CN107958098A

CN107958098A - A kind of bullet train based on spectrum analysis topples method for evaluating hazard

Info

Publication number: CN107958098A
Application number: CN201711058298.1A
Authority: CN
Inventors: 严乃杰; 李永乐; 陈新中; 向活跃; 张志杰
Original assignee: Southwest Jiaotong University
Current assignee: Southwest Jiaotong University; Railway Engineering Research Institute of CARS
Priority date: 2017-11-01
Filing date: 2017-11-01
Publication date: 2018-04-24
Anticipated expiration: 2037-11-01
Also published as: CN107958098B

Abstract

Topple method for evaluating hazard the invention discloses a kind of bullet train based on spectrum analysis, it includes：Relative to the fluctuating wind spectrum computational methods of running train, the recognition methods of train admittance function, running train unsteady aerodynamic force computational methods and train response frequency-domain calculations and capsizing probability evaluation method；Running train fluctuating wind spectrum computational methods solve the problems, such as to calculate different speeds, traffic direction Train wind spectrum based on surface wind spectrum；Train admittance function recognition methods have identified the admittance function on different wind direction fluctuating winds；Running train unsteady aerodynamic force computational methods consider the contribution of down wind, beam wind to, vertical fluctuating wind at the same time；Train responds frequency-domain calculations and capsizing probability evaluation method, specify that the probability distribution of train extreme value response, has quantified the probability of happening that train topples.The present invention has calculated the train probability characteristics wind speed curve PCWC under different capsizing probabilities, can evaluate high wind effect Train safety in operation.

Description

High-speed train overturning risk evaluation method based on spectrum analysis

Technical Field

The invention belongs to the field of high-speed train operation safety analysis, and particularly relates to a high-speed train overturning risk evaluation method based on spectrum analysis.

Background

in the last decade, high-speed trains are rapidly developed in the world due to the advantages of high running speed, high conveying capacity, high safety, high punctuation rate, high comfort, energy conservation, environmental protection and the like, and China high-speed railway construction is in the world leading level.

The pulsating wind field around the train is usually described by using a 'gust equivalent wind speed', such as 'Chinese hat', and only a determined extreme train value response can be obtained by using the method. However, the fluctuating wind load has random characteristics, and the train response under the excitation of the random load also obeys a certain probability distribution. In order to obtain train response with random distribution characteristics, a random pulsating wind field needs to be simulated through a pulsating wind spectrum and a coherence function. Train response analysis is usually performed in a time domain, continuous pulsating wind fields along a line need to be dispersed into wind fields at finite points, correlation exists among the dispersed wind fields, and due to the large number of the dispersed points, the calculation amount of simulation of the wind fields along the line is difficult to complete. On the other hand, the pulse wind spectrum relative to the moving train is different from the pulse wind spectrum relative to the static ground, and the pulse wind time interval relative to the moving train can be simulated by using the pulse wind spectrum on the train, so that the calculation workload can be effectively reduced.

The aerodynamic force of the moving train mainly comprises average wind load and fluctuating wind load (unsteady aerodynamic force), and can be obtained by calculating the aerodynamic coefficient and the admittance function of the train. At present, the pulsating wind load is generally considered to be caused by downwind pulsating wind, however, research shows that transverse and vertical pulsating wind also has important influence. The admittance function is a transfer function of a pulsating wind spectrum and a aerodynamic spectrum, and can be obtained through a wind tunnel test. The traditional identification method considers that the wind fields in the wind tunnels are completely related, and actually the wind fields in the wind tunnels are not completely related, so that the traditional identification method has a reduction effect on the train aerodynamic force under the completely related wind fields. Since the wind field dependency of wind tunnel is obviously different from the actual wind field, it is necessary to remove the reduction effect caused by the incompletely related wind field in the wind tunnel and consider the aerodynamic force dependency in the actual wind field. The admittance function is a function with respect to frequency and is simpler to use in the frequency domain.

