Method for calculating contact resistance of electric connection structure of super / ultra high voltage GIS device contact finger

Abstract

The application provides a calculation method of contact resistance of an electric connection structure of a contact finger of an ultra / extra-high voltage GIS device. The method comprises the following steps: S1, capturing a gray-scale image of a contact area of the contact finger by using MATLAB and a laser confocal microscope, and determining a fractal dimension of the contact area of the contact finger according to the gray-scale image; S2, determining a critical contact area according to the fractal dimension of the contact area of the contact finger and a contact surface characteristic parameter; S3, determining a critical base length and a contact micro-protrusion base diameter according to the critical contact area; S4, calculating the area of a maximum micro-protrusion of the electric connection structure of the contact finger under different loads according to the critical contact area, the critical base length and the contact micro-protrusion base diameter; and S5, determining the contact resistance of the electric connection structure of the contact finger according to the area of the maximum micro-protrusion. In this way, the theoretical calculation of the contact resistance of the electric connection structure of the contact finger of the ultra / extra-high voltage GIS device can be realized, and the method has wide practicability and economy.

Description

Technical Field

[0001] This invention relates to the field of electrical connection structure technology for ultra-high voltage / extra-high voltage GIS equipment, and specifically to a method for calculating the contact resistance of the contact finger electrical connection structure of ultra-high voltage / extra-high voltage GIS equipment. Background Technology

[0002] To address stress concentration caused by thermal expansion and contraction of the central current-carrying conductor in GIS (Gas-Insulated Switchgear) systems, a segmented connection method is adopted. The segmentation points utilize contact finger electrical connection structures of various types, such as springs, straps, and perforated joints, to achieve electrical connection. However, with the continuous development of ultra-high voltage (UHV) power transmission technology in my country and the increasing transmission capacity, the operating current of primary equipment has increased significantly. The contact finger electrical connection structure has become a critical link and weak point affecting the safe and reliable operation of power equipment. In recent years, the contact finger electrical connection structures widely used in GIS equipment have frequently experienced excessive contact resistance and localized thermal stress concentration due to performance degradation in the electrical contact area, ultimately leading to discharge accidents that seriously threaten the safe and stable operation of the power grid.

[0003] The microstructure of the contact finger and conductor surface is not a smooth plane, but rather uneven. The contact surface between the contact finger and conductor is a collection of numerous contact spots (called "conductive spots"), not an ideal planar contact. Therefore, the actual contact area of ​​the contact finger electrical connection structure differs from the nominal contact area. The actual contact area is related to factors such as the roughness of the contact finger and conductor surfaces and the contact pressure load. When current flows through the contact finger electrical connection structure, the current flows through numerous small contact spots, causing a significant current contraction and generating contraction resistance. In addition, a very thin contaminant film layer exists on the conductor and contact finger surfaces, possessing a certain film resistance. Therefore, the contact resistance of the electrical connection structure includes contraction resistance and film resistance, and contact resistance is a key indicator for evaluating the electrical contact state of the electrical connection structure.

[0004] The contact resistance of the watchband's contact finger electrical connection structure originates from the conductive spots generated when current is applied between the irregular contact finger surface and the contact surface of the conductive rod. Due to the irregular microstructure of these contact spots, classical mathematics is insufficient to characterize them. Current technologies can only quantitatively analyze the contact resistance of the contact finger electrical connection structure through experimental measurements, which suffers from inaccurate measurement results. Furthermore, improper contact pressure and slot dimensions in the contact finger electrical connection structure used in GIS equipment can lead to various accidents, causing the GIS equipment to malfunction and become unstable. Summary of the Invention

[0005] This invention provides a method for calculating the contact resistance of the contact finger electrical connection structure of ultra-high voltage / extra-high voltage GIS equipment. This method overcomes the shortcomings of the prior art and can objectively and accurately perform theoretical calculations and evaluation analyses of the contact resistance of the contact finger electrical connection structure of GIS equipment, ensuring the stable operation of GIS equipment and even the entire power system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for calculating the contact resistance of the contact finger electrical connection structure of ultra-high voltage / extra-high voltage GIS equipment, characterized in that the method includes:

[0008] S1. Use MATLAB and laser confocal microscopy to capture grayscale images of the finger contact area, and determine the fractal dimension of the finger contact area based on the grayscale images.

