A method for analyzing interface contact characteristics of crosslinked polyethylene-silicone rubber

Abstract

The application belongs to the technical field of electric power engineering, and discloses a cross-linked polyethylene-silicon rubber interface contact characteristic analysis method, which equates the cross-linked polyethylene-silicon rubber interface contact to the contact of a rough surface and an ideal smooth surface; a random rough surface is constructed by using a spatial frequency synthesis method, and the Ogden model is used to describe the super-elastic stress-strain relationship of the silicon rubber structure to obtain the Ogden model parameters of the random rough surface; a finite element method is used to construct a cross-linked polyethylene-silicon rubber interface contact characteristic analysis model to obtain the contact topography and stress distribution calculation results of the cross-linked polyethylene-silicon rubber insulation interface under different pressure and surface topography conditions. The application can more accurately and effectively analyze the influence law of the material surface roughness, the interface pressure factor, the mesoscale cavity size and the local stress distribution of the interface, and realizes the quantitative analysis of the internal cavity and the local stress distribution of different interface contact conditions under the mesoscale.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electric power engineering, and relates to a cable fault analysis technology, in particular to a cross-linked polyethylene-silicone rubber interface contact characteristic analysis method. BACKGROUND

[0002] With the large-scale application of cross-linked polyethylene (XLPE) cables in power transmission and distribution networks, the demand for cable accessories has also rapidly increased. Among all cable line faults, except for external force damage, cable accessory faults account for more than 86%, and cable accessories have become the weak link of the cable system. The insulation structure of cable accessories is complex, and the installation process requires high. However, cable accessories are usually installed on the construction site, and the installation environment is difficult to control. In addition, the cable operation environment is complex, the cable trench is seriously waterlogged, and overloading and overvoltage phenomena occur frequently.

[0003] Cable accessories use elastomeric insulating materials such as silicone rubber (SiR) to ensure the close fit and overall insulation strength of the interface insulation through interference fit, and also form a solid-solid composite interface insulation structure in the cable accessories. However, even after field sandpaper polishing, there are still micron-level protrusions and depressions on the material surface, and when the two material surfaces are in contact under the action of the holding force, there are still a large number of micron-level cavities between the contact surfaces. In addition, there is a normal electric field with a high tangential component at the insulation interface, resulting in a tangential insulation strength of the solid-solid composite interface of the cable accessory that is much lower than that of the solid insulation body. The contact state and insulation performance of the solid-solid composite interface have become a key factor in determining the insulation level of the cable accessory and even the entire cable system.

[0004] The interface insulation problem of cable accessories has attracted widespread attention from researchers at home and abroad. Researchers have conducted extensive research on key influencing factors and influencing laws of interface insulation performance such as material surface roughness, material mechanical properties, interface contact pressure, and interface filling medium, and have made significant achievements. Researchers at the Norwegian University of Science and Technology used S parameters to characterize the material surface roughness of different grit sandpaper polishing, and found that the interface breakdown field strength increases with the decrease of the material surface roughness. Researchers have also explored the effects of interface pressure and material elastic modulus on interface insulation strength, and found that increasing the interface pressure and reducing the material elastic modulus can effectively improve the interface breakdown voltage. The above studies have shown that each influencing factor affects the interface insulation performance by changing the interface contact topography, and the actual interface contact topography is the key to the insulation performance of the insulation interface.

[0005] Emre Kantar proposed a model for calculating interface contact morphology based on minimum residual potential energy, taking into account factors such as material surface roughness, mechanical properties, and interface pressure. They found that when the interface pressure is high and the material surface is smooth, only isolated closed cavities exist at the interface. However, when the pressure decreases and the roughness increases, the interface produces interconnected gaps formed by large cavities contacting each other. Researchers at Tsinghua University further combined this contact theory with elastic mechanics analysis and proposed a model that correlates the actual contact area ratio with the actual number of contact points and the actual contact area of ​​the contact points. This analytical model advances the study of interface insulation from the influence of external factors to the contact structure within the interface, deepening researchers' understanding of solid-solid composite interface contact and breakdown. However, current models for analyzing solid-solid composite interface contact morphology fail to consider the hyperelastic constitutive relationship of SiR and the effects of internal material stress, resulting in large calculation errors. These models can only characterize the interface contact morphology through the actual contact area ratio parameter, failing to effectively describe the cavity size and local stress distribution characteristics at the mesoscopic scale within the interface, which are key factors affecting the development of interface breakdown and the migration of the filling medium. In addition, related research also lacks direct observation and characterization of the actual contact morphology of the internal interface, and the effectiveness and accuracy of the contact morphology analysis model still need to be verified. Summary of the Invention

[0006] In response to the above-mentioned deficiencies in the prior art, the present invention provides a method for analyzing the contact characteristics of the cross-linked polyethylene-silicone rubber interface, which obtains the pressure distribution under different contact conditions and then analyzes the interface contact situation, providing a new research direction for the mesoscopic analysis of cable insulation, and can also provide effective data support for cable insulation protection and monitoring.

[0007] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0008] A method for analyzing contact characteristics of a cross-linked polyethylene-silicone rubber interface comprises the following steps:

[0009] The cross-linked polyethylene-silicone rubber interface contact is equivalent to the contact between a rough surface and an ideal smooth surface;

[0010] The random rough surface was constructed by spatial frequency synthesis method, and the Ogden model was used to describe the hyperelastic stress-strain relationship of the silicone rubber structure, and the Ogden model parameters of the random rough surface were obtained.

