CN116244980A - Rapid simulation method for three-dimensional dynamic contact behavior of pantograph rigid contact net - Google Patents
Rapid simulation method for three-dimensional dynamic contact behavior of pantograph rigid contact net Download PDFInfo
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Abstract
The invention discloses a quick simulation method of three-dimensional dynamic contact behavior of a pantograph rigid contact net, which specifically comprises the following steps: a rigid contact net model is established by adopting a beam unit and a three-dimensional spring unit, a pantograph reduction mass block model is established, and a pantograph-rigid contact net motion equation is established; calculating an initial equilibrium state of the system under the action of gravity by adopting a Newton iteration method, and calculating an elastic internal force vector, a tangential stiffness matrix and a generalized stiffness matrix of the system at the moment; calculating an arch net contact force vector of the current time step and a system coordinate vector of the next time step; judging whether the calculation of all time steps is finished, if so, outputting a contact force sequence and finishing the calculation, if not, updating the time step index and the system state, and returning to the previous step to perform the calculation of the subsequent time steps. The invention can greatly improve the simulation efficiency of the pantograph-rigid contact net system, obviously reduce the simulation time cost and ensure that the result has extremely high calculation precision.
Description
Technical Field
The invention belongs to the technical field of dynamic simulation of electrified railways, and particularly relates to a quick simulation method of three-dimensional dynamic contact behavior of a pantograph rigid contact net.
Background
The pantograph-rigid catenary system is an important way for an electrified train in a tunnel to acquire electric energy. Limited by the high cost and the harsh test conditions of practical line tests, the field of bow net dynamics is mainly based on finite element models for research work. Zhouning et al (Zhouning, huan, dong, etc.. Urban rail transit bow net system simulation model adaptability research [ J ]. Southwest university of traffic, 2017, 52 (2): 408-423) compares a variable stiffness model and a finite element model of a rigid contact net, and proves that the result obtained by the finite element model is more accurate under high-speed working conditions. Vera et al (C.Vera, B.Suarez, J.Paulin, et al, formulation model for the study of overhead rail current collector systems dynamics, focused on the design of a new conductor rail [ J ]. Veh.Syst.Dyn.2006, 44:595-614) have established a finite element model of rigid catenary using finite element software ANSYS. L. Chen et al (L.Chen, F.Duan, Y.Song, et al, assembly of dynamic interaction performance of high-speed pantograph and overhead conductor rail system [ J ]. IEEE Trans. Instrom. Meas.2022, 71:1-14) established a finite element model of a rigid catenary using Absolute Node Coordinates (ANCF) and solved the dynamic contact force of the catenary using Newmark method. In the existing modeling and simulation research of the pantograph-rigid catenary system, a penalty function method is adopted to simulate the contact behavior of the pantograph. The contact stiffness introduced by the method is an empirical parameter, the value of which significantly influences the simulation result of the model and is difficult to determine a proper value. In addition, the penalty function method also has the problem of virtual penetration between bow nets, so that a displacement result obtained by simulation is inaccurate. In addition, in the pantograph-rigid catenary simulation, only the vertical contact force is considered, and the change of the contact force direction in the three-dimensional space is not considered. Aiming at the problems, L.Chen et al (L.Chen, F.Duan, Y.Song, et al three-dimensional contact formulation for assessment of dynamic interaction of pantograph and overhead conductor rail system [ J ]. Veh.Syst.Dyn.2022:1-24.) establishes an accurate contact model between a pantograph and a rigid contact net based on a Lagrange multiplier constraint method, introduces a three-dimensional vector definition format of contact force in a global coordinate system, calculates normal contact force and tangential contact force, and fully considers the change of contact force direction caused by the vibration of the pantograph net. However, no matter the penalty function method or the accurate contact model is adopted to simulate the bow net contact, gradual iteration is required, a large amount of matrix operation is required to be performed in each iteration step, and the calculation time is long. In the accurate contact model, iteration is needed in the process of calculating the tangential force direction, the whole accurate contact model solving process is an explicit process, a smaller time step is needed to maintain stable convergence of calculation, and the whole calculation efficiency is low. When the optimization design research or batch simulation is carried out, the calculation time cost is huge, and the development of related research work is limited.
