Vortex-induced vibration fatigue damage assessment method for steel pipe member of power transmission tower

Abstract

The invention discloses a power transmission tower steel tube member vortex-induced vibration fatigue damage assessment method. The method comprises the following steps: firstly, establishing a joint probability distribution model between wind speed and wind direction according to historical meteorological data of a place where a power transmission tower is located; secondly, establishing a finite element model of the steel pipe component containing the connecting nodes, and obtaining natural vibration frequency and rotational rigidity of the connecting nodes; calculating vortex-induced vibration displacement of the steel pipe component under different incoming flow conditions based on a wake flow vibrator model; then the nominal bending stress of the steel pipe component is calculated, and the hot spot stress of the connecting joint is determined; and finally, calculating vortex-induced vibration fatigue damage values of the steel pipe member and the connection node thereof in a given period. The method has the remarkable effects that the finite element modeling complexity can be reduced, and the applicability and the prediction reliability and accuracy under the condition of a complex wind field are realized; meanwhile, good calculation efficiency is considered, and vortex-induced vibration fatigue damage of the steel pipe component and the node can be accurately, reliably, efficiently and economically evaluated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of structural wind engineering and power transmission and transformation engineering, and particularly relates to a vortex-induced vibration fatigue damage evaluation method suitable for typical node steel pipe components of a power transmission tower. BACKGROUND

[0002] Steel pipe power transmission towers have been widely used in ultra-high voltage transmission lines due to their significant advantages in economy and technology. However, under the action of natural wind, especially when the incoming flow velocity approaches the natural frequency of the component, the steel pipe component is prone to vortex-induced vibration. At present, the research on vortex-induced vibration fatigue analysis of steel pipe components mainly has the following problems: 1. Difficulty in balancing calculation efficiency and accuracy On the one hand, the existing research usually adopts a CFD simulation method to obtain the vortex-induced vibration response of the steel pipe component. Although this method has high accuracy, the calculation process is complex and resource-consuming, which is difficult to meet the actual needs of rapid prediction and multi-working condition evaluation in engineering. On the other hand, in the process of fatigue damage evaluation, the existing research usually relies on a high-precision finite element model of a full solid element to simulate the stress distribution of the connecting node, so as to extract the hot spot stress for fatigue analysis. Although this modeling method can accurately capture the stress concentration effect, it will lead to a significant increase in calculation burden under the coupling condition of multiple wind speeds and multiple wind directions. Therefore, how to effectively reduce the evaluation cost while ensuring the prediction accuracy is one of the key technical challenges in the current field.

[0003] 2. Incomplete modeling of wind environment randomness In actual engineering application, due to the significant uncertainty of natural wind environment, the vortex-induced vibration and its fatigue damage response of the steel pipe component of the power transmission tower should be considered as a full probability superposition process of damage contribution under different incoming flow conditions. In theory, fatigue life evaluation should be based on the integral calculation of the joint probability distribution of wind speed and wind direction to fully reflect the variation characteristics of environmental load. However, most of the existing researches only consider wind speed as the only random variable, ignoring the randomness of wind direction and its influence on vortex response. At present, there is still a lack of a unified and systematic method to introduce the joint distribution of wind speed and wind direction into the vortex-induced vibration fatigue damage analysis, which limits the applicability and prediction reliability of the existing method under complex wind field conditions. SUMMARY

[0004] To solve the above technical problems, the present application provides a vortex-induced vibration fatigue damage evaluation method for steel pipe components of a power transmission tower, which can efficiently predict the fatigue vortex-induced vibration damage of the steel pipe component and the connecting node while considering the calculation efficiency. The core of the method includes: (1) The wake vortex model is used instead of the high-time-consuming CFD simulation to quickly obtain the vortex-induced vibration response of the steel pipe component under various wind conditions; (2) Introducing the hot spot stress concentration coefficient method and the simplified mechanics model, significantly reducing the complexity of finite element modeling, and realizing efficient estimation of the fatigue damage of the connecting node; (3) Constructing a discrete-continuous hybrid joint probability distribution model of wind speed and wind direction, and based on the total probability formula, the vortex-induced vibration fatigue damage is weighted, so as to comprehensively consider the influence of the randomness of wind speed and wind direction on the vortex-induced vibration fatigue damage.

