CN111368444A - Wheel-rail rolling contact spot analysis method - Google Patents
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Abstract
The invention discloses a wheel-rail rolling contact spot analysis method, which specifically comprises the following steps: establishing a multi-body dynamic simulation model of the wheel-rail rolling contact relation according to the actual wheel-rail rolling contact relation, and outputting wheel-rail rolling contact variables corresponding to wheel-rail rolling contact spots; according to relevant wheel rail rolling contact variables of the wheel rail rolling contact patch, calculating the distribution condition of a total sliding vector in the wheel rail rolling contact patch and defining the condition of a viscous sliding area in the contact patch based on a Kalker linear simplification theory; and calculating the distribution condition of the vertical abrasion loss in the rolling contact spot of the wheel rail based on the Archard abrasion model. The abrasion calculation process of the invention is close to the actual field abrasion condition, the calculation result is accurate, the analysis process of the sliding effect and the abrasion effect of the wheel rail rolling contact patch is efficient and simple, and the invention can be used as the wheel rail rolling contact patch abrasion algorithm interface of multi-body dynamics simulation software such as SIMPACK, GENSYS and the like, and realizes the simulation and calculation of the wheel pair abrasion condition in the running process of the train.
Description
Technical Field
The invention relates to the technical field of wheel-rail rolling contact analysis, in particular to a wheel-rail rolling contact spot analysis method.
Background
With the rapid development of subway systems, the subway systems also face a number of problems. Taking a subway train system as an example, the wheel set is one of important components of a train body, plays a role in guiding the train body to correctly advance and turn along a steel rail in the running process of the train, and is also required to bear all dynamic and static loads from the rail and the train body, so that the problem of wheel set abrasion is one of the most frequently encountered problems of the subway system due to the severe working environment.
The method has the advantages that the wheel set abrasion condition is mastered in real time, the normal service performance of the wheel set is guaranteed, and the method has important significance for guaranteeing the normal safe operation of subway trains. The core of the research on the wheel set abrasion problem lies in analyzing the wheel-rail rolling contact relationship, which reflects the matching state between the wheel rails, and is the basis for analyzing the wheel set abrasion problem, and the expression form of the wheel set abrasion problem is wheel-rail rolling contact spots. In the existing research aiming at the wheel-rail rolling contact spots, the contact spots are regarded as a whole, and the sliding effect and abrasion are analyzed, so that the accuracy of the final analysis result is not high.
Disclosure of Invention
The invention aims to provide an efficient and accurate wheel rail rolling contact patch analysis method capable of realizing analysis of relative sliding effect and abrasion effect between wheel rails.
The technical solution for realizing the purpose of the invention is as follows: a wheel-rail rolling contact spot analysis method comprises the following steps:
and 3, calculating the distribution condition of the vertical abrasion loss in the rolling contact spot of the wheel track based on the Archard abrasion model.
Further, the step 1 of establishing a multi-body dynamic simulation model of the wheel-rail rolling contact relationship according to the actual wheel-rail rolling contact relationship on site, and outputting a wheel-rail rolling contact variable corresponding to the wheel-rail rolling contact patch, specifically as follows:
step 1.1, establishing a wheel pair multi-body dynamics simulation model according to basic contact parameters of a field wheel pair, including wheel diameter, wheel pair transverse displacement, wheel pair rolling head angle and wheel rim inner side distance;
step 1.2, establishing a track multi-body dynamics simulation model according to basic contact parameters of a field track and the geometrical linear condition of the track;
step 1.3, establishing a multi-body dynamic simulation model of the wheel-rail rolling contact relation, simulating the actual wheel-rail rolling contact relation in the running process of the train in real time, and outputting wheel-rail rolling contact variables of wheel-rail rolling contact spots in the process, wherein the wheel-rail rolling contact variables comprise the number np of the contact spots, the transverse η, the longitudinal epsilon and the spin
Creep rate, starting yws and ending ywe positions of contact spots on the wheel, half shaft lengths a and b of the contact spots, contact stress of the contact spots in the vertical direction Qp, and Kalker coefficient C11、C22、C23。
Further, the step 2 of calculating the distribution of the total sliding vector w in the rolling contact patch of the wheel and rail and defining the condition of the viscous sliding area in the contact patch based on the Kalker linear simplification theory according to the relevant rolling contact variable of the rolling contact patch of the wheel and rail, specifically as follows:
step 2.1, obtaining a sliding equation expression under the steady rolling contact state of the wheel rail based on the wheel rail rolling contact variable of the wheel rail rolling contact spot;
step 2.2, carrying out dimensionless operation on the sliding equation expression to realize the conversion from the original wheel track rolling contact spot to the unit circle contact spot and obtain the equation expression of the total sliding vector w;
and 2.3, discretizing the unit circle contact patch into 10 × 10 discrete points, introducing coulomb friction law analysis, and calculating the stick-slip condition and the total slip vector w of each discrete point.
