Spatial reconstruction method for residual stress distribution in epoxy composite insulation

Abstract

The application provides a spatial reconstruction method for residual stress distribution in an epoxy composite insulating part. According to the test result of ultrasonic longitudinal wave speed in the test piece, the shrinkage rate calculation meeting the speed distribution is realized through an inversion algorithm and an elasticity theory, and the residual stress distribution in the test piece is constructed. The method can realize efficient evaluation of the residual stress in the test piece. The inversion method for calculating the internal stress of the material through the ultrasonic speed is first proposed, and the residual stress distribution in the test piece can be effectively evaluated.

Description

Technical Field

[0001] This invention belongs to the field of insulation stress measurement of gas-insulated transmission lines, and specifically relates to a spatial reconstruction method for the internal residual stress distribution of epoxy composite insulation components. Background Technology

[0002] Gas-insulated transmission lines (GILs) are metal-encased transmission equipment widely used in power systems due to their high reliability, strong environmental adaptability, and lack of secondary pollution. Insulators, widely used in GILs, primarily serve insulation and support functions, and their insulation performance largely determines the safety and stability of the GIL. 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-related failures being particularly prominent. Stress concentration and internal defects are important causes of GIL insulator failures. Stress concentration is a significant factor in defect formation, and defects, in turn, promote stress concentration; the two interact, directly inducing phenomena such as partial discharge and abnormal heating in the insulator, accelerating material degradation, and affecting the normal operation of the insulator.

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

[0004] To overcome the shortcomings of the prior art, this invention provides a spatial reconstruction method for the internal residual stress distribution of epoxy composite insulation components. Using a cube specimen cast from epoxy / alumina composite material as a model, the invention enables the detection of the residual stress distribution of the workpiece.

[0005] The technical solution of this invention is a spatial reconstruction method for the internal residual stress distribution of an epoxy composite insulator, comprising the following steps:

[0006] Step 1: Conduct a uniaxial loading test on the test specimen using epoxy resin / alumina composite material to obtain the required material parameters, including the following parameters: (1) acoustoelastic coefficients in the parallel and perpendicular directions; (2) sound velocity of the material under zero stress; (3) strain in the 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, and mesh the model;

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

[0009]

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

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

[0012] Step 4: The internal sound velocity of the epoxy / alumina composite test piece is measured by ultrasonic testing. Based on the sound velocity measurement results at different locations, the average sound velocity distribution matrix in equation (2) is constructed.

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

[0014]

[0015] σ ii τ is the normal stress acting in the i direction. ij To express the shear stress acting in the i-plane along the j-direction, we solve equation (4) and arrange the principal stresses according to the magnitude of the solutions (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 solution iterations for the algorithm model. Use the inversion algorithm proposed in Step 6 to iteratively solve the problem until the tolerance between the specimen sound velocity distribution under the iterated shrinkage distribution and the experimentally measured sound velocity distribution reaches the set condition.

[0020] Step 8: Substitute the shrinkage distribution into the stress field control equation from Step 5 to obtain the residual stress distribution inside the sample at that shrinkage rate.

[0021] During the curing process of epoxy composite materials, the shrinkage rate is continuously distributed. For equation (2), after knowing the sensitivity matrix and the shrinkage rate distribution matrix, the sound velocity distribution matrix can be uniquely determined. By continuously iterating the shrinkage rate, the reconstructed sound velocity matrix satisfies the condition, thereby obtaining an approximate shrinkage rate distribution matrix, which is expressed by equation (5):

[0022] find λ∈[λ min , λ max ]

[0023]

[0024] In the formula, λ min λ is the defined minimum shrinkage rate. max The maximum shrinkage rate as defined; C is the average sound speed distribution matrix constructed from the measurement results. ref Ω represents the normalization coefficient; S is the specimen volume; Ω represents the computational domain.

[0025] The algorithm steps are as follows:

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

[0027] (2) According to equation (2), the constructed shrinkage distribution matrix and the sensitivity matrix S obtained by the finite element method are compared. 1×n Multiplying the matrices yields the average sound speed distribution matrix, which is then substituted into equation (6) for calculation:

[0028]

[0029] In the formula, e is the set tolerance. When the calculation 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 rate distribution matrix, and then return to make a judgment.

[0030] (3) After completing the previous step, it is also necessary to determine whether the shrinkage rate range has reached its optimum; when equation (7) is satisfied, the shrinkage rate distribution matrix at this time is output:

[0031]

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

[0033] .

[0034] The parameters of the epoxy / alumina composite material in step one will change depending on the filler formulation and process during material preparation.

[0035] The epoxy / alumina composite material specimens in step two include basin-shaped and three-pillar-shaped specimens, and the geometry of their internal longitudinal wave velocity was detected.

[0036] The ultrasonic testing method in step four includes ultrasonic longitudinal wave penetration method and ultrasonic reflection wave method to obtain the propagation speed of ultrasonic longitudinal wave inside the specimen.

[0037] The stress distribution described in step five includes the stress forms of normal stress, shear stress, and principal stress.