Disclosure of Invention
In order to improve the simulation calculation efficiency of a pantograph-rigid catenary system when a three-dimensional accurate calculation model is adopted, the invention provides a rapid simulation method of the three-dimensional dynamic contact behavior of the pantograph rigid catenary.
The invention discloses a quick simulation method of three-dimensional dynamic contact behavior of a pantograph rigid contact net, which comprises the following steps:
step 1: the beam unit is adopted to simulate a busbar and a contact line, the spring unit is adopted to simulate a suspension structure and a wire clamp, a rigid contact net finite element model is established, the pantograph model is established by adopting a mass block reduction method, and a pantograph-rigid contact net motion equation is established. The method comprises the following steps:
s11: according to the design parameters of the rigid catenary, adopting beam units to discrete the rigid catenary (the invention is applicable to various beam units), and determining the coordinate vector of each unit and each node; and calculating a mass matrix, a rigidity matrix, a damping matrix and a load vector of each unit according to the beam unit theory.
S12：Taking the suspension structure and the wire clamp as a whole, simulating by adopting a three-dimensional spring unit, and obtaining a mass matrix M of the three-dimensional spring unit s And a stiffness matrix K s The method comprises the following steps of:
wherein m is s K being equivalent mass of suspended structure x ，k y ，k z The equivalent stiffness of the three-dimensional spring on three coordinate axes of the global coordinate system XYZ is respectively.
S13: by adopting a mass block reduction method, a mass block model of the pantograph is established, and a motion equation of the three mass block models of the pantograph is as follows:
wherein m is 1 ,m 2 ,m 3 The mass of the bow head, the upper frame and the lower frame are respectively; c 1 ,c 2 ,c 3 Damping of the bow head, the upper frame and the lower frame respectively; k (k) 1 ,k 2 ,k 3 Rigidity of the bow head, the upper frame and the lower frame respectively; y is 1 ,y 2 ,y 3 The displacement of the bow head, the upper frame and the lower frame are respectively; f (F) L Is a static lifting force applied to the pantograph.
S14: the motion equation of the pantograph-rigid catenary system is constructed by a finite element standard assembly method as follows:
wherein M and C are respectively a mass matrix and a damping matrix of the whole pantograph-rigid catenary system;
the velocity and acceleration vectors of the whole system are respectively; q is the elastic internal force vector of the whole system; p is the external load vector applied to the system; the calculation formula of the elastic internal force vector of the system is as follows:
Q＝Ke (5)
wherein K is a system stiffness matrix, and e is a system coordinate vector.
Step 2: substituting the gravity load into an external load vector in a pantograph-rigid catenary motion equation, and calculating a coordinate vector e of the system in an initial equilibrium state under the action of gravity by adopting a Newton iteration method 0 The method comprises the steps of carrying out a first treatment on the surface of the According to the initial equilibrium state of the bow net system under the action of gravity, the elastic internal force vector Q of the system in the state is calculated in advance 0 System tangential stiffness matrix K in this state assembled t And a generalized stiffness matrix J, and performing sparsification treatment on the generalized stiffness matrix J. The expression of the system generalized stiffness matrix J is as follows:
wherein Δt is the iteration time step in the dynamic simulation process. The zero vector part plays a role of occupying space, and the numerical value of the zero vector part needs to be updated in the subsequent dynamic simulation, so that the memory is allocated in advance to reduce the time cost of memory reallocation.
Step 3: and calculating a contact force vector of the pantograph-rigid catenary system at the current time step and a system coordinate vector of the next time step.
