Method for acquiring pre-tightening force of T-shaped wire clamp bolt of distribution network

Abstract

The invention discloses a method for acquiring the pre-tightening force of a T-shaped wire clamp bolt of a distribution network. The method comprises the following steps of 1, performing mechanical property analysis on the T-shaped wire clamp bolt and a clamped main wire; 2, according to a mechanical property analysis result, obtaining a change rule of the contact surface pressure along with the ascending distance of the bolt; 3, representing the balance relation between the external force, namely the bolt pre-tightening force, and the internal force, namely the contact surface pressure by utilizing three elements, namely stress, strain and displacement in elastic deformation; the degree of local deformation of the contact surface after the contact surface is subjected to the pressure transmitted by the bolt pretightening force; after the contact surface is subjected to the pressure transmitted by the pre-tightening force of the bolt, the position of a mass point on the contact surface is changed; 4, obtaining a control equation of the pre-tightening force of the T-shaped wire clamp bolt, and obtaining initial conditions of calculation; and 5, dispersing the continuous control equation into a linear integral equation, thereby solving the bolt pre-tightening force of the T-shaped wire clamp under mechanical property analysis.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and in particular to the mechanical properties of a T-type line clamp bolt for power distribution networks and a method for calculating its preload. Background Technology

[0002] Calculating the preload of clamp bolts during power outage operations in power distribution networks is a key technology for ensuring the safe operation of power equipment. With the continuous development and upgrading of power grids, power outage operations have gradually become a common practice, especially during the inspection and maintenance of power equipment. As an important connecting component in power distribution networks, the preload of clamp bolts directly affects the stability and safety of the connection. T-type clamps are commonly used in distribution networks; excessive preload will cause excessive pressure on the contact surface between the bolt and the main conductor, leading to puncture of the main conductor and increasing the risk of electric shock to workers. Insufficient preload will result in insufficient contact surface pressure and static friction, causing slippage and clamp detachment, leading to short circuits or open circuits, thus affecting the normal progress of distribution network maintenance. To accurately obtain the preload of T-type clamp bolts, it is necessary to analyze the mechanical properties of the bolts and clarify the factors affecting the preload.

[0003] Therefore, in power outage operations, how to scientifically and rationally calculate and control the preload of clamp bolts has become a technical challenge to ensure the normal operation and safety of power equipment. Summary of the Invention

[0004] The purpose of this invention is to accurately obtain the preload of T-type clamp bolts during power outage operations in distribution networks, so as to ensure the normal operation and safety of power equipment. Therefore, a method for obtaining the preload of T-type clamp bolts in distribution networks is proposed.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for obtaining the preload of a T-type wire clamp bolt in a power distribution network includes the following steps: Step 1: Perform mechanical property analysis on the T-type wire clamp bolt and the main conductor it holds; Step 2: Based on the mechanical property analysis results, obtain the variation law of contact surface pressure with the bolt rising distance; in order to ensure that the T-type clamp does not fall off and the main conductor is not damaged, it is necessary to accurately solve the bolt preload corresponding to the critical point of contact surface pressure. Step 3: Considering that before the bolt preload reaches the critical point of the contact surface pressure, the deformation of the contact surface due to pressure is all elastic deformation, the three elements of stress, strain and displacement in elastic deformation are used to characterize the balance relationship between the external force (bolt preload) and the internal force (contact surface pressure); the degree of local deformation of the contact surface after being subjected to the pressure transmitted by the bolt preload; and the change in the position of the particles on the contact surface after being subjected to the pressure transmitted by the bolt preload. Step 4: Construct stress-strain equation, strain-displacement equation and stress balance equation by using the relationship between the three elements of stress, strain and displacement. Solve the three equations at the same time to obtain the governing equation of the preload of the T-type clamp bolt. Since the governing equation is a partial differential equation, perform a force analysis on the bolt and the boundary of the main line to obtain the initial conditions for calculation. Step 5: Discretize the continuous control equations into linear integral equations to solve for the bolt preload of the T-type clamp under mechanical property analysis.

[0006] In step one, the force analysis of the mechanical properties of the T-type wire clamp bolt and the clamped main conductor includes the supporting force of the main conductor on the bolt. F N Bolt preload F 0. The gravity of the dominant line itself G ; Among them, the main line is supported by the bolt. F N Equal to the pressure of the main line on the bolt F N The total pressure of the dominant line on the bolt is related to the static friction coefficient of the dominant line on the bolt. Static friction is generated on the contact surface under the action. f static friction f It is crucial to ensure that the T-clamp does not fall off, and the force applied in the vertical direction is crucial to ensure that the conductor is not damaged. Preload the bolts F 0 is decomposed into a vertically upward component. F 0y The horizontal component of the bolt preload force F 0x The vertical upward component of the bolt preload force F 0y It is part of the total combined pressure, the horizontal component of the bolt preload. F 0x This will offset part of the static friction. f ; The gravity of the dominant line itself G The pressure of the bolt on the main line in the vertical direction. F N 'The vertically upward component of the bolt preload force' F 0y The total pressure is the key factor affecting static friction.

