A method for predicting residual stress of roll burnishing based on elastic-plastic deformation theory

Abstract

This invention belongs to the field of tumbling finishing technology and aims to solve the problem that current residual stress simulations struggle to simulate workpiece surface material deformation. It provides a method for predicting residual stress in tumbling finishing based on elastoplastic deformation theory, comprising the following steps: equating a blank three-dimensional array to the workpiece's target region; constructing an EDEM simulation model and extracting contact information between the particulate medium and the workpiece; calculating the maximum overlap based on the contact information and dividing the collision into stages; calculating the contact stress distribution corresponding to the overlap at different collision stages; calculating the elastic stress field distribution of the target region at different collision stages based on the contact stress distribution and converting it into elastic loading stress for plastic correction; after loading, calculating the internal stress distribution under the cumulative action of all activated units in the blank three-dimensional array to obtain the residual strain and residual stress of the target region. This invention can simulate the deformation of workpiece surface materials, improving the accuracy of the simulation.

Description

Technical Field

[0001] This invention belongs to the field of tumbling finishing technology, specifically relating to a method for predicting residual stress in tumbling finishing based on the theory of elastic-plastic deformation. Background Technology

[0002] Roll grinding, a surface finishing process that improves surface roughness and introduces residual compressive stress, is widely used in high-end equipment manufacturing industries such as aerospace and vehicle engineering. The introduction of residual compressive stress can promote the transfer of fatigue crack initiation sites from the surface to the subsurface, reduce crack initiation and propagation rates, and effectively improve fatigue life. High-precision prediction of machining residual stress and effective control of residual stress have a crucial impact on the development of surface finishing processes.

[0003] The main methods for predicting residual stress include: experimental measurement, simulation, and theoretical analysis.

[0004] Among them, experimental measurement method is the most widely used in the field of tumbling finishing, but it has problems such as limited model applicability, long time consumption, and high cost. In recent years, simulation method has been gradually applied to the prediction of tumbling residual stress, but it has the problem of low computational efficiency. Due to the complexity and randomness of the action mode of particulate media, as well as the relatively backward research on processing mechanism, theoretical analysis method is relatively lacking in the prediction method of tumbling residual stress.

[0005] Existing methods for simulating residual stress on the surface of workpieces after tumbling finishing involve extracting EDEM (Discrete Element Model) data on the contact between the granular medium and the workpiece using software, and then applying this data as concentrated forces to the nodes of the finite element model to simulate residual stress. However, this method neglects the contact stress distribution characteristics at the instant of contact, making it difficult to simulate the deformation of the workpiece surface material during actual machining, thus reducing the accuracy and reliability of the simulation. Summary of the Invention

[0006] In order to solve at least one of the above-mentioned technical problems in the prior art, the present invention provides a method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation.

[0007] This invention employs the following technical solution: a method for predicting residual stress in tumbling finishing based on elastoplastic deformation theory, comprising the following steps: selecting the area to be predicted on the workpiece and selecting sampling points within the area to be predicted; constructing multiple sets of blank three-dimensional arrays and equating the blank three-dimensional arrays with the area to be predicted; the blank three-dimensional arrays are used to store stress data, strain data, and plastic strain data of the sampling points, and the deformation process is simulated through operations between the arrays; constructing an EDEM simulation model for tumbling finishing, and extracting contact information between the particulate medium and the workpiece in the simulation; the contact information includes the relative velocity and overlap at the instant of contact between the particulate medium and the workpiece; calculating the maximum overlap of the collision during the contact process between the particulate medium and the workpiece based on the contact information, the contact model in the EDEM simulation model, and the differential cyclic iteration method, and dividing the collision stage based on the maximum overlap of the collision, and simulating... The process involves a step-by-step loading of particles during collision. Hertzian contact theory is used to calculate the contact stress distribution corresponding to the overlap at different collision stages. Based on this contact stress distribution and the Boussinesq equation, the elastic stress field distribution of the region to be predicted under contact load at different collision stages is calculated, and this elastic stress field distribution is transformed into incremental elastic loading stress. The elastic loading stress is accumulated step-by-step, and the elastic stress at each collision stage is plastically corrected using radial regression. The plastic strain increment at each stage is calculated, and the accumulated plastic deformation value is obtained by summing the plastic strain increments at each collision stage. After loading, the elements with accumulated plastic deformation values ​​greater than zero in the blank three-dimensional array are activated, and the Galerkin vector method is used to calculate the internal stress distribution under the cumulative action of all activated elements, obtaining the residual strain and residual stress of the region to be predicted.

