A method for calculating the layered stress of steel core aluminum stranded wire under thermal-mechanical coupling

Abstract

The present invention relates to a method for calculating the layered stress of a steel core aluminum stranded wire under the action of thermal coupling, including: calculating the average operating tension of the conductor at the required temperature; substituting the average operating tension of the conductor at the temperature into the axial total strain calculation expression to obtain the conductor axial total strain and the strand strain of the strand; removing the temperature strain from the strand strain to obtain the strand strain of the strand under tension; calculating the axial strain of the strand under tension; multiplying the axial strain of the strand under tension by the elastic modulus of each layer of strand to obtain the axial layered stress of the strand; calculating the layered stress of the steel core and aluminum strand of the conductor under extreme meteorological conditions, and judging whether the conductor meets the safety design and fatigue resistance performance under extreme meteorological conditions. The present invention obtains the layered stress calculation expression of strands of different materials through theoretical derivation, and can obtain the layered stress value of each layer through programming calculation, which provides an important reference for the safety design and selection of overhead lines and the research on fatigue resistance performance.

Description

Technical Field

[0001] The invention relates to the technical field of overhead conductor design calculation, in particular to a method for calculating layered stress of a steel core aluminum stranded wire under the action of thermal-mechanical coupling. Background Art

[0002] With the increase in electricity demand and the large-scale construction of transmission lines, conductor stress under different meteorological conditions is an important indicator for the design and maintenance of overhead conductors. In order to ensure the safe operation of transmission lines, the conductor stress must be controlled within the design range. In actual operation, the cross-sectional stress of steel-core aluminum stranded wire will show obvious stratification effect under the combined action of tension and temperature. In existing projects, construction and design calculations are carried out according to the average stress, ignoring the different properties of the steel core and aluminum strands, the geometric shape of the conductor, extrusion friction, etc.

[0003] At present, the main research work at home and abroad includes: Zheng Liyang and Sun Zuzhi studied the theoretical model of aluminum stranded wire and steel core aluminum stranded wire under tension, and gave a calculation method for stranded wire stress under tension; Lin Jianhua and Zeng Wei simulated the stress distribution law of the conductor after being subjected to tension stress during operation through finite element analysis; Qin Li considered the structure and material properties of carbon fiber composite core conductors, and simulated and analyzed the stress distribution of the outer strands and the contact part of the wire clamp when the conductor was subjected to tension, shear force and bending moment and the extrusion force of the wire clamp during actual operation through finite element analysis; Zhang Qiuhua used theoretical calculation methods, finite element simulation methods and experimental measurement methods to study the stress and stiffness of the conductor under tension load; Rui Xiaoming proposed a new and effective modeling and analysis method, and used Abaqus software to study the proposed method; Raoof et al. calculated the stiffness of different strands by studying the tension-torsion of multi-layer strands; Kumar K studied the axial and bending responses of multi-layer cables under the condition of ignoring friction, and derived the expressions of tensile and torsional stiffness of multi-layer strands; Burks B conducted a numerical study on the aluminum conductor composite core M (ACCC) and obtained the stress distribution of the conductor under heat and load; Xiang L proposed a new model to describe the response of multi-strand steel wire ropes to axial tension and axial torsion, providing new insights into the fatigue and failure behavior of steel strands.

[0004] It can be seen that there are many studies on the distribution of conductor layered stress under tension at home and abroad, but there is a lack of research on the distribution of conductor layered stress under the combined action of temperature and tension. Conductor layered stress affects the safety design and fatigue resistance of overhead conductors. The research on layered stress has important research value for preventing conductor breakage and overturning of transmission towers in large-diameter and large-span transmission lines under extreme climatic conditions. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the layered stress of steel-core aluminum stranded wire under thermal coupling, which takes into account both the average stress and the difference between the strands of each layer of the conductor in the design calculation of the transmission line, can accurately calculate the fatigue damage of the conductor, and ensure the safe design of the overhead conductor under extreme climatic conditions.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for calculating the layered stress of steel core aluminum stranded wire under the action of thermal-mechanical coupling, the method comprising the following steps in order:

[0007] (1) Taking a certain initial state as a reference, the average operating tension of the conductor at the required temperature is calculated by using the state equation of the overhead line at different suspension points;

[0008] (2) Substituting the average operating tension of the conductor at the temperature obtained in step (1) into the calculation expression of the total axial strain, the total axial strain of the conductor is obtained; and the strand strain of the strand is obtained according to the relationship between the axial strain and the strand strain;

[0009] (3) The strand strain under tension is obtained by subtracting the temperature strain from the strand strain.

[0010] (4) According to the relationship between the axial strain and the strand strain and the strand strain under tension, the axial strain of the strand under tension is calculated;

[0011] (5) The axial strain of the strand under tension multiplied by the elastic modulus of each layer of strands gives the axial layer stress of the strand;

[0012] (6) Calculate the layered stress of the conductor steel core and aluminum strands under extreme meteorological conditions, and compare and analyze it with the extreme value of the strand stress required by the specification to determine whether the conductor meets the safety design and fatigue resistance performance under extreme meteorological conditions.

[0013] The step (1) specifically refers to: the calculation formula of the state equation of the unequal height suspension point overhead line is as follows:

[0014]

[0015] Where: 01 , σ 02 They are the stress at the lowest point of the overhead line sag at temperature t1 and temperature t2 respectively;

[0016] γ1 and γ2 are the specific loads of overhead lines at temperature t1 and temperature t2 respectively;

[0017] t1 and t2 are the temperatures of the overhead line at temperature t1 and temperature t2 respectively;

[0018] l and β are the gear distance and height difference angle respectively;

[0019] α and E are the axial comprehensive temperature expansion coefficient and comprehensive elastic modulus of the overhead line, respectively;

[0020] The stress σ at the lowest point of the overhead line sag at temperature t2 is obtained 02 ;

[0021] according to Then the average operating tension of the conductor at the required temperature is obtained, that is, the tension at the lowest sag point of the conductor under the calculation of the annual average temperature; A n is the total cross-sectional area of ​​the nth layer of wire strands, σ 02 is the stress at the lowest point of the overhead line sag at temperature t2, and T is the average operating tension of the conductor.

[0022] The step (2) specifically refers to:

[0023] Substitute the average operating tension of the conductor at the temperature obtained in step (1) into the calculation expression of the total axial strain: Where A is the total cross-sectional area of ​​the conductor, and the total axial strain ε of the conductor is obtained; according to the relationship between the axial strain and the strand strain, the strand strain ε is obtained: n ′=(cos 2 β n -μ n sin 2 β n )ε, where: β n The twist angle is the angle between the strands of wire wound along the axis of the inner core wire and the axial direction.

[0024] The relationship between the strand strain and the axial strain of the strand in step (2) is specifically solved as follows:

[0025] (2a) The parametric equation of the center line of the nth layer of strands is:

[0026]

[0027] y n =R n cosθ n

[0028] z n =R n sinθ n

[0029] Where: R n is the radius of the nth layer; R n =D n -d n ;D n The outer diameter of the strands in the nth layer; d n is the diameter of the strands in the nth layer; Pn is the pitch of the strands in the nth layer; θ n is the central angle of the nth layer of strands wound around the center layer circle;

[0030] (2b) From the geometric relationship, we know that:

[0031]

[0032] In the formula, β n The twist angle is the angle between the strands wound along the inner core axis and the axis direction.

