CN108228940A - The vertical dynamical modeling system of railway transportation Ballast track - Google Patents
The vertical dynamical modeling system of railway transportation Ballast track Download PDFInfo
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- CN108228940A CN108228940A CN201611192537.8A CN201611192537A CN108228940A CN 108228940 A CN108228940 A CN 108228940A CN 201611192537 A CN201611192537 A CN 201611192537A CN 108228940 A CN108228940 A CN 108228940A
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Abstract
The invention discloses a kind of vertical dynamical modeling systems of railway transportation Ballast track, which is characterized in that including：Analysis parameter selectes unit, is used to select the analysis parameter that Ballast track model to be analyzed includes, the analysis parameter includes rail, sleeper and railway roadbed；Analysis equation establishes unit, be used for it is selected analysis parameter carry out force analysis respectively, i.e., list respectively rail, sleeper and railway roadbed respectively corresponding to oscillatory differential equation；Parameter analysis unit is used to set the analytical parameters value corresponding to each analysis parameter；Vertical dynamic model establishes unit, based on the pre-processing module of ANSYS softwares, can create the vertical dynamic model of Ballast track and analyze.The present invention has many advantages, such as that precision is high, function is strong, parameter easily determines, it is easy to calculate, and can fully consider and the closely related influence factor that studies a question.
Description
Technical field
The present invention relates to modeling and simulating technologies, particularly relate to a kind of vertical suitable for railway transportation Ballast track
Dynamical modeling system.
Background technology
With the development of passenger traffic high speed and shipping heavy loading, status of the railway transportation in communications and transportation system is increasingly
It is important.And basis of the track structure as railway transportation, under the repeated action of train load, often will appear fastener failure,
Sleeper hangs the unfavorable defect such as sky, settlement of subgrade.The presence of these defects is very unfavorable to the safe operation of train, and pole
The earth accelerates the fatigue damage of track structure.
Specifically since track is one of major technique equipment of railway, subway, be driving basis, it directly bear by
The load that wheel transmits, and the buildings such as roadbed or bridge tunnel are transferred to, while also play pilot engine vehicle steadily safety
The effect of operation.Therefore with the continuous development of railway technology, track structure is also in continuous improvement and innovation, but generally speaking
There are mainly two types of fundamental types：The non-fragment orbit that traditional Ballast track and recent years is generated along with high-speed railway.Have
Tiny fragments of stone, coal, etc. track has many merits such as be laid with short convenience, low cost, construction period, easy repair, geometry state easily adjust, and is earliest
Apply to the track structure form and the primary structure form of world's railroad track instantly of railway transportation.Ballast track is main
It is made of other auxiliary devices such as rail, fastener, sleeper, railway roadbed, there is associativity and granular media.In the development of nearly 200 years
In history, Ballast track dynamic model is but total after in form by letter to tired, evolution functionally from less to more
Lumped parameter model, beam continuously supported, discrete point bearing beam model etc. can be divided by saying；But existing simulation modeling side
Method is more complicated there are model, at present using less；Or presence can not consider the unevenness and irregularity of track structure, no
It can be used for studying the drawbacks such as influence of the railroad flaws to track vibration.
Invention content
In view of defects in the prior art, the invention aims to provide a kind of novel railway transportation with there is tiny fragments of stone, coal, etc. rail
The vertical dynamical modeling system in road.
To achieve these goals, technical scheme of the present invention：
The vertical dynamical modeling system of railway transportation Ballast track, which is characterized in that including：
Analysis parameter selectes unit, is used to select the analysis parameter that Ballast track model to be analyzed includes, described
It analyzes parameter and includes rail, sleeper and railway roadbed；Wherein rail uses the Euler beams of the discrete dot point of continuous elastic；Sleeper and road
Bed only considers the particle of vertical vibration, and with linear bullet between rail and sleeper, sleeper and railway roadbed and railway roadbed and roadbed
Spring-damping unit connection, and shear spring-damping unit is introduced between adjacent railway roadbed block, to consider each adjacent railway roadbed block
Between shearing effect；
Analysis equation establishes unit, is used to carry out force analysis respectively to selected analysis parameter, i.e., lists respectively
The respective corresponding oscillatory differential equation of rail, sleeper and railway roadbed；
Parameter analysis unit is used to set the analytical parameters value corresponding to each analysis parameter；
And vertical dynamic model establishes unit, is used for the pre-processing module based on ANSYS softwares, creates Ballast track
Vertical dynamic model and analyze the vertical dynamic model of Ballast track established using the pre-processing module of ANSYS softwares,
Wherein rail is carried out discrete using Beam3 beam elements, and sleeper and railway roadbed are simulated using Mass21 mass units, and rail and rail
Combin14 Hookean springs-damping unit is used in connection between pillow, sleeper and railway roadbed, railway roadbed and roadbed and adjacent railway roadbed block
Simulation.
