CN115062506A - Turnout switch rail strain-based train turnout wheel rail passing force identification method - Google Patents
Turnout switch rail strain-based train turnout wheel rail passing force identification method Download PDFInfo
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Abstract
The invention discloses a turnout switch rail strain-based train turnout wheel rail force identification method, wherein a plurality of strain gauges are adhered to different midspan positions of a switch rail and used for sensing and measuring wheel rail force strain response data of the switch rail when a train passes through; establishing a finite element analysis model of a switch point area, deducing and establishing a state transfer equation of point rail strain response and wheel rail force moving load through the finite element analysis model, and solving train turnout wheel rail passing force according to the state transfer equation and wheel rail force strain data. The invention can quickly calculate and identify the force of the train passing through the turnout wheel rail, can quickly know the characteristic signals of the change of the wheel rail force time course, the wheel rail force amplitude and the like when the train passes through a measuring point of the turnout area, can timely know the dynamic situation of the train passing through the turnout, has the advantages of less time consumption, high precision and the like in the identification and analysis process, and has certain guiding significance for the safety evaluation of the turnout area track.
Description
Technical Field
The invention belongs to the technical field of railway turnout detection, and particularly relates to a turnout switch rail force identification method for a train passing through turnout wheels based on turnout switch rail strain.
Background
Wheel-rail interaction is always a hot spot direction concerned in the field of rail engineering, particularly the problem of wheel-rail vibration interaction at a point rail position in a railway turnout system, and the most intuitive embodiment of the wheel-rail interaction is the wheel-rail force. The switch rail of the turnout is an important component in a railway turnout system, in the service process, due to the influence of material characteristics, environment temperature and complex stress between wheel rails, the turnout can be damaged in different degrees such as crushing, side grinding, corrugation, stripping, cracking and the like after long-term use, under the action of wheel rail force, the defect can be more rapidly expanded, failure can be caused suddenly without signs, the switch rail can be damaged even broken under serious conditions, accidents such as train derailment and the like are generated, and casualties and huge economic loss are caused. In order to sense and find the acting force state of the wheel rail at the switch rail in time and avoid further damage to the rail at the switch, the method for monitoring and identifying the acting force of the wheel rail at the switch rail of the switch is found in order to make up for the defects of the prior art, and the method has important significance for ensuring the operation safety of a rail line and improving the allowable safety of a train passing through the switch.
Disclosure of Invention
The invention aims to provide a turnout switch rail force identification method based on turnout switch rail strain, which has the advantages of high convergence speed, less time consumption, high precision and the like. In order to achieve the purpose, the invention adopts the following technical scheme:
according to one aspect of the invention, a turnout switch rail strain-based train turnout wheel rail force identification method is provided, wherein a plurality of strain gauges are pasted on different midspan positions of a switch rail and used for sensing and measuring wheel rail force strain response data of the switch rail when a train passes through; establishing a finite element analysis model of a switch blade area, deducing and establishing a state transfer equation of switch blade strain response and wheel rail force moving load through the finite element analysis model, and solving the force of the train passing through the switch blade according to the state transfer equation and the wheel rail force strain data.
Preferably, the finite element analysis model of the switch blade area satisfies the following conditions:
m, C, K are the mass, damping and stiffness matrices of the point rail, respectively; y is (t) 、
Respectively responding to the displacement, the speed and the acceleration of the wheel track; n is a radical of F(t) F (t) is equivalent node load corresponding to the wheel track at each moment, F (t) is wheel track contact force at any point at each moment, N F(t) And distributing an interpolation function matrix for distributing the wheel-rail contact load at the corresponding moment as the load of the equivalent node load.