[0033] (2c) From the parametric equation of the strand centerline in step (2a), the micro-arc length of the strand in the nth layer is:

[0034]

[0035] (2d) The length of the strand in the nth layer is:

[0036]

[0037] (2e) For S in formula (3), n , R n , P n ,θ n Differentiations are:

[0038]

[0039] (2f) Dividing formula (4) by formula (3) yields:

[0040]

[0041] (2g) The axial strain of the nth layer of strands is:

[0042] Where, u is the axial deformation;

[0043] (2h) The radial strain of the nth layer of strands is:

[0044] Where, μ is the strand Poisson’s ratio;

[0045] (2i) Substituting equations (6) and (7) into equation (5), we obtain:

[0046]

[0047] Among them, μ n is the Poisson's ratio of the nth strand;

[0048] (2j)θ nis the central angle of the nth layer of strands wound on the center circle. When the position of the center circle is determined, it is a constant.

[0049] (2k) Substituting formulas (8) and (9) into formula (5) and taking the limit, we can obtain the relationship between the strand strain and the axial strain:

[0050] That is, the strand strain of the nth layer is:

[0051] The step (3) specifically refers to:

[0052] Strand strain: ε n ′=(cos 2 β n -μ n sin 2 β n )ε, minus the temperature strain: ε t ″=α i (t i -t0), the strand strain under tension is obtained: n ″=(cos 2 β n -μ n sin 2 β n )ε-α i (t i -t0), where: α i is the thermal expansion coefficient of the i-th layer of strands, t i is the temperature of the conductor in a certain state, and t0 is the initial stringing temperature of the conductor.

[0053] The step (4) specifically means that the axial strain of the strand under tension alone is equal to the strand strain multiplied by the cosine of the strand lay angle:

[0054] ε n =ε″ n cosβ n

[0055] In the formula, ε n ″=(cos 2 β n -μ n sin 2 β n )ε-α i (t i -t0) is the strand strain.

[0056] The step (5) specifically refers to:

[0057] Axial strain of the strand under tension: ε n=ε″ n cosβ n , multiplied by the elastic modulus E of each layer of strands n , the axial delamination stress of the strand is obtained:

[0058] σ n =E n ε″ n cosβ n .

[0059] The step (6) specifically refers to: comparing and analyzing the strand stress of each layer calculated from steps (1) to (6) with the strand strength to determine whether the strand meets the strength requirements.

[0060] It can be seen from the above technical scheme that the beneficial effects of the present invention are: first, by considering the different properties of the steel core and the aluminum strands, the influence of the conductor geometry and the combined effects of temperature and tension, the present invention provides a theoretical expression for the cross-sectional layered stress of the steel core aluminum stranded wire under the combined effects of tension and temperature; second, it provides important reference value for the safe design and selection of overhead conductors and the study of fatigue resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flow chart of the method of the present invention;

[0062] Figure 2 It is a conductor structure diagram of the present invention;

[0063] Figure 3 It is a developed diagram of the strands of the present invention;

[0064] Figure 4 It is a schematic diagram of deformation of the strand of the present invention under the action of temperature and tension;

[0065] Figure 5 This is a schematic diagram of the axial mesh division and cross-sectional mesh division of the JL / G1A-400 / 35 conductor;

[0066] Figure 6 This is the axial stress cloud diagram of the middle section (x=50mm) of the JL / G1A-400 / 35 conductor under 20% RTS. DETAILED DESCRIPTION

[0067] like Figure 1 As shown, a method for calculating the layered stress of a steel core aluminum stranded wire under the action of thermal-mechanical coupling comprises the following steps in sequence:

[0068] (1) Taking a certain initial state as a reference, the average operating tension of the conductor at the required temperature is calculated by using the state equation of the overhead line at different suspension points;

[0069] (2) Substituting the average operating tension of the conductor at the temperature obtained in step (1) into the calculation expression of the total axial strain, the total axial strain of the conductor is obtained; and the strand strain of the strand is obtained according to the relationship between the axial strain and the strand strain;

[0070] (3) The strand strain under tension is obtained by subtracting the temperature strain from the strand strain.

