Spatial reconstruction method for internal residual stress distribution of epoxy composite insulator

Abstract

The invention provides a spatial reconstruction method for internal residual stress distribution of an epoxy composite insulator, which is characterized in that according to a test result of internal ultrasonic longitudinal wave sound velocity of a test piece, shrinkage rate calculation meeting sound velocity distribution of the test piece is realized through an inversion algorithm and an elastic mechanics theory, and internal residual stress distribution of the test piece is constructed. The method can realize efficient evaluation of the internal residual stress of the test piece. The invention provides an inversion method for calculating the internal stress through the ultrasonic sound velocity of the material for the first time, and the residual stress distribution in the test piece can be effectively evaluated.

Description

Technical Field

[0001] The present invention belongs to the field of insulation stress measurement of gas-insulated transmission lines, and in particular relates to a method for spatially reconstructing residual stress distribution inside an epoxy composite insulation component. Background Art

[0002] Gas-insulated transmission lines (GILs) are metal-encapsulated transmission equipment widely used in power systems due to their high reliability, strong environmental adaptability, and lack of secondary pollution. The insulators widely used in GILs primarily serve as insulation and support, and their insulation performance largely determines the safety and stability of the GILs. However, with the widespread application of GILs in power transmission and transformation projects, the failure rate of GIL equipment has far exceeded expectations, with insulation-induced failures being particularly prominent. Stress concentration and internal defects are the main causes of GIL insulator failures. Stress concentration is a key factor in defect formation, and defects in turn promote stress concentration. The two interact, directly inducing local discharge and abnormal heating in insulators, accelerating material degradation, and affecting the normal operation of insulators.

[0003] Therefore, exploring effective insulator stress detection methods and achieving efficient and accurate insulator stress detection are of great significance for preventing insulator mechanical failure, avoiding insulation faults, and ensuring the safe and reliable operation of GIL equipment. Currently, mechanical tests are commonly used to test the mechanical properties of test specimens. However, mechanical tests can only assess whether the test specimens pass a certain limit, and cannot measure the residual stress distribution within the test specimens or determine whether the stress is concentrated. When using physical testing methods, the measured data usually only reflects the residual stress on the surface of the insulator, and cannot accurately obtain the residual stress distribution within the insulator. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention provides a spatial reconstruction method for the residual stress distribution inside an epoxy composite insulation part, using a cube specimen cast from epoxy / alumina composite material as a model to realize the detection of the residual stress distribution of the workpiece.

[0005] The technical solution of the present invention is a method for spatially reconstructing the residual stress distribution inside an epoxy composite insulation component, comprising the following steps:

[0006] Step 1: Perform uniaxial loading tests on the test specimens made of epoxy resin / alumina composite materials to obtain the required material parameters, including the following parameters: (1) acoustoelastic coefficients in parallel and perpendicular directions; (2) material sound velocity at zero stress; (3) strains in parallel and perpendicular directions under different stresses;

[0007] Step 2: Prepare the epoxy composite material specimen to be tested, establish a finite element model of the specimen to be tested, and mesh the model;

[0008] Step 3: Define the shrinkage rate of epoxy / alumina composite materials during the curing process as λ. The residual stress generated at different locations inside the specimen can be regarded as caused by the different shrinkage rates of the material at different locations during curing. Based on the relationship between the longitudinal wave sound velocity and the normal stress in the parallel and perpendicular directions in formula (1), the corresponding relationship between the shrinkage rate and the sound velocity is established as shown in formula (2):

[0009]

[0010] In formula (1), K || and K ⊥ are the parallel and perpendicular acoustoelastic coefficients respectively; v0 is the longitudinal wave speed of the material under zero stress; v is the longitudinal wave speed of the material under stress;

[0011] In formula (2), is the average sound velocity distribution matrix of the specimen; S l×n is the sensitivity matrix, obtained by the finite element method; λ n×m is the specimen shrinkage distribution matrix;

[0012] Step 4: Measure the internal sound velocity of the epoxy / alumina composite material to be tested by ultrasonic testing method, and construct the average sound velocity distribution matrix in formula (2) based on the sound velocity measurement results at different positions;

