Cross-linked polyethylene-silicone rubber interface contact characteristic analysis method

Abstract

The invention belongs to the technical field of electric power engineering, and discloses a crosslinked polyethylene-silicone rubber interface contact characteristic analysis method, which is characterized in that crosslinked polyethylene-silicone rubber interface contact is equivalent to contact between a rough surface and an ideal smooth surface; constructing a random rough surface by adopting a spatial frequency synthesis method, and describing a hyperelastic stress-strain relationship of the silicone rubber structure by adopting an Ogden model to obtain Ogden model parameters of the random rough surface; a finite element method is adopted to construct a crosslinked polyethylene-silicone rubber interface contact characteristic analysis model, and contact morphology and stress distribution calculation results of the crosslinked polyethylene-silicone rubber insulation interface under different pressure and surface morphology conditions are obtained. According to the method, the influence rule of the material surface roughness and the interface pressure factor on the mesoscale cavity size and the local stress distribution in the interface can be analyzed more accurately and effectively, and quantitative analysis of the internal cavity and the local stress distribution under different interface contact conditions in the mesoscale is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of electric power engineering, relates to cable fault analysis technology, and specifically relates to a method for analyzing contact characteristics of a cross-linked polyethylene-silicone rubber interface. Background Art

[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 grown rapidly. Among all cable line failures, excluding force damage, cable accessory failures account for more than 86%, and cable accessories have become the weak link in the cable system. The insulation structure of cable accessories is complex and the installation process requirements are high; however, cable accessories are usually installed at the construction site, and the installation environment is difficult to control. In addition, the cable operating environment is complex, the cable trench is seriously flooded, and overload and overvoltage phenomena occur frequently.

[0003] Cable accessories use elastomeric insulating materials such as silicone rubber (SiR), which ensure the close fit of interface insulation and overall insulation strength through interference fit, and also form a solid-solid composite interface insulation structure in the cable accessories. However, even after on-site sandpaper polishing, there are still micron-level protrusions and depressions on the surface of the material. When the two material surfaces are in contact and fit under the action of the clamping force, there are still a large number of micron-level cavities between their contact surfaces. In addition, there is an orthogonal electric field with a high tangential component at the insulation interface, which causes the tangential insulation strength of the solid-solid composite interface of the cable accessories to be much lower than the insulation strength of the solid insulation body. The contact state and insulation performance of the solid-solid composite interface have become key factors in determining the insulation level of cable accessories 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 rules of interface insulation performance, such as material surface roughness, material mechanical properties, interface contact pressure and interface filling medium, and have achieved remarkable results. Researchers from the Norwegian University of Science and Technology used S parameters to characterize the surface roughness of materials polished with sandpaper of different mesh sizes, and found that the interface breakdown field strength increased with the decrease of material surface roughness. Researchers also explored the effects of factors such as interface pressure and material elastic modulus on interface insulation strength, and found that increasing interface pressure and reducing material elastic modulus can effectively increase the interface breakdown voltage. The above studies all show that various influencing factors affect the interface insulation performance by changing the interface contact morphology, and the actual interface contact morphology is the key to the insulation performance of the insulation interface.

[0005] Emre Kantar proposed a calculation model for interface contact morphology based on minimum residual potential energy by combining factors such as material surface roughness, material mechanical properties and interface pressure. It was found that when the interface pressure is high and the material surface is smooth, there are only isolated closed cavities on the interface. When the pressure decreases and the roughness increases, the interface will produce connected gaps formed by the contact of large cavities. Researchers from Tsinghua University further combined the above contact theory with elastic mechanics analysis and proposed a correlation model between the actual contact area ratio of the interface and the actual number of contact points and the contact area of ​​the actual contact points. The above analysis model advances the study of interface insulation problems from the influence of external factors to the contact structure inside the interface, and deepens researchers' understanding of solid-solid composite interface contact and breakdown problems. However, the current solid-solid composite interface contact morphology analysis model does not consider the hyperelastic constitutive relationship of SiR and the internal stress of the material, resulting in large calculation errors. It can only characterize the interface contact morphology through the actual contact area ratio parameter, and cannot effectively describe the cavity size and local stress distribution characteristics of the interface at the mesoscopic scale, which are the key factors affecting the development of interface breakdown and the migration of filling media. 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 view of the above-mentioned deficiencies in the prior art, the present invention provides a method for analyzing the contact characteristics of a cross-linked polyethylene-silicone rubber interface, which obtains the pressure distribution under different contact conditions and then analyzes the interface contact conditions, providing a new research direction for 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 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-silicone rubber interface according to the random rough surface, hyperelastic stress-strain relationship and the Ogden model parameters of the random rough surface. The contact morphology and stress distribution calculation results of the cross-linked polyethylene-silicone rubber insulating interface under different pressures and surface morphologies were obtained.