[0071] (4) According to the relationship between the axial strain and the strand strain and the strand strain under tension, the axial strain of the strand under tension is calculated;

[0072] (5) The axial strain of the strand under tension multiplied by the elastic modulus of each layer of strands gives the axial layer stress of the strand;

[0073] (6) Calculate the layered stress of the conductor steel core and aluminum strands under extreme meteorological conditions, and compare and analyze it with the extreme value of the strand stress required by the specification to determine whether the conductor meets the safety design and fatigue resistance performance under extreme meteorological conditions.

[0074] The step (1) specifically refers to: the calculation formula of the state equation of the unequal height suspension point overhead line is as follows:

[0075]

[0076] Where: 01 , σ 02 They are the stress at the lowest point of the overhead line sag at temperature t1 and temperature t2 respectively;

[0077] γ1 and γ2 are the specific loads of overhead lines at temperature t1 and temperature t2 respectively;

[0078] t1 and t2 are the temperatures of the overhead line at temperature t1 and temperature t2 respectively;

[0079] l and β are the gear distance and height difference angle respectively;

[0080] α and E are the axial comprehensive temperature expansion coefficient and comprehensive elastic modulus of the overhead line, respectively;

[0081] The stress σ at the lowest point of the overhead line sag at temperature t2 is obtained 02 ;

[0082] according to Then the average operating tension of the conductor at the required temperature is obtained, that is, the tension at the lowest sag point of the conductor under the calculation of the annual average temperature; A n is the total cross-sectional area of ​​the nth layer of wire strands, σ 02 is the stress at the lowest point of the overhead line sag at temperature t2, and T is the average operating tension of the conductor.

[0083] The step (2) specifically refers to:

[0084] Substitute the average operating tension of the conductor at the temperature obtained in step (1) into the calculation expression of the total axial strain: Where A is the total cross-sectional area of ​​the conductor, and the total axial strain ε of the conductor is obtained; according to the relationship between the axial strain and the strand strain, the strand strain ε is obtained: n ′=(cos 2 β n -μ n sin 2 β n )ε, where: β n The twist angle is the angle between the strands of wire wound along the axis of the inner core wire and the axial direction.

[0085] like Figure 2 , 3 As shown in , 4, the relationship between the strand strain and the axial strain in step (2) is solved in the following specific steps:

[0086] (2a) The parametric equation of the center line of the nth layer of strands is:

[0087]

[0088] y n =R n cosθ n

[0089] z n =R n sinθ n

[0090] Where: R n is the radius of the nth layer; R n =D n -d n ;D n The outer diameter of the strands in the nth layer; d n is the diameter of the strands in the nth layer; P n is the pitch of the strands in the nth layer; θ n is the central angle of the nth layer of strands wound around the center layer circle;

[0091] (2b) From the geometric relationship, we know that:

[0092]

[0093] In the formula, β n The twist angle is the angle between the strands wound along the inner core axis and the axis direction.

[0094] (2c) From the parametric equation of the strand centerline in step (2a), the micro-arc length of the strand in the nth layer is:

[0095]

[0096] (2d) The length of the strand in the nth layer is:

[0097]

[0098] (2e) For S in formula (3), n , R n , P n ,θ n Differentiations are:

[0099]

[0100] (2f) Dividing formula (4) by formula (3) yields:

[0101]

[0102] (2g) The axial strain of the nth layer of strands is:

[0103] Where, u is the axial deformation;

[0104] (2h) The radial strain of the nth layer of strands is:

[0105] Where, μ is the strand Poisson’s ratio;

[0106] (2i) Substituting equations (6) and (7) into equation (5), we obtain:

[0107]

[0108] Among them, μ n is the Poisson's ratio of the nth strand;

[0109] (2j)θ n is the central angle of the nth layer of strands wound on the center circle. When the position of the center circle is determined, it is a constant.

