Strain energy gradient-based skin stretch springback compensation control method and system

Abstract

The application discloses a skin tension springback compensation control method and system based on strain energy gradient, and belongs to the technical field of thin-walled part plastic forming, and comprises the following steps: a finite element model of tension forming is established to obtain node strain energy and springback displacement; a three-dimensional strain energy gradient field is constructed based on curvature adaptive mesh to distinguish high and low gradient areas; a gradient dynamic correction coefficient is introduced based on a springback reverse vector as a basic direction, and a compensation direction conforming to an energy release path is generated through vector deflection; and after the mold surface is offset, iteration verification is carried out to realize high-precision springback compensation. The application corrects the compensation direction from the essence of strain energy release, avoids the defects of existing technologies such as traditional geometric reverse, sectional segmentation and fixed coefficient, significantly improves the forming precision and surface smoothness of complex hyperbolic skin, reduces the iteration times, is suitable for tension forming die design of various skin materials such as aluminum alloy and titanium alloy, and has engineering application value.

Description

Technical Field

[0001] This invention relates to the field of plastic forming technology for thin-walled parts, and in particular to a skin stretch springback compensation control method and system based on strain energy gradient. Background Technology

[0002] Skin stretch forming is a core manufacturing process for aerodynamic components such as aircraft fuselages, wings, and tail sections. It involves applying tensile loads to sheet metal using clamps and conforming it to the curved surface of a mold to achieve precise forming of complex surfaces. Because skin panels are typically thin-walled, have varying curvatures, and are large in size, the release of elastic strain energy stored within the material after forming and unloading causes significant springback. This directly leads to deviations between the part's surface and the theoretically designed curved surface, affecting assembly accuracy and aerodynamic performance. Therefore, proper compensation for springback, especially precise control of the compensation direction, is crucial for improving the quality of skin forming.

[0003] Currently, the following technical approaches are mainly used for springback compensation in skin stretch forming: Simple reverse compensation method for springback displacement, which directly superimposes the springback displacement vector onto the mold surface without considering the differences in stress and strain energy distribution, easily leading to over- or under-compensation in high curvature areas; Section line segment compensation method, which performs two-dimensional correction along a single section, ignoring three-dimensional bidirectional stress coupling, resulting in a significant deviation between the compensation direction and the actual springback direction; Empirical coefficient compensation method, which uses a fixed proportion to offset the overall surface, unable to adapt to curvature, thickness, and strain hardening distribution, and has poor versatility; Finite element blind iterative compensation method, which repeatedly corrects the mold, but lacks physical constraints on the compensation direction, resulting in blind direction adjustments and numerous iterations.

[0004] Existing technologies do not start from the physical essence of strain energy release generated by springback, and do not establish the intrinsic relationship between the compensation direction and the internal energy distribution, resulting in a mismatch between the compensation direction and the actual springback trend, making it difficult to stably control the forming accuracy of complex skins. Summary of the Invention

[0005] This invention provides a skin stretching springback compensation control method and system based on strain energy gradient, which solves the problem in the prior art that the compensation direction does not match the actual springback trend and that it is difficult to stably control the forming accuracy of complex skins.

[0006] On one hand, embodiments of the present invention provide a skin tensile springback compensation control method based on strain energy gradient, comprising: Establish a finite element model of the entire stretching and forming process of the skin; The forming and unloading springback simulation of the skin is realized based on the material parameters, stretching process parameters, boundary conditions, friction coefficient, and the finite element model of the entire stretching process. The skin mesh is obtained by adaptively refining the mesh based on the surface curvature distribution of the skin. The mesh node parameters of the skin mesh are extracted based on the results of the forming and unloading springback simulation. The three-dimensional strain energy gradient field of the skin mesh is calculated based on the mesh node parameters; The high strain energy gradient region and the low strain energy gradient region are distinguished based on the three-dimensional strain energy gradient field and the gradient threshold. The rebound displacement inverse vector of the node is used as the basic compensation direction. Based on the vector cross product operation and the high strain energy gradient region and low strain energy gradient region, the basic compensation direction is deflected to generate a corrected compensation direction vector that is consistent with the strain energy release trend; The corrected compensation direction vector is re-introduced into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin.

