CN117291077A - Damping compensation-based catenary windproof method - Google Patents
Damping compensation-based catenary windproof method Download PDFInfo
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Abstract
The invention provides a catenary windproof method based on damping compensation, and relates to the technical field of electrified railway catenary. The method comprises the following steps: simulating the large deformation of the contact net under the action of environmental wind; constructing a finite element model of the flexible contact net, and calculating the initial form of the flexible contact net so as to obtain accurate initial dynamic response of the pantograph-contact net; setting a motion equation in an equilibrium state, and calculating the coupling contact pressure of the pantograph and the overhead contact system according to an overhead contact system model under the action of environmental wind; constructing a catenary wind load disturbance model, calculating and obtaining a catenary model under the action of environmental wind according to aerodynamic force acting on catenary cues and initial dynamic response of a pantograph-catenary system; damping compensation is applied to positioning points on the contact net, a damping compensation numerical range that the contact pressure meets constraint conditions is calculated, and the maximum lifting amount is set. The invention can reduce the disturbance influence degree of environmental wind on the contact network on the premise of ensuring stable current receiving of the bow net.
Description
Technical Field
The invention relates to the technical field of electrified railway overhead contact systems, in particular to a overhead contact system windproof method based on damping compensation.
Background
In an electrified railway, the contact net is not only a mechanical slideway of a pantograph of the motor train unit, but also a unique energy channel of the motor train unit. However, the overhead net is very sensitive to environmental disturbance as a high-flexibility and large-span overhead net structure. Particularly, due to the special clue appearance design, the contact net is extremely easy to shake and wave under the action of environmental wind load, so that the pantograph and the contact net cannot keep stable contact, poor power supply and even power interruption of the motor train unit are caused, and the operation safety of a railway is seriously threatened. Therefore, it is needed to find an effective method for suppressing the wind vibration of the contact net environment so as to reduce the influence of the wind field around the line on the running safety of the motor train unit.
The current academic world and the engineering world at home and abroad mainly start to restrain wind vibration of the contact net environment from two aspects of structural parameter optimization and thread section control. If the span and the tension of the overhead contact system are optimized to change the natural frequency of the overhead contact system, the main disturbance frequency of an environmental wind field is avoided, and the wind vibration response of the overhead contact system under the excitation of environmental wind is reduced; the integral rigidity of the contact net is improved, so that the vibration amplitude of the contact net under the disturbance of the environmental wind is reduced. By comparing and analyzing the tension optimization scheme of the overhead contact system under the disturbance of the environmental wind, the improvement of the tension level is found to be an effective overhead contact system windproof measure. However, the improvement of the tension of the contact net not only puts higher demands on the tensile strength of the material of the contact line and the carrier cable, but also inevitably causes the increase of the load of the whole structure of the contact net, thereby shortening the fatigue life of parts and the like.
Damping compensation is a common wind-proof vibration reduction method for high-rise buildings and large-span bridge structures, but the application of the method in electrified railway overhead contact systems is less. When the existing damping compensation mode for the pantograph is directly applied to the overhead contact line, the unreasonable damping compensation value can cause deterioration of the current receiving quality of the pantograph. Therefore, how to introduce additional parameter compensation to reduce the influence degree of the environmental wind disturbance on the contact network on the premise of ensuring the current-carrying stability of the bow net is still to be solved.
Disclosure of Invention
The invention aims to provide a catenary wind prevention method based on damping compensation, which can reduce the disturbance influence degree of environmental wind on a contact network on the premise of ensuring stable current receiving of an arched network.