[0009] S2. Determine the critical contact area based on the fractal dimension of the contact area and the characteristic parameters of the contact surface;

[0010] S3. Determine the critical substrate length and the bottom diameter of the contact micro-protrusion based on the critical contact area;

[0011] S4. Based on the critical contact area, critical base length, and bottom diameter of the contact micro-protrusion, calculate the area of ​​the maximum micro-protrusion of the contact finger electrical connection structure under different loads.

[0012] S5. Determine the contact resistance of the finger electrical connection structure based on the area of ​​the largest micro-protrusion under different loads.

[0013] Furthermore, the step of capturing grayscale images of the finger contact area using MATLAB and laser confocal microscopy, and determining the fractal dimension of the finger contact area based on the grayscale images, includes:

[0014] S21. Use a laser confocal microscope to scan the three-dimensional structure of the finger contact area before and after the test to obtain real-shot, color, and grayscale images;

[0015] S22. Extract a 256×256 pixel grayscale image, use MATLAB to recognize the image, and draw the corresponding 3D model.

[0016] S23. Calculate the fractal dimension D using the difference box method;

[0017] The method of calculating fractal dimension using the difference box method includes:

[0018] S231. An image of size M×N is divided into several k×k sub-blocks of equal size. The gray value at (x,y) of the image is f(x,y), and the total gray levels are... L ;

[0019] S232. Consider the image as a grayscale set (x, y, f(x, y)) of the surface of a three-dimensional object. The XY plane contains a k×k grid, with several boxes stacked on top of each other. The height of each box is... h =( L -1)× k / min(M,N);

[0020] S233. If in the (i,j)th grid, the m-th box contains the minimum gray value within the grid, and the l-th box contains the maximum gray value within the grid, then the number n boxes covering the (i,j)-th grid is... r (i,j)=l-m+1; the number of boxes N covering the entire grid. r = n r (i,j); therefore, the fractal dimension can be calculated as:

[0021] (1)

[0022] Where r = k / min(M,N), a set of N is calculated by changing the size of the grid k. r Then calculate the point pairs {log(1 / r), log(N)} r The slope of the linear regression of )} is the fractal dimension D.

[0023] Furthermore, determining the critical contact area based on the fractal dimension of the finger contact area and the contact surface characteristic parameters includes:

[0024] S31. The deformation of a single micro-protrusion structure is divided into four stages: elastic stage, first elastoplastic stage, second elastoplastic stage, and fully plastic deformation stage. The critical elastic contact area is derived from the deformation process as follows:

[0025] (2)

[0026] in, Indicates the critical elastic contact area; Indicates the hardness coefficient; Indicates the material properties of the contact material; G represents the bottom diameter of the contact micro-protrusion substrate; G represents the fractal roughness expansion coefficient of the rough surface. D This represents the fractal dimension of the contact area between the fingers;

[0027] S32. Based on the fractal dimension of the finger contact area D Input the basic parameters of the contact material and perform iterative calculations to determine the critical contact area;

[0028] S321, Input the elastic modulus of the two materials in the contact area: the rough surface and the rigid plane. E 1. E 2. Poisson's ratio n 1. n 2, and the resistivity of rough surface materials. r 1. r 2. Obtain the equivalent elastic modulus E and equivalent resistivity r :

[0029] (3)

[0030] (4)

[0031] S322, based on hardness coefficient K Poisson's ratio of the rough surface in the contact area n The relationship of 1:

[0032] (5)

[0033] and rough surface region expansion coefficient Relationship with fractal dimension D:

[0034] (6)

[0035] Obtain the critical contact area in the fractal contact model a eco :

[0036] (7)

[0037] in, These are the inherent material parameters in the classical fractal contact model.

[0038] Furthermore, determining the critical substrate length and the bottom diameter of the contact micro-protrusion based on the contact area includes:

[0039] S41, Let the critical elastic contact area be... a ec equal to critical contact area a eco The critical basis length is obtained. l ec ;

[0040] S42. When calculating the contact load of all elastic contact micro-protrusions, the base length is treated as a constant. l ec At this point, the critical basis length serves as a benchmark to describe all micro-bumps. However, the basis lengths of micro-bumps of different sizes differ from the critical basis length by a certain multiple λ. When calculating the basis length integral, it is equivalent to λ. l ec The integral;

[0041] S43. Calculate the critical elastic contact area a ec and critical contact area a eco To satisfy both aec = a eco The formula's equivalent relationship is used to calculate the bottom diameter of the contact micro-protrusion. l， After unifying its dimensions, it becomes l x :

[0042] (8)

[0043] in, A Nominal contact area a This represents the contact area of ​​the micro-convex body.

