A method and system for evaluating vibration response of a wind-vehicle-bridge system with weak lateral stiffness

Abstract

The present invention discloses a vibration response assessment method and system for a wind-vehicle-bridge system with weak lateral stiffness. The method considers the coupling effect of wind loads in a spatiotemporally varying wind field on the vehicle and the weak lateral stiffness track beam, the influence of wind loads on the wheel-rail relationship, and the initial inclination and various forces of the track beam caused by factors such as track beam installation errors and prestressing. A dual-model system of a vehicle subsystem dynamic equation and a track beam finite element model is established. By interacting with the dual models, a dynamic response result after convergence of the vibration analysis is obtained, providing theoretical support for the wind-vehicle-bridge coupling analysis of the weak lateral stiffness track beam, thereby effectively assessing the vibration response of the wind-vehicle-bridge system of a straddle-type monorail, so that the vibration analysis results are consistent with the actual operating conditions, and facilitating designers to take vibration reduction measures in advance to reduce safety risks and improve operational comfort.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration analysis of straddle-type monorails, and more specifically, relates to a vibration response evaluation method and system for a wind-vehicle-bridge system with weak lateral stiffness. Background Art

[0002] The straddle-type monorail is a "beam-track integrated" structure. The vehicle walks on a "single-plank bridge" around the track beam. The vehicle uses rubber tires to achieve running, guidance and stability. The running wheels are supported on the top surface of the track beam to bear the vertical load of the vehicle. During running, the lateral restraint of the vehicle is mainly provided by the guide wheels and stabilizing wheels, and the track beam bears a large torsional load.

[0003] In terms of structural static and dynamic characteristics, the running surface width of the straddle-type monorail track beam is 690 to 850 mm, which is significantly reduced compared to the standard railway gauge of 1435 mm. It has low lateral stiffness and weak stability. When operating at full capacity, the vehicle axle weight is 14 tons, and the vehicle live load accounts for 60% of the total load of the bridge span structure (dead load + live load + second-phase dead load). Compared with the live load ratio of railways and highways, it will increase by 2-5 times. The vehicle-track beam is supported by rubber wheels, and the wheel-rail contact stiffness is insufficient, and the elastic deformation is large. The vehicle-bridge system needs to consider the geometric deformation of the structure and re-establish the nonlinear equilibrium equation, resulting in weak dynamic stability.

[0004] Currently, numerous researchers have conducted extensive research on the vehicle-bridge coupled vibration of steel-wheeled and steel-rail trains, such as high-speed and light rail trains. This is because straddle-type monorail track beams differ from those of conventional trains. Their narrow, high beams have low horizontal stiffness, and the roll effect of the vehicle body is much greater than that of steel-wheeled rail transit. This significantly impacts the vehicle and lateral wind loads, and the vibration of the beam body in turn affects the vibration of the vehicle, thereby affecting driving comfort and safety. Wind loads significantly affect the wheel-rail relationship. Existing technologies consider the effects of wind loads by applying them to the vehicle, failing to fully consider their impact on the beam body. This results in significant discrepancies between the calculated results and actual operating conditions.

[0005] Furthermore, due to the integrated track and beam structure of straddle-type monorail systems, track beam installation requires extremely high precision. Any slight error can cause the track beam to tilt. The structural characteristics of the track beam can also contribute to its tilt (the track beams of straddle-type monorail systems utilize prestressed concrete, which requires consideration of shear and torsional deformations in its design. In actual use, these structural characteristics may cause the track beam to tilt to a certain extent). Previous vehicle-bridge coupled vibration analyses have failed to consider the initial tilt angle of the track beam, resulting in significantly different results from actual conditions.

[0006] Therefore, for the straddle-type monorail structure, it is urgent to design a vibration response evaluation method for the wind-vehicle-bridge system with weak lateral stiffness, so as to effectively evaluate the actual vibration response of the wind-vehicle-bridge system of the straddle-type monorail during operation, so that the vibration analysis results are consistent with the actual operation conditions. Summary of the Invention

[0007] (1) Technical issues to be resolved

[0008] Based on the defects mentioned in the above-mentioned background technology, the present invention discloses a vibration response evaluation method and system for a weak lateral stiffness wind-vehicle-bridge system. The method fully considers the coupling effect of wind load on the vehicle and the weak lateral stiffness track beam, the influence of wind load on the wheel-rail relationship, and the initial inclination and various forces of the track beam caused by factors such as track beam installation error and prestressing, and establishes a dual-model system of the vehicle subsystem dynamic equation and the track beam finite element model. By interacting with the dual models, the dynamic response results after the convergence of the vibration analysis are finally obtained, providing theoretical support for the wind-vehicle-bridge coupling analysis of the weak lateral stiffness track beam, thereby effectively evaluating the vibration response of the wind-vehicle-bridge system of the straddle-type monorail, so that the vibration analysis results are consistent with the actual operating conditions, which facilitates designers to take vibration reduction measures in advance to reduce safety risks and improve operational comfort.

