A high-efficiency simulation method for GIL bellows based on finite elements

Abstract

The application discloses a kind of high-efficiency simulation methods of GIL corrugated pipe based on finite element, comprising the following steps: S1: taking the corrugated pipe in straight line GIL as research object, the geometric modeling of SF6 insulating gas, external air area is carried out to corrugated pipe body;S2: according to the structural parameters of corrugated pipe, corresponding material setting and nonlinear mechanics modeling are carried out;The state of contact surface and the stress distribution of contact body of GIL corrugated pipe structure are influenced mutually in the process of bearing load;Based on three-dimensional nonlinear finite element theory and further analysis method, the large deformation effect of structure is considered, the geometric nonlinear behavior of structure is studied, and the calculation precision is higher relative to analytical calculation method;By the theoretical calculation and definition of the parameters of equal cross-section pipe, the finite element calculation model that can be equivalent to replace the corrugated pipe is established;While guaranteeing the analysis precision, the time used for analysis is greatly shortened, and it is more suitable for the use of GIL in multi-field coupling analysis.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electric power, and particularly relates to a high-efficiency simulation method for a corrugated pipe in a GIL based on finite elements. BACKGROUND

[0002] A gas insulated transmission line (GIL) is a kind of power transmission equipment with a coaxial closed metal shell and a conductor, and adopts compressed gas (SF6 gas or SF6 mixed gas or compressed air) insulation. With the development of a large number of hydropower station constructions, power transmission line river crossings and city underground comprehensive pipe gallery constructions in China, the GIL has been applied more and more due to its advantages of large transmission capacity, low unit loss, small environmental influence, long service life, convenient operation and maintenance and high reliability. As a key component of the power transmission equipment, the corrugated pipe influences the safe and reliable operation of the equipment.

[0003] When the corrugated pipe in the GIL is subjected to multi-field coupling based on the finite element method, the entire analysis process is extremely time-consuming due to the nonlinear characteristics of the corrugated pipe geometry and material, which limits the application of the finite element method in the optimization design of the corrugated pipe in the GIL. SUMMARY

[0004] The purpose of the application is to provide a high-efficiency simulation method for a corrugated pipe in a GIL based on finite elements, which can accurately calculate the influence of thermal expansion and cold contraction of the corrugated pipe in the GIL and strengthen the application of the finite element method in the optimization design of the corrugated pipe in the GIL.

[0005] To achieve the above purpose, the application provides the following technical scheme: a high-efficiency simulation method for a corrugated pipe in a GIL based on finite elements, comprising the following steps: S1: taking a corrugated pipe in a straight-line GIL as a research object, geometrically modeling the corrugated pipe body, SF6 insulation gas and external air area;

[0006] S2: according to the structural parameters of the corrugated pipe, performing corresponding material setting and nonlinear mechanics modeling;

[0007] S3: according to the shell section and the length of the corrugated pipe, performing equivalent modeling;

[0008] S4: according to the model size and material, performing the same mesh division;

[0009] S5: under the same constraint condition, obtaining the axial deformation and stress of different models;

[0010] S6: counting the number of elements and nodes of the two models, and comparing the required time and memory space.

[0011] Preferably, in the step S1, the established geometric model region includes the shell, the flange, the bellows, and the bolt.

[0012] Preferably, in the step S3, the bellows is replaced by a hose with the same cross section as the shell and the same length as the bellows.

[0013] Preferably, in the step S4, different attribute materials are defined for the shell and the cross section pipe respectively, and the same type of element is used for meshing.

[0014] Preferably, in the step S5, the axial displacement of the left end surface of the left shell and the right end surface of the right shell is constrained, and a temperature load of 40℃ is applied to the shell to obtain the axial deformation and stress calculation results of different models.

