Wheel rail adhesion coefficient estimation method

Abstract

The invention provides a wheel-rail adhesion coefficient estimation method, which comprises the following steps of: establishing a local coordinate system at a wheel-rail contact point, and calculating to obtain a rigid contact gap, a contact spot shape and a creep rate between wheel rails by utilizing vertical coordinates of wheels and steel rails under the local coordinate system; importing the rigid contact gap into an EHL model, and calculating to obtain a non-Hertz normal force of the simulated wheel-rail contact interface by combining material parameters and geometric parameters of the wheel-rail contact interface; the shape of the contact spot, the creep rate and the non-Hertz normal force are imported into an ECF model, and tangential stress distribution of the simulated wheel-rail contact interface is obtained through calculation; integrating the wheel-rail contact area by utilizing the tangential stress distribution of the simulated wheel-rail contact interface to obtain the tangential force of the wheel-rail rolling contact, and finally calculating to obtain the wheel-rail adhesion coefficient. According to the method, influence factors of the wheel-rail contact interface are more comprehensively considered, the wheel-rail adhesion calculation accuracy is improved, and the method is suitable for multiple working conditions and has guiding significance for traction and control strategies of trains.

Description

Technical Field

[0001] The invention relates to the technical field of rail transportation, and in particular to a method for estimating a wheel-rail adhesion coefficient. Background Art

[0002] In rail transit systems, the adhesion characteristics between wheels and rails are crucial to the traction and braking performance of trains. In actual scenarios, there are many factors that affect wheel-rail adhesion, such as wheel-rail contact surface conditions, wheel-rail profile wear, contact point coordinates, yaw angle, etc. During the operation of trains, rain and snow and other weather conditions are often encountered. Under humid conditions, the wheel-rail interface may be in a mixed lubrication state, forming interface contamination. The wheel-rail adhesion coefficient decreases sharply with increasing speed. Insufficient adhesion may cause wheel slippage, increased braking distance, potential damage to wheels and tracks, and even ultimately endanger the safety of train operation. Therefore, it is crucial to accurately calculate the wheel-rail adhesion coefficient, especially to improve the prediction accuracy of the interfacial contaminant film thickness, which helps to more effectively utilize the wheel-rail adhesion, thereby improving the efficiency and safety of train operation.

[0003] In the prior art, the elastic fluid mixed lubrication theory (EHL) is introduced into the wheel-rail contact analysis under wet conditions. The EHL theory comprehensively considers aspects such as surface roughness, different lubricants, various interface conditions, and thermal effects. At the same time, the calculation of the adhesion coefficient is also related to the different states of the wheel-rail interface and the elastic-plastic properties of the wheel-rail material. When there is a "third medium" (such as rain, snow, grease, leaves, etc.) between the wheel and the rail, the adhesion coefficient will be significantly reduced; the fluid and solid particles between the wheel and the rail, as well as the surface layer of the wheel and the rail are combined and defined as the third body layer (3BL). The performance of the 3BL and its influence on the traction characteristics are studied through double-disc experiments, and the extended creep force model (ECF) is proposed.

[0004] The elastic mixed lubrication (EHL) theory mainly focuses on the lubrication state of the wheel-rail contact area, describes the contact situation by analyzing parameters such as oil film pressure distribution and thickness, and calculates the values ​​under some special conditions. The extended creep force model (ECF) analyzes the wheel-rail contact from the perspective of creep force, taking into account factors such as wheel-rail material properties, contact surface state, and creep phenomenon, but this model cannot fully cover all aspects of wheel-rail contact. Therefore, the traditional wheel-rail adhesion calculation method has limitations and cannot fully and accurately reflect the actual complex situation of wheel-rail contact. Summary of the invention

[0005] Objective of the invention: The objective of the invention is to provide a method for estimating wheel-rail adhesion coefficient.