[0044] Furthermore, the calculation of the area of ​​the maximum micro-protrusion of the contact finger electrical connection structure under different loads based on the critical contact area, critical substrate length, and contact micro-protrusion bottom diameter includes:

[0045] S51, Given the external load P Through repeated iterations, the magnitudes of the forces acting on the micro-protrusion during its elastic deformation, first elastoplastic deformation, second elastoplastic deformation, and fully plastic deformation stages are calculated using the following formula:

[0046] (9)

[0047] (10)

[0048] (11)

[0049] (12)

[0050] (13)

[0051] In the formula, F re For elastic deformation contact load; F rep1 This is the first elastic-plastic deformation contact load; F rep2 This is the second elastic-plastic deformation contact load; F rp For fully plastic deformation contact load;

[0052] S52. The actual contact area at each deformation stage is calculated using the following formula:

[0053] (14)

[0054] (15)

[0055] (16)

[0056] (17)

[0057] (18)

[0058] In the formula, A re The contact area is the area of ​​elastic deformation; A rep1 This represents the contact area during the first elastic-plastic deformation. A rep2 This represents the contact area during the second elastic-plastic deformation. A rp This represents the contact area under complete plastic deformation.

[0059] S53. Normalize formulas (10)-(18) by dividing both sides by E. A a ,in:

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] In fractal dimension D Under certain conditions, , , All are constants;

[0069] Therefore, regarding material properties i fractal dimension D Structural parameters G When kept constant, the dimensionless contact load is a function of the maximum contact area and the actual contact area;

[0070] S54. By summing the contact loads at different deformation stages, the total contact load on the electrical contact surface can be obtained. P Compared to the actual contact area A r The function expression;

[0071] (19)

[0072] S55, through different actual loads P By forming an equation with equation (19), the parameters for each deformation stage can be obtained; combined with the empirical formula for calculating Holm contact resistance, the formula for calculating contact resistance using fractals is as follows:

[0073] (20)

[0074] (twenty one)

[0075] (twenty two)

[0076] (twenty three)

[0077] (twenty four)

[0078] S56, Assuming external load P If all the force acts during the elastic deformation stage, then the initial elastic deformation pressure is obtained. F rex0 :

[0079] (25)

[0080] Since the entire process is in the elastic deformation stage, the actual contact area can be calculated using the first term of equation (19). A rx0 And the area of ​​the largest micro-convexity is calculated. a l :

[0081] (26)

[0082] In formulas (9) to (26), Fn(a) Let be the contact load distribution function of the micro-convex body. The coefficient for the expansion of the rough surface region. a The single-point contact area of ​​the micro-convex body. The area of ​​the largest micro-convexity. K This is the hardness coefficient. H For material hardness, a epc This represents the first critical elastoplastic contact area. a pc This represents the second critical elastoplastic contact area. n(a) Let be the number distribution density function of micro-convexities. F rxTo correct the contact load, F r For total contact load, l x To unify the dimensions of the normalized micro-convex body base diameter, A rx To correct the actual contact area A r This represents the total actual contact area. A a Nominal contact area a ecx To correct the critical elastic contact area. A re The contact area is adjusted for the elastic stage, where A is the nominal contact area.

[0083] Furthermore, determining the contact resistance of the finger electrical connection structure based on the area of ​​the largest micro-protrusion under different loads includes:

[0084] S61, Area of ​​the largest micro-convexity a 1 and critical elastic contact area a ec Compare;

[0085] S62, if a l <= a ec The external load causes elastic deformation in the contact area, and the total contact resistance is... R ce ;

[0086] S63, if a l > a ec Assuming the load acts on both the elastic deformation stage and the first elastic-plastic deformation stage, the following equation is used for iteration:

[0087] (27)

[0088] By combining equation (27) with the first two terms of equation (19), we can obtain the following calculations. A rx The area of ​​the largest micro-convexity was obtained in the second calculation. a l The area a1 of the largest micro-convexity obtained in the second calculation is judged.

[0089] S64, if a l <=7.1197 a ec The external load causes elastic and first elastoplastic deformation in the contact area, and the total contact resistance is...R ce , R cep1 The sum of parallel connections;

[0090] S65, if a l >7.1197 a ec Assuming the external load acts on the elastic deformation stage, the first elastic-plastic deformation stage, and the second elastic-plastic deformation stage, equation (25) is modified to the following equation for iteration:

[0091] (28)

[0092] By combining equation (28) with the first three terms of equation (19), we can obtain the following calculations. A rx The area of ​​the largest micro-convexity was obtained in the third calculation. a l The area of ​​the largest micro-convexity obtained in the third calculation is then determined.