[0008] Preferably, in the blank three-dimensional array, the array order corresponding to the length of the region to be predicted is the ratio of the length of the region to be predicted to the interval between adjacent sampling points plus one; the array order corresponding to the width of the region to be predicted is the ratio of the width of the region to be predicted to the interval between adjacent sampling points plus one; and the array order corresponding to the width of the region to be predicted is the ratio of the height of the region to be predicted to the interval between adjacent sampling points plus one.

[0009] Preferably, the step of calculating the maximum overlap of the collision between the particulate medium and the workpiece during the contact process based on contact information, the contact model in the EDEM simulation model, and the differential cyclic iterative method is as follows: The relative velocity and overlap of the particulate medium and the workpiece at the instant of contact, extracted from the EDEM simulation, are used as the initial conditions for the cyclic iterative calculation; the first... The relative velocity between the particulate medium and the workpiece at the instant of contact in the iteration step is less than the threshold for relative velocity convergence in the cyclic iteration operation, which is taken as the termination condition of the cyclic iteration operation. The cyclic iteration is performed to iteratively update the relative velocity and overlap between the particulate medium and the workpiece at the instant of contact until the termination condition of the cyclic iteration operation is met. The overlap between the particulate medium and the workpiece at the instant of contact in the current iteration step is output as the maximum overlap of the collision in the contact process between the particulate medium and the workpiece.

[0010] Preferably, the maximum overlap of the collision is divided into: The collision process of particles is simulated by dividing the particles into equal-spaced stages and loading stages into equal-spaced stages. The overlap of each stage during the collision process is obtained. The contact stress distribution of each stage is calculated based on the overlap of each stage during the collision process and Hertzian contact theory.

[0011] Preferably, the step of calculating the elastic stress field distribution of the region to be predicted under the contact load at different collision stages includes: obtaining the elastic stress generated at any point on the workpiece surface under concentrated load using the Boussinesq equation; integrating the elastic stress generated by the load at each contact stress point along the contact region to obtain the elastic stress field distribution under the contact load; and converting the elastic stress field distribution into incremental elastic loading stress includes: subtracting the elastic stress field of each stage from the elastic stress field of the previous stage to convert it into incremental elastic loading stress.

[0012] Preferably, the step of plastically correcting the elastic stress of each collision stage using the radial regression method includes: calculating the test stress of the corresponding stage based on the elastic loading stress of each stage and the stress of the previous stage, and converting the test stress into the deviatoric stress component of the test stress; determining whether the yield condition is satisfied; if not, then the deviatoric stress component of the stress of each stage is equal to the deviatoric stress component of the test stress of the corresponding stage, and the plastic strain of each stage is equal to the plastic strain of the previous stage; calculating the stress of each stage after plastic correction based on the deviatoric stress component of the stress of each stage and the test stress; if satisfied, then performing the following operations: solving the consistency condition equation using the Newton-Raphson method to calculate the plastic strain increment; calculating the plastic strain of each stage after plastic correction based on the deviatoric stress component of the test stress of each stage, the strain of the previous stage, and the plastic strain increment; obtaining the deviatoric stress component of the stress of the corresponding stage based on the deviatoric stress component of the test stress of each stage and the plastic strain increment; calculating the stress of each stage after plastic correction based on the deviatoric stress component of the stress of each stage and the test stress.

