CN105631128A - High-speed railway pantograph-net-train-rail vertical coupling large system dynamic modeling and simulation method - Google Patents

Abstract

The invention discloses a high-speed railway pantograph-net-train-rail vertical coupling large system dynamic modeling and simulation method. Independent dynamic models of a contact net system, a pantograph-train system and a rail system and contact models among the contact net system, the pantograph-train system and the rail system are built. The invention also discloses a coupling integration algorithm to achieve coupling dynamic simulation calculation of a high-speed railway pantograph-net-train-rail large system. Compared with traditional methods, two-way interaction influence rules between a pantograph system and the train rail system can be taken into consideration, simulation calculation better meets practical requirements, and precision and safety of subsequent engineering design can be improved.

Description

A kind of high-speed railway bow-net-Che-rail vertical coupled Iarge-scale system Dynamic Modeling emulation method

Technical field

The invention belongs to the power supply circuit of electric vehicle or the device along rail, especially the Dynamic Modeling simulation technical field of pole line and annex used thereof.

Background technology

High-speed railway bow net dynamic behavior and wheel rail dynamics behavior are all current research focuses, and the former determines the electric energy transmission efficiency of train, and the latter determines the safe operation of train especially, both determines the key factor of highest running speed of train. numerical value emulation method is in research bow net dynamic behaviour and wheel rail dynamics behavior and designs the important channel of its key parameter, but, conventional model is all carried out separately independently carrying out modeling and simulating mostly, the relation that influences each other between the two is usually ignored, in recent years, some scholars consider track vibration to the one-sided impact of bow net, such as Zhai Wan is bright waits people in the paper " motorcycle track coupled vibration is on the dynamic (dynamical) impact of pantograph contact net system " of periodical " railway society " 20 volumes the 1st phase 32-38 page in 1998, establish track and bow net two models respectively, the vibratory response of track is applied to bow net, achieve one-sided Dynamics Coupling. so far, the also relevant report of the not coupling model of net-bow-Che-rail Iarge-scale system, bow net and wheel track bidirectional couple relation therebetween is not yet considered. it is an object of the invention to propose a kind of high-speed railway bow-net-Che-rail Iarge-scale system vertical coupled dynamics modeling method, set up contact system, bow-Che, the kinetic model of track three system independences and contact model each other respectively, and propose the Coupled Dynamics simulation calculation that a kind of coupling point algorithm realizes high-speed railway bow-net-Che-rail Iarge-scale system. the present invention can consider the mutual affecting laws between bow net and track two system, and simulation calculation is more accurate, it is possible to improves accuracy and the security of successive projects design.

Summary of the invention

It is an object of the invention to propose a kind of high-speed railway bow-net-Che-rail Iarge-scale system vertical coupled dynamics modeling method, set up contact system, bow-Che, the kinetic model of track three system independences and contact model each other respectively, and propose the Coupled Dynamics simulation calculation that a kind of coupling point algorithm realizes high-speed railway bow-net-Che-rail Iarge-scale system. Enable to carry out high-speed railway pantograph-contact system-car body-track vertical coupled Iarge-scale system modeling and simulating, the mutual coupling between bow net and track can be reflected, it is possible to consider the contact of bow net contact, wheel track simultaneously and hang the rough non-linear characters such as string different operating state.

The present invention realizes the concrete means of goal of the invention:

A kind of high-speed railway bow-net-Che-rail vertical coupled Iarge-scale system Dynamic Modeling emulation method, high-speed railway pantograph-contact system-car body-track vertical coupled Iarge-scale system modeling and simulating is carried out when considering that bow net contact, wheel track contact and hang the influence factors such as rough non-linear character such as string different operating state simultaneously, with the mutual coupling reflected between bow net and track, comprise following concrete steps:

1) contact system, bow-Che, track kinetic model, is set up respectively;

Step 1. adopts Finite Element Method to set up contact system kinetic model, and its kinetic equation can represent and is:

$M_C{\stackrel{\·\·}{X}}_C\left(t\right)+C_C{\stackrel{\·}{X}}_C\left(t\right)+K_C\left(t\right)X_C\left(t\right)=F_C(x,t)$

Wherein, M_C��C_C��K_CIt is respectively contact system quality, damping, stiffness matrix,X_CT () is respectively contact system acceleration, speed, displacement matrix, F_C(x, t) is dynamic excitation;

