A method for measuring stress distribution of tempered glass insulators

Abstract

A method for measuring the stress distribution of tempered glass insulators, comprising: based on the glass viscoelasticity theory, using CFD software to simulate the fluid field and transient temperature field in the tempering cooling, importing the temperature field results into FEA software, and solving the residual stress field in combination with the generalized Maxwell model. Selecting the disk-shaped area of ​​the insulator, using a photoelastic stress measurement device to obtain stress data, and comparing with the simulation results to verify the reliability of the model. Based on the verified model, the overall residual stress distribution of the insulator is output, and the high tensile stress concentration area is identified. According to the stress distribution, the cooling process parameters are adjusted, and the simulation prediction is re-performed and verified through photoelastic measurement to achieve iterative process optimization. The method of the present invention deeply integrates numerical simulation and experimental measurement to form a closed-loop optimization process, which can more comprehensively and accurately grasp the stress distribution of tempered glass insulators, thereby effectively overcoming the limitations of the existing technology and achieving precise guidance and optimization of the tempering process.

Description

Technical Field

[0001] The present invention relates to a manufacturing and detection technology of a tempered glass insulator in the field of power transmission and transformation, and in particular to a stress distribution measurement method of a tempered glass insulator. Background Art

[0002] Glass insulators are widely used in transmission lines due to their "zero-value self-destruction" characteristics, long lifespan, and excellent insulation performance. However, the problem of self-destruction of tempered glass insulators is becoming increasingly prominent, especially in large-tonnage insulators, seriously impacting the safe and stable operation of power grids. One of the main causes of self-destruction is stress concentration caused by impurities within the glass (such as nickel sulfide and aluminum sulfide). When the combined internal tensile stress and defect stress exceed the intrinsic strength of the glass, rupture occurs.

[0003] Traditional stress testing methods for tempered glass, such as photoelastic testing, are primarily used to detect the risk of self-explosion in flat architectural glass. However, glass insulators have complex geometries, varying wall thicknesses in different areas, and significant curvature. The varying thicknesses at different locations, and the significant curvature at the corners between the head and the disc, result in a far more complex internal stress distribution than that of flat glass. Existing methods often lack mature defect detection methods for insulators. Manufacturers' factory inspections are often destructive and rely on manual experience, lacking standardized data support, resulting in poor test consistency. Traditional flat glass stress distribution models cannot simply be applied to the complex stress fields of glass insulators.

[0004] Currently, research on the mechanism of self-explosion in glass insulators, particularly on residual stress distribution, remains insufficient. Although numerical simulation methods have been used to simulate the tempering process and obtain residual stress distributions, and the simulation results can be verified using photoelastic methods, existing photoelastic measurement equipment (such as the SCALP series stress analyzers) has limitations when measuring complex structures like insulators. Their measurement depth and measurable area are limited, limited to the disc-shaped, quasi-flat plate, and the measurement depth does not exceed 5 mm. This means that photoelastic methods alone cannot fully capture stress information across the entire insulator's size and thickness. Therefore, a method that combines the advantages of simulation and measurement to more comprehensively and accurately determine the stress distribution of tempered glass insulators is urgently needed, which can guide the optimization of the tempering process.

[0005] It should be noted that the information disclosed in the above background technology section is only used to understand the background of this application, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0006] The main purpose of the present invention is to overcome the defects existing in the above-mentioned background technology and provide a method for measuring stress distribution of tempered glass insulators.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A stress distribution measurement method for a tempered glass insulator based on a combination of simulation and measurement includes the following steps:

[0009] S1. Based on the viscoelasticity theory of glass, computational fluid dynamics (CFD) software was used to simulate the fluid field and transient temperature field of the insulator during the tempering cooling process. The temperature field results were then imported into finite element analysis (FEA) software. Combined with the time-varying laws of material properties and structural relaxation effects described by the generalized Maxwell model, the residual stress field distribution was solved.

[0010] S2. Select a measurable disc-shaped area in the insulator and obtain surface and thickness stress data using a photoelastic stress measurement device. Compare and verify the data with the simulation results of the corresponding area. When the error does not exceed the set threshold, the reliability of the simulation model is confirmed.

[0011] S3. Based on the verified simulation model, output the residual stress distribution of the entire insulator, including the disc and head, and identify the areas of high tensile stress concentration;

[0012] S4. Adjust the cooling process parameters based on the stress distribution results, re-simulate and predict the optimization effect, and verify the actual sample through photoelastic measurement to achieve an iterative optimization closed loop of the tempering process.

[0013] Furthermore, in step S1, simulating the fluid field and the transient temperature field of the insulator during the tempering cooling process includes:

[0014] Set differential pressure boundary conditions for the upper and lower wind grids;

[0015] The non-uniform flow field and temperature field are solved by coupling the fluid continuity equation, Navier-Stokes equation and energy equation;

[0016] The non-uniform convection heat transfer coefficient on the insulator surface is calculated based on the temperature field results.