[0006] Technical solution: A method for estimating wheel-rail adhesion coefficient, comprising the following steps:

[0007] (1) Establish a local coordinate system at the wheel-rail contact point and calculate the rigid contact gap, contact spot shape, and creep rate between the wheel and rail;

[0008] (2) the rigid contact gap obtained in step (1) is introduced into the elastic fluid mixed lubrication model, and the non-Hertzian normal force of the simulated wheel-rail contact interface is calculated by combining the material parameters and geometric parameters of the wheel-rail contact interface;

[0009] (3) introducing the contact spot shape and creep rate obtained in step (1) and the non-Hertzian normal force obtained in step (2) into the extended creep force model to calculate the tangential stress distribution of the simulated wheel-rail contact interface;

[0010] (4) The tangential stress distribution of the simulated wheel-rail contact interface is integrated over the wheel-rail contact area to obtain the tangential force of the wheel-rail rolling contact. The ratio of the tangential force to the non-Hertzian normal force is calculated to obtain the wheel-rail adhesion coefficient.

[0011] Specifically, in step (1), the rigid contact gap between the wheel and the rail is:

[0012] h=z cw -z cr

[0013] Where: h is the rigid contact gap between wheel and rail, z cw is the ordinate of the wheel in the local coordinate system at the contact point, z crw is the ordinate of the rail in the local coordinate system at the contact point.

[0014] Specifically, in step (2), the elastic fluid mixed lubrication model includes: solving the dimensionless Reynolds equation, the dimensionless film thickness equation, the dimensionless density equation, the dimensionless viscosity equation and the dimensionless load equation to obtain the non-Hertzian normal force.

[0015] Specifically, the dimensionless Reynolds equation is:

[0016]

[0017] λ=(8πUk e R x ) / (Wa eqv )

[0018] k e =b eqv / a eqv

[0019] Where: X, Y are dimensionless coordinate values; P is the dimensionless normal force; H is the dimensionless water film thickness; is the dimensionless viscosity, is the dimensionless density; W is the dimensionless load; R x is the radius of curvature in the x direction at the contact point; k e is the equivalent ellipticity, aeqv is the major axis of the equivalent ellipse, b eqv is the minor axis of the equivalent ellipse; U is the dimensionless velocity;

[0020] The dimensionless film thickness equation is:

[0021]

[0022] Where: H0 is the dimensionless initial center film thickness; G(X,Y) is the dimensionless rigid contact gap; V is the dimensionless elastic deformation; S1 is the roughness of the wheel surface, and S2 is the roughness of the rail surface;

[0023] The dimensionless viscosity equation is:

[0024]

[0025] Where: η0 is the environmental viscosity; η i (i=1, 2, 3, 4) are the fitting coefficients of the polynomial;

[0026] The dimensionless density equation is:

[0027]

[0028] Where: p0 is the maximum normal pressure;

[0029] The dimensionless load equation is:

[0030]

[0031] Where: P f (X,Y) is the pressure carried by the dimensionless fluid, P a (X,Y) is the dimensionless solid pressure, k e is the equivalent ellipticity.

[0032] Specifically, in the dimensionless film thickness equation, the dimensionless elastic deformation V(X,Y) is:

[0033]

[0034] λ1=2p0R x / πE′a eqv

[0035] Where: p0 is the maximum normal pressure; R x is the equivalent radius of curvature; E' is the comprehensive elastic modulus; P f is the pressure carried by the dimensionless fluid, P a is the pressure on the dimensionless solid, a eqv is the major axis of the equivalent ellipse.

[0036] Specifically, step (3) includes:

[0037] The wheel-rail contact interface is divided into several discrete units, and the displacement of each discrete unit is as follows:

[0038]

[0039] Where: u(x i ,y j ) is the displacement of the discrete unit, u x (x i ,y j ) is the displacement of the discrete unit in the x-axis direction, u y (x i ,y j ) is the displacement of the discrete unit in the y-axis direction; x i and i is the horizontal and vertical coordinates of the discrete unit; ξ x is the longitudinal creep rate; y is the lateral creep rate; φ is the spin creep rate;

[0040] The shear stress analysis of the medium at the wheel-rail contact interface is carried out. When the shear stress is less than the elastic limit shear stress, the medium material undergoes elastic deformation. The formula is as follows:

[0041]

[0042] Where: τ(x i ,y j ) is shear stress, L e is the flexibility coefficient; L x , L y , L φ is the Kalker coefficient;

[0043] When the shear stress is greater than the elastic limit shear stress and less than the plastic limit shear stress, the dielectric material undergoes plastic deformation. The shear stress formula is as follows:

[0044] τ 3BL =τ c1 +(τ c2 -τ c1 )(1-exp((-u+τ c1 L e ) / L p ))