[0007] In one possible implementation, the mesh node parameters include elastic strain energy density, total strain energy, node coordinates, and springback displacement vector.

[0008] In one possible implementation, the skin mesh is obtained by adaptively refining the mesh based on the surface curvature distribution of the skin, including: The mesh density of the skin grid is dynamically allocated according to the curvature of the skin. The skin mesh is either a tetrahedral linear element or a shell element.

[0009] In one possible implementation, calculating the three-dimensional strain energy gradient field of the skin mesh based on the mesh node parameters includes: The strain energy gradient vector is obtained based on the total strain energy and the nodal coordinates. The continuous three-dimensional strain energy gradient field is obtained by interpolating the strain energy gradient vector using element shape functions.

[0010] In one possible implementation, the gradient threshold is determined by the material, thickness, and maximum curvature of the skin.

[0011] In one possible implementation, before generating a corrected compensation direction vector consistent with the strain energy release trend by deflecting the basic compensation direction according to the vector cross product operation and the high strain energy gradient region and the low strain energy gradient region, a dynamic correction coefficient for the strain energy gradient is also introduced.

[0012] In one possible implementation, re-importing the corrected compensation direction vector into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin includes: The correction compensation direction vector is used for mold surface offset; The error was obtained by re-importing the mold surface offset into the finite element model of the entire stretching forming process for iteration and simulation verification. The stretching and springback compensation control of the skin is completed based on the error.

[0013] On the other hand, embodiments of the present invention also provide a skin tensile springback compensation control system based on strain energy gradient, comprising: The finite element simulation interface module is used to establish a finite element model of the entire stretching process of the skin; based on the material parameters, stretching process parameters, boundary conditions, friction coefficient of the skin and the finite element model of the entire stretching process, the forming and unloading springback simulation of the skin is realized; The gradient field calculation module is used to adaptively refine the mesh according to the surface curvature distribution of the skin to obtain the skin mesh; extract the mesh node parameters of the skin mesh according to the results of the forming and unloading springback simulation; calculate the three-dimensional strain energy gradient field of the skin mesh according to the mesh node parameters; and distinguish between high strain energy gradient regions and low strain energy gradient regions according to the three-dimensional strain energy gradient field and gradient threshold. The compensation direction correction module is used to take the rebound displacement reverse vector of the node as the basic compensation direction; based on the vector cross product operation and the high strain energy gradient region and low strain energy gradient region, the basic compensation direction is deflected to generate a corrected compensation direction vector consistent with the strain energy release trend; the corrected compensation direction vector is re-imported into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin.

[0014] The skin tensile springback compensation control method and system based on strain energy gradient of the present invention has the following advantages: (1) The compensation direction is in line with the physical mechanism and consistent with the strain energy release path, thus avoiding the directional deviation of traditional geometric reverse compensation from the root.

[0015] (2) The compensation direction has a clear physical basis, which significantly shortens the mold development cycle.

