Transmission tower displacement calculation method based on virtual work principle

Abstract

The invention relates to the technical field of power transmission towers, aims to solve the problems that an existing tower displacement calculation method based on finite element software analysis is complex in model processing and low in efficiency, and provides a power transmission tower displacement calculation method based on a virtual work principle, which comprises the following steps: S1, establishing a power transmission tower model, and independently modeling each rod piece of a power transmission tower; s2, assuming that the initial bolt slippage of the power transmission tower is 0; s3, applying a load in the power transmission tower model, and calculating the axial force of each rod piece; s4, in the power transmission tower model, applying unit force in the pre-solving direction of the pre-solving node, and calculating virtual internal force of each rod piece; s5, calculating an elastic deformation value of the overall rod piece; s6, identifying the types of the rod pieces and the number of connection points of the end heads of the rod pieces; s7, selecting a bolt slippage model; s8, calculating a total bolt slippage deformation value; and S9, calculating the total displacement of the pre-solved node of the power transmission tower in the pre-solved direction, wherein the total displacement is the sum of the total elastic deformation value and the total bolt slippage deformation value.

Description

Technical Field

[0001] The invention relates to the technical field of power transmission towers, and in particular to a method for calculating the displacement of a power transmission tower based on the principle of virtual work. Background Art

[0002] Angle steel towers are the most commonly used tower form for power transmission lines because of their light individual components, easy manufacturing, transportation and installation. Angle steel towers are composed of many components, especially for 500kV and above lines, where there are more than a thousand components in a tower. The components are mainly connected by bolts. Except for anchor bolts, flange bolts and hanging point bolts, most bolts are mainly subjected to shear loads. To ensure smooth installation, the screw hole diameters of M16, M20 and M24 common bolts commonly used in angle steel towers are generally required to be the nominal diameter of the bolt plus 1.5mm. Due to the influence of domestic processing accuracy, the gap between the bolt and the screw hole is generally greater than 1.5mm. Since the bolts of angle steel towers are mainly subjected to shear, this structural feature determines that when the shear force is greater than the friction between the connected components, slippage will occur between the bolted components.

[0003] The current general tower design software uses a spatial truss model or a beam-truss model for calculation and analysis, without considering the effect of bolt slip on the tower deformation and stress. Due to bolt slip, the measured value of the overall tower deformation is much greater than the software calculation and analysis value, and the internal force of the rod will also be significantly different from the calculated value.

[0004] According to the "Electric Power Engineering Design Manual", the bolt slip and structural stress deformation of the plane truss are calculated based on the principle of virtual work according to the following formula. However, some scholars have found through analysis that the following formula only considers the influence of the bolt hole, but does not consider the influence of factors such as hole wall deformation and preload force, and cannot accurately calculate the deformation of the three-dimensional space structure, which is very different from the actual test results.

[0005]

[0006] In the formula, Δ is the deformation value, Δ p is the stress deformation value, δ is the bolt slip value, is the virtual internal force of each member under the unit force in the desired deformation direction, N p is the internal force of each rod under the action of load P, L is the length of each rod, E is the elastic modulus, A is the cross-sectional area of ​​each rod, n is the number of connection points of each rod, and e is the difference between the bolt hole diameter and the bolt diameter, which is generally 1.5-2.0mm.

[0007] In response to the theoretical problem of bolt slip, domestic and foreign scholars have conducted a series of related studies and proposed a bolt slip index model and a polynomial model. Based on the bolt slip index model and polynomial model, some scholars used finite element software such as ANSYS and ABAQUS combined with spring units to conduct modeling and analysis, and achieved good results in the deformation analysis of the real test tower. This calculation method requires the stiffness or node processing of the rod in the finite element software. Due to the large number of transmission tower rods, complex structure and low efficiency, it is mostly used for comparative analysis of measured displacements in real test.

[0008] It can be seen that the existing tower displacement calculation method based on finite element software analysis has complex model processing and low efficiency. It is mostly used for comparative analysis and research with real-type tests. It cannot be promoted and applied in the tower design stage to optimize the structural design method and deformation performance and improve the safety and reliability of the tower structure. Summary of the invention

[0009] The present invention aims to provide a method for calculating the displacement of a transmission tower based on the principle of virtual work, so as to solve the problems of complex model processing and low efficiency of the existing method for calculating the displacement of the tower based on finite element software analysis.