[0093] S66, if a l <=205.3827 a ec ,but a epc =7.1197 a ec , a pc =205.3827 a ec ;

[0094] External loads cause elastic, first elastoplastic, and second elastoplastic deformations in the contact area, resulting in a contact resistance of... R ce , R cep1 , R cep2 The sum of parallel connections; among which, a epc This represents the first critical elastoplastic contact area. a pc This represents the second critical elastoplastic contact area.

[0095] S67, if a l >205.3827 a ec Assuming the external load acts on the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, and the fully plastic deformation stage, equation (25) is modified to the following equation for iteration:

[0096] (29)

[0097] By combining equation (29) with the first two terms of equation (19), we can obtain the following calculations. A rx The area of ​​the largest micro-convexity was obtained in the fourth calculation. a l ;

[0098] If an external load causes elastic, first elastoplastic, second elastoplastic, and fully plastic deformation in the contact area, then the total contact resistance is: R ce , R cep1 , R cep2 , R cp The sum of parallel connections.

[0099] The beneficial effects of this invention are as follows:

[0100] (1) In view of the shortcomings of existing technologies that can only quantitatively analyze the contact resistance of the finger electrical connection structure through experimental measurement, and cannot objectively and accurately calculate the contact resistance of the finger electrical connection structure for GIS equipment, this invention uses MATLAB and laser confocal microscopy to capture grayscale images of the contact area, obtains the nominal contact area and fractal dimension of the finger contact area, and uses fractal theory model to finally realize the theoretical calculation of the contact resistance of the finger electrical connection structure for ultra-high voltage / extra-high voltage GIS equipment. It has wide applicability and economy.

[0101] (2) This invention comprehensively considers the four stages of elastic deformation, first elastic-plastic deformation, second elastic-plastic deformation and plastic deformation in the process of electric contact of the finger, and obtains the influence of different fractal dimensions on the actual contact area of ​​the electric contact of the finger. It makes up for the fact that existing research can only obtain the macroscopic contact resistance parameters of the finger used in GIS equipment through experimental measurement, and reduces or avoids various accidents caused by improper contact pressure and slot size of the electric connection structure of the finger used in GIS equipment, and ensures the safe and reliable operation of GIS equipment and even the stable operation of the entire power system.

[0102] It should be understood that the description in the Summary Section is not intended to limit the key or essential features of the invention, nor is it intended to restrict the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0103] The above and other features, advantages, and aspects of the various embodiments of the present invention will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0104] Figure 1 A flowchart illustrating the calculation method for the contact resistance of the finger electrical connection structure in ultra-high voltage / extra-high voltage GIS equipment according to the present invention is shown. Detailed Implementation

[0105] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0106] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0107] Fractal theory provides a method for studying irregular sets in nature. It can reveal the intrinsic laws governing these natural phenomena through self-similar fractals. With the development of nonlinear science, fractal theory has been applied to the microscopic level, enabling the creation of more accurate contact models for rough surfaces. This invention, based on a fractal theory model, uses MATLAB to identify grayscale images and obtain the fractal dimension of the watch strap's finger contact surface. D Simultaneously considering the four deformation states of the micro-protrusion—elasticity, first elastoplasticity, second elastoplasticity, and complete plasticity—the theoretical calculation of the contact resistance of the watchband's contact finger electrical connection structure under different pressure states was finally realized.

[0108] Step 1: First, use a laser confocal microscope to capture a 3D real-world image and height map of the contact area of ​​the GIS equipment's touch point. Then, based on the real-world image, convert the image into a grayscale image. During the contact process, the higher the contact point and the smoother the surface, the closer it is to white in the grayscale image; when there are pits or slopes on the surface, it is closer to black in the grayscale image. Therefore, the fractal dimension of the contact area can be obtained from the extracted grayscale image. D .

[0109] fractal dimension D The acquisition involves the following steps:

[0110] The three-dimensional structure of the contact area before and after the experiment was scanned using a laser confocal microscope to obtain real-shot, color, and grayscale images;

[0111] Extract a 256×256 pixel grayscale image, use MATLAB to recognize the image, and draw the corresponding 3D model.

[0112] The fractal dimension was obtained by using the difference box method. D .