S31: system elastic internal force Q of current time step is calculated by adopting linearization idea i And calculate the generalized load vector
The calculation formulas are respectively as follows:
Q i ＝Q 0 +K t (e i -e 0 ) (7)
wherein the index i is a time step index. At the initial moment, i.e. i=0, e i-1 Calculated from the following formula:
s32: calculating a contact force direction vector n using the estimated relative velocity i The calculation formula is
Wherein mu is the Coulomb friction coefficient between bow net and n n,i As a normal contact force direction vector,
wherein A is p,i And A c,i Tangential vectors of the pantograph head and the contact line, respectively.
n t,i For the estimated tangential force direction vector,
wherein v is i The estimated relative speed between the bow head and the contact line at the contact point is as follows:
wherein v is t Is a vehicle operating speed vector. G is a contact constraint matrix and is written
Defining the forward direction of the pantograph as the front, the reverse direction as the rear, n 1 The number of degrees of freedom, n, of all nodes behind the beam unit in contact on the rigid contact network 2 The number of degrees of freedom of all nodes in front of the beam unit in a contact state on the rigid contact net; s is S c A matrix of shape functions of the beam units in contact with each other, S p The method is used for calculating an auxiliary matrix of the vertical position of the bow head, and writing:
s33: assuming that the bow net system is in a contact state, updating the last row and the last column of the generalized stiffness matrix of the system, and carrying out LU decomposition on the final row and the last column, wherein the updating format is as follows:
wherein Δt is an iteration time step, i is an iteration index, and t= [ 0.1.0]Is an auxiliary vector. LU decomposition is carried out on J to obtain an upper triangular matrix J U And lower triangular matrix J L Satisfy J L ·J U ＝J。
S34: calculating the system coordinate vector of the current contact force and the next time step, wherein the calculation formula is as follows:
wherein U is i The coordinate vector and the contact force of the system are included, namely:
f i for the current time step total contact forceIs calculated from the following equation:
F i ＝f i ·n i (19)
judging the actual contact state between the pantograph and the rigid contact net by the positive and negative contact force, if f i If the bow net is not less than 0, the bow net is in a contact state, and the step 4 is entered; if f i And (3) if the bow net is less than 0, the bow net is in an off-line state, and the step S35 is performed.
S35: let f i ＝0，F i ＝[0 0 0] T And calculating the coordinate vector e of the next time step when the pantograph-catenary system is in an off-line state i+1 The calculation formula is
Step 4: judging whether the calculation of the contact force of all time steps is finished, if so, outputting a bow net contact force sequence of all time steps, and ending the calculation; if not, updating the position of the pantograph according to the running speed of the vehicle, updating the iteration time step index and the pantograph network state, returning to the step 3, and carrying out calculation of the next time step.
Compared with the prior art, the invention has the beneficial technical effects that:
the invention adopts a method for estimating the relative movement speed of the bow net, thereby avoiding the iteration link required by determining the contact force direction; the system is subjected to linearization treatment in an initial equilibrium state, so that the system rigidity matrix assembly process required by calculating the elastic internal force in each time step is avoided; sparse processing is carried out on the main matrix, LU decomposition is carried out on the system generalized stiffness matrix, and the calculation complexity is reduced; by delaying the contact state determination link, the additional calculation amount required for the contact state determination is avoided. Compared with the traditional pantograph-rigid contact net simulation method, the method can greatly improve the system simulation calculation efficiency, remarkably reduce the time cost required by simulation, and ensure that the result has extremely high calculation precision.
Drawings
Fig. 1 is a flow chart of a rapid simulation method of three-dimensional dynamic contact behavior of a pantograph rigid catenary.
