CN108345724A - A kind of optimum design method of tramcar embedded tracks road structure - Google Patents
A kind of optimum design method of tramcar embedded tracks road structure Download PDFInfo
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Abstract
The present invention relates to a kind of design methods of tramcar embedded tracks road structure, it is fully investigating existing streetcar track roadbed design data, it is basic to grasp tramcar vehicle, on the basis of the design parameter of track and roadbed, experiment is carried out using response phase method and regression analysis is carried out to structure, and then obtain rail vertical deviation, track plates vertical bending moment, bedding top surface deforms and the functional relation of bedding top surface dynamic stress and each main design parameters, and the evaluation and optimization of embedded tracks road structure design scheme are carried out according to the functional relation, finally obtain the design scheme of economical rationality.
Description
Technical field
The present invention relates to a kind of methods of optimization design tramcar embedded tracks road structure, belong to city rail friendship
Logical field.
Background technology
Modern tram belongs to urban track traffic scope, has more similarity with subway and light rail, but simultaneously
But also with its own exclusive technology and operation feature.Modern tram type of vehicle is unique, right of way form is complicated and under
Portion's embedded tracks structure has larger difference (as shown in Figure 1) compared with Conventional plate-type non-fragment orbit, therefore in design, construction and supports
Shield repair etc. cannot blindly apply mechanically the design standard of subway and light rail.However, since China's modern tram is studied
It the reasons such as starts late, the design of modern tram track bed at present and builds and have no unified standard, mostly answered with reference to foreign countries
With situation or use for reference other urban track traffic modes.Therefore, the co-design for studying embedded tracks roadbed system, will have
Conducive to modern tram system safe and stable operation is ensured, extension wire service life, promotion China's modern tram is not
Disconnected development, has good economic results in society.Therefore there is an urgent need for propose a kind of simple and efficient optimization design embedded tracks road
The method of based structures.
Invention content
The present invention for currently to embedded tracks roadbed design parameter to every design objective affecting laws theory and
Research is insufficient, to improve the economy and reasonability of track bed design, provides a kind of simple Optimal Design embedded tracks road
The method that based structures are set.The present invention can correctly reflect influence of each crucial track bed parameter to design objective, while big
Improve design efficiency greatly, further compensated for the deficiency of modern tram embedded tracks Design Method for Subgrade, have compared with
Strong practicability and extensive engineering application foreground.
In view of the above and other objects, the present invention is achieved through the following technical solutions:
A kind of optimum design method of tramcar embedded tracks road structure, which is characterized in that include the following steps:
Step 1: existing streetcar track roadbed design data is fully investigated, it is basic to grasp tramcar vehicle, rail
The design parameter in road and roadbed, mainly includes:Tramcar axis is heavy (A/t), high molecular material used by embedded tracks
Elasticity modulus (B/MPa), track plate thickness (C/m), subgrade bed overall thickness (D/m) and bedding Compaction K30(E/
(MPa/m)), so that it is determined that the reasonable value range of design parameter;
Step 2: according to the tramcar embedded tracks roadbed knot of design parameter track plates length collected by step 1
Structure finite element model;
Step 3: carrying out track bed structure ginseng using single-factor quantity method according to the finite element model that step 2 is established
Number impact analysis, determines crucial effect parameter;
Step 4: carrying out the design of response surface experiments scheme using Box-Behnken test design methods;
Step 5: using stepwise regression analysis method to data carry out regression analysis, to obtain rail vertical deviation,
Letter between key influence factor described in track plates vertical bending moment, the deformation of bedding top surface and bedding top surface dynamic stress and step 3
Number relationship.
Further, it is characterised in that:The tramcar embedded tracks of three pieces of track plates length are established in step 2
Road structure finite element model, using the track bed structure corresponding to intermediate one piece of track plates as research object.