Further, the step 2.1 obtains a sliding equation expression in the steady rolling contact state of the wheel rail based on the wheel rail rolling contact variable of the wheel rail rolling contact patch, specifically as follows:
step 2.1.1, calculating the longitudinal and transverse contact spot cuts respectivelyDirection force px、py：
Wherein, C11、C22、C23Is Kalker coefficient, G is the synthetic shear modulus of the wheel-rail material, η, epsilon,
Respectively the transverse creep rate, the longitudinal creep rate and the spin creep rate, wherein a and b are the semiaxial length of the elliptical contact patch;
step 2.1.2, respectively calculating the material flexibility coefficients L of the contact patch in the longitudinal direction and the transverse directionx、Ly：
Step 2.1.3, obtaining a sliding equation expression under the steady rolling contact state of the wheel rail based on the Kalker linear simplification theory:
wherein v isx、vyRespectively longitudinal and transverse sliding speed, vvFor the running speed of the locomotive, Lx、LyRespectively longitudinal and transverse material compliance coefficient, px、pyRespectively longitudinal and transverse tangential forces, and x and y are coordinate points in the contact patch based on a wheel-track coordinate system.
Further, the step 2.2 of performing dimensionless operation on the sliding equation expression to realize the conversion from the original wheel track rolling contact patch to the unit circle contact patch and obtain the equation expression of the total sliding vector w, which is specifically as follows:
step 2.2.1, carrying out dimensionless operation on the sliding equation expression to realize the conversion from the rolling contact spot of the original wheel track to the unit circle contact spot, and ordering:
wherein N is the resultant force in the contact patch in the normal direction, f is the friction coefficient of the wheel track, x 'is the abscissa after non-dimensionalization, y' is the ordinate after non-dimensionalization, z0Is the maximum value of normal force in contact patch, p'x、p′yFor the non-dimensionalized internal contact force of the contact patch, nx、nyIs the displacement amount in a contact patch, L'yIs a material compliance coefficient in the transverse direction after non-dimensionalization,
is the non-dimensionalized spin creep rate component, wiIs the sliding amount;
step 2.2.2, obtaining a new sliding equation expression as follows:
step 2.2.3, converting the new sliding equation expression into a matrix vector form:
wherein w ═ wxwy) As a result of the total sliding vector,
in the form of a rigid sliding vector, the sliding vector,
is an elastic sliding vector.
Further, in step 2.3, the unit circle contact patch is discretized into 10 × 10 discrete points, coulomb friction law analysis is introduced, and the stick-slip condition and the total slip vector w of each discrete point are calculated as follows:
step 2.3.1, taking any strip on the unit circle, which is parallel to the x 'axis and has the width dy', and taking a point x on the strip1’＝x0' -h to x0' integrate, when h goes to 0, convert the matrix vector expression to:
w1/2＝s1/2+p′1-p′0
wherein,
is a point x1' AND Point x0' the total sliding vector between the two elements,
is a point x1' AND Point x0'rigid sliding vector between p'1＝p'(x'1) Is a point x1'elastic slip vector of, p'0＝p'(x'0) Is a point x0The elastic sliding vector at, h is the point x1' AND Point x0'Length between, x'1/2Is a point x1' AND Point x0' midpoint between;
step 2.3.2, h take 1/10 with belt length from right belt boundary
Initially, the force at the boundary is idealized as 0, so p' (x)0') (00) backwards according to
Solving rigid sliding vectors of the whole strip in sequence to realize the discretization of the unit circle contact patch into 10 × 10 discrete points;
step 2.3.3, coulomb friction law analysis is introduced, and the stick-slip condition and the total slip vector w of each discrete point are calculated, namely any point in a unit circle contact spot meets the following conditions:
definition z ═ p/z0，pH＝p0’-s│xo’-h/2，
1) If | pH|≤fz’Then the spot is in an adhesive state, p1’＝pHAnd w |xo’-h/2＝(0 0)；
2) If | pH|>fz', then the point is in a sliding state, p1’＝(fz’/|pH|)×pHAnd w |xo’-h/2＝-λp1', where λ ═ pHI/(fz') -1 and λ>0。
Further, the distribution situation of the vertical abrasion loss in the rolling contact patch of the wheel rail is calculated based on the Archard abrasion model in the step 3, which is specifically as follows:
step 3.1, aiming at the sliding area in the rolling contact spot of the wheel rail, calculating the vertical abrasion loss delta z (x, y) of each sliding discrete point based on an Archard abrasion model as follows:
wherein Qp is the normal contact force, H is the hardness of the softer material of the two contact materials, kwΔ x is the length of the discrete point on the abscissa for a dimensionless wear coefficient;
and 3.2, regarding the adhesion area in the rolling contact spot of the wheel track, and setting the default delta z (x, y) to be 0.