[0011] The finite element method was used to construct an analysis model of the contact characteristics of the cross-linked polyethylene (XLPE)-silicone rubber interface based on the random rough surface, hyperelastic stress-strain relationship, and the Ogden model parameters of the random rough surface. The contact morphology and stress distribution of the XLPE-silicone rubber insulating interface under different pressure and surface morphology conditions were obtained.

[0012] Preferably, a random rough surface is constructed using a spatial frequency synthesis method, comprising the following steps:

[0013] Each spatial site of the random rough surface is formed by superposition of fundamental waves of different frequencies;

[0014] Construct random rough surfaces at various spatial sites.

[0015] Preferably, the basic wave is expressed as:

[0016]

[0017] A mn =1 / (ν x 2 +ν y 2 ) β / 2

[0018]

[0019] Among them, A mn is the amplitude, is the wave vector, is the spatial location, x and y are the spatial coordinates, is the phase angle, v x 、v y are the spatial frequencies in the x and y directions respectively, β is the spectrum harmonic index, k x 、k y are the wave vectors in the x and y directions respectively, and m and n are the frequency numbers in the x and y directions respectively.

[0020] Preferably, the random rough surface is represented by:

[0021]

[0022] Among them, M and N are the spatial cutoff frequencies in the x and y directions respectively. is a uniform random value between 0 and π.

[0023] Preferably, the stress-strain relationship of the silicone rubber structure is expressed as:

[0024]

[0025] Among them, P is the principal stress, λ is the deformation rate, α is the i and μ i is the material parameter, and i is the order.

[0026] Preferably, obtaining the Ogden model parameters of the random rough surface comprises the following steps:

[0027] 制作硅橡胶试样;

[0028] Conduct tensile tests on silicone rubber specimens to obtain corresponding stress-strain curves;

[0029] The stress-strain curve of the silicone rubber sample was fitted to obtain the Ogden model parameters of the random rough surface.

[0030] Preferably, a finite element method is used to construct a cross-linked polyethylene-silicone rubber interface contact characteristic analysis model based on the Ogden model parameters of the random rough surface, comprising the following steps:

[0031] The finite element method is used to construct a rough surface contact simulation model consisting of a rough entity and a rigid smooth entity;

[0032] Set the rough entity as a hyperelastic material and set the hyperelastic parameters according to the Ogden model parameters of the random rough surface;

[0033] Set the contact interface between the rough solid and the rigid smooth solid as a contact pair;

[0034] Set the rigid smooth body as a fixed domain constraint and apply a set displacement to the non-contacting surface of the rough body.

[0035] Preferably, the side length of the rigid smooth solid is greater than the side length of the rough solid.

[0036] Preferably, the rough surface of the rough entity is a random rough surface constructed by using a spatial frequency synthesis method. mn The random rough surfaces with different roughness and morphology are obtained by combining the spectral harmonic index.

[0037] The present invention has the following beneficial effects:

[0038] The XLPE-SiR interface contact characteristics analysis model based on the equivalent roughness law and hyperelastic constitutive relationship in the present invention can more accurately and effectively analyze the influence of material surface roughness and interface pressure factors on the cavity size and local stress distribution at the mesoscopic scale inside the interface, and realize quantitative analysis of the internal cavity and local stress distribution under different interface contact conditions at the mesoscale. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic flow chart of a method for analyzing contact characteristics of a cross-linked polyethylene-silicone rubber interface provided by an embodiment of the present invention;

[0040] Figure 2 为等效粗糙度法则示意图;

[0041] Figure 3Schematic diagram of SiR stress-strain curve;

[0042] Figure 4 Schematic diagram of the sample surface morphology; among them, (a) is a schematic diagram of the surface morphology of the sample polished with XLPE-100 mesh sandpaper, (b) is a schematic diagram of the surface morphology of the sample polished with SiR-100 mesh sandpaper, (c) is a schematic diagram of the surface morphology of the sample polished with XLPE-800 mesh sandpaper, and (d) is a schematic diagram of the surface morphology of the sample polished with SiR-800 mesh sandpaper;

[0043] Figure 5 Schematic diagram of the interface sample (a) and the schematic diagram of the interface contact morphology observation results (b);

[0044] Figure 6 Schematic diagram of rough surface contact simulation model;

[0045] Figure 7 The simulation results of the cross-linked polyethylene-silicone rubber interface are shown in Figure 2. (a) is a schematic diagram of the interface contact morphology simulation results, and (b) is a schematic diagram of the stress distribution simulation results.

[0046] Figure 8 The contact morphology reconstructed based on Micro-CT observation results of XLPE-SiR interface samples; (a) is a schematic diagram of the three-dimensional contact morphology calculation results, and (b) is a schematic diagram of the two-dimensional contour calculation results;

[0047] Figure 9 The three-dimensional schematic diagram and two-dimensional contour diagram of the contact morphology obtained by simulation of the cross-linked polyethylene-silicone rubber interface; among them, (a) is a three-dimensional schematic diagram of the interface contact morphology with a roughness of 20 degrees, Figure 9 (b) is a two-dimensional contour diagram of the interface contact morphology with a roughness of 20 degrees, (c) is a three-dimensional schematic diagram of the interface contact morphology with a roughness of 10 degrees, (d) is a two-dimensional contour diagram of the interface contact morphology with a roughness of 10 degrees, (e) is a three-dimensional schematic diagram of the interface contact morphology with a roughness of 5 degrees, (f) is a two-dimensional contour diagram of the interface contact morphology with a roughness of 5 degrees, (g) is a three-dimensional schematic diagram of the interface contact morphology with a roughness of 2 degrees, and (h) is a two-dimensional contour diagram of the interface contact morphology with a roughness of 2 degrees; the two-dimensional contour diagram is obtained by projecting the three-dimensional diagram of the interface contact morphology, where the area surrounded by the dotted line is determined by the area where the stress is not 0;