[0009] (2) Technical solution

[0010] The present invention discloses a method for evaluating the vibration response of a wind-vehicle-bridge system with weak lateral stiffness, comprising the following steps:

[0011] For straddle-type monorail, establish a vehicle subsystem dynamic equation and a track beam finite element model that considers the initial inclination of the track beam. The vehicle subsystem dynamic equation takes into account the track irregularity excitation and wind load excitation, but does not take into account the influence of the track beam displacement, to obtain the wheel-rail force time history curve F1 in the initial state of the track beam. The wheel-rail force time history curve F1 is imported into the track beam finite element model, and a vibration response analysis is performed under wind load excitation to obtain the displacement time history curve S1 of each wheel-rail contact point in the bridge subsystem dynamic model. The wheel-rail contact point displacement time history curve S1 is assigned as an influence value to each wheel in the vehicle subsystem dynamic equation as the initial value of this stage, and the wheel-rail force time history curve F2 of the next stage is updated through vibration analysis. When n≥1, determine whether the condition is met. δ is the preset control index. When the wheel-rail force time history When the wheel-rail force time history curve F2 is continuously imported into the track beam finite element model and vibration response analysis is performed to obtain the wheel-rail contact point displacement time history curve S2 → the wheel-rail contact point displacement time history curve S2 is assigned as the influence value to each wheel of the vehicle subsystem dynamic equation as the initial value of this stage, and the wheel-rail force time history curve F3 of the next stage is updated through vibration analysis → until the condition is met , the vibration analysis converges and the vehicle and track beam coupled vibration analysis results are output.

[0012] In addition, the present invention also discloses a vibration response evaluation system for a weak lateral stiffness wind-vehicle-bridge system, comprising:

[0013] at least one processor; and at least one memory communicatively coupled to the processor, wherein:

[0014] The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute any of the above-mentioned methods for evaluating vibration response of a wind-vehicle-bridge system with weak lateral stiffness.

[0015] (3) Beneficial effects

[0016] (1) The present invention establishes an accurate mathematical model of the straddle-type monorail vehicle (i.e., the dynamic equation of the vehicle subsystem). The model fully considers the coupling effect of wind load on the vehicle and the weak lateral stiffness track beam, the influence of wind load on the wheel-rail relationship, and the initial inclination of the track beam caused by factors such as track beam installation error and prestressing. The model also simulates and restores the changing lateral wind field of the bidirectional straddle-type monorail. In addition, considering that the track beam is generally a multiply indeterminate structure, the method of establishing a finite element physical model of the track beam in combination with the vehicle mathematical model can greatly improve the efficiency and applicability of the vibration response evaluation.

[0017] (2) The present invention fully combines the respective advantages of the two models to simulate the vibration stress conditions of the straddle-type monorail, so that the two models can be interactively updated and iterated under the initial action of external forces. The wheel-rail force time history is introduced into the track beam finite element model and a vibration response analysis is performed to obtain the wheel-rail contact point displacement time history. The wheel-rail contact point displacement time history of the track beam finite element model under the simulated wind field is introduced into the vehicle subsystem dynamic equation, and the vibration analysis is updated to obtain the various wheel-rail force time histories of the next stage. After the wheel-rail force time history is continuously output stably, the dynamic response results of the vehicle and track beam after the dual model state is finally output, thereby providing theoretical support for the wind-vehicle-bridge coupling analysis of the weak lateral stiffness track beam, and effectively evaluating the actual vibration response of the wind-vehicle-bridge system of the straddle-type monorail, so that relevant designers can take measures in advance to reduce safety risks and improve operational comfort.

[0018] (3) In addition, in order to make the vibration analysis results as consistent as possible with the vibration conditions during actual operation, the present invention also specifically performs mathematical modeling of the force balance of the vehicle subsystem dynamic equation, and specifically simulates the wind load conditions of the vehicle and track beam of the two-way straddle-type monorail at different speeds and position relationships to reflect the temporal and spatial variation relationship of the wind field. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the present invention or the prior art, the following briefly introduces the drawings required for the embodiments:

[0020] Figure 1 Flowchart of the vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to the present invention;

[0021] Figure 2 Schematic diagram of various degrees of freedom of the vehicle body space coordinate system in the present invention;

[0022] Figure 3 Schematic diagram of force balance of the vehicle body space coordinate system in the present invention;

[0023] Figure 4 Schematic diagram of the wheelset displacement of the vehicle in the present invention, wherein Figure (a) is a schematic diagram of the transverse displacement of the wheelset coordinate system, and Figure (b) is a schematic diagram of the rotational displacement of the wheelset coordinate system;

[0024] Figure 5 Schematic diagram of wind loads when the clearance between two trains running in opposite directions is S>L on the bidirectional straddle-type monorail in the present invention;

[0025] Figure 6 Schematic diagram of wind load on the bidirectional straddle-type monorail when the clearance S≤L between two trains running in opposite directions in the present invention. DETAILED DESCRIPTION

[0026] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0027] like Figure 1 As shown, the present invention provides a method for evaluating the vibration response of a wind-vehicle-bridge system with weak lateral stiffness. The working process of the method is as follows:

[0028] First, for the straddle-type monorail, establish the vehicle subsystem dynamic equation and track beam finite element model respectively, taking into account the initial inclination of the track beam. → The vehicle subsystem dynamic equation takes into account the track irregularity excitation and wind load excitation, but does not take into account the influence of the track beam displacement, to obtain the wheel-rail force time history curve F1 in the initial state of the track beam. → The wheel-rail force time history curve F1 is imported into the track beam finite element model, and a vibration response analysis is performed under wind load excitation to obtain the displacement time history curve S1 of each wheel-rail contact point in the bridge subsystem dynamic model. → The wheel-rail contact point displacement time history curve S1 is assigned as the influence value to each wheel in the vehicle subsystem dynamic equation as the initial value of this stage, and the wheel-rail force time history curve F2 of the next stage is updated through vibration analysis. → When n ≥ 1, determine whether the condition is met. δ is the preset control index. When the wheel-rail force time history When the wheel-rail force time history curve F2 is imported into the track beam finite element model and vibration response analysis is performed to obtain the wheel-rail contact point displacement time history curve S2 → the wheel-rail contact point displacement time history curve S2 is assigned as the influence value to each wheel of the vehicle subsystem dynamic equation as the initial value of this stage, and the wheel-rail force time history curve F3 of the next stage is obtained through vibration analysis → ... (loop to determine whether the conditions are met Otherwise, the wheel-rail force time history curve F n+1 Import the track beam finite element model and perform vibration response analysis to obtain the wheel-rail contact point displacement time history curve S n+1 , and n=n+1 to update the wheel-rail force time history curve Fn +2 , continue with the condition until the condition is met , the vibration analysis converges and the vehicle and track beam coupled vibration analysis results are output.