The scheme is further preferable, and the step of solving the train turnout-passing wheel rail force according to the state transfer equation and the wheel rail force strain data comprises the following steps:
the method comprises the following steps: equivalently simplifying the wheel-rail contact force into a form of wheel-rail force moving load F (t), and dispersing the point rail part structure into a plurality of supporting units according to sleeper support;
step two: the wheel-rail force moving load at any time on each supporting unit is supplemented with an interpolation function N F 1，N F 2、N F 3 and N F 4；
Step three: introducing integration parameters gamma and beta according to a Newmark display expression method, selecting a time step delta t, and calculating an integration constant, wherein the parameters gamma and beta respectively satisfy the following conditions:
γ≥0.50,β≥0.25(0.5+γ) 2
step four: and (3) solving the dynamic response at the ith delta t moment by combining a finite element analysis model and a Newmark method formula, wherein the dynamic response equation at the ith delta t moment is as follows:
in general, when the initial state response of the track is 0, i.e., when i is 0, y is 0 ＝ 0、
The above formula is finally expressed as:
step five: calculating the dynamic response y of the structural node in the finite element analysis model according to the dynamic response equation (t) 、
Converting the node dynamic response into two-side node displacement response corresponding to each monitoring point, and then solving the final mid-span monitoring point displacement response through two-side node displacement;
step six: and solving a state transfer equation of the wheel-rail force moving load according to the corresponding relation between the mid-span monitoring point displacement response and the corresponding node displacement response, and solving the train turnout wheel-rail force according to the state transfer equation.
Preferably, in step six, the corresponding relationship between the mid-span displacement response of the monitoring point and the displacement response of the corresponding node is converted into a mid-span displacement response w (x) w(t) T) and strain response to node ε (x) w(t) The relationship of (i), (ii), (iii), (iv),the midspan displacement response and the strain response relation meet the following conditions:
in the formula y f The vertical distance between the strain gauge and the neutral axis of the switch rail is defined;
the monitoring point mid-span displacement response meets the following conditions:
W(t)＝N w(t) Z(t)＝N w(t) H L F(t)；
N w(t) an interpolation function matrix for converting node displacement into transmid displacement, Z (t) is the output response at the corresponding node of the final monitoring point across, H L A final transfer coefficient matrix of the strain response and the moving load;
the moving load of the wheel rail force, namely the final expression of the force of the train passing through the turnout wheel rail, meets the following conditions:
the above solution is further preferred, where the output response z (t) at the node corresponding to the final monitoring point across satisfies:
wherein R is a In response to acceleration
Corresponding extraction matrix, R v Is speed response
Corresponding extraction matrix, R d In response to displacement y (t) The extraction matrix of (1).
Preferably, the interpolation function N is a function of a number of pixels in the image F 1，N F 2、N F 3 and N F 4 respectively satisfy:
wherein x is F(t) The distance between the unit where the wheel-rail contact force is located and the left node at any moment is l, which is the length of one supporting unit; n is a radical of F 1、N F 2 is a displacement interpolation function and a corner interpolation function of the left node of the corresponding unit, N F 3、N F And 4, respectively representing a displacement interpolation function and a corner interpolation function of the right node of the corresponding unit.
In a further preferred aspect of the foregoing solution, in the first step, the point rail partial structure is discretized into a plurality of support units according to sleeper support as follows: the number of the corresponding equivalent node loads at each moment is dispersed into a plurality of supporting units for the whole wheel rail according to the sleeper support according to the form of the train wheel pair, and each supporting unit only acts on one wheel contact at most.
In summary, due to the adoption of the technical scheme, the invention has the following technical effects:
the stress condition of the turnout wheel rail when a train passes through is rapidly calculated and identified through the rail turnout strain condition, characteristic signals such as wheel rail force time-course change, wheel rail force amplitude and the like when the train passes through a turnout area measuring point can be rapidly known, dynamic conditions of the train passing through the turnout can be identified and analyzed, convergence factors are introduced in the calculation and identification processes to correct wheel rail contact force, and the corrected time domain algorithm has the advantages of simplicity, high convergence speed, less time consumption, high precision and the like. The identification method has certain guiding significance for the safety evaluation of the tracks in the turnout zone.
Drawings
FIG. 1 is a schematic diagram of the strain bonding of a steel rail at a measuring point according to the present invention;
FIG. 2 is a schematic structural diagram of a finite element analysis model of a vehicle track according to the present invention;
FIG. 3 is a schematic diagram of the division of the switch rail into model structural units;
FIG. 4 is a schematic diagram of load distribution of nodes corresponding to loads at any time;
FIG. 5 is a schematic diagram of monitoring point displacement response and node response allocation according to the present invention;
FIG. 6 is a schematic diagram of the arrangement of the strain gauges in the turnout zone of the present invention;
fig. 7 is a schematic diagram of the wheel-rail force time course curve of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings by way of examples of preferred embodiments. It should be noted, however, that the numerous details set forth in the description are merely for the purpose of providing the reader with a thorough understanding of one or more aspects of the present invention, which may be practiced without these specific details.