[0110] (2k) Substituting formulas (8) and (9) into formula (5) and taking the limit, we can obtain the relationship between the strand strain and the axial strain:

[0111] That is, the strand strain of the nth layer is:

[0112] The step (3) specifically refers to:

[0113] Strand strain: ε n′=(cos 2 β n -μ n sin 2 β n )ε, minus the temperature strain: ε t ″=α i (t i -t0), the strand strain under tension is obtained: n ″=(cos 2 β n -μ n sin 2 β n )ε-α i (t i -t0), where: α i is the thermal expansion coefficient of the i-th layer of strands, t i is the temperature of the conductor in a certain state, and t0 is the initial stringing temperature of the conductor.

[0114] The step (4) specifically means that the axial strain of the strand under tension alone is equal to the strand strain multiplied by the cosine of the strand lay angle:

[0115] ε n =ε″ n cosβ n

[0116] In the formula, ε n ″=(cos 2 β n -μ n sin 2 β n )ε-α i (t i -t0) is the strand strain.

[0117] β n The twist angle is the angle between the strands of wire wound along the axis of the inner core wire and the axial direction.

[0118] The step (5) specifically refers to:

[0119] Axial strain of the strand under tension: ε n =ε″ n cosβ n , multiplied by the elastic modulus E of each layer of strands n , the axial delamination stress of the strand is obtained:

[0120] σ n =E n ε″ n cosβ n .

[0121] The step (6) specifically refers to: comparing and analyzing the strand stress of each layer calculated from the steps (1) to (6) with the strand strength to determine whether the strand meets the strength requirement. The strand strength is determined based on the breaking force of steel core or aluminum strand in GB / T 1179-2008, which is a safer rule: the stress at 250 mm gauge length and 1% elongation.

[0122] The following combination Figures 1 to 6 The present invention is further described.

[0123] On the basis of theoretical derivation, a certain actual project was taken as an example to conduct comparative verification through finite element simulation analysis. The study shows that: under the action of tension alone, the axial stress of the steel-core aluminum stranded wire will show an obvious stratification effect. The stress borne by the steel core layer in the steel-core aluminum stranded wire is significantly greater than that of the aluminum strand layer, which is about 3 to 4 times that of the aluminum strand; under the combined action of tension and temperature, the operating tension of the conductor decreases with the increase of temperature; at the same time, as the temperature increases, the stress of the steel core layer increases, and the stress of the aluminum strand layer decreases. The precise analysis of the stress stratification effect of the conductor under the combined action of temperature and tension is of great significance to the safety design of the conductor and the study of its anti-fatigue performance.

[0124] When theoretically deriving the layered stress calculation, the premise assumption is: ignore the extrusion and friction between the strands to ensure the coordination of axial deformation, that is, the axis of each strand is in the same circular cross-section, the strands in the same layer are subjected to the same stress state, and the Poisson effect of the strands is considered.

[0125] Embodiment 1

[0126] Conductor geometry model and material parameters: The selected conductor model is: JL / G1A-400 / 35, the elastic modulus of the steel core is 190 Gpa, and the Poisson's ratio is 0.3; the elastic modulus of the aluminum strand is 55 Gpa, and the Poisson's ratio is 0.3; the geometric parameters of the conductor are shown in Table 1.

[0127] Table 1 Geometric modeling parameters of steel core aluminum stranded wire JL / G1A-400 / 35

[0128]

[0129] Meshing and boundary conditions: The geometric model of the wire JL / G1A-400 / 35 was completed in Solid Works and imported into ANSYS for finite element analysis. The wire length was set to 100 mm and the mesh was divided as follows: Figure 5 shown.

[0130] Boundary conditions: contact is set as binding constraint; a fixed end is set on the x=0mm section at the end of the wire to constrain all degrees of freedom in the X, Y, and Z directions; only the wire is considered to be symmetrically pulled in the axial direction (x direction), and the influence of gravity is ignored. A rigid domain is established at the x=100mm section at the other end of the wire to ensure that the nodes on the x=100mm section have the same axial displacement; finally, a concentrated force is applied to the x=100mm section. When studying the stress stratification effect of the wire under tension, the added concentrated force is: 20% RTS (rated breaking force).