[0029] It should be pointed out that if Figure 1 As shown, at the first cycle of n = 0, based on the vehicle subsystem dynamic equation in the initial state of the track beam (taking into account the track irregularity excitation and wind load excitation, and not taking into account the track beam displacement), the wheel-rail force time history curve F1 can be obtained. The wheel-rail force time history curve F1 needs to be imported into the track beam finite element model, and a vibration response analysis is performed under wind load excitation to obtain the displacement time history curve S1 of each wheel-rail contact point in the bridge subsystem dynamic model. The wheel-rail contact point displacement time history curve S1 is then assigned as an influence value to each wheel of the vehicle subsystem dynamic equation as the initial value of this stage, and the wheel-rail force time history curve F2 of the next stage is obtained through vibration analysis. When n≥1, The judgment procedure of the condition, and if the condition is not met, the interactive update iteration between the two models will continue until the condition is met. The vibration analysis is determined to have converged and the loop is terminated. Based on the current vehicle subsystem dynamic equations and the track beam finite element model, the system outputs the coupled vehicle and track beam vibration analysis results, obtaining accurate vibration data for the straddle-type monorail system. Furthermore, if the output vibration analysis results do not meet expectations, designers can implement additional vibration reduction measures to mitigate the vibration.

[0030] In another embodiment, the control index δ can be set to different values ​​according to the accuracy requirements, such as thresholds of 3%, 5%, etc. The wheel-rail force time history curve F of all wheels on the straddle-type monorail is n Corresponding to the wheel force in Table 2 below, and the wheel-rail contact point displacement time history curve S n Wheel-rail force time history curve F n The action points in the track beam finite element model correspond to each other. It is also worth mentioning that because the wheel-rail force history F n and wheel-rail contact point displacement time history S n The forms of expression may vary due to the consideration of the actual situation of the project, the constraints of the track beams and the vehicle formation, and there are many other factors that may need to be considered according to the actual situation. Therefore, the present invention does not use a fixed mathematical model framework to reflect their respective forms, thereby causing unnecessary limitations.

[0031] like Figure 2-6 As shown, in order to make the vibration analysis results as consistent as possible with the vibration conditions during actual operation, the present invention also specifically performs mathematical modeling of the force balance of the vehicle subsystem dynamic equation, and specifically simulates the wind loads on the vehicle and track beam of the bidirectional straddle-type monorail at different speeds and positions to reflect the temporal and spatial variation relationship of the wind field.

[0032] In another embodiment, Figure 2-4 As shown, the present invention establishes the following vehicle subsystem dynamic equation:

[0033] Through finite element calculation (prestressed tensioning, storage beam) and field testing, the maximum possible inclination angle α0 of the track beam is determined. Therefore, when the vehicle runs on this beam section, it will generate a component of force parallel to the bridge deck of Mgsinα0≈Mgα0 and a component of force perpendicular to the track beam of Mgcosα0.

[0034] like Figure 2 As shown in Figure 1, according to the characteristics of straddle-type monorail vehicles, the vehicle body and bogie both have five degrees of freedom: yaw, sink, roll, head shake, and pitch. One car has two bogies, so each car has 10 degrees of freedom, as shown in Table 1.

[0035] Table 1 Vehicle degree of freedom settings

[0036] structure sideways Ups and downs Roll Shake your head nod body <![CDATA[y c ]]> <![CDATA[z c ]]> <![CDATA[θ c ]]> <![CDATA[φ c ]]> <![CDATA[ψ c ]]> Bogie (i=1, 2) <![CDATA[y ti ]]> <![CDATA[z ti ]]> <![CDATA[θ ti ]]> <![CDATA[φ ti ]]> <![CDATA[ψ ti ]]>

[0037] Vibration characteristics of running tires

[0038]

[0039] Where K is the tire radial stiffness, C is the tire radial damping, X and are the radial relative displacement and relative velocity of the wheel and rail, respectively.

[0040] The longitudinal slip force during tire movement is Where Δδ is the slip displacement, v c is the vehicle speed, r c is the radius of the running wheel.

[0041] Tire cornering force F y =K rβ β, aligning torque M β =-K′ rβ β, where β is the slip angle, K rβ , K′ rβ They are the tire's cornering and righting stiffness respectively.

[0042] The dynamic equation of the vehicle subsystem mainly needs to consider establishing the dynamic balance equation of the vehicle, and the straddle-type monorail coupling system mainly includes the following forces: ① vehicle wheel force; ② vehicle frame force; ③ force caused by the initial inclination of the track beam; ④ wind load.