[0007] In step two, the variation of the contact surface pressure with the bolt's upward distance, combined with the mechanical characteristic analysis in step one, shows that in the first stage, the bolt is subjected to an upward preload. Since it is not yet in contact with the main guide line, the contact surface has not yet formed. Therefore, the pressure on the contact surface at this time is low. FN ' The value is 0; when the bolt preload increases to F At point 1, partial contact begins between the bolt and the main guideline, and the pressure surpasses the initial point, entering the second stage. In the initial contact phase, due to the continuous increase in the contact area and rapid deformation of the contact surface, the contact surface pressure increases. F N ' The growth rate is relatively fast; when the bolt preload increases to F 2. This refers to the bolt's yield point. At this point, due to the curvature of the dominant line, the increase in the contact area gradually slows down, and the increase in contact pressure also gradually slows down. The contact pressure at this point... F N ' Static friction generated f Insufficient force to hold the main conductor firmly in the slot will cause slippage between the T-clamp and the main conductor, eventually leading to the clamp falling off; when the bolt preload increases to F At 3 o'clock, the main guide line and the bolt contact surface reach the third stage, that is, they are exactly in complete contact, and the contact surface pressure... F N ' When the critical point is reached, the static friction force generated f It can just press the main line into the slot; when the bolt preload exceeds the critical point, the contact surface between the main line and the bolt enters the fourth stage, that is, the bolt breaks through the contact surface and punctures the main line, eventually causing damage to the main line.

[0008] In step four, obtaining the control equation for the preload of the T-type wire clamp bolt specifically includes the following steps: Step 4-1: Since stress analysis is to construct the balance relationship between external and internal forces, that is, to characterize the pressure distribution per unit area of ​​the contact surface after the bolt preload is transmitted to the contact surface, stress balance equations need to be constructed to characterize the above balance relationship. Step 4-2: Then, the bolt preload is transmitted to the pressure distribution per unit area of ​​the contact surface, which will cause deformation on the contact surface, that is, the relationship between stress and strain. To characterize the degree of this deformation, a stress-strain equation needs to be constructed. Step 4-3: Based on this, deformation will cause the position of each particle on the contact surface to change, that is, the relationship between strain and displacement. In order to characterize the degree of position change, a strain-displacement equation needs to be constructed. Step 4-4: By combining the stress balance equation, stress-strain equation and strain-displacement equation, the governing equation for the preload of the T-type clamp bolt can be obtained.

[0009] In step 4-1, the stress balance equation can be expressed as: (1); in, The normal stress generated by the bolt preload transmitted to the contact surface is respectively... x , y , z Components on the axis; The shear stress generated by the bolt preload transmitted to the contact surface is respectively... x , y , z Components on the axis; The weight per unit volume of the contact surface is respectively... x , y , z Components on the axis; These are, respectively, the shear stress acting on the plane normal to the y-axis along the x-axis; the shear stress acting on the plane normal to the z-axis along the x-axis; the shear stress acting on the plane normal to the z-axis along the y-axis; the shear stress acting on the plane normal to the x-axis along the z-axis; and the shear stress acting on the plane normal to the y-axis along the z-axis. In step 4-2, the stress-strain equation can be expressed as: (2); in, This is the strain tensor of the bolt preload transmitted to the contact surface. For the Kronecker delta function, This represents the normal strain tensor of the particles at the contact surface after deformation. This represents the shear strain tensor of the particles at the contact surface after deformation. and Let Lamé constant be . E The Young's modulus of the contact surface material. The Poisson's ratio of the contact surface material; In step 4-3, the strain-displacement equation can be expressed as: (3); in, These are the points on the contact surface after deformation along the contact surface. x , y , z Displacement in the axial direction; These are the points on the contact surface after deformation along the contact surface. x , y , z Normal strain in the axial direction; , , These are the points on the contact surface after deformation along the contact surface. x O y , y O z , z O x Shear strain in the planar direction; In step 4-4, the simultaneous stress equilibrium equations, stress-strain equations, and strain-displacement equations can be expressed as: (4); The relationship between bolt preload and contact surface pressure is as follows: (5); In the formula: m This is the transmission coefficient of bolt preload, typically taken as 0.6~0.7. This is the critical value of the contact surface pressure. This is the critical value of the contact surface stress. A It is the effective force-bearing area of ​​the contact surface between the main conductor and the bolt; among which, stress characterizes the pressure distribution of the bolt preload per unit area on the contact surface, and has a direct conversion relationship with pressure; Combining equations (4) and (5), the controlling equation for the preload of the T-type clamp bolt can be expressed as: (6).

[0010] In step four, after obtaining the governing equation for the preload of the T-type wire clamp bolt by utilizing the relationship between the three elements of stress, strain, and displacement through the above steps, it is necessary to determine the initial conditions for the governing equation, which includes the following steps: Step s4-1) Determine the computational domain for the initial conditions; Step s4-2) Calculate the initial conditions of the governing equations using the surface stress properties of the computational region; In step s4-1), after the preload is applied to the bolt head, it exerts pressure on the contact surface between the bolt and the main guideline, generating surface stress. Therefore, the bolt's upper surface, where surface stress is generated, forms the boundary for calculating the preload, and the distribution of surface stress constitutes the boundary condition for the bolt preload. This boundary condition is also the initial condition for the governing equation. The bolt's upper surface is high... z A cylinder approaching 0, about xOz and yOz Planar symmetry; to simplify the region of repetitive calculations, the symmetry of the initial conditions is calculated, and the domain of the calculated boundary conditions is defined. Reduced to 1 / 4 of its original size to facilitate subsequent measurement using the mirror method. The initial conditions.

[0011] In step s4-2), stress characterizes the equilibrium relationship between external and internal forces, therefore for the 1 / 4 domain... The surface stress also satisfies the equilibrium equation, therefore the surface stress at the boundary surface satisfies: (7); In the formula: t i Here are the components of the surface stress vector of the boundary force-bearing surface. These components are known quantities. i = x , y , z , n i Here are the components of the normal vector of the boundary force surface, where i = x , y , z ; Since the surface stress acts vertically upwards, its component in the normal vector direction is 0, therefore... t x and t y If both are 0, then equation (7) can be rewritten as: (8); In the formula: Let be the tensor form of surface stress, where i = x , y ; j = x , y , z ; This is the unit normal vector of the boundary surface subjected to force. Since the domain of the boundary in equation (8) is only 1 / 4; By calculating the symmetry properties of the boundary surface in step one, it can be seen that the normal stress and shear stress must be the same in magnitude in other octaves, only the direction is opposite, that is, the sign is positive or negative; Since the surface stress in the normal direction is 0, substituting the remaining part into equation (8) can reveal that the tensor form will not change due to different directions, so equation (8) is the initial condition of the bolt preload control equation.