[0012] Preferably, a random rough surface is constructed by 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] Making silicone rubber samples;

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

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

[0030] Preferably, a finite element method is used to construct a cross-linked polyethylene-silicone rubber interface contact characteristic analysis model according to 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 including 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 characteristic analysis model based on the equivalent roughness law and the hyperelastic constitutive relationship 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 It is a schematic diagram of the equivalent roughness law;

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

[0042] Figure 4 Schematic diagram of the sample surface morphology; wherein, (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 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; (a) is a schematic diagram of the interface contact morphology simulation calculation results, and (b) is a schematic diagram of the stress distribution simulation calculation results;

[0046] Figure 8 The contact morphology reconstructed based on the Micro-CT observation results of the XLPE-SiR interface sample; (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] Fig. 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, Fig. 9 (b) is a schematic diagram of the two-dimensional contour line of the interface contact morphology with a roughness of 20 degrees, (c) is a schematic diagram of the three-dimensional contour line of the interface contact morphology with a roughness of 10 degrees, (d) is a schematic diagram of the two-dimensional contour line of the interface contact morphology with a roughness of 10 degrees, (e) is a schematic diagram of the three-dimensional contour line of the interface contact morphology with a roughness of 5 degrees, (f) is a schematic diagram of the two-dimensional contour line of the interface contact morphology with a roughness of 5 degrees, (g) is a schematic diagram of the three-dimensional contour line of the interface contact morphology with a roughness of 2 degrees, (h) is a schematic diagram of the two-dimensional contour line of the interface contact morphology with a roughness of 2 degrees; the two-dimensional contour line schematic 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] Fig.10 Schematic diagram of the change of interface contact characteristics with interface roughness;

[0049] Fig.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; wherein, (a) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.01MPa, (b) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.01MPa, (c) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.1MPa, (d) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.1MPa, (e) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.2MPa, (f) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.2MPa, (g) is a three-dimensional schematic diagram of the interface contact morphology under a pressure of 0.3MPa, and (h) is a two-dimensional contour diagram of the interface contact morphology under a pressure of 0.3MPa;

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

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

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

[0053] Fig.15 Schematic diagram of the effect of roughness and pressure on interface stress distribution;

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

[0055] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept 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. A random rough surface is constructed by using a spatial frequency synthesis method, and the Ogden model is used 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 random rough surfaces, hyperelastic stress-strain relationships and Ogden model parameters of random rough surfaces, 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 characteristic analysis model based on the equivalent roughness law and the hyperelastic constitutive relationship 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 has a large number of micron-sized protrusions and depressions, the contact process between the two rough surfaces is complicated, involving dynamic motion, deformation, and relaxation of a large number of contact points. The amount of computation for this complex process is huge and it is not easy to converge. Adopting corresponding simplified methods can greatly reduce the amount of computation and the difficulty of computation. Although the cable accessories are cylindrical coaxial structures at the macroscopic scale, at the micron scale, their local contact areas can be regarded as microelements of the curved surface, and the curved surface contact problem can be converted into the contact between 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 the two rough surfaces are independent of each other and randomly distributed with the standard deviation of the 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 roughness of the surfaces 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 XLPE and SiR constituting the insulating interface are independent of each other and obey 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, which can greatly reduce the difficulty of theoretical analysis and the amount of numerical calculation.

[0069] In an optional embodiment of the present invention, this embodiment adopts 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 conventional rough surface construction method based on approximate fractal dimension has the problem of limited spatial scale resolution. Therefore, this embodiment adopts the spatial frequency synthesis method to construct a random rough surface, that is, it is considered that each spatial position of the rough surface is composed of the superposition of basic waves of different frequencies, and 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 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 values ​​uniformly and randomly between 0 and π.

[0080] In this embodiment, the amplitude proportional 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 will have a tendency to return to their original state, thereby generating internal stress inside the material. The stress-strain relationship of an isotropic material can be described by the generalized Hooke's law, as shown in the following formula:

[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 stress 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 above generalized Hooke's law defines the stress-strain relationship of the material through the elastic modulus and Poisson's ratio, but it is only applicable to describing the linear elastic deformation of the material. The elastic deformation range of rubber is large, 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 the hyperelastic body is defined by the strain energy density function, among which the Ogden model can be used for the case where the strain reaches 700%, and has good simulation capabilities within 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, and λ3 are the deformation rates in the three principal strain directions, and α i and μ i is the material parameter and i is the order.