Further, it is characterised in that:The crucial effect parameter is macromolecule packing material elasticity modulus (A/MPa),
Track plate thickness (B/m), subgrade bed overall thickness (C/m) and bedding Compaction K30(D/(MPa/m))
Further, it is characterised in that:The rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface and
Bedding top surface dynamic stress and the functional relation of five kinds of factors described in step 1 are respectively:
R1=1.51700-0.24148*A+0.44218*B+0.15034*C-0.00061*D-0.000 95*C*D
+0.02037*A^2
R2=-3.58416+0.35598*A+85.28571*B+0.52415*C-0.012728*D+0. 71429*A*B
-0.00524*C*D-0.036296*A^2-136.05442*B^2
R3=0.17848+0.018201*A+0.58503*B+0.17381*C-0.00166*D-0.04 7619*A*B
-0.00095*C*D-0.02381*C^2
R4=18.86752+0.18712*A-45.02721*B-7.61395*C+0.086799*D+2. 24490*B*C
-0.066667*B*D-0.014286*C*D+85.03401*B^2+3.08503*C^2
Wherein:R1, R2, R3, R4 indicate rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface, bedding respectively
Top surface dynamic stress, A are high molecular material elasticity modulus, and B is track plate thickness, and C is bedding overall thickness, and D is bedding Compaction
K30。
Further, it is characterised in that:Further include that the error in equation is analyzed and corrected after step 5.
Further, it is characterised in that:The error analysis and amendment include step 6:With coefficient of multiple correlation R2, correct
Multiple correlation coefficientIt is that evaluation index carries out error analysis with P values, if error analysis result is unqualified, returns to step
Rapid four re-start plan design.
Further, it is characterised in that:The error analysis and amendment include step 7:Respectively with rail vertical deviation,
The minimum value of track plates vertical bending moment, the deformation of bedding top surface and bedding top surface dynamic stress is optimization aim, using the BP based on GA
Neural network optimizes analysis to gained functional relation in step 5,
Further, it is characterised in that:The error analysis and amendment include step 8:It is built according to analytic hierarchy process (AHP)
Judgment matrix, and consistency check is carried out to judgment matrix, and using the feature vector of MATLAB Program judgment matrixs.
Further, it is characterised in that:The error analysis and amendment include step 9:By weight system obtained by step 8
It is several that processing is weighted to step 7, to obtain optimal embedded tracks roadbed design scheme.
The tramcar embedded tracks road structure finite element model is according to collected design parameter by having
Limit meta software ANSYS is established, and groove-shape rail, high molecular material, track plates, plain concrete supporting course and roadbed are all made of
Solid element is simulated, and train load is simulated by the concentrated force that a pair acts in track plate.The tramcar of foundation
Embedded tracks roadbed finite element model is as shown in Figure 2.
Advantages of the present invention:
1) it is directed to the theory and the not perfect situation of method that existing embedded tracks road structure designs, in track
On the basis of roadbed finite element model, result of finite element and Principle of Statistics are taken full advantage of, it is proposed that a kind of easy to be fast
The method of prompt optimization design embedded tracks road structure, can carry out the design scheme of embedded tracks road structure
Evaluation and optimization, so that design scheme is more economically reasonable.
2) response phase method can obtain a series of evaluation indexes using less test number (TN), and be obtained by regression analysis
Quadratic regression equation between each evaluation index and factor, thus on the basis for ensureing regression equation correctness significantly
Save valuable time.
3) qualitative and quantitative analysis of designer can be combined by analytic hierarchy process (AHP), so that designer can
To be very easily adjusted to embedded tracks roadbed design scheme according to previous engineering experience and actual demand.
Description of the drawings
Fig. 1 is the flow chart of the present invention
Fig. 2 is embedded tracks road structure schematic diagram
Fig. 3 is embedded tracks road structure finite element model figure
It is marked in figure as follows:1- rail, 2- macromolecule packing materials, 3- track plates, 4- plain concrete supporting courses, the roads 5-
Base.