[0016] (3) It is highly versatile and applicable to various skin materials such as aluminum alloy and titanium alloy. It can be used for stretch forming, stretch bending forming and other processes. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating an overall process for a skin tensile springback compensation control method based on strain energy gradient, as provided in an embodiment of this application. Figure 2 A structural diagram of a skin tensile springback compensation control system based on strain energy gradient is provided in an embodiment of this application; Figure 3 A schematic diagram of the skin strain energy gradient field distribution in an embodiment of a skin tensile springback compensation control method based on strain energy gradient provided in this application. Figure 4 This is a schematic diagram illustrating the compensation direction vector correction principle of a skin tensile springback compensation control method based on strain energy gradient, provided in an embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Figure 1 This is a flowchart illustrating a skin tensile springback compensation control method based on strain energy gradient, provided by an embodiment of the present invention. The embodiment of the present invention provides a skin tensile springback compensation control method based on strain energy gradient, comprising: Establish a finite element model of the entire stretching and forming process of the skin; The forming and unloading springback simulation of the skin is realized based on the material parameters, stretching process parameters, boundary conditions, friction coefficient, and the finite element model of the entire stretching process. The skin mesh is obtained by adaptively refining the mesh based on the surface curvature distribution of the skin. The mesh node parameters of the skin mesh are extracted based on the results of the forming and unloading springback simulation. The three-dimensional strain energy gradient field of the skin mesh is calculated based on the mesh node parameters; The high strain energy gradient region and the low strain energy gradient region are distinguished based on the three-dimensional strain energy gradient field and the gradient threshold. The rebound displacement inverse vector of the node is used as the basic compensation direction. Based on the vector cross product operation and the high strain energy gradient region and low strain energy gradient region, the basic compensation direction is deflected to generate a corrected compensation direction vector that is consistent with the strain energy release trend; The corrected compensation direction vector is re-introduced into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin.

[0021] The grid node parameters include elastic strain energy density, total strain energy, node coordinates, and springback displacement vector.

[0022] The skin mesh is obtained by adaptively refining the mesh based on the surface curvature distribution of the skin, including: The mesh density of the skin grid is dynamically allocated according to the curvature of the skin. The skin mesh is either a tetrahedral linear element or a shell element.

[0023] The calculation of the three-dimensional strain energy gradient field of the skin mesh based on the mesh node parameters includes: The strain energy gradient vector is obtained based on the total strain energy and the nodal coordinates. The continuous three-dimensional strain energy gradient field is obtained by interpolating the strain energy gradient vector using element shape functions.

[0024] The gradient threshold is determined by the material, thickness, and maximum curvature of the skin.

[0025] Before generating a corrected compensation direction vector consistent with the strain energy release trend by deflecting the basic compensation direction based on the vector cross product operation and the high strain energy gradient region and the low strain energy gradient region, a dynamic correction coefficient for the strain energy gradient is introduced.

[0026] The process of re-importing the corrected compensation direction vector into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin includes: The correction compensation direction vector is used for mold surface offset; The error was obtained by re-importing the mold surface offset into the finite element model of the entire stretching forming process for iteration and simulation verification. The stretching and springback compensation control of the skin is completed based on the error.

[0027] For example, a finite element model of the entire process of skin stretching and forming is first established, and material parameters, stretching path, boundary conditions and friction coefficient are applied. The loading forming and unloading springback simulation is completed, and the elastic strain energy density, total strain energy, node coordinates and springback displacement vector of the skin mesh nodes are extracted.

[0028] Then, the mesh is adaptively refined based on the curvature distribution of the skin surface, the strain energy gradient vector of each node is calculated, a three-dimensional strain energy gradient field is constructed, and the high strain energy gradient region and the low strain energy gradient region are distinguished according to the gradient threshold.

[0029] Then, based on the nodal rebound displacement reverse vector as the basic compensation direction, a strain energy gradient dynamic correction coefficient is introduced. The corrected rebound compensation direction vector is generated by performing spatial vector operations between the gradient vector and the basic compensation direction.

[0030] Finally, the compensated mold surface is re-imported into the finite element model for simulation verification, and the forming error is calculated. If the error exceeds the allowable range, the gradient field is updated and the compensation direction is iteratively corrected until the accuracy requirements are met.

[0031] Among them, adaptive mesh density is dynamically allocated according to the curvature: when the local curvature is greater than 1 / 500 mm - ¹ When the mesh cell size is 0.5mm to 1.0mm; when the local curvature is less than or equal to 1 / 500mm - ¹When the mesh element size is 2.0mm to 3.0mm, the mesh type is tetrahedral linear element or shell element.