[0017] Furthermore, step S1 specifically includes the following fluid-heat-solid coupling numerical simulation:

[0018] Establish a 3D CFD model including the air fluid domain and insulator geometry, set up the turbulence model and non-equilibrium wall function;

[0019] In FEA, the mesh is refined along the thickness of the insulator to capture the temperature gradient, and the accuracy is ensured through mesh independence verification;

[0020] The simple thermorheological characteristics and structural relaxation effect of glass are determined, the fictitious temperature is calculated using the Tool-Narayanaswamy model, and the thermal-mechanical coupled stress field is solved based on the viscoelastic constitutive equation.

[0021] Furthermore, the construction of the viscoelastic constitutive equation includes:

[0022] The generalized Maxwell model is used to describe the time dependence of shear modulus and bulk modulus;

[0023] A temperature offset function is introduced to convert the temperature effect into a scaled time variable;

[0024] The thermal expansion strain is calculated using the fictitious temperature and substituted into the stress integral expression to solve the transient stress.

[0025] Furthermore, the structural relaxation effect is quantified by a fictitious temperature model:

[0026] The fictitious temperature is calculated by integrating the current temperature and the historical temperature;

[0027] Thermal strain is determined by multiplying the difference in liquid / solid thermal expansion coefficients by the change in imaginary temperature.

[0028] Furthermore, in step S2:

[0029] The measurement area is limited to a disc-shaped quasi-flat plate structure, and the measurement depth is ≤5mm;

[0030] Quantitative verification is achieved by comparing the root mean square error of stress curves at multiple points in the thickness direction.

[0031] Furthermore, in step S2, when the error is ≤10%, it is confirmed that the simulation model is reliable.

[0032] Furthermore, the stress distribution identified in step S3 is used to guide the optimization of pressurization parameters for the water pressure test inside the head, and / or to provide a fracture resistance basis for the disc structure design.

[0033] Furthermore, the process optimization in step S4 includes:

[0034] For the high tensile stress concentration area at the connection, the stress peak is reduced by adjusting the nozzle pressure distribution, local cooling intensity or cooling rate;

[0035] The optimized parameters include heating temperature, cooling time and regional differentiated wind pressure.

[0036] Furthermore, the method further comprises the following steps:

[0037] Online monitoring is performed based on the full-scale stress distribution, and the risk of self-explosion is predicted by tracking and identifying stress changes in key areas.

[0038] The present invention has the following beneficial effects:

[0039] The present invention provides a stress distribution measurement method for tempered glass insulators. By combining numerical simulation with photoelastic non-destructive measurement technology, the internal stress distribution of tempered glass insulators can be accurately obtained in full size, thereby guiding the closed-loop control optimization of the tempering process.

[0040] Specifically, the present invention provides a method based on coupled simulation of computational fluid dynamics (CFD) and finite element analysis (FEA) combined with local photoelastic non-destructive measurement. Compared with the existing technology, which relies solely on photoelastic measurement and cannot fully obtain the stress information of complex-shaped insulators, and the simulation results lack comprehensive verification of measured data, the method of the present invention deeply integrates numerical simulation and experimental measurement to form a closed-loop optimization process, which can more comprehensively and accurately grasp the stress distribution of tempered glass insulators, thereby effectively overcoming the limitations of the existing technology and achieving precise guidance and optimization of the tempering process.

[0041] The present invention not only lays the foundation for the study of the self-explosion mechanism of insulators, but also can predict and prevent self-explosion by online monitoring and tracking stress changes in key areas. Experimental results show that the present invention is of great significance to the design and manufacture of glass insulators. For example, based on the method of the present invention, the stress concentration and self-explosion rate at the connection can be reduced by optimizing the cooling process, and the mechanical properties of the insulator can be improved by improving the toughness of the material or adopting local reinforcement technology. It can also provide a basis for the development of an online monitoring system to prevent self-explosion. In short, the present invention provides a powerful means for the study of the self-explosion mechanism of glass insulators, and also provides reliable support for the improvement of the tempering process and the selection of water pressure values ​​for internal water pressure tests.

[0042] Other beneficial effects of the embodiments of the present invention will be further described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The figure is an overall flow chart of the stress distribution measurement method of the tempered glass insulator of the present invention.

[0044] FIG. 2( a ) is a distribution diagram of the maximum principal stress in the disk region along the thickness direction according to an embodiment of the present invention.

[0045] FIG. 2( b ) is a distribution diagram of the maximum principal stress in the disk region along the length direction according to an embodiment of the present invention.

[0046] FIG3( a ) is a distribution diagram of the maximum principal stress in the rib region of an embodiment of the present invention.

[0047] FIG3( b ) is a distribution diagram of the maximum principal stress in the head region according to an embodiment of the present invention.

[0048] FIG4( a ) is a distribution diagram of stress components of the quasi-cylindrical structure in the head region according to an embodiment of the present invention.

[0049] FIG4( b ) is a distribution diagram of stress components at the corners of the head region according to an embodiment of the present invention.