FIG. 2 is a graph showing the comparison of the results of the fast simulation method according to the present invention and the conventional method.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
The embodiment is a simulation case of dynamic contact between a 30-span rigid contact net and a pantograph in a straight line section, and the running speed of a vehicle is 200km/h. The method provided by the invention is applicable to various beam units, in the embodiment, an Absolute Node Coordinate (ANCF) beam unit is adopted to establish a model of the rigid contact net, and a standard pantograph-rigid contact net three-dimensional contact force simulation method is respectively adopted to calculate the pantograph-rigid contact net contact force with the quick simulation method of the pantograph-rigid contact net three-dimensional dynamic contact behavior provided by the invention, and the calculation results of the two methods are compared. The specific parameters in the examples are shown in tables 1 and 2, and the coefficient of friction between the bow and the contact line is 0.3. In this embodiment, a right-hand rectangular coordinate system is adopted, and the forward direction of the train is set as the positive direction X, the positive direction Y is the vertical upward direction, and the direction Z is vertical to the track line center line.
Table 1 parameters of rigid catenary in examples
Table 2 example pantograph parameters
The flow of the invention is shown in figure 1, and the specific implementation process is as follows:
step 1: according to the parameters of the rigid catenary shown in table 1, a rigid catenary finite element model is established by adopting an absolute node coordinate beam unit (the invention is applicable to various beam units) and a three-dimensional spring unit, a pantograph model is established by adopting a mass block reduction method according to the parameters of the pantograph shown in table 2, and a pantograph-rigid catenary motion equation is established. The specific implementation method comprises the following steps:
s11: and taking the busbar and the contact line as a whole, dispersing the busbar and the contact line by adopting absolute node coordinate beam units according to the design parameters of the rigid contact net, and determining the coordinate vector of each unit and each node. And calculating a mass matrix, a rigidity matrix, a damping matrix and a load vector of each unit according to the absolute node coordinate beam unit theory.
S12: taking the suspension structure and the wire clamp as a whole, simulating by adopting a three-dimensional spring unit, and obtaining a mass matrix M of the three-dimensional spring unit s And a stiffness matrix K s The method comprises the following steps of:
wherein m is s K being equivalent mass of suspended structure x ，k y ，k z Equivalent stiffness of the three-dimensional spring on three coordinate axes of the global coordinate system XYZ is respectively shown;
s13: according to the parameters shown in table 2, a mass block model of the pantograph is established by adopting a mass block reduction method, and a motion equation of the three mass block models of the pantograph is as follows:
wherein m is 1 ,m 2 ,m 3 The mass of the bow head, the upper frame and the lower frame are respectively; c 1 ,c 2 ,c 3 Damping of the bow head, the upper frame and the lower frame respectively; k (k) 1 ,k 2 ,k 3 Rigidity of the bow head, the upper frame and the lower frame respectively; y is 1 ,y 2 ,y 3 The displacement of the bow head, the upper frame and the lower frame are respectively; f (F) L The static lifting force is applied to the pantograph;
s14: the motion equation of the pantograph-rigid catenary system is constructed by a finite element standard assembly method as follows:
wherein M and C are respectively a mass matrix and a damping matrix of the whole pantograph-rigid catenary system;
the velocity and acceleration vectors of the whole system are respectively; q is the elastic internal force vector of the whole system; p is the external load vector applied to the system; the calculation formula of the elastic internal force vector of the system is as follows:
wherein K is a system stiffness matrix, and e is a system coordinate vector.
Step 2: substituting the gravity load into an external load vector in a pantograph-rigid catenary motion equation, and calculating a coordinate vector e of the system in an initial equilibrium state under the action of gravity by adopting a Newton iteration method 0 The method comprises the steps of carrying out a first treatment on the surface of the According to the initial equilibrium state of the bow net system under the action of gravity, the elastic internal force vector Q of the system in the state is calculated in advance 0 System tangential stiffness matrix K in this state assembled t And a generalized stiffness matrix J, and performing sparsification treatment on the generalized stiffness matrix J. The expression of the system generalized stiffness matrix J is as follows:
wherein Δt is the iteration time step in the dynamic simulation process. The zero vector part plays a role of occupying space, and the numerical value of the zero vector part needs to be updated in the subsequent dynamic simulation, so that the memory is allocated in advance to reduce the time cost of memory reallocation.
