CN115510577B - Rapid prediction method for rolling contact fatigue of wheel track - Google Patents

Rapid prediction method for rolling contact fatigue of wheel track Download PDF

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CN115510577B
CN115510577B CN202211171212.7A CN202211171212A CN115510577B CN 115510577 B CN115510577 B CN 115510577B CN 202211171212 A CN202211171212 A CN 202211171212A CN 115510577 B CN115510577 B CN 115510577B
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安博洋
孙耀亮
王平
柯妍
胡家龙
赖洪翔
陈嵘
徐井芒
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Southwest Jiaotong University
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Abstract

The invention discloses a wheel-rail rolling contact fatigue rapid prediction method, which comprises the following steps: introducing a saturation concept on the basis of the stability diagram, and expanding the stability diagram to obtain an expanded stability diagram; the normal stress and tangential stress distribution of the surface of the steel rail are utilized, and the stress-strain field distribution in the wheel rail body under the steady-state rolling condition is solved by adopting a potential function method; selecting a proper fatigue model by combining the extended stability diagram, and predicting the fatigue life by utilizing the stress strain amplitude based on a critical plane method; according to the invention, the stability diagram is expanded by introducing the concept of saturation, so that the creeping state of any wheel rail can be considered; and secondly, the potential function method is utilized to obtain the stress-strain field distribution in the steel rail body required by the rolling contact fatigue prediction of the wheel rail, and compared with a typical fatigue prediction method, the calculation efficiency is greatly improved.

Description

Rapid prediction method for rolling contact fatigue of wheel track
Technical Field
The invention relates to the technical fields of railway engineering wheel-rail relation and material performance, in particular to a method for rapidly predicting rolling contact fatigue of a wheel rail.
Background
Wheel rail systems are key components in railway transportation, and traction, running and braking of a train are realized through rolling contact of wheel rails. Many scholars have conducted related studies on the problem of fatigue damage generated during the rolling contact process of wheel tracks, and have proposed various wheel track rolling contact fatigue prediction models. These models can be broadly divided into two categories: the first category is guided by engineering applications, and mainly includes a stability chart of Johnson professor, a surface contact fatigue index and an abrasion number-based damage function, which are proposed by Ekberg, etc., and the Johnson professor starts with the Hertz contact theory, establishes a stability theory, and obtains a stability curve, as shown in fig. 1. The stability diagram provided by the stability diagram takes the normal force of rolling contact of the wheel rail and the longitudinal and transverse creep force as an evaluation index for defining the bearing capacity of the wheel rail, so that the safety of the wheel rail under different running conditions can be intuitively and rapidly compared. The abscissa in fig. 1 is defined as the ratio of the total tangential force to the total normal force of the wheel-rail contact as the coefficient of friction, as shown in the following equation:
Figure GDA0004210023770000011
wherein F is x And F y Longitudinal and transverse creep forces of contact of wheel and rail respectively, F n Is the wheel rail contact normal force.
Ekberg et al define the surface fatigue index on the basis of the stability theory to quantitatively analyze the rolling contact fatigue damage problem, when presented on the stability diagram, i.e., the surface fatigue index FIsurf is the horizontal distance from the working point WP to the plastic stability limit BC, and the calculated expression is as follows:
Figure GDA0004210023770000012
wherein a and b are respectively long and short half shafts of the contact spots of the wheel track; p is p 0 Maximum normal stress in the contact patch of the wheel track; k is the pure shear yield strength. As is evident from FIG. 1, when FI surf At > 0, the local material response of the wheel track is in the ratcheting region where plastic strain of the wheel track can build up all the time, eventually leading to its loss of toughness and fatigue failure. The wheel-rail material response is determined by the coefficient of friction under actual operating conditions and the maximum normal contact pressure within the contact patch.
The second type is directed by fine modeling, and the model is often predicted by combining a critical plane method, wherein stress strain time course data required by the method is often obtained by solving by adopting a finite element method, deng Xiangyun et al establish a three-dimensional wheel-rail transient rolling finite element model, calculate and solve the stress-strain field distribution of a steel rail when a wheel rolls once, and predict the wheel-rail rolling contact fatigue by combining the critical plane method. J iang and Wen et al simulated the multiple passes of cyclic loading on the rail surface using the finite element method on this basis and performed fatigue life predictions.