[0113] The principle of the difference box method is to divide an image of size M×N into several k×k sub-blocks of equal size, where the gray value at (x,y) is f(x,y), and the total gray levels are... L At this point, the image is viewed as a grayscale set (x, y, f(x, y)) of the surface of a three-dimensional object. The XY plane contains a k×k grid, with several boxes stacked on top of each other. The height of each box is... h =( L -1)× k / min(M,N). If in the (i,j)th grid, the m-th box contains the minimum gray value within the grid, and the l-th box contains the maximum gray value within the grid, then the number n boxes covering the (i,j)-th grid is... r (i,j)=l-m+1. The number of boxes N covering the entire grid. r = n r (i,j). Therefore, the fractal dimension can be calculated as:

[0114] (1)

[0115] Where r = k / min(M,N). A set of N values ​​is calculated by changing the size of the grid k. r Then calculate the point pairs {log(1 / r), log(N)} r The slope of the linear regression of )} is the fractal dimension D.

[0116] Step 2: The contact between two rough planes can be equivalent to the contact between a rigid smooth plane and a rough surface. The rough surface can be considered as a collection of multiple micro-protrusions distributed over a certain area. The deformation of a single micro-protrusion structure can be divided into four stages: elastic stage, first elastoplastic stage, second elastoplastic stage, and fully plastic deformation stage. The critical elastic contact area is derived from the deformation process as follows:

[0117] (2)

[0118] Obtaining the fractal dimension of the finger contact area D Based on this, the basic parameters of the contact materials are input for subsequent iterative calculations. First, the elastic moduli of the two materials in the contact region—the rough surface and the rigid plane—are input. E 1. E 2. Poisson's ratio n 1. n 2, and the resistivity of rough surface materials. r 1. r 2. Obtain the equivalent elastic modulus E and equivalent resistivity r .

[0119] (3)

[0120] (4)

[0121] Then, based on the hardness coefficient K Poisson's ratio of the rough surface in the contact area n The relationship of 1:

[0122] (5)

[0123] and rough surface region expansion coefficient Relationship with fractal dimension D:

[0124] (6)

[0125] Finally, the critical contact area in the MB analysis model was obtained. a eco for:

[0126] (7)

[0127] Step 3, due to the length of the micro-protrusion substrate l The substrate length varies with the contact area; that is, for different micro-protrusions, the substrate length varies. l Different, and base length l The relationship between the contact area and the micro-protrusion substrate length is not a known linear one, making it impossible to calculate the integral over all micro-protrusion substrate lengths. To solve this problem, the critical elastic contact area is set... a ec Equal to the critical contact area given by the MB fractal contact model a eco This will allow us to determine the critical basis length. l ec Therefore, when calculating the contact load of all elastic contact micro-protrusions, the base length is treated as a constant. l ec At this point, the critical basis length serves as a benchmark to describe all micro-protrusions. The basis lengths of micro-protrusions of different sizes differ from the critical basis length by a certain multiple λ. Therefore, when calculating the basis length integral, it can be equivalent to λ. l ec The integral. Therefore, by calculating the two critical contact areas. a ec= a eco The formula is equivalent, and the bottom diameter of the contact micro-protrusion is calculated by reverse calculation. l。 To facilitate subsequent calculations, its dimensions are standardized as follows: l x .

[0128] (8)

[0129] Step 4, due to externally applied load P It is the result of all the deformation effects of the micro-convexity, therefore P It is the sum of the pressures during the left and right deformation stages. Therefore, given the known external load... P Through repeated iterations, the magnitudes of the forces acting on the micro-protrusion during its elastic deformation, first elastoplastic deformation, second elastoplastic deformation, and fully plastic deformation stages are calculated using the following formula:

[0130] (9)

[0131] (10)

[0132] (11)

[0133] (12)

[0134] (13)

[0135] In the formula, F re For elastic deformation contact load; F rep1 This is the first elastic-plastic deformation contact load; F rep2 This is the second elastic-plastic deformation contact load; F rp For fully plastic deformation contact load.

[0136] Similarly, the actual contact area between the rough surface of the finger and the electrode. A r It is the sum of the contact areas of all micro-protrusions. Depending on the size of the micro-protrusions and the load they bear, the deformation of the micro-protrusions is classified into elastic deformation, first elastoplastic deformation, second elastoplastic deformation, and complete plastic deformation. Therefore, the actual contact area... A r This is the sum of the deformed contact areas mentioned above. When the actual contact area falls within the corresponding range, the true contact area and contact load at that moment can be uniquely obtained. The formula for calculating the true contact area is:

[0137] (14)

[0138] (15)

[0139] (16)

[0140] (17)

[0141] (18)

[0142] In the formula, A re The contact area is the area of ​​elastic deformation; A rep1 This represents the contact area during the first elastic-plastic deformation. A rep2 This represents the contact area during the second elastic-plastic deformation. A rp This represents the contact area under complete plastic deformation.