Under the excitation of wind load and track irregularity load, the dynamic response of the train system can be simulated by a multi-degree-of-freedom train numerical model. The method is used for evaluating the stability performance of the train in the transverse wind direction, whether the train overturns or not is not derailed, so that the nonlinear wheel-rail contact can be simplified into linear contact or is directly ignored. In addition, the research shows that the influence of the freedom degree of the train model on the stability analysis result of the train transverse wind is small. Therefore, in the train transverse wind stability analysis, a simplified train model can be used, and train non-linear characteristics are ignored.

The overturning of the train is generally judged by using the wheel set load shedding rate, and when the maximum load shedding of the wheel set on the windward side of the train reaches a limit value, the corresponding average wind speed is the critical wind speed. The overturning critical wind speed of the train is a function of the vehicle speed and the initial wind direction angle, and a single critical wind speed curve, namely a Characteristic wind speed curve (CWC), can be obtained by using a traditional time domain method. If the random characteristics of the pulsating Wind and the track irregularity and the uncertainties of other parameters are considered, a characteristic Wind speed Curve under different failure probabilities (overturning probabilities), namely a probability characteristic Wind speed Curve (PCWC), can be obtained. The wind environment along the railway is constantly changing, and the wind speed and wind direction angle of a certain area can be generally described by a specific probability distribution, such as a Weibull distribution. The probability of the train overturning along the whole railway line under different wind speeds and wind direction angles is integrated, so that the probability of the train overturning along the whole railway line under the action of strong wind can be obtained.

Disclosure of Invention

The invention aims to solve the technical problem of providing a high-speed train overturning danger evaluation method based on spectrum analysis, which is used for determining the probability distribution and the overturning probability of the train response extreme value, calculating a train probability characteristic wind speed curve PCWC under different overturning probabilities and evaluating the train operation safety under the action of strong wind based on probability analysis.

In order to solve the technical problems, the invention adopts the technical scheme that:

a high-speed train overturning risk evaluation method based on spectrum analysis comprises the following steps:

step 1: testing different wind direction angles through a wind tunnel testaerodynamic coefficient of train average wind load under wind attack angle αThe average wind load aerodynamic coefficient of the train is tested by using the wind tunnel, and the unsteady aerodynamic coefficient C of the moving train in the downwind direction is calculated by a derived formula_iuTransverse wind direction unsteady aerodynamic coefficient C_ivVertical unsteady aerodynamic coefficient C_iwAnd identifying the admittance function χ_iξ0(f)；

Wherein,at an initial wind direction angle, V_trIs the vehicle speed, U is the average wind speed,is the average wind speed relative to the moving train;

according to theoretical derivation, neglecting the influence of the pulse wind cross spectrum, the train admittance function is identified by the following formula:

wherein,is aerodynamic force F_i(t) and the pulsatile wind component ξ (t) (ξ ═ u, v, w) of the cross-spectrum, χ_iξ0(f) Is the admittance function to be identified; ρ is air density, H is train height, C_iξIs the unsteady aerodynamic wind load coefficient of the train, S_ξξ(f) is the self-spectrum of the pulsating wind ξ (t) in wind tunnel, J_ξξ(f) the method is characterized in that a joint acceptance function is provided for an impulse wind component ξ (t) in the wind tunnel, and is used for reflecting the reduction effect of a transverse incompletely related wind field in the wind tunnel, and the calculation is carried out according to the following formula:

in the above formulaL is the train length; coh_ξξ(y, f) is a coherence function of xi-direction pulsating wind under the condition that the distance in the wind tunnel is y;

step 2: establishing a vehicle numerical model, and calculating the wheel-rail contact force F under the static state of the train₀；

Wherein, Y_D(t) is a train dynamic response displacement vector;is Y_D(t) first derivative;is Y_D(t) second derivative; m_V、C_V、K_VRespectively are train system mass, damping and rigidity matrixes; f_W(t)、F_T(t) are pulsating wind load and track irregularity load vector respectively;

and step 3: determining a ground wind field characteristic, comprising: average wind speed U and downwind turbulence intensity I_uIntensity of cross wind turbulence I_vAnd vertical turbulence intensity I_wDownwind turbulence integral scale L_uTransverse wind direction turbulence integral scale L_vVertical turbulence integral scale L_wSelf-spectrum S of downwind pulsating wind on ground_u(f) Ground transverse wind direction pulsating wind self-spectrum S_v(f) Self-spectrum S of ground vertical pulsating wind_w(f) And the ground pulse wind coherence function Coh_u(Δy,f)；