However, the prior method has the defects in the wheel-rail rolling contact fatigue prediction: on one hand, rolling and sliding behaviors in actual wheel-rail contact are ignored on the theoretical basis when a prediction model taking engineering application as a guide is established, and the fatigue life of the wheel-rail contact cannot be accurately predicted; on the other hand, a model guided by scientific research needs to be predicted by combining more detailed wheel-rail contact stress strain time course data, and the data are often obtained through finite element simulation, so that the calculation efficiency is low. The concrete steps are as follows: the stability profile taught by Johnson can determine four responses (i.e., elastic stability, plastic stability, and ratcheting) of the wheel-rail material, but it has two drawbacks in predicting wheel-rail rolling contact fatigue. First, the existing stability diagram is obtained in a full sliding state, without considering the case of partial sliding or even rolling. The wheel rim is usually in full slip contact with the rail, but in actual operation, it is the portion of the wheel tread that is in contact with the rail that is typically sliding. Second, since the existing stability profile does not take into account the detailed contact creep rate of the wheel rail, the creep rate has a very important impact on the fatigue life of the wheel rail. In the transient finite element method, only a single pass of the wheel can be simulated, and the obtained stress-strain time course data in the wheel track body can not reflect the real material response condition. And J iang adopts a finite element method to simulate the condition of multiple rolling of a cyclic load, so that the calculation cost is high, and a single prediction model is adopted instead of a prediction model which is more suitable according to different choices of wheel track material responses.
Therefore, it is necessary to provide a wheel-rail rolling contact fatigue rapid prediction method which combines calculation accuracy and efficiency.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a wheel-rail rolling contact fatigue rapid prediction method, which comprises the steps of firstly expanding a stability diagram by introducing a concept of saturation so as to consider the creeping state of any wheel rail; and secondly, the potential function method is utilized to obtain the stress-strain field distribution in the steel rail body required by the rolling contact fatigue prediction of the wheel rail, and compared with a typical fatigue prediction method, the calculation efficiency is greatly improved.
In order to achieve the above purpose, the invention adopts the following technical scheme: a wheel-rail rolling contact fatigue rapid prediction method comprises the following steps:
step 1, introducing a saturation concept on the basis of a stability diagram, and expanding the stability diagram to obtain an expanded stability diagram;
step 2, utilizing the normal stress and tangential stress distribution of the surface of the steel rail, and solving the stress-strain field distribution in the wheel rail under the steady-state rolling condition by adopting a potential function method;
and 3, selecting a proper fatigue model by combining the extended stability diagram in the step 1, and predicting the fatigue life by using the stress strain amplitude obtained in the step 2 based on a critical plane method.
As a further improvement of the present invention, in step 1, the saturation is specifically as follows:
the ratio of the longitudinal creep force to the tangential traction force is defined as saturation in the same coordinate system, and the specific expression is as follows:
Figure GDA0004210023770000031
wherein: u is saturation, the value is 0-1, the contact state between wheel tracks is rolling state when the saturation is 0, and the contact state between wheel tracks is full sliding state when the saturation is 1; f (F) x Is the longitudinal creep force; f is the coefficient of friction; f (F) n Is the total normal force.
As a further improvement of the present invention, the step 1 is specifically as follows:
solving the stress-strain field distribution of the wheel-rail contact interface based on the Hertz contact theory and the Carter two-dimensional rolling contact theory; establishing a two-dimensional local steel rail finite element model, and considering an eight-node secondary plane strain unit and a plane strain infinite element, wherein the two-dimensional local steel rail finite element model adopts translation of normal and tangential stress distribution in a rolling direction to simulate a circulating rolling process; and (3) repeatedly rolling and calculating the load on the surface of the steel rail for multiple times based on a finite element method to obtain a stress-strain curve, determining the wheel-rail material response corresponding to the stress-strain curve, and then obtaining an expanded stability diagram.
As a further improvement of the invention, when the stress-strain field distribution of the contact interface of the wheel rail is solved, the half width of the rolling contact spot of the wheel rail and the maximum contact pressure in the contact spot are preferentially solved, and the calculation expression is as follows:
Figure GDA0004210023770000041
/>
Figure GDA0004210023770000042
wherein: r is R 11 And R is 22 Longitudinal curvature radius of the wheels and the steel rail respectively; e (E) 1 And E is 2 The elastic modulus of the wheels and the steel rails are respectively; upsilon (v) 1 And v 2 Poisson ratios of wheels and rails respectively; p is p 0 Is the maximum contact pressure stress; a is the half width of the contact patch; p (P) z Is the normal contact force in the transverse unit length;
according to the division of the adhesion area and the sliding area in the contact spots and the tangential force distribution of the adhesion area and the sliding area, the expression equation of the tangential force of the adhesion area is obtained:
Figure GDA0004210023770000043
wherein: p is p 1 Tangential force of the stick-slip region; x is x 1 Is an abscissa variable; a, a 1 Is half-width of the adhesive area; x's' 1 ＝x 1 -a+a 1 ，s 1 For longitudinal creep rate, the function Sign (s 1 ) Is defined as follows:
Figure GDA0004210023770000051
and (3) performing finishing programming on the formulas (1) - (4), and calculating to obtain normal contact stress distribution and tangential contact stress distribution under different friction coefficients, saturation and steady-state maximum contact pressure.