[0043] like Figure 3-4 As shown, the definitions of the parameters in the dynamic balance equation are as follows:

[0044] K rr , K gr , K sr are the radial stiffness of the running wheel, guide wheel and stabilizing wheel respectively;

[0045] K 2x , K 2y , K 2z are the stiffness of the front and rear bogies in the x, y, and z axes of the air suspension, respectively;

[0046] C 2x 、C 2y , C 2z are the damping of the front and rear bogies in the x, y, and z axes of the air suspension, respectively;

[0047] β is the sideslip angle, K rβ , K′ rβ They are the tire's cornering and righting stiffness respectively;

[0048] C rr 、C gr 、C sr They are the radial damping of the running wheel, guide wheel and stabilizing wheel respectively;

[0049] L c is the distance between bogies in the same carriage;

[0050] L t 、L g are the distances from the running wheels and stabilizing wheels of the same bogie to the center of gravity of the bogie;

[0051] h1 is the distance from the center of gravity of the bogie to the center of gravity of the air suspension; h3 is the distance from the center of gravity of the air suspension to the center of gravity of the vehicle body;

[0052] h t h is the distance from the center of gravity of the bogie to the top surface of the beam; r is the distance from the center of gravity of the bogie to the center of gravity of the running wheels;

[0053] h L h is the distance between the top surface of the track beam and the center of gravity of the track beam; g h is the distance between the bogie's center of gravity and the guide wheel; gg h is the distance between the center of gravity of the track beam and the guide wheel; s h is the distance between the center of gravity of the bogie and the running wheels; ss is the distance between the center of gravity of the track beam and the running wheels; b is the distance of the running wheels in the transverse direction of the bridge; b1 is the distance from the edge of the bogie in the transverse direction of the bridge to the axial direction of the track beam; b2 is 1 / 2 of the width of the track beam; b3 is the distance between the air suspensions in the transverse direction of the bridge;

[0054] ① The forces acting on the vehicle wheels are shown in Table 2 below

[0055] Table 2 Vehicle wheel forces

[0056]

[0057] (j=1, 2 represents the front and rear positions of the tires according to the driving direction, R and L represent the right and left tires respectively)

[0058] It can be seen that the wheel force of the running wheel is:

[0059]

[0060]

[0061] The wheel force on the guide wheel is:

[0062]

[0063] The wheel force of the stabilizing wheel is:

[0064]

[0065] ② The vehicle frame forces are shown in Table 3

[0066] Table 3 Vehicle frame forces

[0067]

[0068] It can be seen that the force acting on the vehicle frame is:

[0069] F xtR11 =-K 2x (h3φ c -b3ψ c +h1φ t1 +b3ψ t1 )

[0070] F xtL1 =-K 2x (h3φ c +b3ψ c +h1φ t1 -b3ψ t1 )

[0071] F xtR2 =-K 2x (h3φ c -b3ψ c +h1φ t2 +b3ψ t2 )

[0072] F xtL2 =-K 2x (h3φ c +b3ψ c +h1φ t2 -b3ψ t2 )

[0073]

[0074] According to the D'Alembert principle, the vehicle dynamic balance equation can be established through the balance equations of the front and rear bogies and the vehicle body, and used as Figure 1The vehicle subsystem dynamic equations in the vehicle subsystem include the bogie motion equations and the car body motion equations. The bogie motion equations specifically include the bogie transverse motion balance equation, the bogie heave motion balance equation, the bogie roll motion balance equation, the bogie nodding motion balance equation and the bogie head shaking motion balance equation. The car body motion equations specifically include the car body transverse motion balance equation, the car body heave motion balance equation, the car body roll motion balance equation, the car body nodding motion balance equation and the car body head shaking motion balance equation.

[0075] (1) Bogie motion equation

[0076] A) Bogie transverse motion equilibrium equation: bogie transverse inertia force + frame system force + tilt additional force

[0077] For the front bogie (i=1), the bogie inertia force is: Additional force on the bogie in the transverse direction of the bridge caused by the bridge tilt - M t1 gsinα0≈-M t1 gα0;

[0078] Wheel force: F1(y t1 )=F yrR11 +F yrL11 +F yrR12 +F yrL12 +F ygR11 +F ygL11 +F ygR12 +F ygL12 +F ysR11 +F ysL11

[0079] Frame force: F2(y t1 )=F ytR1 +F ytL1

[0080] The equilibrium equation of motion is Right now (To avoid redundancy, similar equations in the following text will omit this substitution process)

[0081] Simplifying, we get:

[0082] in, C1=2C 2y ;D1=2h3C 2y ; E1=2L c C 2y ; F1 = -4K gr -2K sr -2K2y ; G1 = -4h g K gr -2K sr h s +2K 2y h1; H1 = -4K rβ ; I1=2K 2y ; J1 = 2K 2y h3; K1 = 2K 2y L c .

[0083] For the rear bogie (i=2), the bogie inertia force is: Additional force on the bogie in the transverse direction of the bridge caused by the bridge tilt - M t2 gsinα0≈-M t2 gα0;

[0084] Wheel force: F1(y t2 )=F yrR21 +F yrL21 +F yrR22 +F yrL22 +F ygR21 +F ygL21 +F ygR22 +F ygL22 +FysR 21 +Fys L21

[0085] Frame force: F2(y t2 )=F ytR2 +F ytL2

[0086] The equilibrium equation of motion is

[0087] Simplifying, we get:

[0088] in, C6=2C 2y ;D6=2h3C 2y ; E6 = -2L c C 2y ; F6 = -4K gr -2K sr -2K 2y ; G6 = -4h g K gr -2K sr h s +2K 2y h1;H6=-4K rβ ; I6=2K 2y ; J6 = 2K2y h3; K6 = -2K 2y L c .