[0048] Figure 10 Schematic diagram of the change of interface contact characteristics with interface roughness;

[0049] Figure 11The three-dimensional schematic diagram and two-dimensional contour diagram of the contact morphology obtained by simulating the cross-linked polyethylene-silicone rubber interface under different interface pressures; among them, (a) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.01 MPa, (b) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.01 MPa, (c) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.1 MPa, (d) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.1 MPa, (e) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.2 MPa, (f) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.2 MPa, (g) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.3 MPa, and (h) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.3 MPa.

[0050] Figure 12 Schematic diagram of the change of interface contact characteristics with interface contact pressure;

[0051] Figure 13 Schematic diagram of the influence of roughness and pressure on the actual contact area ratio of the interface;

[0052] Figure 14 Schematic diagram of local stress distribution obtained by simulation of cross-linked polyethylene-silicone rubber interface under different interface pressures; among them, (a) is a schematic diagram of local stress distribution of the interface under the contact condition of 5μm-0MPa, (b) is a schematic diagram of local stress distribution of the interface under the contact condition of 5μm-0.1MPa, (c) is a schematic diagram of local stress distribution of the interface under the contact condition of 5μm-0.2MPa, and (d) is a schematic diagram of local stress distribution of the interface under the contact condition of 5μm-0.3MPa.

[0053] Figure 15 Schematic diagram of the influence of roughness and pressure on interface stress distribution;

[0054] Figure 16 Schematic diagram of the uneven contact at the solid-solid composite insulation interface. DETAILED DESCRIPTION

[0055] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0056] Example

[0057] like Figure 1As shown, an embodiment of the present invention provides a method for analyzing contact characteristics of a cross-linked polyethylene-silicone rubber interface, comprising the following steps S1 to S3:

[0058] S1. The cross-linked polyethylene-silicone rubber interface contact is equivalent to the contact between a rough surface and an ideal smooth surface;

[0059] S2. Use the spatial frequency synthesis method to construct a random rough surface, and use the Ogden model to describe the hyperelastic stress-strain relationship of the silicone rubber structure to obtain the Ogden model parameters of the random rough surface;

[0060] S3. The finite element method is used to construct a cross-linked polyethylene-silicone rubber interface contact characteristic analysis model based on the random rough surface, hyperelastic stress-strain relationship and the Ogden model parameters of the random rough surface, and the stress distribution calculation results of the cross-linked polyethylene-silicone rubber insulation interface under different pressure and surface morphology conditions are obtained.

[0061] The XLPE-SiR interface contact characteristics analysis model based on the equivalent roughness law and hyperelastic constitutive relationship in the present invention can more accurately and effectively analyze the influence of material surface roughness and interface pressure factors on the cavity size and local stress distribution at the mesoscopic scale inside the interface, and realize quantitative analysis of the internal cavity and local stress distribution under different interface contact conditions at the mesoscale.

[0062] In an optional embodiment of the present invention, since the surface of the solid insulation is rough and there are a large number of micron-sized protrusions and depressions, the contact process between the two rough surfaces is complicated, involving the dynamic movement, deformation and relaxation of a large number of contact points. The computational complexity of this complex process is huge and not easy to converge. The corresponding simplified method can greatly reduce the computational complexity and computational difficulty. Although the cable accessories are cylindrical coaxial structures at the macroscopic scale, at the micron scale, their local contact areas can be regarded as infinitesimals of the surface, and the surface contact problem can be converted into the contact of two planes. According to the "equivalent roughness law" proposed by Greenwood, as long as the surface morphologies of the rough surfaces are independent of each other and obey the Gaussian distribution, the contact between the two rough surfaces can be simplified to the contact between an equivalent rough surface and a smooth rigid plane, such as Figure 2 If the surface morphologies of two rough surfaces are independent of each other and randomly distributed with the standard deviation of roughness, it can be expressed as:

[0063]

[0064] in, is the probability that the surface profile height is less than z, σ is the standard deviation of the surface profile height z, that is, the surface profile root mean square roughness S q .

[0065] Then the roughness σ′ and elastic modulus E′ of the equivalent rough surface can be calculated by the following two formulas respectively:

[0066]

[0067] Among them, σ1 and σ2 are the surface roughness of the two materials, respectively, in μm; E1 and E2 are the elastic moduli of the two materials, respectively, in MPa; v1 and v2 are the Poisson's ratios of the two materials, respectively, in 1.

[0068] The surface morphologies of the XLPE and SiR components of the insulating interface are independent and follow a Gaussian distribution. Therefore, this embodiment uses the equivalent rough surface method to transform the contact between two rough surfaces into the contact between a rough surface and an ideal smooth surface, significantly reducing the difficulty of theoretical analysis and the amount of numerical calculations required.

[0069] In an optional embodiment of the present invention, this embodiment uses a spatial frequency synthesis method to construct a random rough surface, including the following steps:

[0070] Each spatial site of the random rough surface is formed by superposition of fundamental waves of different frequencies;

[0071] Construct random rough surfaces at various spatial sites.