[0087] The strain energy function is derived from the deformation rate to obtain the corresponding stress component, that is, the stress-strain relationship of the Ogden model is expressed as:

[0088]

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

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

[0091] Making silicone rubber samples;

[0092] Conduct tensile tests on silicone rubber specimens to obtain corresponding stress-strain curves;

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

[0094] In this embodiment, a tensile test is performed on an XLPE sample and a SiR sample for comparison.

[0095] The XLPE sample is made of commercial power cable insulation XLPE pellets blended with a peroxide cross-linking agent and vacuum pressed. The processing conditions are vacuum preheating treatment at 120°C and 5MPa pressure for 10 minutes, and then vacuum cross-linking treatment at 170°C and 15MPa pressure for 5 minutes. After natural cooling, the experimental sample is obtained. The obtained XLPE sample is degassed in a vacuum drying oven at 60°C for 24 hours.

[0096] The SiR sample was selected from commercial two-component liquid silicone rubber and vulcanized at high temperature in vacuum after mixing. The processing conditions were as follows: silicone rubber liquid A and liquid B (brand: SYLGARD 184 Silicone Elastomer) were fully mixed at a volume ratio of 10:1, and then allowed to stand at 25°C in a vacuum drying oven for 30 minutes for exhaust treatment, and then vulcanized at 80°C in a vacuum drying oven for 2 hours. After the sample was naturally cooled, it was taken out to obtain an experimental sample. The obtained SiR sample was degassed in a vacuum drying oven at 60°C for 24 hours.

[0097] According to the experimental and test requirements, the sample was punched into the required size, and the surface of the sample was evenly polished for 1 min using a grinder equipped with sandpaper of different mesh sizes. Then, acetone and deionized water were used to wash away impurities on the surface of the sample, and the sample was dried at 60 °C in a vacuum drying oven for 12 h before being taken out for use.

[0098] In order to test the mechanical properties of the prepared XLPE and SiR samples, the samples were cut into dumbbell-shaped thin sheet samples of national standard 1A type, and the effective tensile area length × width × thickness was 20mm × 4mm × 2mm. The tensile test was carried out using INSTRON-5967 universal material testing machine, with a test temperature of 20℃ and a tensile rate of 50mm / min. The stress-strain curve of the sample was measured as follows Figure 3 The relevant mechanical parameters are shown in Table 1.

[0099] Table 1 Mechanical parameters

[0100]

[0101] In this embodiment, according to the superelastic stress-strain relationship given above, Figure 3 The stress-strain curve of SiR shown in the figure was fitted, and the Ogden model parameters were obtained as shown in Table 2.

[0102] Table 2 Parameters of Ogden model for equivalent rough surface

[0103]

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

[0105]

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

[0107] Table 3 Surface morphology distribution parameters

[0108]

[0109] In this embodiment, micro computed tomography (Micro-CT) is used to observe the actual contact morphology of the rough XLPE-SiR interface sample. First, XLPE and SiR samples with a size of 8 mm × 8 mm × 3 mm are prepared, and the sample surfaces are polished with 100-mesh sandpaper respectively, and stacked to form Figure 5 (a) shows the interface sample, and an interface pressure of 0.1 MPa is applied. The interface sample is scanned by a Micro-CT of model SKYSCAN 1272 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 (b) shows that the gray convex points are interface cavities, and it can be found that there are still a large number of non-contact cavities at the XLPE-SiR contact interface. The cavity analysis function of the Micro-CT instrument is further used to perform statistical analysis on the distribution of cavities of different sizes in the interface, and the results are shown in Table 4.

[0111] Table 4 Cavity distribution parameters

[0112]

[0113] The interface contact characteristics including contact morphology and stress distribution are key factors in determining the insulation performance and water barrier performance of the solid-solid insulation interface. However, there is currently a lack of fast and effective calculation and analysis methods for interface contact characteristics. This embodiment establishes a three-dimensional finite element analysis model of interface contact characteristics 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 including 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 adjusted by adjusting the amplitude A of the fundamental wave with different frequencies. mn , random rough surfaces with different roughness and morphology are obtained. Based on the determined random rough surface, the root mean square roughness (roughness for short) of the rough surface can be determined, and then the morphology of the rough surface can be determined.