[0089] B) Bogie heaving and floating equilibrium equation: bogie heaving and floating inertia force + frame system force + tilt additional force

[0090] For the front bogie (i=1), the bogie inertia force is: Additional force in the bogie z direction due to bridge tilt - M t1 gcosα0;

[0091] Wheel force: F1(z t1 )=F zrR11 +F zrL11 +F zrR12 +F zrL12

[0092] Frame force: F2(z t11 )=F ztR1 +F ztL1

[0093] The equilibrium equation of motion is

[0094] Simplifying, we get:

[0095] Where A2 = -4C rr -2C 2z ; B2=2C 2z ; C2=-2L c C 2z ; D2 = -4K rr -2K 2z ; E2=2K 2z ; F2 = -2L c K 2z .

[0096] For the rear bogie (i=2), the bogie inertia force is: Additional force in the bogie z direction due to bridge tilt - M t2 gcosα0;

[0097] Wheel force: F1(z t2 )=F zrR21 +F zrL21 +F zrR22 +F zrL22

[0098] Frame force: F2(z t2 )=F ztR2 +F ztL2

[0099] The equilibrium equation of motion is

[0100] Simplifying, we get:

[0101] Where A7=-4C rr -2C 2z ; B7=2C 2z ; C7=2L c C 2z ;D7=-4K rr -2K 2z ; E7 = 2K 2z ;F7=2L c K 2z .

[0102] C) Bogie rolling motion equilibrium equation: bogie rolling inertia force + frame system force + tilt additional force

[0103] For the front bogie (i=1), the bogie rolling inertia force is: Additional rolling force on the bogie caused by bridge tilt -M t1 gα0h t ;

[0104] Wheel force M1(z t1 )=(F yrR11 +F yrL11 +F yrR1 2+F yrL12 )h t +(F ygR11 +F ygL11 +F ygR12 +F ygL12 )h g +(F ysR11 +F ysL11 )h s +(-F zrR11 -F zrL11 +F zrR12 +F zrL12 )b;

[0105] Frame force M2(z t1 )=(F ztL1 -F ztR1 )b3-(F ytR1 +F ytL1 )h1

[0106] Depend on

[0107] Available

[0108] in C3=-2h1C 2y ; E3=-2h1L c C 2y ; F3 = -4h g K gr -2h s K sr +2h1K 2y ; H3=-4h t K ra ; I3=-2h1K 2y ; K3=-2h1L c K 2y .

[0109] For the rear bogie (i=2), the bogie rolling inertia force is: Additional rolling force on the bogie caused by bridge tilt -M t2 gα0h t ;

[0110] Wheel force M1(z t2 )=(F yrR21 +F yrL21 +F yrR22 +F yrL22 )h t +(F ygR21 +F ygL21 +F ygR22 +F ygL22 )h g +(F ysR21 +F ysL21 )h s +(-F zrR21 -F zrL21 +F zrR22 +F zrL22 )b;

[0111] Frame force M2(z t2 )=(F ztL2 -F ztR2 )b3-(F ytR2 +F ytL2 )h1

[0112] From the dynamic balance equation

[0113] Available

[0114] in C8=-2h1C 2y ; E8=2h1L c C 2y ; F8 = -4h g K gr -2h s K sr +2h1K 2y ; H8=-4h t K ra ; I8=-2h1K 2y ; K8=2h1L c K 2y .

[0115] D) Bogie nodding motion equilibrium equation: bogie nodding inertia force + frame system force

[0116] For the front bogie (i=1), the bogie nodding inertia force is:

[0117] Wheel force M1(y t1 )=(-F zrR11 -F zrL11 +F zrR12 +F zrL12 )L t -(F xrR11 +F xrL11 +F xrR12 +F xrL12 )h t ;

[0118] Frame force M2(y t1 )=-(F xtR1 +F xtL1 )h1

[0119] From the dynamic balance equation

[0120] Available

[0121] in C4=-2h1h3K 2x .

[0122] For the rear bogie (i=2), the bogie nodding inertia force is:

[0123] Wheel force M1(y t2 )=(-F zrR21 -FzrL21 +F zrR22 +F zrL22 )L t -(F xrR21 +F xrL21 +F xrR22 +F xrL22 )h t ;

[0124] Frame force M2(y t2 )=-(F xtR2 +F xtL2 )h1

[0125] From the dynamic balance equation

[0126] Available

[0127] in C9=-2h1h3K 2x .

[0128] E) Bogie sway motion equilibrium equation: bogie sway inertia force + frame system force

[0129] For the front bogie (i=1), the bogie nodding inertia force is:

[0130] Wheel force M1(z t1 )=(F ygR11 +F ygL11 -F ygR12 -F ygL12 )L g +(F yrR11 +F yrL11 -F yrR12 -F yrL12 )L t +(F xrR11 +F xrL11 -F xrR12 -F xrL12 )b+(M zrR11 +M zrL11 +M zrR12 +M zrL12 );

[0131] Frame force M2(z t1 )=(F xtR1 -F xtL1 )b3

[0132] From the dynamic balance equation

[0133] Available

[0134]

[0135] For the front bogie (i=2), the bogie nodding inertia force is:

[0136] Wheel force M1(z t2 )=(F ygR21 +F ygL21 -F ygR22 -F ygL22 )L g +(F yrR21 +F yrL21 -F yrR22 -F yrL22 )L t +(F xrR21 +F xrL21 -F xrR22 -F xrL22 )b+(M zrR21 +M zrL21 +M zrR22 +M zrL22 );