The invention is realized in the following way:
in a first aspect, the present application provides a method for preventing wind of a catenary based on damping compensation, including the following steps:
constructing a beam unit model of the flexible contact net by an absolute node coordinate method, and simulating the large deformation of the absolute node of the contact net under the action of environmental wind;
constructing a finite element model of the flexible contact net, and calculating the initial form of the flexible contact net according to the deformation of the contact net under the gravity load so as to obtain the accurate initial dynamic response of a pantograph-contact net system;
setting a motion equation in a balance state, and calculating motion constraint of the pantograph and the overhead line according to an overhead line model under the action of environmental wind, namely coupling contact pressure of the pantograph and the overhead line, so as to evaluate the current receiving quality of a pantograph-overhead line system under the environmental wind;
constructing a catenary wind load disturbance model, calculating aerodynamic force acting on catenary cues, and obtaining a catenary model under the action of environmental wind according to the aerodynamic force acting on the catenary cues and the initial dynamic response of a pantograph-catenary system;
damping compensation is applied to positioning points on the contact net, a damping compensation numerical range that the coupling contact pressure of the pantograph and the contact net under the action of environmental wind meets constraint conditions is calculated, and the maximum lifting amount of the contact line at the positioning points is set.
Further, the constructing the absolute node coordinate method beam unit model of the flexible contact net comprises the following steps of:
according to the formula:
obtaining a beam unit e of the flexible contact net; wherein χ is the local position variable of the beam unit, the range is [0,l ], and l is the unit length; i is a node label; j is a node label; (x, y, z) is the three-dimensional spatial coordinates of the node.
Further, the construction of the finite element model of the flexible contact net, and the calculation of the initial form of the flexible contact net according to the deformation of the contact net under the gravity load so as to obtain the accurate initial dynamic response of the pantograph-contact net system, comprises the following steps:
according to the formula:
r＝S e
obtaining an initial form matrix r of the flexible contact net; wherein S is a shape function matrix,
wherein S is 1 ＝1-3ξ 2 +2ξ 3 ，S 2 ＝l(ξ-2ξ 2 +ξ 3 )，S 3 ＝3ξ 2 -2ξ 3 ，S 4 ＝l(ξ 3 -ξ 2 ) The method comprises the steps of carrying out a first treatment on the surface of the ζ=χ/l; l is the unit length;
according to the formula:
obtaining the strain capacity U of the catenary cue unit and the generalized elastic unit Q of the catenary cue unit; wherein,e is Young's modulus of a contact net thread unit, A is thread sectional area, and I is moment of inertia of the contact net thread; k (K) e Representing a cell stiffness matrix;
integrating generalized elastic units Q of the contact net clue units to obtain a correlation matrix K of the degree of freedom increment delta e of the contact net T And an initial length increment Δl 0 Is a correlation matrix K of (1) L ；
According to the formula:
obtaining a node unbalanced force increment delta F; wherein Δe represents the degree of freedom increment;
according to the formula:
obtaining the increment delta F of the global unbalance force of the node unbalance force increment delta F G The method comprises the steps of carrying out a first treatment on the surface of the Wherein,a global stiffness matrix that is a displacement delta vector; />A global stiffness matrix that is an initial length increment; deltaU c The stress increment matrix is the stress increment matrix of the contact net;
delta DeltaF according to global imbalance force G And obtaining the displacement and the initial length of all nodes of the contact net, and obtaining the initial form of the contact net.
Further, the above equation of motion under the equilibrium state is set, and the motion constraint of the pantograph and the catenary, that is, the coupling contact pressure of the pantograph and the catenary, is calculated according to the catenary model under the action of the environmental wind, so as to evaluate the current-collecting quality of the pantograph-catenary system under the environmental wind, including the following steps:
the equation of motion in equilibrium is as follows:
wherein,representing the pantograph head speed; />Representing the speed of the upper frame of the pantograph; />Representing the speed of the lower frame of the pantograph; />Indicating the acceleration of the lower frame of the pantograph; />Representing the upper frame acceleration of the pantograph; />Representing the pantograph head acceleration; m represents the pantograph reduction mass, c represents the pantograph reduction damping, k represents the pantograph reduction stiffness, including ( 1 Bow head, (. Cndot.) the head of the bow 2 Upper frame, ( 3 Lower frame (.) 12 Coupling parameters for the bow and the upper frame; (. Cndot. 21 Parameters for coupling the upper frame with the bow head, (-) 23 The upper frame and the lower frame are coupled with parameters; (. Cndot. 32 Coupling parameters for the lower frame and the upper frame;
according to the formula:
F C ＝K S ·(y 1 -y c )
obtaining the coupling contact pressure F of the pantograph and the contact net c The method comprises the steps of carrying out a first treatment on the surface of the Wherein y is 1 For vertical displacement of bow head, y c For vertical displacement of contact line and bow head contact point, K S Is equivalent coupling rigidity between the pantograph head and the contact line.