[0121] The rough entity is constructed by stretching a random rough surface. The side length of the rough entity is set to 100 μm. To ensure that the rough entity and the rigid entity can fully contact, the side length of the rigid entity needs to be slightly larger than the rough entity and is set to 120 μm. The rough geometric entity B1 and the rigid entity B2 are assembled to complete the geometric entity 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 material mechanical properties measured in Table 1, the elastic modulus of SiR is much smaller than that of XLPE, and 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 on the rough surface R2 and the smooth surface S1, it is 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 conditions are set.

[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 built, 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, and then the stress distribution of the cross-linked polyethylene-silicone rubber insulation interface is obtained. And the average 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, by adjusting the amplitude A of the fundamental wave with different frequencies mn , and obtain random rough surfaces with different roughness and morphology. At the same time, the displacement applied to the rough surface R1 of the rough entity is regulated by controlling the grid displacement. The displacement is applied from the highest convex peak of the rough interface facing the rigid smooth entity. When the interface pressure reaches the design value, the displacement is stopped; then, the stress distribution of the cross-linked polyethylene-silicone rubber insulation interface is obtained through the superelastic stress-strain relationship of the silicone rubber structure, and the interface contact morphology is determined.

[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 of this surface roughness is constructed to calculate the surface morphology and stress distribution when the interface pressure is 0.1 MPa. Figure 7 As shown in the figure, the area where the local contact stress is greater than 0 MPa is counted as the actual contact area. It can be found that when the 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 1, 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 1. 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%. The simulation model of solid-solid interface contact characteristics can effectively simulate and calculate the actual contact morphology of the XLPE-SiR insulating interface.

[0131] This experimental example uses the established cross-linked polyethylene-silicone rubber interface contact characteristic analysis model to study the influence of material surface roughness on the interface contact morphology. Equivalent rough surfaces with surface roughness of 20μm, 10μm, 5μm and 2μm are constructed respectively, and specified displacements are applied to equivalent rough entities with different roughness to obtain double-layer media with different roughness.

[0132] Depend on Fig. 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 shown in Figure 2. Fig.10 shown.

[0133] When the contact interface roughness is 20μm, the interface mainly has medium-sized cavities of 15 to 35μm, and there are 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 above 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, there are only cavities below 15μm 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 at pressures of 0.01MPa, 0.1MPa, 0.2MPa and 0.3MPa, respectively, as shown in the figure. Fig.11 shown.

[0135] Depend on Fig.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 comes into contact (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 further contacts, the interface pressure is borne by the actual contact peaks that come into contact 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 actual contact area ratio of the interface increases. The actual contact area ratio and cavity size distribution of the 5μm roughness surface under different interface pressures are further statistically analyzed, as shown in the figure. Fig.12 shown.

[0136] Depend on Fig.12 It can be found that the actual contact area ratio of the interface increases approximately linearly with the interface pressure. Under a pressure of 0.01MPa, the interface is mainly composed of air gap through-channels formed by connecting medium and small cavities of 15-35μm and a small number of large cavities larger than 35μm, and the actual contact area accounts for only 20.12%; when the interface pressure reaches 0.1MPa and 0.2MPa, the number of contact peaks increases, the contact area increases rapidly, and the actual contact area accounts for 46.89% and 58.41% respectively. At this time, there are a large number of small cavities with a diameter of less than 15μm and some medium cavities of 15-35μm on the interface, and the area and width of the air gap through-channel are reduced; when the interface pressure reaches 0.3MPa, the proportion of small cavities increases further, and cavities larger than 25μm disappear, and the actual contact area accounts for 72.85%. At this time, the air gap through-channel is blocked, 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 Fig.13 As shown, 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 protrusion peaks, the contact time and contact stress of different protrusion peaks are different, resulting in the uneven local contact stress of each actual contact point. Based on the cross-linked polyethylene-silicone rubber interface contact characteristic analysis model, the stress distribution characteristics of the contact interface under the action of different material surface roughness and interface pressure are obtained. Fig.14It can be found that under different interface contact conditions, the local stresses borne by each actual contact point are quite different. 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 Fig.14 The local contact stress distribution of the actual contact interface under different conditions is statistically analyzed. The results are as follows Fig.15 As shown, it can be found that the local stress distribution of the actual contact interface under different material surface roughness and different interface pressure conditions is approximately consistent with 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 of the interface. The smaller the value, the smaller the dispersion of the local contact stress of the interface.