[0012] Step five specifically includes the following steps: Step 5-1: First, divide the solution domain of the partial differential equation of bolt preload into a grid to define the solution domain of each grid in the discretized integral equation. Step 5-1: Considering that the governing equation of bolt preload is a nonlinear partial differential equation, and that nonlinear partial differential equations have strong continuity, when solving analytically, the cross terms of variables in the equation will severely hinder the separation of variables, thus failing to satisfy linear superposition and making it impossible to construct a general solution by combining simple particular solutions; at this time, it is necessary to use numerical methods to obtain an approximate solution to replace the original analytical solution; and by meshing the large and continuous solution domain, the calculation results of the governing equation can be initially approximated. Step 5-2: Select the weight function based on the magnitude of the error generated by each grid cell in the solution domain for the approximate solution according to the integral equation. This forces the error to zero under the weighting of the weighting function, thereby eliminating the error caused by the cross term and obtaining the weak integral equation of the bolt preload. Step 5-3: The solution domain of the discretized integral equation has been defined during mesh generation. The mesh can be characterized by its shape, i.e., its shape function. N ( x To avoid approximate solution errors caused by the mismatch between the shape function and the weight function of the mesh element in the integral equation, the shape function can be adjusted accordingly. N ( x ) and weight function By performing the same form of discretization, it is ensured that the shape function and the grid weight function in the solution domain of the integral equation are mutually mapped; Step 5-4: Further discretize the weak form integral equation of bolt preload to obtain a linear integral equation consisting only of low-order polynomials. Solving this linear equation system will yield the bolt preload solution based on mechanical properties.

[0013] In step 5-3, for the shape function N ( x ) and weight function Discretizing in the same form can be represented as: (9); In the formula: a and b These represent the contact surface stress and the discretized mesh nodes after weighting function. N The total number of grid nodes for discretizing the contact surface stress tensor; and These are the shape functions of the contact surface stress tensor and the weighting function, respectively. and Let be the nodal stress values ​​of the contact surface stress tensor and weighting function.

[0014] In step 5-4, the weak-form integral equation of the bolt preload can be expressed as follows: (10); In the formula: It is the first invariant of the contact surface stress; Substituting equation (9) into equation (10) and expanding further, we obtain a linear integral equation consisting only of low-order polynomials, which is also the unit equation: (11); in: Let be the stress tensor component at the a-th node, and k and l represent the normal direction of the stress surface and the stress direction, respectively. This represents the equivalent nodal load component at the b-th node; Element stiffness matrix The interaction between nodes in the solution domain of the integral equation is characterized as follows: (12); in, Let be the shape function of the a-th node. Let be the shape function of the b-th node. Let m be the coordinate variable in the m-direction of the spatial coordinate system. Let be the coordinate variable in the i-direction of the spatial coordinate system. Let be the coordinate variable in the j-direction of the spatial coordinate system. For the Kronecker function, For the Kronecker function, The Kronecker function; Element load terms The influence of surface stress on the contact surface stress within the solution domain is characterized as follows: (13); in, Let be the component of the unit normal vector of the boundary force-bearing surface in the j-direction. This refers to the boundary region where surface forces act; Finally, the element stiffness matrices of all contact surface stresses are filled into the global stiffness matrix of bolt preload as elements according to their positions on the bolt preload degree of freedom during mesh generation: (14); In the formula: K The global stiffness matrix of the bolt preload. The load vector consists of all surface stress load terms; the only unknown is the bolt preload. F 0, Substitute the surface stress equation (8) into the load vector and solve the linear equation system to obtain the bolt preload of the T-type clamp under mechanical property analysis.

[0015] Compared with the prior art, the present invention has the following technical effects: This invention takes into account the mechanical characteristics of the preload of T-type clamp bolts and fully considers the relationship between the three elements of elastic deformation, thereby improving the accuracy of bolt preload calculation results and providing a new calculation approach for the preload setting of clamp bolts during power outage operations in power distribution networks. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 A schematic diagram of the T-type wire clamp bolt structure and the application of its preload; Figure 2 A schematic diagram illustrating the mechanical properties of the contact surface between the bolt and the main guideline; Figure 3 This is a schematic diagram illustrating how the contact surface pressure changes with the bolt preload. Figure 4 A schematic diagram illustrating the initial conditions for obtaining the control equation of bolt preload. Figure 5 This is a flowchart of the present invention. Detailed Implementation

[0017] like Figure 1 As shown, a method for obtaining the preload of a T-type clamp bolt in a power distribution network specifically includes the following steps: Step 1: The mechanical properties of the T-type wire clamp bolt and the clamped main conductor were analyzed, such as... Figure 1 and Figure 2 As shown, the key to clarifying the preload analysis of T-type clamp bolts lies in the analysis of the pressure on the contact surface between the bolt and the main guide line; Step Two: Based on the mechanical property analysis results, further analyze the variation law of contact surface pressure with the bolt rising distance. It is determined that to ensure the T-clamp does not fall off and the main conductor is not damaged, the bolt preload corresponding to the critical point of contact surface pressure needs to be accurately calculated. Its variation law is as follows: Figure 3 As shown; Step 3: Considering that before the bolt preload reaches the critical point of the contact surface pressure, the deformation of the contact surface due to pressure is all elastic deformation, the three elements of stress, strain and displacement in elastic deformation are used to characterize the balance relationship between external force (bolt preload) and internal force (contact surface pressure); the degree of local deformation of the contact surface after being subjected to the pressure transmitted by the bolt preload; and the change in the position of the particles on the contact surface after being subjected to the pressure transmitted by the bolt preload. Step 4: Construct stress-strain equation, strain-displacement equation and stress balance equation by utilizing the relationship between the three elements of stress, strain and displacement. Solve the three equations simultaneously to obtain the governing equation of the preload of the T-type wire clamp bolt.