Further, the constructing the catenary wind load disturbance model, calculating aerodynamic force acting on catenary clues, and obtaining the catenary model under the action of environmental wind according to the aerodynamic force acting on catenary clues and initial dynamic response of the pantograph-catenary system comprises:
according to the formula:
obtaining aerodynamic force F acting in the transverse direction of the contact net wire x And act asAerodynamic force F used in longitudinal direction of contact net wire y The method comprises the steps of carrying out a first treatment on the surface of the Wherein F is D Aerodynamic resistance of the catenary wire; f (F) L The aerodynamic lift force of the contact net clue is that alpha is the wind attack angle;
aerodynamic force F acting in transverse direction of contact net wire x And aerodynamic force F acting on the contact net wire in the longitudinal direction y And (5) sending the model into a finite element model of the flexible contact net to obtain the contact net model under the action of environmental wind.
Further, the above-mentioned applying damping compensation at the setpoint on the contact net, calculating the damping compensation numerical range that the coupling contact pressure of the pantograph and the catenary under the effect of the environmental wind satisfies the constraint condition, setting the maximum lifting amount of the contact line at the setpoint includes: f (F) max ≤F m +3σ，F min And the maximum lifting amount of the contact line at the positioning point is less than 120mm and is more than or equal to 20N. Wherein F is max For maximum contact pressure, F m For the average contact pressure, F min Sigma is the standard deviation of the contact pressure, which is the minimum value of the contact pressure.
In a second aspect, the present application provides an electronic device comprising a memory for storing one or more programs; a processor; the method according to any of the first aspects is implemented when the one or more programs are executed by the processor.
Compared with the prior art, the invention has at least the following advantages or beneficial effects:
the invention provides a catenary windproof method based on damping compensation, which provides a calculation method of a catenary damping compensation numerical range, simplifies calculation of the catenary damping compensation numerical range, reduces influence of environmental wind disturbance on a contact network on the premise of ensuring stable current receiving of a pantograph catenary system, and is beneficial to enhancing operation stability and operation safety of an electrified railway motor train unit in a high wind area; the current-receiving quality of the arch net is ensured, and the damping compensation value is more reasonable.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a catenary windproof method based on damping compensation according to the invention;
fig. 2 is a schematic diagram of a catenary beam unit model based on an absolute node coordinate method in an embodiment of the present invention;
fig. 3 is a schematic diagram of an initial form calculation result of a finite element model of a catenary in an embodiment of the present invention;
fig. 4 is a schematic diagram of a damping compensation application position of a catenary according to an embodiment of the present invention;
FIG. 5 is a graph showing minimum distribution of contact pressure statistics under different damping compensations according to an embodiment of the present invention;
FIG. 6 is a graph of the standard differential distribution of contact pressure under different damping compensations in an embodiment of the present invention;
fig. 7 is a graph showing the variation of the contact line lifting amount of the contact line at the locating point of the contact line before and after damping compensation in the embodiment of the invention;
FIG. 8 is a graph showing the time domain distribution of contact pressure of an archwire system under the influence of environmental wind before and after damping compensation in an embodiment of the present invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, which are generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, as provided in the accompanying drawings, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, are intended to be within the scope of the present application. Some embodiments of the present application are described in detail below with reference to the accompanying drawings. The various embodiments and features of the embodiments described below may be combined with one another without conflict.