[0013] Step 5: Establish the stress field control equation to describe the stress distribution during the curing process of epoxy composite materials. The residual stress generated at different locations inside the specimen can be regarded as caused by the different shrinkage rates of the material at different locations during curing. For the microelement, the stress tensor including normal stress and shear stress shown in formula (3) is used to describe its stress state:

[0014]

[0015] σ ii is the normal stress acting in the i direction, τ ij is the shear stress acting on plane i along direction j. By solving equation (4), the principal stresses are arranged according to the magnitude of the obtained solution (σ1, σ2, σ3):

[0016]

[0017] Based on the static equilibrium equation, for any specimen, when the stress distribution in the x, y, and z directions is measured, the corresponding shear stress and principal stress can be determined;

[0018] Step 6: Establish a spatial distribution inversion algorithm to invert the residual stress distribution inside the specimen;

[0019] Step 7: Set the shrinkage range, initial shrinkage distribution matrix, optimization tolerance, and maximum number of model solutions for the algorithm model. Use the inversion algorithm proposed in step 6 to iterate and solve until the tolerance between the sound velocity distribution of the specimen under the iterated shrinkage distribution and the experimentally measured sound velocity distribution meets the set conditions.

[0020] Step 8: Substitute the shrinkage rate distribution into the stress field control equation in step 5 to obtain the residual stress distribution inside the sample under the shrinkage rate.

[0021] During the curing process of epoxy composite materials, the shrinkage rate is continuously distributed. For formula (2), after the sensitivity matrix and the shrinkage rate distribution matrix are known, the sound velocity distribution matrix can be uniquely determined. By continuously iterating the shrinkage rate, the reconstructed sound velocity matrix satisfies the conditions and an approximate shrinkage rate distribution matrix is obtained, which is expressed by formula (5) as follows:

[0022] find λ∈[λ min ,λ max ]

[0023]

[0024] Where λ min is the minimum value of the defined shrinkage rate, λ max is the maximum value of the defined shrinkage rate; is the average sound velocity distribution matrix constructed from the measurement results, C ref is the normalization coefficient; S is the specimen volume; Ω represents the calculation domain;

[0025] The algorithm steps are as follows:

[0026] (1) At the beginning of the algorithm process, set the initial interval [λ min ,λ max ], construct the initial shrinkage rate distribution matrix;

[0027] (2) According to formula (2), the constructed shrinkage distribution matrix is compared with the sensitivity matrix S obtained by the finite element method. 1×n Multiply to get the average sound velocity distribution matrix, and substitute it into formula (6) for calculation:

[0028]

[0029] Where e is the set tolerance. When the calculated result is less than or equal to e, proceed to the next step. If it is greater than e, it is necessary to use an iterative algorithm to iterate the shrinkage distribution matrix and then return to the judgment.

[0030] (3) After completing the judgment in the previous step, it is necessary to determine whether the current shrinkage rate range has reached the optimal value. When formula (7) is satisfied, the shrinkage rate distribution matrix at this time is output:

[0031]

[0032] Where ε is the set tolerance. When the condition is not met, the shrinkage range is iterated again through formula (8), and then the previous step is returned to make a judgment until the condition is met. The shrinkage distribution matrix at this time is output:

[0033]

[0034] The parameters of the epoxy / alumina composite material in step 1 may vary depending on the filler formulation and process used in the preparation of the material.

[0035] The epoxy / alumina composite material test pieces in step 2 include a basin type and a three-pillar type, and the geometric shapes of the longitudinal wave speed inside the test pieces are detected.

[0036] The ultrasonic testing method in step 4 includes an ultrasonic longitudinal wave penetration method and an ultrasonic reflection wave method to obtain the propagation speed of the ultrasonic longitudinal wave inside the test piece.

[0037] The stress distribution described in step 5 includes stress forms such as normal stress, shear stress, and principal stress.

[0038] In the inversion algorithm process (2) established in step 6, the algorithm for iterating the shrinkage rate matrix includes a genetic algorithm and a particle swarm algorithm.