Compared with the prior art, the method has the obvious advantages that (1) the abrasion of the wheel rail rolling contact spots is discretized into abrasion distribution of 10 × 10 discrete points, the abrasion calculation process is closer to the actual field abrasion condition, and the calculation result is more accurate, and (2) the sliding effect and abrasion effect analysis process of the wheel rail rolling contact spots is efficient and simple, the analysis result is accurate, and the method can be used as a wheel rail rolling contact spot abrasion algorithm interface of multi-body dynamics simulation software such as SIMPACK and GENSYS, and the simulation and calculation of the wheel pair abrasion condition in the train running process are realized.
Drawings
FIG. 1 is a schematic flow chart of a wheel-rail rolling contact patch analysis method according to the present invention.
FIG. 2 is a schematic diagram of a multi-body dynamic simulation model of a wheel-rail rolling contact relationship in an embodiment of the invention.
FIG. 3 is a schematic diagram of the de-dimensionalization and discretization of the rolling contact patch of the wheel and rail according to an embodiment of the present invention.
FIG. 4 is a schematic diagram of the definition of the rolling contact patch viscous-smooth area of the wheel track according to the embodiment of the invention.
FIG. 5 is a schematic diagram of the vertical wear distribution of the rolling contact patch of the wheel track in the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
With reference to fig. 1, the wheel-rail rolling contact patch analysis method of the present invention includes the following steps:
step 1.1, establishing a wheel pair multi-body dynamics simulation model according to basic contact parameters of a field wheel pair, including wheel diameter, wheel pair transverse displacement, wheel pair rolling head angle and wheel rim inner side distance;
step 1.2, establishing a track multi-body dynamics simulation model according to basic contact parameters of a field track and the geometrical linear condition of the track;
step 1.3, establishing a multi-body dynamic simulation model of the wheel-rail rolling contact relation, simulating the actual wheel-rail rolling contact relation in the running process of the train in real time, and outputting wheel-rail rolling contact variables of wheel-rail rolling contact spots in the process, wherein the wheel-rail rolling contact variables comprise the number np of the contact spots, the transverse η, the longitudinal epsilon and the spin
Creep rate, starting yws and ending ywe positions of contact spots on the wheel, half shaft lengths a and b of the contact spots, contact stress of the contact spots in the vertical direction Qp, and Kalker coefficient C11、C22、C23。
step 2.1, obtaining a sliding equation expression under the steady rolling contact state of the wheel rail based on the wheel rail rolling contact variable of the wheel rail rolling contact spot, which is specifically as follows:
step 2.1.1, respectively calculating the longitudinal and transverse tangential forces of the contact patch:
wherein, C11、C22、C23Is Kalker coefficient, G is the synthetic shear modulus of the wheel-rail material, η, epsilon,
Respectively the transverse creep rate, the longitudinal creep rate and the spin creep rate, wherein a and b are the semiaxial length of the elliptical contact patch;
step 2.1.2, respectively calculating the material flexibility coefficients of the contact spots in the longitudinal direction and the transverse direction:
step 2.1.3, obtaining a sliding equation expression under the steady rolling contact state of the wheel rail based on the Kalker linear simplification theory:
wherein v isx、vyRespectively longitudinal and transverse sliding speed, vvFor the running speed of the locomotive, Lx、LyRespectively longitudinal and transverse material compliance coefficient, px、pyRespectively longitudinal and transverse tangential forces, and x and y are coordinate points in the contact patch based on a wheel-track coordinate system.