[0131] Engineering example: For an overhead conductor with unequal height suspension points, the span is l=400m, the height difference is h=50m, and the conductor model is JL / G1A-400 / 35. The basic parameters and mechanical indicators of the conductor are shown in Table 2.

[0132] Table 2 JL / G1A-400 / 35 conductor parameters

[0133]

[0134] When calculating the conductor delamination stress in the temperature field, firstly, based on the conductor state equation, take 20℃ as the annual average operating tension as the starting point, and calculate the conductor tension at each temperature as shown in Table 3.

[0135] Table 3 Conductor tension values ​​at different temperatures

[0136]

[0137] It can be seen from Table 3 that the conductor running tension decreases with increasing temperature and increases with decreasing temperature.

[0138] Depend on Figure 6 It can be seen that the stress borne by the steel core layer in the steel core aluminum stranded wire is significantly greater than that of the aluminum strand layer, which is about 3 to 4 times that of the aluminum strand; this is consistent with the actual working conditions of the steel core aluminum stranded wire: the steel core bears the main tension, and the aluminum strand mainly transmits electrical energy.

[0139] The average value of the axial stress of each layer of the conductor is extracted in the finite element simulation software and compared with the theory to obtain the following Table 4.

[0140] Table 4 Finite element and theoretical values ​​of axial stress of each layer of JL / G1A-400 / 35 conductor at 20% RTS

[0141]

[0142]

[0143] It can be seen from Table 4 that the error between the finite element simulation value and the theoretical value of the layered stress of the steel core aluminum stranded wire is within 3%, which meets the actual requirements of the project and further illustrates the correctness and accuracy of the finite element simulation. The stress borne by the steel core layer in the steel core aluminum stranded wire is significantly greater than that of the aluminum strand layer, about 3 to 4 times that of the aluminum strand; the strand tension of the steel core is greater than that of the aluminum strand, which is consistent with the actual working conditions of the steel core aluminum stranded wire. The reason for the error between the finite element simulation value and the theoretical value is that the theoretical derivation ignores the friction and extrusion effect, and the finite element simulation takes into account the extrusion and the tension-torsion coupling effect of the stranded wire.

[0144] my country's design specifications stipulate that the allowable operating temperature of ordinary steel core aluminum stranded wire is between -40℃ and 70℃. Therefore, in the case analysis, -40℃ and 70℃ are used for verification. The results of theoretical calculation and finite element analysis are shown in Table 5.

[0145] Table 5 Axial delamination stress of JL / G1A-400 / 35 strand at different temperatures and corresponding tensions

[0146]

[0147]

[0148] It can be seen from Table 5 that the error between the finite element simulation value and the theoretical value of the delamination stress of steel core aluminum stranded wire at different temperatures is within 5%, which meets the actual requirements of the project and further illustrates the correctness and accuracy of the finite element simulation. Figure 5 It can be seen that as the temperature rises, the stress of the steel core layer increases, while the stress of the aluminum strand layer decreases. The reason for the above phenomenon is that the thermal expansion coefficient of the aluminum strand is about twice that of the steel core. Under the action of temperature, the aluminum strand expands quickly, while the steel core expands slowly. In order to maintain deformation coordination between the steel core and the aluminum strand, the steel core layer applies pressure to the aluminum strand layer, while the aluminum strand layer applies tension to the steel core layer; thus, the stress of the steel core layer increases with the increase of temperature, while the stress of the aluminum strand layer decreases with the increase of temperature.