And 4, step 4: calculating the vehicle speed V_trAnd initial wind direction angleDownwind pulsating wind self-spectrum S of lower moving train_u′u′(f) Transverse wind direction pulsating wind self-spectrum S of moving train_v′v′(f) Vertical pulsating wind self-spectrum S of mobile train_w′w′(f) Further calculating the pulsating wind joint acceptance function J on the moving train_ξ′ξ′(f)；

S_uu(Δy,f)＝Coh_u(Δy,f)S_u(f)

Wherein R is_uu(Deltay, tau + tau') represents the downwind correlation function of the ground pulsating wind, S_uu(delta y, f) represents the cross spectrum of the downwind fluctuating wind on the ground, f is frequency, tau is time interval, tau' is freezing time of the fluctuating wind, and delta y is the transverse wind direction distance of the ground point; r_u′u′(Delta η, tau) represents the relevant function of the pulsating wind of the train, Delta η is the distance between points on the train, S_u(f) For the downwind pulsating wind self-spectrum of the ground, Coh_u(Δ y, f) is a ground pulsating wind coherence function; s_u′u′(delta η, f) is the downwind fluctuating wind cross spectrum of the moving train, and the same method is adopted to obtain the upwind fluctuating wind cross spectrum S of the moving train_v′v′(Δ η, f), vertical pulsation wind cross-spectrum S_w′w′(Δη,f)；

S_vv(Δy,f)＝Coh_u(Δy,f)S_v(f)

Wherein R is_vv(Deltay, tau + tau') represents the correlation function of the transverse wind direction of the ground pulsating wind, S_vv(Δ y, f) represents the ground cross wind direction fluctuating wind cross spectrum;

S_ww(Δy,f)＝Coh_u(Δy,f)S_w(f)

wherein R is_vv(Deltay, tau + tau') represents the vertical correlation function of the ground fluctuating wind, S_vv(Δ y, f) represents the ground vertical pulsatile wind cross-spectrum;

further calculating a pulsating wind joint acceptance function J on the moving train_ξ′ξ′(f)；

And 5: by average wind speed relative to the moving trainDownwind pulsating wind self-spectrum S of moving train_u′u′(f) Transverse wind direction pulsating wind self-spectrum S of moving train_v′v′(f) Vertical pulsating wind self-spectrum S of mobile train_w′w′(f) Admittance function χ_iξ0(f) And the downwind unsteady aerodynamic coefficient C of the moving train_iuTransverse wind direction unsteady aerodynamic coefficient C_ivVertical unsteady aerodynamic coefficient C_iwCalculating the average wind load of the moving trainAnd calculating the fluctuating wind load spectrum on the moving trainTrack irregularity load spectrum

Wherein,for moving the average wind load of the train, A_W(f) Is a matrix composed of aerodynamic coefficients and admittances;is a pulsating wind load matrix,A track irregularity load matrix; s_W(f) For pulsating wind power spectrum matrix, S_X(f) A track irregularity power spectrum matrix;

step 6: load the average windFluctuating wind load spectrumTrack irregularity load spectrumLoading the displacement vector to a train numerical model, and calculating the static displacement vector Y of the train under the static wind load_STrain dynamic response spectrumFurther calculating the wheel set load shedding under the action of calculating the static wind load on the windward sideDynamic response spectrum for wheel set load shedding

K_VY_S＝F_S

Wherein, K_VIs a train system stiffness matrix, Y_SThe static displacement vector of the train under the static wind load is obtained; f_SIs a static wind load vector; a. the_W(f) Is a matrix composed of aerodynamic coefficients and admittances;respectively are aerodynamic force and track irregularity excitation power spectrum matrixes; s_W(f) For pulsating wind power spectrum matrix, S_X(f) A track irregularity power spectrum matrix;a train dynamic response spectrum; h (f) is the train system response transfer function, H^*(f) A conjugate transpose matrix of H (f);

and 7: calculating corresponding average wind speed U and initial wind direction angle according to extreme value obeying extreme value I type Gunn Bell distribution of Gaussian processProbability of overturn of lower train