Step 2.2, carrying out dimensionless operation on the sliding equation expression to realize the conversion from the original wheel track rolling contact patch to the unit circle contact patch and obtain the equation expression of the total sliding vector w, which is specifically as follows:
step 2.2.1, carrying out dimensionless operation on the sliding equation expression to realize the conversion from the rolling contact spot of the original wheel track to the unit circle contact spot, and ordering:
wherein N is the resultant force in the contact patch in the normal direction, f is the friction coefficient of the wheel track, x 'is the abscissa after non-dimensionalization, y' is the ordinate after non-dimensionalization, z0Is the maximum value of normal force in contact patch, p'x、p′yFor the non-dimensionalized internal contact force of the contact patch, nx、nyIs the displacement amount in a contact patch, L'yIs a material compliance coefficient in the transverse direction after non-dimensionalization,
is the non-dimensionalized spin creep rate component, wiIs the sliding amount;
step 2.2.2, obtaining a new sliding equation expression as follows:
step 2.2.3, converting the new sliding equation expression into a matrix vector form:
wherein w ═ wxwy) As a result of the total sliding vector,
in the form of a rigid sliding vector, the sliding vector,
as elastic sliding vector
Step 2.3, discretizing the unit circle contact patch into 10 × 10 discrete points, introducing coulomb friction law analysis, and calculating the stick-slip condition and the total slip vector w of each discrete point, wherein the method specifically comprises the following steps:
step 2.3.1, taking any strip on the unit circle, which is parallel to the x 'axis and has the width dy', and taking a point x on the strip1’＝x0' -h to x0' integrate, when h goes to 0, convert the matrix vector expression to:
w1/2＝s1/2+p′1-p′0
wherein,
is a point x1' AND Point x0' the total sliding vector between the two elements,
is a point x1' AND Point x0'rigid sliding vector between p'1＝p'(x'1) Is a point x1'elastic slip vector of, p'0＝p'(x'0) Is a point x0The elastic sliding vector at, h is the point x1' AND Point x0'Length between, x'1/2Is a point x1' AND Point x0' midpoint between;
step 2.3.2, h take 1/10 with belt length from right belt boundary
Initially, the force at the boundary is idealized as 0, so p' (x)0') (00) backwards according to
Solving rigid sliding vectors of the whole strip in sequence to realize the discretization of the unit circle contact patch into 10 × 10 discrete points;
step 2.3.3, coulomb friction law analysis is introduced, and the stick-slip condition and the total slip vector w of each discrete point are calculated, namely any point in a unit circle contact spot meets the following conditions:
definition z ═ p/z0，pH＝p0’-s│xo’-h/2，
1) If | pHIf | ≦ fz', the dot is in an adhesive state, p1’＝pHAnd w |xo’-h/2＝(0 0)；
2) If | pH|>fz', then the point is in a sliding state, p1’＝(fz’/|pH|)×pHAnd w |xo’-h/2＝-λp1', where λ ═ pHI/(fz') -1 and λ>0。
step 3.1, aiming at the sliding area in the rolling contact spot of the wheel rail, calculating the vertical abrasion loss of each sliding discrete point based on an Archard abrasion model as follows:
wherein Qp is the normal contact force, H is the hardness of the softer material of the two contact materials, kwΔ x is the length of the discrete point on the abscissa for a dimensionless wear coefficient;
and 3.2, regarding the adhesion area in the rolling contact spot of the wheel track, and setting the default delta z (x, y) to be 0.
Example 1
In this embodiment, a train in a next trip of the guangzhou subway line network is taken as an example for specific explanation, and the process includes the following steps:
in order to realize the simulation of the actual wheel-rail contact effect, firstly, a wheel-pair/rail multi-body dynamic model is established, wheel/rail basic parameters which have obvious influence on the wheel-rail contact relation are determined, and parameters which have little influence are ignored. According to the actual wheel set condition on site, the measured S10002 type profile is adopted as the initial profile of the wheel set, the nominal diameter of the wheel is set to be 840mm, and the inner side distance of the wheel rim is set to be 1353 mm. Considering that the slight elastic deformation on the wheel set can directly influence the contact relation of the wheel and the rail, the wheel set is set as an elastic body; similarly, the actual situation of the rail on site is combined, the initial profile of the rail adopts an actually measured UIC60 profile, the bottom slope of the rail is set to be 1:40, the gauge is set to be 1435mm, and the friction coefficient of the wheel rail is set to be 0.4. Similarly to wheel set modeling, the elastic deformation occurs when the rail is made of an elastic body. Because the track line shapes with different curve radiuses can generate different wheel-track contact relations, a track line model is required to be established according to the actual line condition, wherein the total length of the line is about 14.4km, different sections of the track have different curve radiuses, and each section has a specified ultrahigh value. The final wheel-rail rolling contact relation multi-body dynamic simulation model is shown in figure 2. The model after the simulation can output the wheel-rail rolling contact variable corresponding to the wheel-rail rolling contact patch, as shown in table 1.