Specific implementation mode
A kind of method of simple Optimal Design embedded tracks road structure described in present embodiment includes the following steps:
Step 1: existing streetcar track roadbed design data is fully investigated, it is basic to grasp streetcar track roadbed
The design parameter of structure.By taking certain tramcar Practical Project as an example, tramcar axis weight is 12.5t, desin speed 70km/
H, the coefficient of impact 1.5, high molecular material elasticity modulus are 3MPa, and track plates length is 6m, and track plates width is 2.1m, rail
Road plate thickness is 0.22m, and supporting course width is 2.1m, and bearing layer thickness is 0.2m, and roadbed overall thickness is 1.5m, Compaction
K30For 110MPa/m.
Step 2: the Track desigh parameter and roadbed design parameter according to step 1 establish the embedded rail of tramcar
Road Base structural finite element model;Preferably, to eliminate influence of the boundary effect to result of calculation, three pieces of rail plate longs are established
The tramcar embedded tracks road structure finite element model of degree, with the track bed knot corresponding to intermediate one piece of track plates
Structure is research object;
Step 3: carrying out track bed structure ginseng using single-factor quantity method according to the finite element model that step 2 is established
Number impact analysis, so that it is determined that going out key influence factor.
Show by the research and test result of applicant:
(1) with the increase of macromolecule packing material elasticity modulus, rail vertical deviation is substantially reduced;
(2) track plates length and width is insensitive to every evaluation index, and with the increase of track plate thickness, rail
Guidance tape vertical bending moment gradually increases, and bedding top surface dynamic stress is gradually reduced, and other two index amplitude of variation is smaller;
(3) supporting course width and thickness influences every evaluation index smaller;
(4) with the increase of roadbed overall thickness and Compaction K30, the deformation of bedding top surface is gradually reduced, and bedding top surface
Dynamic stress gradually increases.
Accordingly, it is determined that macromolecule packing material elasticity modulus (A/MPa), track plate thickness (B/m), subgrade bed total thickness
Spend (C/m) and bedding Compaction K30(D/ (MPa/m)) is crucial effect parameter.Meanwhile it is existing embedding both at home and abroad by investigating
The design scheme for entering formula track bed structure determines that the reasonable value range of above-mentioned five kinds of factors is as shown in table 1.
1 five kinds of factor reasonable value ranges of table
Step 4: since Box-Behnken test design methods can more accurately be depicted each influence factor and comment
Non-linear relation between valence index, and required test number (TN) is less compared with Central Composite designs, therefore use Box-
Behnken test design methods carry out the design of response surface experiments scheme, and testing program is as shown in table 2:
2 response surface experiments scheme of table
Step 5: being tested according to the table 2 in step 4, then data are returned using stepwise regression analysis method
Return analysis, to obtain rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface and bedding top surface dynamic stress and step
Functional relation between rapid 3 four kinds of key influence factors.
Rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface and the bedding top surface dynamic stress and step
The functional relation of one five kinds of factors is respectively:
Rail vertical deviation calculation formula
R1=1.51700-0.24148*A+0.44218*B+0.15034*C-0.00061*D-0.000 95*C*D
+0.02037*A^2
Track plates vertical bending moment calculation formula
R2=-3.58416+0.35598*A+85.28571*B+0.52415*C-0.012728*D+0. 71429*A*B
-0.00524*C*D-0.036296*A^2-136.05442*B^2
Bedding top surface deforms calculation formula
R3=0.17848+0.018201*A+0.58503*B+0.17381*C-0.00166*D-0.04 7619*A*B
-0.00095*C*D-0.02381*C^2
Bedding top surface Stress Calculation formula
R4=18.86752+0.18712*A-45.02721*B-7.61395*C+0.086799*D+2. 24490*B*C
-0.066667*B*D-0.014286*C*D+85.03401*B^2+3.08503*C^2
Wherein:R1, R2, R3, R4 indicate rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface, bedding respectively
Top surface dynamic stress, A are high molecular material elasticity modulus, and B is track plate thickness, and C is bedding overall thickness, and D is bedding Compaction
K30。
Preferably, further include the steps that the regression equation is verified and corrected, specific bag includes:
Step 6: respectively with the general coefficient of multiple correlation R of response phase method2, modified multiple correlation coefficientIt is to comment with P values
Valence index carries out error analysis to the functional relation of gained in step 5, and step is carried out after being verified, and otherwise increases new
Sampled point or delete infeasible sampled point, return to step 4 and re-start plan design;
Error analysis is as shown in table 3:
3 regression equation error analysis of table
Analytical table 3 it is found that four response regression equations multiple correlation coefficient and correct multiple correlation coefficient be all higher than 0.85,
And in close proximity to 1.Meanwhile the P values of each regression equation are respectively less than 0.01, therefore illustrate the correct of established regression equation
Property is very high.