Step 2. adopt mode respectively method set up track kinetic model, its kinetic equation can represent and is:

$M_T{\stackrel{\·\·}{X}}_T\left(t\right)+C_T{\stackrel{\·}{X}}_T\left(t\right)+K_T{X}_T\left(t\right)=F_T\left(t\right)$

Wherein, M_T��C_T��K_TIt is respectively track quality, damping, stiffness matrix,X_TT () is respectively orbital acceleration, speed, displacement matrix, F_TT () is dynamic excitation;

Step 3. adopts many body dynamics method establishment pantograph-body powered model, and its kinetic equation can represent and is:

$M_V{\stackrel{\·\·}{X}}_V\left(t\right)+C_V{\stackrel{\·}{X}}_V\left(t\right)+K_V{X}_V\left(t\right)=F_V\left(t\right)$

Wherein, M_V��C_V��K_VIt is respectively bow-Che quality, damping, stiffness matrix,X_VT () is respectively bow-Che acceleration, speed, displacement matrix, F_VT () is dynamic excitation;

2) bow net, track contact model, is built respectively

Step 1. adopts penalty function method to build bow net contact model:

$f_c\left(t\right)=\left\{\begin{array}{cc}{K}_S\left(y_1\right(t)-y_c(t\left)\right)& y_1\left(t\right)\&GreaterEqual;y_c\left(t\right)\\ 0& y_1\left(t\right)<y_c\left(t\right)\end{array}\right.$

Wherein, K_SFor bow net contact rigidity, y₁The displacement of (t) pantograph collector head, y_cT () is osculatory point of contact vertical deviation, f_cT () is bow net contact power,

Step 2. is according to hertz the Theory Construction Wheel-rail contact model:

$f_{wj}\left(t\right)=\left\{\begin{array}{cc}{\{\frac{1}{G}\&lsqb;w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)\&rsqb;\}}^{1.5}& w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)\&GreaterEqual;0\\ 0& w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)<0\end{array}\right.$

Wherein G is hertz constant, f_wjT () is the contact force of jth wheel and track; w_r(x_wj, t) it is the vertical deviation of jth wheel, Z_wjT () is the vertical deviation of jth wheel; w₀T () is the static irregularity of track;

3), by method of value solving bow-net-Che-rail complicated coupling kinetics system being solved, the iterative algorithm in each time walks is as follows:

(1) point of contact of bow net and wheel track is determined according to running velocity and current time;

(2) reactive force f between track is calculated by Wheel-rail contact model_wj(t);

(3) adopt bow net coupling model coupling net-bow-truck system, and wheel rail force is applied in bow-net-truck system and calculates contact system response X_C(t) and pantograph-car body response X_V(t);

(4) X is responded according to car body_VT () and Wheel-rail contact model upgrade reactive force f between track_wj(t);

(5) track reactive force is applied to track model, calculates track response X_T(t), and judge convergency, if met, entering future time step, then returning step (2) if do not met;

4), display or subsequent processing device is inputed to by emulating result above.

For clearly illustrating that theoretical foundation and the acquisition process of above technique means, special by as follows to each step particular content and method of design detailed description:

For bow-net-Che-rail system, as shown in Figure 1,1. set up independent contact system, bow-Che, wheel rail dynamics model respectively.

Step 1. adopts Finite Element Method to set up contact system kinetic model, wherein osculatory and carrier cable are regarded Euler's Bernoulli Jacob's beam element as, are hung string and regard that spring unit, other suspension system regard lumped mass, rigidity point as, the stiffness matrix of each unit can with reference to correlated finite element books, by Finite Element Method integrated after, its kinetic equation of contact system can represent and is:

$M_C{\stackrel{\&CenterDot;\&CenterDot;}{X}}_C\left(t\right)+C_C{\stackrel{\&CenterDot;}{X}}_C\left(t\right)+K_C\left(t\right)X_C\left(t\right)=F_C(x,t)---\left(1\right)$

Wherein, M_T��C_T��K_TIt is respectively track quality, damping, stiffness matrix,X_TT () is respectively orbital acceleration, speed, displacement matrix, F_TT () is dynamic excitation.