As a further improvement of the present invention, the step 2 specifically includes the steps of:
(1) Establishing a solid model of the load acting on the surface of the half-space based on the half-space assumption, the isotropic elastic half-space being represented by a coordinate system (x, y, z), wherein the surface is represented by z=0; the applied normal load and tangential load are distributed in the curved surface area S, and a loading point S is loaded in the loading area S 2 (x 2 ,y 2 0) applying a load normal component P respectively 1 (x 2 ,y 2 0), tangential component of load P 2 (x 2 ,y 2 0), and P 3 (x 2 ,y 2 0), wherein at any point S in the rail body 1 (x 1 ,y 1 ,z 1 ) From the load application point S 2 (x 2 ,y 2 Distance r of 0), the calculation expression is as follows:
Figure GDA0004210023770000052
(2) When solving the elastic field of any point in the steel rail body, defining potential function
Figure GDA0004210023770000053
The expression is as follows:
Figure GDA0004210023770000054
wherein, the expression of Ω and χ is:
Ω＝z 1 ln(r+z 1 )-r
χ＝ln(r+z 1 ) (7)
and these nine potential functions also need to satisfy:
Figure GDA0004210023770000055
introduces an auxiliary potential function psi (m) (m=0, 1) whose expression is as follows:
Figure GDA0004210023770000061
Figure GDA0004210023770000062
(3) According to the definition of the potential function and the auxiliary potential function in the step (2), a calculation formula of the elastic displacement of any point in the steel rail body can be obtained, and the calculation formula is as follows:
Figure GDA0004210023770000063
Figure GDA0004210023770000064
Figure GDA0004210023770000065
wherein G is the shear modulus of elasticity; v is poisson's ratio;
the corresponding stress expression obtained by hooke's law is:
Figure GDA0004210023770000066
Figure GDA0004210023770000067
Figure GDA0004210023770000068
Figure GDA0004210023770000069
Figure GDA00042100237700000610
Figure GDA00042100237700000611
the corresponding strain is obtained from the ratio of stress to elastic modulus E or shear elastic modulus G;
(4) And replacing the maximum stress-strain amplitude obtained by the classical finite element method with the obtained maximum stress-strain value of the steel rail at a certain moment.
As a further development of the invention, in step 3, the fatigue model includes a Fatemi-society model for elastic stabilization, a KBW model for plastic stabilization and a Jiang-Sehitoglu model for ratcheting.
As a further improvement of the invention, the calculation expression of the artemi-society model and the corresponding fatigue life calculation expression are as follows:
Figure GDA0004210023770000071
Figure GDA0004210023770000072
wherein, C is a fatigue damage parameter; n is a material parameter, reflects the sensitivity degree of normal stress of different materials to the influence of fatigue life, and is obtained by carrying out a uniaxial test on the same material; Δγ max Is the maximum shear strain amplitude; sigma (sigma) n,max Maximum normal stress on the plane of maximum shear strain; sigma (sigma) y Is the yield stress; upsilon (v) e And v p Respectively the elastic and plastic Poisson ratios; sigma'. f And epsilon' f Fatigue strength coefficient and fatigue ductility coefficient, respectively; b and c are the fatigue strength index and the fatigue ductility index, respectively; e and N f Elastic modulus and fatigue life, respectively.
As a further improvement of the present invention, the calculation expression of the KBW model and the corresponding fatigue life calculation expression are as follows:
Figure GDA0004210023770000073
Figure GDA0004210023770000074
wherein, deltay max Is the maximum shear strain amplitude; delta epsilon n The maximum normal strain amplitude on the plane of maximum shear strain amplitude; s is an empirical parameter.
As a further improvement of the invention, the computational expression of the Jiang-Sehitoglu model and the corresponding fatigue life computational expression are as follows:
Figure GDA0004210023770000075
Figure GDA0004210023770000076
Figure GDA0004210023770000081
wherein F is P Is a fatigue damage parameter; f (F) Pmax Is the maximum value of fatigue damage parameters;<>is MacCauley brackets; sigma (sigma) max Maximum normal stress in the crack initiation plane; delta epsilon is crack initiationNormal strain amplitude in the green plane; Δτ is the shear stress amplitude in the crack initiation plane; Δγ is the shear strain amplitude in the crack initiation plane; the constant J is obtained by a tensile/torsional test; τ' f And gamma' f The shear fatigue strength coefficient and the shear fatigue ductility coefficient, respectively.
As a further improvement of the present invention, the step 3 is specifically as follows:
the rail stress strain field obtained based on potential function method is distributed into stress tensor sigma ij (i, j=1, 2) and strain tensor epsilon ij (i, j=1, 2), and calculating the stress tensor sigma 'of any slope at any node according to the coordinate axis rotation transformation formula' ij (i, j=1, 2) and strain tensor ε' ij (i, j=1, 2), wherein the specific expressions of the stress tensor and the strain tensor are respectively:
Figure GDA0004210023770000082
Figure GDA0004210023770000083
the coordinate transformation matrix is as follows:
Figure GDA0004210023770000084
the transformation relationship between the tensors is then:
Figure GDA0004210023770000085
according to the stress state of a point, tensor coordinate transformation is carried out on the point by taking 1 degree as a step length, so as to obtain the stress-strain state of any two-dimensional inclined plane of the point, and the fatigue damage parameter value of the inclined plane is obtained according to the selected fatigue prediction model, so that the maximum value of the fatigue damage parameter is found, and then the fatigue life prediction value is obtained.