Wherein,is the average wind speed U and the initial wind direction angleProbability of overturning under working conditions;for dynamic extreme value response ofCumulative probability distribution of time; k is a radical of_lThe wheel set load shedding rate limit value;the wheel set is subjected to load reduction under the action of static wind load; f_D(t) wheel pair deloading under the action of pulsating wind and track irregularity; v. of₀The crossing rate of the stable Gaussian process at zero mean value;the standard deviation is the extreme value response standard deviation of the wheel-rail contact force;

and 8: adjusting initial wind direction angleIn the range of [0,2 π]Average wind speed in the range of 0, U_max]，U_maxRecalculating the restricted train wind speed from the step 3 until the initial wind direction angle reaches 2 pi and the average wind speed reaches U_maxObtaining different average wind speed U and initial wind direction angleA lower train operation overturning probability curve;

and step 9: taking into account the corresponding initial wind direction angleLower average wind speed U occurrence probabilityInitial wind direction angleProbability of occurrenceCalculating the average wind speed U and the initial wind direction angleProbability of train overturning under combined working conditionFinally calculating the overturning probability of the train running along the line under the fixed speed

Step 10: taking the probability of failure as a fixed value p_fSelecting a vehicle speed V from the overturning probability curve obtained in the step 8_trInitial wind direction angleLower overturning wind speed U_cAnd obtaining a probability characteristic wind speed curve of the train, wherein the probability characteristic wind speed curve is used as a reference basis for ensuring the safe operation of the train under the action of strong wind.

Compared with the prior art, the invention has the beneficial effects that: the probability distribution of the response extreme value of the train and the overturning probability are determined, the probability characteristic wind speed curve PCWC of the train under different overturning probabilities is calculated, and the running safety of the train under the action of strong wind can be evaluated.

Drawings

FIG. 1 is a schematic flow chart of the evaluation method of the present invention.

Fig. 2 is a schematic view (perspective view) showing the relationship between the wind field of the mobile train and the ground wind field.

Fig. 3 is a schematic diagram (top view) of the relationship between the wind field of the moving train and the ground wind field.

Fig. 4 is a vector diagram of the wind speed of the moving train in the invention.

FIG. 5 is a chart of a ground and train wind spectrum according to the present invention.

FIG. 6 is a wind field joint acceptance function in a wind tunnel according to the present invention.

FIG. 7 is an admittance function (lateral force admittance) identified by the method of the present invention.

FIG. 8 is an admittance function (lift admittance) identified by the method of the invention.

Fig. 9 is an admittance function (lateral force admittance) identified by a conventional method.

Fig. 10 is an admittance function (lift admittance) identified by a conventional method.

Fig. 11 is a train aerodynamic spectrum (lateral force) in the present invention.

Fig. 12 is a train aerodynamic spectrum (lift) of the present invention.

Fig. 13 shows response spectra under the excitation of the uneven orbit and the pulsating wind in the present invention (under the action of the uneven orbit).

FIG. 14 shows the response spectrum (under the action of the pulsating wind) of the present invention when the orbit is not smooth and the pulsating wind is excited.

FIG. 15 is a graph of the probability of failure at different vehicle speeds in the present invention.

FIG. 16 shows PCWC (initial wind direction angle 90) at different failure probabilities in the present invention.

FIG. 17 shows PCWC (vehicle speed 70m/s) at different failure probabilities in the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. The method combines a pulsating wind spectrum calculation method, a train admittance function identification method, a moving train unsteady aerodynamic force calculation method, a train response frequency domain calculation and an overturning probability evaluation method relative to a moving train, applies pulsating wind and track irregularity excitation to a train system in a load spectrum mode, calculates a moving train response spectrum, determines the probability distribution and the overturning probability of a train response extreme value based on probability analysis, calculates a train probability characteristic wind speed curve under different overturning probabilities, and evaluates the train operation safety under the action of strong wind.