[0018] In step one, the force analysis of the T-type wire clamp bolt and the clamped main conductor in step one includes the supporting force of the main conductor on the bolt. F N Bolt preload F 0. The gravity of the dominant line itself G .

[0019] The main line is supported by the bolt. F N Equal to the pressure of the main line on the bolt F N The total pressure of the dominant line on the bolt is related to the static friction coefficient of the dominant line on the bolt. Static friction is generated on the contact surface under the action. f static friction f The key to ensuring that the T-clamp does not fall off is that the force applied in the vertical direction is the key to ensuring that the conductor is not damaged.

[0020] Bolt preload F 0 can be decomposed into the vertically upward component of the bolt preload. F 0y The horizontal component of the bolt preload force F 0x The vertical upward component of the bolt preload force F 0y It is part of the total combined pressure, the horizontal component of the bolt preload. F 0x This will offset part of the static friction. f .

[0021] The gravity of the dominant line itself G The pressure of the bolt on the main line in the vertical direction. F N 'The vertically upward component of the bolt preload force' F 0y The total pressure is the key factor affecting static friction.

[0022] The variation of contact surface pressure with the bolt's upward distance in step two, combined with the mechanical property analysis in step one, shows that in the first stage, the bolt is subjected to an upward preload. Since it is not yet in contact with the main guideline, the contact surface has not yet formed. Therefore, the pressure on the contact surface at this time... F N ' It is 0. When the bolt preload increases to F At point 1, partial contact begins between the bolt and the main guideline, and the pressure surpasses the initial point, entering the second stage. In the initial contact phase, due to the continuous increase in the contact area and rapid deformation of the contact surface, the contact surface pressure increases. F N 'The growth rate is relatively fast. When the bolt preload increases to F 2. This refers to the bolt's yield point. At this point, due to the curvature of the dominant line, the increase in the contact area gradually slows down, and the increase in contact pressure also gradually slows down. The contact pressure at this point... F N ' Static friction generated f Insufficient force to hold the main conductor firmly in the slot will cause slippage between the T-clamp and the main conductor, eventually leading to the clamp falling off. When the bolt preload increases to... F At 3 o'clock, the main guide line and the bolt contact surface reach the third stage, that is, they are exactly in complete contact, and the contact surface pressure... F N ' When the critical point is reached, the static friction force generated f It can just press the main guide line tightly into the slot. When the bolt preload exceeds the critical point, the contact surface between the main guide line and the bolt enters the fourth stage, that is, the bolt breaks through the contact surface and pierces the main guide line, eventually causing damage to the main guide line.

[0023] Step four includes the following steps: Step 4-1): Since stress analysis establishes the equilibrium relationship between external and internal forces, that is, characterizes the pressure distribution per unit area of ​​the contact surface after the bolt preload is transmitted to the contact surface, a stress equilibrium equation needs to be constructed to characterize the above equilibrium relationship. The stress equilibrium equation can be expressed as: (1); Step 4-2): Subsequently, the bolt preload is transmitted to the pressure distribution per unit area of ​​the contact surface, which will cause deformation on the contact surface, i.e., the relationship between stress and strain. To characterize the degree of this deformation, a stress-strain equation needs to be constructed. The stress-strain equation can be expressed as: (2); Step 4-3): Based on this, deformation will cause positional changes in each particle on the contact surface, i.e., the relationship between strain and displacement. To characterize the degree of positional change, a strain-displacement equation needs to be constructed. The strain-displacement equation can be expressed as: (3); in, These are the points on the contact surface after deformation along the contact surface. x , y , z Displacement in the axial direction; These are the points on the contact surface after deformation along the contact surface. x , y , z Normal strain in the axial direction; , , These are the points on the contact surface after deformation along the contact surface. x O y , y O z , z O x Shear strain in the planar direction; Step 4-4): By combining the stress balance equation, stress-strain equation, and strain-displacement equation, the governing equation for the preload of the T-type wire clamp bolt can be obtained. The stress-strain equation and strain-displacement equation can be expressed as: (4); The relationship between bolt preload and contact surface pressure is as follows: (5); In the formula: m This is the transmission coefficient of bolt preload, typically taken as 0.6~0.7. This is the critical value of the contact surface pressure. This is the critical value of the contact surface stress. A This refers to the effective force-bearing area of ​​the contact surface between the main conductor and the bolt. Stress characterizes the pressure distribution of the bolt preload per unit area of ​​the contact surface and has a direct conversion relationship with pressure.

[0024] Combining equations (4) and (5), the controlling equation for the preload of the T-type clamp bolt can be expressed as: (6); By utilizing the relationship between the three elements of stress, strain, and displacement through the above steps, the governing equation for the preload of the T-type wire clamp bolt is obtained.

[0025] After obtaining the governing equation for the preload of the T-type wire clamp bolt by utilizing the relationship between the three elements of stress, strain, and displacement through the above steps, it is still necessary to determine the initial conditions for the governing equation, such as... Figure 4 As shown, it includes the following steps: Step (1): Determine the computational domain for the initial conditions; In step (1), after the preload is applied to the bolt head, it exerts pressure on the contact surface between the bolt and the main guideline. This pressure generates surface stress on the contact surface. Therefore, the upper surface of the bolt where surface stress is generated is the boundary for calculating the preload, and the distribution of surface stress is the boundary condition for the bolt preload. This boundary condition is the initial condition for the governing equation. The upper surface of the bolt is high... z A cylinder approaching 0, about xOz and yOz Planar symmetry. To simplify the repetitive calculation domain, the symmetry of the initial conditions is calculated, and the domain of the calculated boundary conditions is defined. Reduced to 1 / 4 of its original size, and finally obtained using the mirror method. The initial conditions.

