig. 2 is a geometric schematic of an equivalent post-rotation rectangular section profile.
Fig. 3 is a schematic drawing of pretension reloading.
Fig. 4 is a fully elastically deformed.
Fig. 5 shows the elastic deformation of the outer plastic inner layer.
Fig. 6 shows the inner layer plastically compressing the outer layer elastically deforming.
Fig. 7 shows plastic deformation of the outer layer by plastic stretching and the inner layer by plastic compression.
Fig. 8 is a comparison of theoretical calculated rebound values with experimental results.
Detailed Description
The invention is further illustrated by the following figures and examples
The theoretical calculation method for resilience prediction of the three-dimensional stretch-bending formed part is introduced as follows:
the whole flow chart of the method is shown in fig. 1, and in the example, AA6082 aluminum alloy rectangular section bar is selected as a study object.
Examples:
step 1:
Three-dimensional stretch bending (bending in horizontal and vertical directions respectively) of a rectangular section profile with the section size of 40mm multiplied by 40mm, the wall thickness of 4mm and the length of 2.2m is equivalently abstracted into space two-dimensional bending of a rotary rectangular section profile, as shown in figure 2. Since the rotation radius and the rotation angle in the horizontal direction and the vertical direction are the same, the cross section is defined as a diamond cross section.
Step 2:
Taking the equivalent diamond-shaped section as a new stretch-bending section, establishing a coordinate system ouvw, and determining an outermost fiber point A, an innermost fiber point B, a section height h, a distance c from the point A to a neutral layer, a section total length L, a section width B (u) at each position (changing along with the change of the coordinate u) and a section area A of the diamond-shaped section under the coordinate system; material parameters determined according to tensile test: stress sigma, strain epsilon, elastic modulus E, plastic modulus D, elastic limit strain epsilon s, yield stress sigma s. Table 1 shows the geometric parameters of diamond cross section, and Table 2 shows the performance parameters of AA6082 material.
TABLE 1 rhombic section geometry parameters
TABLE 2 AA6082 Material Performance parameters
Step 3:
The pre-stretching stress just reaches the yield stress, sigma T=σS = 155.44MPa, the arc bending radius of the target forming part is 5402.2958mm, and the bending radius rho of the geometric neutral layer of the profile in the stretch bending deformation process is 5430.5758mm. In the stretching and bending process of the profile, the single loading stress-strain relation is:
Wherein σ S=εS E. The plastic stretching region, the elastic loading region and the plastic compression region are divided according to the stress strain distribution of the section, and different loading modes can be generated according to different stretching stresses and bending radiuses. The expression of strain and total stress in the strain neutral layer coordinate system xOz is
The strain and total stress expression under the geometrical neutral layer coordinate system wou is
Balance relation between internal force and external load after stretch bending deformation
T=∫AσdA (6)
M=∫AσudA (7)
Obtaining
The areas of the neutral layer plastic compression area, the elastic area and the outer layer stretching area of the profile are respectively A 1、A2 and A 3, the static moments on the v axis are respectively S 1、S2 and S 3, and the moments of inertia on the v axis are respectively I 1、I2 and I 3. According to the geometrical properties of the plane
Step 4:
Based on the determined conditions, the tensile stress sigma T is solved to be within the sigma T2(ρ)<σT=σS range, and the deformation type is that the outer layer is plastic, the inner layer is elastically deformed, and the c 0 = -4.6854 is solved.
Step 5:
outer plastic inner layer elastic deformation:
Step 6:
Based on the solved rho ε, M and geometric parameters and technological parameters, the method is based on a stretch bending rebound equation
And solving the bending radius rho p after rebound. The stretch bending and rebound results are shown in Table 3
TABLE 3 stretch bending rebound results
Step 7
And according to the comparison of the calculated bending radius rho p after rebound with the target bending radius rho, a corresponding rebound value is calculated, and compared with an experimental value, the relative error and the absolute error are calculated. The theoretical calculation result is compared with the experimental value as shown in the figure.
