Weak transverse stiffness wind-vehicle-bridge system vibration response evaluation method and system

Abstract

The invention discloses a vibration response evaluation method and system for a weak transverse stiffness wind-vehicle-bridge system. According to the method, the coupling effect of a wind load of a spatio-temporal variation wind field on a vehicle and a weak transverse stiffness track beam, the influence of the wind load on a wheel-rail relation, and track beam initial inclination and various acting forces caused by factors such as track beam installation errors and prestress tension are considered; a dual-model system of a vehicle subsystem dynamic equation and a track beam finite element model is established, a dynamic response result after vibration analysis convergence is obtained through interaction of the dual models, theoretical support is provided for wind-vehicle-bridge coupling analysis of the weak transverse stiffness track beam, and the dynamic response result is obtained. Therefore, the vibration response condition of the wind-vehicle-bridge system of the straddle type monorail is effectively evaluated, so that the vibration analysis result is consistent with the real operation condition, and designers can conveniently take vibration reduction measures in advance to reduce the safety risk and improve the operation 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 weak lateral stiffness wind-vehicle-bridge system. 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 track beam of the straddle-type monorail is 690-850mm, which is significantly reduced compared to the standard railway gauge of 1435mm, with 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), which is 2-5 times higher than the live load ratio of railways and highways. The vehicle-track beam is supported by rubber wheels, 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, and the dynamic stability is weak.

[0004] At present, many scholars have conducted extensive research on the vehicle-bridge coupled vibration of steel wheel and rail trains such as high-speed rail and light rail. Because the track beam of straddle-type monorail transportation has its own particularity that is different from that of general trains, its narrow and high beam has low horizontal stiffness, and the roll effect of the car body is much greater than that of steel wheel rail transportation. The effect on the vehicle and lateral wind load is obvious, and the vibration of the beam body will in turn affect the vibration of the vehicle, thereby affecting the comfort and safety of driving. Wind load has a great impact on the wheel-rail relationship. The existing technology considers the impact of wind load by adding wind load to the vehicle, but fails to fully consider the impact of wind load on the beam body, resulting in a great discrepancy between the calculation results and the actual operation conditions.

[0005] On the other hand, due to the structural characteristics of the straddle-type monorail, the track beam installation accuracy is very high, and any slight error may cause the track beam to tilt; the structural characteristics of the track beam may also cause it to tilt (the track beam of the straddle-type monorail adopts a prestressed concrete structure, and the design of this structure needs to consider the effects of shear deformation and torsional deformation. In actual use, these structural characteristics may cause the track beam to tilt to a certain extent). Previous vehicle-bridge coupled vibration analysis did not consider the initial tilt angle of the track beam, resulting in analysis results that are very different from the actual situation.

[0006] Therefore, it is urgent to design a vibration response evaluation method for the wind-vehicle-bridge system with weak lateral stiffness for the straddle-type monorail structure, 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 operating 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, which provides 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 is convenient for designers to take vibration reduction measures in advance to reduce safety risks and improve operational comfort.

[0009] (II) Technical solution

[0010] The present invention discloses a method for evaluating vibration response of a weak lateral stiffness wind-vehicle-bridge system, 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 and does not take into account the influence of the track beam displacement, and obtains the wheel-rail force time history curve F1 in the initial state of the track beam → Import the wheel-rail force time history curve F1 into the track beam finite element model, and perform vibration response analysis under wind load excitation to obtain the displacement time history curve S1 of each wheel-rail contact point in the bridge subsystem dynamic model → Assign the wheel-rail contact point displacement time history curve S1 as an influence value to each wheel of the vehicle subsystem dynamic equation as the initial value of this stage, and update the wheel-rail force time history curve F2 of the next stage 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 curve F2 is continuously 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 curve S2 → the wheel-rail contact point displacement time history curve S2 is 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 F3 of the next stage is obtained through vibration analysis update → until the condition is met , the vibration analysis converges and the coupled vibration analysis results of the vehicle and track beam 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 in communication with the processor, wherein:

[0014] The memory stores program instructions executable 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] (III) Beneficial effects

[0016] (1) The present invention establishes an accurate vehicle mathematical model of a straddle-type monorail (i.e., the dynamic equation of the vehicle subsystem), which 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, and 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 hyperstatic structure, the method of establishing a finite element physical model of the track beam combined with a vehicle mathematical model can greatly improve the efficiency and applicability of vibration response evaluation.