The basic theory involved in the present invention is as follows:

one, moving train wind field model

Based on the assumption that the mean wind speed is far greater than the pulsating wind speed, the pulsating wind speed is considered to be unchanged in a certain time and space range, that is, the vortex has not yet been evolved in time within the freezing time tau' of the pulsating wind, and the distance deltax is traveled under the carrying of the mean wind. Based on this, the above-ground pulsating wind cross-correlation function R can be used_uu(Deltay, tau + tau') represents the cross-correlation function R of the pulsating wind on the moving train_u′u′(Δ η, τ) (as shown in FIGS. 2 and 3), i.e.

u(x_k′,y_k′,t+τ)＝u(x_m,y_m,t+τ+τ′)＝u(x_j,y_j-Δy,t+τ+τ′) (1)

R_u′u′(Δη,τ)＝E[u(x_j,y_j,t)u(x_j,y_j-Δy,t+τ+τ′)]＝R_uu(Δy,τ+τ′) (2)

Wherein,

S_uu(Δy,f)＝Coh_u(Δy,f)S_u(f) (4)

then, the pulsatile wind cross-spectrum with respect to the moving train is:

in the above formula S_u(f)、Coh_u(delta y, f) is the self-spectrum and coherence function of the pulsating wind on the ground, delta eta is the distance between two points on the train, S_u′u′(delta η, f) is the reciprocal spectrum of the fluctuating wind on the moving train, the integral in the formula has no analytic solution and needs to be solved by numerical calculation, and the reciprocal spectrum S of the transverse fluctuating wind and the vertical fluctuating wind of the moving train can be obtained by adopting the same method_v′v′(Δη,f)、S_w′w′(Δη,f)。

By the numerical method, the average wind speed U and the initial wind direction angle can be calculated by any type of ground wind spectrum and coherent functionAnd vehicle speed V_trAnd (5) a lower moving train wind spectrum. Compared with the von-Karman spectrum based mobile train wind spectrum proposed by Cooper and the Kaimal spectrum based mobile train wind spectrum proposed by Wumeng snow, the method is not limited by the ground wind spectrum and the type of coherence function.

Second, moving train aerodynamic model

When the vehicle speed V is_trAt an angle of U with respect to the mean wind speedThe instantaneous wind speed "felt" by the moving train is (as shown in fig. 4):

the average wind load of the moving train is as follows:

by theoretical derivation, if the contributions of downwind direction, crosswind direction and vertical pulsating wind are considered at the same time, the unsteady aerodynamic force of the moving train can be expressed as:

wherein,

in the above formula, i is S, and L represents a lateral force or a lift force; if get V_tr＝0、Then obtaining an unsteady aerodynamic expression of the static train, which can be used for identifying the aerodynamic admittance function obtained by the static train model test.

Third, admittance function identification

According to theoretical derivation, neglecting the influence of the pulse wind cross spectrum, the train admittance function can be identified by the following formula:

in the above formula, the first and second carbon atoms are,is aerodynamic force F_i(t) and the pulsatile wind component ξ (t) (ξ ═ u, v, w) of the cross-spectrum, χ_iξ0(f) Is the admittance function to be identified; j. the design is a square_ξξ(f) the method is a joint acceptance function of the pulsating wind component ξ (t) in the wind tunnel and is used for reflecting the reduction effect of a transverse incompletely related wind field in the wind tunnel, and can be calculated by the following formula:

in the above formulaL is the train length; coh (hydrogen sulfide)_ξξand (y, f) is a coherent function of xi-direction pulsating wind under the condition that the distance in the wind tunnel is y.

J for removing incompletely correlated wind fields in wind tunnels_ξξ(f) Then, calculating the unsteady aerodynamic force of the moving train, and considering the joint acceptance function J of the actual wind field_ξ′ξ′(f) The method can be obtained by the coherent function integral of the wind field of the moving train, namely:

equation of motion of four-wheel train system

The train system consists of 1 train body and 2 bogies, and has 5 freedom degrees of transverse, vertical, side rolling, nodding and shaking. The train response can be divided into static response and dynamic response, and the train motion equations under the action of static and dynamic loads are respectively as follows:

K_VY_S＝F_S(16)

in the above formula, Y_SIs a static displacement vector of the train under the static wind load, Y_D(t) is a train dynamic response displacement vector; m_V、C_V、K_VRespectively are train system mass, damping and rigidity matrixes; f_S、F_W(t)、F_TAnd (t) is static wind load, fluctuating wind load and track irregularity load vector respectively.