[0050] FIG5( a ) is a comparison diagram of stress measurement results and calculation results corresponding to the left direction in FIG2( a ) according to an embodiment of the present invention.

[0051] FIG5( b ) is a comparison diagram of stress measurement results and calculation results corresponding to the middle direction of FIG2( a ) according to an embodiment of the present invention.

[0052] FIG5( c ) is a comparison diagram of stress measurement results and calculation results corresponding to the right side direction of FIG2( a ) according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following is a detailed description of the embodiments of the present invention. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present invention and its application.

[0054] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element. In addition, connection can be used for both fixing and coupling or communication.

[0055] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0056] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0057] The present invention provides a method for acquiring the stress distribution of tempered glass insulators and optimizing the tempering process. This method deeply integrates numerical simulation with experimental measurement to form a closed-loop optimization process. This method aims to overcome the limitations of the existing technology, such as the inability to fully obtain stress information of complex-shaped insulators by relying solely on photoelastic measurement, and the lack of comprehensive verification of simulation results with measured data, thereby achieving precise guidance and optimization of the tempering process.

[0058] See Figure 1 The embodiment of the present invention provides a stress distribution measurement method for a tempered glass insulator based on a combination of simulation and measurement, comprising the following steps:

[0059] Step S1, fluid-heat-solid coupling numerical simulation: Based on the viscoelasticity theory of glass, the fluid field and the transient temperature field of the insulator during the tempering cooling process are simulated using computational fluid dynamics (CFD) software. The temperature field results are then imported into finite element analysis (FEA) software. Combined with the time-varying laws of material properties and structural relaxation effects described by the generalized Maxwell model, the residual stress field distribution is solved.

[0060] In some embodiments, in step S1, the simulation of the fluid field and the transient temperature field of the insulator during the tempering cooling process includes: setting differentiated pressure boundary conditions for the upper and lower wind grids; solving the non-uniform flow field and temperature field by coupling the fluid continuity equation, the Navier-Stokes equation and the energy equation; and calculating the non-uniform convection heat transfer coefficient of the insulator surface based on the temperature field results.

[0061] In some embodiments, in step S1, the fluid-thermal-solid coupling numerical simulation specifically includes: establishing a three-dimensional CFD model including an air fluid domain and an insulator geometry, setting a turbulence model and a non-equilibrium wall function; in FEA, encrypting the grid along the thickness direction of the insulator to capture the temperature gradient, and ensuring accuracy through grid independence verification; determining the simple thermorheological characteristics and structural relaxation effects of the glass, calculating the fictitious temperature using the Tool-Narayanaswamy model, and solving the thermal-mechanical coupling stress field based on the viscoelastic constitutive equation.

[0062] The construction of the viscoelastic constitutive equation specifically includes: using the generalized Maxwell model to describe the time dependence of the shear modulus and bulk modulus; introducing a temperature offset function to convert the temperature effect into a scaled time variable; calculating the thermal expansion strain through a fictitious temperature, and substituting it into the stress integral expression to solve the transient stress.

[0063] In some embodiments, the structural relaxation effect is quantified by a fictitious temperature model: the fictitious temperature is calculated by integrating the current temperature and the historical temperature; and the thermal strain is determined by multiplying the difference in liquid / solid thermal expansion coefficients by the fictitious temperature change.

[0064] Step S2, photoelastic measurement and simulation verification of key areas: Select a measurable disk-shaped area in the insulator, obtain surface and thickness stress data using a photoelastic stress measurement device, and compare and verify with the simulation results of the corresponding area. When the error does not exceed the set threshold, the reliability of the simulation model is confirmed.

[0065] In some embodiments, the measurement area is limited to a disk-shaped quasi-flat plate structure, and the measurement depth is ≤5 mm; quantitative calibration is achieved by comparing the root mean square error of stress curves at multiple points in the thickness direction.

[0066] In some embodiments, in step S2, the simulation model is confirmed to be reliable when the error is ≤10%.

[0067] Step S3, full-size stress distribution identification: Based on the verified simulation model, the residual stress distribution of the entire insulator, including the disc and the head, is output to identify the high tensile stress concentration area.

[0068] In some embodiments, the identified stress distribution is used to guide the optimization of pressurization parameters during the hydrostatic test inside the head. Furthermore, the identified stress distribution is used to provide a basis for the design of the disk structure to prevent fracture.

[0069] Step S4, closed-loop optimization of the tempering process: adjust the cooling process parameters according to the stress distribution results, re-simulate and predict the optimization effect, and verify the actual sample through photoelastic measurement to form an iterative optimization closed loop.

[0070] In some embodiments, the process optimization in step S4 includes: reducing the stress peak in the high tensile stress concentration area at the connection by adjusting the nozzle pressure distribution, local cooling intensity or cooling rate; the optimization parameters include heating temperature, cooling time and regional differentiated wind pressure.

[0071] In some embodiments, the stress distribution measurement method for tempered glass insulators based on a combination of simulation and measurement further includes: performing online monitoring based on full-size stress distribution, and predicting the risk of self-explosion by tracking and identifying stress changes in key areas.