Examples
Referring to fig. 1, the method for preventing wind of the overhead contact system based on damping compensation comprises the following steps:
constructing a beam unit model of the flexible contact net by an absolute node coordinate method, and simulating the large deformation of the absolute node of the contact net under the action of environmental wind;
as shown in fig. 2, constructing a beam unit model of a flexible catenary by an absolute node coordinate method, and simulating large deformation of an absolute node of the catenary under the action of environmental wind comprises:
according to the formula:
obtaining a beam unit e of the flexible contact net; wherein χ is the local position variable of the beam unit, the range is [0,l ], and l is the unit length; i is a node label; j is a node label; (x, y, z) is the three-dimensional spatial coordinates of the node.
The overhead contact line clue is provided with beam units, and the deformation of the overhead contact line calculated by the beam units can reflect the large deformation behavior of the overhead contact line under the action of environmental wind, so that the subsequent calculation is convenient.
Constructing a finite element model of the flexible contact net, and calculating the initial form of the flexible contact net according to the deformation of the contact net under the gravity load so as to obtain the accurate initial dynamic response of a pantograph-contact net system;
as shown in fig. 3, constructing a finite element model of the flexible catenary, and calculating an initial form of the flexible catenary according to deformation of the catenary under a gravity load to obtain an accurate initial dynamic response of a pantograph-catenary system, wherein the method comprises the following steps:
according to the formula:
r＝S e
obtaining an initial form matrix r of the flexible contact net; wherein S is a shape function matrix,
wherein S is 1 ＝1-3ξ 2 +2ξ 3 ，S 2 ＝l(ξ-2ξ 2 +ξ 3 )，S 3 ＝3ξ 2 -2ξ 3 ，S 4 ＝l(ξ 3 -ξ 2 ) The method comprises the steps of carrying out a first treatment on the surface of the ζ=χ/l; l is the unit length;
according to the formula:
obtaining the strain capacity U of the catenary cue unit and the generalized elastic unit Q of the catenary cue unit; wherein,e is Young's modulus of a contact net thread unit, A is thread sectional area, and I is moment of inertia of the contact net thread; k (K) e Representing a cell stiffness matrix;
integrating generalized elastic units Q of the contact net clue units to obtain a correlation matrix K of the degree of freedom increment delta e of the contact net T And an initial length increment Δl 0 Is a correlation matrix K of (1) L ；
According to the formula:
obtaining a node unbalanced force increment delta F; wherein Δe represents the degree of freedom increment;
according to the formula:
obtaining the increment delta F of the global unbalance force of the node unbalance force increment delta F G The method comprises the steps of carrying out a first treatment on the surface of the Wherein,a global stiffness matrix that is a displacement delta vector; />A global stiffness matrix that is an initial length increment; deltaU c The stress increment matrix is the stress increment matrix of the contact net;
delta DeltaF according to global imbalance force G And obtaining the displacement and the initial length of all nodes of the contact net, and obtaining the initial form of the contact net.
The initial form of the contact net is calculated, so that the deformation of the contact net caused by environmental wind can be obtained, the initial form of the contact net is calculated through the strain capacity and the generalized elastic unit of the contact net clue unit, and the form of the contact net can be reflected accurately.
Constructing a catenary wind load disturbance model, calculating aerodynamic force acting on catenary cues, and obtaining a catenary model under the action of environmental wind according to the aerodynamic force acting on the catenary cues and the initial dynamic response of a pantograph-catenary system;
constructing a catenary wind load disturbance model, calculating aerodynamic force acting on catenary cues, and obtaining a catenary model under the action of environmental wind according to the aerodynamic force acting on the catenary cues and the initial dynamic response of a pantograph-catenary system, wherein the method comprises the following steps of:
according to the formula:
obtaining aerodynamic force F acting in the transverse direction of the contact net wire x And aerodynamic force F acting on the contact net wire in the longitudinal direction y The method comprises the steps of carrying out a first treatment on the surface of the Wherein F is D Aerodynamic resistance of the catenary wire; f (F) L The aerodynamic lift force of the contact net clue is that alpha is the wind attack angle;
aerodynamic force F acting in transverse direction of contact net wire x And aerodynamic force F acting on the contact net wire in the longitudinal direction y And (5) sending the model into a finite element model of the flexible contact net to obtain the contact net model under the action of environmental wind.