[0026] Step (2): Calculate the initial conditions of the governing equations using the surface stress properties of the computational domain. To simplify the repetitive calculation domain, calculate the symmetry characteristics of the initial conditions and define the domain of the calculated boundary conditions. Reduced to 1 / 4 of its original size, and finally obtained using the mirror method. Initial conditions on the domain. The surface stress also satisfies the equilibrium equation, therefore the surface stress at the boundary surface satisfies: (7); In the formula: t i This is a component of the surface stress vector of the boundary force-bearing surface; this component is a known quantity. n i Here are the components of the normal vector of the boundary force surface, where i = x , y , z .

[0027] Since the surface stress acts vertically upwards, its component in the normal vector direction is 0, therefore... t x and t y If both are 0, then equation (7) can be rewritten as: (8); In the formula: Let be the tensor form of surface stress, where i = x , y ; j = x , y , z .

[0028] Equation (8) is the initial condition for the bolt preload control equation.

[0029] Step 5: Discretize the continuous governing equations into linear integral equations to solve for the bolt preload of the T-clamp under mechanical property analysis. This includes the following steps: Step 5-1): First, divide the solution domain of the partial differential equation of bolt preload into a grid to define the solution domain of each grid in the discretized integral equation; In step 5-1), considering that the governing equation for bolt preload is a nonlinear partial differential equation, and that nonlinear partial differential equations have strong continuity, the cross-terms of variables in the equation will severely hinder the separation of variables when solving analytically, thus failing to satisfy linear superposition and making it impossible to construct a general solution by combining simple particular solutions. Therefore, a numerical solution is needed to obtain an approximate solution to replace the original analytical solution. Discretizing the large and continuous solution domain through mesh generation can provide a preliminary approximation of the calculation results of the governing equation.

[0030] Step 5-2): Select the weight function based on the magnitude of the error generated by each grid cell in the solution domain for the approximate solution according to the integral equation. This forces the error to zero under the weighting of the weighting function, thereby eliminating the error caused by the cross term and obtaining the weak integral equation of the bolt preload. Step 5-3): The solution domain of the discretized integral equation has been defined during mesh generation. The mesh can be functionally represented by its shape, i.e., the shape function. N ( x To avoid approximate solution errors caused by the mismatch between the shape function and the weight function of the mesh element in the integral equation, the shape function can be adjusted accordingly. N ( x ) and weight function By performing the same form of discretization, it is ensured that the shape function and the grid weight function in the solution domain of the integral equation are mutually mapped; For shape functions N ( x ) and weight function Discretizing in the same form can be represented as: (9); In the formula: a and b These represent the contact surface stress and the discretized mesh nodes after weighting function. N This represents the total number of mesh nodes for discretizing the stress tensor at the contact surface. and These are the shape functions of the contact surface stress tensor and the weighting function, respectively. and Let be the nodal stress values ​​of the contact surface stress tensor and weighting function.

[0031] Step 5-4): Further discretize the weak form integral equation of bolt preload to obtain a linear integral equation consisting only of low-order polynomials. Solving this linear equation system will yield the bolt preload solution based on mechanical properties.

[0032] The weak integral equation for bolt preload can be expressed as follows: (10); In the formula: It is the first invariant of the contact surface stress.

[0033] Substituting equation (9) into equation (10) and expanding further, we obtain a linear integral equation consisting only of low-order polynomials, which is also the unit equation: (11); in: Element stiffness matrix The interaction between nodes in the solution domain of the integral equation is characterized as follows: (12); Element load terms The influence of surface stress on the contact surface stress within the solution domain is characterized as follows: (13); Finally, the element stiffness matrices of all contact surface stresses are filled into the global stiffness matrix of bolt preload as elements according to their positions on the bolt preload degree of freedom during mesh generation.

[0034] (14); In the formula: K The global stiffness matrix of the bolt preload. This is the load vector consisting of all surface stress load terms. The only unknown quantity is the bolt preload. F 0. Substitute the surface stress equation (8) into the load vector and solve the linear equation system to obtain the bolt preload of the T-type clamp under mechanical property analysis.

[0035] Example: This invention conducted a solution and verification experiment for the warning force of the T-type clamp bolt in the power distribution network, as detailed below: Experimental objects: Commonly used T-type clamps for power distribution networks (model: JBTL-120), M12 stainless steel bolts, LGJ-120 / 20 steel-cored aluminum stranded wire (main conductor); Experimental tools: torque wrench (accuracy ±0.1 N*m), laser displacement sensor (accuracy ±0.01 mm), stress strain gauge (accuracy ±1 μβ), ANSYS finite element simulation software; Experimental parameters: static friction coefficient μ=0.4 (standard value for copper-aluminum contact surface), preload transmission coefficient m=0.65, dominant linear elastic modulus E=200GPa, effective force-bearing area of ​​contact surface A=120mm² (actual contact dimension between bolt and wire).

[0036] 1. Verification of the relationship between contact surface pressure and preload: The bolt preload was gradually applied using a torque wrench, while simultaneously measuring the bolt rise distance, contact surface pressure, and static friction. The data is shown in the table below. Figure 1As shown, the rationality of the "four-stage change law" is verified: Table 1 Data corresponding to contact surface pressure, preload, and bonding state.

[0037] Analysis: When F0 = 1.75kN, FN' = 1.5kN, and f = 0.60kN (μ = 0.4). Combined with F0x = 0.875kN and F0y = 1.51kN, the mechanical equilibrium of "total pressure = G + FN' + F0y" is satisfied, verifying that "the third stage is the optimal preload". When F0 ≥ 2.0kN, the bolt punctures the main line, matching the description of "damage risk in the fourth stage".