Step 3: and calculating a contact force vector of the pantograph-rigid catenary system at the current time step and a system coordinate vector of the next time step.
S31: system elastic internal force Q of current time step is calculated by adopting linearization idea i And calculate the generalized load vector
The calculation formulas are respectively as follows:
Q i ＝Q 0 +K t (e i -e 0 ) (7)
wherein the index i is a time step index. At the initial moment, i.e. i=0, e i-1 Calculated from the following formula:
s32: calculating a contact force direction vector n using the estimated relative velocity i The calculation formula is
Wherein mu is the Coulomb friction coefficient between bow net and n n,i As a normal contact force direction vector,
wherein A is p,i And A c,i Tangential vectors of the pantograph head and the contact line, respectively.
n t,i For the estimated tangential force direction vector,
wherein v is i The estimated relative speed between the bow head and the contact line at the contact point is as follows:
wherein v is t Is a vehicle operating speed vector. G is a contact constraint matrix and is written
Defining the forward direction of the pantograph as the front, the reverse direction as the rear, n 1 The number of degrees of freedom, n, of all nodes behind the beam unit in contact on the rigid contact network 2 The number of degrees of freedom of all nodes in front of the beam unit in a contact state on the rigid contact net; s is S c A matrix of shape functions of the beam units in contact with each other, S p The method is used for calculating an auxiliary matrix of the vertical position of the bow head, and writing:
s33: assuming that the bow net system is in a contact state, updating the last row and the last column of the generalized stiffness matrix of the system, and carrying out LU decomposition on the final row and the last column, wherein the updating format is as follows:
wherein Δt is an iteration time step, i is an iteration index, and t= [ 0.1.0]Is an auxiliary vector. LU decomposition is carried out on J to obtain an upper triangular matrix J U And lower triangular matrix J L Satisfy J L ·J U ＝J。
S34: calculating the system coordinate vector of the current contact force and the next time step, wherein the calculation formula is as follows:
wherein U is i Coordinate vector and contact force magnitude comprising system
f i For the magnitude of the total contact force for the current time step, the total contact force vector is calculated by the following equation:
F i ＝f i ·n i (19)
judging the actual contact state between the pantograph and the rigid contact net by the positive and negative contact force, if f i If the bow net is not less than 0, the bow net is in a contact state, and the step 4 is entered; if f i And (3) if the bow net is less than 0, the bow net is in an off-line state, and the step S35 is performed.
S35: let f i ＝0，F i ＝[0 0 0] T And calculating the coordinate vector e of the next time step when the pantograph-catenary system is in an off-line state i+1 The calculation formula is
Step 4: judging whether the calculation of the contact force of all time steps is finished, if so, outputting a bow net contact force sequence of all time steps, and ending the calculation; if not, updating the position of the pantograph according to the running speed of the vehicle, updating the iteration time step index and the pantograph network state, returning to the step 3, and carrying out calculation of the next time step.
Through the steps, the contact pressure between the pantograph and the rigid catenary can be rapidly calculated. The simulation of the model in table 1 and table 2 is carried out by adopting a standard pantograph-rigid catenary three-dimensional contact force simulation method, the results are compared with the results of the quick simulation method provided by the invention, the total contact force obtained by the two methods is compared with the total contact force obtained by the two methods, as shown in fig. 2, and the statistical comparison of the results is shown in table 3.
Table 3 comparison of the results obtained by the two methods
It can be seen that the result obtained by the rapid simulation method is basically coincident with the result obtained by the standard calculation method, and the absolute value of the relative deviation of the total contact force is only 0.48% at maximum, which shows that the rapid simulation method provided by the invention hardly affects the result precision. The calculation time required by the standard simulation method is 2092.89s, and the calculation time of the quick simulation method is 48.75s, which is only 2.33% of the standard method, so that the calculation time cost of 97.67% is saved. The result shows that the quick simulation method for the three-dimensional dynamic contact behavior of the pantograph-rigid catenary can obviously reduce the calculation time cost of simulation on the basis of basically not influencing the result precision.