TABLE 1 model output wheel-track contact variables
after the wheel track rolling contact variable of the wheel track rolling contact patch at a certain sampling point is obtained as shown in table 1, the wheel track rolling contact variable is input into a contact patch analysis algorithm flow to realize the dimensionless treatment of the original elliptic wheel track rolling contact patch into a unit circle contact patch, the subsequent discretization is carried out on the basis of the unit circle contact patch into 10 × 10 discrete points, the total sliding vector w of each discrete point is respectively calculated, and the result is shown in table 2.
TABLE 2 Total sliding vector distribution in Unit circle contact patch (part)
And 3, calculating the distribution situation of the vertical abrasion loss in the rolling contact spot of the wheel rail based on the Archard abrasion model:
on the basis of defining the sticky and slippery area of the wheel rail contact patch, the vertical abrasion amount of each sliding point in the wheel rail contact patch after the wheel rolls for one circle is calculated based on the Archard abrasion model, so as to obtain the vertical abrasion distribution of the whole contact patch, as shown in FIG. 5.
In conclusion, the abrasion of the wheel rail rolling contact spots can be discretized into abrasion distribution of 10 × 10 discrete points, the abrasion calculation process is closer to the actual field abrasion condition, the calculation result is more accurate, the sliding effect and abrasion effect analysis process of the wheel rail rolling contact spots is efficient and simple, the analysis result is accurate, and the wheel rail rolling contact spot abrasion calculation method can be used as a wheel rail rolling contact spot abrasion algorithm interface of multi-body dynamics simulation software such as SIMPACK (simple interactive simulation and dynamic simulation system) and GENSYS (generalized information system) and the like to realize the simulation and calculation of the abrasion condition of the wheel pair in the running process of the train.
Claims (7)
1. A wheel-rail rolling contact spot analysis method is characterized by comprising the following steps:
step 1, establishing a multi-body dynamic simulation model of a wheel-rail rolling contact relation according to the actual wheel-rail rolling contact relation on site, and outputting wheel-rail rolling contact variables corresponding to wheel-rail rolling contact spots;
step 2, calculating the distribution condition of the total sliding vector w in the wheel rail rolling contact spot and defining the condition of a viscous sliding area in the contact spot based on a Kalker linear simplification theory according to the relevant wheel rail rolling contact variable of the wheel rail rolling contact spot;
and 3, calculating the distribution condition of the vertical abrasion loss in the rolling contact spot of the wheel track based on the Archard abrasion model.
2. The wheel-rail rolling contact patch analysis method according to claim 1, wherein the step 1 is to establish a multi-body dynamic simulation model of the wheel-rail rolling contact relationship according to the actual wheel-rail rolling contact relationship on site, and output a wheel-rail rolling contact variable corresponding to the wheel-rail rolling contact patch, specifically as follows:
step 1.1, establishing a wheel pair multi-body dynamics simulation model according to basic contact parameters of a field wheel pair, including wheel diameter, wheel pair transverse displacement, wheel pair rolling head angle and wheel rim inner side distance;
step 1.2, establishing a track multi-body dynamics simulation model according to basic contact parameters of a field track and the geometrical linear condition of the track;
step 1.3, establishing a multi-body dynamic simulation model of the wheel-rail rolling contact relation, simulating the actual wheel-rail rolling contact relation in the running process of the train in real time, and outputting wheel-rail rolling contact variables of wheel-rail rolling contact spots in the process, wherein the wheel-rail rolling contact variables comprise the number np of the contact spots, the transverse η, the longitudinal epsilon and the spin
Creep rate, starting yws and ending ywe positions of contact spots on the wheel, half shaft lengths a and b of the contact spots, contact stress of the contact spots in the vertical direction Qp, and Kalker coefficient C11、C22、C23。
3. The wheel-rail rolling contact patch analysis method according to claim 1, wherein the step 2 is to calculate the distribution of the total sliding vector w in the wheel-rail rolling contact patch and define the condition of the sticky-sliding area in the contact patch based on the Kalker linear simplification theory according to the relevant wheel-rail rolling contact variables of the wheel-rail rolling contact patch, and specifically includes the following steps:
step 2.1, obtaining a sliding equation expression under the steady rolling contact state of the wheel rail based on the wheel rail rolling contact variable of the wheel rail rolling contact spot;
step 2.2, carrying out dimensionless operation on the sliding equation expression to realize the conversion from the original wheel track rolling contact spot to the unit circle contact spot and obtain the equation expression of the total sliding vector w;
and 2.3, discretizing the unit circle contact patch into 10 × 10 discrete points, introducing coulomb friction law analysis, and calculating the stick-slip condition and the total slip vector w of each discrete point.