[0013] Preferably, the steps of obtaining the residual strain and residual stress of the region to be predicted include:

[0014] In the blank three-dimensional array storing plastic strain data, cells with a cumulative plastic deformation value greater than zero are counted and marked as active.

[0015] The Galerkin vector method was used to calculate the internal strain generated at the sampling points of all activated elements;

[0016] The residual strain is obtained by summing the internal strains generated by all activated elements.

[0017] The residual stress is calculated using the generalized Hooke's law and the residual strain.

[0018] Compared with the prior art, the beneficial effects of the present invention are:

[0019] This invention discloses a method for predicting residual stress in tumbling grinding based on the theory of elastic-plastic deformation. First, the local area of ​​the workpiece surface under study is discretized into multiple three-dimensional arrays to store stress data, strain data, and plastic strain data, respectively. An EDEM simulation model of tumbling grinding is established to obtain the relative velocity and overlap between the particulate medium and the workpiece at the moment of contact. The maximum overlap is calculated using the Hertz-Mindlin contact model through iterative calculations, and the collision stages are defined. The contact stress distribution under different collision stages is calculated based on the Hertz contact model. The elastic stress field distribution of the workpiece surface and below under contact loads at different collision stages is calculated based on the Boussinesq equation and converted into an incremental form. The elastic stress at each stage is plastically corrected using the radial regression method, and the cumulative value of plastic deformation is calculated. Finally, the internal stress distribution under the cumulative action of all elements with a cumulative plastic deformation value greater than zero is calculated using the Galerkin vector method, yielding residual strain and residual stress.

[0020] This invention can simulate the deformation of workpiece surface materials during actual processing, thereby improving the accuracy and reliability of the simulation. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments 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.

[0022] Figure 1 This is a flowchart of a method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation, as proposed in this invention.

[0023] Figure 2 This is a schematic diagram illustrating the construction principle of a discretized three-dimensional array in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of the EDEM simulation model in an embodiment of the present invention;

[0025] Figure 4 This is a flowchart illustrating the calculation of the maximum overlap in an embodiment of the present invention.

[0026] Figure 5 This is a diagram showing the calculation results of the maximum overlap in an embodiment of the present invention;

[0027] Figure 6 This is a flowchart illustrating the calculation of elastic stress increment in an embodiment of the present invention;

[0028] Figure 7 This is a flowchart illustrating the calculation of stress after plastic correction in an embodiment of the present invention;

[0029] Figure 8 The diagram shows the calculated stress (dynamic stress in the X direction) after plastic correction in an embodiment of the present invention.

[0030] Figure 9 The diagram shows the calculated stress (Z-axis dynamic stress) after plastic correction in this embodiment of the invention.

[0031] Figure 10 The diagram shows the calculated stress (equivalent stress) after plastic correction in the embodiments of the present invention.

[0032] Figure 11 This is a flowchart illustrating the calculation of residual stress in an embodiment of the present invention;

[0033] Figure 12 The figure shows the calculation results of the residual stress in the X direction in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described 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 implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationships, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should fall within the scope of the technical content disclosed in the present invention. It should be noted that in this specification, relational terms such as "first" and "second" are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0036] This invention provides an embodiment:

[0037] like Figures 1 to 12 As shown, this invention provides a method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation. The calculation process of this invention consists of four parts: contact mechanics, elasticity mechanics, plasticity mechanics, and internal stress balance, including the following steps:

[0038] S1: Select the area of ​​the workpiece to be predicted and select several sampling points within the area to be predicted to construct multiple sets of blank three-dimensional arrays, and treat the blank three-dimensional arrays as equivalent to the area to be predicted; the blank three-dimensional arrays are used to store the stress data of the sampling points. Strain data and plastic strain data The transformation process is simulated through operations between arrays.