As shown in fig. 1 and fig. 2, according to the train turnout switch rail force identification method based on the turnout switch rail strain provided by the invention, a plurality of strain gauges are pasted on different midspan positions of the switch rail and used for sensing and measuring the wheel rail force strain response data of the switch rail when the train passes through; establishing a finite element analysis model of a turnout switch rail area, deducing and establishing a state transfer equation of switch rail strain response and wheel rail force moving load through the finite element analysis model, and solving the turnout wheel rail passing force of the train according to the state transfer equation and wheel rail force strain data; in the invention, the finite element analysis model of the switch blade area meets the following conditions:
m, C, K are the mass, damping and stiffness matrices of the point rail, respectively; y is (t) 、
Respectively responding to the displacement, the speed and the acceleration of the wheel track; n is a radical of F(t) F (t) is the equivalent node load corresponding to the wheel track at each moment, F (t) is the wheel track contact force at any point at each moment, N F(t) And distributing an interpolation function matrix for distributing the wheel-rail contact load at the corresponding moment as the load of the equivalent node load.
In the invention, solving the train turnout-passing wheel rail force according to the state transfer equation and the wheel rail force strain data comprises the following steps:
the method comprises the following steps: equivalently simplifying the wheel-rail contact force into a form of wheel-rail force moving load F (t), and dispersing the structure of the switch rail part into a plurality of supporting units according to sleeper support, as shown in FIG. 2; the point rail part structure is separated into a plurality of supporting units according to sleeper support according to the following steps: the number of the corresponding equivalent node loads at each moment is divided into a plurality of supporting units for supporting the sleepers of the whole wheel rail according to the form of train wheel pairs, and each supporting unit is contacted with at most one wheel;
step two: an interpolation function N is used for assisting the wheel-rail force moving load at any time on each single supporting element F 1，N F 2、N F 3 and N F 4; the interpolation function N F 1，N F 2、N F 3 and N F 4 respectively satisfy:
wherein x is F(t) The distance between the unit where the wheel-rail contact force is located and the left node at any moment is l, which is the length of one supporting unit; n is a radical of F 1、N F 2 is a displacement interpolation function and a corner interpolation function of the left node of the corresponding unit, N F 3、N F 4 displacement interpolation function of right node of corresponding unitAnd a corner interpolation function.
Converting the mobile load at any moment into the node equivalent load, wherein the N corresponds to the required load at the moment F (t), and N F (t) includes N corresponding to the time F 1，N F 2、N F 3、N F 4, an interpolation function; in the invention, as shown in fig. 2, the sleeper support position is taken as a node, one span between two sleepers represents one support unit, one support unit has two nodes, and the load at any moment between every two support units needs to be distributed to the unit node in the calculation process to be equivalent to the load of the corresponding unit node. Considering the vertical displacement and the rotation angle at the node, the moving load at any moment on each single supporting element is assisted by an interpolation function N F 1，N F 2、N F 3 and N F 4, obtaining the equivalent node load N of the unit where the arbitrary load is positioned F (t) F (t), as shown in FIG. 4. The equivalent node load of the whole structure is obtained by sequentially calculating the corresponding equivalent node load of the moving load on each unit and grouping;
step three: introducing integration parameters gamma and beta according to a Newmark display expression method, selecting a time step delta t, and calculating an integration constant, wherein the time step is determined according to parameters gamma and beta controlled by integration precision and stability, and the parameters gamma and beta respectively meet the following requirements:
γ≥0.50,β≥0.25(0.5+γ) 2 ；
step four: and (3) solving the dynamic response at the ith time delta t by combining the formula (1) and a Newmark explicit formula, namely a solving equation of displacement, speed and acceleration (dynamic response), wherein the dynamic response equation at the ith time delta t is as follows:
in general, when the track initial state response is 0, i.e. when i is 0, y 0 ＝0、
The above formula is finally expressed as:
wherein, the expression is related to O (O) 0 、O d 、O v 、O a )、P(P 0 、P d 、P v 、 P a )、Q(Q 0 、Q d 、Q v 、Q a ) The response coefficient transfer matrix of (a) is:
the same reasoning can be used for the derivation of the correlation equation to obtain the integral constant c 0 To c 7 And β and γ; and