[0072] The proposed stress distribution measurement method for tempered glass insulators, based on a combination of simulation and measurement, addresses the challenge of accurately obtaining the full-scale stress distribution of complex tempered glass insulators by deeply integrating CFD-FEA fluid-thermal-solid coupled simulation with local photoelastic nondestructive measurement technology. A generalized Maxwell model and structural relaxation effect simulation framework, constructed based on glass viscoelasticity theory, combined with a thickness-direction mesh refinement strategy, achieve high-precision residual stress calculations in irregularly shaped areas, such as the insulator disc and head. Stress data is verified within the measurable disc-shaped area using photoelasticity (e.g., an error of ≤10% verifies model reliability), overcoming the limitation of traditional photoelastic technology limited to flat surfaces and establishing a bidirectional simulation-measurement verification mechanism. Based on the full-scale stress distribution, high tensile stress concentration areas (e.g., a peak of 90 MPa at the joint) are identified to guide the closed-loop optimization of process parameters, such as nozzle pressure distribution and regional differentiated cooling, significantly reducing the risk of spontaneous explosion. This method also provides a scientific basis for studying the mechanism of insulator spontaneous explosion, optimizing internal water pressure test parameters, and developing online monitoring systems, fundamentally improving power grid safety and stability while reducing reliance on destructive testing.

[0073] The following further describes specific embodiments of the present invention, its algorithm examples and experimental verification.

[0074] A stress distribution measurement method for tempered glass insulators is based on coupled computational fluid dynamics (CFD) and finite element analysis (FEA) simulation combined with local photoelastic nondestructive measurement. This method deeply integrates numerical simulation and experimental measurement to form a closed-loop optimization process, which specifically includes the following steps:

[0075] Step 1: Fluid-thermal-solid coupled numerical simulation of the insulator tempering process:

[0076] Based on the viscoelasticity of glass, CFD software is used to accurately calculate the cooling fluid field and insulator temperature field during the tempering process. Specifically, the impact of complex structures such as the insulator disc and head on the cooling airflow path is considered. This includes the phenomenon that protrusions accelerate heat dissipation, while recessed areas may form low-speed zones, leading to heat accumulation and slow cooling.

[0077] The transient temperature field results obtained by CFD calculation are imported into FEA software for thermal-structural coupling analysis to solve the residual stress field distribution generated by the insulator during the tempering cooling process.

[0078] In FEA modeling, special attention is paid to the mesh density along the thickness direction to accurately capture the temperature gradient that is critical to the formation of residual stresses.

[0079] Step 2: Photoelastic measurement and simulation verification of key areas:

[0080] Key areas of the glass insulator that can be measured by photoelastic method and are representative of the risk of self-explosion are selected. Non-destructive measurements are performed using photoelastic stress measurement equipment to obtain stress distribution data in these areas.

[0081] The photoelastic measurement results were compared and verified with the simulation results for the corresponding areas to verify the accuracy and reliability of the simulation model. When the error between the two is within 10%, the simulation model is considered to have high confidence in the full-scale and full-thickness stress distribution of the glass insulator.

[0082] Step 3: Obtain full-size stress distribution and identify key stress concentration areas:

[0083] Based on a simulation model validated with photoelastic measurements, obtain residual stress distribution maps across the entire glass insulator scale, including all complex geometries on the disk and head.

[0084] Step 4: Optimization guidance and verification of tempering process:

[0085] Based on the full-scale stress distribution results obtained, especially the distribution and values ​​of high tensile stress areas and stress concentration points, specific optimization suggestions are made for tempering process parameters (such as heating temperature, cooling rate, nozzle pressure distribution, cooling time, etc.). For example, by optimizing the cooling process, stress concentration at the joint can be reduced.

[0086] Targeted cooling strategies are adjusted to reduce tensile stress peaks in critical high-tensile stress areas.

[0087] The optimized process parameters are used to perform fluid-thermal-solid coupling simulation again to predict the stress distribution under the new process. The insulator samples produced by the new process are verified using the photoelastic method, forming an iterative optimization closed loop until the expected stress distribution and performance indicators are achieved.

[0088] This method provides a basis for subsequent research on the mechanism of insulator self-explosion and supports the development of an online monitoring system to predict and prevent self-explosion by tracking stress changes in key areas.

[0089] In this embodiment, the specific methods of operations such as three-dimensional modeling, simulation analysis, and process optimization are as follows.

[0090] Establishment and meshing of 3D geometric model:

[0091] According to the three-dimensional dimensions of the tempered glass insulator to be tested, an accurate geometric model is established in the CAD software.

[0092] The geometric model was imported into the meshing software, and unstructured meshing was performed on the insulator model. In particular, local mesh refinement was performed in areas with sharp changes in thickness and stress gradients to ensure the accuracy of stress calculations.

[0093] Fluid field and temperature field simulation (CFD):

[0094] In the CFD software, the air fluid domain model in the tempering cooling furnace is established, and the inlet and outlet boundary conditions are set.