4. The wheel-rail rolling contact patch analysis method according to claim 3, wherein the wheel-rail rolling contact variable based on the wheel-rail rolling contact patch in step 2.1 is used to obtain a sliding equation expression in a steady-state rolling contact state of the wheel rail, specifically as follows:
step 2.1.1, respectively calculating the longitudinal and transverse tangential forces p of the contact patchx、py：
Wherein, C11、C22、C23Is Kalker coefficient, G is the synthetic shear modulus of the wheel-rail material, η, epsilon,
Respectively the transverse creep rate, the longitudinal creep rate and the spin creep rate, wherein a and b are the semiaxial length of the elliptical contact patch;
step 2.1.2, respectively calculating the material flexibility coefficients L of the contact patch in the longitudinal direction and the transverse directionx、Ly：
Step 2.1.3, obtaining a sliding equation expression under the steady rolling contact state of the wheel rail based on the Kalker linear simplification theory:
wherein v isx、vyRespectively longitudinal and transverse sliding speed, vvFor the running speed of the locomotive, Lx、LyRespectively longitudinal and transverse material compliance coefficient, px、pyRespectively longitudinal and transverse tangential forces, and x and y are coordinate points in the contact patch based on a wheel-track coordinate system.
5. The wheel-track rolling contact patch analysis method according to claim 3, wherein the sliding equation expression in step 2.2 is subjected to non-dimensionalization operation to realize conversion from the original wheel-track rolling contact patch to a unit circle contact patch and obtain an equation expression of a total sliding vector w, which is as follows:
step 2.2.1, carrying out dimensionless operation on the sliding equation expression to realize the conversion from the rolling contact spot of the original wheel track to the unit circle contact spot, and ordering:
wherein N is the resultant force in the contact patch in the normal direction, f is the friction coefficient of the wheel track, x 'is the abscissa after non-dimensionalization, y' is the ordinate after non-dimensionalization, z0Is the maximum value of normal force in contact patch, p'x、py' is the non-dimensionalized internal contact force of the contact patch, nx、nyIs the displacement amount in a contact patch, L'yIs a material compliance coefficient in the transverse direction after non-dimensionalization,
is the non-dimensionalized spin creep rate component, wiIs the sliding amount;
step 2.2.2, obtaining a new sliding equation expression as follows:
step 2.2.3, converting the new sliding equation expression into a matrix vector form:
wherein w ═ wxwy) As a result of the total sliding vector,
in the form of a rigid sliding vector, the sliding vector,
is an elastic sliding vector.