[0143] Normalize equations (10)-(18) by dividing both sides by E. A a ,in: ; ; ; ; . , , .

[0144] Given a fixed fractal dimension , , All are constants. Therefore, for material properties... i fractal dimension D Structural parameters G When constant, the dimensionless contact load is a function of the maximum contact area and the actual contact area. By summing the contact loads at different deformation stages, the total contact load on the electrical contact surface can be obtained. P Compared to the actual contact area A r The function expression:

[0145] (19)

[0146] Through different actual loads P By forming an equation with equation (19), the parameters for each deformation stage can be obtained, laying the foundation for subsequent contact resistance calculations. Combining the Holm contact resistance calculation empirical formula, the formula for calculating contact resistance using fractals is as follows:

[0147] (20)

[0148] (twenty one)

[0149] (twenty two)

[0150] (twenty three)

[0151] (twenty four)

[0152] Step 5, assuming external load P If all the forces act during the elastic deformation stage, then the initial elastic deformation pressure can be obtained. F rex0 :

[0153] (25)

[0154] Since the entire process is in the elastic deformation stage, the actual contact area can be calculated using the first term of equation (19). A rx0 And the area of ​​the largest micro-protrusion can be calculated. a l .

[0155] (26)

[0156] Ⅰ: If a l <= a ec External loads cause elastic deformation in the contact area, resulting in a total contact resistance of R ce ;

[0157] II: If a l > a ec Then, re-enter step 5 and iterate using equation (25) as follows:

[0158] (27)

[0159] in, A Nominal contact area a This represents the contact area of ​​the micro-protrusion;

[0160] The corrected true contact area is calculated using equation (27) and the first two terms of equation (19). A rx And the area of ​​the largest micro-convexity can be calculated a second time. a l .

[0161] III: If a l <=7.1197 a ec External loads cause elastic and first elastoplastic deformation in the contact area, resulting in a total contact resistance of... R ce , R cep1 The sum of parallel connections;

[0162] IV: If a l > a ec Then, re-enter step 5 and iterate using equation (25) as follows:

[0163] (28)

[0164] The corrected true contact area is calculated using equation (28) and the first three terms of equation (19). A rx And the area of ​​the largest micro-convexity can be calculated a second time. a l .

[0165] V: If a l <=205.3827 a ec And a l >7.1197a ec ,but a epc =7.1197 a ec , a pc =205.3827 a ec .

[0166] External loads cause elastic, first elastoplastic, and second elastoplastic deformations in the contact area, resulting in a contact resistance of... R ce , R cep1 , R cep2 The sum of parallel connections;

[0167] VI: If a l >205.3827 a ec Then, re-enter step 5 and iterate using equation (25) as follows:

[0168] (29)

[0169] The corrected true contact area is calculated using equation (29) and the first two terms of equation (19). A rx And the area of ​​the largest micro-convexity can be calculated a second time. a l .

[0170] Based on this, if the external load causes elastic, first elastoplastic, second elastoplastic, and fully plastic deformation in the contact area, then the total contact resistance is: R ce , R cep1 , R cep2 , R cp The sum of parallel connections.

[0171] In summary, the contact resistance under different external loads P can be calculated.

[0172] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0173] Furthermore, although the operations are described in a specific order, this should be understood as requiring that such operations be performed in the specific order shown or in sequential order, or requiring that all illustrated operations be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of the invention. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0174] Although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.