[0032] Strain energy gradient vector From total strain energy The partial derivatives with respect to the spatial coordinates (x, y, z) of the node are shown in the following formula: ; These represent the rates of change of total strain energy along the x, y, and z coordinate axes, respectively.

[0033] A continuous strain energy gradient field is obtained by interpolation of element shape functions.

[0034] Gradient threshold The skin material, thickness, and maximum curvature are jointly determined to satisfy the following: ; in The curvature coefficient is taken as 0.0005 to 0.002; It is the elastic modulus; Skin thickness; This represents the maximum curvature of the skin.

[0035] The basic compensation direction is the unit reverse vector of the rebound displacement vector. ,satisfy: ; in This represents the three-dimensional rebound displacement vector of the current node; The springback displacement modulus.

[0036] Dynamic correction coefficient The expression is: ; in The strain sensitivity coefficient is 0.3–0.6 for aluminum alloys and 0.5–0.8 for titanium alloys. The gradient magnitude of the current node. This represents the maximum gradient modulus of the entire skin.

[0037] Corrected compensation direction vector satisfy: ; in It is a vector cross product; the compensation direction in the high gradient region is deflected along the direction of strain energy decrease, with a deflection angle of 6° to 15°, and the deflection angle in the low gradient region does not exceed 5°.

[0038] The allowable range of forming error is ±0.1mm. The iteration termination condition is that the springback error of all nodes is less than 0.1mm and the error in the high gradient region is less than 0.08mm.

[0039] In one possible embodiment, springback compensation is performed on the hyperbolic fuselage skin of a certain aircraft model: 1. Process and model parameters; Component material: 2024-T3 aluminum alloy; Skin thickness: 1.2mm; Surface type: hypercurvature surface, principal curvature radii R500mm and R800mm; Forming method: Clamp-type stretch forming; Finite element software: Abaqus / Standard; Element type: Four-node shell element.

[0040] 2. Forming and springback simulation; Establish a finite element model of the entire stretch forming process and set the elastic modulus. With a Poisson's ratio of 0.33 and a yield strength of 345 MPa, isotropic strain hardening is considered. After completing the loading forming and unloading springback calculations, the springback displacement vector and total strain energy at each node are extracted. and spatial coordinates.

[0041] 3. Adaptive mesh and strain energy gradient field construction; Curvature greater than 1 / 500mm - ¹The mesh in one region was refined to 0.8 mm, while the mesh in the remaining regions remained at 2.0 mm; to quantitatively describe the rate of change and release direction of strain energy in space, a strain energy gradient vector was constructed. It is defined as the total strain energy. Calculate the strain energy gradient vector at each node using a three-dimensional vector formed by the first-order partial derivatives along the three directions (x, y, z) of the node's spatial coordinates: ; in: These represent the rates of change of total strain energy along the x, y, and z coordinate axes, respectively. gradient vector The direction of the increase in strain energy is the direction in which the modulus increases the most. It reflects the degree of non-uniformity of the spatial distribution of strain energy. The larger the modulus, the higher the energy concentration in the region, the more violent the rebound trend, and the more sensitive the direction.

[0042] The gradient threshold is determined based on the material, thickness, and curvature. Divide the region into high gradient region and low gradient region.

[0043] 4. Calculation of compensation direction; After obtaining the springback displacements of each node from the finite element simulation output, the basic compensation direction of each node is first determined. (Node springback displacement vector) It represents the spatial displacement vector of the skin after unloading from the molded position to the free state. Its direction represents the actual springback trend of the material, and the mold length represents the magnitude of the springback displacement.

[0044] To pre-offset the mold surface in the opposite direction of springback to counteract springback deformation after unloading, the basic compensation direction is defined as the reverse unit vector of the springback displacement, expressed as: ; in: This represents the three-dimensional rebound displacement vector of the current node; This is the magnitude of the springback displacement vector, i.e., the amplitude of the nodal springback displacement; The negative sign indicates that the compensation direction is opposite to the rebound direction, thus achieving reverse pre-compensation for the rebound displacement; Normalization make It is a unit vector that only represents the compensation direction and does not include the compensation displacement amplitude, which facilitates subsequent independent control of the compensation amount and compensation direction.