Claims (4)
1. A quick simulation method of three-dimensional dynamic contact behavior of a pantograph rigid contact net is characterized by comprising the following steps:
step 1: simulating a busbar and a contact line by adopting a beam unit, simulating a suspension structure and a wire clamp by adopting a spring unit, establishing a finite element model of the rigid contact net, establishing a pantograph model by adopting a mass block reduction method, and constructing a pantograph-rigid contact net motion equation;
step 2: substituting the gravity load into an external load vector in a pantograph-rigid catenary motion equation, and calculating a coordinate vector of the system in an initial equilibrium state under the action of gravity by adopting a Newton iteration method; according to an initial equilibrium state of the bow net system under the action of gravity, an elastic internal force vector of the system in the state is calculated in advance, a system tangential stiffness matrix and a generalized stiffness matrix in the state are assembled, and sparse processing is carried out on the system tangential stiffness matrix and the generalized stiffness matrix;
step 3: calculating a contact force vector of a pantograph-rigid catenary system at the current time step and a system coordinate vector of the next time step;
step 4: judging whether the calculation of the contact force of all time steps is finished, if so, outputting a bow net contact force sequence of all time steps, and ending the calculation; if not, updating the position of the pantograph according to the running speed of the vehicle, updating the iteration time step index and the pantograph network state, returning to the step 3, and carrying out calculation of the next time step.
2. The method for rapidly simulating three-dimensional dynamic contact behavior of a pantograph rigid catenary according to claim 1, wherein the step 1 is specifically:
s11: dispersing the rigid catenary by adopting beam units according to the design parameters of the rigid catenary, and determining coordinate vectors of each unit and each node; according to the beam unit theory, calculating a mass matrix, a rigidity matrix, a damping matrix and a load vector of each unit;
s12: taking the suspension structure and the wire clamp as a whole, simulating by adopting a three-dimensional spring unit, and obtaining a mass matrix M of the three-dimensional spring unit s And a stiffness matrix K s The method comprises the following steps of:
wherein m is s K being equivalent mass of suspended structure x ，k y ，k z Equivalent stiffness of the three-dimensional spring on three coordinate axes of the global coordinate system XYZ is respectively shown;
s13: by adopting a mass block reduction method, a mass block model of the pantograph is established, and a motion equation of the three mass block models of the pantograph is as follows:
wherein m is 1 ,m 2 ,m 3 The mass of the bow head, the upper frame and the lower frame are respectively; c 1 ,c 2 ,c 3 Damping of the bow head, the upper frame and the lower frame respectively; k (k) 1 ,k 2 ,k 3 Rigidity of the bow head, the upper frame and the lower frame respectively; y is 1 ,y 2 ,y 3 The displacement of the bow head, the upper frame and the lower frame are respectively; f (F) L The static lifting force is applied to the pantograph;
s14: the motion equation of the pantograph-rigid catenary system is constructed by a finite element standard assembly method as follows:
wherein M and C are respectively a mass matrix and a damping matrix of the whole pantograph-rigid catenary system;
the velocity and acceleration vectors of the whole system are respectively; q is the elastic internal force vector of the whole system; p is the external load vector applied to the system; the calculation formula of the elastic internal force vector of the system is as follows:
Q＝Ke (5)
wherein K is a system stiffness matrix, and e is a system coordinate vector.
3. The rapid simulation method of three-dimensional dynamic contact behavior of a pantograph rigid catenary according to claim 2, wherein the expression of the system generalized stiffness matrix J in step 2 is:
wherein Δt is the iteration time step in the dynamic simulation process.