[0005] The specific steps are as follows: Step 1: According to the historical meteorological data of the site of the power transmission tower, a joint probability distribution model between continuous wind speed and discrete wind direction is established, forming a discrete-continuous hybrid distribution; Step 2: Establish a finite element model of the steel pipe member containing the connecting node, and obtain the natural frequency through modal analysis to identify the rotational stiffness of the connecting node; Step 3: Based on the wake oscillator model, the vortex-induced vibration displacement of the steel pipe member under different flow conditions is calculated; Step 4: Using the vortex-induced vibration displacement, the nominal bending stress of the steel pipe member is calculated according to the Euler beam theory, and the hot spot stress of the connecting node is determined by the hot spot stress concentration coefficient method; Step 5: Combined with the wind speed-wind direction joint probability distribution model, the vortex-induced vibration fatigue damage value of the steel pipe member and its connecting node in a given period is calculated according to the total probability formula. BRIEF DESCRIPTION OF DRAWINGS

[0006] Figure 1 is the wind rose diagram of the site of the power transmission tower; Figure 2 is the probability density function (PDF) curve of the wind speed under a typical direction (NE); Figure 3 is the finite element model diagram of the steel pipe member containing the C-type node; Figure 4 is the stress distribution diagram of the connecting node; Figure 5 is the wind speed and wind direction time history data curve of a certain place in a certain period of time; Figure 6 is the change process curve of the cumulative vortex-induced vibration fatigue damage of a certain C-type node steel pipe member in one year. DETAILED DESCRIPTION

[0007] The present application will be further described below in combination with the embodiments and the drawings.

[0008] Example 1: A vortex-induced vibration fatigue damage evaluation method for steel pipe members of a power transmission tower, comprising the following steps: Step 1, according to the historical meteorological data of the site of the power transmission tower, the joint probability distribution model between continuous wind speed and discrete wind direction is established, and the discrete-continuous mixed distribution is formed.

[0009] Step 2, the finite element model of steel pipe member containing connecting node is established, and the natural frequency is obtained through modal analysis, so as to identify the rotational stiffness of connecting node. Specifically, the finite element model of steel pipe member of "C" type connecting node is established; and the end of steel pipe member is taken as the coordinate origin, and the axial direction of steel pipe member is taken as the coordinate direction The coordinate system is established; and the subsequent steps are carried out. Rotational stiffness of connecting node of steel pipe member The formula (1) is used to calculate and obtain: Formula (1); Wherein: ; L is the length of steel pipe member, EI is the bending stiffness of steel pipe member, P is the axial force of steel pipe member, m is the unit mass of steel pipe member, ω is the natural circular frequency of steel pipe member, , ω is the natural frequency of steel pipe member.

[0010] Step 3, the vortex-induced vibration displacement of steel pipe member under different flow conditions is calculated based on the wake oscillator model. The vortex-induced vibration displacement According to formula (2), the vortex-induced vibration displacement is calculated: Formula (2); X is the axial coordinate, t is the time; m is the unit mass, , m is the unit mass of steel pipe member, m is the fluid added mass, , ρ is the flow density, D is the outer diameter of steel pipe member, C is the system damping, , C is the structural damping, C is the fluid damping, , K is the stall parameter, , C is the average resistance coefficient, 1.2 is taken, St is the Strouhal number, Take 0.2, is the vortex shedding frequency, , is the average velocity of the flow relative to the normal direction of the member, , is the average velocity of the flow, is the angle of the flow direction relative to the axial direction of the steel tube member, is the reference value of the amplitude of the lift coefficient, is a transient variable representing the wake flow dynamics; the transient variable representing the wake flow dynamics is calculated according to the following formula (3): , formula (3); is a nonlinear damping coefficient, is a coupling coefficient; and are both empirical parameters in the wake oscillator model; When calculating the vortex-induced vibration displacement, the boundary conditions are specified according to formula (4): , formula (4); is the vortex-induced vibration displacement at time t at the "0" coordinate along the axial direction of the steel tube member; is the vortex-induced vibration displacement at time t at the "L" coordinate along the axial direction of the steel tube member.