Step 2. adopts mode decomposition method to set up track kinetic model, and track can also regard Euler's Bernoulli Jacob's beam element as, and its motion partial differential equation can be written as

${\mathrm{EI}}_r\frac{{\&part;}^4{w}_r}{\&part;x^4}(x,t)+{\mathrm{\&rho;}}_r\frac{{\&part;}^2{w}_r}{\&part;t^2}(x,t)=\underset{i=1}{\overset{n_r}{\&Sigma;}}{f}_{ri}\mathrm{\&delta;}(x-x_r^i)+\underset{j=1}{\overset{4}{\&Sigma;}}{f}_{wj}\mathrm{\&delta;}(x-x_{wj})---\left(2\right)$

Wherein, EI_rIt is curved in tracks rigidity, ��_rIt is linear density, f_riWithIt is the external force position of i-th bracing or strutting arrangement respectively, n_rIt is the quantity of bracing or strutting arrangement, x_wjIt it is the point of contact of jth wheel and track. w_r(x, t) represents track vertical deviation. Pass through mode decomposition, it is possible to represent and be

$w_r(x,t)=\underset{u=1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&psi;}}_u\left(x\right)q_u\left(t\right)---\left(3\right)$

Wherein, q_uT () is the broad sense displacements of u rank, ��_uX () is corresponding mode function. By bringing formula (3) into formula (2), the kinetic equation that can obtain track is:

$M_T{\stackrel{\&CenterDot;\&CenterDot;}{X}}_T\left(t\right)+C_T{\stackrel{\&CenterDot;}{X}}_T\left(t\right)+K_T{X}_T\left(t\right)=F_T\left(t\right)---\left(4\right)$

Wherein, M_T��C_T��K_TIt is respectively track quality, damping, stiffness matrix,X_TT () is respectively orbital acceleration, speed, displacement matrix, F_TT () is dynamic excitation.

Step 3. adopts many body dynamics method establishment pantograph-body powered model. Its kinetic equation can directly topological framework according to Fig. 1 write out:

$M_V{\stackrel{\&CenterDot;\&CenterDot;}{X}}_V\left(t\right)+C_V{\stackrel{\&CenterDot;}{X}}_V\left(t\right)+K_V{X}_V\left(t\right)=F_V\left(t\right)---\left(5\right)$

Wherein, M_V��C_V��K_VIt is respectively bow-Che quality, damping, stiffness matrix,X_VT () is respectively bow-Che acceleration, speed, displacement matrix, F_VT () is dynamic excitation;

2, penalty function method is adopted to build bow net contact model:

$f_c\left(t\right)=\left\{\begin{array}{cc}{K}_S\left(y_1\right(t)-y_c(t\left)\right)& y_1\left(t\right)\&GreaterEqual;y_c\left(t\right)\\ 0& y_1\left(t\right)<y_c\left(t\right)\end{array}\right.---\left(6\right)$

Wherein, K_SFor bow net contact rigidity, y₁The displacement of (t) pantograph collector head, y_cT () is osculatory point of contact vertical deviation, f_cT () is bow net contact power, according to hertz the Theory Construction Wheel-rail contact model:

$f_{wj}\left(t\right)=\left\{\begin{array}{cc}{\{\frac{1}{G}\&lsqb;w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)\&rsqb;\}}^{1.5}& w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)\&GreaterEqual;0\\ 0& w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)<0\end{array}\right.---\left(7\right)$

Wherein G is hertz constant, f_wjT () is the contact force of jth wheel and track; w_r(x_wj, t) it is the vertical deviation of jth wheel, Z_wjT () is the vertical deviation of jth wheel; w₀T () is the static irregularity of track.

3, by method of value solving, bow-net-Che-rail complicated coupling kinetics system is solved. Iterative algorithm in each time walks is as follows:

(1) according to running velocity v and current time t, it is determined that the point of contact of bow net and wheel track;

(2) matrix X is moved according to bow-parking stall_V(t) and track displacement matrix X_T(t), it is determined that the displacement Z of each wheel_wjThe track displacement w of (t) and point of contact_r(x_wj, t),

(3) reactive force f between track is calculated by the Wheel-rail contact model shown in formula (6)_wj(t);

(4) simultaneous equations (1), (5-6) are coupled bow-net-Che Coupled Dynamics model, and the wheel rail force f that will obtain in step 3_wjT () is applied in bow-net-truck system to calculate contact system response X_C(t) and pantograph-car body response X_V(t);

(5) X is responded according to car body_V(t) and track displacement matrix X_TT (), the Wheel-rail contact model of combined type (6), upgrades reactive force f between track_wj(t);

(6) track reactive force is applied to track model, calculates track response X_T(t), and judge convergency: X_TDoes t () < �� set up? if setting up, then enter future time step, as being false, return step 2.