[0039] Beneficial effects:

[0040] The present invention realizes the reconstruction of the residual stress field inside the test piece based on the spatial distribution inversion algorithm and elastic mechanics calculation, and can detect the residual stress inside the test piece more efficiently and accurately.

[0041] The present invention is combined with a physical testing method, and an algorithm model that can describe the residual stress distribution inside the epoxy / alumina composite material specimen is constructed by inverting the ultrasonic longitudinal wave speed data inside the specimen measured by the ultrasonic testing method.

[0042] Based on the test results of the longitudinal wave sound velocity inside the epoxy / alumina composite material specimen, the present invention uses a spatial distribution inversion algorithm to calculate the shrinkage rate that meets the longitudinal wave sound velocity distribution inside the specimen, and constructs the residual stress distribution inside the specimen based on elastic mechanics calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flow chart of the method of the present invention;

[0044] Figure 2 This is the material calibration experiment result diagram of the present invention

[0045] Figure 3 This is a physical picture of the test piece of the present invention;

[0046] Figure 4 It is an experimental schematic diagram of the present invention;

[0047] Figure 5 is a flow chart of the inversion algorithm of the present invention;

[0048] Figure 6 This is a diagram showing the inversion results of the residual stress distribution inside the sample of the present invention. DETAILED DESCRIPTION

[0049] The present invention is further described below in conjunction with the accompanying drawings.

[0050] refer to Figure 1 This is a spatial reconstruction method for the internal residual stress distribution of epoxy composite insulation components. The method is based on the inversion of the internal residual stress of the epoxy / alumina composite material specimen based on the ultrasonic penetrating longitudinal wave sound velocity. The specific steps include:

[0051] Step 1: Perform uniaxial loading test on the test specimen using epoxy resin / alumina composite material to obtain the required material parameters, including the following parameters: (1) acoustic elastic coefficient in parallel and perpendicular directions; (2) material sound velocity under zero stress; (3) strain in parallel and perpendicular directions under different stresses. The calibration results are as follows: Figure 2 As shown;

[0052] Step 2: Prepare the epoxy / alumina composite material specimen to be tested, such as Figure 3 As shown, a finite element model of the test piece is established and the model is meshed;

[0053] Step 3: Define the shrinkage rate of epoxy / alumina composite materials during the curing process as λ. The residual stress generated at different locations inside the specimen can be regarded as caused by the different shrinkage rates of the material at different locations during curing. Based on the relationship between the longitudinal wave sound velocity and the normal stress in the parallel and perpendicular directions in formula (1), the corresponding relationship between the shrinkage rate and the sound velocity is established as shown in formula (2):

[0054]

[0055] In formula (1), K || and K ⊥ are the parallel and perpendicular acoustoelastic coefficients respectively; v0 is the longitudinal wave speed of the material under zero stress; v is the longitudinal wave speed of the material under stress;

[0056] In formula (2), is the average sound velocity distribution matrix of the specimen; S 1×n is the sensitivity matrix, obtained by the finite element method; λ n×m is the specimen shrinkage distribution matrix;

[0057] Step 4: Measure the internal sound velocity of the epoxy / alumina composite material to be tested by ultrasonic testing. Based on the sound velocity measurement results at different positions, construct the average sound velocity distribution matrix in formula (2). The experimental schematic diagram is shown in the figure: Figure 4 As shown;

[0058] Step 5: Establish the stress field control equation to describe the stress distribution during the curing process of epoxy composite materials. The residual stress generated at different locations inside the specimen can be regarded as caused by the different shrinkage rates of the material at different locations during curing. For the microelement, the stress tensor including normal stress and shear stress shown in formula (3) is used to describe its stress state:

[0059]

[0060] σ ii is the normal stress acting in the i direction, τ ij is the shear stress acting on plane i along direction j. By solving equation (4), the principal stresses are arranged according to the magnitude of the obtained solution (σ1, σ2, σ3):

[0061]

[0062] Based on the static equilibrium equation, for any specimen, when the stress distribution in the x, y, and z directions is measured, the corresponding shear stress and principal stress can be determined;