[0095] Import the glass insulator model into the fluid domain and set up a coupled heat transfer interface between the glass and air.

[0096] An appropriate turbulence model is used to simulate the fluid field during the cooling process and the transient temperature field inside the glass insulator.

[0097] Stress Field Simulation (FEA):

[0098] The transient temperature field data of glass insulators obtained by CFD simulation is imported into FEA software.

[0099] The material properties are defined according to the viscoelastic theory of glass, including the temporal variation of the shear modulus G and bulk modulus K, which can be described using the generalized Maxwell model.

[0100] Considering the thermorheological simplicity (TS) characteristics and structural relaxation effect of glass, the temperature dependence of material parameters is defined.

[0101] Thermal-mechanical coupling calculations are performed to solve the residual stress distribution of glass insulators caused by internal and external temperature differences and uneven volume shrinkage during the cooling process.

[0102] Photoelastic measurement and simulation verification:

[0103] Prepare the tempered glass insulator sample to be tested and select an area on it suitable for photoelastic measurement.

[0104] The SCALP-05 photoelastic stress measurement device can be used to non-destructively measure surface stress or stress in the thickness direction of a selected area.

[0105] Quantitatively compare the measured stress curve or value with the FEA simulation results, calculate the root mean square error or other evaluation indicators, and evaluate the accuracy of the simulation results.

[0106] Stress distribution analysis and tempering process optimization:

[0107] Once the simulation results were fully verified by photoelastic measurements, the simulation model was used to comprehensively analyze the residual stress distribution in various parts of the insulator, focusing on the areas of maximum tensile stress and stress concentration points.

[0108] Based on the analysis results, for example, if the tensile stress in a certain area is found to be too high, the cooling intensity or cooling rate in that area can be adjusted specifically (such as by changing the nozzle aperture, air flow speed, distance, or increasing the local cooling air volume, etc.) to reduce the tensile stress.

[0109] The optimized process parameters are re-entered into the simulation model for prediction and evaluation of the optimization effect. Multiple simulation-analysis-optimization iterations are performed until the optimal residual stress distribution is achieved.

[0110] Finally, the optimized tempering process parameters are applied to the actual production line, and their effectiveness is verified again through sampling photoelastic measurement or destructive testing.

[0111] Examples and verification results

[0112] Computational fluid dynamics (CFD) software was used to calculate the flow and temperature fields during the glass tempering process. The temperature field results were then imported into finite element analysis (FEA) software for structural analysis to determine the stress field. The simulation model is detailed below.

[0113] According to on-site investigation, the upper air grid pressure of the tempering cooling equipment is 1.4 bar, and the lower air grid pressure is 0.6 bar. According to the basic equations of fluid mechanics, the continuity equation (1) and the Navier-Stokes equation (2) can be obtained.

[0114] (1)

[0115] Where, r is the fluid density, u , v , w are the velocity components in the x, y, and z directions respectively. (2)

[0116] Where, p For pressure, m is the dynamic viscosity, fx is the volume force in the x-direction. The equations for the y- and z-directions are similar.

[0117] The Realizable k-ε model is used as the turbulence model. This model is advantageous for simulating heat transfer phenomena associated with impinging jets while requiring relatively low computational resources. Furthermore, a nonequilibrium wall function is used as the wall function.

[0118] During the tempering process, glass components typically cool rapidly from an initial temperature of approximately 680°C to 300°C within 160 seconds. The tempering process is a three-dimensional transient temperature field problem. To simplify the problem, this paper assumes that the glass has isotropic properties and ignores the heat generated by glass deformation and thermal radiation. Equation (3) is the heat conduction equation:

[0119] (3)

[0120] Where, r gis the density of glass, T is the temperature, is the spatial coordinate ( x , y , z ) and time t function, c p is the specific heat capacity, l is the thermal conductivity of the material.

[0121] Glass is an amorphous material with short-range order and long-range disorder in its atomic arrangement, similar to a liquid but retaining a specific shape like a solid. The temperature at which glass begins to exhibit solid properties during its transition from liquid to solid is called the transition temperature. Tg , which is related to the cooling rate. From the perspective of mechanical response, glass is also a viscoelastic material, and its mechanical properties are related to both temperature and time.

[0122] When a constant shear strain is applied to a viscoelastic material, the ratio of the stress response to the strain is called the shear modulus. This value slowly decreases, a phenomenon known as relaxation. If a constant stress is applied and the corresponding strain changes are observed, the corresponding variable is defined as compliance, and this process is known as creep.

[0123] If the applied stress or strain is a variable, the Boltzmann superposition principle must be introduced to describe the mechanical behavior of linear viscoelastic materials. Combining the definitions of relaxation and creep, the constitutive relation of linear viscoelastic materials can be obtained:

[0124] (4)

[0125] Where, s and P are shear stress and hydrostatic pressure, G and K are the shear and bulk moduli, c and e kk are shear and normal strains, t is the actual time, t ′ is the integral variable, which represents the elapsed time. It can be expressed in tensor form as shown in Equation (5):

[0126] (5)

[0127] in, s ij is the stress tensor, e ij is the deviatoric strain, d ij is the Kronecker symbol.