[0137] Frame force M2(z t2 )=(F xtR2 -F xtL2 )b3

[0138] From the dynamic balance equation

[0139] Available

[0140]

[0141] ② Vehicle motion equation

[0142] A) Transverse motion equilibrium equation of the vehicle body: Transverse inertia force of the vehicle body + force of the frame system + additional tilt force + wind load

[0143] Vehicle inertia force: Additional force on the bogie in the transverse direction of the bridge caused by the bridge tilt - M c gsinα0≈-M c gα0;

[0144] Transverse static wind resistance:

[0145] Frame force: F2(y c )=-(F ytR1 +F ytL1 +F ytR2 +FytL2 )

[0146] The equilibrium equation of motion is

[0147] Simplified

[0148] Among them A 11 =4C 2y ; B 11 =-4C 2y ; C 11 =-4C 2y ;D 11 =-4h3C 2y ;E 11 =4K 2y ; F 11 =-4K 2y ; G 11 =-4K 2y ;H 11 =-4h3K 2y .

[0149] B) Equilibrium equation for vehicle body sinking and floating motion: vehicle body inertia force + frame system force + tilt additional force + wind load lift

[0150] Vehicle inertia force: Additional force on the bogie in the transverse direction of the bridge caused by the bridge tilt - M c gcosα0;

[0151] Transverse static wind lift:

[0152] Frame force: F2(z c )=-(F ztR1 +F ztL1 +F ztR2 +F ztL2 )

[0153] The equilibrium equation of motion is

[0154] Simplified

[0155] Among them A 12 =2C 2z ; B 12 =-2b3C 2z ; C 12 =2C 2z ;D 12 =-2b3C 2z ;E 12 =-4C 2z ; F12 =2K 2z ; G 12 =-2b3K 2z ;H 12 =2K 2z ;I 12 =-2b3K 2z ; J 12 =-4K 2z .

[0156] C) Vehicle roll motion equilibrium equation: vehicle inertia force + frame system force + tilt additional force + wind load

[0157] Vehicle inertia force: Additional rolling force on the bogie caused by bridge tilt -M c gα0h3;

[0158] Transverse static wind moment:

[0159] Frame force: M2(z c )=(F ztR1 +F ztR2 -F ztL1 -F ztL2 )b3+(F ytR1 +F ytL1 +F ytR1 +F ytL1 )h3

[0160] The equilibrium equation of motion is

[0161] have to

[0162] Among them A 13 =-4C 2y ; B 13 =4h1C 2y ; C 13 =4C 2y ; E 13 =-4K 2y ; F 13 =4h1K 2y ; G 13 =4K 2y ;

[0163] D) The equilibrium equation of the vehicle's nodding motion: vehicle inertia force + frame system force

[0164] Vehicle inertia force:

[0165] Frame force: M2(y c )=(F ztR1 +F ztL1 -F ztR2 -F ztL2 )L c +(F xtR1 +F xtL1 +F xtR1 +F xtL1 )h3

[0166] The equilibrium equation of motion is

[0167] have to

[0168] Among them A 14 =-2L c C 2z ; B 14 =2L c C 2z ; D 14 =-2L c K 2z ;E 14 =-2h1h3K 2x ; F 14 =2L c K 2z ; G 14 =-2h1h3K 2x ;

[0169] E) Balance equation of vehicle body shaking motion: vehicle body inertia force + frame system force

[0170] Vehicle inertia force:

[0171] Frame force: M2(z c )=(F xtL1 +F xtL2 -F xtR1 -F xtR2 )b3+(F ytR2 +F ytL2 -F ytR1 -F ytL1 )L c

[0172] The equilibrium equation of motion is

[0173] have to

[0174] Among them A15 =-4L c C 2y ; B 15 =4b3K 2x ; C 15 =-4L c K 2y -4b3K 2x .

[0175] Based on the various equilibrium equations of the straddle-type monorail vehicle, the dynamic equations of the straddle-type monorail vehicle subsystem are established. The wheel-rail contact relationship has taken into account the influence of the track inclination angle α0. The dynamic equations of the vehicle subsystem are obtained from the motion equations of the bogies and the vehicle body:

[0176]

[0177] Among them, h t is the distance from the center of gravity of the bogie to the top surface of the beam, h3 is the distance from the center of gravity of the air suspension to the center of gravity of the car body, α0 is the track inclination angle, g is the acceleration of gravity, and The wind loads are the lateral static wind resistance, lateral static wind lift and lateral static wind moment, M t1 、M t2 、M c are the masses of the front bogie, rear bogie and car body respectively, J t1x 、J t1y 、J t1z , are respectively the rolling inertia, nodding inertia and yaw inertia of the front bogie, J t2x 、J t2y 、J t2z They are respectively the rolling inertia, nodding inertia and yaw inertia of the rear bogie, J cx 、J cy 、J cz They are the rolling inertia, nodding inertia and yaw inertia of the vehicle body. * ~K * are the simplified physical parameters of the above bogie motion equations and vehicle body motion equations; the angles of each degree of freedom are shown in Table 1.

[0178] Establishment of the track beam finite element model: For complex structures such as double-track bridges, the traditional method of establishing vibration differential equations is difficult to simulate the actual situation of the bridge structure. Therefore, the track beam finite element model preferentially uses commercial software for modal analysis to establish the bridge subsystem dynamic model. The bridge subsystem dynamic model can perform vibration response analysis by importing the wheel-rail force time history to obtain the displacement time history of the wheel-rail contact point on the track beam.