[0063] Step 6: Establish a spatial distribution inversion algorithm to invert the residual stress distribution inside the specimen. During the curing process of epoxy composite materials, the shrinkage rate is continuously distributed; for formula (2), after the sensitivity matrix and the shrinkage rate distribution matrix are known, the sound velocity distribution matrix can be uniquely determined; and when the sound velocity distribution matrix and the sensitivity matrix are known, since the sensitivity matrix is not in the form of a square matrix, it cannot be inverted, and n>l, so the shrinkage rate can only be continuously iterated so that the reconstructed sound velocity matrix meets the conditions to obtain an approximate shrinkage rate distribution matrix, which is the main goal of the inversion algorithm. The algorithm flow is as follows Figure 5 As shown, it can be specifically expressed by formula (5):

[0064] find λ∈[λ min ,λ max ]

[0065]

[0066] Where λ min is the minimum value of the defined shrinkage rate, λ max is the maximum value of the defined shrinkage rate; is the average sound velocity distribution matrix constructed from the measurement results, C ref is the normalization coefficient; S is the specimen volume; Ω represents the calculation domain.

[0067] (1) At the beginning of the algorithm process, set the initial interval [λ min ,λ max ], construct the initial shrinkage rate distribution matrix;

[0068] (2) According to formula (2), the constructed shrinkage distribution matrix is compared with the sensitivity matrix S obtained by the finite element method. 1×n Multiply to get the average sound velocity distribution matrix, and substitute it into formula (6) for calculation:

[0069]

[0070] Where e is the set tolerance. If the calculated result is less than or equal to e, proceed to the next step. If it is greater than e, it is necessary to iterate the shrinkage distribution matrix using an iterative algorithm and then return to the judgment.

[0071] (3) After completing the judgment in the previous step, it is necessary to determine whether the current shrinkage rate range has reached the optimal value. When formula (7) is satisfied, the shrinkage rate distribution matrix at this time is output:

[0072]

[0073] Where ε is the set tolerance. When the condition is not met, the shrinkage range is iterated again through formula (8), and then the previous step is returned to make a judgment until the condition is met. The shrinkage distribution matrix at this time is output:

[0074]

[0075] Step 7: Set the shrinkage rate range, initial shrinkage rate distribution matrix, optimization tolerance, and maximum number of model solutions for the algorithm model, and use the inversion algorithm proposed in step 6 to iteratively solve the problem until the tolerance between the sound velocity distribution of the specimen under the iterated shrinkage rate distribution and the experimentally measured sound velocity distribution meets the set conditions.

[0076] Step 8: Substitute the shrinkage rate distribution into the stress field control equation of step 5 to obtain the residual stress distribution inside the sample under the shrinkage rate. The result is as follows: Figure 6 shown.

[0077] It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive. Therefore, the present invention includes but is not limited to the embodiments described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of the present invention also fall within the scope of protection of the present invention.