[0011] Step 4, using the vortex-induced vibration displacement, calculate the nominal bending stress of the steel tube member according to the Euler beam theory, and determine the hot spot stress of the connection node by the hot spot stress concentration factor method; The hot spot stress of the transmission tower connection node is obtained by the following steps: first, obtain the stress distribution of the connection node by finite element analysis; then, calculate the hot spot stress and nominal stress at the weld toe to obtain the hot spot stress concentration factor SCF; and calculate the actual weld toe nominal stress using the vortex-induced vibration displacement; finally, obtain the hot spot stress of the connection node.

[0012] Specifically, the nominal bending stress at time t at the "L" coordinate along the axial direction of the steel tube member is calculated according to the following formula (5): Z T , formula (5); is the elastic modulus; The hot spot stress of the transmission tower connection node​​​​​​ According to formula (6); , formula (6); SCF is the hot spot stress concentration factor; is the nominal stress at the weld toe; ; is the bending normal stress, is the cross-section bending modulus at the hot spot, is the distance from the end of the C-type joint to the weld toe, ; is the vortex-induced vibration displacement at the time of along the "x" coordinate of the steel pipe member, is the cross-section width of the connecting plate, is the cross-section height of the connecting plate; Step 5, according to the wind speed-wind direction joint probability distribution model, the vortex-induced vibration fatigue damage value of the steel pipe member and its connecting joint in a given period is calculated according to the total probability formula; Specifically, the vortex-induced vibration fatigue damage value of the steel pipe member and its connecting joint in a given period is calculated according to formula (7); , formula (7); is the number of sections divided according to the wind direction interval, which can be determined according to the statistical data of the meteorological station; is the number of sections divided according to the wind speed interval, wherein the wind speed interval range is defined as 0.8 -1.2 , is the wind speed corresponding to the maximum value of the vortex-induced vibration of the steel pipe member, which can be calculated by ; is the average wind speed of the interval, is the average wind direction of the interval; The probability of the occurrence of the wind direction , which can be obtained through the rose diagram of the wind at the location of the transmission tower; is the joint probability density function of the wind speed and wind direction, which can be obtained by least square fitting according to the statistical data of the meteorological station; is the joint probability density function value under the condition of the wind speed and the wind direction ; is the wind speed​ and wind direction Vortex-induced vibration fatigue damage under the condition can be calculated according to formula (8); , formula (8); is the number of stress cycles, which can be obtained according to the rainflow counting method; is the number of cycles of fatigue limit, , and are the parameters of S-N curve, which can be taken as =1012.164 and =3 for steel pipe members, and =1012.49, =3.089 for connection nodes; is the stress amplitude, which can be obtained by using the rainflow counting method to count the stress time history and , so as to obtain the stress amplitude of steel pipe members and connection nodes respectively.

[0013] Example 2: Taking the Yangtze River large-span transmission tower of Bahe Tan-Zhejiang UHV transmission line (Anhui section) as the engineering background, and combining with the local meteorological data, the vortex-induced vibration fatigue damage analysis of the steel pipe member of the transmission tower prone to vortex-induced vibration is carried out.

[0014] A vortex-induced vibration fatigue damage evaluation method for steel pipe members of a transmission tower, comprising the following steps: Step 1, first, according to the historical meteorological statistical data of Chizhou City in Anhui Province where the large-span line is located, the measured average wind speed data from 2000 to 2020 is selected, which contains 16 average wind speed samples under different wind direction directions. For the wind speed data under each wind direction, a Gumbel distribution model is used for modeling to form a discrete-continuous mixed distribution; the wind rose diagram of the place where the transmission tower is located is shown in Figure 1 , and the probability density function (PDF) curve of wind speed under a typical direction (NE) is shown in Figure 2 .

