Fast solution method for volume coefficient matrix in residual stress field inference and application

Abstract

The application provides a volume coefficient matrix fast solving method for residual stress field deduction and application, and relates to the technical field of material stress measurement and characterization. The method comprises the following steps: step S1: calculating the unconstrained node sub-stiffness matrix inverse matrix of the initial state of a part; step S2: calculating the unconstrained node sub-stiffness matrix change caused by material removal of the part at each step; step S3: calculating the unconstrained node sub-stiffness matrix inverse matrix of the part at each step; step S4: calculating the volume coefficient matrix of the part at each step; and step S5: assembling the volume coefficient matrix of the part at each step into a volume coefficient matrix. The method solves residual stress by using the volume coefficient matrix in residual stress field deduction. The application significantly improves the calculation efficiency of the volume coefficient matrix, and effectively solves the problem of low calculation efficiency of the volume coefficient matrix in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material stress measurement and characterization, in particular to a volume coefficient matrix fast solving method for residual stress field inference and application. BACKGROUND

[0002] Under the background of rapid development of aerospace technology, the new generation of aircraft structural parts are developing towards more complex and more precise, and the manufacturing cycle is required to be shortened day by day, which puts forward higher requirements on the processing quality. However, the workpiece needs to go through heat treatment, machining and other processes in the manufacturing process, which inevitably produces residual stress in the blank. Residual stress will have a significant impact on machining accuracy, material strength, dimensional stability and fatigue resistance of parts, and may even cause deformation or failure of the workpiece. Therefore, accurately evaluating the residual stress field distribution and optimizing the processing technology have become the key link to improve the processing quality of parts, and also the focus of current manufacturing research.

[0003] After searching the existing technical documents, it is found that patent document CN114154364A discloses an initial residual stress field inference method based on deformation force. The method uses the influence of the unbalanced stress field in the non-cutting state under the equivalent clamping constraint of the deformation force on the deformation trend, and establishes the mechanical relationship between a series of deformation forces monitored in multiple non-cutting states and the residual stress field according to the virtual work principle, that is, (wherein, represents the volume coefficient matrix; represents the residual stress, represents the deformation force). The method is an effective means to infer the residual stress field. However, the calculation of the volume coefficient matrix, which is a key parameter for inferring the residual stress from the deformation force, completely depends on finite element simulation, resulting in low calculation efficiency and difficulty in meeting the needs of engineering applications.

[0004] Therefore, there is an urgent need for an innovative method that can significantly improve the calculation efficiency of the volume coefficient matrix to overcome the limitations of existing technology. SUMMARY

[0005] The purpose of the present application is to provide a volume coefficient matrix fast solving method for residual stress field inference and application, which can solve the problem of low calculation efficiency of the volume coefficient matrix in the prior art and reduce the calculation time.

[0006] To achieve the above-mentioned purpose, the present application provides a volume coefficient matrix fast solving method for residual stress field inference, which comprises the following steps:

[0007] Step S1: calculating the inverse matrix of the non-constrained node sub-stiffness matrix of the initial state of the part;

[0008] Step S2: Calculate the change in the sub-stiffness matrix of the unconstrained nodes caused by the material removal of the parts in each process step;

[0009] Step S3: Calculate the inverse matrix of the unconstrained node sub-stiffness matrix of each step part;

[0010] Step S4: Calculate the volume coefficient matrix of the parts in each process step;

[0011] Step S5: Assemble the volume coefficient matrices of the parts in each process step into a volume coefficient matrix.

[0012] Preferably, in step S3, the specific expression of the inverse matrix of the unconstrained node sub-stiffness matrix of each step part is:

[0013] ;

[0014] ;

[0015] in, Indicates the The overall stiffness matrix of the work step; Indicates the Unconstrained node sub-stiffness matrix of the work step parts; Indicates the Unconstrained-constrained node sub-stiffness matrix of the work step part; Indicates the Constrained-unconstrained node sub-stiffness matrix of the work step parts; Indicates the The constraint node sub-stiffness matrix of the work step parts; represents the identity matrix; Indicates the The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the The change in the stiffness matrix of the unconstrained nodes caused by the material removal of the work step parts; Indicates the number of work steps.