Claims

1. A method for spatial reconstruction of residual stress distribution inside epoxy composite insulation, characterized in that: The steps include: Step 1: Perform uniaxial loading tests on the test specimens made of epoxy resin / alumina composite materials to obtain the required material parameters, including the following parameters: (1) acoustoelastic coefficients in parallel and perpendicular directions; (2) material sound velocity at zero stress; (3) strains in parallel and perpendicular directions under different stresses; Step 2: Prepare the epoxy composite material specimen to be tested, establish a finite element model of the specimen to be tested, and mesh the model; Step 3: Define the shrinkage rate of epoxy / alumina composite materials during the curing process as λ. The residual stress generated at different locations inside the specimen can be regarded as caused by the different shrinkage rates of the material at different locations during curing. Based on the relationship between the longitudinal wave sound velocity and the normal stress in the parallel and perpendicular directions in formula (1), the corresponding relationship between the shrinkage rate and the sound velocity is established as shown in formula (2): In formula (1), K || and K ⊥ are the parallel and perpendicular acoustoelastic coefficients respectively; v0 is the longitudinal wave speed of the material under zero stress; v is the longitudinal wave speed of the material under stress; In formula (2), is the average sound velocity distribution matrix of the specimen; S l×n is the sensitivity matrix, obtained by the finite element method; λ n×m is the specimen shrinkage distribution matrix; Step 4: Measure the internal sound velocity of the epoxy / alumina composite material to be tested by ultrasonic testing method, and construct the average sound velocity distribution matrix in formula (2) based on the sound velocity measurement results at different positions; Step 5: Establish the stress field control equation to describe the stress distribution during the curing process of epoxy composite materials. The residual stress generated at different locations inside the specimen can be regarded as caused by the different shrinkage rates of the material at different locations during curing. For the microelement, the stress tensor including normal stress and shear stress shown in formula (3) is used to describe its stress state: σ ii is the normal stress acting in the i direction, τ ij is the shear stress acting on plane i along direction j. By solving equation (4), the principal stresses are arranged according to the magnitude of the obtained solution (σ1, σ2, σ3): Based on the static equilibrium equation, for any specimen, when the stress distribution in the x, y, and z directions is measured, the corresponding shear stress and principal stress can be determined; Step 6: Establish a spatial distribution inversion algorithm to invert the residual stress distribution inside the specimen; Step 7: Set the shrinkage range, initial shrinkage distribution matrix, optimization tolerance, and maximum number of model solutions for the algorithm model. Use the inversion algorithm proposed in step 6 to iterate and solve until the tolerance between the sound velocity distribution of the specimen under the iterated shrinkage distribution and the experimentally measured sound velocity distribution meets the set conditions. Step 8: Substitute the shrinkage rate distribution into the stress field control equation in step 5 to obtain the residual stress distribution inside the sample under the shrinkage rate.

2. The method according to claim 1, characterized in that During the curing process of epoxy composite materials, the shrinkage rate is continuously distributed. For formula (2), after the sensitivity matrix and the shrinkage rate distribution matrix are known, the sound velocity distribution matrix can be uniquely determined. By continuously iterating the shrinkage rate, the reconstructed sound velocity matrix satisfies the conditions and an approximate shrinkage rate distribution matrix is obtained, which is expressed by formula (5) as follows: findλ∈[λ min ,l max ] Where λ min is the minimum value of the defined shrinkage rate, λ max is the maximum value of the defined shrinkage rate; is the average sound velocity distribution matrix constructed from the measurement results, C ref is the normalization coefficient; S is the specimen volume; Ω represents the calculation domain; The algorithm steps are as follows: (1) At the beginning of the algorithm process, set the initial interval [λ min ,λ max ], construct the initial shrinkage rate distribution matrix; (2) According to formula (2), the constructed shrinkage distribution matrix is compared with the sensitivity matrix S obtained by the finite element method. l×n Multiply to get the average sound velocity distribution matrix, and substitute it into formula (6) for calculation: Where e is the set tolerance. When the calculated result is less than or equal to e, proceed to the next step. If it is greater than e, it is necessary to use an iterative algorithm to iterate the shrinkage distribution matrix and then return to the judgment. (3) After completing the judgment in the previous step, it is necessary to determine whether the current shrinkage rate range has reached the optimal value. When formula (7) is satisfied, the shrinkage rate distribution matrix at this time is output: Where ε is the set tolerance. When the condition is not met, the shrinkage range is iterated again through formula (8), and then the previous step is returned to make a judgment until the condition is met. The shrinkage distribution matrix at this time is output:

3. The method according to claim 1, characterized in that The parameters of the epoxy / alumina composite material in step 1 may vary depending on the filler formulation and process used in the preparation of the material.

4. The method according to claim 1, wherein The epoxy / alumina composite material test pieces in step 2 include a basin type and a three-pillar type, and the geometric shapes of the longitudinal wave speed inside the test pieces are detected.

5. The method according to claim 1, wherein The ultrasonic testing method in step 4 includes an ultrasonic longitudinal wave penetration method and an ultrasonic reflection wave method to obtain the propagation speed of the ultrasonic longitudinal wave inside the test piece.

6. The method according to claim 1, characterized in that The stress distribution described in step 5 includes stress forms such as normal stress, shear stress, and principal stress.

7. The method according to claim 1, characterized in that In the inversion algorithm process (2) established in step 6, the algorithm for iterating the shrinkage rate matrix includes a genetic algorithm and a particle swarm algorithm.

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