[0015] Preferably, the step S2 further includes: S21, the axial stiffness of the bellows is:

[0016]

[0017] In the formula, K is the axial stiffness of the bellows, N / mm; N is the wave number of the bellows; D m is the average diameter of the bellows, mm; E b t is the elastic modulus of the bellows material at the design temperature, MPa; E0 is the elastic modulus of the bellows material at room temperature, MPa; δ m is the actual wall thickness of a single layer of the bellows, mm; n is the number of layers of the bellows; h is the wave height, mm; C f is the shape correction coefficient of the bellows.

[0018] S22, whether the material is nonlinear or the geometry is nonlinear, the finite element equation is nonlinear:

[0019] ψ(u)=P(u)-R=0

[0020] Wherein, R is the equivalent node force vector of the external load, and P is the equivalent node force vector of the internal force.

[0021] The nonlinear finite element equation cannot be solved by using the direct method; the incremental method is used.

[0022] In the displacement finite element solution of the incremental method, u is the displacement increment vector of the structure.

[0023] ψ(u)=K(u)u-R=0

[0024] One advantage of using the incremental method is that some intermediate numerical results of the entire load change process can be obtained. When the nature of the problem is related to the history of the load, the incremental method must be used.

[0025] A load factor λ is usually introduced in the incremental method to represent the load, so that the nonlinear finite element equation can be written as:

[0026]

[0027] Load factor λ:

[0028] 0 = λ0< λ1< λ2<... < λ M = 1

[0029] Corresponding to different loads.

[0030] If the solution corresponding to the load factor λ = λ n has been obtained, denoted as u = u n , then

[0031]

[0032] Let u n+1 = u n + Δu be its solution, so that

[0033]

[0034] Taylor expand Ψ(u n + Δu, λ n + Δλ) at u n , λ n , we have

[0035]

[0036] Let

[0037]

[0038] Considering , the above equation can be approximated as

[0039]

[0040] If it is considered that the solution u = u n corresponding to the load factor λ = λ n is not the exact solution, i.e.

[0041]

[0042] Then the solution of the equation is

[0043]

[0044] ​S51, define the elastic modulus E1 of the equal cross-section tube material according to the stiffness of the bellows, so that the bellows has the same mechanical properties, i.e. the same elongation under the same tension. Assuming that the length of the equal cross-section tube and the bellows is L, the same axial tension F, N is applied to the two end faces; the elastic modulus of the equal cross-section tube is E, MPa, the cross-sectional area is A, mm 2 , the deformation amount of the equal cross-section tube is ΔL1, mm; the stiffness of the bellows is K, and the deformation amount is ΔL2, mm.

[0045]

[0046] S52, the equal cross-section tube will generate a large axial strain ε x1 , μ1 = -ε y1 / ε x1 (μ1 is the axial Poisson's ratio of the equal cross-section tube material). The length of the equal cross-section tube is L1, mm; the length of the left shell is L2, mm; the length of the right shell is L3, mm; the linear expansion coefficient of the shell material is α, mm / (mm·℃); the shrinkage strain of the shell perpendicular to the axial direction caused by the temperature difference is ε y1 , the wall thickness is δ, mm; the temperature difference from the working temperature to the ambient temperature is ΔT; assuming that the sum of the shrinkage deformation amounts of the left and right shells is the tensile deformation amount of the equal cross-section tube, the following is obtained:

[0047]

[0048] Compared with the prior art, the beneficial effects of the present application are that: the state of the contact surface and the stress distribution of the contact body of the bellows structure in the GIL are mutually influenced during the load bearing process; based on the three-dimensional nonlinear finite element theory and further analysis method, the large deformation effect of the structure is considered, the geometric nonlinear behavior of the structure is studied, and the calculation precision is higher than that of the analytical calculation method; through the theoretical calculation and definition of the parameters of the equal cross-section tube, the finite element calculation model which can be equivalent to replace the bellows is established; while ensuring the analysis precision, the analysis time is greatly shortened, and the method is more suitable for the use of the GIL in the multi-field coupling analysis. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 It is a flowchart of the high-efficiency simulation method of the bellows in the GIL based on the finite element of the present application;

[0050] Figure 2 It is a schematic diagram of the bellows structure of the GIL researched by the embodiment of the present application.