[0045] Where: τ 3BL is the shear stress, τ c1 is the elastic limit shear stress; τ c2 is the plastic limit shear stress; u is the displacement; L e is the flexibility coefficient; Lp is the plasticity factor;

[0046] Calculate the temperature of the dielectric material at a given time:

[0047]

[0048] Where: T(x i ,y j ) is the temperature of the dielectric material, T0 is the ambient temperature, β W is the heat penetration coefficient of the wheel; q W is the friction heat flowing to the wheel; v W is the circumferential speed of the wheel, n is the total number of divided grids;

[0049] The elastic limit shear stress, plastic limit shear stress, compliance coefficient and plasticity factor are corrected using the calculated temperature of the medium material, and the shear stress calculation is performed again. The above steps are repeated until the temperature error is less than the set convergence accuracy to obtain the tangential stress distribution of the simulated wheel-rail contact interface.

[0050] Specifically, in step (3), the elastic limit shear stress and plastic limit shear stress formulas of the medium are as follows:

[0051]

[0052] Where: τ c1 is the elastic limit shear stress, τ c2 is the plastic limit shear stress, and are all constants, p is the non-Hertzian normal force, T is the temperature of the medium, and T0 is the ambient temperature.

[0053] Specifically, in step (3), the formulas for the flexibility coefficient and plasticity factor are as follows:

[0054]

[0055] Where: L e is the flexibility coefficient, L p is the plasticity factor, p is the non-Hertzian normal force, are constants, T 3BL is the temperature of the medium, and T0 is the ambient temperature.

[0056] Specifically, step (4) includes:

[0057] Calculate the solid load and fluid load of the simulated wheel-rail contact interface separately:

[0058] W a =∫∫P a (x,y)dxdy

[0059] W f =∫∫P f (x,y)dxdy

[0060] Where: W a is the solid support, W f is the fluid load, P a (x, y) is the dimensionless pressure on the solid, P f (x,y) is the pressure carried by the dimensionless fluid;

[0061] The tangential force is obtained by integrating the tangential stress in the wheel-rail contact area, and the formula is:

[0062] F T =∫∫τ(x i ,y j )dxdy

[0063] Where: F T is the tangential force, τ(x i ,y j ) is (x i ,y j ) at the shear stress;

[0064] Calculate the wheel-rail adhesion coefficient f:

[0065]

[0066] Preferably, the above method further comprises the following steps:

[0067] (5) The wheel-rail adhesion coefficient obtained in step (4) is compared with the wheel-rail adhesion coefficient calculated using the FASTSIM model or the POLACH model. The accuracy is evaluated by calculating the root mean square error. The smaller the root mean square error, the higher the accuracy. The root mean square error calculation formula is as follows:

[0068]

[0069] Where: RMSE is the root mean square error, n is the number of samples, f i is the wheel-rail adhesion coefficient obtained in step (4), f i * It is the wheel-rail adhesion coefficient calculated by FASTSIM model or POLACH model.

[0070] Beneficial effect: Compared with the prior art, the significant effect of the present invention is that the present invention proposes a method for estimating the wheel-rail adhesion coefficient which comprehensively considers the wheel-rail interface roughness and different interface conditions, combines the advantages of the elastic fluid mixed lubrication model (EHL) and the extended creep force model (ECF), and more comprehensively takes into account various actual influencing factors of the wheel-rail contact interface, significantly improves the accuracy of wheel-rail adhesion calculation, and is applicable to a variety of different working conditions rather than being limited to calculations under specific conditions. It has better universality and practicality, and has practical guiding significance for the traction and control strategies of trains. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a flow chart of the method of the present invention.

[0072] Figure 2 It is a schematic diagram of the wheel-rail contact geometry.

[0073] Figure 3 It is a schematic diagram of the wheel-rail local coordinate system.

[0074] Figure 4 is the rigid contact gap diagram under different lateral displacements.

[0075] Figure 5 It is a schematic diagram of the stress-displacement relationship of the elastic-plastic behavior of 3BL.

[0076] Figure 6 This is a schematic diagram of the 3BL independent brush model.

[0077] Figure 7 It is a schematic diagram of creep curves of FASTSIM model, POLACH model and ECF model. DETAILED DESCRIPTION

[0078] A preferred embodiment of the present invention is further described below in conjunction with the accompanying drawings.