Claims

1. A method for calculating the contact resistance of the contact finger electrical connection structure of ultra-high voltage / extra-high voltage GIS equipment, characterized in that, The method includes: S1. Use MATLAB and laser confocal microscopy to capture grayscale images of the finger contact area, and determine the fractal dimension of the finger contact area based on the grayscale images. S2. Determine the critical contact area based on the fractal dimension of the contact area and the characteristic parameters of the contact surface; S3. Determine the critical substrate length and the bottom diameter of the contact micro-protrusion based on the critical contact area; S4. Based on the critical contact area, critical base length, and bottom diameter of the contact micro-protrusion, calculate the area of ​​the maximum micro-protrusion of the contact finger electrical connection structure under different loads. S5. Determine the contact resistance of the finger electrical connection structure based on the area of ​​the largest micro-protrusion. The determination of the critical contact area based on the fractal dimension of the finger contact area and the characteristic parameters of the contact surface includes: S31. The deformation of a single micro-protrusion structure is divided into four stages: elastic stage, first elastoplastic stage, second elastoplastic stage, and fully plastic deformation stage. The critical elastic contact area is derived from the deformation process as follows: (2) in, Indicates the critical elastic contact area; Indicates the hardness coefficient; Indicates the material properties of the contact material; G represents the bottom diameter of the contact micro-protrusion substrate; G represents the fractal roughness expansion coefficient of the rough surface. D This represents the fractal dimension of the contact area between the fingers; S32. Based on the fractal dimension of the finger contact area D Input the basic parameters of the contact material and perform iterative calculations to determine the critical contact area; S321, Input the elastic modulus of the two materials in the contact area: the rough surface and the rigid plane. E 1. E 2. Poisson's ratio ν 1. ν 2, and the resistivity of rough surface materials. ρ 1. ρ 2. Obtain the equivalent elastic modulus E and equivalent resistivity ρ : (3) (4) S322, based on hardness coefficient K Poisson's ratio of the rough surface in the contact area ν The relationship of 1: (5) and rough surface region expansion coefficient Relationship with fractal dimension D: (6) Obtain the critical contact area in the fractal contact model a eco : (7) in, These are the inherent material parameters in the classical fractal contact model; The determination of the critical substrate length and the bottom diameter of the contact micro-protrusion based on the critical contact area includes: S41, Let the critical elastic contact area be... a ec equal to critical contact area a eco The critical basis length is obtained. l ec ; S42. When calculating the contact load of all elastic contact micro-protrusions, the base length is treated as a constant. l ec At this point, the critical basis length serves as a benchmark to describe all micro-bumps. However, the basis lengths of micro-bumps of different sizes differ from the critical basis length by a certain multiple λ. When calculating the basis length integral, it is equivalent to λ. l ec The integral; S43. By calculating the critical elastic contact area a ec and critical contact area a eco To satisfy both a ec = a eco The formula's equivalent relationship is used to calculate the bottom diameter of the contact micro-protrusion. l， After unifying its dimensions, it becomes l x : (8)； in, A Nominal contact area a This represents the contact area of ​​the micro-protrusion; The calculation of the maximum micro-protrusion area of ​​the contact finger electrical connection structure under different loads, based on the critical contact area, critical substrate length, and contact micro-protrusion bottom diameter, includes: S51, Given the external load P Through repeated iterations, the magnitudes of the forces acting on the micro-protrusion during its elastic deformation, first elastoplastic deformation, second elastoplastic deformation, and fully plastic deformation stages are calculated using the following formula: (9) (10) (11) (12) (13) In the formula, F re For elastic deformation contact load; F rep1 This is the first elastic-plastic deformation contact load; F rep2 This is the second elastic-plastic deformation contact load; F rp For fully plastic deformation contact load; S52. The actual contact area at each deformation stage is calculated using the following formula: (14) (15) (16) (17) (18) In the formula, A re The contact area is the area of ​​elastic deformation; A rep1 This represents the contact area during the first elastic-plastic deformation. A rep2 This represents the contact area during the second elastic-plastic deformation. A rp This represents the contact area under complete plastic deformation. S53. Normalize formulas (10)-(18) by dividing both sides by E. A a ,in: ； ； ； ； ； ； ； ； In fractal dimension D Under certain conditions, , , All are constants; Therefore, regarding material properties θ fractal dimension D Structural parameters G When kept constant, the dimensionless contact load is a function of the maximum contact area and the actual contact area; S54. By summing the contact loads at different deformation stages, the total contact load on the electrical contact surface can be obtained. P Compared to the actual contact area A r The function expression; (19) S55, through different actual loads P By forming an equation with equation (19), the parameters for each deformation stage can be obtained; combined with the empirical formula for calculating Holm contact resistance, the formula for calculating contact resistance using fractals is as follows: (20) (21) (22) (23) (24) S56, Assuming external load P If all the force acts during the elastic deformation stage, then the initial elastic deformation pressure is obtained. F rex0 : (25) Since the entire process is in the elastic deformation stage, the actual contact area can be calculated using the first term of equation (19). A rx0 And the area of ​​the largest micro-convexity is calculated. a l : (26) In formulas (9) to (26), Fn(a) Let be the contact load distribution function of the micro-convex body. The coefficient for the expansion of the rough surface region. a The single-point contact area of ​​the micro-convex body. The area of ​​the largest micro-convexity. K This is the hardness coefficient. H For material hardness, a epc This represents the first critical elastoplastic contact area. a pc This represents the second critical elastoplastic contact area. n(a) Let be the number distribution density function of micro-convexities. F rx To correct the contact load, F r For total contact load, l x To unify the dimensions of the normalized micro-convex body base diameter, A rx To correct for the actual contact area, A r This represents the total actual contact area. A a Nominal contact area a ecx To correct the critical elastic contact area. A re The contact area is adjusted for the elastic stage, where A is the nominal contact area.