[0039] Specifically, the region to be predicted is a local area at and below the workpiece surface, and the size of the region to be predicted is... ; Select an interval of in the region to be predicted. Several sampling points, stress data of the sampling points stored in a blank three-dimensional array. Strain data and plastic strain data The order of the array in the array satisfies:

[0040]

[0041] These are the length, width, and height of the prediction region, respectively. These are the array orders corresponding to the length, width, and height of the prediction region, respectively; The interval between adjacent sampling points.

[0042] In this embodiment, a size of [size missing] was selected. The workpiece surface and the local area below it are taken as the research object, based on the interval. Sampling points were selected, and a three-dimensional blank array was constructed to store the stress data. Strain data Plastic strain data ,like Figure 2 As shown.

[0043] S2: Construct an EDEM simulation model for tumbling finishing and extract the contact information between the particulate medium and the workpiece in the simulation. The contact information includes the relative velocity and overlap between the particulate medium and the workpiece at the moment of contact. Based on the contact information, the contact model in the EDEM simulation model, and the differential cyclic iteration method, calculate the maximum overlap of the collision during the contact process between the particulate medium and the workpiece. Divide the collision stages based on the maximum overlap and simulate the step-by-step loading process during the collision of the particulate medium. The contact model in the EDEM simulation model is the Hertz-Mindlin contact model, which is a model for calculating interparticle contact force.

[0044] In this embodiment, the following is constructed: Figure 3 The EDEM discrete element simulation model shown is a numerical model of a particle system constructed based on the discrete element method. The particle medium material is alumina, and its relevant parameters are shown in Table 1; the workpiece material is TC4, and its relevant parameters are shown in Table 2; the container material is nylon, and its relevant parameters are shown in Table 3; finally, the contact parameters and motion parameters between the particle medium and the workpiece are set, as shown in Table 4. Figure 3 middle , These represent the vibration frequency and amplitude, respectively. The sphere represents the granular medium, the square block above the sphere represents the workpiece, the shell outside the granular medium and the workpiece represents the container, and the square platform below the container is the vibration table.

[0045] The preset parameters in the EDEM simulation model include: particulate medium parameters, workpiece parameters, container parameters, particulate medium-container contact parameters, and vibration parameters; the particulate medium parameters include the density, elastic modulus, Poisson's ratio, and diameter of the particulate medium; the workpiece and container parameters both include density, elastic modulus, and Poisson's ratio; the particulate medium-container contact parameters and vibration parameters include the collision recovery coefficient, friction coefficient, vibration frequency, and amplitude between the particulate medium and the workpiece; the three-dimensional model in the EDEM simulation model includes three-dimensional models of the workpiece and the container.

[0046] Table 1. Parameters of Particulate Media

[0047]

[0048] Table 2 Workpiece Parameters

[0049]

[0050] Table 3 Container Parameters

[0051]

[0052] Table 4 Contact parameters and vibration parameters between particulate media and container

[0053]

[0054] By extracting the relative velocity between the particulate medium and the workpiece at the instant of contact in the simulation. With overlap Based on contact information, the Hertz-Mindlin contact model, and the differential cyclic iterative method, the maximum collision overlap during the contact process between particulate media and the workpiece is calculated. The calculation process is as follows: Figure 4 As shown.

[0055] The steps for calculating the maximum collision overlap during the contact process between particulate media and workpiece based on contact information, the Hertz-Mindlin contact model, and the differential cyclic iterative method are as follows:

[0056] S221: Determine the initial conditions for the iterative loop operation:

[0057]

[0058]

[0059] In the formula, This represents the initial overlap between the particulate medium and the workpiece during the iterative calculation. The initial relative velocity between the particulate medium and the workpiece; , These represent the relative velocity and overlap between the particulate medium and the workpiece at the instant of contact, extracted from EDEM simulation.