Setting a motion equation in a balance state, and calculating motion constraint of the pantograph and the overhead line according to an overhead line model under the action of environmental wind, namely coupling contact pressure of the pantograph and the overhead line, so as to evaluate the current receiving quality of a pantograph-overhead line system under the environmental wind;
setting a motion equation in a balance state and calculating motion constraint of the pantograph and the overhead contact line comprises the following steps:
the equation of motion in equilibrium is as follows:
wherein,representing the pantograph head speed; />Representing the speed of the upper frame of the pantograph; />Representing the speed of the lower frame of the pantograph; />Indicating the acceleration of the lower frame of the pantograph; />Representing the upper frame acceleration of the pantograph; />Representing the pantograph head acceleration; m represents the pantograph reduction mass, c represents the pantograph reduction damping, k represents the pantograph reduction stiffness, including ( 1 Bow head, (. Cndot.) the head of the bow 2 Upper frame, ( 3 Lower frame (DEG)) 12 Coupling parameters for the bow and the upper frame; (. Cndot. 21 Parameters for coupling the upper frame with the bow head, (-) 23 The upper frame and the lower frame are coupled with parameters; (. Cndot. 32 Coupling parameters for the lower frame and the upper frame;
according to the formula:
F C ＝K S ·(y 1 -y c )
obtaining the coupling contact pressure F of the pantograph and the contact net c The method comprises the steps of carrying out a first treatment on the surface of the Wherein y is 1 For vertical displacement of bow head, y c For vertical displacement of contact line and bow head contact point, K S Is equivalent coupling rigidity between the pantograph head and the contact line.
The pressure of wind that the contact net receives includes the pressure of pantograph in addition to the exemplary, combines the two, can obtain the contact net hand size that has more practical meaning, and when setting up damping compensation, it is more accurate, more convincing.
As shown in fig. 4, damping compensation is applied to a positioning point on the contact net, a damping compensation numerical range that the coupling contact pressure of the pantograph and the contact net under the action of environmental wind meets constraint conditions is calculated, and the maximum lifting amount of the contact line at the positioning point is set.
Damping compensation is applied to a positioning point on a contact net, a damping compensation numerical range that the coupling contact pressure of a pantograph and the contact net under the action of environmental wind meets constraint conditions is calculated, and the maximum lifting amount of the contact line at the positioning point is set, wherein the maximum lifting amount comprises the following steps: f (F) max ≤F m +3σ，F min And the maximum lifting amount of the contact line at the positioning point is less than 120mm and is more than or equal to 20N. Wherein F is max For maximum contact pressure, F m For the average contact pressure, F min Sigma is the standard deviation of the contact pressure, which is the minimum value of the contact pressure.
The minimum distribution of the contact pressure of the bow net system obtained by the method under the environmental wind excitation shown in figure 5 can know that the reasonable numerical range of damping compensation is in the range of 40-320 N.s/m according to constraint conditions; FIG. 6 shows standard deviation distribution of contact pressure of the bow net system under different damping compensations, wherein the reasonable numerical range of the damping compensations is within 250 N.m/s according to constraint conditions, and the reasonable numerical range of the damping compensations of the contact net is set within 40-250 N.m/s; fig. 7 shows that the contact line lifting amount at the contact line positioning point under damping compensation meets the constraint condition, namely the maximum lifting amount of the contact line at the positioning point is less than 120mm, and the damping compensation can obviously reduce the contact line lifting amount at the positioning point; fig. 8 shows the comparison result of the time domain statistics of the contact pressure of the front and rear bow net systems under the damping compensation of the environmental wind disturbance, and it can be seen that the contact pressure fluctuation caused by the high-speed operation of the environmental wind and the bow net can be effectively reduced after the damping compensation of the contact net is performed.