[0051] Figure 3 It is a diagram of the axial displacement amount of the bellows and the equal cross-section tube of the GIL researched by the embodiment of the present application with the cross-section position.

[0052] Figure 4The object researched by the embodiment of the present application is a GIL bellows and a stress change diagram with a cross-section position of an equal cross-section pipe. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the present application.

[0054] Please refer to Figures 1 to 4 The present application provides a technical solution: as Figure 1 A high-efficiency simulation method of a bellows in a GIL based on finite elements, comprising the following steps:

[0055] S1: taking the bellows in a straight-line GIL as a research object, geometrically modeling the shell, the expansion joint and the flange;

[0056] S2: according to the structural parameters of the bellows, performing corresponding material setting and nonlinear mechanics modeling;

[0057] S3: according to the shell cross-section and the bellows length, performing equivalent modeling;

[0058] S4: according to the model size and the material, performing the same mesh division;

[0059] S5: under the same constraint condition, obtaining the axial deformation and stress of different models;

[0060] S6: counting the number of elements and the number of nodes of the two models, and comparing the time and memory space required for calculation.

[0061] More specifically, as Figure 2 shown, the geometric model region established in step S1 includes the shell, the expansion joint and the flange.

[0062] More specifically, step S2 includes the following steps:

[0063] The shell material is 5083-H112, the shell wall thickness is 6mm, and the bellows material is 06Cr18Ni11Ti.

[0064] S21: referring to the empirical formula in GB / T12777-2008, the axial stiffness of the bellows is:

[0065]

[0066] In the formula, K is the axial stiffness of the bellows, N / mm; N is the wave number of the bellows; D mD is the average diameter of the bellows, mm; E is the elastic modulus of the bellows material at design temperature, MPa; E0 is the elastic modulus of the bellows material at room temperature, MPa; δ is the thickness of the bellows material, mm; n is the number of layers of the bellows; h is the wave height, mm; C and C are the shape correction factors of the bellows. b t D is the average diameter of the bellows, mm; E is the elastic modulus of the bellows material at design temperature, MPa; E0 is the elastic modulus of the bellows material at room temperature, MPa; δ is the thickness of the bellows material, mm; n is the number of layers of the bellows; h is the wave height, mm; C and C are the shape correction factors of the bellows. m D is the average diameter of the bellows, mm; E is the elastic modulus of the bellows material at design temperature, MPa; E0 is the elastic modulus of the bellows material at room temperature, MPa; δ is the thickness of the bellows material, mm; n is the number of layers of the bellows; h is the wave height, mm; C and C are the shape correction factors of the bellows. f D is the average diameter of the bellows, mm; E is the elastic modulus of the bellows material at design temperature, MPa; E0 is the elastic modulus of the bellows material at room temperature, MPa; δ is the thickness of the bellows material, mm; n is the number of layers of the bellows; h is the wave height, mm; C and C are the shape correction factors of the bellows.

[0067] S22: Regardless of the material nonlinear problem or the geometric nonlinear problem, the finite element equation is nonlinear:

[0068] ψ(u) = P(u) - R = 0

[0069] Wherein, R is the equivalent node force vector of external load, P is the equivalent node force vector of internal force.

[0070] For nonlinear finite element equation system, the direct method cannot be used to obtain its solution. Generally, various mathematical numerical methods are used to approximate the solution of nonlinear equation system with a series of linear equation systems. Common numerical solution methods are generally divided into three categories, namely direct iteration method, Newton method and incremental method.

[0071] In the displacement finite element solution method of the incremental method, u is the displacement increment vector of the structure.

[0072] ψ(u) = K(u)u - R = 0

[0073] One advantage of using the incremental method is that some intermediate numerical results of the entire load change process can be obtained. When the nature of the problem is related to the history of the load, the incremental method must be used.