[0017] (2) The present invention fully combines the 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 force. The wheel-rail force time history is introduced into the track beam finite element model and the 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 wheel-rail force time history of the next stage is obtained through vibration analysis update. 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 bidirectional straddle-type monorail at different speeds and position relationships, so as 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 in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments:

[0020] Figure 1 It is a flow chart of the vibration response evaluation method of the weak lateral stiffness wind-vehicle-bridge system of 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 It is a schematic diagram of the force balance of the vehicle body space coordinate system in the present invention;

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

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

[0025] Figure 6 It is a schematic diagram of wind load when the clear distance between two trains running in opposite directions of the bidirectional straddle-type monorail in the present invention is S≤L. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. 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 making creative work 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 weak lateral stiffness wind-vehicle-bridge system, and the working process of the method is as follows:

[0028] First, for the straddle-type monorail, the vehicle subsystem dynamic equation and the track beam finite element model considering the initial inclination of the track beam are established respectively. The vehicle subsystem dynamic equation takes into account the track irregularity excitation and wind load excitation and does not take into account the influence of the track beam displacement, and obtains 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 the consideration of 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 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, it is judged whether the condition is met. δ is the preset control index. 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 obtained through vibration analysis update → ... (loop to determine whether the condition is met If 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 coupled vibration analysis results of the vehicle and track beam are output.

[0029] It should be pointed out that if Figure 1 As shown in the figure, at the first cycle of n = 0, based on the dynamic equation of the vehicle subsystem in the initial state of the track beam (taking into account the track unevenness 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 update, and when n≥1, The judgment procedure of the condition continues to cycle through the interactive update iterations between the two models when the condition is not met until the condition is met. The vibration analysis is judged to have converged and the cycle is stopped when the current vehicle subsystem dynamic equation and track beam finite element model are used to output the vehicle and track beam coupled vibration analysis results, and obtain accurate vibration data of the straddle-type monorail. In addition, if the output vibration analysis results do not meet expectations, designers can take other vibration reduction measures to reduce vibration.

[0030] In another embodiment, the control index δ can be set to different values ​​according to the accuracy requirements, such as 3%, 5% and other thresholds. The wheel-rail force time history curve F of all wheels on the straddle-type monorail 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 It is also worth mentioning that because the wheel-rail force time 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 may be many other factors that 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 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.

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

[0033] Through finite element calculation (prestressing, 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, according to the vehicle characteristics of the straddle-type monorail, the vehicle body and bogie both contain five degrees of freedom: yaw, float, roll, shake and nod. One car has two bogies, so each car has 10 degrees of freedom, as shown in Table 1 below.

[0035] Table 1 Vehicle degree of freedom settings

[0036] structure Swing 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 of the tire during running 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, self-aligning torque M β =-K′ rβ β, where β is the slip angle, K rβ , K′ rβ They are the tire's cornering and self-centering 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 They 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 slip angle, K rβ , K′ rβ They are the tire's cornering and self-centering 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 wheel and stabilizing wheel of the same bogie to the center of gravity of the bogie respectively;

[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 center of gravity of the bogie and the guide wheel; gg h is the distance from the center of gravity of the track beam to 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 wheel; b is the distance of the running wheel 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 suspension in the transverse direction of the bridge;

[0054] ① The wheel forces of the vehicle are shown in Table 2 below

[0055] Table 2 Vehicle wheel forces

[0056]

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

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

[0059]

[0060]

[0061] The wheel force of 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 it can be 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 and float 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 and float 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 inclination of the bridge - 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 inclination of the bridge - 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 +FyS 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 motion 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 balance 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 shaking motion balance equation: bogie shaking 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) Equilibrium equation of vehicle body transverse motion: inertial force of vehicle body transverse motion + force of 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 inclination of the bridge - 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) The equilibrium equation of 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 inclination of the bridge - M c gcosα0;

[0151] Lateral 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) The vehicle body rolling motion equilibrium equation: vehicle body 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 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 equation of the vehicle subsystem of the straddle-type monorail is established, in which the wheel-rail contact relationship has taken into account the influence of the track inclination angle α0. The dynamic equation of the vehicle subsystem is obtained from the motion equations of each bogie and the 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 They are the lateral static wind resistance, lateral static wind lift and lateral static wind moment of the wind load, 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 the rolling inertia, nodding inertia and yaw inertia of the front bogie, J t2x , J t2y , J t2z are 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 car body motion equations respectively; the angles of each degree of freedom are shown in Table 1.

[0178] Establishment of the finite element model of the track beam: 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 finite element model of the track beam preferably uses commercial software for modal analysis to establish the dynamic model of the bridge subsystem. The dynamic model of the bridge subsystem 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 of the wind field is used as the excitation input of the dynamic equation of the vehicle subsystem and the finite element model of the track beam. The size 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, which cannot provide 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 dynamic spatiotemporal simulation of the wind load of a bidirectional straddle-type monorail (i.e., a double-track running vehicle) in actual operation, the method for determining the wind load of the vehicle and the track beam under different speed and position relationships in the present invention is as follows:

[0181] 1) Check the on-site wind field conditions → Use CFD to establish a fluid model to simulate the wind field conditions → Conduct wind tunnel tests on the scaled axle model (pressure measuring holes are arranged on the vehicle section, and a six-component balance is arranged under each car) to determine the wind load conditions of the train and track beams under various working conditions (single-line with trains, double-line trains) when the train is stationary → Verify the correctness of the CFD simulation through model test data and correct the basic parameters of the model → Determine the wind loads on the train and track beams under various working conditions through CFD model calculations.