[0079] Example 1

[0080] See also Figure 1 As shown, this embodiment provides a wheel-rail adhesion coefficient estimation method, comprising the following steps:

[0081] (1) A local coordinate system is established at the wheel-rail contact point. The rigid contact gap, contact spot shape, and creep rate between the wheel and rail are calculated using the coordinates of the wheel and rail in the local coordinate system.

[0082] See also Figure 2As shown in the figure, the wheel-rail contact point under different working conditions is determined by the trace method. After the contact point is determined, in order to solve the three-dimensional geometric gap near the contact point, the wheel-rail surface needs to be meshed. Considering the wheel as a rotating body, the height h(x, y) corresponding to the x-coordinate and y-coordinate of any point on the wheel can be obtained:

[0083]

[0084] Where: R(y) is the radius of the wheel rolling circle at the corresponding coordinate.

[0085] The above formula is the expression in the wheel coordinate system. After considering the yaw angle and roll angle, the expression of the wheel surface in the wheel-rail absolute coordinate system can be obtained through the following coordinate transformation: w (x,y):

[0086]

[0087] Where: x, y, h are the longitudinal, transverse and vertical coordinates of the wheel surface in the wheel coordinate system; x1, y1, h1 are the longitudinal, transverse and vertical coordinates of the wheel surface in the wheel-rail absolute coordinate system; ψ w To shake the head angle; is the roll angle; Δy is the lateral displacement of the wheelset; R0 is the standard rolling circle radius.

[0088] For the expression of the rail in the absolute coordinate system, assuming that the rail does not undergo a sudden change in the longitudinal direction, the rail profile can be regarded as a function only related to y, expressed as h r (x,y):

[0089] h r (x,y)=f r (y)

[0090] Where: f r (y) is the rail interface profile.

[0091] See also Figure 3 As shown in the figure, to solve the wheel-rail rigid contact gap in the local coordinate system of the wheel-rail contact point, it is necessary to transform both the wheel surface and the rail surface into the local coordinate system of the wheel-rail rolling contact. w 、h r The coordinate transformation is performed based on the relative distance of each point from the contact point to obtain the ordinate z of the wheel-rail surface in the local coordinate system. cw 、z cr :

[0092]

[0093] The rigid contact gap between any wheel and rail is calculated as follows:

[0094] h=zcw -z cr

[0095] Where: h is the rigid contact gap between the wheel and rail, that is, the geometric gap without considering the wheel and rail deformation, z cw is the ordinate of the wheel in the local coordinate system at the contact point, z crw is the ordinate of the rail in the local coordinate system at the contact point.

[0096] Please refer to Figure 4 As shown, it is the contour map corresponding to the rigid contact gap under different lateral displacements of this embodiment, which is the visualization result obtained by the above contact geometry calculation. It can be intuitively seen that the distribution of the rigid contact gap under different lateral displacements is different.

[0097] The creep rate refers to the ratio of the difference between the actual distance traveled by the wheel and the distance traveled in pure rolling to the distance traveled in pure rolling when the wheel rolls on the rail due to the tangential force between the wheel and the rail. In this embodiment, the above modeling and data are directly input into the wheel dynamics simulation software (such as UM) to output the creep rate.

[0098] The contact patch shape is obtained by inputting the contact gap into the NORM algorithm, which was proposed by Kalker based on the linear creep theory. In this embodiment, the contact patch shape is directly calculated using the S-CONTACT software, which combines the NORM algorithm with the tangential algorithm to accurately solve the contact patch shape.

[0099] (2) The rigid contact gap obtained in step (1) is introduced into the elastic fluid hybrid lubrication model (EHL), and the non-Hertzian normal force of the simulated wheel-rail contact interface is calculated by combining the material parameters and geometric parameters of the wheel-rail contact interface.

[0100] The mutual movement between the wheel and rail will form a mixed lubrication in which fluid lubrication and solid direct contact coexist. At this time, the load between the wheel and rail is jointly borne by the fluid pressure and the solid contact pressure. When analyzing the mixed lubrication, it is necessary to solve the Reynolds equation, the film thickness equation, the density equation, the viscosity equation and the load equation at the same time. In order to reduce the number of unknown quantities and maintain the stability of the numerical calculation, the above equations are converted into a dimensionless mode for calculation. In the present invention, the Hertz calculation area in the conventional EHL model is corrected. Since the radius of curvature at the contact point in the actual wheel-rail contact is not constant, it is more reasonable to use the non-Hertz calculation area. At the same time, the non-Hertz gap calculated in step (1) is used to correct the film thickness equation in the EHL model.