[0010] The present invention is achieved by adopting the following technical solutions:

[0011] The present invention provides a method for calculating the displacement of a transmission tower based on the virtual work principle, comprising the following steps:

[0012] S1: Establish a transmission tower model, and model each member of the transmission tower separately;

[0013] S2: Assuming that the transmission tower is assembled, the initial bolt slip is 0;

[0014] S3: Apply loads to the transmission tower model and calculate the axial forces of each member;

[0015] S4: In the transmission tower model, a unit force is applied at the pre-determined node and in the pre-determined direction to calculate the virtual internal force of each member;

[0016] S5: Calculate the overall elastic deformation value of the rod;

[0017] S6: Identify the type of bar and the number of connection points at the ends of the bar;

[0018] S7: Select the bolt sliding model;

[0019] S8: Calculate the overall bolt slip deformation value;

[0020] S9: Calculate the total displacement of the transmission tower in the expected direction of the expected node. The total displacement is the sum of the overall elastic deformation value and the overall bolt sliding deformation value.

[0021] As the preferred technical solution:

[0022] Step S1 specifically includes:

[0023] In the universal tower design software, a spatial truss or beam truss model is established for each member one by one.

[0024] As the preferred technical solution:

[0025] The general tower design software includes Daoheng tower full stress analysis software and SmartTower tower design software.

[0026] As the preferred technical solution:

[0027] In step S3, the axial force of each member is calculated using a solver in the general tower design software.

[0028] As the preferred technical solution:

[0029] In step S4, the virtual internal force of each member is calculated using the solver in the general tower design software.

[0030] As the preferred technical solution:

[0031] In step S5, the overall elastic deformation value of the rod is calculated using the general tower design software, or calculated using the following formula based on the virtual work principle:

[0032]

[0033] In the formula, Δ p To calculate the elastic deformation value of the overall member in the direction of the node, is the virtual internal force of each member under the action of unit force in the pre-determined direction at the pre-determined node, N p is the axial force of each member under the action of load P, L is the length of each member, E is the elastic modulus, and A is the cross-sectional area of ​​each member.

[0034] As the preferred technical solution:

[0035] Step S6 specifically includes: classifying the rods, and determining the number of connection points of the rod ends according to the rod categories.

[0036] As the preferred technical solution:

[0037] In step S7, the bolt slip model adopts the Ungkurapinan polynomial model.

[0038] As the preferred technical solution:

[0039] In step S8, the overall bolt sliding deformation value is calculated according to the virtual work principle as follows:

[0040]

[0041] Where Δ is the overall bolt slip deformation value, which is divided into two parts: δ and ∑Δ c , where δ is the relative value of bolt slip in this working condition relative to that before loading, ∑Δ c is the residual value of bolt slip before loading in this working condition, is the virtual internal force of each member under the action of unit force in the pre-determined direction of the pre-determined node, n is the number of connection points of each member end; Δ s is the bolt slip value of the rod joint under load P, Δ s The calculation is performed using an exponential model or a polynomial model.

[0042] For controlled working conditions (working conditions that can cause more than 70% of the rod bolts to slip), the residual value of bolt slip can be ignored. For uncontrolled working conditions, the residual value of bolt slip of the preceding load needs to be considered.

[0043] As the preferred technical solution:

[0044] Step S2 specifically includes: assuming that after the transmission tower is assembled, no slippage occurs to the bolts at each node, the bolts are located at the center of the screw holes, and the initial bolt slippage is 0.

[0045] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0046] The invention is based on the principle of virtual work, takes into account the influence of loading time history, decomposes the deformation of the iron tower into three parts: the elastic deformation value of the rod, the residual value of bolt slip and the relative value of bolt slip, and calculates them separately. By taking into account the bolt slip, the calculation formula of the iron tower deformation is corrected. Combined with the internal force calculation results of the iron tower general design software, the deformation of each node and direction of the iron tower after the bolt slip is considered can be quickly calculated, and the deformation influencing factors are analyzed, providing a reference for the design and optimization of the iron tower. After the bolt slip formula is corrected, the calculated value is close to the measured value. Compared with the measured value, the difference between the calculated displacement and the test displacement under different working conditions can be controlled within 10%, providing a basis for the real test data analysis and the optimization design of the iron tower; it overcomes the problems of complex model processing and low efficiency in the prior art, and can quickly identify the displacement influencing factors, so as to analyze and control the deformation when designing the iron tower, and further improve the safety and reliability of the iron tower structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The present invention is a flowchart of a method for calculating the displacement of a transmission tower based on the principle of virtual work.

[0048] Figure 2 This is a schematic diagram of the displacement observation points of the real test.

[0049] Figure 3It is a comparison chart between the measured displacement and the calculated displacement under the wire break condition.

[0050] Figure 4 This is a comparison chart of the measured displacement and the calculated displacement under 60° strong wind conditions.

[0051] Figure 5 It is a comparison chart between the measured displacement and the calculated displacement of the uneven ice-torsion condition without considering the residual deformation correction.