The beneficial effects of the invention are as follows: the stability diagram proposed by Johnson professor is extended by first introducing the concept of saturation so that it can take into account any creep state of the wheel track rolling contact. In order to quickly calculate the stress-strain amplitude required to predict fatigue, an approximation assumption is proposed and demonstrated that the maximum in-vivo stress-strain of the material under steady-state rolling conditions is approximately equal to the maximum stress-strain amplitude under transient rolling conditions. Therefore, a potential function method proposed by LOVE is adopted to replace a finite element method to obtain the stress-strain field distribution in the wheel track body required by the wheel track rolling contact fatigue prediction. And finally, determining four responses (namely elasticity, elastic stability, plastic stability and ratchet effect) of the wheel track material through the expanded stability diagram, rapidly determining a proper model for fatigue prediction based on a potential function method, and improving the calculation efficiency on the premise of ensuring the calculation accuracy.
Drawings
FIG. 1 is a Johnson-stability diagram;
FIG. 2 is a graph showing the distribution of Carter versus stick-slip region in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a two-dimensional steady-state rolling finite element model in an embodiment of the present invention;
FIG. 4 is a graph showing the partial material response of two contact bodies under cyclic reciprocating load in accordance with an embodiment of the present invention;
FIG. 5 is an extended stability diagram in an embodiment of the present invention;
FIG. 6 is a schematic diagram of a semi-infinite solid model for LOVE in an embodiment of the invention;
FIG. 7 is a diagram showing the equivalent stress of the potential function method and the finite element method according to the embodiment of the present invention;
FIG. 8 is a diagram illustrating node stress coordinate transformation in accordance with an embodiment of the present invention;
FIG. 9 is a graph showing the comparison of predicted fatigue life for two methods with different coefficients of friction in an embodiment of the present invention;
FIG. 10 is a graph showing the comparison of predicted fatigue life for two methods at different maximum contact pressures in an embodiment of the present invention;
FIG. 11 is a graph showing the comparison of predicted fatigue life for two methods at different saturation levels in an embodiment of the present invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Examples
A wheel-rail rolling contact fatigue rapid prediction method comprises the following steps:
step 1, introducing a concept of saturation on the basis of a stability diagram of the teaching of Johnson, and expanding the saturation:
(1) Firstly, in this embodiment, the two-dimensional wheel-rail rolling contact (without considering the transverse and spin creep rate of the wheel-rail contact) is defined in the same coordinate system, and the ratio of the longitudinal creep force to the tangential traction force is defined as saturation, and the specific expression is:
Figure GDA0004210023770000101
wherein: u is saturation, the value is 0-1, the contact state between wheel tracks is rolling state when the saturation is 0, and the contact state between wheel tracks is full sliding state when the saturation is 1; f (F) x Is the longitudinal creep force; f is the coefficient of friction; f (F) n Is the total normal force.
(2) And secondly, solving the stress-strain field distribution of the wheel-rail contact interface based on the Hertz contact theory and the Carter two-dimensional rolling contact theory. When the distribution is solved, the half width of the rolling contact spots of the wheel track and the maximum contact pressure in the contact spots are obtained preferentially, and the calculation expression is shown in the formula (2) and the formula (3).
Figure GDA0004210023770000102
Figure GDA0004210023770000103
Wherein: r is R 11 And R is 22 Longitudinal curvature radius of the wheels and the steel rail respectively; e (E) 1 And E is 2 The elastic modulus of the wheels and the steel rails are respectively; upsilon (v) 1 And v 2 Poisson ratios of wheels and rails respectively; p is p 0 Is the maximum contact pressure stress; a is the half width of the contact patch; p (P) z Is the normal contact force per unit length in the lateral direction.
In addition, carter also considers the division of the adhesion and sliding zones in the contact patch and their tangential force distribution, as shown in FIG. 2. He proposes a representation of the tangential force of the stick-slip region as in equation (4).
Figure GDA0004210023770000111
Wherein: p is p 1 Tangential force of the stick-slip region; x is x 1 Is the abscissa variable in fig. 2; a, a 1 Is half-width of the adhesive area; x's' 1 ＝x 1 -a+a 1 ，s 1 For longitudinal creep rate, the function Sign (s 1 ) Is defined as follows:
Figure GDA0004210023770000112
and (3) performing finishing programming on the formulas (1) - (4), and calculating to obtain normal contact stress distribution and tangential contact stress distribution under different friction coefficients, saturation and steady-state maximum contact pressure.