K. m, C matrix vs. other O d i 、O v i 、O a i ；P d i 、P v i 、P a i ；Q d i 、 Q v i 、Q a i The expression of the response coefficient transfer matrix, i.e. the O, P, Q matrix at each instant. In general, the stiffness, mass and damping matrix K at each moment i 、M i And C i All are constant matrix, then equivalent stiffness matrix
Also a constant matrix, each time is composed of
K i 、M i And C i The ideographic O, P, Q response coefficient transfer matrix is also a constant matrix. At the same time, N F(i-j) Indicating the load distribution interpolation function at the i-j times of deltat, F i-j Represents any moving load (wheel track force) at the ith-jth time delta t, and i and j represent the accumulation process of the time step delta t, namely the several time delta t;
step five: calculating the dynamic response y of the structural node in the finite element analysis model according to the dynamic response equation (t) 、
Namely node displacement (including node vertical displacement and rotation angle), speed (including vertical direction and rotation angle direction) and acceleration (including vertical direction and rotation angle direction) response matrixes; and extracting response data needed to be used from the response. Deducing and calculating a transfer equation of the strain of the mid-span monitoring point and the wheel-track force (moving load), and solving the dynamic response of all nodes of the model structure, wherein for this purpose, data to be extracted should be displacement responses (including node vertical displacement and corners) of nodes at two sides corresponding to each monitoring point, the mid-span displacement response is obtained through the displacement (including node vertical displacement and corners) of the nodes at two sides, and then the displacement is converted into the strain response according to the relationship between the mid-span displacement and the strain; for this reason, the node dynamic response is converted into two-side node displacement response corresponding to each monitoring point, then the displacement response of the final mid-span monitoring point is solved through the displacement of the two-side nodes, and at the moment, the output response Z (t) of the node corresponding to the final mid-span monitoring point meets the following requirements:
wherein R is a In response to acceleration
Corresponding extraction matrix, R v Is speed response
Corresponding extraction matrix, R d In response to displacement y (t) Extracting the matrix; in the present invention, R is the node displacement response extracted a 、R v The matrix is a zero matrix, and R d The matrix is a non-zero matrix, and R d The matrix should satisfy the requirement of extracting the node displacement response (including the vertical displacement and the rotation angle of the node) corresponding to each monitoring point at each moment.
Let R ═ R d 、R v 、R a ]Substituting the formula (5) to obtain:
let the response coefficient matrix H K Comprises the following steps:
H L ＝N F (t)H K ， (11)；
the relationship between the response z (t) (including the vertical displacement and the rotation angle of the node) at the corresponding node of the final monitoring point and the state transfer equation of the moving load satisfies the following conditions:
Z(t)＝H L F(t) (12)
wherein the content of the first and second substances,
step six: according to the corresponding relation (packet) between the displacement response of the monitoring point and the displacement response of the corresponding nodeIncluding the corresponding relation between the vertical displacement of the node and the corner), solving a state transfer equation of the wheel-rail force moving load, solving the relation between the midspan displacement response and the state transfer equation of the moving load by solving the force of the train passing through the turnout wheel rail according to the state transfer equation, wherein the corresponding schematic diagram of the midspan displacement load and the node displacement (including the vertical displacement of the node and the corner) is shown in fig. 5. In the invention, the corresponding relation between the mid-span displacement response of the monitoring point and the displacement response of the counter node is converted into the mid-span displacement response w (x) w(t) T) and strain response to node ε (x) w(t) And t), the monitoring point mid-span displacement response satisfies the following conditions:
W(t)＝N w(t) Z(t)＝N w(t) H L F(t)， (14)；
wherein N is w(t) An interpolation function matrix for converting node displacement into transmid displacement, Z (t) is the output response at the corresponding node of the final monitoring point across, H L The final transmission coefficient matrix of the strain response and the moving load; like the load interpolation function, the node dynamic response comprises displacement and a corner, one support unit is provided with two nodes, and therefore the interpolation function N is used for assisting the displacement and the corner of the node at any moment on each support unit w1(t) ,N w2(t) ,N w3(t) And N w4(t) Then, the displacement expression of any position on the unit at any time can be obtained, which is shown in FIG. 5; if the displacement response of a certain measuring point at a certain moment is as follows:
W(t1)＝N w1(t1) Zz(t1)+N w2(t1) θz(t1)+N w3(t1) Zy(t1)+N w4(t1) θy(t1)， (15)；