[0128] The variation of G and K with time t needs to be described by the generalized Maxwell model. The generalized Maxwell model consists of multiple parallel Maxwell units. Each Maxwell unit has its own shear modulus G i and viscosity η i , and the corresponding relaxation time τ i The relationship between the three is given by equation (6):

[0129] (6)

[0130] These parallel elements in the generalized Maxwell model are simultaneously subjected to externally applied stress or strain, as shown in Equation (7):

[0131] (7)

[0132] With the help of Laplace transform, the overall shear modulus and bulk modulus of the generalized Maxwell model can be obtained (8):

[0133] (8)

[0134] Among them, G0 and K0 are the values ​​of G and K at t=0, g i and k i is the normalized value. In fact, g i 、k i and τ i These are exactly the parameters needed to define a viscoelastic material.

[0135] The behavior of linear viscoelastic materials at constant temperature has been described above. However, the tempering process of glass is related to both time and temperature, not just a function of time. In order to more accurately define the nonlinear temperature-dependent viscoelastic properties of glass, glass is considered as a thermorheological simple (TS) material. Therefore, the change of relaxation modulus with time at different temperatures can be expressed by the Arrhenius shift function (9) and the scaled time. x (10) Obtain:

[0136] (9)

[0137] (10)

[0138] Where, T and T ref are the instantaneous temperature and the reference temperature, D is the material coefficient, which depends on the reference temperature T ref After introducing temperature dependence, the viscoelastic constitutive equation under temperature change conditions can be obtained:

[0139] (11)

[0140] (12)

[0141] in, e th is the thermal strain, α is the coefficient of thermal expansion.

[0142] Also expressed in tensor form, the constitutive equation is shown as (13):

[0143] (13)

[0144] Structural relaxation of glass refers to the process by which the internal structure of glass approaches a thermodynamically stable state over time. This phenomenon occurs because glass, as an amorphous material, is not in a thermodynamic equilibrium. Structural relaxation is most evident in the volume of glass decreasing during cooling, indicating an increase in density, which undoubtedly affects the formation of residual stresses in the glass.

[0145] The fictive temperature is a hypothetical temperature used to describe the structural state of glass relative to its thermodynamic equilibrium state. The structural relaxation model, called the Tool-Narayanaswamy (TN) model, describes the structural relaxation of materials under varying temperature conditions. This model uses the fictive temperature as a core variable to describe the behavior of glass under complex thermal histories. The expression for the fictive temperature is:

[0146] (14)

[0147] in, M ( t ) is the response function, obtained experimentally. After obtaining the fictitious temperature using equation (14), the liquid and solid thermal expansion coefficients can be used α 1 and α g , the thermal strain is calculated by equation (15):

[0148] (15)

[0149] To determine the temperature distribution of the glass insulator after tempering and forced convection heat transfer, a three-dimensional CFD model of the glass components was constructed using computational fluid dynamics software for coupled flow-heat analysis. Based on manufacturer information and on-site survey results, the upper air grille pressure was set to 1.4 bar, while the lower air grille pressure was set to 0.6 bar.

[0150] Calculations of the flow and temperature fields during the tempering process reveal significant differences in the cooling rate of different parts of glass insulators. The insulator's structure, such as the disc and head, alters the cooling airflow path. Protruding sections accelerate the airflow, rapidly dissipating heat, while recessed sections obstruct the flow, potentially creating low-velocity areas or eddies that accumulate heat and slow the cooling rate.

[0151] Glass material properties were defined using a finite element analysis subroutine, and coupled thermal-mechanical calculations were performed within the finite element analysis software. Temperature gradients along the thickness are a key factor in the formation of tempered residual stresses, necessitating a sufficient mesh size across the thickness of the insulator. By gradually refining the mesh size (starting with an initial 10 mm), the stress variation was less than 1% when the mesh size was reduced to 2 mm, demonstrating mesh independence. Furthermore, symmetry constraints were set along the x and z axes to limit the calculation to a single quarter of the insulator.

[0152] Based on its structural and thermal properties, the disk can be further divided into a quasi-flat plate portion and a ribbed joint. The cooling rate of the latter is significantly slower than that of the former. When the time reaches 160 seconds, the temperature of the quasi-flat plate portion drops to approximately 100°C, while the temperature of the joint remains around 200°C. The existence of this temperature gradient will affect the distribution of residual stresses. The five labeled arrows in Figures 2(a) and 2(b) indicate the observed directions of maximum principal stresses: three directions along the plate thickness and two directions in the middle layer.

[0153] The head and ribs can be considered as quasi-cylindrical structures. For these areas, the values ​​of the stress components of the head will also be paid attention to in order to provide a reference for the implementation of the internal water pressure test of the head. Figures 3(a) and 3(b) show the maximum principal stress distribution of the ribs and the head along the directions marked by the arrows in the figures, respectively. Figures 4(a) and 4(b) show the components of the stress tensor including s 11 、 s 22 、 s 33 、 s 12 、 s 13 、 s 23 It is worth mentioning that in Figure 4(a) s 12 and s 23 The values ​​are almost equal, so the curves are not clearly distinguished.