[0182] Working condition a: see Figure 5 As shown in the figure, for double-track vehicles, the critical distance L of interference 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] Among them, 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 body drag coefficient, lift coefficient and torsional moment coefficient, respectively. 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 during the operation of the two trains. 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 running trains, the wind load in the time-space varying wind field is also related to the running speeds of the two vehicles. Based on this relationship, the load time history of the wind load can be established, and the wind load is added to the dynamic equation of the vehicle subsystem and the finite element model of the track beam according to the time history.

[0193] Input of wind load: The specific method for establishing the load history of wind loads on vehicles and track beams under different speeds and position relationships 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 bidirectional vehicle speeds, so

[0195] ① When condition b is met

[0196] Vehicle wind load Wind load on track beam

[0197] ③ When the working condition a is met

[0198] Vehicle wind load Wind load on track beam

[0199] (2) If the initial clearance distance between two-way running trains is S>L, the initial non-interference and mutual interference distances between the two trains are (SL) and (L c +2L), the time is It can be seen that the vehicle and track load time history is as follows

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

[0201] Vehicle wind load Wind load on track beam

[0202] ② When condition b is met

[0203] Vehicle wind load Wind load on track beam

[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 function unit is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor (processor) to perform some steps of the method described in each example of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), disk or optical disk and other media that can store program codes.

[0205] Finally, it is 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 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 and does not take into account the influence of the track beam displacement, and obtains the wheel-rail force time history curve F1 in the initial state of the track beam → Import the wheel-rail force time history curve F1 into the track beam finite element model, and perform vibration response analysis under wind load excitation to obtain the displacement time history curve S1 of each wheel-rail contact point in the bridge subsystem dynamic model → Assign the wheel-rail contact point displacement time history curve S1 as an influence value to each wheel of the vehicle subsystem dynamic equation as the initial value of this stage, and update the wheel-rail force time history curve F2 of the next stage 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 curve F2 is continuously 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 curve S2 → the wheel-rail contact point displacement time history curve S2 is 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 F3 of the next stage is obtained through vibration analysis update → until the condition is met , the vibration analysis converges and the coupled vibration analysis results of the vehicle and track beam are output.

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

3. The vibration response evaluation method of a weak lateral stiffness wind-vehicle-bridge system according to claim 1, characterized in that: Wheel-rail force time history curve F of all wheels on straddle-type monorail n Corresponds to the wheel forces in the following table Where j = 1, 2 represents the front and rear positions of the tires 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 It corresponds to the action point in the finite element model of the track beam.

4. The vibration response evaluation method of a weak lateral stiffness wind-vehicle-bridge system according to claim 3 is characterized in that: Based on the various equilibrium equations of the straddle-type monorail vehicle, the dynamic equation of the vehicle subsystem of the straddle-type monorail is established, in which the wheel-rail contact relationship has taken into account the influence of the track inclination angle α0. The dynamic equation of the vehicle subsystem is obtained from the motion equations of each bogie and the body: 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 of gravity, and They are the lateral static wind resistance, lateral static wind lift and lateral static wind moment of the wind load, 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 the rolling inertia, nodding inertia and yaw inertia of the front bogie, J t2x , J t2y , J t2z are 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, A * ~K * are the simplified physical parameters of the bogie motion equations and the car body motion equations respectively; y c 、z c ,θ c ,φ c , c They are the yaw, sink, roll, shake and nod angles of the vehicle body; ti 、z ti ,θ ti ,φ ti , ti are the yaw, sink, roll, pitch and nod angles of the bogie respectively. The subscript i represents the front and rear bogies respectively.

5. The method for evaluating vibration response of a wind-vehicle-bridge system with weak lateral stiffness according to claim 1, characterized in that: The track beam finite element model uses commercial software for 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 wheel-rail contact point displacement time history on the track beam.

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

7. The method for evaluating vibration response of a wind-vehicle-bridge system with weak lateral stiffness according to claim 6, characterized in that: The working conditions when the train is stationary include: Working condition a: Determine the critical distance L between vehicles. 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 Where ρ is the air density and 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 body drag coefficient, lift coefficient and torsional moment coefficient, respectively. H v is the distance between the center of mass of the vehicle body and the top surface of the track beam, and The dynamic equations used to apply to the vehicle subsystem are 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 be applied to the finite element model of the track beam; Working condition b: When the clear distance between two trains running in opposite directions is S≤L, the wind load on the opposite vehicle will be disturbed during the operation of the two trains. 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 8. The method for evaluating vibration response of a wind-vehicle-bridge system with weak lateral stiffness according to claim 7, 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 speeds 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 bidirectional 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 is S>L, the initial non-interference and mutual interference distances between the two trains are (SL) and (L c +2L), the time is It can be seen that the vehicle and track load time history is as follows ① and When , working condition a is met; ② When , working condition b is met.

9. 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 in communication with the processor, wherein: The memory stores program instructions executable 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 8.

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