In summary, the embodiment of the application provides the method for calculating the damping compensation numerical range of the overhead contact system based on the damping compensation, so that the calculation of the damping compensation numerical range of the overhead contact system is simplified, the influence of environmental wind-induced disturbance on the overhead contact system is reduced on the premise of ensuring the stable current-carrying of the overhead contact system of the pantograph, and the running stability and the running safety of the electrified railway motor train unit in a high wind area are improved; the current-receiving quality of the arch net is ensured, and the damping compensation value is more reasonable.
It will be evident to those skilled in the art that the present application is not limited to the details of the foregoing illustrative embodiments, and that the present application may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Claims (7)
1. The catenary windproof method based on damping compensation is characterized by comprising the following steps of:
constructing a beam unit model of the flexible contact net by an absolute node coordinate method, and simulating the large deformation of the absolute node of the contact net under the action of environmental wind;
constructing a finite element model of the flexible contact net, and calculating the initial form of the flexible contact net according to the deformation of the contact net under the gravity load so as to obtain the accurate initial dynamic response of a pantograph-contact net system;
constructing a catenary wind load disturbance model, calculating aerodynamic force acting on catenary cues, obtaining a catenary model under the action of environmental wind according to the aerodynamic force acting on the catenary cues and the initial dynamic response of a pantograph-catenary system, and obtaining a catenary model under the action of the environmental wind according to the aerodynamic force acting on the catenary cues and the initial dynamic response of the pantograph-catenary system;
setting a motion equation in a balance state, and calculating motion constraint of the pantograph and the overhead line according to an overhead line model under the action of environmental wind, namely coupling contact pressure of the pantograph and the overhead line;
damping compensation is applied to positioning points on the contact net, a damping compensation numerical range that the coupling contact pressure of the pantograph and the contact net under the action of environmental wind meets constraint conditions is calculated, and the maximum lifting amount of the contact line at the positioning points is set.
2. The method for preventing wind of a catenary based on damping compensation according to claim 1, wherein the constructing a beam unit model of an absolute node coordinate method of the flexible catenary, and simulating the large deformation of the absolute node of the catenary under the action of environmental wind comprises:
according to the formula:
obtaining a beam unit e of the flexible contact net; wherein χ is the local position variable of the beam unit, the range is [0,l ], and l is the unit length; i is a node label; j is a node label; (x, y, z) is the three-dimensional spatial coordinates of the node.
3. The method for preventing wind of a catenary based on damping compensation according to claim 2, wherein the constructing a finite element model of the catenary, calculating an initial shape of the catenary according to deformation of the catenary under a gravity load, so as to obtain an accurate initial dynamic response of a pantograph-catenary system, comprises the following steps:
according to the formula:
r＝Se
obtaining an initial form matrix r of the flexible contact net; wherein S is a shape function matrix,
wherein S is 1 ＝1-3ξ 2 +2ξ 3 ，S 2 ＝l(ξ-2ξ 2 +ξ 3 )，S 3 ＝3ξ 2 -2ξ 3 ，S 4 ＝l(ξ 3 -ξ 2 ) The method comprises the steps of carrying out a first treatment on the surface of the ζ=χ/l; l is the unit length;
according to the formula:
obtaining the strain capacity U of the catenary cue unit and the generalized elastic unit Q of the catenary cue unit; wherein,e is Young's modulus of a contact net thread unit, A is thread sectional area, and I is moment of inertia of the contact net thread; k (K) e Representing a cell stiffness matrix;
integrating generalized elastic units Q of the contact net clue units to obtain a correlation matrix K of the degree of freedom increment delta e of the contact net T And an initial length increment Δl 0 Is a correlation matrix K of (1) L ；
According to the formula:
obtaining a node unbalanced force increment delta F; wherein Δe represents the degree of freedom increment;
according to the formula:
obtaining the increment delta F of the global unbalance force of the node unbalance force increment delta F G The method comprises the steps of carrying out a first treatment on the surface of the Wherein,a global stiffness matrix that is a displacement delta vector; />A global stiffness matrix that is an initial length increment; deltaU c The stress increment matrix is the stress increment matrix of the contact net;
delta DeltaF according to global imbalance force G And obtaining the displacement and the initial length of all nodes of the contact net, and obtaining the initial form of the contact net.