From the main contents of the present invention it may be seen that separated modeling method different from the past, the present invention establishes complete bow-net-Che-rail coupling vertical dynamics model, and gives its iterative method. The inventive method can carry out high-speed railway pantograph-contact system-car body-track vertical coupled Iarge-scale system modeling and simulating, the mutual coupling between bow net and track can be reflected, it is possible to consider the contact of bow net contact, wheel track simultaneously and hang the rough non-linear characters such as string different operating state.

Accompanying drawing explanation

Fig. 1 is bow-net-Che-rail vertical coupled model schematic

Fig. 2 is bow net contact power calculation result figure

Fig. 3 is pantograph collector head displacement figure

Fig. 4 is osculatory point of contact displacement figure

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are elaborated: the present embodiment is implemented under premised on technical solution of the present invention, give detailed implementation process, but protection scope of the present invention is not limited to following embodiment.

The present embodiment is to design train running speed as the Beijing-Tianjin railway contact line of 350Km/h and DSA380 type pantograph, contact system and pantograph parameters all come from document [Dynamicperformanceofpantograph/overheadlineinteractionfo r4spanoverlaps TPS/OCSportion.SIEMENS, 2006:4-21.], track parameter comes from document [Zhai Wanming, vehicle. orbit coupling kinetics .2007.], track irregularity parameter choose U.S. AAR1-6 level track spectrum, the emulation speed of a motor vehicle is chosen for 350km/h. The dynamic response of high-speed railway bow-net-Che-rail is carried out simulation calculation by the emulation method adopting the present invention to propose.

First according in specification sheets and claim 1) step, step 1, adopts Euler's Bernoulli Jacob's beam element simulating contact line and carrier cable, its parameter choose Beijing-Tianjin inter-city contact system, and according to Finite Element Method assembling quality and stiffness matrix, its kinetic equation is:

$M_C{\stackrel{\&CenterDot;\&CenterDot;}{X}}_C\left(t\right)+C_C{\stackrel{\&CenterDot;}{X}}_C\left(t\right)+K_C\left(t\right)X_C\left(t\right)=F_C(x,t)$

Wherein, M_T��C_T��K_TIt is respectively track quality, damping, stiffness matrix,X_TT () is respectively orbital acceleration, speed, displacement matrix, F_TT () is dynamic excitation.

Then according to 1) 1 step 2 in step, set up track model by modal superposition method, its kinetic equation is:

$M_T{\stackrel{\&CenterDot;\&CenterDot;}{X}}_T\left(t\right)+C_T{\stackrel{\&CenterDot;}{X}}_T\left(t\right)+K_T{X}_T\left(t\right)=F_T\left(t\right)$

Wherein, M_T��C_T��K_TIt is respectively track quality, damping, stiffness matrix,X_TT () is respectively orbital acceleration, speed, displacement matrix, F_TT () is dynamic excitation.

Again according to 1) in step 3 and Fig. 1, set up bow-vehicle dynamics model:

$M_V{\stackrel{\&CenterDot;\&CenterDot;}{X}}_V\left(t\right)+C_V{\stackrel{\&CenterDot;}{X}}_V\left(t\right)+K_V{X}_V\left(t\right)=F_V\left(t\right)$

Wherein, M_V��C_V��K_VIt is respectively bow-Che quality, damping, stiffness matrix,X_VT () is respectively bow-Che acceleration, speed, displacement matrix, F_VT () is dynamic excitation;

Subsequently, according to 2) method sets up track and bow net contact model, the mutual relationship between equation of constraint respectively in step, and the size of hertz constant G is chosen forWherein r is radius of wheel; Contact stiffness K_SIt is chosen for 82300N/m.

Last according to 3) in integral algorithm entirety bow-net-Che-rail system is solved. Fig. 2 lists the calculation result of bow net contact power, and Fig. 3 lists pantograph Uplifting amount, and Fig. 4 lists the displacement of osculatory point of contact. Can clearly be seen that from this three width figure the bow net response adopting the inventive method to calculate is very big by the impact of track quality, wherein fluctuate under AAR1 orbital plane quality maximum, and it is minimum to fluctuate under AAR6 orbital plane quality.