[0060] S222: Set the loop iteration termination condition: In the formula, This is the threshold for relative velocity convergence in iterative loop operations. For the first k The relative velocity between the particulate medium and the workpiece at the instant of contact corresponding to the iteration step;

[0061] S223: Perform iterative loops; where the first... k The calculation of the iteration step is as follows:

[0062]

[0063]

[0064]

[0065] In the formula, For differentiation operations; For particulate media mass; It is the elastic force coefficient; It is the inelastic force coefficient; For the first k The amount of overlap between the particulate medium and the workpiece at the instant of contact corresponding to the iteration step;

[0066] S224: When the iteration termination condition is met, output the maximum overlap of collisions between the particulate medium and the workpiece. In the formula, This represents the maximum overlap during collisions. The curve showing the evolution of overlap over time throughout the entire collision cycle in the particulate medium is obtained, as shown below. Figure 5 As shown, E in the coordinate system represents powers of 10.

[0067] Maximum overlap of collisions Divided into N The system uses equidistant stages to simulate the progressive loading process during particle collisions, with each stage having an incremental overlap. satisfy: .

[0068] S3: Calculate the contact stress distribution corresponding to the overlap at different collision stages using Hertzian contact theory;

[0069] The contact stress distribution at each stage is calculated based on the overlap increments at each stage of the collision process and Hertzian contact theory; Contact stress distribution at each stage The calculation formula is:

[0070]

[0071]

[0072]

[0073] In the formula, Contact stress; The distance from the point of application to the center of contact; This represents the maximum contact stress. The contact radius; Where the particle radius is; It is the equivalent elastic modulus; For the increment of overlap, The value represents the level of the collision phase, taking values ​​of Any integer in the range.

[0074] S4: Based on the contact stress distribution and the Boussinesq equation, calculate the elastic stress field distribution of the region to be predicted under the contact load at different collision stages, and transform the elastic stress field distribution into an incremental form of elastic loading stress; the Boussinesq equation is a class of nonlinear partial differential equations used to simulate shallow water wave motion.

[0075] like Figure 6 As shown, the steps for calculating the elastic stress field distribution of the region to be predicted under contact loads at different collision stages include: obtaining the point of application on the workpiece surface using the Boussinesq equation. any point under concentrated load Developed elastic stress , The coordinates of the points where the loads act on the workpiece surface are located; the elastic stress generated by the loads at each point of contact stress is then distributed along the contact area. By performing integral calculations, the elastic stress field distribution under contact load is obtained. :

[0076]

[0077] Subtracting the elastic stress field of each stage from the previous stage transforms it into an incremental form of elastic loading stress. :

[0078]

[0079] S5: Accumulate the elastic loading stress step by step, and perform plastic correction on the elastic stress at each collision stage using the radial regression method, while simultaneously calculating the cumulative value of plastic deformation; such as Figure 7 As shown, the specific steps are as follows:

[0080] S521: Calculate the test stress based on the elastic loading stress, and convert the test stress into a deviatoric stress form:

[0081] Calculate the test stress :

[0082]

[0083] Transform it into the form of deviatoric stress:

[0084]

[0085] In the formula, The deviatoric stress component of the test stress; For the summation of normal stresses for the stress tensor; It is a second-order unit tensor;

[0086] S522: Determine whether the yield condition is met. The parameters of the workpiece material hardening model are shown in Table 5:

[0087]

[0088]

[0089] In the formula, For tensor 2-norm operations; For material hardening model; Equivalent plastic strain; A This represents the initial yield strength. B It is the strain hardening modulus; The strain hardening index is denoted as .

[0090] Table 5. Parameters of the workpiece material hardening model

[0091]

[0092] If the yield condition is not met, then the deviatoric stress components of the stress at each stage are equal to the deviatoric stress components of the test stress at the corresponding stage, and the plastic strain at each stage is equal to the plastic strain at the previous stage, as shown in the following formula:

[0093]

[0094]

[0095] In the formula, For the deviatoric stress component of the stress, Plastic strain;

[0096] The stress at each stage after plastic correction is calculated based on the deviatoric stress components and the test stress at each stage, using the following formula:

[0097]

[0098] In the formula, For stress.