[0015] Step 2, as shown in Figure 3 , a finite element model of a steel pipe member containing a C-type node is established, and the left end of the steel pipe member is taken as the coordinate origin, and the axial direction of the steel pipe member is taken as the direction to establish the coordinate system; the physical parameters of the steel pipe member are: the unit mass of the steel pipe member =23.305 kg / m, the bending stiffness of the steel pipe member =2.732×10 5 , and the length of the steel pipe member =10.12m, axial force of steel tube member =0, and model parameters , , ; its natural frequency is obtained by modal analysis 5.92Hz; According to formula (1), the rotational stiffness of the connecting node is calculated ; , formula (1); , ; The rotational stiffness is calculated =1.925×10 5 kN / m; Step 3, according to formula (2), (3), (4) in example 1, the vortex-induced vibration displacement of steel tube member under different flow conditions is calculated ; , formula (2); is the axial coordinate, is the time; is the unit mass, , is the unit mass of steel tube member, is the fluid added mass, , is the flow density, is the outer diameter of steel tube member, is the system damping, , is the structural damping, is the fluid damping, , is the stall parameter, , is the average drag coefficient, 1.2, is the Strohals number, 1.2, is the vortex shedding frequency, , is the average velocity of the flow relative to the normal direction of the member, , is the average velocity of the flow, is the angle of the flow direction relative to the axial direction of the steel tube member, is the reference value of the amplitude of the lift coefficient, is the instantaneous variable representing the wake dynamics; the instantaneous variable of the wake flow dynamics is calculated according to the following equation (3); equation (3); is a nonlinear damping coefficient, is a coupling coefficient; and are both empirical parameters in the wake oscillator model; When calculating the vortex-induced vibration displacement, the boundary condition is specified according to equation (4): equation (4); is the vortex-induced vibration displacement of the left end of the steel pipe member at time ; is the vortex-induced vibration displacement of the right end of the steel pipe member at time .

[0016] Step 4, calculate the nominal bending stress at time at the axial coordinate of the steel pipe member according to the following equation (5): equation (5); is the elastic modulus; The stress distribution of the connecting joint obtained by finite element analysis is shown in FIG. 3, and the hot spot stress concentration coefficient of the C-type connecting joint is determined according to the ratio of the hot spot stress to the nominal stress, SCF = 2.27; The hot spot stress of the connecting joint of the power transmission tower is calculated according to equation (6): Figure 4 equation (6); SCF is the hot spot stress concentration coefficient; is the nominal stress at the weld toe; ; is the bending normal stress, is the bending modulus of section at the hot spot, is the distance from the end of the C-type joint to the weld toe, ; is the vortex-induced vibration displacement at time at the midpoint position along the steel pipe member, is the sectional width of the connecting plate, is the sectional height of the connecting plate.

[0017] ​​​Step 5, calculate the vortex-induced vibration fatigue damage value of steel tube member and its connection joint in given period according to formula (7) ; , formula (7) is the number of wind direction interval division, according to the statistical data of meteorological station, determine = 16 is the number of wind speed interval division, the calculation results of several instances show that when the wind speed interval > 10, the vortex-induced vibration fatigue damage value of joint and steel tube member hardly changes obviously with the increase of . Considering the calculation accuracy and calculation efficiency, it is suggested that = 10, and 0.8 ≤ ≤ 1.2 , ; is the average wind speed of the interval, is the average wind direction of the interval is the probability of wind direction occurrence, which is obtained by Figure 1 ; is the joint probability density function value under the condition of wind speed and wind direction , which is obtained by least square fitting according to the statistical data of meteorological station; is the vortex-induced vibration fatigue damage under the condition of wind speed and wind direction , which can be calculated according to formula (8) , formula (8) is the stress cycle number, which can be obtained according to rain flow counting method; is the cycle number of fatigue limit, , and are the parameters of S-N curve, for steel tube member, it can be taken as = 1012.164 and = 3, and for connection joint, it can be taken as = 1012.49, = 3.089 For stress amplitude, the rainflow counting method can be used to count the stress time history and Statistics are performed to obtain the stress amplitude of the steel pipe member and the connection node, respectively.