Step 7: using the response of four kinds of embedded tracks roadbeds described in step 5 as optimization aim, using based on
The BP neural network of GA optimizes analysis to gained functional relation in step 5, when four kinds of responses of gained distinguish optimal
Embedded tracks roadbed design scheme is as shown in table 4.
4 prioritization scheme of table
Step 8: the importance degree of the response of four kinds of embedded tracks roadbeds according to step 5, uses
Analytic hierarchy process (AHP) determines the weight coefficient of four kinds of responses respectively.
It is analyzed it is found that since track plate thickness is to track plates maximum vertical bending moment and bedding top surface dynamic stress shadow by step 3
Sound is larger, and smaller to rail vertical displacement and bedding top surface Influence of Displacement.Rail is directly resulted in view of track plates moment of flexure is excessive
Road Structural Engineering cost dramatically increases, therefore track vertical bending moment importance is greater than bedding top surface dynamic stress.Meanwhile rail
Displacement has great influence for the comfortableness and security of driving, therefore steel rail displacement importance is slightly above bedding top surface position
It moves, hence it is evident that be less than bedding top surface dynamic stress.Construct judgment matrix as follows.
The feature vector of judgment matrix is solved, result of calculation is as follows:
W=(0.085,0.583,0.043,0.289)T
Consistency check is carried out to judgment matrix according to the relative theory of analytic hierarchy process (AHP), checking procedure is as follows:
1. calculating the Maximum characteristic root λ of judgment matrixmax:
2. calculating coincident indicator CI and CR
Therefore judgment matrix meets coherence request.
Wherein:RI is Aver-age Random Consistency Index, is taken as 0.9.
Thus may determine that rail vertical deviation, track plates vertical bending moment, the displacement of bedding top surface and dynamic stress weight system
Number is respectively 0.085,0.583,0.043,0.289.
Step 9: be weighted processing to four kinds of embedded tracks roadbed design schemes obtained by step 7, and by step 8
Gained weight coefficient is multiplied by each row in table 4 respectively, the embedded tracks road structure scheme after final optimization pass, such as 5 institute of table
Show.
5 final optimization pass scheme of table
From example as can be seen that the carried tramcar embedded tracks road structure design objective calculation formula of the present invention can
Preferably to describe affecting laws of each key parameter to design objective, the reliability of the put forward calculation formula of the present invention is demonstrated.
Meanwhile the carried embedded tracks road structure design objective calculation formula of the integrated use present invention and method for optimization analysis can
Ensureing to make the stress of embedded tracks road structure more reasonable on basis reasonable for structure, and to a certain extent
Reduce project cost.
In conclusion method of the present invention to a kind of simple Optimal Design embedded tracks road structure proposed, it can
To correctly reflecting the functional relation between each design parameter and evaluation index, existing embedded rail is largely compensated for
The shortcoming of Road Base design method, it is ensured that the reasonability and economy of design scheme.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications
It should be regarded as protection scope of the present invention.In addition, although having used some specific terms in this specification, these terms are only
Explanation merely for convenience, does not limit the present invention in any way.