[0099] If the yield condition is met, proceed to the next step of calculating the plastic strain increment.

[0100] S523: Solving the consistency condition equations using the Newton-Raphson method Calculate the plastic strain increment The cumulative value of plastic deformation is obtained by summing the plastic strain increments at each collision stage.

[0101]

[0102] In the formula, Shear modulus of the workpiece; This represents the plastic strain increment.

[0103] S524: Calculate the stress after plastic correction With plastic strain The calculation results are as follows Figure 8 , Figure 9 , Figure 10 As shown, the calculation formula is as follows:

[0104]

[0105]

[0106]

[0107] .

[0108] S6: After loading, activate the elements in the blank 3D array whose cumulative plastic deformation value is greater than zero, and use the Galerkin vector method to calculate the internal stress distribution under the cumulative action of all activated elements, thereby obtaining the residual strain and residual stress in the region to be predicted. The Galerkin vector method is a semi-analytical numerical method in elasticity based on a vector potential function.

[0109] The calculation process for residual stress and residual strain is as follows: Figure 11 As shown, statistical plastic strain data Plastic deformation elements with a value greater than 0 are identified and marked as active states. The Galerkin vector method is then used to calculate the plastic deformation elements for any active state. At the sampling point The generated internal strain :

[0110]

[0111]

[0112] In the formula, This is the Galerkin vector method function; This is a relative position vector.

[0113] The residual strain is obtained by accumulating the internal strain generated by the plastic deformation unit; the formula for calculating the residual strain is:

[0114] In the formula, This represents residual strain; This is the Galerkin vector method function;

[0115] The residual stress is calculated using the generalized Hooke's law, and the formula for calculating the residual stress is as follows:

[0116]

[0117] In the formula, This is residual stress; , These are the workpiece's elastic modulus and Poisson's ratio, respectively. This represents the normal strain component in the residual strain; This is the Kronecker operator. The calculation results are as follows: Figure 12 As shown.

[0118] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation, characterized in that, Includes the following steps: Select the area to be predicted of the workpiece and select sampling points in the area to be predicted to construct multiple sets of blank three-dimensional arrays, and convert the blank three-dimensional arrays into the area to be predicted; The blank three-dimensional array is used to store stress data, strain data, and plastic strain data of the sampling points, and the deformation process is simulated through operations between the arrays; An EDEM simulation model of the tumbling finishing process is constructed, and the contact information between the particulate medium and the workpiece is extracted in the simulation. The contact information includes the relative velocity and overlap between the particulate medium and the workpiece at the moment of contact. Based on the contact information, the contact model in the EDEM simulation model, and the differential cyclic iteration method, the maximum overlap of the collision between the particulate medium and the workpiece is calculated, and the collision stages are divided based on the maximum overlap of the collision to simulate the step-by-step loading process in the collision process of the particulate medium. The contact stress distribution corresponding to the overlap at different collision stages was calculated using Hertzian contact theory. Based on the contact stress distribution and the Boussinesq equation, the elastic stress field distribution of the region to be predicted under the contact load at different collision stages is calculated, and the elastic stress field distribution is transformed into an incremental form of elastic loading stress. The elastic loading stress is accumulated step by step, and the elastic stress of each collision stage is plastically corrected by radial regression method. The plastic strain increment of the stage is calculated, and the cumulative value of plastic deformation is obtained by accumulating the plastic strain increment of each collision stage. After loading, the elements with cumulative plastic deformation values ​​greater than zero in the blank three-dimensional array are activated, and the internal stress distribution under the cumulative action of all activated elements is calculated using the Galerkin vector method to obtain the residual strain and residual stress in the region to be predicted.