(3) Again, a two-dimensional local rail finite element model was built, taking into account the eight-node secondary plane strain cell and plane strain infinite element, as shown in fig. 3. The translation of the normal and tangential stress distributions in the rolling direction is used in the model to simulate the cyclic rolling process. The top surface of the steel rail in the two-dimensional model is smooth, normal stress and tangential stress do not change with time, and the stress distribution is obtained in the first two steps. The cyclic moving load of the top surface of the steel rail is realized by self-programming and modifying inp files, and the rolling direction is shown in figure 3. At the initial rolling position a, the contact load is gradually increased by 10 incremental steps, and then the contact load is gradually moved in the longitudinal direction toward the end point B, the contact load is moved by 0.5mm in one incremental step, and the total rolling distance is 40mm. After 80 steps of scrolling, the contact patch will reach point B and finally be unloaded to zero by 10 incremental steps. Therefore, the rolling process of the wheel is completed once, multiple simulated rolling is realized, and the process is repeated.
(4) And finally, repeatedly rolling and calculating the load on the surface of the steel rail for a plurality of times based on a finite element method to obtain a stress-strain curve, and determining the corresponding wheel-rail material response, as shown in fig. 4. An expanded stability diagram is then obtained as shown in fig. 5.
Step 2, solving the normal stress and tangential stress distribution of the surface of the steel rail by using the solving method in the steps 1 to 1, and solving the stress-strain field distribution in the wheel rail under the steady-state rolling condition by using the potential function method of LOVE:
(1) Live builds a solid model of the load acting on the half-space surface based on the half-space assumption, as shown in fig. 6, the isotropic elastic half-space volume is represented by a coordinate system (x, y, z), where the surface is represented by z=0; the applied normal load and tangential load are distributed in the curved surface area S, and a loading point S is loaded in the loading area S 2 (x 2, y 2, 0) Where the normal components P of the load are applied respectively 1 (x 2 ,y 2 0), tangential component of load P 2 (x 2 ,y 2 0), and P 3 (x 2 ,y 2 0), wherein at any point S in the rail body 1 (x 1 ,y 1 ,z 1 ) From the load application point S 2 (x 2 ,y 2 Distance r of 0), the calculation expression is as follows:
Figure GDA0004210023770000121
(2) When solving the elastic field (displacement field and stress field) of any point in the steel rail body, a potential function is defined
Figure GDA0004210023770000122
The expression is as follows:
Figure GDA0004210023770000123
wherein, the expression of Ω and χ is:
Ω＝z 1 ln(r+z 1 )-r
χ＝ln(r+z 1 ) (7)
and these nine potential functions also need to satisfy:
Figure GDA0004210023770000124
since the expression of the potential function is relatively complex, an auxiliary potential function ψ is introduced (m) (m=0, 1) whose expression is as follows:
Figure GDA0004210023770000131
Figure GDA0004210023770000132
(3) According to the definition of the potential function and the auxiliary potential function in the step (2), a calculation formula of the elastic displacement of any point in the steel rail body can be obtained, and the calculation formula is as follows:
Figure GDA0004210023770000133
/>
Figure GDA0004210023770000134
Figure GDA0004210023770000135
wherein G is the shear modulus of elasticity; v is poisson's ratio.
The corresponding stress expression obtained by hooke's law is:
Figure GDA0004210023770000136
Figure GDA0004210023770000137
Figure GDA0004210023770000138
Figure GDA0004210023770000139
Figure GDA00042100237700001310
Figure GDA00042100237700001311
the corresponding strain is obtained from the ratio of stress to the elastic modulus E or shear elastic modulus G.
(4) The maximum stress-strain value of the rail at a certain time is used for replacing the maximum stress-strain amplitude obtained by the classical finite element method, and a schematic diagram is shown in fig. 7.
Step 3: selecting a proper fatigue model by combining the extended stability diagram in the step 1, and predicting the fatigue life by using the stress strain amplitude obtained in the step 2 based on a critical plane method
(1) Three fatigue prediction models are selected in the invention: the model Fatemi-society for elastic stabilization is applicable to the model KBW for plastic stabilization and to the model Jiang-Sehitoglu for ratcheting.
The calculation expression of the Fatemi-society model and the corresponding fatigue life calculation expression are as follows:
Figure GDA0004210023770000141
Figure GDA0004210023770000142
wherein, C is a fatigue damage parameter; n is a material parameter, reflects the sensitivity degree of normal stress of different materials to the influence of fatigue life, and is obtained by carrying out a uniaxial test on the same material; Δγ max Is the maximum shear strain amplitude; sigma (sigma) n,max Maximum normal stress on the plane of maximum shear strain; sigma (sigma) y Is the yield stress; upsilon (v) e And v p Respectively the elastic and plastic Poisson ratios; sigma'. f And epsilon' f Fatigue strength coefficient and fatigue ductility coefficient, respectively; b and c are the fatigue strength index and the fatigue ductility index, respectively; e and Nf are the modulus of elasticity and fatigue life, respectively.
The computational expression of the KBW model and the corresponding fatigue life computational expression are as follows:
Figure GDA0004210023770000143
Figure GDA0004210023770000144
wherein, deltay max Is the maximum shear strain amplitude; delta epsilon n The maximum normal strain amplitude on the plane of maximum shear strain amplitude; s is an empirical parameter.