[0154] Photoelasticity is one of the effective means of nondestructive testing of tempered glass. It can not only measure surface stress, but also measure the stress distribution in the thickness direction of the glass. However, this method has certain limitations. It can only measure flat glass, and the measurement depth does not exceed 5mm. For glass insulators, only the quasi-flat part of the disk meets the measurement requirements. The present invention selects the three observation directions in Figure 2(a) for photoelastic stress measurement and compares them with the simulation results. Figure 5(a) to Figure 5(c) By comparing the experimental and simulation data, it is found that the two are highly consistent, with the root mean square errors of the three comparisons being 7.916MPa, 7.932MPa, and 11.768MPa, respectively.

[0155] The distribution of residual stress in tempered glass insulators is crucial for understanding their spontaneous explosion mechanism. Experiments show that the maximum tensile stress in the disc region is concentrated in the middle layer, reaching approximately 73 MPa, while the tensile stress at the joints is even higher, at approximately 90 MPa. According to Griffith crack theory, the critical stress for crack propagation is closely related to the fracture toughness of the material. The higher tensile stress at the joints indicates that this area is more susceptible to spontaneous explosion, which is consistent with the high failure rate observed in the field.

[0156] Compared to previous research focused primarily on flat glass, this study comprehensively analyzes the residual stress distribution in complex glass insulators. The results show that despite the non-flat geometry of the head and ribs, the maximum principal stress distribution generally follows a parabolic pattern. The tensile stress in the ribs ranges from 85 to 95 MPa, while the surface compressive stress ranges from 90 to 120 MPa.

[0157] These results demonstrate the significant implications of the method presented in this paper for the design and manufacture of glass insulators. For example, optimizing the cooling process during tempering can reduce stress concentration at the joints, thereby lowering the spontaneous explosion rate. Furthermore, increasing material toughness or employing localized reinforcement techniques can further improve the mechanical properties of insulators. In practical applications, these results can also provide a basis for the development of online monitoring systems that can predict and prevent spontaneous explosions by tracking stress changes in critical areas.

[0158] If the flat glass is regarded as a superposition of thin layers in the thickness direction, with the Z axis representing the thickness direction, then each thin layer is located in the XY plane, and only the normal stress related to the z value exists on it. ,and Cut .

[0159] The stress observation results of the quasi-cylindrical structure of the head are consistent with the above model characteristics: in the observation area, the X axis can be regarded as the thickness direction. Of course, the stress components is not strictly zero, and The shear stress in this area is almost zero (its magnitude is the normal stress one-tenth of the total).

[0160] The stress components at the corners are more complicated. The X axis cannot be considered as the thickness direction, so The value of is no longer close to 0. The value of is close to the maximum principal stress because it can be regarded as the normal stress of the differential surface. In addition, the other two shear stress values ​​at the corners are also approximately zero.

[0161] The internal hydrostatic test is a destructive test that applies water pressure to the head to eliminate inferior insulators. A detailed analysis of the residual stress distribution in the head region provides valuable insights into the mechanical behavior of glass insulators under internal pressure. These findings provide a theoretical basis for optimizing test parameters, such as pressure limit and loading rate, to improve test accuracy and safety.

[0162] In summary, the high spontaneous explosion rate of glass insulators stems from failure of the glass matrix caused by volume expansion of impurities in the tensile stress layer. The method presented in this paper uses fluid-thermal-solid coupled simulation to obtain the tempered residual stress distribution of the glass insulator. The surface stress of a specific region of the disk is then measured using photoelasticity. Based on viscoelasticity theory, numerical simulation of the tempering process of the glass components of the glass insulator is performed to obtain the tempered residual stress distribution. The simulated results are then compared with measurements using the SCALP-05 photoelastic stress measurement device to verify the accuracy of the simulation results. The results show that in the disk region, the surface compressive stress of the quasi-flat plate is approximately 170 MPa, while the maximum tensile stress in the middle layer is approximately 73 MPa. The maximum tensile stress at the connection is approximately 90 MPa, with no significant difference in surface compressive stress between the quasi-flat plate and the ribs. The maximum principal stress distribution in the head and ribs exhibits a generally parabolic pattern, with tensile stresses of approximately 85–95 MPa in the ribs and surface compressive stresses of approximately 90–120 MPa. Stress components also exhibit differences in different regions of the head. The accuracy of the simulation results is verified using photoelasticity.

[0163] The following conclusions were drawn from the experimental summary:

[0164] (1) In the disc area, the surface compressive stress of the quasi-flat plate is about 170 MPa, the maximum tensile stress in the middle layer is about 73 MPa, and the maximum tensile stress at the connection is even higher, about 90 MPa. Its surface compressive stress is not significantly different from that of the quasi-flat plate.