Considering the phase difference of the rail irregularity of each wheel pair at the same time, the rail irregularity excitation can be expressed as:

Y_Tj(t)＝[y_w(t+τ_j),z_w(t+τ_j),φ_w(t+τ_j)]^T(j＝1,2,3,4) (20)

wherein, K_T、C_TRespectively is a rigidity matrix and a damping matrix corresponding to the irregularity of the track; y is_TAnd (t) is a track irregularity matrix. The phase difference between the rail irregularities of the respective wheel pairs can be expressed as:

in the above formula, Y_T(t) is a track irregularity matrix; y is_Tj(t) unevenness of track of jth wheel setA vector direction;

under the action of fluctuating wind load and track irregularity, the dynamic response power spectrum of the train is as follows:

H(f)＝[-M_V(2πf)²+C_Vi2πf+K_V]^-1(23)

wherein,

in the above formula, A_W(f) Is a matrix composed of aerodynamic coefficients and admittances;respectively are aerodynamic force and track irregularity excitation power spectrum matrixes; s_W(f)、S_X(f) The power spectrum matrixes are pulsating wind and track irregularity respectively;dynamically responding to a power spectrum for the train; e_T(f) Is composed ofA diagonal matrix is formed.

Fifth, response evaluation

The irregularity of the pulsating wind and the orbit is generally smoothAnd the Gaussian process, namely the corresponding stable Gaussian process with zero mean train response. Therefore, based on the Poisson assumption, the extreme value F of the wheel-rail contact force_DmaxThe cumulative probability distribution of (c) is:

in the above formulaWherein,

the extreme value of the wheel-rail contact force at the assurance rate p is:

when the maximum load shedding rate of the wheels on the windward side exceeds a critical value k_lAnd then, considering that the train overturns:

in the above formula F₀The contact force of the wheel rail is the contact force of the train in the static state.

For a given wind speed, initial wind angle, and vehicle speed, the probability of a train overturning can be expressed as:

and calculating the overturning probability of the train under different wind speeds and initial wind direction angles. Finally, the probability of overturning the train along the whole railway line is as follows:

table 1 the symbol definitions referred to herein

The feasibility and the beneficial technical effects of the method of the invention are verified by the specific examples below. The near-surface Kaimal spectrum is used as a target spectrum, a wind tunnel test data is combined, the aerodynamic spectrum of the moving train is simulated, a typical Chinese high-speed railway train is taken as an example, the train overturning probability under the action of strong wind is analyzed, and PCWC under different overturning probabilities is obtained.

1) Movable train wind field

The downwind, crosswind and vertical near-surface Kaimal spectra are as follows:

in the above formula:to reduce the frequency; l is_ξIs a turbulence integral scale; sigma_ξIs the standard deviation of the pulsating wind. The relationship between the integral scale and standard deviation of the turbulence of downwind, crosswind and vertical pulsating wind is shown in Table 2, wherein σ is₁Is the standard deviation of₁Is a turbulence integral scale parameter. In order to truly reflect the near-surface wind field, the method is takenL_u40 m. Using the Davenport coherence function, the attenuation coefficient takes 7. Taking downwind pulsating wind as an example, the ground upwind spectrum (the speed ratio is 0) and the moving train wind spectrum under different speed ratios are shown in fig. 5. As can be seen from the figure, the energy distribution of the wind spectrum of the mobile train is obviously different from that of the ground wind spectrum.