[0018] The accumulated vortex-induced vibration fatigue damage of the connection node (predicted node) in the region between January 1, 2024 and December 31, 2024 is 0.216, and the accumulated vortex-induced vibration fatigue damage of the steel pipe member (predicted member) is 0.0083.

[0019] Example 3 In order to verify the effectiveness of the method of the present application, the same node and the same steel pipe member in the same region and the same time range in Example 2 are analyzed by the traditional step-by-step method (i.e., fatigue damage analysis is performed every hour in a year), and a number of fatigue damage analysis results are obtained, which are continuously stacked and accumulated to obtain the accumulated vortex-induced vibration fatigue damage in 2024.

[0020] First, the wind speed and wind direction time history data of the region from January 1, 2024 to December 31, 2024 are analyzed, as shown in Figure 5 , which details the hourly average wind speed and wind direction changes throughout the year, totaling 8784 data samples.

[0021] This example uses fatigue damage analysis every 1h, and the vortex-induced vibration fatigue damage change process curve is as shown in Figure 6 ; it can be seen from Figure 6 that the predicted node vortex-induced vibration fatigue damage value calculated by the present application in 2024 is very close to the actual predicted node vortex-induced vibration fatigue damage value "0.252" measured by the traditional step-by-step method in 2024. The predicted member vortex-induced vibration fatigue damage value calculated by the present application in 2024 is also relatively close to the actual predicted member vortex-induced vibration fatigue damage value "0.0099" measured by the traditional step-by-step method in 2024. The above verification shows that the method of the present application has high accuracy and reliability for predicting and evaluating the vortex-induced vibration fatigue damage of steel pipe members and nodes.

[0022] At the same time, since the traditional step-by-step method requires analysis at each time, the calculation amount is relatively large, specifically 8760 (365 days * 24h / day * 1 time / h) times in this example; in contrast, the number of analyses required by the method of the present application is 160 (10 * 16) times. It can be seen that the method of the present application can reduce a large number of analysis calculation times, significantly improve the calculation efficiency, and reduce the calculation cost.​

[0023] Beneficial effects: the method of the application can significantly reduce the complexity of finite element modeling, realize the applicability and prediction reliability and accuracy under complex wind field conditions, and at the same time, consider better calculation efficiency. The vortex-induced vibration fatigue damage of the steel pipe member and the node can be evaluated more accurately, reliably, efficiently and economically.

[0024] Finally, it should be noted that the above description is only for the preferred embodiments of the application, and those skilled in the art can make various similar expressions under the inspiration of the application without departing from the purpose of the application and the claims, and such changes fall within the protection scope of the application.

Claims

1. A method for assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower, characterized by The method comprises the following steps: Step 1, a joint probability distribution model between continuous wind speed and discrete wind direction is established according to historical meteorological data of the site of the power transmission tower, forming a discrete-continuous mixed distribution; Step 2, a finite element model of the steel pipe member containing a connecting node is established, and the natural frequency is obtained through modal analysis to identify the rotational stiffness of the connecting node; Step 3, the vortex-induced vibration displacement of the steel pipe member under different flow conditions is calculated based on the wake oscillator model; Step 4, the nominal bending stress of the steel pipe member is calculated according to the Euler beam theory using the vortex-induced vibration displacement, and the hot spot stress of the connecting node is determined by the hot spot stress concentration factor method; Step 5, the vortex-induced vibration fatigue damage value of the steel pipe member and the connecting node within a given period is calculated according to the total probability formula combined with the wind speed-wind direction joint probability distribution model.