N w1(t) ,N w2(t) ,N w3(t) and N w4(t) The values of (A) are respectively as follows:
x w(t) indicates the position of the monitoring point from the node on the left side when x w(t) When l/2, the displacement response across the monitoring point is expressed. Zz (t) is the vertical displacement response of the left node in the corresponding node response Z (t) of the monitoring point unitθ z (t) is the corner response of the left node in the node response Z (t) corresponding to the monitoring point unit; zy (t) is the vertical displacement response of the right side node in the node response Z (t) corresponding to the monitoring point unit, and theta y (t) is the corner response of the right side node in the node response Z (t) corresponding to the monitoring point unit. To this end, a response w (x) is based on the mid-span displacement w(t) T) and strain response ε (x) w(t) T) the relationship determines the final state transfer equation. The midspan displacement response and the strain response relation meet the following conditions:
wherein y in the formula f The vertical distance between the strain gauge and the neutral axis of the switch rail is defined;
then equation (14) is combined with equation (17) to determine the final state transfer equation that satisfies:
and the wheel-rail force moving load is the train turnout-passing wheel-rail force, and the final expression of the train turnout-passing wheel-rail force calculation is as follows:
and substituting the measured switch rail part strain response into a formula (19), namely solving a state transfer equation, and calculating to obtain the rail force of the train passing through the turnout wheel.
In the invention, data measured by a strain gauge (strain sensor) is connected to an NI-9031 acquisition instrument through a lead, the acquisition instrument acquires strain at a turnout steel rail measuring point by adopting a trigger sampling mode, when a train passes through the measuring point, a trigger system starts to acquire data and finishes acquisition after the train runs away, the acquisition instrument is in charge of acquiring and storing the measuring point strain when the train runs through the turnout zone through connection with the strain sensor, and the mounting statistics of the strain gauge are shown in an attached table 1;
TABLE 1 Strain gage installation position distribution Table
The turnout area strain gauge layout is shown in figure 6, steel rail strain at a measuring point is pasted as shown in figure 1, strain gauges are installed on a switch rail and a stock rail in the turnout area, a straight stock rail and a curved stock rail with the same section are respectively provided with one strain gauge, all train wheel rail force signals passing through the section can be measured, a rail is simulated into a continuously supported beam unit, vehicle load is simulated into moving point load, and the strain gauges are pasted on different positions of the switch rail and used for sensing and measuring wheel rail force strain response data of the switch rail when a train passes through. The number of sections is selected according to actual conditions, the measured actual strain data is processed through MATLAB software, and the wheel-rail force time-course change is obtained by directly solving the combined formula (19);
through the calculation of the formula, a wheel-rail force time-course curve is obtained, as shown in fig. 7, characteristic signals such as wheel-rail force time-course change, wheel-rail force amplitude and the like when the train passes through a turnout zone measuring point can be obtained from fig. 7, and further, dynamic conditions of train turnout passing can be identified and analyzed.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be construed as the protection scope of the present invention.
Claims (7)
1. A force identification method for a train passing through a turnout wheel rail based on turnout switch rail strain is characterized by comprising the following steps: pasting a plurality of strain gauges on different span-middle positions of the switch rail for sensing and measuring wheel rail force strain response data of the switch rail when a train passes through; establishing a finite element analysis model of a switch blade area, deducing and establishing a state transfer equation of switch blade strain response and wheel rail force moving load through the finite element analysis model, and solving the force of the train passing through the switch blade according to the state transfer equation and the wheel rail force strain data.
2. The turnout switch rail force-passing train wheel rail force identification method based on turnout switch rail strain is characterized in that: the finite element analysis model of the switch blade area meets the following conditions:
m, C, K are the mass, damping and stiffness matrices of the point rail, respectively; y is (t) 、
Respectively responding to the displacement, the speed and the acceleration of the wheel track; n is a radical of F(t) F (t) is equivalent node load corresponding to the wheel track at each moment, F (t) is wheel track contact force at any point at each moment, N F(t) And distributing an interpolation function matrix for distributing the wheel-rail contact load at the corresponding moment as the load of the equivalent node load.