[0140] Table 5 Distribution parameters of local contact stress on the interface under different conditions

[0141]

[0142] Depend on Fig.14 It can be found that the maximum local contact stress of the interface is mainly determined by the overall pressure of the interface. When the overall pressure of the interface is fixed at 0.1MPa and the surface roughness of the material changes in the range of 2-10μm, the maximum local contact stress of the interface remains basically unchanged, all around 0.5MPa. When the surface roughness of the material is fixed, the maximum local contact stress appears at the highest convex peak on the material surface. As the interface pressure increases, the two material surfaces are closer, all actual contact points are further compressed, and the elastic compression of the highest convex peak increases. Therefore, the maximum local contact stress changes positively with the overall pressure of the interface. The dispersion of local contact stress is affected by both the surface roughness of the material and the overall pressure of the interface. When the surface roughness of the material increases or the overall pressure of the interface increases, the difference in elastic compression generated by convex peaks of different heights on the material surface increases. Therefore, the dispersion of local contact stress on the interface changes positively with both the surface roughness of the material and the overall pressure of the interface.

[0143] The proportion of contact points with different contact strengths (i.e., local contact stress at each contact point) is further statistically analyzed. According to the distribution characteristics of local stress at the interface and the contact strength of each actual contact point, all actual contact points are divided into weak contact points (contact strength at (0, 0.5P]), average contact points (contact strength at (0.5P, P+κ]) and strong contact points (contact strength at (P+κ, +∞)). Based on the above contact point division, the proportion of each type of contact point in all actual contact points is calculated according to the distribution characteristics of local contact stress at the interface under different contact conditions. The calculation results are shown in Table 5. It can be found that under all the above interface contact conditions, the proportion of weak contact points is between 10% and 20%, the proportion of average contact points is between 61% and 67%, and the proportion of strong contact points is between 16% and 23%. In general, under various contact conditions, the proportion of weak contact points, average contact points and strong contact points at the solid-solid composite insulation interface is approximately around 1:3:1.

[0144] Schematic diagram of the non-uniform contact characteristics of the solid-solid composite insulation interface Fig.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 compressive deformation under the action of the contact stress; as the interface pressure increases, the two solid insulating materials get closer, more high peaks come into contact, and bear the contact stress and undergo compressive deformation, resulting in an increase in the actual contact area of ​​the interface; in this process, the difference in elastic compression produced by peaks of different heights increases, resulting in unevenly distributed local contact stresses 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, the solid-solid interface contact characteristics analysis model was established. The calculated result of the actual contact area ratio of the interface had an error of less than 5% compared with the Micro-CT observation value, which enabled the 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 material surface roughness, but increases linearly with the increase of the interface pressure. Increasing the interface pressure can effectively improve the actual contact conditions 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 approximately 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 flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, 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 flowchart and / or block diagram. 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 capable of directing a computer or other programmable data processing device to operate 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 A 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 operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions 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] The present invention uses specific embodiments 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 idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on 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 should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for analyzing the 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 silicone rubber structure, and the Ogden model parameters of the random rough surface were obtained. The finite element method was used to construct an analysis model of the contact characteristics of the cross-linked polyethylene (PE)-silicone rubber interface according to the random rough surface, hyperelastic stress-strain relationship and the Ogden model parameters of the random rough surface. The stress distribution calculation results of the cross-linked polyethylene-silicone rubber insulation interface under different pressures and surface morphologies were obtained.

2. The method for analyzing the contact characteristics of the cross-linked polyethylene-silicone rubber interface according to claim 1, characterized in that: The random rough surface is constructed by 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.

3. The method for analyzing the contact characteristics of the cross-linked polyethylene-silicone rubber interface according to claim 2, 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.

4. The method for analyzing the contact characteristics of the cross-linked polyethylene-silicone rubber interface according to claim 3, characterized in that: A random rough surface is represented by: 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.

5. The cross-linked polyethylene-silicone rubber interface contact characteristics analysis method 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.

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

7. The method for analyzing the contact characteristics of the cross-linked polyethylene-silicone rubber interface 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 the Ogden model parameters of the random rough surface, including the following steps: The finite element method is used to construct a rough surface contact simulation model including 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.

8. The method for analyzing the contact characteristics of the cross-linked polyethylene-silicone rubber interface according to claim 7, characterized in that: The edge length of a rigid smooth body is greater than the edge length of a rough body.

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

10. The method for analyzing cross-linked polyethylene-silicone rubber interface contact characteristics according to claim 9, 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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