[0074] In the incremental method, a load factor λ is usually introduced, and the load is represented by , so the nonlinear finite element equation can be written as:

[0075]

[0076] Load factor λ:

[0077] 0 = λ0 < λ1 < λ2 < … < λ M = 1

[0078] Corresponding to different loads.

[0079] If the solution corresponding to the load factor λ = λ n is obtained, denoted as u = u n , then

[0080]

[0081] Let u n+1 = un + Δu is its solution, so that:

[0082]

[0083] Let Ψ(u n + Δu, λ n + Δλ) be Taylor expanded at u n , λ n :

[0084]

[0085] Let us denote:

[0086]

[0087] Taking into account that the above equation can be approximated as

[0088]

[0089] Taking into account that the solution u = u n corresponding to the load factor λ = λ n is not the exact solution, i.e.:

[0090]

[0091] The solution of the equation is then:

[0092]

[0093] More specifically, in step S3 in the middle, the bellows are replaced by a hose (sectional tube) having the same section as the shell and the same length as the bellows.

[0094] More specifically, in step S4 in the middle, different property materials are defined for the shell and the sectional tube, respectively, and the mesh is divided using the same type of element (Solid 186).

[0095] More specifically, step S5 comprises the following steps:

[0096] S51 : define the modulus of elasticity E1 of the material of the sectional tube according to the stiffness of the bellows, so that it has the same mechanical properties as the bellows, i.e. the same elongation under the same tensile force. Let the length of the sectional tube and the bellows be L, the same axial tensile force be F, N, the modulus of elasticity of the sectional tube be E, MPa, the cross-sectional area be A, mm 2 , the deformation be ΔL1, mm, and the stiffness of the bellows be K, the deformation be ΔL2, mm.

[0097]

[0098] S52: large axial strain ε will be generated in the cold shrinking process of the equal cross-section tube x1 μ1=-ε y1 / ε x1 (μ1 is the axial Poisson's ratio of the equal cross-section tube material). The equal cross-section tube has a length of L1, mm; the left shell has a length of L2, mm; the right shell has a length of L3, mm; the linear expansion coefficient of the shell material is α, mm / (mm·℃); the shrinkage strain of the shell perpendicular to the axial direction caused by the temperature difference is ε y1 , the wall thickness is δ, mm; the temperature difference from the working temperature to the ambient temperature is ΔT; the sum of the shrinkage deformation of the left and right shells is set to be the tensile deformation of the equal cross-section tube, and the following equation is obtained:

[0099]

[0100] The axial displacement of the left end surface of the left shell and the right end surface of the right shell is constrained (the displacement of the left end surface of the left shell is 0), and a temperature load of 40℃ is applied to the shell (the initial temperature is set to -15℃), and the axial deformation of different models, the axial displacement and stress change with the cross-section position are obtained, as shown in Figures 3-4 .

[0101] More specifically, in step S6, the number of elements, the number of nodes, the time required for calculation and the memory usage space related to the calculation efficiency of the corrugated pipe and the equal cross-section tube finite element are counted, as shown in Figure 4 .

[0102] The calculation efficiency of the GIL corrugated pipe and the equal cross-section tube model studied in this embodiment is compared as shown in the following table.

[0103]

[0104]