[0072] Specifically, the traditional rough surface construction method based on approximate fractal dimension has the problem of limited spatial scale resolution. Therefore, this embodiment uses the spatial frequency synthesis method to construct a random rough surface. That is, each spatial location of the rough surface is considered to be composed of the superposition of fundamental waves of different frequencies. Each wave component is expressed as:

[0073]

[0074] A mn =1 / (ν x 2 +ν y 2 ) β / 2

[0075]

[0076] Among them, A mn is the amplitude, wave vector, is the spatial location, x, y spatial coordinates, is the phase angle, v x 、v y are the spatial frequencies in the x and y directions respectively, β is the spectrum harmonic index, k x 、k y are the wave vectors in the x and y directions respectively, and m and n are the frequency numbers in the x and y directions respectively.

[0077] The random rough surface constructed by the superposition of multiple basic waves is expressed as:

[0078]

[0079] Among them, M and N are the spatial cutoff frequencies in the x and y directions respectively, (x, y) are the spatial coordinates in the x and y directions, and m and n are the frequency numbers in the x and y directions respectively. is the phase angle, which takes a random value uniformly between 0 and π.

[0080] In this embodiment, the amplitude scaling factor A is adjusted mn , you can get surfaces with different roughness and profiles.

[0081] In an optional embodiment of the present invention, after a solid material is deformed under external stress, its internal molecular chains tend to return to their original state, thereby generating internal stress within the material. The stress-strain relationship of an isotropic material can be described by the generalized Hooke's law, as shown in the following equation:

[0082]

[0083] Among them, ε x , ε y , ε z are the normal strains in each spatial direction, σ x , σ y , σ z are the normal stresses in each spatial direction, γ xy , γ zx , γ yz are the shear strains in each direction, σ xy , σ zx , σ yz are the shear stresses in each direction, E is the elastic modulus of the material, G is the shear modulus of the material, and ν is the Poisson's ratio of the material.

[0084] The generalized Hooke's law defines the stress-strain relationship of a material through the elastic modulus and Poisson's ratio, but it is only applicable to describing the linear elastic deformation of the material. Rubber has a wide range of elastic deformation, and the stress-strain relationship has obvious nonlinear characteristics. Therefore, this embodiment uses a hyperelastic model to describe the stress-strain behavior of the silicone rubber structure. The stress-strain relationship of a hyperelastic body is defined by the strain energy density function. The Ogden model can be used for strains up to 700% and has good simulation capabilities over the entire strain range of the rubber. Its strain energy function is expressed as:

[0085]

[0086] where W is the elastic energy density, λ1, λ2, λ3 are the deformation rates of the three principal strain directions, α i and μ i are material parameters, and i is the order.

[0087] The stress components are obtained by partial derivation of the strain energy function with respect to the deformation rate, and the stress-strain relationship of the Ogden model is expressed as:

[0088]

[0089] where P is the principal stress, W is the elastic energy density, λ is the total deformation rate (i.e. the percentage of the change after strain relative to the percentage before strain), α i and μ i are material parameters, and i is the order.

[0090] Since the elastic modulus of SiR is much lower than that of XLPE, and according to the formula of the elastic modulus of the equivalent rough surface, when the elastic modulus of the two materials is quite different, the mechanical properties of the equivalent rough surface will be determined by the material with the smaller elastic modulus, i.e. SiR. Therefore, the steps for obtaining the Ogden model parameters of the random rough surface in this embodiment include the following steps:

[0091] A silicon rubber sample is prepared;

[0092] The silicon rubber sample is subjected to tensile testing to obtain the corresponding stress-strain curve;

[0093] The stress-strain curve of the silicon rubber sample is fitted to obtain the Ogden model parameters of the random rough surface.

[0094] In this embodiment, XLPE samples and SiR samples are subjected to tensile testing for comparison.

[0095] The XLPE sample is prepared by vacuum compression molding of commercial power cable insulation XLPE pellets blended with a peroxide crosslinking agent, with the processing conditions being vacuum preheating at 120°C and 5MPa pressure for 10min, followed by vacuum crosslinking at 170°C and 15MPa pressure for 5min, and then natural cooling to obtain the experimental sample, and the obtained XLPE sample is subjected to degassing treatment in a vacuum drying oven at 60°C for 24h.

[0096] The SiR sample is selected from a commercial two-component liquid silicone rubber, which is mixed and then vacuum high-temperature vulcanized. The processing conditions are as follows: the silicone raw rubber A liquid and B liquid (brand: SYLGARD 184 Silicone Elastomer) are mixed uniformly at a volume ratio of 10:1, and then placed in a vacuum drying oven at 25°C for 30 min for exhaust treatment, and then subjected to vulcanization treatment at 80°C in a vacuum drying oven for 2 h. After the sample is naturally cooled, the sample piece is taken out for use. The obtained SiR sample piece is degassed in a vacuum drying oven at 60°C for 24 h.

[0097] According to the experimental and test requirements, the sample piece is punched into the required size, and the surface of the sample is uniformly polished for 1 min using a polisher equipped with sandpaper of different mesh sizes. Then, the sample surface is washed with acetone and deionized water in turn to remove impurities, and then dried in a vacuum drying oven at 60°C for 12 h before being taken out for standby use.