[0038] 2. Verification of the relationship between the three elements of elastic deformation Based on the above experiments, the stress, strain, and particle displacement of the contact surface under different preloads were measured and compared with the theoretical calculations to verify the accuracy of the "stress-strain-displacement correlation model". The data are shown in Table 2. Table 2. Comparison of Simulation and Theoretical Data for the Three Elements of Elastic Deformation

[0039] Analysis: The relative error between the simulation and theoretical displacement is <3.5%, and the error at the critical point (1.75kN) is 1.82%. The error originates from the influence of temperature on E (E=67GPa at 60℃). When F0=1.75kN, σ=19.1MPa and ε=0.282×10⁻³, which conforms to equation (2) "E=σ / ε≈67.7GPa" (the error is 1.9% compared with the actual E=69GPa), verifying the "stress-strain-displacement three-element correlation model".

[0040] 3. Verification of the effectiveness of the preload calculation method The superiority of the "discrete integration method" of this invention is verified by comparing the solution results with those of traditional analytical methods and finite element methods. The data are shown in Table 3. Table 3 Comparison of preload results from different solution methods

[0041] Analysis: The discrete integration method of this invention has a relative error of 0.57% (compared to 5.71% for the traditional analytical method) due to the elimination of variable cross terms through weighting functions; it takes 12.5 seconds (compared to 35.8 seconds for the finite element method) due to the reduction of the solution domain by 1 / 4. This verifies the principle of "balancing accuracy and efficiency," addresses the pain points of traditional methods, and meets the needs of power distribution network operations.

[0042] 4. Stability data of critical preload value F3 under different working conditions Considering the actual operating conditions of the power distribution network (temperature, icing), the stability of the critical preload value F3 was tested to verify the environmental adaptability of the method. The data are shown in Table 4. Table 4. Stability data of critical preload value F3 under different working conditions

[0043] Analysis: The coefficient of variation of F3 for each operating condition is <0.6%: high temperature (60℃) F3 = 1.70kN, low temperature (-20℃) F3 = 1.80kN, and icing F3 = 1.95kN. The data meet the requirements, verifying the applicability to complex environments.

[0044] In summary, the method proposed in this invention first analyzes the mechanical properties of the T-type wire clamp bolt and the clamped main conductor, clarifying that the key to analyzing the preload of the T-type wire clamp bolt lies in analyzing the pressure on the contact surface between the bolt and the main conductor. Secondly, based on the results of the mechanical property analysis, it further analyzes the variation law of the contact surface pressure with the bolt's rising distance, clarifying that to ensure the T-type wire clamp does not fall off and the main conductor is not damaged, it is necessary to accurately solve for the bolt preload corresponding to the critical point of the contact surface pressure. Thirdly, considering that before the bolt preload reaches the critical point of the contact surface pressure, the deformation of the contact surface due to pressure is all elastic deformation, the three elements of stress, strain, and displacement in elastic deformation are used to characterize the balance relationship between external force (bolt preload) and internal force (contact surface pressure); the degree of local deformation of the contact surface after being subjected to the pressure transmitted by the bolt preload; and the change in the position of the mass points on the contact surface after being subjected to the pressure transmitted by the bolt preload. Then, by utilizing the relationship between the three elements, stress-strain equations, strain-displacement equations, and stress balance equations are constructed. Solving these three equations simultaneously yields the governing equation for the preload of the T-type clamp bolt. Since the governing equation is a partial differential equation, a force analysis is performed on the bolt and the boundary of the dominant line to obtain the initial conditions for calculation. Finally, the continuous governing equation is discretized into a linear integral equation, thereby solving for the bolt preload of the T-type clamp under mechanical property analysis. This invention considers the mechanical properties of the T-type clamp bolt preload and fully considers the relationship between the three elements of elastic deformation, improving the accuracy of the bolt preload calculation results and providing a new calculation approach for the preload setting of clamp bolts during power outage operations in distribution networks.

Claims

1. A method for obtaining the preload of a T-type clamp bolt in a power distribution network, characterized in that, Includes the following steps: Step 1: Perform mechanical property analysis on the T-type wire clamp bolt and the main conductor it holds; Step 2: Based on the mechanical property analysis results, obtain the variation law of contact surface pressure with the bolt rising distance; in order to ensure that the T-type clamp does not fall off and the main conductor is not damaged, it is necessary to accurately solve the bolt preload corresponding to the critical point of contact surface pressure. Step 3: Considering that before the bolt preload reaches the critical point of the contact surface pressure, the deformation of the contact surface due to pressure is all elastic deformation, the three elements of stress, strain and displacement in elastic deformation are used to characterize the balance relationship between the bolt preload and the internal force, i.e., the contact surface pressure; the degree of local deformation of the contact surface after being subjected to the pressure transmitted by the bolt preload; and the change in the position of the particles on the contact surface after being subjected to the pressure transmitted by the bolt preload. Step 4: Construct stress-strain equation, strain-displacement equation and stress balance equation by using the relationship between the three elements of stress, strain and displacement. Solve the three equations at the same time to obtain the governing equation of the preload of the T-type clamp bolt. Since the governing equation is a partial differential equation, perform a force analysis on the bolt and the boundary of the main line to obtain the initial conditions for calculation. Step 5: Discretize the continuous control equations into linear integral equations to solve for the bolt preload of the T-type clamp under mechanical property analysis.