Further, analysis equation establishes the rail, sleeper and railway roadbed in unit respectively corresponding vibration differential
Equation is respectively：
The ordinary differential system of the rail vibration coordinate of the rail
The oscillatory differential equation of the sleeper
The oscillatory differential equation of the railway roadbed
Formula (1.15), (1.18) and (1.21) synthesis is obtained into the oscillatory differential equation group of track structure, exponent number simultaneously
For M+2N.
Further, the partial parameters in parameter analysis unit can be obtained directly by empirical data, and another part parameter is led to
It crosses railway roadbed centrum load-bearing hypothesis to be calculated, calculating process includes：
According to the computed altitude h of centrum lap0To judge whether adjacent railway roadbed block interference phenomenon occurs, and select accordingly
Institute's calculation formula to be used is selected, wherein, h0Concrete form it is as follows
Work as h0When≤0, without interference phenomenon between adjacent railway roadbed block, at this time
Kf=(le+2hbtanα)(lb+2hbtanα)Ef (1.25)
Work as h0>When 0, there are interference phenomenon between adjacent railway roadbed block, at this time
Wherein
And roadbed support stiffness
Kf=ls(le+2hbtanα)Ef (1.30)。
Compared with prior art, beneficial effects of the present invention：
The present invention supports beam model using discrete point and has fully considered three layers of (steel of shearing effect between adjacent railway roadbed block
Rail-sleeper-railway roadbed-roadbed) discrete point bearing beam model, so as to ensure that this method has the function of that precision is high, strong, parameter is easily true
Determine, calculate the advantages that easy, and can fully consider and the closely related influence factor that studies a question.
Description of the drawings
Fig. 1 is the corresponding flow chart of steps of the method for the invention；
Fig. 2 is the corresponding flow chart of steps of the method for the invention；
Fig. 3 is the corresponding Ballast track model structure schematic diagram of the method for the invention.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, below in conjunction with attached in the embodiment of the present invention
Figure, is clearly and completely described technical scheme of the present invention, it is clear that described embodiment is that a part of the invention is real
Example is applied, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art are not making creation
Property labour under the premise of all other embodiments obtained, shall fall within the protection scope of the present invention.
Rational dynamic analysis modeling is the key that Ballast track structural vibration analysis, should have precision height, function
By force, parameter easily determines, calculates the advantages that easy, and can fully consider with study a question closely related influence because
Element, so as to ensure the reliability of result of calculation and accuracy.Therefore, the method for the invention is establishing the vertical power of Ballast track
During model, it then follows following principle：
(1) lumped parameter model is primarily adapted for use in qualitative analysis, and beam continuously supported can not consider track structure
Non even supporting, thus the present invention using discrete point support beam model.
(2) it fails to simulate fastener, sleeper hangs the track structures defects such as empty and settlement of subgrade, present invention consideration
Three layers of (rail-sleeper-railway roadbed-roadbed) discrete point bearing beam model of shearing effect between adjacent railway roadbed block.
(3) for simulation rail generally using two kinds of models of Euler beams and Timoshenko beams, Timoshenko beams consider beam
Shearing and rotatory inertia effect, for can be obtained during rail oscillometry it is more accurate as a result, but theory analysis very
Complexity, and Euler beams calculate easy, to be obtained in rail low-frequency analysis with Timoshenko beam models result almost one
It causes.The present invention simulates rail using Euler beams, calculating process can be made greatly simple while enough numerical precisions are ensured
Change.
Based on above-mentioned principle, as shown in Figs. 1-2, modeling of the present invention includes the following steps：
Analysis parameter selectes unit：Select the analysis parameter that Ballast track model to be analyzed includes, the analysis ginseng
Amount includes rail, sleeper and railway roadbed；Wherein, the vertical dynamic model of Ballast track considers as shown in Fig. 2, in the model trajectory
The common ginseng of rail, sleeper and railway roadbed is shaken；Wherein, rail is simulated with the Euler beams of the discrete dot point of continuous elastic, sleeper
It is regarded as only considering the particle of vertical vibration with railway roadbed, and between rail and sleeper, sleeper and railway roadbed and railway roadbed and roadbed
It is connected with Hookean spring-damping unit, and shear spring-damping unit is introduced between adjacent railway roadbed block, to consider it
Between shearing effect.