[0165] (2) The maximum principal stress distribution of the insulators conforms to the parabolic characteristics, among which the ratio of the tensile stress (85~95MPa) to the compressive stress (90~120MPa) in the ribs is relatively large.

[0166] (3) The quasi-cylindrical structure of the head can still be regarded as a flat plate model, but the stress components at the corners of the head are more complex.

[0167] The present invention provides a technical tool for studying the self-explosion mechanism of glass insulators, and also provides reliable support for improving their tempering process and selecting water pressure values ​​for internal water pressure tests.

[0168] The above description further details the present invention in conjunction with specific / preferred embodiments, and the specific implementation of the present invention should not be construed as being limited to these descriptions. Persons skilled in the art will appreciate that, without departing from the spirit of the present invention, they may make various substitutions or modifications to the described embodiments, and these substitutions or modifications should be considered to fall within the scope of protection of the present invention. Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "preferred embodiments," "examples," "specific examples," or "some examples" indicates that the specific features, structures, materials, or characteristics described in conjunction with such embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Persons skilled in the art may combine and assemble the different embodiments or examples described in this specification, as well as features of different embodiments or examples, without conflicting opinions. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions, and modifications may be made within the scope of protection of the patent application.

Claims

1. A method for measuring stress distribution of a tempered glass insulator, characterized in that: The following steps are involved: S1. Based on the viscoelasticity theory of glass, computational fluid dynamics (CFD) software was used to simulate the fluid field and transient temperature field of the insulator during the tempering cooling process. The temperature field results were then imported into finite element analysis (FEA) software. Combined with the time-varying laws of material properties and structural relaxation effects described by the generalized Maxwell model, the residual stress field distribution was solved. S2. Select a measurable disc-shaped area in the insulator and obtain surface and thickness stress data using a photoelastic stress measurement device. Compare and verify the data with the simulation results of the corresponding area. When the error does not exceed the set threshold, the reliability of the simulation model is confirmed. S3. Based on the verified simulation model, output the residual stress distribution of the entire insulator, including the disc and head, and identify the areas of high tensile stress concentration; S4. Adjust cooling process parameters based on stress distribution results, re-simulate and predict optimization results, and verify actual samples through photoelastic measurements to achieve an iterative optimization closed loop for the tempering process. Step S1 specifically includes the following fluid-thermal-solid coupling numerical simulation: Establish a 3D CFD model including the air fluid domain and insulator geometry, set up the turbulence model and non-equilibrium wall function; In FEA, the mesh is refined along the thickness of the insulator to capture the temperature gradient, and the accuracy is ensured through mesh independence verification; The simple thermorheological characteristics and structural relaxation effects of glass were determined, the fictive temperature was calculated using the Tool-Narayanaswamy model, and the thermo-mechanical coupled stress field was solved based on the viscoelastic constitutive equation. The construction of the viscoelastic constitutive equation includes: The generalized Maxwell model is used to describe the time dependence of shear modulus and bulk modulus; A temperature offset function is introduced to convert the temperature effect into a scaled time variable; The thermal expansion strain is calculated using the fictitious temperature and substituted into the stress integral expression to solve the transient stress.

2. The method according to claim 1, wherein In step S1, the simulation of the fluid field and the transient temperature field of the insulator during the tempering cooling process includes: Set differential pressure boundary conditions for the upper and lower wind grids; The non-uniform flow field and temperature field are solved by coupling the fluid continuity equation, Navier-Stokes equation and energy equation; The non-uniform convection heat transfer coefficient on the insulator surface is calculated based on the temperature field results.

3. The method according to claim 1, wherein The structural relaxation effect is quantified by a fictitious temperature model: The fictitious temperature is calculated by integrating the current temperature and the historical temperature; Thermal strain is determined by multiplying the difference in liquid / solid thermal expansion coefficients by the change in imaginary temperature.

4. The method according to any one of claims 1 to 3, wherein In step S2: The measurement area is limited to a disc-shaped quasi-flat plate structure, and the measurement depth is ≤5mm; Quantitative verification is achieved by comparing the root mean square error of stress curves at multiple points in the thickness direction.

5. The method according to any one of claims 1 to 3, characterized in that In step S2, when the error is ≤10%, it is determined that the simulation model is reliable.

6. The method according to any one of claims 1 to 3, wherein: The stress distribution identified in step S3 is used to guide the optimization of pressurization parameters for the water pressure test inside the head, and / or to provide a fracture resistance basis for the disc structure design.

7. The method according to any one of claims 1 to 3, characterized in that The process optimization in step S4 includes: For the high tensile stress concentration area at the connection, the stress peak is reduced by adjusting the nozzle pressure distribution, local cooling intensity or cooling rate; The optimized parameters include heating temperature, cooling time and regional differentiated wind pressure.

8. The method according to any one of claims 1 to 3, wherein: The following steps are also included: Online monitoring is performed based on the full-scale stress distribution, and the risk of self-explosion is predicted by tracking and identifying stress changes in key areas.

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