TABLE 2 pulsating wind parameters

2) Admittance function identification

According to the deduced aerodynamic model of the stationary train, the influence of downwind direction, transverse wind direction and vertical pulsating wind is considered at the same time, the admittance function of the typical high-speed railway train in China is tested through a wind tunnel test, and the joint acceptance function of a wind field in the wind tunnel is calculated, as shown in FIG. 6. As can be seen from the figure, the combined acceptance function of the wind fields in the wind tunnel is far less than 1, which indicates that incompletely related wind fields in the wind tunnel have a significant reduction effect on the aerodynamic force of the train. Through analysis, the phase of the admittance function has no influence on the overturning performance of the train, so the imaginary part of the admittance function can be ignored, and the amplitude of the transverse force and lift admittance function at a typical wind direction angle is shown in fig. 7 and 8. According to the conventional method, only the influence of downwind pulsating wind is considered, and the identified admittance functions are shown in fig. 9 and 10. Through comparison, the admittance functions identified by the new method and the traditional method have obvious difference, and the pulsating wind admittance functions in different directions also have obvious difference.

3) Aerodynamic spectrum of moving train

And taking the speed of the train to be 70m/s and the wind speed to be 25m/s, substituting the calculated wind spectrum of the moving train into the deduced aerodynamic model of the moving train, and considering the identified admittance function to obtain the unsteady aerodynamic spectrum of the moving train. By adopting the same method, the admittance function identified by the traditional method (only considering the influence of downwind pulsating wind) is substituted into the traditional aerodynamic model of the moving train, and the aerodynamic spectrum of the moving train can also be calculated. The aerodynamic force spectra calculated by the two methods are shown in fig. 11 and 12, and it can be seen from the graphs that the aerodynamic force spectra of the moving train calculated by the two methods have significant difference. Theoretically, if the actual wind field is identical to the wind field of the wind tunnel, the aerodynamic spectra of the moving train calculated by the two methods should be identical. However, in nature, wind field dependence is different from that in wind tunnels. In order to obtain a more reasonable aerodynamic spectrum of the moving train, the influence of downwind direction, transverse wind direction and vertical pulsating wind needs to be considered at the same time.

4) Train overturn risk analysis under strong wind action

And (3) identifying an admittance function and calculating the unsteady aerodynamic force of the moving train by adopting a new method. And (3) loading the train system by taking the train aerodynamic force spectrum and the track irregularity excitation spectrum obtained by calculation as external loads, so as to calculate the windward side wheel-rail contact force response spectrum. Due to the adoption of a linear system, the excitation of track irregularity and the excitation of pulsating wind can be independently applied, and the calculated independent response and the total response meet the SRSS superposition principle. A train response spectrum under the conditions of 70m/s of train speed, different train speed ratios, different initial wind direction angles, unsmooth track and independent excitation of pulsating wind is shown in the graph 13 and the graph 14.

Taking T as 120min, the initial wind direction angle as 90 °, the train overturning probability under different vehicle speeds and wind speeds is calculated, as shown in fig. 15. The probability of overturning was 5%, 10%/, 43%, and PCWC at different vehicle speeds and different wind angles was obtained as shown in fig. 16 and 17. As can be seen from the figure, the probability of the train overturning at a specific speed, wind speed and initial wind direction angle can be quantified through calculation by a frequency domain method, and PCWC under different overturning probabilities can be obtained.

Claims

1. A high-speed train overturning risk evaluation method based on spectrum analysis is characterized by comprising the following steps:

step 1: testing different wind direction angles through a wind tunnel testaerodynamic coefficient of train average wind load under wind attack angle αUsing windThe average wind load aerodynamic coefficient of the train tested by the tunnel is calculated by a derived formula to obtain the unsteady aerodynamic coefficient C of the moving train in the downwind direction_iuTransverse wind direction unsteady aerodynamic coefficient C_ivVertical unsteady aerodynamic coefficient C_iwAnd identifying the admittance function χ_iξ0(f)；

<mrow> <msub> <mi>J</mi> <mrow> <mi>&xi;</mi> <mi>&xi;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>L</mi> <mo>&prime;</mo> </msup> </mfrac> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <msup> <mi>L</mi> <mo>&prime;</mo> </msup> </msubsup> <msub> <mi>coh</mi> <mrow> <mi>&xi;</mi> <mi>&xi;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>y</mi> </mrow>