[0098] In order to test the mechanical properties of the prepared XLPE and SiR samples, the samples are respectively cut into dumbbell-shaped thin sheet samples according to the national standard 1A, and the effective tensile area is 20 mm x 4 mm x 2 mm. The tensile test is carried out by using an INSTRON-5967 universal material testing machine, and the test temperature is 20°C and the tensile rate is 50 mm / min. The stress-strain curve of the sample is shown in Figure 3 , and the related mechanical parameters are shown in Table 1.

[0099] Table 1 Mechanical parameter table

[0100]

[0101] In this embodiment, according to the super-elastic stress-strain relationship given above, the Ogden model parameters of the SiR stress-strain curve shown in Figure 3 are obtained by fitting, as shown in Table 2.

[0102] Table 2 Ogden model parameters of equivalent rough surface

[0103]

[0104] In an optional embodiment of the present application, 100-mesh and 800-mesh sandpaper are selected to polish the surfaces of the XLPE and SiR samples, and a Zeiss-LSM700 laser confocal microscope is used to observe the surface morphology of the reconstructed sample, with a z-axis stepping accuracy of 10 nm and a resolution of 0.2 μm. The obtained surface morphology of the sample is shown in Figure 4 . According to the obtained three-dimensional surface morphology of the sample, the surface morphology distribution parameters are calculated and expressed as:

[0105]

[0106] Among them, S a 、S q are the arithmetic mean roughness and the root mean square roughness of the profile, J is the number of measurement points, z j is the profile height of the measurement point. The measured surface topography distribution parameters are shown in Table 3.

[0107] Table 3 Surface morphology distribution parameters

[0108]

[0109] In this example, micro-computed tomography (Micro-CT) was used to observe the actual contact morphology of rough XLPE-SiR interface samples. First, XLPE and SiR samples with a size of 8 mm × 8 mm × 3 mm were prepared, and the sample surfaces were polished with 100-grit sandpaper respectively, and stacked to form the following Figure 5 The interface sample shown in (a) was subjected to an interface pressure of 0.1 MPa. The interface sample was scanned using a SKYSCAN 1272 Micro-CT scanner with a scanning resolution of 5 μm.

[0110] The contact morphology of the XLPE-SiR interface sample obtained by scanning is as follows: Figure 5 As shown in Figure (b), the gray bumps represent interfacial cavities. It can be seen that a large number of non-contact cavities still exist at the XLPE-SiR interface. The cavity analysis function of the Micro-CT instrument was further used to statistically analyze the distribution of cavities of different sizes within the interface. The results are shown in Table 4.

[0111] Table 4 Cavity distribution parameters

[0112]

[0113] Interfacial contact characteristics, including contact morphology and stress distribution, are key factors in determining the insulation and water barrier properties of solid-solid insulation interfaces. However, a rapid and effective computational analysis method for these interfacial contact characteristics is currently lacking. This example establishes a three-dimensional finite element analysis model for the XLPE-SiR interface based on the equivalent roughness method and the hyperelastic constitutive relationship.

[0114] This embodiment uses the finite element method to construct a cross-linked polyethylene-silicone rubber interface contact characteristic analysis model based on random rough surfaces, hyperelastic stress-strain relationships, and Ogden model parameters of random rough surfaces, including the following steps:

[0115] The finite element method is used to construct a rough surface contact simulation model consisting of a rough entity and a rigid smooth entity;

[0116] Set the rough entity as a hyperelastic material and set the hyperelastic parameters according to the Ogden model parameters of the random rough surface;

[0117] Set the contact interface between the rough solid and the rigid smooth solid as a contact pair;

[0118] Set the rigid smooth body as a fixed domain constraint and apply a set displacement to the non-contacting surface of the rough body.

[0119] Specifically, this embodiment constructs a rough surface contact simulation model in COMSOL Multiphysics finite element simulation software based on random rough surfaces. Figure 6 As shown, it mainly includes a rough entity B1 and a rigid smooth entity B2.

[0120] The random rough surface constructed by the spatial frequency synthesis method given above is obtained by adjusting the amplitude A of the fundamental wave with different frequencies. mn , obtaining random rough surfaces with different roughness and morphology. Based on the determined random rough surface, the root mean square roughness (roughness) of the rough surface can be determined, and then the rough surface morphology can be determined.

[0121] The rough solid is constructed by stretching a random rough surface. The side length of the rough solid is set to 100 μm. To ensure sufficient contact between the rough solid and the rigid solid, the side length of the rigid solid needs to be slightly larger than the rough solid, set to 120 μm. The rough geometric solid B1 and the rigid solid B2 are assembled to complete the geometric solid construction.

[0122] The ideal rigid entity B2 is set as a linear elastic body, and the material is set as structural steel in the built-in material library. According to the mechanical properties of the materials measured in Table 1, the elastic modulus of SiR is much smaller than that of XLPE. The mechanical properties of the equivalent rough entity will be mainly determined by SiR. Therefore, the rough entity B1 is set as a hyperelastic material, and the hyperelastic parameters are shown in Table 2. Since the contact between the two entities occurs between the rough surface R2 and the smooth surface S1, they are set as a contact pair P1, in which the rigid surface S1 is set as the contact source boundary and the rough surface R2 is set as the contact target boundary. The contact pair P1 is the contact interface that needs to be paid attention to in this embodiment. Finally, the rigid entity B2 is set as a fixed domain constraint, and a specified displacement is applied to the surface R1 of the rough entity, that is, all boundary condition settings are completed.