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

[0039] Beneficial effects:

[0040] This invention reconstructs the internal residual stress field of a specimen based on a spatial distribution inversion algorithm and elasticity calculations, enabling more efficient and accurate detection of internal residual stress in the specimen.

[0041] This invention combines physical testing methods and constructs an algorithmic model that can describe the distribution of residual stress inside epoxy / alumina composite material specimens by inverting the ultrasonic longitudinal wave velocity data inside the specimens obtained by ultrasonic testing methods.

[0042] This invention is based on the test results of the longitudinal wave velocity inside the epoxy / alumina composite material specimen. It uses a spatial distribution inversion algorithm to calculate the shrinkage rate that satisfies the longitudinal wave velocity distribution inside the specimen, and constructs the residual stress distribution inside the specimen based on elasticity calculations. Attached Figure Description

[0043] Figure 1 This is a flowchart of the method of the present invention;

[0044] Figure 2 This is a diagram showing the material calibration test results of the present invention.

[0045] Figure 3 This is a photograph of the test specimen of the present invention;

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

[0047] Figure 5 This is a flowchart 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 Implementation

[0049] The present invention will be further described in detail below with reference to 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, based on the inversion of the longitudinal wave velocity through ultrasonic penetration to retrieve the internal residual stress of epoxy / alumina composite material specimens. The method specifically includes the following steps:

[0051] Step 1: A uniaxial loading test was conducted on the test specimen using epoxy resin / alumina composite material to obtain the required material parameters, including the following parameters: (1) acoustoelastic coefficients in the parallel and perpendicular directions; (2) sound velocity of the material under zero stress; (3) strain in the 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 λ during the curing process of epoxy / alumina composite material. The residual stress generated at different locations inside the specimen can be regarded as being caused by the different shrinkage rates at different locations during material curing. Based on the relationship between longitudinal wave velocity and normal stress in the parallel and perpendicular directions in equation (1), establish the correspondence between shrinkage rate and sound velocity shown in equation (2):

[0054]

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

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

[0057] Step 4: The internal sound velocity of the epoxy / alumina composite test piece is measured using ultrasonic testing. Based on the sound velocity measurement results at different locations, the average sound velocity distribution matrix in equation (2) is constructed. The experimental schematic diagram is shown below. 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 material. The residual stress generated at different locations inside the specimen can be regarded as being caused by the different shrinkage rates at different locations during material curing. For the micro-element, the stress tensor containing normal stress and shear stress shown in equation (3) is used to describe its stress state:

[0059]

[0060] σ ii τ is the normal stress acting in the i direction. ij To express the shear stress acting in the i-plane along the j-direction, we solve equation (4) and arrange the principal stresses according to the magnitude of the solutions (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 Six: 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 equation (2), after knowing the sensitivity matrix and the shrinkage rate distribution matrix, the sound velocity distribution matrix can be uniquely determined; however, 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. Therefore, it is only possible to obtain an approximate shrinkage rate distribution matrix by iterating the shrinkage rate continuously, so that the reconstructed sound velocity matrix satisfies the conditions. This is the main goal of the inversion algorithm. The algorithm flow is as follows: Figure 5 As shown, it can be specifically expressed by equation (5):

[0064] find λ∈[λ min , λ max ]

[0065]

[0066] In the formula, λ min λ is the defined minimum shrinkage rate. max The maximum shrinkage rate as defined; C is the average sound speed distribution matrix constructed from the measurement results. ref Ω represents the normalization coefficient; S is the specimen volume; Ω represents the computational domain.

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

[0068] (2) According to equation (2), the constructed shrinkage distribution matrix and the sensitivity matrix S obtained by the finite element method are compared. 1×n Multiplying the matrices yields the average sound speed distribution matrix, which is then substituted into equation (6) for calculation:

[0069]

[0070] In the formula, e is the set tolerance. When the calculation 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 make a judgment.

[0071] (3) After completing the previous step, it is also necessary to determine whether the shrinkage rate range has reached its optimum; when equation (7) is satisfied, the shrinkage rate distribution matrix at this time is output:

[0072]

[0073] In the formula, ε is the set tolerance. When this condition is not met, the shrinkage rate range is iterated again by formula (8), and then the previous step is returned to make a judgment until the condition is met. Then the shrinkage rate 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 solution iterations for the algorithm model. Use the inversion algorithm proposed in Step 6 to iteratively solve the problem until the tolerance between the specimen sound velocity distribution under the iterated shrinkage rate distribution and the experimentally measured sound velocity distribution reaches the set condition.

[0076] Step 8: Substitute the shrinkage distribution into the stress field governing equation from Step 5 to obtain the residual stress distribution inside the sample at that shrinkage rate. The results are as follows: Figure 6 As shown.