[0016] Preferably, in step S3,

[0017] Based on the idea of ​​block matrix, through elementary row transformation, Convert to upper triangular matrix , the specific expression is:

[0018] ;

[0019] in, express The number of rows of the block matrix composed of non-zero elements in .

[0020] Accordingly, through the conversion The same elementary row transformation will Convert to , the specific expression is:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] in, Indicates the first The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the first -1 Inverse matrix of the non-constrained node stiffness matrix of the step part; express The block sub-matrix of ; express The block sub-matrix of ; Represents the row block index, ; Represents the column block index, ; The number of rows is , The number of rows and columns is based on Perform calculations; represents transpose;

[0026] Finally, through the conversion The opposite elementary row transformation will Transform again to get .

[0027] Preferably, in step S4, the specific expression of the volume coefficient matrix of the parts in each process step is:

[0028] ;

[0029] in, Indicates the The sub-geometry matrix corresponding to the work step constraint node; Indicates the The sub-geometry matrix corresponding to the non-constrained nodes of the work step; Indicates the Volume coefficient matrix of process step parts.

[0030] Preferably, in step S5, the specific expression of assembling the volume coefficient matrix of the parts in each process step into the volume coefficient matrix is:

[0031] ;

[0032] in, represents the volume coefficient matrix.

[0033] The present invention also provides an application of the above-mentioned method for quickly solving the product coefficient matrix in residual stress field inference, using the volume coefficient matrix to solve the residual stress. The specific expression is:

[0034] ;

[0035] in, represents residual stress; Indicates deformation force.

[0036] Therefore, the present invention adopts the above-mentioned method and application for quickly solving the volume coefficient matrix for residual stress field inference, and the beneficial technical effects are as follows:

[0037] The present invention reduces the dimension of matrix inversion in the process of solving the volume coefficient matrix through block matrix inversion and iterative update algorithm, significantly improves the calculation efficiency of the volume coefficient matrix, and effectively solves the problem of low calculation efficiency of the volume coefficient matrix in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is the parts model drawing;

[0039] Figure 2 It is the finite element model diagram of some working steps; among them, Figure 2 (a) is the finite element model of the second step; Figure 2 (b) is the finite element model of the 5th step; Figure 2 (c) is the finite element model of the 10th step; Figure 2 (d) is the finite element model of the 16th step;

[0040] Figure 3 Comparison chart of residual stress results;

[0041] Figure 4 The present invention provides a flow chart of a method for quickly solving a volume coefficient matrix for residual stress field inference and its application. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0043] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0044] Example 1

[0045] like Figure 1 As shown in the figure, the part selected in this embodiment is a rectangular blank of aluminum alloy with a length of 32 mm, a width of 16 mm, and a height of 20 mm, and its material density is 2830 kg / m 3 , Young's modulus is 71.7 GPa, and Poisson's ratio is 0.33.

[0046] Three fixed constraint points were selected at the bottom of the part and fixed constraints were applied to simulate fixed clamping. Spring element points in the z direction were set at the four corners of the part to simulate the constraints of the deformation force monitoring device on the workpiece and obtain deformation force data.

[0047] The part is divided into 2mm grids and 16 areas are selected as material removal areas. A material removal operation is performed in each process step. The material removal process of each process step is simulated by the function of ABAQUS finite element software. After completing the boundary condition setting, the finite element model file in inp format is exported. The finite element model of some process steps is as follows: Figure 2 As shown. Among them, Figure 2 (a) is the finite element model of the second step; Figure 2 (b) is the finite element model of the 5th step; Figure 2 (c) is the finite element model of the 10th step; Figure 2 (d) in the figure is the finite element model of the 16th process step.