The computational expression of the Jiang-Sehitoglu model and the corresponding fatigue life computational expression are as follows:
Figure GDA0004210023770000145
Figure GDA0004210023770000146
Figure GDA0004210023770000151
wherein F is P Is a fatigue damage parameter; f (F) Pmax Is the maximum value of fatigue damage parameters;<>is MacCauley brackets; sigma (sigma) max Maximum normal stress in the crack initiation plane; delta epsilon is the normal strain amplitude in the crack initiation plane; Δτ is the shear stress amplitude in the crack initiation plane; Δγ is the shear strain amplitude in the crack initiation plane; the constant J can be obtained by a tensile/torsional test; τ' f And gamma' f The shear fatigue strength coefficient and the shear fatigue ductility coefficient, respectively. .
And (3) selecting the most suitable fatigue prediction model based on the maximum contact stress and saturation obtained by actual observation by using the extended stability diagram obtained in the step (1).
(2) The rail stress strain field obtained based on the potential function method in the step 2 is distributed into a stress tensor sigma ij (i, j=1, 2) and strain tensor epsilon ij (i, j=1, 2), and calculating the stress tensor sigma 'of any slope at any node according to the coordinate axis rotation transformation formula' ij (i, j=1, 2) and strain tensor ε' ij (i, j=1, 2), as shown in fig. 8. The specific expressions of the stress tensor and the strain tensor are respectively as follows:
Figure GDA0004210023770000152
Figure GDA0004210023770000153
the coordinate transformation matrix is as follows:
Figure GDA0004210023770000154
the transformation relationship between the tensors is then:
Figure GDA0004210023770000155
/>
according to the stress state of a point, tensor coordinate transformation is carried out on the point by taking 1 degree as a step length, so as to obtain the stress-strain state of any two-dimensional inclined plane of the point, and the fatigue damage parameter value of the inclined plane is obtained according to the selected fatigue prediction model, so that the maximum value of the fatigue damage parameter is found, and then the fatigue life prediction value is obtained. It should be noted that if the fatigue prediction model is selected as the Jiang-Sehitoglu model, it is also necessary to quantitatively analyze the specific gravity of the two components of normal stress-strain and shear stress-strain, so that a specific model formula can be selected.
This embodiment is further described below:
the present embodiment expands the stability diagram for the case of friction coefficients f=0.2 and f=0.4, as shown in fig. 5. And the comparative analysis of rolling contact fatigue life of wheel track under different friction coefficients and the comparative analysis of time consumption prediction are carried out on the method of the embodiment and the classical finite element method, as shown in fig. 9 and table 1. Similarly, comparative analyses were also performed on rolling contact fatigue life and predicted time consumption of the wheel track at different maximum contact pressures and at different saturation levels for the two methods, see fig. 10, 11 and tables 2 and 3, respectively. In the figure, FE represents a finite element method, and PF represents a method of the present embodiment. It can be found that 1) the method of the embodiment is consistent with the finite element method in the prediction result of the rolling contact fatigue life of the wheel track, and the error rate can be controlled within 15%; 2) Compared with the prediction time consumption, the method of the embodiment can reduce the typical fatigue prediction calculation cost from a few hours to a few seconds, and the calculation efficiency is remarkably improved.
TABLE 1 time consuming prediction of fatigue life by two methods with different coefficients of friction
Figure GDA0004210023770000161
TABLE 2 time consuming prediction of fatigue life for two methods at different maximum contact pressures
Figure GDA0004210023770000162
Figure GDA0004210023770000171
TABLE 3 time consuming prediction of fatigue life for two methods at different saturation levels
Figure GDA0004210023770000172
An application case for predicting the rolling contact fatigue life of a wheel track by the method of the present embodiment is exemplified herein.
S1, assuming that the wheel profile is LMA, the steel rail profile is CN60, taking the elastic modulus e=206 GPa, poisson ratio v=0.3, the friction coefficient f=0.4, the saturation u=0.8, the pure shear yield strength k=265 MPa, and the normal force 13.4kN in consideration of the coincidence of the steel rail and the wheel material.
S2, the expression of the half width of the contact patch and the maximum contact stress in the contact patch is as follows:
Figure GDA0004210023770000173
Figure GDA0004210023770000174
wherein R is 11 ＝430mm，R 22 = infinity, the expression reduces to:
Figure GDA0004210023770000175
Figure GDA0004210023770000176
due to P z =13.4 kN, then a=8mm, p 0 =1060 Mpa, i.e. p 0 And/k.apprxeq.4. According to u=0.8, p 0 With/k=4, the material response in this case is ratcheting, as is seen in the extended stability diagram of fig. 5 with f=0.4, and the fatigue prediction model chosen should be the Jiang-Sehitoglu model.