[0045] This basic compensation direction The initial directional reference constituting the springback compensation embodies the core idea of ​​traditional geometric compensation. However, this invention does not directly use this direction as the final compensation direction, but instead uses it as the initial reference direction. Subsequently, it is spatially deflected and corrected by strain energy gradient, thereby overcoming the shortcomings of traditional simple reverse compensation with a single direction and mismatch with stress release path.

[0046] 5. Dynamic correction coefficient: ; Take the material sensitivity coefficient High gradient region ≈1.30~1.42, low gradient region ≈1.05~1.15.

[0047] Correction compensation direction vector: ; In the high gradient region, the compensation direction deflects by 6° to 12°, and in the low gradient region, it deflects by 1° to 4°, deflecting along the decreasing trend of strain energy.

[0048] 6. Iterative verification results After the first iteration, the maximum error was 0.14 mm; after the second fine-tuning of the compensation direction, the maximum error across the entire surface was 0.07 mm, meeting the design tolerance requirement of ±0.1 mm. The skin fit was good, with no warping or torsion, and the mold was machined in one go, eliminating the need for trial molding and rework.

[0049] Figure 2 This invention provides a structural diagram of a skin tensile springback compensation control system based on strain energy gradient, according to an embodiment of the present invention. The embodiment of the present invention provides a skin tensile springback compensation control system based on strain energy gradient, comprising: The finite element simulation interface module is used to establish a finite element model of the entire stretching process of the skin; based on the material parameters, stretching process parameters, boundary conditions, friction coefficient of the skin and the finite element model of the entire stretching process, the forming and unloading springback simulation of the skin is realized; The gradient field calculation module is used to adaptively refine the mesh according to the surface curvature distribution of the skin to obtain the skin mesh; extract the mesh node parameters of the skin mesh according to the results of the forming and unloading springback simulation; calculate the three-dimensional strain energy gradient field of the skin mesh according to the mesh node parameters; and distinguish between high strain energy gradient regions and low strain energy gradient regions according to the three-dimensional strain energy gradient field and gradient threshold. The compensation direction correction module is used to take the rebound displacement reverse vector of the node as the basic compensation direction; based on the vector cross product operation and the high strain energy gradient region and low strain energy gradient region, the basic compensation direction is deflected to generate a corrected compensation direction vector consistent with the strain energy release trend; the corrected compensation direction vector is re-imported into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin.

[0050] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0051] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A skin tensile springback compensation control method based on strain energy gradient, characterized in that, include: Establish a finite element model of the entire stretching and forming process of the skin; The forming and unloading springback simulation of the skin is realized based on the material parameters, stretching process parameters, boundary conditions, friction coefficient, and the finite element model of the entire stretching process. The skin mesh is obtained by adaptively refining the mesh based on the surface curvature distribution of the skin. The mesh node parameters of the skin mesh are extracted based on the results of the forming and unloading springback simulation. The three-dimensional strain energy gradient field of the skin mesh is calculated based on the mesh node parameters; The high strain energy gradient region and the low strain energy gradient region are distinguished based on the three-dimensional strain energy gradient field and the gradient threshold. The rebound displacement inverse vector of the node is used as the basic compensation direction. Based on the vector cross product operation and the high strain energy gradient region and low strain energy gradient region, the basic compensation direction is deflected to generate a corrected compensation direction vector consistent with the strain energy release trend, including: Corrected compensation direction vector satisfy: ； in For vector cross product, The strain energy gradient vector, Unit reverse vector, The compensation direction in the high gradient region deflects along the direction of strain energy decrease, while the deflection angle in the low gradient region does not exceed 5°. The basic compensation direction is the unit reverse vector of the rebound displacement vector. ,satisfy: ； in This represents the three-dimensional rebound displacement vector of the current node; The springback displacement modulus; Dynamic correction coefficient The expression is: ； in The material strain sensitivity coefficient, The gradient magnitude of the current node. The maximum gradient modulus of the entire skin; The corrected compensation direction vector is re-introduced into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin.