2. The method according to claim 1, characterized in that, In step one, the force analysis of the mechanical properties of the T-type wire clamp bolt and the clamped main conductor includes the support force of the main conductor on the bolt. F N Bolt preload F 0. The gravity of the dominant line itself G ; Among them, the main line is supported by the bolt. F N Equal to the pressure of the main line on the bolt F N The total pressure of the dominant line on the bolt is related to the static friction coefficient of the dominant line on the bolt. Static friction is generated on the contact surface under the action. f static friction f It is crucial to ensure that the T-clamp does not fall off, and the force applied in the vertical direction is crucial to ensure that the conductor is not damaged. Preload the bolts F 0 is decomposed into a vertically upward component. F 0y The horizontal component of the bolt preload force F 0x The vertically upward component of the bolt preload force F 0y It is part of the total combined pressure, the horizontal component of the bolt preload. F 0x This will offset part of the static friction. f ; The gravity of the dominant line itself G Pressure of the bolt on the main line in the vertical direction F N 'The vertically upward component of the bolt preload force' F 0y The total pressure is the key factor affecting static friction.

3. The method according to claim 1 or 2, characterized in that, In step two, the variation of the contact surface pressure with the bolt's upward distance, combined with the mechanical characteristic analysis in step one, shows that in the first stage, the bolt is subjected to an upward preload. Since it is not yet in contact with the main guide line, the contact surface has not yet formed. Therefore, the pressure on the contact surface at this time is low. F N ' The value is 0; when the bolt preload increases to F At point 1, partial contact begins between the bolt and the main guideline, and the pressure surpasses the initial point, entering the second stage. In the initial contact phase, due to the continuous increase in the contact area and rapid deformation of the contact surface, the contact surface pressure increases. F N ' The growth rate is relatively fast; when the bolt preload increases to F 2. This refers to the bolt's yield point. At this point, due to the curvature of the dominant line, the increase in the contact area gradually slows down, and the increase in contact pressure also gradually slows down. The contact pressure at this point... F N ' Static friction generated f Insufficient force to hold the main conductor firmly in the slot will cause slippage between the T-clamp and the main conductor, eventually leading to the clamp falling off; when the bolt preload increases to F At 3 o'clock, the main guide line and the bolt contact surface reach the third stage, that is, they are exactly in complete contact, and the contact surface pressure... F N ' When the critical point is reached, the static friction force generated f It can just press the main line into the slot; when the bolt preload exceeds the critical point, the contact surface between the main line and the bolt enters the fourth stage, that is, the bolt breaks through the contact surface and punctures the main line, eventually causing damage to the main line.

4. The method according to claim 1, characterized in that, In step four, obtaining the control equation for the preload of the T-type wire clamp bolt specifically includes the following steps: Step 4-1: Since stress analysis is to construct the balance relationship between external and internal forces, that is, to characterize the pressure distribution per unit area of ​​the contact surface after the bolt preload is transmitted to the contact surface, stress balance equations need to be constructed to characterize the above balance relationship. Step 4-2: Then, the bolt preload is transmitted to the pressure distribution per unit area of ​​the contact surface, which will cause deformation on the contact surface, that is, the relationship between stress and strain. To characterize the degree of this deformation, a stress-strain equation needs to be constructed. Step 4-3: Based on this, deformation will cause the position of each particle on the contact surface to change, that is, the relationship between strain and displacement. In order to characterize the degree of position change, a strain-displacement equation needs to be constructed. Step 4-4: By combining the stress balance equation, stress-strain equation and strain-displacement equation, the governing equation for the preload of the T-type clamp bolt can be obtained.

5. The method according to claim 4, characterized in that, In step 4-1, the stress balance equation can be expressed as: （1）； in, The normal stress generated by the bolt preload transmitted to the contact surface is respectively... x , y , z Components on the axis; The shear stress generated by the bolt preload transmitted to the contact surface is respectively... x , y , z Components on the axis; The weight per unit volume of the contact surface is respectively... x , y , z Components on the axis; These are, respectively, the shear stress acting on the plane normal to the y-axis along the x-axis; the shear stress acting on the plane normal to the z-axis along the x-axis; the shear stress acting on the plane normal to the z-axis along the y-axis; the shear stress acting on the plane normal to the x-axis along the z-axis; and the shear stress acting on the plane normal to the y-axis along the z-axis. In step 4-2, the stress-strain equation can be expressed as: （2）； in, This is the strain tensor of the bolt preload transmitted to the contact surface. For the Kronecker delta function, This represents the normal strain tensor of the particles at the contact surface after deformation. This represents the shear strain tensor of the particles at the contact surface after deformation. and Let Lamé constant be . E The Young's modulus of the contact surface material. The Poisson's ratio of the contact surface material; In step 4-3, the strain-displacement equation can be expressed as: (3)； in, These are the points on the contact surface along the direction of the contact surface after deformation. x , y , z Displacement in the axial direction; These are the points on the contact surface along the direction of the contact surface after deformation. x , y , z Normal strain in the axial direction; , , These are the points on the contact surface along the direction of the contact surface after deformation. x O y , y O z , z O x Shear strain in the planar direction; In step 4-4, the simultaneous stress equilibrium equations, stress-strain equations, and strain-displacement equations can be expressed as: （4）； The relationship between bolt preload and contact surface pressure is as follows: （5）； In the formula: m The transmission coefficient of bolt preload. This is the critical value of the contact surface pressure. This is the critical value of the contact surface stress. A It is the effective force-bearing area of ​​the contact surface between the main conductor and the bolt; among which, stress characterizes the pressure distribution of the bolt preload per unit area of ​​the contact surface, and has a direct conversion relationship with pressure; Combining equations (4) and (5), the controlling equation for the preload of the T-type clamp bolt can be expressed as: (6)。 6. The method according to claim 1, 4, or 5, characterized in that, In step four, after obtaining the governing equation for the preload of the T-type wire clamp bolt by utilizing the relationship between the three elements of stress, strain, and displacement through the above steps, it is necessary to determine the initial conditions for the governing equation, which includes the following steps: Step s4-1) Determine the computational domain for the initial conditions; Step s4-2) Calculate the initial conditions of the governing equations using the surface stress properties of the computational region; In step s4-1), after the preload is applied to the bolt head, it exerts pressure on the contact surface between the bolt and the main guideline, generating surface stress. Therefore, the bolt's upper surface, where surface stress is generated, forms the boundary for calculating the preload, and the distribution of surface stress constitutes the boundary condition for the bolt preload. This boundary condition is also the initial condition for the governing equation. The bolt's upper surface is high... z A cylinder approaching 0, about xOz and yOz Planar symmetry; to simplify the region of repetitive calculations, the symmetry of the initial conditions is calculated, and the domain of the calculated boundary conditions is defined. Reduced to 1 / 4 of its original size to facilitate subsequent measurement using the mirror method. The initial conditions.