S3, solving the distribution of the stress-strain field of the steel rail by using a potential function method of LOVE, performing tensor coordinate change on the maximum stress amplitude based on a critical plane method, wherein normal stress-strain takes the dominant role, and then solving the maximum fatigue damage parameter value on the critical plane, namely F based on the parameters in Table 4 and a fatigue damage parameter solving formula in a Jiang-Sehitoglu model Pmax ＝2.798MPa。
Table 4 fatigue life prediction formula parameter table
Figure GDA0004210023770000181
And S4, solving and calculating the fatigue life based on a tensile fatigue life prediction formula in the Jiang-Sehitoglu model after obtaining the maximum value of the fatigue damage parameters. The expression is as follows:
Figure GDA0004210023770000182
obtaining a fatigue life value N through programming iteration solution f 16785 times (number of passes of wheel over rail).
S5, finally, the fatigue life value obtained by the method is found to be equal to the fatigue life value N obtained by a classical finite element method f Results of 18771 times are matched, and prediction error is not large; but the prediction takes only 1.6 seconds compared with the 1.5 hours of the finite element method, and the calculation efficiency is remarkably improved.
The foregoing examples merely illustrate specific embodiments of the invention, which are described in greater detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention.

Claims (5)

1. The method for rapidly predicting the rolling contact fatigue of the wheel track is characterized by comprising the following steps of:
step 1, introducing a saturation concept on the basis of a stability diagram, and expanding the stability diagram to obtain an expanded stability diagram;
step 2, utilizing the normal stress and tangential stress distribution of the surface of the steel rail, and solving the stress-strain field distribution in the wheel rail under the steady-state rolling condition by adopting a potential function method;
step 3, selecting a proper fatigue model by combining the expansion stability diagram in the step 1, and predicting the fatigue life by using the stress strain amplitude obtained in the step 2 based on a critical plane method;
in step 1, the saturation is specifically as follows:
the ratio of the longitudinal creep force to the tangential traction force is defined as saturation in the same coordinate system, and the specific expression is as follows:
Figure FDA0004217229030000011
wherein: u is saturation, the value is 0-1, the contact state between wheel tracks is rolling state when the saturation is 0, and the contact state between wheel tracks is full sliding state when the saturation is 1; f (F) x Is the longitudinal creep force; f is the coefficient of friction; f (F) n Is the total normal force;
the step 1 specifically comprises the following steps:
solving the stress-strain field distribution of the wheel-rail contact interface based on the Hertz contact theory and the Carter two-dimensional rolling contact theory; establishing a two-dimensional local steel rail finite element model, and considering an eight-node secondary plane strain unit and a plane strain infinite element, wherein the two-dimensional local steel rail finite element model adopts translation of normal and tangential stress distribution in a rolling direction to simulate a circulating rolling process; repeatedly rolling and calculating the load on the surface of the steel rail for a plurality of times based on a finite element method to obtain a stress-strain curve, determining the wheel-rail material response corresponding to the stress-strain curve, and then obtaining an expanded stability diagram;
the step 2 specifically comprises the following steps:
(1) Establishing a solid model of the load acting on the surface of the half-space based on the half-space assumption, the isotropic elastic half-space being represented by a coordinate system (x, y, z), wherein the surface is represented by z=0; the applied normal load and tangential load are distributed in the curved surface area S, and the load applying point S is in the curved surface area S 2 (x 2 ,y 2 0) applying a load normal component P respectively 1 (x 2 ,y 2 0), tangential component of load P 2 (x 2 ,y 2 0), and P 3 (x 2 ,y 2 0), wherein at any point S in the rail body 1 (x 1 ,y 1 ,z 1 ) From the load application point S 2 (x 2 ,y 2 Distance r of 0), the calculation expression is as follows:
Figure FDA0004217229030000021
(2) When solving the elastic field of any point in the steel rail body, defining potential function
Figure FDA0004217229030000022
Figure FDA0004217229030000023
The expression is as follows:
Figure FDA0004217229030000024
Figure FDA0004217229030000025
Figure FDA0004217229030000026
wherein, the expression of Ω and χ is:
Ω＝z 1 ln(r+z 1 )-r
χ＝ln(r+z 1 )
and these nine potential functions also need to satisfy:
Figure FDA0004217229030000027
introduces an auxiliary potential function psi (m) M=0, 1, and its expression is as follows:
Figure FDA0004217229030000028
Figure FDA0004217229030000029
(3) According to the definition of the potential function and the auxiliary potential function in the step (2), a calculation formula of the elastic displacement of any point in the steel rail body is obtained, and the calculation formula is as follows:
Figure FDA0004217229030000031
Figure FDA0004217229030000032
Figure FDA0004217229030000033
wherein G is the shear modulus of elasticity; v is poisson's ratio;
the corresponding stress expression obtained by hooke's law is:
Figure FDA0004217229030000034
Figure FDA0004217229030000035
Figure FDA0004217229030000036
Figure FDA0004217229030000037
Figure FDA0004217229030000038
Figure FDA0004217229030000039
the corresponding strain is obtained from the ratio of stress to elastic modulus E or shear elastic modulus G;
(4) Replacing the maximum stress-strain amplitude value obtained by the finite element method with the obtained maximum stress-strain value of the steel rail at a certain moment;
in step 3, the fatigue model comprises a Fatemi-society model suitable for elastic stabilization, a KBW model suitable for plastic stabilization and a Jiang-Sehitoglu model suitable for ratcheting;
the step 3 specifically comprises the following steps:
converting the distribution of the rail stress strain field obtained based on the potential function method into a stress tensor sigma ij I, j=1, 2 and the strain tensor epsilon ij I, j=1, 2, and calculating the stress tensor sigma 'of any inclined plane at any node according to the coordinate axis rotation transformation formula' ij I, j=1, 2 and strain tensor ε' ij I, j=1, 2, wherein the specific expressions of the stress tensor and the strain tensor are respectively:
Figure FDA0004217229030000041
Figure FDA0004217229030000042
the coordinate transformation matrix is as follows:
Figure FDA0004217229030000043
the transformation relationship between the tensors is then:
Figure FDA0004217229030000044
according to the stress state of a point, tensor coordinate transformation is carried out on the point by taking 1 degree as a step length, so as to obtain the stress-strain state of any two-dimensional inclined plane of the point, and the fatigue damage parameter value of the inclined plane is obtained according to the selected fatigue prediction model, so that the maximum value of the fatigue damage parameter is found, and then the fatigue life prediction value is obtained.