[0105] Although the embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and alterations can be made thereto without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for efficient simulation of a corrugated tube in a GIL based on finite elements, characterized in that: It comprises the following steps: S1: taking the bellows in straight line GIL as the research object, geometrically modeling the bellows body, SF6 insulating gas and external air area; S2: according to the structural parameters of the bellows, performing corresponding material setting and nonlinear mechanics modeling; S3: according to the shell section and the length of the bellows, performing equivalent modeling; S4: according to the model size and material, performing the same mesh division; S5: under the same constraint condition, obtaining the axial deformation and stress of different models; S6: counting the number of elements and nodes of the two models, comparing the time and memory space required for calculation; The step S2 further comprises S21: the axial stiffness of the bellows is: where K is the axial stiffness of the bellows, N / mm; N is the wave number of the bellows; D m is the average diameter of the bellows, mm; E b t is the modulus of elasticity of the bellows material at the design temperature, MPa; E0is the modulus of elasticity of the bellows material at room temperature, MPa; δ m is the actual wall thickness of a single layer of the bellows, mm; n is the number of layers of the bellows; h is the wave height, mm; C and C f are the shape correction factors of the bellows; S22: The finite element equation is nonlinear regardless of the material nonlinear problem or the geometric nonlinear problem: ψ (u) = P (u) - R = 0 Wherein, R is the equivalent node force vector of external load, P is the equivalent node force vector of internal force; For nonlinear finite element equation group, direct method cannot be used to obtain its solution; and incremental method is used; In the displacement finite element solution of the incremental method, u is the displacement increment vector of the structure; ψ (u) = K (u) u - R = 0 An advantage of using the incremental method is that some intermediate numerical results of the whole load change process can be obtained; when the nature of the problem and the history of the load are related, the incremental method must be used; A load factor λ is usually introduced in the incremental method to express the load, p, as and the nonlinear finite element equation can be written as Load factor λ: 0 = λ0< λ1< λ2<... < λ M = 1 Corresponding to different loads; If the solution corresponding to the load factor λ = λ n has been found, denoted by u = u n , then Let u n+1 = u n + Δu be a solution, then we have: Ψ(u) n +Δu,λ n +Δλ) in u n ,λ n Taylor expansion yields: If it is recorded as: Taking into account The above equation can thus be approximated as If the solution u = u n corresponding to the load factor λ = λ n is not the exact solution, i.e.: Then the solution of the equation is:

2. The method for efficient simulation of bellows in GIL based on finite elements according to claim 1, characterized in that: In the step S1, the geometric model area established includes shell, flange, bellows and bolt.

3. The method for efficient simulation of bellows in GIL based on finite elements according to claim 1, characterized in that: In the step S3, the bellows is replaced by a hose with the same section as the shell and the same length as the bellows.

4. The method for efficient simulation of bellows in a GIL based on finite elements according to claim 1, characterized in that: In the step S4, different attribute materials are defined for the shell and the equal-section pipe respectively, and the same type of element is used for mesh division.

5. The method for efficient simulation of bellows in a GIL based on finite elements according to claim 1, characterized in that: In the step S5, the axial displacement of the left end surface of the left shell and the right end surface of the right shell is constrained, and a temperature load of 40℃ is applied to the shell, to obtain the axial deformation and stress calculation results of different models.

6. The method for efficient simulation of bellows in a GIL based on finite elements according to claim 1, characterized in that: The step S5 further comprises: S51: define the elastic modulus E1 of the equal cross-section tube material according to the bellows stiffness, so that it has the same mechanical properties as the bellows; assume that the length of the equal cross-section tube and the bellows is L, the same axial tension F, N is applied to the two end faces; the elastic modulus of the equal cross-section tube is E, MPa, the cross-sectional area is A, mm 2 , the deformation amount is ΔL1, mm; the stiffness of the bellows is K, and the deformation amount is ΔL2, mm; S52: large axial strain ε will be generated in the cold shrinking process of the equal cross-section tube x1 , μ1 = -ε y1 / ε x1， μ1 is the axial Poisson's ratio of the equal cross-section tube material; the length of the equal cross-section tube is L1, mm; the length of the left shell is L2, mm; the length of the right shell is L3, mm; the linear expansion coefficient of the shell material is α, mm / (mm·℃); the shrinkage strain of the shell perpendicular to the axial direction caused by the temperature difference is ε y1 , the wall thickness is δ, mm; the temperature difference from the working temperature to the ambient temperature is ΔT; it is assumed that the sum of the shrinkage deformation amounts of the left and right shells is the tensile deformation amount of the equal cross-section tube, and the following is obtained:

Images