[0149] The theoretical value of the conductor delamination stress of steel core aluminum stranded wire in the temperature field was obtained by deduction and verified by finite element simulation comparison, and the following conclusions were obtained:

[0150] The error between the finite element simulation value and the theoretical value of the delamination stress of the steel core aluminum stranded wire at different temperatures is within 5%, which meets the actual engineering requirements and further illustrates the correctness and accuracy of the finite element simulation and theoretical derivation.

[0151] Only under the action of tension, the axial stress of steel core aluminum stranded wire will show obvious stratification effect. The stress borne by the steel core layer in the steel core aluminum stranded wire is significantly greater than that of the aluminum strand layer, about 3 to 4 times that of the aluminum strand; the strand tension of the steel core is greater than that of the aluminum strand, which is in line with the actual working conditions of the steel core aluminum stranded wire.

[0152] Under the combined effect of tension and temperature, the conductor running tension decreases as the temperature rises; at the same time, as the temperature rises, the stress of the steel core layer increases, while the stress of the aluminum strand layer decreases. When the temperature exceeds a certain value (inflection point temperature), the aluminum strand will not be stressed, and the steel core will bear all the tension.

[0153] The existing theories for solving conductor stress under different meteorological conditions often use the state equation of overhead lines with unequal height suspension points to obtain the average stress of the conductor, ignoring the differences between the geometric properties and material properties of the strands; the comparison between the two is shown in Table 6:

[0154] Table 6 Axial layering stress and average stress of JL / G1A-400 / 35 strand at different temperatures and corresponding tensions

[0155]

[0156] It can be seen from Table 6 that the axial stress of the steel core layer in the conductor is much greater than the axial stress of the aluminum strand layer; the average axial stress is between the aluminum strand stress and the steel core stress, but the difference between the two is large and cannot be ignored when considering the strength damage of the wire strand.

[0157] In summary, the present invention obtains the layered stress calculation expression of stranded wires of different materials through theoretical derivation, and the layered stress value of each layer can be obtained through programming calculation, which provides an important reference for the safe design and selection of overhead lines and the study of fatigue resistance. Steel core aluminum stranded wire is one of the main products of overhead conductors, and the steel core and aluminum strands jointly bear the conductor tension. In actual work, the steel core mainly plays the role of increasing strength, and the aluminum stranded wire mainly plays the role of transmitting electrical energy. During actual operation, the cross-sectional stress of the steel core aluminum stranded wire will show an obvious layered effect under the combined action of tension and temperature. By considering the different properties of the steel core and aluminum strands, the combined effect of the conductor geometry and temperature and tension. The stress layering effect of the conductor under the combined action of thermal forces is analyzed, which provides important reference value for the safe design and selection of overhead conductors and the study of fatigue resistance.

Claims

1. A method for calculating the layered stress of steel core aluminum stranded wire under thermal-mechanical coupling, characterized in that: The method comprises the following steps in order: (1) Taking a certain initial state as a reference, the average operating tension of the conductor at the required temperature is calculated by using the state equation of the overhead line at different suspension points; (2) Substituting the average operating tension of the conductor at the temperature obtained in step (1) into the calculation expression of the total axial strain, the total axial strain of the conductor is obtained; According to the relationship between the axial strain and the strand strain, the strand strain is obtained; (3) The strand strain under tension is obtained by subtracting the temperature strain from the strand strain. (4) Based on the relationship between the axial strain and the strand strain and the strand strain under tension, calculate the axial strain of the strand under tension; (5) The axial strain of the strand under tension multiplied by the elastic modulus of each layer of strands gives the axial layer stress of the strand; (6) Calculate the delamination stress of the conductor steel core and aluminum strands under extreme meteorological conditions, and compare and analyze it with the extreme value of the strand stress required by the specification to determine whether the conductor meets the safety design and fatigue resistance performance under extreme meteorological conditions; The step (1) specifically refers to: the calculation formula of the state equation of the unequal height suspension point overhead line is as follows: ； Where: Temperature ,temperature The stress at the lowest point of overhead line sag under two conditions; Temperature ,temperature Specific load of overhead lines under two conditions; Temperature ,temperature Temperature of overhead lines in two states; are the gear distance and height difference angle respectively; are the axial comprehensive temperature expansion coefficient and comprehensive elastic modulus of the overhead line respectively; get Stress at the lowest point of overhead line sag at different temperatures ; according to Then the average operating tension of the conductor at the required temperature is obtained, that is, the tension at the lowest sag point of the conductor under the calculation of the annual average temperature; For the Total cross-sectional area of ​​layer strands, for The stress at the lowest point of the overhead line sag at the temperature, T is the average operating tension of the conductor; The step (2) specifically refers to: Substitute the average operating tension of the conductor at the temperature obtained in step (1) into the calculation expression for the total axial strain: , where is the total cross-sectional area of ​​the conductor, and the total axial strain of the conductor is obtained ; According to the relationship between axial strain and strand strain, the strand strain is obtained: , where: The twist angle is the angle between the strands of wire wound along the axis of the inner core wire and the axial direction.