Claims (9)
1. a kind of optimum design method of tramcar embedded tracks road structure, which is characterized in that include the following steps:
Step 1: existing streetcar track roadbed design data is fully investigated, it is basic to grasp tramcar vehicle, track and road
The design parameter of base, mainly includes:Tramcar axis is heavy (A/t), high molecular material springform used by embedded tracks
It measures (B/MPa), track plate thickness (C/m), subgrade bed overall thickness (D/m) and bedding Compaction K30(E/ (MPa/m)), from
And determine the reasonable value range of design parameter;
Step 2: being had according to the tramcar embedded tracks road structure of design parameter track plates length collected by step 1
Limit meta-model;
Step 3: carrying out track bed structural parameters shadow using single-factor quantity method according to the finite element model that step 2 is established
Analysis is rung, determines crucial effect parameter;
Step 4: carrying out the design of response surface experiments scheme using Box-Behnken test design methods;
Step 5: regression analysis is carried out to data using stepwise regression analysis method, to obtain rail vertical deviation, track plates
Functional relation between key influence factor described in vertical bending moment, the deformation of bedding top surface and bedding top surface dynamic stress and step 3.
2. optimum design method according to claim 1, it is characterised in that:Three pieces of track plates length are established in step 2
Tramcar embedded tracks road structure finite element model, be with the track bed structure corresponding to intermediate one piece of track plates
Research object.
3. optimum design method according to claim 1, it is characterised in that:The crucial effect parameter is filled for macromolecule
Elasticity modulus of materials (A/MPa), track plate thickness (B/m), subgrade bed overall thickness (C/m) and bedding Compaction K30(D/
(MPa/m))。
4. according to claim 1-3 any one of them optimum design methods, it is characterised in that:The rail vertical deviation,
Track plates vertical bending moment, the deformation of bedding top surface and bedding top surface dynamic stress and the functional relation of five kinds of factors described in step 1 are distinguished
For:
R1=1.51700-0.24148*A+0.44218*B+0.15034*C-0.00061*D-0.000 95*C*D+0.02037*A
^2
R2=-3.58416+0.35598*A+85.28571*B+0.52415*C-0.012728*D+0. 71429*A*B-
0.00524*C*D-0.036296*A^2-136.05442*B^2
R3=0.17848+0.018201*A+0.58503*B+0.17381*C-0.00166*D-0.04 7619*A*B-
0.00095*C*D-0.02381*C^2
R4=18.86752+0.18712*A-45.02721*B-7.61395*C+0.086799*D+2. 24490*B*C-
0.066667*B*D-0.014286*C*D+85.03401*B^2+3.08503*C^2
Wherein:R1, R2, R3, R4 indicate rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface, bedding top surface respectively
Dynamic stress, A are high molecular material elasticity modulus, and B is track plate thickness, and C is bedding overall thickness, and D is bedding Compaction K30。
5. optimum design method according to claim 4, it is characterised in that:Further include to the equation after step 5
Error analysis and amendment.
6. optimum design method according to claim 5, it is characterised in that:The error analysis and amendment include step
Six:With coefficient of multiple correlation R2, modified multiple correlation coefficientIt is that evaluation index carries out error analysis with P values, if error analysis
As a result it is unqualified, then returns to step 4 and re-start plan design.
7. optimum design method according to claim 6, it is characterised in that:The error analysis and amendment include step
Seven:It is respectively excellent with the minimum value of rail vertical deviation, track plates vertical bending moment, the deformation of bedding top surface and bedding top surface dynamic stress
Change target, analysis is optimized to gained functional relation in step 5 using the BP neural network based on GA.
8. optimum design method according to claim 7, it is characterised in that:The error analysis and amendment include step
Eight:Consistency check is carried out according to analytic hierarchy process (AHP) development of judgment matrix, and to judgment matrix, and uses MATLAB Programs
The feature vector of judgment matrix.
9. optimum design method according to claim 7, it is characterised in that:The error analysis and amendment include step
Nine:Weight coefficient obtained by step 8 is weighted processing to step 7, to obtain more preferably embedded tracks roadbed design
Scheme.
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