[0101] The dimensionless Reynolds equation is:

[0102]

[0103] λ=(8πUk e R x ) / (Wa eqv )

[0104] k e =b eqv / a eqv

[0105] Where: X, Y are dimensionless coordinate values; P is the dimensionless normal force; H is the dimensionless water film thickness; is the dimensionless viscosity, is the dimensionless density; W is the dimensionless load; R x is the radius of curvature in the x direction at the contact point; k e is the equivalent ellipticity, a eqv is the major axis of the equivalent ellipse, b eqv is the minor axis of the equivalent ellipse; U is the dimensionless velocity;

[0106] The dimensionless film thickness equation is:

[0107]

[0108] Where: H0 is the dimensionless initial center film thickness; G(X,Y) is the dimensionless rigid contact gap; V is the dimensionless elastic deformation; S1 is the roughness of the wheel surface, and S2 is the roughness of the rail surface;

[0109] The dimensionless viscosity equation is:

[0110]

[0111] Where: η0 is the environmental viscosity; η i (i=1, 2, 3, 4) are the fitting coefficients of the polynomial;

[0112] The dimensionless density equation is:

[0113]

[0114] Where: p0 is the maximum normal pressure;

[0115] The dimensionless load equation is:

[0116]

[0117] Where: P f (X,Y) is the pressure carried by the dimensionless fluid, P a (X,Y) is the dimensionless pressure on the solid, k e is the equivalent ellipticity.

[0118] In this embodiment, the dimensionless elastic deformation V(X,Y) in the dimensionless film thickness equation is:

[0119]

[0120] λ1=2p0R x / πE′a eqv

[0121] Where: p0 is the maximum normal pressure; R x is the equivalent radius of curvature; E' is the comprehensive elastic modulus; P f is the pressure carried by the dimensionless fluid, P a is the pressure on the dimensionless solid, a eqv is the major axis of the equivalent ellipse.

[0122] Solving the above equations at the same time, we obtain the non-Hertzian normal force P.

[0123] (3) The contact spot shape obtained in step (1) and the non-Hertzian normal force obtained in step (2) are introduced into the extended creep force model to calculate the tangential stress distribution of the simulated wheel-rail contact interface.

[0124] The extended creep force model (ECF model) is used to solve the wheel-rail tangential problem. This model treats the "third medium" at the wheel-rail interface as a third body (3BL) and considers the effects of pressure and temperature on the elastic-plastic behavior of the material. The elastic-plastic behavior of the material is as follows: Figure 4 As shown in the figure, when the shear stress is less than the elastic limit shear stress τ c1 When the shear stress is greater than τ c1 And it does not exceed its plastic limit shear stress τ c2 When , 3BL undergoes plastic deformation. The elastic and plastic limit shear stresses of 3BL are also affected by pressure and temperature. The specific expressions are as follows:

[0125]

[0126] Where: τ c1 is the elastic limit shear stress, τ c2 is the plastic limit shear stress, and are all constants obtained from experiments, p is the non-Hertzian normal force calculated in step (2), T is the temperature of the medium, and T0 is the ambient temperature.

[0127] The flexibility coefficient L in the shear characteristic curve of 3BL e and plasticity factor L p The expression is as follows:

[0128]

[0129] Where: L e is the flexibility coefficient, L p is the plasticity factor, p is the non-Hertzian normal force, are constants, T 3BL is the temperature of the medium, and T0 is the ambient temperature.