4. The rapid simulation method of three-dimensional dynamic contact behavior of a pantograph rigid catenary according to claim 3, wherein the step 3 is specifically:
s31: system elastic internal force Q of current time step is calculated by adopting linearization idea i And calculate the generalized load vector
The calculation formulas are respectively as follows:
Q i ＝Q 0 +K t (e i -e 0 ) (7)
wherein, the subscript i is a time step index, e 0 Is the coordinate vector of the system in the initial equilibrium state under the action of gravity, Q 0 Is the elastic internal force vector, K, of the system in this state t The tangential stiffness matrix of the system in this state; p (P) i An external load vector representing step i;
at the initial moment, i.e. i=0, e i-1 Calculated from the following formula:
s32: calculating a contact force direction vector n using the estimated relative velocity i The calculation formula is as follows:
wherein mu is the Coulomb friction coefficient between bow net and n n,i As a normal contact force direction vector,
wherein A is p,i And A c,i Tangential vectors of the pantograph head and the contact line respectively;
n t,i for the estimated tangential force direction vector,
wherein v is i The estimated relative speed between the bow head and the contact line at the contact point is as follows:
wherein v is t Is a vehicle operating speed vector; g is a contact constraint matrix, written:
defining the forward direction of the pantograph as the front, the reverse direction as the rear, n 1 The number of degrees of freedom, n, of all nodes behind the beam unit in contact on the rigid contact network 2 The number of degrees of freedom of all nodes in front of the beam unit in a contact state on the rigid contact net; s is S c A matrix of shape functions of the beam units in contact with each other, S p The method is used for calculating an auxiliary matrix of the vertical position of the bow head, and writing:
s33: assuming that the bow net system is in a contact state, updating the last row and the last column of the generalized stiffness matrix of the system, and carrying out LU decomposition on the final row and the last column, wherein the updating format is as follows:
wherein Δt is an iteration time step, i is an iteration index, and t= [010 ]]As auxiliary vector, LU decomposition is carried out on J to obtain an upper triangular matrix J U And lower triangular matrix J L Satisfy J L ·J U ＝J；
S34: calculating the system coordinate vector of the current contact force and the next time step, wherein the calculation formula is as follows:
wherein U is i The coordinate vector and the contact force of the system are included, namely:
f i for the magnitude of the total contact force for the current time step, the total contact force vector is calculated by the following equation:
F i ＝f i ·n i (19)
judging the actual contact state between the pantograph and the rigid contact net by the positive and negative contact force, if f i If the bow net is not less than 0, the bow net is in a contact state, and the step 4 is entered; if f i If the bow net is less than 0, the bow net is in an off-line state, and the step S35 is performed;
s35: let f i ＝0，F i ＝[000] T And calculating the coordinate vector e of the next time step when the pantograph-catenary system is in an off-line state i+1 The calculation formula is
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117610383A (en) * | 2024-01-22 | 2024-02-27 | 中铁电气化勘测设计研究院有限公司 | Rigid contact net parameter selection method and parameter result based on bow net coupling simulation |
| CN117894471A (en) * | 2024-03-15 | 2024-04-16 | 柏意慧心(杭州)网络科技有限公司 | Method, computing device, and medium for simulating the configuration of a stent release contact |
-
2022
- 2022-12-06 CN CN202211552706.XA patent/CN116244980A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117610383A (en) * | 2024-01-22 | 2024-02-27 | 中铁电气化勘测设计研究院有限公司 | Rigid contact net parameter selection method and parameter result based on bow net coupling simulation |
| CN117610383B (en) * | 2024-01-22 | 2024-05-17 | 中铁电气化勘测设计研究院有限公司 | Rigid contact net parameter selection method based on bow net coupling simulation |
| CN117894471A (en) * | 2024-03-15 | 2024-04-16 | 柏意慧心(杭州)网络科技有限公司 | Method, computing device, and medium for simulating the configuration of a stent release contact |
| CN117894471B (en) * | 2024-03-15 | 2024-06-07 | 柏意慧心(杭州)网络科技有限公司 | Method, computing device, and medium for simulating the configuration of a stent release contact |
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