3. The turnout switch rail strain-based train turnout wheel rail force identification method according to claim 1, characterized in that: solving the train turnout-passing wheel rail force according to the state transfer equation and the wheel rail force strain data comprises the following steps:
the method comprises the following steps: equivalently simplifying the wheel-rail contact force into a form of wheel-rail force moving load F (t), and dispersing the point rail part structure into a plurality of supporting units according to sleeper support;
step two: an interpolation function N is used for assisting the wheel-rail force moving load at any time on each supporting unit F 1，N F 2、N F 3 and N F 4；
Step three: introducing integration parameters gamma and beta according to a Newmark display expression method, selecting a time step delta t, and calculating an integration constant, wherein the parameters gamma and beta respectively satisfy the following conditions:
γ≥0.50,β≥0.25(0.5+γ) 2
step four: and (3) solving the dynamic response at the ith delta t moment by combining a finite element analysis model and a Newmark method formula, wherein the dynamic response equation at the ith delta t moment is as follows:
when the initial state response of the track is 0, i.e., i is 0, y 0 ＝0、
The above formula is finally expressed as:
step five: calculating the dynamic response y of the structural node in the finite element analysis model according to the dynamic response equation (t) 、
Converting the node dynamic response into two-side node displacement response corresponding to each monitoring point, and then solving the final mid-span monitoring point displacement response through two-side node displacement;
step six: and solving a state transfer equation of the wheel-rail force moving load according to the corresponding relation between the midspan monitoring point displacement response and the corresponding node displacement response, and solving the train turnout wheel-rail force according to the state transfer equation.
4. The method for identifying the force of the turnout switch rail passing through the turnout wheel based on the strain of the turnout switch rail as claimed in claim 3, wherein the method comprises the following steps: in step six, the corresponding relation between the mid-span displacement response of the monitoring point and the displacement response of the corresponding node is converted into a mid-span displacement response w (x) w(t) T) and strain response to node ε (x) w(t) And t), the midspan displacement response and the strain response relation satisfy the following conditions:
in the formula y f The vertical distance between the strain gauge and the neutral axis of the switch rail is formed by bonding the strain gauge;
the monitoring point mid-span displacement response meets the following conditions:
W(t)＝N w(t) Z(t)＝N w(t) H L F(t)；
N w(t) an interpolation function matrix for converting node displacement into transmid displacement, Z (t) is the output response at the corresponding node of the final monitoring point across, H L The final transmission coefficient matrix of the strain response and the moving load;
the moving load of the wheel rail force, namely the final expression of the force of the train passing through the turnout wheel rail, meets the following conditions:
5. the method for identifying the force of a train passing through a switch wheel rail based on the strain of a switch blade as claimed in claim 4, wherein: and output response Z (t) at the corresponding node of the final monitoring point in the span satisfies the following conditions:
wherein R is a In response to acceleration
Corresponding extraction matrix, R v Is speed response
Corresponding extraction matrix, R d Is a displacement response y (t) The extraction matrix of (1).
6. The method for identifying the force of the turnout switch rail passing through the turnout wheel based on the strain of the turnout switch rail as claimed in claim 3, wherein the method comprises the following steps: the interpolation function N F 1，N F 2、N F 3 and N F 4 respectively satisfy:
wherein x is F(t) L is the length of a supporting unit, and is the position of the unit where the wheel-rail contact force is located at any moment and the left node; n is a radical of F 1、N F 2 is a displacement interpolation function and a corner interpolation function of the left node of the corresponding unit, N F 3、N F 4 are each independentlyAnd the displacement interpolation function and the corner interpolation function of the right node of the corresponding unit.
7. The method for identifying the force of the turnout switch rail passing through the turnout wheel based on the strain of the turnout switch rail as claimed in claim 2, wherein the method comprises the following steps: in the first step, the point rail part structure is dispersed into a plurality of supporting units according to the sleeper support, and the method comprises the following steps: the number of the corresponding equivalent node loads at each moment is dispersed into a plurality of supporting units for the whole wheel rail according to the sleeper support according to the form of the train wheel pair, and each supporting unit only acts on one wheel contact at most.
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