[0179] The wind load in the wind field serves as the excitation input for the dynamic equations of the vehicle subsystem and the finite element model of the track beam. The magnitude and input method of the wind load are key technical points for obtaining the wind-vehicle-bridge coupled vibration response. Existing research results have failed to systematically propose a method for obtaining and inputting wind loads for bidirectional straddle-type monorail, and therefore cannot provide a reference for the construction of actual projects.

[0180] See also Figure 1 and Figure 5-6 It can be seen that in order to perform a dynamic spatiotemporal simulation of the wind load on a bidirectional straddle-type monorail (i.e., a vehicle running on two lines) in actual operation, the method for determining the wind load on the vehicle and track beam under different speed and position relationships in the present invention is as follows:

[0181] 1) Detect on-site wind conditions → Use CFD to build a fluid model to simulate wind conditions → Conduct wind tunnel tests on a scaled-down axle model (with pressure gauges on the vehicle cross-section and a six-component balance under each carriage) to determine the wind loads on the train and track beams under various operating conditions (single-track with trains on it, double-track with trains passing) when the train is stationary → Verify the accuracy of the CFD simulation using model test data and modify the basic model parameters → Determine the wind loads on the train and track beams under various operating conditions using the CFD model.

[0182] Working condition a: see Figure 5 As shown in the figure, for double-track vehicles, the critical interference distance L between vehicles is first determined. When the clearance S>L between two trains running in opposite directions, they can be equivalent to one-way trains running on both sides without interfering with each other. The lateral static wind resistance acting on the train is lateral static wind lift and transverse static wind moment The specific value is

[0183]

[0184] Where ρ is the air density; A is the windward surface area of ​​the vehicle body; The relative wind speed acting on the vehicle body, is the average wind acting perpendicular to the track beam, v is the train speed; are the vehicle body drag coefficient, lift coefficient and torsional moment coefficient, H v is the distance between the center of mass of the vehicle body and the top surface of the track beam, and Used to apply to the vehicle subsystem dynamic equations.

[0185] Wind load acting on the centroid of the windward surface of the track beam for

[0186]

[0187] Among them, C gz is the resistance coefficient of the track beam, For application to track beam finite element models.

[0188] Working condition b: see Figure 6 As shown in the figure, when the clear distance between two trains running in opposite directions is S≤L, the wind load of the opposite vehicle will be interfered with during the double-train operation. Because the time is short, the interference coefficient is uniformly set to δ x , δ x Including δ zx , δ sx , δ Mx and δ gx , δ x is a coefficient related to the position of the double-track vehicle, determined by CFD calculation. At this time, the lateral static wind resistance acting on the train is lateral static wind lift and transverse static wind moment The value is

[0189]

[0190] Wind load acting on the centroid of the windward surface of the track beam for

[0191]

[0192] From the analysis and research of the above two cases, it can be seen that in addition to the positional relationship between the critical interference distance L between vehicles and the clear distance S between two-way trains, the wind load in the spatiotemporal wind field is also related to the driving speed of the two vehicles. Based on this relationship, a load history of the wind load can be established, and the wind load can be added to the vehicle subsystem dynamic equation and the track beam finite element model according to the time history.

[0193] Wind load input: The specific method for establishing the load history of wind loads on vehicles and track beams under different speeds and positions is as follows:

[0194] (1) If the initial clearance between two-way trains is S≤L, the mutual interference distance between the two trains is S+L c +L, the interference time is L c is the vehicle length, V1 and V2 are the two-way vehicle speeds, so

[0195] ① When the working condition b is met

[0196] Vehicle wind load Track beam wind load

[0197] ③ When the working condition a is satisfied

[0198] Vehicle wind load Track beam wind load

[0199] (2) If the initial clearance distance between two-way running trains S>L, the initial non-interference and mutual interference distances of the two trains are (SL) and (L c +2L), the time is The vehicle and track load time series are as follows:

[0200] ① and When the working condition a is satisfied

[0201] Vehicle wind load Track beam wind load

[0202] ② When the working condition b is met

[0203] Vehicle wind load Track beam wind load

[0204] In the examples provided above, each step in the vibration response evaluation method of the present invention can also be implemented in the form of a software program, which can be stored in a computer-readable storage medium or system. The above-mentioned software functional unit is stored in a storage medium and includes a number of instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) or a processor to execute some of the steps of the method described in each example of the present invention. The aforementioned storage medium includes: a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., various media that can store program code.