[0048] Based on the finite element model, the following data were extracted: .

[0049] in, Indicates the The overall stiffness matrix of the work step; Indicates the The sub-geometry matrix corresponding to the work step constraint node; Indicates the The sub-geometry matrix corresponding to the non-constrained nodes of the work step; , Indicates the number of work steps.

[0050] like Figure 4 As shown, the present invention proposes a method for quickly solving the volume coefficient matrix for residual stress field inference, comprising the following steps:

[0051] Step S1: According to the node constraints, the overall stiffness matrix is ​​divided into four sub-stiffness matrices. The specific expression is:

[0052] ;

[0053] wherein, denotes the non-constrained node sub-stiffness matrix of the part in the step i; denotes the non-constrained-constrained node sub-stiffness matrix of the part in the step i; denotes the constrained-non-constrained node sub-stiffness matrix of the part in the step i; denotes the constrained node sub-stiffness matrix of the part in the step i.

[0054] The non-constrained node sub-stiffness matrix of the part in the initial state is calculated by the non-constrained node sub-stiffness matrix of the part in the initial state , and the non-constrained node sub-stiffness matrix inverse matrix of the part in the initial state is calculated by the non-constrained node sub-stiffness matrix of the part in the initial state .

[0055] Step S2: The non-constrained node sub-stiffness matrix change amount caused by the material removal of the part in each step is calculated, and the specific expression is as follows:

[0056] ;

[0057] wherein, denotes the non-constrained node sub-stiffness matrix change amount caused by the material removal of the part in the step i.

[0058] In the embodiment, .

[0059] Step S3: The non-constrained node sub-stiffness matrix inverse matrix of the part in each step is calculated, and the specific expression is as follows:

[0060] ;

[0061] wherein, denotes the non-constrained node sub-stiffness matrix inverse matrix of the part in the step i; denotes the non-constrained node sub-stiffness matrix inverse matrix of the part in the step i. Based on the block matrix idea, the non-constrained node sub-stiffness matrix inverse matrix

[0062] is converted into an upper triangular matrix by elementary row transformation, and the specific expression is as follows:

[0063] ;

[0064] wherein, denotes the ​The number of rows of the block matrix composed of non-zero elements in .

[0065] Accordingly, through the conversion The same elementary row transformation will Convert to , the specific expression is:

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] in, Indicates the first The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the first -1 Inverse matrix of the non-constrained node stiffness matrix of the step part; express The block sub-matrix of ; express The block sub-matrix of ; Represents the row block index, ; Represents the column block index, ; The number of rows is , The number of rows and columns is based on Perform calculations; Indicates transpose.

[0071] Finally, through the conversion The opposite elementary row transformation will Transform again to get .

[0072] Step S4: Calculate the volume coefficient matrix of the parts in each process step. The specific expression is:

[0073] ;

[0074] in, Indicates the The sub-geometry matrix corresponding to the work step constraint node; Indicates the The sub-geometry matrix corresponding to the non-constrained nodes of the work step; Indicates the Volume coefficient matrix of process step parts.

[0075] Step S5: Assemble the volume coefficient matrices of the parts in each process step into a volume coefficient matrix. The specific expression is:

[0076] ;

[0077] in, represents the volume coefficient matrix.

[0078] The volume coefficient matrix was calculated using a computer with an Intel(R) Core(TM) i7-9700F processor and 16GB of memory. The traditional inversion method took 817.5 seconds to calculate the volume coefficient matrix, while the method of the present invention took only 433 seconds, with a 47% improvement in computational efficiency. This strongly demonstrates that the method of the present invention has significant advantages in improving the efficiency of volume coefficient matrix calculation.

[0079] Monitor the deformation force data of parts in real time during the processing of parts, and solve the residual stress based on the solved volume coefficient matrix The specific expression is:

[0080] ;

[0081] in, represents residual stress; Indicates deformation force.