[0123] When dividing the mesh, considering that the deformation caused by the contact force mainly acts on the rough elastic body B1 and the main interface contact morphology occurs on the rough surface R2, in order to reduce the amount of calculation, the rigid body B2 is coarsened and divided into 2522 meshes; the rough elastic body B1 is refined and divided into 8818 meshes.

[0124] After the model is constructed, the deformation rate of the corresponding position can be determined by applying a specified displacement to the surface R1 of the rough entity, and then the stress at the corresponding position is calculated through the superelastic stress-strain relationship of the silicone rubber structure, thereby obtaining the stress distribution of the cross-linked polyethylene-silicone rubber insulation interface. The average value of the contact stress is used as the interface pressure. By adjusting the displacement applied to the rough surface R1 of the rough entity, the stress distribution characteristics of the solid-solid insulation interface under different pressure conditions can be obtained. In this embodiment, the place where the stress is not 0 is also used as the contact area to obtain the contact morphology of the cross-linked polyethylene-silicone rubber insulation interface; the actual contact area ratio of the interface can also be determined by counting the interface contact area.

[0125] Experimental example

[0126] In order to verify the effectiveness of the present invention, this test example compares and analyzes the simulation calculation results of the interface contact morphology and the actual observation results obtained by using Micro-CT.

[0127] In this experimental example, based on the spatial frequency synthesis method, the fundamental wave amplitude A of different frequencies is adjusted. mn , obtaining randomly rough surfaces of varying roughness and morphology. Simultaneously, the displacement applied to the rough surface R1 of the rough solid is regulated by controlling the grid displacement. Displacement is applied starting from the highest peak of the rough interface facing the rigid smooth solid and stopping when the interface pressure reaches the designed value. The stress distribution at the cross-linked polyethylene (XLPE)-silicone rubber insulation interface is then determined through the hyperelastic stress-strain relationship of the silicone rubber structure, thereby determining the interface contact morphology.

[0128] It can be found from Table 3 that the surface roughness of the material polished with 100-grit sandpaper is about 20 μm. Therefore, a surface contact simulation model with this surface roughness is constructed to calculate the surface morphology and stress distribution when the interface pressure is 0.1 MPa. Figure 7 By counting the area where the local contact stress is greater than 0 MPa as the actual contact area, it can be found that when an interface pressure of 0.1 MPa is applied, the actual contact area of ​​the 20 μm rough surface accounts for 12.80% of the simulation value.

[0129] In order to more intuitively compare the contact interface morphology obtained by the simulation model and the actual observation, the contact morphology of the 100-mesh interface obtained by Micro-CT observation in the 400 μm × 400 μm area under the interface pressure of 0.1 MPa was reconstructed, as shown in Figure 2. Figure 8 As shown in Figure 2, the highest contact peak height is 59 μm. The area within 10% of the maximum peak height is selected as the actual contact area, as shown in Figure 2. Figure 8 As shown in the dotted box in (b), the area accounts for 17.46%.

[0130] The above comparative analysis shows that the error between the actual contact area ratio calculated by the simulation model and the actual Micro-CT observation result is 4.66%. This solid-solid interface contact characteristic simulation model can effectively simulate and calculate the actual contact morphology of the XLPE-SiR insulating interface.

[0131] This experiment uses a model for analyzing the contact characteristics of a cross-linked polyethylene (XLPE)-silicone rubber interface to investigate the effect of surface roughness on the interface contact morphology. Equivalent rough surfaces with surface roughnesses of 20 μm, 10 μm, 5 μm, and 2 μm were constructed. Prescribed displacements were applied to these equivalent rough entities to create dual-layer dielectrics with varying roughness.

[0132] Depend on Figure 9 It can be seen that when the interface pressure is 0.1MPa, there are large-area air gap through-channels on the high-roughness surface. As the surface roughness decreases, the actual contact points on the interface increase, the actual contact area continues to increase, and the air gap through-channels are blocked and separated, forming multiple closed cavities isolated from each other. The actual contact area ratio and cavity size distribution of surfaces with different roughness under 0.1MPa interface pressure are further statistically analyzed. When calculating the cavity size distribution, non-overlapping circles of different diameters are used to fit the non-contact areas in the contour map to obtain the cavity size and number. The statistical results are as follows: Figure 10 shown.

[0133] When the contact interface roughness is 20μm, the interface mainly has medium-sized cavities of 15 to 35μm, and a small number of large-sized cavities larger than 45μm. The overall number of cavities is small, but the cavities are connected to each other to form a large-area through-channel. When the interface roughness is reduced to 10μm, the proportion of medium-sized cavities of 15 to 35μm and large-sized cavities larger than 35μm on the interface decreases, and the proportion of small-sized cavities below 15μm increases. When the interface roughness is reduced to 5μm, the total number of cavities increases, and the main cavities are small-sized cavities below 15μm. When the roughness is reduced to 2μm, only cavities below 15μm exist on the interface, and the number of cavities is significantly reduced.

[0134] This experimental example continues to use the established cross-linked polyethylene-silicone rubber interface contact characteristic analysis model to further explore the influence of different interface pressures on the interface contact morphology. Taking into account that in the actual cable accessories installation process, 300-400 mesh sandpaper is generally used to polish the XLPE surface. According to the observation results, the surface roughness is about 5μm at this time. Therefore, an interface contact model with a roughness of 5μm is constructed to study the contact morphology of the interface under different interface pressures. A uniformly increasing normal displacement is applied to the rough entity to obtain the interface contact morphology and stress distribution when the pressure is 0.01MPa, 0.1MPa, 0.2MPa and 0.3MPa, respectively, as shown in the following figure. Figure 11 shown.