Analysis equation establishes unit：To it is selected analysis parameter carry out force analysis respectively, i.e., list respectively rail,
The respective corresponding oscillatory differential equation of sleeper and railway roadbed；
The oscillatory differential equation of the rail is simulated for rail with Euler beams, wherein, Pi(i=1~4) are wheel rail force,
Train speed is v；Frsi(i=1~N) is rail chair support reaction, and N is the sleeper number in model trajectory；OxZrFor rail's coordinate
System, x0For initial time train wheel-rail force P1Coordinate, xiFor sleeper support reaction FrsiCoordinate；2lc、2ltRespectively vehicle
Spacing and wheel-base bogie, l are rail length；
According to the force diagram of rail, can list its oscillatory differential equation is
Wherein
xi=ils(i=1~N) (1.3)
In formula, Zr(x, t) is the vibration displacement of rail, and wherein t is time variable；
δ (x) is Dirac functions, wherein as x=0, δ (x)=1, and as x ≠ 0, δ (x)=0；
xwi(i=1~4) are the coordinates of motion of each wheel-rail force, are followed successively by
Zsi(t) it is the vibration displacement of sleeper, lsFor sleeper spacing；
Since formula (1.1) is fourth order PDEs, needs to be translated into second order ordinary differential equation group, can just use number
Value method is solved, and according to Ritz methods, the solution of equation (1.1) can be written as form
In formula, φk(x) it is the rail vibration shape, specially
qk(t) for rail canonical vibration coordinate, M is the rail rank number of mode that is intercepted；
Formula (1.5) is substituted into formula (1.1) to obtain
φ is multiplied by equation 1 above .7 both sides are sameh(x) (h=1,2 ..., M), and x is integrated along entire rail length,
Ensure the orthogonality of mode
Then
By equation 1 above .9, can obtain
And because
So formula (1.10) becomes
Further, steel rail displacement representative formula (1.5) is substituted into formula (1.2), obtained
Then, rail vibration coordinate second order ordinary differential equation group can be obtained
The oscillatory differential equation of the sleeper：
The stress of No. i-th sleeper is set, wherein, FsriIt is rail to the reaction force of sleeper, FsbiIt is lower section railway roadbed to rail
The active force of pillow, the oscillatory differential equation that can list sleeper accordingly are
Wherein
In formula, Zbi(t) it is the vibration displacement of railway roadbed.
Above formula is substituted into equation (2.16) and arranged, the Pumping ties differential equation can be obtained
The oscillatory differential equation of the railway roadbed：
The stress of No. i-th railway roadbed block is set, wherein, FbsiIt is top sleeper to the active force of railway roadbed, FbfiFor lower section roadbed
To the active force of railway roadbed, FbbliFor the shear force of left side railway roadbed block, FbbriFor the shear force of right side railway roadbed, accordingly may be used
The oscillatory differential equation for listing railway roadbed is
Wherein
Above formula is substituted into (1.19) and arranged, the ballast bed vibration differential equation can be obtained
Formula (1.15), (1.18) and (1.21) is comprehensive, the oscillatory differential equation group of track structure, exponent number can be obtained
For M+2N.
Parameter analysis unit：Set the analytical parameters value corresponding to each analysis parameter；Since some parameters are such as in model
mr、EI、Kpi、Cpi、Msi、Cbi、Kwi、Cwi、CfiThe value of each parameter can be obtained directly from experience table, other are such as Mbi、KbiAnd
KfiValue then need by railway roadbed centrum load-bearing assume obtain, it is described be railway roadbed centrum load-bearing assume from sleeper to railway roadbed transmit
Load, it is approximate in granular ballast bed to be transmitted downwards with cone distribution, and until road bed, and except centrum
Railway roadbed is substantially at unstress state, and specific calculating process is：
First, according to the computed altitude h of centrum lap0Judge whether adjacent railway roadbed block interference phenomenon occurs, and
The institute of selection accordingly calculation formula to be used.Wherein, h0Concrete form it is as follows
Work as h0When≤0, without interference phenomenon between adjacent railway roadbed block, at this time
Kf=(le+2hbtanα)(lb+2hbtanα)Ef (1.25)
Work as h0>When 0, there are interference phenomenon between adjacent railway roadbed block, at this time
Wherein
And roadbed support stiffness
Kf=ls(le+2hbtanα)Ef (1.30)
According to above formula and empirical value, M can be calculatedbi、KbiAnd KfiValue.So far, the vertical power of Ballast track
Each parameter value in model has determined that.