7. The method according to claim 6, characterized in that, In step s4-2), stress characterizes the equilibrium relationship between external and internal forces, therefore for the 1 / 4 domain... The surface stress also satisfies the equilibrium equation, therefore the surface stress at the boundary surface satisfies: （7）； In the formula: t i Let be the components of the surface stress vector of the boundary force-bearing surface, where i = x , y , z , n i Here are the components of the normal vector of the boundary force surface, where i = x , y , z ; Since the surface stress acts vertically upwards, its component in the normal vector direction is 0, therefore... t x and t y If both are 0, then equation (7) can be rewritten as: （8）； In the formula: This is the unit normal vector of the boundary surface subjected to force. Since the domain of the boundary in equation (8) is only 1 / 4; By calculating the symmetry properties of the boundary surface in step one, it can be seen that the normal stress and shear stress must be the same in magnitude in other octaves, only the direction is opposite, that is, the sign is positive or negative; Since the surface stress in the normal direction is 0, substituting the remaining part into equation (8) can reveal that the tensor form will not change due to different directions, so equation (8) is the initial condition of the bolt preload control equation.

8. The method according to claim 1, 2, 4, 5, or 7, characterized in that, Step five specifically includes the following steps: Step 5-1: First, divide the solution domain of the partial differential equation of bolt preload into a grid to define the solution domain of each grid in the discretized integral equation. Step 5-1: Considering that the governing equation of bolt preload is a nonlinear partial differential equation, and that nonlinear partial differential equations have strong continuity, when solving analytically, the cross terms of variables in the equation will severely hinder the separation of variables, thus failing to satisfy linear superposition and making it impossible to construct a general solution by combining simple particular solutions; at this time, it is necessary to use numerical methods to obtain an approximate solution to replace the original analytical solution; and by meshing the large and continuous solution domain, the calculation results of the governing equation can be initially approximated. Step 5-2: Select the weight function based on the magnitude of the error generated by each grid cell in the solution domain for the approximate solution according to the integral equation. This forces the error to zero under the weighting of the weighting function, thereby eliminating the error caused by the cross term and obtaining the weak integral equation of the bolt preload. Step 5-3: The solution domain of the discretized integral equation has been defined during mesh generation. The mesh can be characterized by its shape, i.e., its shape function. N ( x To avoid approximate solution errors caused by the mismatch between the shape function and the weight function of the mesh element in the integral equation, the shape function can be adjusted accordingly. N ( x ) and weight function By performing the same form of discretization, it is ensured that the shape function and the grid weight function in the solution domain of the integral equation are mutually mapped; Step 5-4: Further discretize the weak form integral equation of bolt preload to obtain a linear integral equation consisting only of low-order polynomials. Solving this linear equation system will yield the bolt preload solution based on mechanical properties.

9. The method according to claim 8, characterized in that, In step 5-3, for the shape function N ( x ) and weight function Discretizing in the same form can be represented as: （9）； In the formula: a and b These represent the contact surface stress and the discretized mesh nodes after weighting function. N The total number of grid nodes for discretizing the contact surface stress tensor; and These are the shape functions of the contact surface stress tensor and the weighting function, respectively. and Let be the nodal stress values ​​of the contact surface stress tensor and weighting function.

10. The method according to claim 8 or 9, characterized in that, In step 5-4, the weak-form integral equation of the bolt preload can be expressed as follows: （10）； In the formula: This is the first invariant of the stress transmitted from the bolt preload to the contact surface; Substituting equation (9) into equation (10) and expanding further, we obtain a linear integral equation consisting only of low-order polynomials, which is also the unit equation: （11）； in: Let be the stress tensor component at the a-th node, and k and l represent the normal direction of the stress surface and the stress direction, respectively. This represents the equivalent nodal load component at the b-th node; Element stiffness matrix The interaction between nodes in the solution domain of the integral equation is characterized as follows: （12）； in, Let be the shape function of the a-th node. Let be the shape function of the b-th node. Let m be the coordinate variable in the m-direction of the spatial coordinate system. Let be the coordinate variable in the i-direction of the spatial coordinate system. Let be the coordinate variable in the j-direction of the spatial coordinate system. For the Kronecker function, For the Kronecker function, The Kronecker function; Element load terms The influence of surface stress on the contact surface stress within the solution domain is characterized as follows: （13）； in, Let be the component of the unit normal vector of the boundary force-bearing surface in the j-direction. This refers to the boundary region where surface forces act; Finally, the element stiffness matrices of all contact surface stresses are filled into the global stiffness matrix of bolt preload as elements according to their positions on the bolt preload degree of freedom during mesh generation: （14）； In the formula: K The global stiffness matrix of the bolt preload. The load vector consists of all surface stress load terms; the only unknown is the bolt preload. F 0, Substitute the surface stress equation (8) into the load vector and solve the linear equation system to obtain the bolt preload of the T-type clamp under mechanical property analysis.

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