6. The wheel-track rolling contact patch analysis method according to claim 3, wherein the discretization of the unit circle contact patch in step 2.3 is performed to 10 × 10 discrete points, and coulomb friction law analysis is introduced to calculate the stick-slip condition and the total slip vector w of each discrete point, which are as follows:
step 2.3.1, taking any strip on the unit circle, which is parallel to the x 'axis and has the width dy', and taking a point x on the strip1’＝x0' -h to x0' integrate, when h goes to 0, convert the matrix vector expression to:
w1/2＝s1/2+p′1-p′0
wherein,
is a point x1' AND Point x0' the total sliding vector between the two elements,
is a point x1' AND Point x0'rigid sliding vector between p'1＝p'(x'1) Is a point x1'elastic slip vector of, p'0＝p'(x'0) Is a point x0The elastic sliding vector at, h is the point x1' AND Point x0'Length between, x'1/2Is a point x1' AND Point x0' midpoint between;
step 2.3.2, h take 1/10 with belt length from right belt boundary
Initially, the force at the boundary is idealized as 0, so p' (x)0') (00) backwards according to
Solving rigid sliding vectors of the whole strip in sequence to realize the discretization of the unit circle contact patch into 10 × 10 discrete points;
step 2.3.3, coulomb friction law analysis is introduced, and the stick-slip condition and the total slip vector w of each discrete point are calculated, namely any point in a unit circle contact spot meets the following conditions:
definition z ═ p/z0，pH＝p0’-s|xo’-h/2，
1) If | pHIf | ≦ fz', the dot is in an adhesive state, p1’＝pHAnd w-xo’-h/2＝(0 0)；
2) If | pH|>fz', then the point is in a sliding state, p1’＝(fz’/|pH|)×pHAnd w-xo’-h/2＝-λp1', where λ ═ pHI/(fz') -1 and λ>0。
7. The wheel-rail rolling contact patch analysis method according to claim 1, wherein the vertical wear distribution in the wheel-rail rolling contact patch is calculated based on the Archard wear model in step 3, and specifically as follows:
step 3.1, aiming at the sliding area in the rolling contact spot of the wheel rail, calculating the vertical abrasion loss delta z (x, y) of each sliding discrete point based on an Archard abrasion model as follows:
wherein Qp is the normal contact force, H is the hardness of the softer material of the two contact materials, kwΔ x is the length of the discrete point on the abscissa for a dimensionless wear coefficient;
and 3.2, regarding the adhesion area in the rolling contact spot of the wheel track, and setting the default delta z (x, y) to be 0.
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Cited By (7)
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| CN113503197A (en) * | 2021-07-12 | 2021-10-15 | 哈尔滨工程大学 | Marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration |
| CN114541196A (en) * | 2022-02-18 | 2022-05-27 | 西南交通大学 | Rail grinding period design method considering turnout service performance evolution |
| CN114781158A (en) * | 2022-04-21 | 2022-07-22 | 西南交通大学 | Equivalent method for simplifying non-Hertz tangential contact calculation of wheel track |
| CN114969886A (en) * | 2022-04-07 | 2022-08-30 | 西南交通大学 | Steel rail rolling contact fatigue prediction method |
| CN115630554A (en) * | 2022-11-15 | 2023-01-20 | 西南交通大学 | Wheel-rail two-dimensional rolling contact force calculation method considering material nonuniformity |
| CN116542023A (en) * | 2023-04-12 | 2023-08-04 | 西南交通大学 | Computing method, system and storage medium for simulating conformal contact of wheel track |
| CN117744236A (en) * | 2023-11-07 | 2024-03-22 | 西南交通大学 | Method and device for estimating calculation of contact boundary elements of acceleration wheel track |
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| CN113503197A (en) * | 2021-07-12 | 2021-10-15 | 哈尔滨工程大学 | Marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration |
| CN114541196A (en) * | 2022-02-18 | 2022-05-27 | 西南交通大学 | Rail grinding period design method considering turnout service performance evolution |
| CN114969886A (en) * | 2022-04-07 | 2022-08-30 | 西南交通大学 | Steel rail rolling contact fatigue prediction method |
| CN114969886B (en) * | 2022-04-07 | 2023-03-28 | 西南交通大学 | Steel rail rolling contact fatigue prediction method |
| CN114781158A (en) * | 2022-04-21 | 2022-07-22 | 西南交通大学 | Equivalent method for simplifying non-Hertz tangential contact calculation of wheel track |
| CN114781158B (en) * | 2022-04-21 | 2023-05-05 | 西南交通大学 | Equivalent method for simplifying non-Hertz tangential contact calculation of wheel track |
| CN115630554A (en) * | 2022-11-15 | 2023-01-20 | 西南交通大学 | Wheel-rail two-dimensional rolling contact force calculation method considering material nonuniformity |
| CN116542023A (en) * | 2023-04-12 | 2023-08-04 | 西南交通大学 | Computing method, system and storage medium for simulating conformal contact of wheel track |
| CN116542023B (en) * | 2023-04-12 | 2024-02-06 | 西南交通大学 | Computing method, system and storage medium for simulating conformal contact of wheel track |
| CN117744236A (en) * | 2023-11-07 | 2024-03-22 | 西南交通大学 | Method and device for estimating calculation of contact boundary elements of acceleration wheel track |
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