[0135] Depend on Figure 11 It can be found that when the surface roughness is 5μm, due to the small peak-to-valley difference of the equivalent rough surface, when the interface just contacts (the contact pressure is 0.01MPa), there are already multiple contact peaks, but the interface is still mainly a large area of ​​air gap through-channel. When the interface contacts further, the interface pressure is borne by the actual contact peak that contacts first. These contact peaks are compressed under the action of pressure, resulting in an increase in the contact area of ​​a single contact peak, and the number of actual contact peaks increases, and the proportion of the actual contact area of ​​the interface increases. Further statistics on the actual contact area ratio and cavity size distribution of the 5μm roughness surface under different interface pressures are shown as follows: Figure 12 shown.

[0136] Depend on Figure 12 It can be found that the actual contact area ratio of the interface increases approximately linearly with the interface pressure. At a pressure of 0.01MPa, the interface is mainly composed of air gap through-channels connected by medium and small cavities of 15-35μm and a small number of large cavities larger than 35μm, with an actual contact area of ​​only 20.12%. When the interface pressure reaches 0.1MPa and 0.2MPa, the number of contact peaks increases and the contact area increases rapidly, with the actual contact area ratio reaching 46.89% and 58.41%, respectively. At this time, there are a large number of small cavities with diameters less than 15μm and some medium cavities of 15-35μm on the interface, and the area and width of the air gap through-channels are reduced. When the interface pressure reaches 0.3MPa, the proportion of small cavities further increases, and cavities larger than 25μm disappear, with an actual contact area ratio of 72.85%. At this time, the air gap through-channels are isolated, forming multiple closed cavities.

[0137] Further fitting analysis is performed on the actual contact area ratio of the interface under different material surface roughness and interface pressure, such as Figure 13 As shown in the figure, it can be found that the actual contact area ratio of the interface decreases exponentially with the increase of the surface roughness of the material, but increases linearly with the increase of the interface pressure.

[0138] In addition to the contact morphology, the local stress distribution of the solid-solid composite contact interface is also an important feature of the interface contact. During the contact process between two solid insulating materials, due to the height difference of the convex peaks, the contact time and contact stress borne by different convex peaks are different, resulting in the unevenness of the local contact stress at each actual contact point. Based on the cross-linked polyethylene-silicone rubber interface contact characteristic analysis model, the contact interface stress distribution characteristics under the action of different material surface roughness and interface pressure are obtained as follows: Figure 14It can be found that under different interface contact conditions, the local stresses borne by each actual contact point vary greatly. When the overall contact pressure of the interface is 0.1 MPa, the local contact stress actually borne by some contact points inside the interface can reach several MPa.

[0139] Further Figure 14 The local contact stress distribution of the actual contact interface under different conditions is statistically analyzed. The results are as follows Figure 15 As shown in Figure 5, it can be found that the local stress distribution at the actual contact interface under different material surface roughness and different interface pressure conditions approximately conforms to the normal distribution characteristics. The normal distribution parameters of the interface stress under various contact conditions are shown in Table 5, where the scale parameter κ represents the dispersion of the local contact stress at the interface. A smaller value indicates a smaller dispersion of the local contact stress at the interface.

[0140] Table 5 Interface local contact stress distribution parameters under different conditions

[0141]

[0142] Depend on Figure 14 It can be found that the maximum local contact stress at the interface is primarily determined by the overall interface pressure. When the overall interface pressure is fixed at 0.1 MPa and the material surface roughness varies between 2 and 10 μm, the maximum local contact stress at the interface remains essentially unchanged, remaining around 0.5 MPa. However, when the surface roughness is constant, the maximum local contact stress occurs at the highest surface peak. As the interface pressure increases, the two surfaces move closer together, all actual contact points are further compressed, and the elastic compression of the highest surface peak increases. Therefore, the maximum local contact stress varies positively with the overall interface pressure. The dispersion of local contact stress is affected by both the surface roughness and the overall interface pressure. When the surface roughness or the overall interface pressure increases, the difference in elastic compression generated by surface peaks of different heights increases. Therefore, the dispersion of local contact stress at the interface is positively correlated with both the surface roughness and the overall interface pressure.

[0143] A statistical analysis was further performed on the proportion of contact points with different interface contact strengths (i.e., local contact stress at each contact point). Based on the distribution characteristics of local interface stress and the contact strength of each actual contact point, all actual contact points were divided into weak contact points (contact strength between (0, 0.5P]), average contact points (contact strength between (0.5P, P+κ]), and strong contact points (contact strength between (P+κ, +∞)). Based on this contact point classification and the distribution characteristics of local interface contact stress under different contact conditions, the proportion of each type of contact point among all actual contact points was calculated. The results are shown in Table 5. It can be found that under all the above interface contact conditions, the proportion of weak contact points ranged from 10% to 20%, the proportion of average contact points ranged from 61% to 67%, and the proportion of strong contact points ranged from 16% to 23%. Overall, the proportion of weak contact points, average contact points, and strong contact points at the solid-solid composite insulation interface under various contact conditions was approximately 1:3:1.