2. The method for calculating the contact resistance of the contact finger electrical connection structure of ultra / extra-high voltage GIS equipment according to claim 1, characterized in that, The process involves capturing grayscale images of the finger contact area using MATLAB and a laser confocal microscope, and determining the fractal dimension of the finger contact area based on these images, including: S21. Use a laser confocal microscope to scan the three-dimensional structure of the finger contact area before and after the test to obtain real-shot, color, and grayscale images; S22. Extract a 256×256 pixel grayscale image, use MATLAB to recognize the image, and draw the corresponding 3D model. S23. Calculate the fractal dimension D using the difference box method; The method of calculating fractal dimension using the difference box method includes: S231. An image of size M×N is divided into several k×k sub-blocks of equal size. The gray value at (x,y) of the image is f(x,y), and the total gray levels are... L ; S232. Consider the image as a grayscale set (x, y, f(x, y)) of the surface of a three-dimensional object. The XY plane contains a k×k grid, with several boxes stacked on top of each other. The height of each box is... h =( L -1)× k / min(M,N); S233. If in the (i,j)th grid, the m-th box contains the minimum gray value within the grid, and the l-th box contains the maximum gray value within the grid, then the number n boxes covering the (i,j)-th grid is... r (i,j)=l-m+1; the number of boxes N covering the entire grid. r = n r (i,j); therefore, the fractal dimension can be calculated as: (1) Where r = k / min(M,N), a set of N is calculated by changing the size of the grid k. r Then calculate the point pairs {log(1 / r), log(N)} r The slope of the linear regression of )} is the fractal dimension D.

3. The method for calculating the contact resistance of the contact finger electrical connection structure of ultra-high voltage / extra-high voltage GIS equipment according to claim 1, characterized in that, The determination of the contact resistance of the finger electrical connection structure based on the area of ​​the largest micro-protrusion includes: S61, Area of ​​the largest micro-convexity a 1 and critical elastic contact area a ec Compare; S62, if a l <= a ec The external load causes elastic deformation in the contact area, and the total contact resistance is... R ce ; S63, if a l > a ec Assuming the load acts on both the elastic deformation stage and the first elastic-plastic deformation stage, the following equation is used for iteration: (27) in, A Nominal contact area a This represents the contact area of ​​the micro-protrusion; The corrected true contact area is calculated using equation (27) and the first two terms of equation (19). A rx The area of ​​the largest micro-convexity was obtained in the second calculation. a l The area a1 of the largest micro-convexity obtained in the second calculation is judged. S64, if a l <=7.1197 a ec The external load causes elastic and first elastoplastic deformation in the contact area, and the total contact resistance is... R ce , R cep1 The sum of parallel connections; S65, if a l >7.1197 a ec Assuming the external load acts on the elastic deformation stage, the first elastic-plastic deformation stage, and the second elastic-plastic deformation stage, equation (25) is modified to the following equation for iteration: (28) The corrected true contact area is calculated using equation (28) and the first three terms of equation (19). A rx The area of ​​the largest micro-convexity was obtained in the third calculation. a l The area of ​​the largest micro-convexity obtained in the third calculation is then determined. S66, if a l <=205.3827 a ec ,but a epc =7.1197 a ec , a pc =205.3827 a ec ; External loads cause elastic, first elastoplastic, and second elastoplastic deformations in the contact area, resulting in a contact resistance of... R ce , R cep1 , R cep2 The sum of parallel connections; in, a epc This represents the first critical elastoplastic contact area. a pc This represents the second critical elastoplastic contact area. S67, if a l >205.3827 a ec Assuming the external load acts on the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, and the fully plastic deformation stage, equation (25) is modified to the following equation for iteration: (29) The corrected true contact area is calculated using equation (29) and the first two terms of equation (19). A rx The area of ​​the largest micro-convexity was obtained in the fourth calculation. a l ; If an external load causes elastic, first elastoplastic, second elastoplastic, and fully plastic deformation in the contact area, then the total contact resistance is: R ce , R cep1 , R cep2 , R cp The sum of parallel connections.

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