2. The method for predicting residual stress in rolling finishing based on elastoplastic deformation theory according to claim 1, characterized in that: In the blank three-dimensional array, the array order corresponding to the length of the region to be predicted is the ratio of the length of the region to be predicted to the interval of adjacent sampling points plus one; the array order corresponding to the width of the region to be predicted is the ratio of the width of the region to be predicted to the interval of adjacent sampling points plus one; and the array order corresponding to the width of the region to be predicted is the ratio of the height of the region to the interval of adjacent sampling points plus one.

3. The method for predicting residual stress in rolling finishing based on elastoplastic deformation theory according to claim 1, characterized in that: The steps for calculating the maximum collision overlap during the contact process between particulate media and the workpiece, based on contact information, the contact model in the EDEM simulation model, and the differential cyclic iterative method, are as follows: The relative velocity and overlap between the particulate medium and the workpiece at the instant of contact, extracted from EDEM simulation, are used as the initial conditions for iterative calculations; the... The relative velocity between the particulate medium and the workpiece at the instant of contact corresponding to the iteration step is less than the threshold of relative velocity convergence in the cyclic iteration operation, which is used as the termination condition of the cyclic iteration operation. Perform iterative updates on the relative velocity and overlap between the particulate medium and the workpiece at the moment of contact until the termination condition of the iterative operation is met. Output the overlap between the particulate medium and the workpiece at the moment of contact corresponding to the current iteration step as the maximum overlap of the collision during the contact process between the particulate medium and the workpiece.

4. The method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation according to claim 3, characterized in that: The maximum overlap of the collision is divided into The system uses equidistant stages to simulate the progressive loading process during particle collision, thus obtaining the overlap of each stage during the collision process. The contact stress distribution at each stage is calculated based on the overlap at each stage of the collision process and Hertzian contact theory.

5. The method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation according to claim 4, characterized in that: The steps for calculating the elastic stress field distribution of the region to be predicted under contact loads at different collision stages include: obtaining the elastic stress generated at any point on the workpiece surface under concentrated loads using the Boussinesq equation; and integrating the elastic stress generated by the loads at each contact stress point along the contact region to obtain the elastic stress field distribution under contact loads. The step of converting the elastic stress field distribution into incremental elastic loading stress includes: subtracting the elastic stress field of each stage from the elastic stress field of the previous stage to convert it into incremental elastic loading stress.

6. The method for predicting residual stress in rolling finishing based on elastoplastic deformation theory according to claim 5, characterized in that: The step of plastically correcting the elastic stress at each collision stage using the radial regression method includes: The test stress of the corresponding stage is calculated based on the elastic loading stress of each stage and the stress of the previous stage, and the test stress is converted into the deviatoric stress component of the test stress. Determine whether the yield condition is met. If not, the deviatoric stress component of the stress at each stage is equal to the deviatoric stress component of the test stress at the corresponding stage, and the plastic strain at each stage is equal to the plastic strain at the previous stage. Calculate the stress at each stage after plastic correction based on the deviatoric stress component of the stress at each stage and the test stress. If the condition is met, perform the following operations: solve the consistency condition equation using the Newton-Raphson method to calculate the plastic strain increment; calculate the plastic strain at each stage after plastic correction based on the deviatoric stress component of the test stress at each stage, the strain at the previous stage, and the plastic strain increment; obtain the deviatoric stress component of the stress at the corresponding stage based on the deviatoric stress component of the test stress at each stage and the plastic strain increment; calculate the stress at each stage after plastic correction based on the deviatoric stress component of the stress at each stage and the test stress.

7. The method for predicting residual stress in rolling finishing based on the theory of elastic-plastic deformation according to claim 6, characterized in that: The steps for obtaining the residual strain and residual stress of the region to be predicted include: In the blank three-dimensional array storing plastic strain data, cells with a cumulative plastic deformation value greater than zero are counted and marked as active. The Galerkin vector method was used to calculate the internal strain generated at the sampling points of all activated elements; The residual strain is obtained by summing the internal strains generated by all activated elements. The residual stress is calculated using the generalized Hooke's law and the residual strain.

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