Claims (1)

1. high-speed railway bow-net-Che-rail vertical coupled Iarge-scale system Dynamic Modeling emulation method, high-speed railway pantograph-contact system-car body-track vertical coupled Iarge-scale system modeling and simulating is carried out when considering that bow net contact, wheel track contact and hang the influence factors such as rough non-linear character such as string different operating state simultaneously, with the mutual coupling reflected between bow net and track, comprise following concrete steps:

1) contact system, bow-Che, track kinetic model, is set up respectively;

Step 1. adopts Finite Element Method to set up contact system kinetic model, and its kinetic equation can represent and is:

$M_C{\stackrel{\&CenterDot;\&CenterDot;}{X}}_C\left(t\right)+C_C{\stackrel{\&CenterDot;}{X}}_C\left(t\right)+K_C\left(t\right)X_C\left(t\right)=F_C(x,t)$

Wherein, M_C��C_C��K_CIt is respectively contact system quality, damping, stiffness matrix,It is respectively contact system acceleration, speed, displacement matrix, F_C(x, t) is dynamic excitation;

Step 2. adopt mode respectively method set up track kinetic model, its kinetic equation can represent and is:

$M_T{\stackrel{\&CenterDot;\&CenterDot;}{X}}_T\left(t\right)+C_T{\stackrel{\&CenterDot;}{X}}_T\left(t\right)+K_T{X}_T\left(t\right)=F_T\left(t\right)$

Wherein, M_T��C_T��K_TIt is respectively track quality, damping, stiffness matrix,It is respectively orbital acceleration, speed, displacement matrix, F_TT () is dynamic excitation;

Step 3. adopts many body dynamics method establishment pantograph-body powered model, and its kinetic equation can represent and is:

$M_V{\stackrel{\&CenterDot;\&CenterDot;}{X}}_V\left(t\right)+C_V{\stackrel{\&CenterDot;}{X}}_V\left(t\right)+K_V{X}_V\left(t\right)=F_V\left(t\right)$

Wherein, M_V��C_V��K_VIt is respectively bow-Che quality, damping, stiffness matrix,It is respectively bow-Che acceleration, speed, displacement matrix, F_VT () is dynamic excitation;

2) bow net, track contact model, is built respectively

Step 1. adopts penalty function method to build bow net contact model:

$f_c\left(t\right)=\left\{\begin{array}{cc}{K}_S\left(y_1\right(t)-y_c(t\left)\right)& y_1\left(t\right)\&GreaterEqual;y_c\left(t\right)\\ 0& y_1\left(t\right)<y_c\left(t\right)\end{array}\right.$

Wherein, K_SFor bow net contact rigidity, y₁The displacement of (t) pantograph collector head, y_cT () is osculatory point of contact vertical deviation, f_cT () is bow net contact power,

Step 2. is according to hertz the Theory Construction Wheel-rail contact model:

$f_{wj}\left(t\right)=\left\{\begin{array}{cc}{\{\frac{1}{G}\&lsqb;w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)\&rsqb;\}}^{1.5}& w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)\&GreaterEqual;0\\ 0& w_r(x_{wj},t)-Z_{wj}\left(t\right)-w_0\left(t\right)<0\end{array}\right.$

Wherein G is hertz constant, f_wjT () is the contact force of jth wheel and track; w_r(x_wj, t) it is the vertical deviation of jth wheel, Z_wjT () is the vertical deviation of jth wheel; w₀T () is the static irregularity of track;

3), by method of value solving bow-net-Che-rail complicated coupling kinetics system being solved, the iterative algorithm in each time walks is as follows:

(1) point of contact of bow net and wheel track is determined according to running velocity and current time;

(2) reactive force f between track is calculated by Wheel-rail contact model_wj(t);

(3) adopt bow net coupling model coupling net-bow-truck system, and wheel rail force is applied in bow-net-truck system and calculates contact system response X_C(t) and pantograph-car body response X_V(t);

(4) X is responded according to car body_VT () and Wheel-rail contact model upgrade reactive force f between track_wj(t);

(5) track reactive force is applied to track model, calculates track response X_T(t), and judge convergency, if met, entering future time step, then returning step (2) if do not met;

4), display or subsequent processing device is inputed to by emulating result above.