[0052] Figure 6 It is a comparison chart between the measured displacement and the calculated displacement of the non-uniform ice-torsion condition considering the residual deformation correction. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] Example 1

[0055] like Figure 1 As shown, this embodiment proposes a method for calculating the displacement of a transmission tower based on the principle of virtual work, comprising the following steps:

[0056] S1: A transmission tower model is established in the general tower design software, and each member of the transmission tower is modeled separately.

[0057] Specifically, a spatial truss or beam truss model is established for each member in the tower general design software, and each member is modeled separately in order to propose the axial force N of each member. p Among them, the general tower design software includes Daoheng Tower Full Stress Analysis Software, SmartTower Tower Design Software, etc. The purpose of establishing a spatial truss or beam-truss model member by member is to accurately obtain the internal force of each member under different working conditions, and avoid the excessive internal force value of some members due to the simplified modeling of unified materials.

[0058] S2: Assume that after the transmission tower is assembled, the initial bolt slip is 0.

[0059] S3: Apply loads in the spatial truss or beam-truss model and use the solver in the tower general design software to calculate the axial forces of each member.

[0060] S4: In the spatial truss or beam-truss model, a unit force is applied at the pre-determined node and in the pre-determined direction, and the virtual internal force of each member is calculated using the solver in the general tower design software.

[0061] S5: Calculate the overall member elastic deformation value.

[0062] The overall elastic deformation value of the rod can be directly calculated using the general tower design software, or it can be calculated in combination with the virtual internal force using the following formula:

[0063]

[0064] In the formula, Δ p To calculate the elastic deformation value of the overall member in the direction of the node, is the virtual internal force of each member under the action of unit force in the pre-determined direction at the pre-determined node, N p is the axial force of each member under the action of load P, L is the length of each member, E is the elastic modulus, and A is the cross-sectional area of ​​each member.

[0065] S6: Identify the type of member and the number of connection points at the ends of the member.

[0066] The types of rods and the number of connection points at the ends of the rods can be counted according to the following table:

[0067]

[0068] S7: Select the bolt sliding model.

[0069] In view of the fact that the Kitipornchai exponential model and the domestic modified exponential model are only applicable to M16 and M20 bolts, when calculating the M24 bolts and the sliding deformation of the main material of the tower body, the displacement value will be seriously too large. Therefore, the bolt sliding model preferably adopts the Ungkurapinan polynomial model.

[0070] S8: According to the number of connection points at the ends of the rod and the bolt slip model, combined with the virtual internal force, the overall bolt slip deformation value in the expected direction of the node is obtained.

[0071] Considering the influence of residual deformation, number of connection points of rod ends, preload, bolt gap, rod internal force, and hole wall deformation, the calculation formula for the overall bolt slip deformation value is as follows:

[0072]

[0073] Where Δ is the cumulative value of bolt slip deformation, that is, the overall bolt slip deformation value, which is divided into two parts: δ and ∑Δ c , where δ is the relative value of bolt slip in this working condition relative to that before loading, ∑Δ c is the residual value of bolt slip before loading in this working condition, is the virtual internal force of each member under the action of unit force in the pre-determined direction of the pre-determined node, n is the number of connection points of each member end; Δ s is the bolt slip value of the rod joint under load P, Δ sThe calculation is performed using an exponential model or a polynomial model.

[0074] For controlled working conditions (working conditions that can cause more than 70% of the rod bolts to slip), the residual value of bolt slip can be ignored. For uncontrolled working conditions, the residual value of bolt slip of the preceding load needs to be considered.

[0075] S9: Calculate the total displacement of the transmission tower in the expected direction of the expected node. The total displacement is the sum of the overall elastic deformation value and the overall bolt sliding deformation value.

[0076] Next, combined with examples, the three typical control conditions of broken wire, 60° strong wind and uneven ice twist are analyzed for the 500kV line ZNC33153B landscape tower. The applicability of the invention is verified by comparing the real-type test with the node displacement calculated based on the virtual work principle.

[0077] In order to study the influence of bolt slip on the deformation of transmission tower, the displacements of 11 nodes under three typical control conditions were compared. Figure 2 The node location and number are shown. Figure 3 The comparison between the measured displacement and the calculated displacement under the wire break condition is shown. Figure 4 The comparison between the measured displacement and the calculated displacement under the 60° strong wind condition is shown. Figure 5 , Figure 6 The comparison between the measured displacement and the calculated displacement under the non-uniform ice-torsion condition without considering the residual deformation correction and considering the residual deformation correction is shown respectively.