2. The method for rapidly predicting wheel-rail rolling contact fatigue according to claim 1, wherein when the wheel-rail contact interface stress-strain field distribution is solved, the half width of the wheel-rail rolling contact spot and the maximum contact pressure in the contact spot are firstly obtained, and the calculation expression is as follows:
Figure FDA0004217229030000045
Figure FDA0004217229030000046
wherein: r is R 11 And R is 22 Longitudinal curvature radius of the wheels and the steel rail respectively; e (E) 1 And E is 2 The elastic modulus of the wheels and the steel rails are respectively; upsilon (v) 1 And v 2 Poisson ratios of wheels and rails respectively; p is p 0 Is the maximum contact pressure stress; a is the half width of the contact patch; p (P) z Is the normal contact force in the transverse unit length;
according to the division of the adhesion area and the sliding area in the contact spots and the tangential force distribution of the adhesion area and the sliding area, the expression equation of the tangential force of the adhesion area is obtained:
Figure FDA0004217229030000051
wherein: p is p 1 Tangential force of the stick-slip region; x is x 1 Is an abscissa variable; a, a 1 Is half-width of the adhesive area; x is x 1 ′＝x 1 -a+a 1 ，s 1 For longitudinal creep rate, the function Sign (s 1 ) Is defined as follows:
Figure FDA0004217229030000052
and calculating to obtain normal contact stress distribution and tangential contact stress distribution under different friction coefficients, saturation and steady-state maximum contact pressure.
3. The wheel-rail rolling contact fatigue rapid prediction method according to claim 2, wherein the calculation expression of the artemi-society model and the corresponding fatigue life calculation expression are as follows:
Figure FDA0004217229030000053
Figure FDA0004217229030000054
wherein, C is a fatigue damage parameter; n is a material parameter, reflects the sensitivity degree of normal stress of different materials to the influence of fatigue life, and is obtained by carrying out a uniaxial test on the same material; Δγ max Is the maximum shear strain amplitude; sigma (sigma) n,max Maximum normal stress on the plane of maximum shear strain; sigma (sigma) y Is the yield stress; upsilon (v) e And v p Respectively the elastic and plastic Poisson ratios; sigma'. f And epsilon' f Fatigue strength coefficient and fatigue ductility coefficient, respectively; b and c are the fatigue strength index and the fatigue ductility index, respectively; e and N f Elastic modulus and fatigue life, respectively.
4. The method for rapidly predicting rolling contact fatigue of a wheel track according to claim 3, wherein the calculation expression of the KBW model and the corresponding fatigue life calculation expression are as follows:
Figure FDA0004217229030000061
Figure FDA0004217229030000062
wherein, deltay max Is the maximum shear strain amplitude; delta epsilon n The maximum normal strain amplitude on the plane of maximum shear strain amplitude; s is an empirical parameter.
5. The method for rapidly predicting rolling contact fatigue of a wheel track according to claim 4, wherein the computational expression of the Jiang-Sehitoglu model and the corresponding fatigue life computational expression are as follows:
Figure FDA0004217229030000063
Figure FDA0004217229030000064
Figure FDA0004217229030000065
wherein F is P Is a fatigue damage parameter; f (F) Pmax Is the maximum value of fatigue damage parameters;<>is MacCauley brackets; sigma (sigma) max Maximum normal stress in the crack initiation plane; delta epsilon is the normal strain amplitude in the crack initiation plane; Δτ is the shear stress amplitude in the crack initiation plane; Δγ is the shear strain amplitude in the crack initiation plane; the constant J is obtained by a tensile/torsional test; τ' f And gamma' f The shear fatigue strength coefficient and the shear fatigue ductility coefficient, respectively.
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