2. The method for assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 1, characterized in that: In step 2, a finite element model of the steel pipe member of the "C" type connection node is established; and the end of the steel pipe member is taken as the coordinate origin, and the axial direction of the steel pipe member is taken as the coordinate direction The coordinate system is established.

3. The method of assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 1, wherein: In step 4, the hot spot stress of the connecting node of the power transmission tower is obtained by the following steps: First, the stress distribution of the connecting node is obtained by finite element analysis; Then, the hot spot stress and nominal stress at the weld toe are calculated to obtain the hot spot stress concentration factor SCF; The actual nominal stress at the weld toe is calculated using the vortex-induced vibration displacement; Finally, the hot spot stress of the connecting node is obtained.

4. The method of assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 2 or 3, characterized in that: In the step 2, the rotational stiffness of the steel pipe member connecting joint is obtained by formula (1) ; , equation (1); ； the length of the steel pipe member, the flexural rigidity of the steel pipe member, the axial force of the steel pipe member, the unit mass of the steel pipe member, the natural circular frequency of the steel pipe member, , the natural frequency of the steel pipe member.

5. The method of assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 4, wherein: In step 3, the vortex-induced vibration displacement of the steel pipe member under different incoming flow conditions is calculated according to formula (2) ; , equation (2); is an axial coordinate, is time; m, for unit mass of the steel pipe member, , m, for unit mass of the steel pipe member, m, for fluid added mass, , m, for incoming flow density, m, for outer diameter of the steel pipe member, m, for system damping, , m, for structural damping, m, for fluid damping, , m, for stall parameter, , m, for average drag coefficient, m, for Strouhal number, m, for vortex shedding frequency, , m, for average velocity of the incoming flow relative to the normal direction of the member, , m, for average velocity of the incoming flow, m, for angle of the incoming flow direction relative to the axial direction of the steel pipe member, m, for reference value of the amplitude of the lift coefficient, m, for instantaneous variable characterizing the wake dynamics.

6. The method for assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 5, characterized in that: instantaneous variables of the wake flow dynamics According to the following equation (3); , equation (3); is the nonlinear damping coefficient, is the coupling coefficient.

7. The method of assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 5, wherein: In step 3, the boundary conditions are specified according to formula (4): , equation (4); the vortex-induced vibration displacement at the time when the "0" coordinate along the axial direction of the steel pipe member is at the time when the "0" coordinate along the axial direction of the steel pipe member is at Vortex-induced vibration displacement at time t along the steel pipe member axis ” coordinates are at time t.

8. The method for assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 5, characterized in that: In the step 4, the nominal bending stress at the time T at the coordinate Z along the axial direction of the steel pipe member is calculated according to the following equation (5) ; , equation (5); E is the modulus of elasticity.

9. A method of assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 8, characterized in that: In step 4, the hot spot stress of the connection node of the power transmission tower is calculated according to formula (6) ; , equation (6); SCF is the hot spot stress concentration factor; is the nominal stress at the weld toe; ; is the bending normal stress, is the cross-sectional bending modulus at the hot spot, is the distance from the end of the C-node to the weld toe, ; is the vortex-induced vibration displacement of the steel pipe member at the time of the moment is the coordinate of the connection plate in the direction of the axis of the steel pipe member is the vortex-induced vibration displacement of the steel pipe member at the time of the moment is the sectional width of the connection plate is the sectional height of the connection plate 10. A method of assessing vortex-induced vibration fatigue damage of a steel tube member of a power transmission tower according to claim 9, characterized in that: In step 5, the vortex-induced vibration fatigue damage value of the steel pipe member and its connecting joint in a given period is calculated according to formula (7) ; , equation (7); the number of segments for the wind direction interval, the number of segments for the wind speed interval, the average wind speed of the first interval, the average wind direction of the first interval, the probability of the wind direction appearing, the joint probability density function value of the first wind speed and wind direction condition, the vortex-induced vibration fatigue damage of the first wind speed and wind direction condition.

Images