[0205] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for evaluating the vibration response of a wind-vehicle-bridge system with weak lateral stiffness, characterized in that: The following steps are involved: For straddle-type monorail, establish a vehicle subsystem dynamic equation and a track beam finite element model that considers the initial inclination of the track beam. The vehicle subsystem dynamic equation takes into account the track irregularity excitation and wind load excitation, but does not take into account the influence of the track beam displacement, to obtain the wheel-rail force time history curve F1 in the initial state of the track beam. The wheel-rail force time history curve F1 is imported into the track beam finite element model, and a vibration response analysis is performed under wind load excitation to obtain the displacement time history curve S1 of each wheel-rail contact point in the bridge subsystem dynamic model. The wheel-rail contact point displacement time history curve S1 is assigned as an influence value to each wheel in the vehicle subsystem dynamic equation as the initial value of the current stage, and the wheel-rail force time history curve F2 of the next stage is updated through vibration analysis. When n≥1, determine whether the condition is met. δ is the preset control index. When the wheel-rail force time history When the wheel-rail force time history curve F2 is continuously imported into the track beam finite element model and vibration response analysis is performed to obtain the wheel-rail contact point displacement time history curve S2 → the wheel-rail contact point displacement time history curve S2 is assigned as the influence value to each wheel of the vehicle subsystem dynamic equation as the initial value of the current stage, and the wheel-rail force time history curve F3 of the next stage is updated through vibration analysis → until the condition is met When , the vibration analysis converges and the vehicle and track beam coupled vibration analysis results are output; Based on the various equilibrium equations of the straddle-type monorail vehicle, the dynamic equations of the straddle-type monorail vehicle subsystem are established. The wheel-rail contact relationship has taken into account the influence of the track inclination angle α0. The dynamic equations of the vehicle subsystem are obtained from the various bogie motion equations and the vehicle body motion equations as follows: Among them, h t is the distance from the center of gravity of the bogie to the top surface of the beam, h3 is the distance from the center of gravity of the air suspension to the center of gravity of the vehicle body, g is the acceleration due to gravity, and The wind loads are the lateral static wind resistance, lateral static wind lift and lateral static wind moment, M t1 、M t2 、M c are the masses of the front bogie, rear bogie and car body respectively, J t1x 、J t1y 、J t1z , are respectively the rolling inertia, nodding inertia and yaw inertia of the front bogie, J t2x 、J t2y 、J t2z They are respectively the rolling inertia, nodding inertia and yaw inertia of the rear bogie, J cx 、J cy 、J cz are the rolling inertia, nodding inertia, and yawing inertia of the vehicle body, respectively; A*~K* are the simplified physical parameters of the motion equations of each bogie and the vehicle body; y c 、z c ,θ c 、φ c , ψ c are the yaw, sink, roll, head shake and nod angles of the vehicle body; ti 、z ti ,θ ti 、φ ti , ψ ti are the yaw, heave, roll, pitch and nod angles of the bogie, and the subscript i represents the front and rear bogies, respectively.

2. The vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to claim 1, characterized in that: The control index δ is 3% or 5%.

3. The vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to claim 1, characterized in that: Wheel-rail force time history curve F of all wheels on straddle-type monorail n Corresponding to the wheel forces in the following table Where j = 1, 2 represents the front and rear positions of the tire in the driving direction, R and L represent the right and left tires respectively, and the wheel-rail contact point displacement time history curve S n Wheel-rail force time history curve F n The corresponding points of action in the finite element model of the track beam.

4. The vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to claim 1, characterized in that: Commercial software is used in the track beam finite element model to perform modal analysis to establish a bridge subsystem dynamics model. The bridge subsystem dynamics model can perform vibration response analysis by importing the wheel-rail force time history to obtain the displacement time history of the wheel-rail contact point on the track beam.

5. The vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to claim 1, characterized in that: The wind load excitation for the bidirectional straddle-type monorail system is specifically the wind load on the vehicle and track beam under different speeds and positions. The determination method is as follows: Detect on-site wind conditions → Use CFD to build a fluid model to simulate wind conditions → Conduct wind tunnel tests on scaled axle models to determine wind loads on the train and track beams under various operating conditions when the train is stationary → Verify the accuracy of the CFD simulation using model test data and correct basic model parameters → Determine wind loads on the train and track beams under various operating conditions using CFD model calculations.

6. The vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to claim 5, characterized in that: The operating conditions when the train is stationary include: Working condition a: Determine the critical distance L between vehicles. When the clearance S between two trains running in opposite directions is greater than L, they can be equivalent to one-way trains running on both sides without interfering with each other. The lateral static wind resistance acting on the train is lateral static wind lift and transverse static wind moment The specific value is Where ρ is the air density, A is the windward surface area of ​​the vehicle body, The relative wind speed acting on the vehicle body, is the average wind acting perpendicular to the track beam, v is the train speed; are the vehicle body drag coefficient, lift coefficient and torsional moment coefficient, H v is the distance between the center of mass of the vehicle body and the top surface of the track beam, and Used to apply to the vehicle subsystem dynamic equations, Wind load acting on the centroid of the windward surface of the track beam for Among them, C gz is the resistance coefficient of the track beam, Used to apply to the track beam finite element model, Working condition b: When the clearance between two trains running in opposite directions is S≤L, the wind load on the opposite vehicle will be interfered with during the double-train operation. The interference coefficient is uniformly set as δ x , δ x Including δ zx , δ sx , δ Mx and δ gx , δ x is a coefficient related to the position of the double-track vehicle, determined by CFD calculation. At this time, the lateral static wind resistance acting on the train is lateral static wind lift and transverse static wind moment The value is Wind load acting on the centroid of the windward surface of the track beam for 7. The vibration response evaluation method of a wind-vehicle-bridge system with weak lateral stiffness according to claim 6, characterized in that: Input of wind load excitation: The specific method for establishing the load history of wind loads on vehicles and track beams under different speed and position relationships is as follows: (1) If the initial clearance between two-way trains is S≤L, the mutual interference distance between the two trains is S+L c +L, the interference time is L c is the vehicle length, V1 and V2 are the two-way vehicle speeds, so ① When , the working condition b is met; ② When , working condition a is met; (2) If the initial clearance distance between two-way running trains S>L, the initial non-interference and mutual interference distances of the two trains are (SL) and (L c +2L), the time is The vehicle and track load time series are as follows: ① and When , working condition a is met; ② When , working condition b is met.

8. A vibration response evaluation system for a weak lateral stiffness wind-vehicle-bridge system, characterized in that: include: at least one processor; and at least one memory communicatively connected to the processor, wherein: The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the vibration response evaluation method of a weak lateral stiffness wind-vehicle-bridge system according to any one of claims 1 to 7.

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