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

Claims

1. A spatial reconstruction method of the internal residual stress distribution of an epoxy composite insulator, characterized in that, Comprising the following steps: Step one: uniaxial loading test is conducted on the test specimen with epoxy / alumina composite material, and the required material parameters are obtained, including the following parameters: (1) the acoustic-elastic coefficients in parallel and vertical directions; (2) the material acoustic velocity under zero stress; (3) the strain in parallel and vertical directions under different stresses; Step two: prepare the epoxy composite specimen to be tested, and establish the finite element model of the test specimen, and perform mesh partitioning on the model; Step three: define the shrinkage rate of the epoxy / alumina composite material during the curing process as λ, and the residual stress generated at different positions in the test specimen can be regarded as being caused by the different shrinkage rates at different positions of the material during curing, and according to the relationship between the longitudinal wave acoustic velocity and the normal stress in the parallel and vertical directions in formula (1), the corresponding relationship between the shrinkage rate and the acoustic velocity is established as shown in formula (2): In formula (1), K || and K ⊥ are the parallel and perpendicular acoustic-elastic coefficients, respectively; v0is the longitudinal wave acoustic speed of the material under zero stress; and v is the longitudinal wave acoustic speed of the material under stress. In formula (2), S is the average sound velocity distribution matrix of the test piece; S l×n is the sensitivity matrix, which is obtained by the finite element method; λ n×m is the shrinkage distribution matrix of the test piece; Step four: measure the internal acoustic velocity of the epoxy / alumina composite test specimen by ultrasonic testing method, and based on the acoustic velocity measurement results at different positions, the average acoustic velocity distribution matrix in formula (2) is constructed; Step five: establish a stress field control equation for describing the stress distribution in the curing process of the epoxy composite material, and the residual stress generated at different positions in the test specimen can be regarded as being caused by the different shrinkage rates at different positions of the material during curing, and for a micro-element, the stress tensor containing the 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 in the j direction on the i plane, by solving equation (4), the principal stresses are arranged in the order of the magnitude of the solution (σ1, σ2, σ3): Based on the static equilibrium equation, for any test sample, when the stress distribution in x, y, and z directions is measured, the corresponding shear stress and principal stress can be determined; Step six: establish a spatial distribution inversion algorithm for inverting the residual stress distribution in the test specimen; Step seven: set the shrinkage rate range, initial shrinkage rate distribution matrix, and optimization tolerance and maximum number of model solutions for the algorithm model, and iteratively solve by using the inversion algorithm proposed in step six until the tolerance between the acoustic velocity distribution of the test specimen under the iteratively obtained shrinkage rate distribution and the experimentally measured acoustic velocity distribution reaches the set condition; Step eight: substitute the shrinkage rate distribution into the stress field control equation in step five to obtain the residual stress distribution in the test sample under the shrinkage rate.

2. The method of claim 1, wherein, In the curing process of the epoxy composite material, the shrinkage rate is continuously distributed, and for formula (2), after the sensitivity matrix and the shrinkage rate distribution matrix are known, the acoustic velocity distribution matrix can be uniquely determined; by continuously iterating the shrinkage rate, the reconstructed acoustic velocity matrix satisfies the condition to obtain the approximate shrinkage rate distribution matrix, which is represented by formula (5): find λ ∈ [λ min , λ max ] where λ min is the minimum defined shrinkage, λ max is the maximum defined shrinkage; is the average sound velocity distribution matrix constructed from the measurement results, C ref is the normalization coefficient; S is the volume of the test piece; Ω represents the calculation domain; The algorithm steps are as follows: (1) At the beginning of the algorithm flow, set the initial interval [λ min , λ max ] and construct the initial shrinkage rate distribution matrix; (2) According to formula (2), the constructed shrinkage rate distribution matrix is multiplied with the sensitivity matrix S obtained by the finite element method l×n to obtain the average sound velocity distribution matrix, which is substituted into formula (6) for calculation: In the formula, e is the set tolerance, when the calculation result is less than or equal to e, enter the next step; if it is greater than e, the shrinkage rate distribution matrix needs to be iterated by using the iteration algorithm, and then return to the judgment; (3) After completing the judgment of the above step, it is also necessary to judge whether the shrinkage rate range at this time has reached the optimum; when formula (7) is satisfied, the shrinkage rate distribution matrix at this time is output: In the formula, ε is the set tolerance, when the condition is not satisfied, the shrinkage rate range is iterated again by formula (8), and then returned to the previous step for judgment until the condition is satisfied, and the shrinkage rate distribution matrix at this time is output: 。 3. The method of claim 1, wherein, The parameters of the epoxy / alumina composite material in step one will change with the filler formula and process during material preparation.

4. The method of claim 1, wherein, The epoxy / alumina composite material test piece in step two includes a basin type and a three-column type, and the internal longitudinal wave velocity is detected according to the geometry.

5. The method of claim 1, wherein, The ultrasonic detection method in step four includes ultrasonic longitudinal wave penetration and ultrasonic reflection wave method to obtain the propagation velocity of ultrasonic longitudinal wave in the test piece.

6. The method of claim 1, wherein, The stress distribution described in step five includes normal stress, shear stress and principal stress.

7. The method of claim 1, wherein, In the inversion algorithm flow (2) established in step six, the iteration shrinkage rate matrix algorithm includes genetic algorithm and particle swarm algorithm.

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