4. The method for preventing wind of a catenary based on damping compensation according to claim 3, wherein the constructing a catenary wind load disturbance model, calculating aerodynamic forces acting on catenary cues, and obtaining the catenary model under the action of environmental wind according to the aerodynamic forces acting on the catenary cues and initial dynamic responses of a pantograph-catenary system comprises:
according to the formula:
obtaining aerodynamic force F acting in the transverse direction of the contact net wire x And aerodynamic force F acting on the contact net wire in the longitudinal direction y The method comprises the steps of carrying out a first treatment on the surface of the Wherein F is D Aerodynamic resistance of the catenary wire; f (F) L Is connected withThe aerodynamic lift force of the touch net clue, alpha is the wind attack angle;
aerodynamic force F acting in transverse direction of contact net wire x And aerodynamic force F acting on the contact net wire in the longitudinal direction y And (5) sending the model into a finite element model of the flexible contact net to obtain the contact net model under the action of environmental wind.
5. The method for preventing wind of a catenary based on damping compensation according to claim 3, wherein the step of setting a motion equation in a balanced state and calculating motion constraint of the pantograph and the catenary according to a catenary model under the action of ambient wind, namely coupling contact pressure of the pantograph and the catenary comprises the following steps:
the equation of motion in equilibrium is as follows:
wherein,representing the pantograph head speed; />Representing the speed of the upper frame of the pantograph; />Representing the speed of the lower frame of the pantograph;indicating the acceleration of the lower frame of the pantograph; />Representing the upper frame acceleration of the pantograph; />Representing the pantograph head acceleration; m represents the pantograph reduction mass, c represents the pantograph reduction damping,k represents the pantograph reduced stiffness, including (·) 1 Parameters of bow head, (. Cndot.) for bow head 2 Is the upper frame parameter, ( 3 Parameters of the lower frame (.) 12 Coupling parameters for the bow and the upper frame; (. Cndot. 21 Parameters for coupling the upper frame with the bow head, (-) 23 The upper frame and the lower frame are coupled with parameters; (. Cndot. 32 Coupling parameters for the lower frame and the upper frame;
according to the formula:
F C ＝K S ·(y 1 -y c )
obtaining the coupling contact pressure F of the pantograph and the contact net c The method comprises the steps of carrying out a first treatment on the surface of the Wherein y is 1 For vertical displacement of bow head, y c For vertical displacement of contact line and bow head contact point, K S Is equivalent coupling rigidity between the pantograph head and the contact line.
6. The method for preventing wind of overhead contact line based on damping compensation according to claim 1, wherein the positioning points on the overhead contact line apply damping compensation, the coupled contact pressure of the pantograph and the overhead contact line under the action of environmental wind is calculated to satisfy the damping compensation numerical range of constraint conditions, and the setting of the maximum lifting amount of the overhead contact line at the positioning points comprises: f (F) max ≤F m +3σ，F min And the maximum lifting amount of the contact line at the positioning point is less than 120mm and is more than or equal to 20N. Wherein F is max For maximum contact pressure, F m For the average contact pressure, F min Sigma is the standard deviation of the contact pressure, which is the minimum value of the contact pressure.
7. An electronic device, comprising:
a memory for storing one or more programs;
a processor;
the method of any of claims 1-6 is implemented when the one or more programs are executed by the processor.
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