2. The skin tensile springback compensation control method based on strain energy gradient according to claim 1, characterized in that, The grid node parameters include elastic strain energy density, total strain energy, node coordinates, and springback displacement vector.

3. The skin tensile springback compensation control method based on strain energy gradient according to claim 1, characterized in that, The skin mesh is obtained by adaptively refining the mesh based on the surface curvature distribution of the skin, including: The mesh density of the skin grid is dynamically allocated according to the curvature of the skin. The skin mesh is either a tetrahedral linear element or a shell element.

4. The skin tensile springback compensation control method based on strain energy gradient according to claim 2, characterized in that, The calculation of the three-dimensional strain energy gradient field of the skin mesh based on the mesh node parameters includes: The strain energy gradient vector is obtained based on the total strain energy and the nodal coordinates. The continuous three-dimensional strain energy gradient field is obtained by interpolating the strain energy gradient vector using element shape functions.

5. The skin tensile springback compensation control method based on strain energy gradient according to claim 1, characterized in that, The gradient threshold is determined by the material, thickness, and maximum curvature of the skin.

6. The skin tensile springback compensation control method based on strain energy gradient according to claim 1, characterized in that, Before generating a corrected compensation direction vector consistent with the strain energy release trend by deflecting the basic compensation direction based on the vector cross product operation and the high strain energy gradient region and the low strain energy gradient region, a dynamic correction coefficient for the strain energy gradient is introduced.

7. The skin tensile springback compensation control method based on strain energy gradient according to claim 1, characterized in that, The process of re-importing the corrected compensation direction vector into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin includes: The correction compensation direction vector is used for mold surface offset; The error was obtained by re-importing the mold surface offset into the finite element model of the entire stretching forming process for iteration and simulation verification. The stretching and springback compensation control of the skin is completed based on the error.

8. A skin tensile springback compensation control system based on strain energy gradient, characterized in that, include: The finite element simulation interface module is used to build a finite element model of the entire stretching and forming process of the skin. The forming and unloading springback simulation of the skin is realized based on the material parameters, stretching process parameters, boundary conditions, friction coefficient, and the finite element model of the entire stretching process. The gradient field calculation module is used to adaptively refine the mesh according to the surface curvature distribution of the skin to obtain the skin mesh; The mesh node parameters of the skin mesh are extracted based on the results of the forming and unloading springback simulation; the three-dimensional strain energy gradient field of the skin mesh is calculated based on the mesh node parameters; and the high strain energy gradient region and the low strain energy gradient region are distinguished based on the three-dimensional strain energy gradient field and the gradient threshold. The compensation direction correction module is used to take the rebound displacement reverse vector of the node as the basic compensation direction; based on the vector cross product operation and the high strain energy gradient region and low strain energy gradient region, it deflects the basic compensation direction to generate a corrected compensation direction vector consistent with the strain energy release trend, including: Corrected compensation direction vector satisfy: ； in For vector cross product, The strain energy gradient vector, Unit reverse vector, The compensation direction in the high gradient region deflects along the direction of strain energy decrease, while the deflection angle in the low gradient region does not exceed 5°. The basic compensation direction is the unit reverse vector of the rebound displacement vector. ,satisfy: ； in This represents the three-dimensional rebound displacement vector of the current node; The springback displacement modulus; Dynamic correction coefficient The expression is: ； in The material strain sensitivity coefficient, The gradient magnitude of the current node. The maximum gradient modulus of the entire skin is used; the corrected compensation direction vector is re-introduced into the finite element model of the entire stretching forming process to complete the stretching springback compensation control of the skin.

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