[0082] The part is divided into 10 layers along the thickness direction, and residual stress (including residual stress in the x-direction and residual stress in the y-direction) is preset in each layer. The residual stress of the part is solved based on the method of the present invention, and the obtained residual stress result is compared with the preset residual stress. The comparison results are as follows: Figure 3 The mean absolute error of the residual stress inference in the x-direction is 4.3 MPa, and the mean absolute error of the residual stress inference in the y-direction is 2.6 MPa. These comparisons demonstrate the excellent prediction accuracy of the proposed method, verifying its effectiveness and reliability in residual stress field inference.

[0083] Therefore, the present invention adopts the above-mentioned method and application of rapid solution of volume coefficient matrix for residual stress field inference. Through an innovative matrix operation solution method, while ensuring the calculation accuracy, it significantly improves the calculation efficiency of the volume coefficient matrix, and effectively solves the problem of low calculation efficiency of the volume coefficient matrix in the existing technology.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for quickly solving the volume coefficient matrix for residual stress field inference, characterized in that: The following steps are involved: Step S1: Calculate the inverse matrix of the non-constrained node sub-stiffness matrix of the initial state of the part; Step S2: Calculate the change in the sub-stiffness matrix of the unconstrained nodes caused by the material removal of the parts in each process step; Step S3: Calculate the inverse matrix of the unconstrained node sub-stiffness matrix of each step part; Step S4: Calculate the volume coefficient matrix of the parts in each process step; Step S5: Assemble the volume coefficient matrices of the parts in each process step into a volume coefficient matrix; In step S3, the specific expression of the inverse matrix of the unconstrained node sub-stiffness matrix of each step part is: ； ； in, Indicates the The overall stiffness matrix of the work step; Indicates the Unconstrained node sub-stiffness matrix of the work step parts; Indicates the Unconstrained-constrained node sub-stiffness matrix of the work step part; Indicates the Constrained-unconstrained node sub-stiffness matrix of the work step parts; Indicates the The constraint node sub-stiffness matrix of the work step parts; represents the identity matrix; Indicates the The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the The change in the stiffness matrix of the unconstrained nodes caused by the material removal of the work step parts; Indicates the number of work steps.

2. A method for rapidly solving a volume coefficient matrix for residual stress field inference according to claim 1, characterized in that: In step S3, Based on the idea of ​​block matrix, through elementary row transformation, Convert to upper triangular matrix , the specific expression is: ； in, express The number of rows of the block matrix composed of non-zero elements in ; Accordingly, through the conversion The same elementary row transformation will Convert to , the specific expression is: ； ； ； ； in, Indicates the first The inverse matrix of the non-constrained node stiffness matrix of the work step parts; Indicates the first The inverse matrix of the non-constrained node stiffness matrix of the work step parts; express The block sub-matrix of ; express The block sub-matrix of ; Represents the row block index, ; Represents the column block index, ; The number of rows is , The number of rows and columns is based on Perform calculations; represents transpose; Finally, through the conversion The opposite elementary row transformation will Transform again to get .

3. A method for rapidly solving the volume coefficient matrix for residual stress field inference according to claim 2, characterized in that: In step S4, the specific expression of the volume coefficient matrix of the parts in each process step is: ； in, Indicates the The sub-geometry matrix corresponding to the work step constraint node; Indicates the The sub-geometry matrix corresponding to the non-constrained nodes of the work step; Indicates the Volume coefficient matrix of process step parts.

4. A method for rapidly solving a volume coefficient matrix for residual stress field inference according to claim 3, characterized in that: In step S5, the volume coefficient matrix of each step part is assembled into a specific expression of the volume coefficient matrix: ； in, represents the volume coefficient matrix.

5. An application of the method for quickly solving the volume coefficient matrix according to any one of claims 1 to 4 in residual stress field inference, characterized in that: The volume coefficient matrix is ​​used to solve the residual stress. The specific expression is: ； in, represents residual stress; Indicates deformation force.

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