[0130] See also Figure 5 As shown in the figure, the third body layer is composed of many independent brushes perpendicular to the wheel-rail contact surface. Assuming that the normal stress and tangential stress along each brush are constant, when the brush enters the contact from the leading edge of the contact patch and leaves the contact patch at the trailing edge, the normal stress, tangential stress and temperature will change. Figure 5 The displacements u1, u2, and u3 corresponding to the three brushes B1, B2, and B3 increase successively. At the same time, the corresponding normal stresses P1, P1, and P1 and tangential stresses τ1, τ2, and τ3 and temperatures T1, T2, and T3 also vary. As the displacement increases, the elastic deformation of the brushes changes to plastic deformation. In order to obtain the tangential stress distribution and creep force of the wheel-rail rolling contact, the contact area can be divided into several discrete units for study. For any discrete unit (i, j), let the normal stress of the discrete unit be p(x i ,y j ), the displacement is u(x i ,y j ), the tangential stress is τ(x i ,y j ), the temperature is T(x i ,y j ), the expression of total displacement is as follows:

[0131]

[0132] Where: u(x i ,y j ) is the displacement of the discrete unit, u x (x i ,y j ) is the displacement of the discrete unit in the x-axis direction, u y (x i ,y j ) is the displacement of the discrete unit in the y-axis direction;

[0133] The shear stress analysis of the medium at the wheel-rail contact interface is carried out. When the shear stress is less than the elastic limit shear stress τ c1 When , the dielectric material undergoes elastic deformation, and the formula is as follows:

[0134]

[0135] Where: τ(x i ,y j ) is shear stress, L e is the flexibility coefficient; ξ x is the longitudinal creep rate; y is the lateral creep rate; φ is the spin creep rate; L x , L y , L φ is the Kalker coefficient;

[0136] As the displacement increases, 3BL changes from elastic deformation to plastic deformation. When the shear stress is greater than the elastic limit shear stress τ c1 and is less than the plastic limit shear stress τ c2 When the dielectric material undergoes plastic deformation, the displacement of the wheel and rail is very small relative to the displacement of the 3BL, so they can be ignored. To calculate the tangential stress of plastic deformation, the Voce material hardening law is used, and the formula is as follows:

[0137] τ 3BL =τ c1 +(τ c2 -τ c1 )(1-exp((-u+τ c1 L e ) / L p ))

[0138] Where: τ 3BL is the shear stress, τ c1 is the elastic limit shear stress; τ c2 is the plastic limit shear stress; u is the displacement; L e is the flexibility coefficient; L p is the plasticity factor;

[0139] When the speed is greater than 0.05m / s, calculate the temperature of the dielectric material at a given moment:

[0140]

[0141] Where: T(x i ,y j ) is the temperature of the dielectric material, T0 is the ambient temperature, β W is the heat penetration coefficient of the wheel; q W is the friction heat flowing to the wheel; v W is the circumferential speed of the wheel, and n is the total number of grids divided into the calculation area, which is used here to mark different intervals for iteration and accumulation when calculating the temperature change.

[0142] The elastic limit shear stress, plastic limit shear stress, compliance coefficient and plasticity factor are corrected using the calculated temperature of the medium material, and the shear stress calculation is performed again. The above steps are repeated until the temperature error is less than the set convergence accuracy ERR (ERR is 0.01°C in this embodiment) to obtain the tangential stress distribution of the simulated wheel-rail contact interface.

[0143] (4) The tangential stress distribution of the simulated wheel-rail contact interface is integrated over the wheel-rail contact area to obtain the tangential force of the wheel-rail rolling contact. The wheel-rail adhesion coefficient is calculated by combining the solid bearing pressure and the fluid bearing pressure obtained in step (2).

[0144] Calculate the solid load and fluid load of the simulated wheel-rail contact interface separately:

[0145] W a =∫∫P a (x,y)dxdy

[0146] W f =∫∫P f (x,y)dxdy

[0147] Where: W a is the solid support, W f is the fluid load, P a (x, y) is the dimensionless pressure on the solid, P f (x,y) is the pressure carried by the dimensionless fluid;

[0148] The tangential force is obtained by integrating the tangential stress in the wheel-rail contact area, and the formula is:

[0149] F T =∫∫τ(x i ,y j )dxdy

[0150] Where: F T is the tangential force, τ(x i ,y j ) is (x i ,y j ) at the shear stress;

[0151] Calculate the wheel-rail adhesion coefficient f:

[0152]

[0153] (5) The wheel-rail adhesion coefficient obtained in step (4) is compared with the wheel-rail adhesion coefficient calculated using the FASTSIM model or the POLACH model. The accuracy is evaluated by calculating the root mean square error between the two. The smaller the root mean square error, the higher the accuracy. The root mean square error calculation formula is as follows:

[0154]

[0155] Where: RMSE is the root mean square error, n is the number of samples, f i is the wheel-rail adhesion coefficient obtained in step (4), f i * It is the wheel-rail adhesion coefficient calculated by FASTSIM model or POLACH model.