<mrow> <msub> <mi>M</mi> <mi>V</mi> </msub> <msub> <mover> <mi>Y</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mi>V</mi> </msub> <msub> <mover> <mi>Y</mi> <mo>&CenterDot;</mo> </mover> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mi>V</mi> </msub> <msub> <mi>Y</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mi>W</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>F</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>R</mi> <mrow> <mi>u</mi> <mi>u</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>&tau;</mi> <mo>+</mo> <msup> <mi>&tau;</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <msub> <mi>S</mi> <mrow> <mi>u</mi> <mi>u</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&lsqb;</mo> <mn>2</mn> <mi>&pi;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>+</mo> <msup> <mi>&tau;</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mi>d</mi> <mi>f</mi> </mrow>

S_uu(Δy,f)＝Coh_u(Δy,f)S_u(f)

<mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>&infin;</mi> </msubsup> <msub> <mi>R</mi> <mrow> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&pi;</mi> <mi>f</mi> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&tau;</mi> </mrow>

<mrow> <msub> <mi>R</mi> <mrow> <mi>v</mi> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>&tau;</mi> <mo>+</mo> <msup> <mi>&tau;</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <msub> <mi>S</mi> <mrow> <mi>v</mi> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&lsqb;</mo> <mn>2</mn> <mi>&pi;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>+</mo> <msup> <mi>&tau;</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mi>d</mi> <mi>f</mi> </mrow>

S_vv(Δy,f)＝Coh_u(Δy,f)S_v(f)

<mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>v</mi> <mo>&prime;</mo> </msup> <msup> <mi>v</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>&infin;</mi> </msubsup> <msub> <mi>R</mi> <mrow> <msup> <mi>v</mi> <mo>&prime;</mo> </msup> <msup> <mi>v</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&pi;</mi> <mi>f</mi> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&tau;</mi> </mrow>

<mrow> <msub> <mi>R</mi> <mrow> <mi>w</mi> <mi>w</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>&tau;</mi> <mo>+</mo> <msup> <mi>&tau;</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <msub> <mi>S</mi> <mrow> <mi>w</mi> <mi>w</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&lsqb;</mo> <mn>2</mn> <mi>&pi;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>+</mo> <msup> <mi>&tau;</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mi>d</mi> <mi>f</mi> </mrow>

S_ww(Δy,f)＝Coh_u(Δy,f)S_w(f)

<mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>w</mi> <mo>&prime;</mo> </msup> <msup> <mi>w</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>&infin;</mi> </msubsup> <msub> <mi>R</mi> <mrow> <msup> <mi>w</mi> <mo>&prime;</mo> </msup> <msup> <mi>w</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&pi;</mi> <mi>f</mi> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&tau;</mi> </mrow>

<mrow> <msub> <mi>J</mi> <mrow> <msup> <mi>&xi;</mi> <mo>&prime;</mo> </msup> <msup> <mi>&xi;</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>L</mi> <mo>&prime;</mo> </msup> </mfrac> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <msup> <mi>L</mi> <mo>&prime;</mo> </msup> </msubsup> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>&eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> <msup> <mi>u</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>d</mi> <mi>y</mi> </mrow>

K_VY_S＝F_S

Wherein, K_VIs a train system stiffness matrix, Y_SFor static displacement of train under static wind loadVector quantity; f_SIs a static wind load vector; a. the_W(f) Is a matrix composed of aerodynamic coefficients and admittances;is a pulsating wind load matrix,A track irregularity load matrix; s_W(f) For pulsating wind power spectrum matrix, S_X(f) A track irregularity power spectrum matrix;a train dynamic response spectrum; h (f) is the train system response transfer function, H^*(f) A conjugate transpose matrix of H (f);

Wherein,is the average wind speed U and the initial wind direction angleProbability of overturning under working conditions;the dynamic load shedding extreme value is the wheel-rail contact force; k is a radical of_lThe wheel set load shedding rate limit value; f₀The contact force of the wheel track is the contact force of the wheel track in the static state of the train;the wheel set is subjected to load reduction under the action of static wind load; f_D(t) wheel pair deloading under the action of pulsating wind and track irregularity; v. of₀The crossing rate of the stable Gaussian process at zero mean value;the standard deviation is the extreme value response standard deviation of the wheel-rail contact force;