Claims (1)
1. Rebound prediction theoretical calculation method for three-dimensional stretch-bending formed part
The method comprises the following steps:
step 1: the new method for calculating the three-dimensional stretch bending rebound theory is provided, namely, the three-dimensional stretch bending rectangular section bar is equivalently abstracted into the space two-dimensional bending of a rotary rectangular section bar;
Step 2: taking the equivalent rotary rectangular section as a new stretch bending section, establishing a coordinate system ouvw, and determining an outermost fiber point A, an innermost fiber point B, a section height h, a distance c from the point A to a neutral layer, a section total length L, a section width B (u) and a section area A of the rotary rectangular section under the coordinate system; material parameters determined according to tensile test: stress sigma, strain epsilon, elastic modulus E, plastic modulus D, elastic limit strain epsilon s, yield stress sigma s;
Step 3: pre-stretching to enable the profile to reach an elastic stage, and then stretch-bending the profile, wherein the pre-stretching stress is sigma T, the axial tension T, R is the bending radius ρ of a bending die and is the bending radius of a geometric neutral layer of the profile, and M is the total bending moment born by the profile after stretch bending deformation; wherein ρ=r+h-c, t=σ T a; in the stretching and bending process of the profile, the single loading stress-strain relation is:
Wherein sigma s=εs E is divided into a plastic stretching area, an elastic loading area and a plastic compression area according to the stress strain distribution of the section, and different loading modes can be generated according to different stretching stress and bending radius, and stretch bending deformation can be divided into 'complete elastic deformation', 'outer plastic inner layer elastic deformation', 'inner plastic compression outer layer elastic deformation' and 'outer plastic stretching inner layer plastic compression deformation'; the expression of strain and total stress in the strain neutral layer coordinate system xOz is
The strain and total stress expression under the geometrical neutral layer coordinate system wou is
Balance relation between internal force and external load after stretch bending deformation
T=∫AσdA (6)
M=∫AσudA (7)
Obtaining
The areas of a neutral layer plastic compression area, an elastic area and an outer layer stretching area of the profile are respectively A 1、A2 and A 3, the static moments on the v axis are respectively S 1、S2 and S 3, and the moments of inertia on the v axis are respectively I 1、I2 and I 3; according to the geometrical properties of the plane
Step 4: four different types of stretch bending deformation are possible when the pre-stretching stress is less than or equal to the yield stress; different stress strains of the inner layer fiber and the outer layer fiber can cause different results to occur, and the different conditions are divided into the following judging conditions:
P4-1 complete elasticity determination condition: when the fiber stress of the innermost layer and the fiber stress of the outermost layer simultaneously meet sigma T1(ρ)≤σT≤σT0 (rho), wherein
Elastic deformation of the P4-2 outer plastic inner layer: when the fiber stress of the innermost layer and the fiber stress of the outermost layer are simultaneously satisfied
max{σT0(ρ),σT2(ρ)}<σT≤σS (12)
Wherein σ T2 (ρ) solves the equation
Elastic deformation of the inner plastic layer and the outer plastic layer of the P4-3: when the fiber stress of the innermost layer and the fiber stress of the outermost layer are simultaneously satisfied
0<σT<min{σT1(ρ),σT3(ρ)} (14)
Wherein σ T3 (ρ) solves the equation
P4-4 outer layer plastic stretching inner layer plastic compression: when the fiber stress of the innermost layer and the fiber stress of the outermost layer are simultaneously satisfied
max{σT0(ρ),σT3(ρ)}<σT<min{σT1(ρ),σT2(ρ)} (16)
Step 5: based on the judgment condition of the step 4, the following expressions of the bending radius and the total bending moment of the four strain neutral layers are obtained:
p5-1 is completely elastically deformed:
elastic deformation of the P5-2 outer plastic inner layer:
p5-3 elastic deformation of inner plastic layer:
p5-4 outer layer plastic stretching inner layer plastic compression:
step 6: based on the solved rho ε, M and geometric parameters and technological parameters, the method is based on a stretch bending rebound equation
Solving a bending radius rho p after rebound;
Step 7: and according to the comparison of the calculated bending radius rho p after rebound with the target bending radius rho, a corresponding rebound value is calculated, and compared with an experimental value, the relative error and the absolute error are calculated.
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CN107704697A (en) * | 2017-10-18 | 2018-02-16 | 西南交通大学 | A kind of section bar three-dimensional bending formability prediction and evaluation optimization method |
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JP2008266903A (en) * | 2007-04-17 | 2008-11-06 | Shimizu Corp | Method for estimating amount of rebound in excavated ground, and ground excavation method |
CN104281725A (en) * | 2013-07-13 | 2015-01-14 | 西安嘉业航空科技有限公司 | Three-dimensional multi-curvature part bending method |
CN104866641A (en) * | 2014-12-10 | 2015-08-26 | 太原科技大学 | Model for predicting resilience of bar subjected to two roll straightening |
JP2018108593A (en) * | 2017-01-05 | 2018-07-12 | Jfeスチール株式会社 | Spring-back amount prediction method |
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