Vertical dynamic model establishes unit：Based on the pre-processing module of ANSYS softwares, the vertical power of Ballast track is created
Model is simultaneously analyzed.It is main since ANSYS softwares are that molten bonding structure, fluid, electric field etc. are analyzed in the large-scale general finite element software of one
To include three front processor, solver and preprocessor parts.Wherein, front processor have the function of powerful solid modelling and
Abundant mesh generation tool, user can easily construct finite element model, and also have Numerous in the cell library of software
Cell type, can realize the simulation to a variety of materials in engineering and structure.Pre-treatment that is of the invention then utilizing ANSYS softwares
Module establishes the vertical dynamic model of Ballast track, and wherein rail is carried out discrete using Beam3 beam elements, and sleeper and railway roadbed are adopted
It is simulated with Mass21 mass units, and between rail and sleeper, sleeper and railway roadbed, railway roadbed and roadbed and adjacent railway roadbed block
Connection is simulated with Combin14 Hookean springs-damping unit.
So far, you can the required vertical dynamic model of Ballast track.
Said program is merely preferred embodiments of the present invention, but protection scope of the present invention is not limited thereto,
Any one skilled in the art in the technical scope disclosed by the present invention, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (3)
1. the vertical dynamical modeling system of railway transportation Ballast track, which is characterized in that including：
Analysis parameter selectes unit, is used to select the analysis parameter that Ballast track model to be analyzed includes, the analysis
Parameter includes rail, sleeper and railway roadbed；Wherein rail uses the Euler beams of the discrete dot point of continuous elastic；Sleeper and railway roadbed are equal
Only consider the particle of vertical vibration, and Hookean spring-resistance is used between rail and sleeper, sleeper and railway roadbed and railway roadbed and roadbed
Buddhist nun's unit connects, and introduces shear spring-damping unit between adjacent railway roadbed block, to consider between each adjacent railway roadbed block
Shearing effect；
Analysis equation establishes unit, be used for it is selected analysis parameter carry out force analysis respectively, i.e., list respectively rail,
The respective corresponding oscillatory differential equation of sleeper and railway roadbed；
Parameter analysis unit is used to set the analytical parameters value corresponding to each analysis parameter；
And vertical dynamic model establishes unit, is used for the pre-processing module based on ANSYS softwares, creates hanging down for Ballast track
It is that the vertical dynamic model of Ballast track is established using the pre-processing module of ANSYS softwares to dynamic model and analysis, wherein
Rail is carried out discrete using Beam3 beam elements, and sleeper and railway roadbed are simulated using Mass21 mass units, and rail and sleeper,
Combin14 Hookean springs-damping unit mould is used in connection between sleeper and railway roadbed, railway roadbed and roadbed and adjacent railway roadbed block
Intend.
2. the vertical dynamical modeling system of railway transportation Ballast track according to claim 1, it is characterised in that：
Respectively corresponding oscillatory differential equation is respectively the rail, sleeper and the railway roadbed that analysis equation is established in unit：
The ordinary differential system of the rail vibration coordinate of the rail
The oscillatory differential equation of the sleeper
The oscillatory differential equation of the railway roadbed
Formula (1.15), (1.18) and (1.21) synthesis is obtained into the oscillatory differential equation group of track structure, exponent number M+ simultaneously
2N。
3. the vertical dynamical modeling system of railway transportation Ballast track according to claim 2, it is characterised in that：
Partial parameters in parameter analysis unit can be obtained directly by empirical data, another part parameter by railway roadbed centrum by
Lotus is assumed to be calculated, and calculating process includes：
According to the computed altitude h of centrum lap0To judge whether adjacent railway roadbed block interference phenomenon occurs, and select institute accordingly
Calculation formula to be used, wherein, h0Concrete form it is as follows
Work as h0When≤0, without interference phenomenon between adjacent railway roadbed block, at this time
Kf=(le+2hb tanα)(lb+2hb tanα)Ef (1.25)
Work as h0>When 0, there are interference phenomenon between adjacent railway roadbed block, at this time
Wherein
And roadbed support stiffness
Kf=ls(le+2hb tanα)Ef (1.30)。
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| GB2601847A (en) * | 2020-11-30 | 2022-06-15 | Reckitt Benckiser Health Ltd | Personal care compositions |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| GB2601847A (en) * | 2020-11-30 | 2022-06-15 | Reckitt Benckiser Health Ltd | Personal care compositions |
| GB2601847B (en) * | 2020-11-30 | 2023-05-10 | Reckitt Benckiser Health Ltd | Sanitising/cleansing personal care composition |
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