2. The method for calculating the layered stress of the steel core aluminum stranded wire under the action of thermal-mechanical coupling according to claim 1 is characterized in that: The relationship between the strand strain and the axial strain in step (2) is solved in the following specific steps: (2a) The parametric equation of the center line of the nth layer of strands is: ； ； ； Where: is the radius of the nth strand; ; The outer diameter of the strands in the nth layer; is the strand diameter of the nth layer; is the strand pitch of the nth layer; is the central angle of the nth layer of strands wound around the center layer circle; (2b) From the geometric relationship, we know that: （1） In the formula, The twist angle is the angle between the strands wound along the inner core axis and the axis direction. (2c) From the parametric equation of the strand centerline in step (2a), the micro-arc length of the strand in the nth layer is: （2） (2d) The length of the strand in the nth layer is: （3） (2e) For equation (3) , , , Differentiations are: （4） (2f) Dividing formula (4) by formula (3) yields: （5） (2g) The axial strain of the nth strand is: (6) Where, u is the axial deformation; (2h) The radial strain of the nth layer of strands is: (7) in, is the strand Poisson’s ratio; (2i) Substituting equations (6) and (7) into equation (5), we obtain: （8） in, is the Poisson's ratio of the nth strand; (2j) is the central angle of the nth layer of strands wound on the center circle. When the position of the center circle is determined, it is a constant. ； （9） (2k) Substituting formulas (8) and (9) into formula (5) and taking the limit, we can obtain the relationship between the strand strain and the axial strain: That is, the strand strain of the nth layer is: .

3. The method for calculating the layered stress of steel core aluminum stranded wire under thermal-mechanical coupling according to claim 1, characterized in that: The step (3) specifically refers to: Strand strain: , minus the temperature strain: , the strand strain of the strand under tension is obtained: ,in: is the thermal expansion coefficient of the i-th layer of strands, t i is the temperature of the conductor in a certain state, and t0 is the initial stringing temperature of the conductor.

4. The method for calculating the layered stress of steel core aluminum stranded wire under thermal-mechanical coupling according to claim 1, characterized in that: The step (4) specifically refers to: The axial strain of a strand under tension only is equal to the strand strain multiplied by the cosine of the strand lay angle: ； In the formula, is the strand strain.

5. The method for calculating the layered stress of steel core aluminum stranded wire under thermal-mechanical coupling according to claim 1, characterized in that: The step (5) specifically refers to: Axial strain of a strand under tension: , multiplied by the elastic modulus of each layer of strands , the axial delamination stress of the strand is obtained: 。 6. The method for calculating the layered stress of steel core aluminum stranded wire under thermal-mechanical coupling according to claim 1, characterized in that: The step (6) specifically refers to: comparing and analyzing the strand stress of each layer calculated from steps (1) to (6) with the strand strength to determine whether the strand meets the strength requirements.

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