[0078] from Figure 3 It can be seen that under the condition of wire breakage, the displacement value calculated by the truss model (without considering bolt slippage) is much smaller than the measured value, and the calculated value of the present invention is generally equivalent to the measured value, which proves the applicability of the calculation method of the present invention. Therefore, under the condition of wire breakage, the calculation method of the present invention is applicable.

[0079] from Figure 4 It can be seen that under the 60-degree high wind condition, the displacement value calculated by the truss model (without considering bolt slippage) is much smaller than the measured value, and the calculated value of the present invention is generally equivalent to the measured value, which proves the applicability of the calculation method of the present invention. Therefore, under the 60-degree high wind condition, the calculation method of the present invention is applicable.

[0080] from Figure 5 It can be seen that under the non-uniform ice-torsion condition, the displacement value calculated by the truss model (without considering bolt slip) is much smaller than the measured value; if the residual deformation correction is not considered, the calculated value of the present invention is quite different from the measured value; after considering the residual deformation correction (such as Figure 6 As shown in the figure, the calculated values ​​of the present invention are generally equivalent to the measured values, which proves the applicability of the calculation method of the present invention.

[0081] The applicability of the transmission tower displacement calculation method based on the virtual work principle was verified through a real-type test. By comparing and analyzing three typical working conditions, namely, wire breakage, 60° strong wind, and uneven ice torsion, it can be seen that under controlled working conditions (wire breakage, 60° strong wind), even without considering the influence of residual deformation, the node displacement under the design load obtained by the present invention is consistent with the measured value; for uncontrolled working conditions (uneven ice torsion), after considering the influence of residual deformation and correction, the node displacement under the design load obtained by the present invention is basically consistent with the measured value. Compared with the measured displacement, the displacement calculated by the present invention has a smaller error, which solves the problem of complex model processing and low efficiency in the prior art, and can quickly identify the factors affecting the displacement, so as to analyze and control the deformation during the tower design, and further improve the safety and reliability of the tower structure.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the displacement of a transmission tower based on the principle of virtual work, characterized in that: The following steps are involved: S1: Establish a transmission tower model, and model each member of the transmission tower separately; S2: Assuming that the transmission tower is assembled, the initial bolt slip is 0; S3: Apply loads to the transmission tower model and calculate the axial forces of each member; S4: In the transmission tower model, a unit force is applied at the pre-determined node and in the pre-determined direction to calculate the virtual internal force of each member; S5: Calculate the overall elastic deformation value of the rod; S6: Identify the type of bar and the number of connection points at the ends of the bar; S7: Select the bolt sliding model; S8: Calculate the overall bolt slip deformation value; S9: Calculate the total displacement of the transmission tower in the expected direction of the expected node. The total displacement is the sum of the overall elastic deformation value and the overall bolt sliding deformation value.

2. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1, characterized in that: Step S1 specifically includes: In the universal tower design software, a spatial truss or beam truss model is established for each member one by one.

3. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1, characterized in that: The general tower design software includes Daoheng tower full stress analysis software and SmartTower tower design software.

4. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1 is characterized in that: In step S3, the axial force of each member is calculated using a solver in the general tower design software.

5. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1 is characterized in that: In step S4, the virtual internal force of each member is calculated using the solver in the general tower design software.

6. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1 is characterized in that: In step S5, the overall elastic deformation value of the rod is calculated using the general tower design software, or calculated using the following formula based on the virtual work principle: In the formula, Δ p To calculate the elastic deformation value of the overall member in the direction of the node, is the virtual internal force of each member under the action of unit force in the pre-determined direction at the pre-determined node, N p is the axial force of each member under the action of load P, L is the length of each member, E is the elastic modulus, and A is the cross-sectional area of ​​each member.

7. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1 is characterized in that: Step S6 specifically includes: classifying the rods, and determining the number of connection points of the rod ends according to the rod categories.

8. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1, characterized in that: In step S7, the bolt slip model adopts the Ungkurapinan polynomial model.

9. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1, characterized in that: In step S8, the overall bolt sliding deformation value is calculated according to the virtual work principle as follows: Where Δ is the overall bolt slip deformation value, which is divided into two parts: δ and ∑Δ c , where δ is the relative value of bolt slip in this working condition relative to that before loading, ∑Δ c is the residual value of bolt slip before loading in this working condition, is the virtual internal force of each member under the action of unit force in the pre-determined direction of the pre-determined node, n is the number of connection points of each member end; Δ s is the bolt slip value of the rod joint under load P, Δ s The calculation is performed using either an exponential model or a polynomial model.

10. The method for calculating the displacement of a transmission tower based on the virtual work principle according to claim 1, characterized in that: Step S2 specifically includes: assuming that after the transmission tower is assembled, no slippage occurs to the bolts at each node, the bolts are located at the center of the screw holes, and the initial bolt slippage is 0.

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