[0144] Schematic diagram of the uneven contact characteristics of the solid-solid composite insulation interface Figure 16 As shown in the figure, when the interface pressure increases, the highest peak on the material surface comes into contact first and bears the contact stress, and the contact peak undergoes compression deformation under the action of the contact stress; as the interface pressure increases, the two solid insulating materials get closer, and more high peaks come into contact and bear the contact stress and undergo compression deformation, resulting in an increase in the actual contact area ratio of the interface; in this process, the difference in elastic compression generated by peaks of different heights increases, resulting in unevenly distributed local contact stress at each actual contact point on the interface.

[0145] In summary, the present invention can achieve the following effects:

[0146] (1) Based on the spatial frequency synthesis method and the hyperelastic constitutive relationship, a solid-solid interface contact characteristic analysis model was established. The calculated results of the actual contact area ratio of the interface were less than 5% different from the Micro-CT observation value, which achieved quantitative analysis of the internal cavity and local stress distribution under different interface contact conditions at the mesoscopic scale.

[0147] (2) The actual contact area ratio of the solid-solid composite insulation interface decreases exponentially with the increase of the surface roughness of the material, but increases linearly with the increase of the interface pressure. Increasing the interface pressure can effectively improve the actual contact situation of the interface. When the interface pressure is 0.3 MPa, the actual contact area ratio of interfaces with different roughness can reach about 70%.

[0148] (3) The local contact stress at the solid-solid composite insulation interface presents an uneven distribution characteristic. The local contact stress of the interface generally conforms to the normal distribution. Under different contact conditions, the ratio of weak contact points, average contact points and strong contact points on the interface is around 1:3:1.

[0149] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0150] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0151] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0152] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0153] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for analyzing contact characteristics of a cross-linked polyethylene-silicone rubber interface, characterized in that: The following steps are involved: The cross-linked polyethylene-silicone rubber interface contact is equivalent to the contact between a rough surface and an ideal smooth surface; The random rough surface was constructed by spatial frequency synthesis method, and the Ogden model was used to describe the hyperelastic stress-strain relationship of the silicone rubber structure, and the Ogden model parameters of the random rough surface were obtained. The random rough surface is constructed using the spatial frequency synthesis method, which includes the following steps: Each spatial site of the random rough surface is formed by superposition of fundamental waves of different frequencies; Construct random rough surfaces at various spatial sites; The finite element method was used to construct an analysis model of the contact characteristics of the cross-linked polyethylene (XLPE)-silicone rubber interface based on random rough surfaces, hyperelastic stress-strain relationship, and Ogden model parameters of random rough surfaces. The stress distribution calculation results of the XLPE-silicone rubber insulation interface under different pressure and surface morphology conditions were obtained.

2. The cross-linked polyethylene-silicone rubber interface contact characteristics analysis method according to claim 1, characterized in that: The basic wave is expressed as: A mn =1 / (ν x 2 +n y 2 ) β / 2 Among them, A mn is the amplitude, is the wave vector, is the spatial location, x and y are the spatial coordinates, is the phase angle, v x 、v y are the spatial frequencies in the x and y directions respectively, β is the spectrum harmonic index, k x 、k y are the wave vectors in the x and y directions respectively, and m and n are the frequency numbers in the x and y directions respectively.

3. The cross-linked polyethylene-silicone rubber interface contact characteristics analysis method according to claim 2, characterized in that: A random rough surface is represented as: Among them, M and N are the spatial cutoff frequencies in the x and y directions respectively. is a uniform random value between 0 and π.

4. The method for analyzing cross-linked polyethylene-silicone rubber interface contact characteristics according to claim 1, characterized in that: The hyperelastic stress-strain relationship of the silicone rubber structure is expressed as: Among them, P is the principal stress, λ is the deformation rate, α is the i and μ i is the material parameter, and i is the order.

5. The cross-linked polyethylene-silicone rubber interface contact characteristics analysis method according to claim 1, characterized in that: Obtaining the Ogden model parameters for a random rough surface involves the following steps: Prepare silicone rubber samples; Conduct tensile tests on silicone rubber specimens to obtain corresponding stress-strain curves; The stress-strain curve of the silicone rubber sample was fitted to obtain the Ogden model parameters of the random rough surface.

6. The cross-linked polyethylene-silicone rubber interface contact characteristics analysis method according to claim 1, characterized in that: The finite element method is used to construct a cross-linked polyethylene-silicone rubber interface contact characteristic analysis model based on random rough surfaces, hyperelastic stress-strain relationships, and Ogden model parameters of random rough surfaces. The model includes the following steps: The finite element method is used to construct a rough surface contact simulation model consisting of a rough entity and a rigid smooth entity; Set the rough entity as a hyperelastic material and set the hyperelastic parameters according to the Ogden model parameters of the random rough surface; Set the contact interface between the rough solid and the rigid smooth solid as a contact pair; Set the rigid smooth body as a fixed domain constraint and apply a set displacement to the non-contacting surface of the rough body.

7. The method for analyzing cross-linked polyethylene-silicone rubber interface contact characteristics according to claim 6, characterized in that: The edge lengths of rigid smooth bodies are greater than those of rough bodies.

8. The method for analyzing cross-linked polyethylene-silicone rubber interface contact characteristics according to claim 6 or 7, characterized in that: The rough surface of the rough entity is a random rough surface constructed by adopting a spatial frequency synthesis method.

9. The method for analyzing cross-linked polyethylene-silicone rubber interface contact characteristics according to claim 8, characterized in that: By adjusting the amplitude A of the fundamental wave of different frequencies mn , random rough surfaces with different roughness and morphology are obtained.

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