[0156] See also Figure 7 As shown, under the conditions of a normal force of 110 kN and a speed of 20 m / s, creep curves were simulated based on the FASTSIM model, the POLACH model and the calculation model provided in this embodiment (hereinafter referred to as the ECF model).

[0157] from Figure 7 It can be seen from the partial enlarged graph of the curve in that when the creep rate is less than 0.5%, the creep curves simulated by the FASTSIM model and the ECF model are almost the same, both showing an approximately linear growth trend. After that, the curve simulated by the FASTSIM model tends to saturate and remain stable.

[0158] Unlike the above models, the creep curve simulated by the POLACH model has an initial downward slope in the small creep stage. It reaches a saturation value when the creep rate increases to about 4%, and then shows a negative slope characteristic. However, when the creep rate is greater than about 30%, the downward trend of the curve gradually slows down. The advantages of the ECF model are highlighted here. After the creep rate exceeds 0.5%, the creep curve of the ECF model does not tend to saturation directly like the FASTSIM model, but begins to rise slowly until it reaches the saturation value. Moreover, when the creep rate increases further, although the curve will also decline, compared with the POLACH model, the downward trend of the curve simulated by the ECF model is more obvious, which can more finely reflect the changes in the creep process, and show unique advantages in simulating the creep curve.

Claims

1. A wheel-rail adhesion coefficient estimation method, characterized in that: The following steps are involved: (1) Establish a local coordinate system at the wheel-rail contact point and calculate the rigid contact gap, contact spot shape, and creep rate between the wheel and rail; (2) the rigid contact gap obtained in step (1) is introduced into the elastic fluid mixed lubrication model, and the non-Hertzian normal force of the simulated wheel-rail contact interface is calculated by combining the material parameters and geometric parameters of the wheel-rail contact interface; (3) introducing the contact spot shape and creep rate obtained in step (1) and the non-Hertzian normal force obtained in step (2) into the extended creep force model to calculate the tangential stress distribution of the simulated wheel-rail contact interface; (4) The tangential stress distribution of the simulated wheel-rail contact interface is integrated over the wheel-rail contact area to obtain the tangential force of the wheel-rail rolling contact. The ratio of the tangential force to the non-Hertzian normal force is calculated to obtain the wheel-rail adhesion coefficient.

2. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: In the step (1), the rigid contact gap between the wheel and the rail is: h=z cw -z cr Where: h is the rigid contact gap between wheel and rail, z cw is the ordinate of the wheel in the local coordinate system at the contact point, z crw is the ordinate of the rail in the local coordinate system at the contact point.

3. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: In the step (2), the elastic fluid mixed lubrication model includes: solving the dimensionless Reynolds equation, the dimensionless film thickness equation, the dimensionless density equation, the dimensionless viscosity equation and the dimensionless load equation to obtain the non-Hertzian normal force.

4. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: The dimensionless Reynolds equation is: λ=(8πUk e R x ) / (Wa eqv ) k e =b eqv / a eqv Where: X, Y are dimensionless coordinate values; P is the dimensionless normal force; H is the dimensionless water film thickness; is the dimensionless viscosity, is the dimensionless density; W is the dimensionless load; R x is the radius of curvature in the x direction at the contact point; k e is the equivalent ellipticity, a eqv is the major axis of the equivalent ellipse, b eqv is the minor axis of the equivalent ellipse; U is the dimensionless velocity; The dimensionless film thickness equation is: Where: H0 is the dimensionless initial center film thickness; G(X,Y) is the dimensionless rigid contact gap; V is the dimensionless elastic deformation; S1 is the roughness of the wheel surface, and S2 is the roughness of the rail surface; The dimensionless viscosity equation is: Where: η0 is the environmental viscosity; η i (i=1, 2, 3, 4) are the fitting coefficients of the polynomial; The dimensionless density equation is: Where: p0 is the maximum normal pressure; The dimensionless load equation is: Where: P f (X,Y) is the pressure carried by the dimensionless fluid, P a (X,Y) is the dimensionless solid pressure, k e is the equivalent ellipticity.

5. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: In the dimensionless film thickness equation, the dimensionless elastic deformation V(X,Y) is: λ1=2p0R x / πE′a eqv Where: p0 is the maximum normal pressure; R x is the equivalent radius of curvature; E' is the comprehensive elastic modulus; P f is the pressure carried by the dimensionless fluid, P a is the pressure on the dimensionless solid, a eqv is the major axis of the equivalent ellipse.

6. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: The step (3) comprises: The wheel-rail contact interface is divided into several discrete units, and the displacement of each discrete unit is as follows: Where: u(x i ,y j ) is the displacement of the discrete unit, u x (x i ,y j ) is the displacement of the discrete unit in the x-axis direction, u y (x i ,y j ) is the displacement of the discrete unit in the y-axis direction; x i and i is the horizontal and vertical coordinates of the discrete unit; ξ x is the longitudinal creep rate; y is the lateral creep rate; φ is the spin creep rate; The shear stress analysis of the medium at the wheel-rail contact interface is carried out. When the shear stress is less than the elastic limit shear stress, the medium material undergoes elastic deformation. The formula is as follows: Where: τ(x i ,y j ) is shear stress, L e is the flexibility coefficient; L x , L y , L φ is the Kalker coefficient; When the shear stress is greater than the elastic limit shear stress and less than the plastic limit shear stress, the dielectric material undergoes plastic deformation. The shear stress formula is as follows: t 3BL =t c1 +(t c2 -t c1 )(1-exp((-u+τ c1 L e ) / L p )) Where: τ 3BL is the shear stress, τ c1 is the elastic limit shear stress; τ c2 is the plastic limit shear stress; u is the displacement; L e is the flexibility coefficient; L p is the plasticity factor; Calculate the temperature of the dielectric material at a given time: Where: T(x i ,y j ) is the temperature of the dielectric material, T0 is the ambient temperature, β W is the heat penetration coefficient of the wheel; q W is the friction heat flowing to the wheel; v W is the circumferential speed of the wheel, n is the total number of divided grids; The elastic limit shear stress, plastic limit shear stress, compliance coefficient and plasticity factor are corrected using the calculated temperature of the medium material, and the shear stress calculation is performed again. The above steps are repeated until the temperature error is less than the set convergence accuracy to obtain the tangential stress distribution of the simulated wheel-rail contact interface.

7. The wheel-rail adhesion coefficient estimation method according to claim 6, characterized in that: In the step (3), the elastic limit shear stress and plastic limit shear stress formulas of the medium are as follows: Where: τ c1 is the elastic limit shear stress, τ c2 is the plastic limit shear stress, and are all constants, p is the non-Hertzian normal force, T is the temperature of the medium, and T0 is the ambient temperature.

8. The wheel-rail adhesion coefficient estimation method according to claim 6, characterized in that: In the step (3), the formulas for the flexibility coefficient and the plasticity factor are as follows: Where: L e is the flexibility coefficient, L p is the plasticity factor, p is the non-Hertzian normal force, are constants, T 3BL is the temperature of the medium, and T0 is the ambient temperature.

9. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: The step (4) comprises: Calculate the solid load and fluid load of the simulated wheel-rail contact interface separately: W a =∫∫P a (x,y)dxdy W f =∫∫P f (x,y)dxdy Where: W a is the solid support, W f is the fluid load, P a (x, y) is the dimensionless pressure on the solid, P f (x,y) is the pressure carried by the dimensionless fluid; The tangential force is obtained by integrating the tangential stress in the wheel-rail contact area, and the formula is: F T =∫∫τ(x i ,and j )dxdy Where: F T is the tangential force, τ(x i ,y j ) is (x i ,y j ) at the shear stress; Calculate the wheel-rail adhesion coefficient f:

10. The wheel-rail adhesion coefficient estimation method according to claim 1, characterized in that: The following steps are also included: (5) The wheel-rail adhesion coefficient obtained in step (4) is compared with the wheel-rail adhesion coefficient calculated using the FASTSIM model or the POLACH model. The accuracy is evaluated by calculating the root mean square error. The smaller the root mean square error, the higher the accuracy. The root mean square error calculation formula is as follows: Where: RMSE is the root mean square error, n is the number of samples, f i is the wheel-rail adhesion coefficient obtained in step (4), f i * It is the wheel-rail adhesion coefficient calculated by FASTSIM model or POLACH model.

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