Three-dimensional wheel-rail wear map construction method taking ambient temperatures and material properties into consideration

Abstract

The present invention relates to the technical field of wheel-rail material friction and wear. Provided is a three-dimensional wheel-rail wear map construction method taking ambient temperatures and material properties into consideration. The method comprises: 1) on the basis of wheel-rail rolling friction and wear experiments under different contact parameters, obtaining the friction and wear performance of a wheel material under the condition of different ambient temperatures and different wheel-rail hardness ratios, and constructing a function relationship between a wheel wear rate and the dissipated energy per unit area of a wheel-rail contact patch under a series of conditions with different ambient temperatures and wheel-rail hardness ratios; 2) performing function fitting on experimental data to respectively obtain a three-dimensional wheel wear map taking ambient temperatures into consideration and a three-dimensional wheel wear map taking wheel-rail material hardness ratios into consideration; and 3) selecting a two-dimensional reference wear map, and by means of normalization processing, constructing a three-dimensional wheel wear map simultaneously taking ambient temperatures and material hardness ratios into consideration. On the basis of a constructed wear map, the present invention can preferably predict a wheel wear behavior under the condition of different ambient temperatures and different material properties.

Description

A wheel-rail three-dimensional wear map construction method considering environmental temperature and material characteristics TECHNICAL FIELD

[0001] The present application relates to the field of wheel-rail material friction and wear technology, and provides a wheel-rail three-dimensional wear map construction method considering environmental temperature and material characteristics. BACKGROUND

[0002] With the gradual high-speed and heavy-load of railway transportation, as one of the most core components to ensure the safety of train operation, the friction and wear behavior of wheel-rail materials will become more serious, which poses a challenge to the wear resistance, service life and safety reliability of wheel-rail materials. At the same time, the wheel-rail system serves in a relatively open environment, and the complex and variable operating conditions will also affect the friction and wear behavior of wheel-rail materials.

[0003] The wear model is a research method commonly used in tribological systems, which can comprehensively and intuitively integrate various tribological information of the friction pair materials, and is essentially a comprehensive information database containing wear rate data and wear surface morphology data, providing convenient data reference for wear and life prediction research of friction pair materials. At present, Archard wear model and Tgamma / A-wear rate model are the two most commonly used wear models for wheel-rail systems. Among them, the Tgamma / A-wear rate model is based on a large number of wheel-rail friction and wear test results in the laboratory, and its continuous input value of wear rate can more accurately study the friction and wear behavior of the wheel-rail system. However, the existing Tgamma / A-wear rate model only considers the two-dimensional function relationship between material wear rate and energy dissipation work (Tgamma / A), but different wheel-rail material characteristics and external environmental temperature will also greatly affect the wear behavior of wheel-rail materials. Therefore, it is necessary to develop a three-dimensional wear model considering the material characteristics (internal factors) and environmental temperature (external factors) of wheel-rail materials, and further draw a three-dimensional wear map reflecting the wear rate of wheel-rail materials with energy dissipation work, material hardness and environmental temperature. At the same time, based on the constructed three-dimensional wear model, wheel-rail wear prediction considering environmental temperature and material characteristics can be further carried out. SUMMARY

[0004] The present application provides a wheel-rail three-dimensional wear map construction method considering environmental temperature and material characteristics, which can solve the problem that the existing two-dimensional wear map cannot reflect the internal factors (material characteristics) and external factors (environmental temperature) affecting the wear behavior of wheel-rail materials in engineering practical applications.

[0005] According to the wheel-rail three-dimensional wear map construction method considering environmental temperature and material characteristics, the following steps are included:

[0006] 1) based on the wheel-rail rolling friction and wear experiments under different contact parameters, the friction and wear properties of the wheel material under different environmental temperatures and different wheel-rail hardness ratios are obtained, and a functional relationship between the wheel wear rate and the unit area wheel-rail contact spot dissipation energy under a series of different environmental temperatures and wheel-rail hardness ratios is constructed;

[0007] 2) the experimental data is fitted by MATLAB software, and the wheel three-dimensional wear map considering the environmental temperature and the wheel three-dimensional wear map considering the wheel-rail material hardness ratio are obtained respectively;

[0008] 3) a two-dimensional reference wear map is selected and a wheel three-dimensional wear map considering the environmental temperature and the material hardness ratio is constructed through normalization processing.

[0009] As preferred, in step 1), the functional relationship between the wheel wear rate and the unit area wheel-rail contact spot dissipation energy under a series of different environmental temperatures and wheel-rail hardness ratios is Tγ / A-wear rate functional relationship, wherein the wheel wear rate is the wear amount divided by the product of the running distance and the wheel-rail contact area A; the unit area wheel-rail contact spot dissipation energy Tγ / A is the product of the wheel-rail interface tangential force T and the creep rate γ divided by the wheel-rail contact area A; the Tγ / A-wear rate functional relationship is divided into two regions I and II according to the curve change slope.

[0010] As preferred, in step 2), the Tγ / A-wear rate curve I and II region line segment slope and the I and II region intersection point abscissa under different environmental temperatures are fitted by MATLAB software with environmental temperature as the independent variable, the wheel wear model considering the environmental temperature Tt is obtained, and the wheel three-dimensional wear map considering the environmental temperature 3DMAP(Tt) is constructed based on the wheel wear model considering the environmental temperature Tt with wear rate, Tγ / A and environmental temperature Tt as coordinate parameters;

[0011] The Tγ / A-wear rate curve I and II region slope under different wheel-rail hardness ratios is fitted, the wheel wear model considering the material hardness ratio Hv is obtained, and the wheel three-dimensional wear map considering the wheel-rail material hardness ratio 3DMAP(Hv) is constructed based on the wheel wear model considering the material hardness ratio Hv with wear rate, Tγ / A and wheel-rail hardness ratio as coordinate parameters; the wheel two-dimensional wear map 2DMAP(Tt) and 2DMAP(Hv) under a certain environmental temperature or material hardness ratio condition is obtained from the wheel three-dimensional wear map 3DMAP(Tt) and the wheel three-dimensional wear map 3DMAP(Hv).

[0012] As preferred, in step 2), the fitting functions of the I and II region line segment slopes in the wheel wear model considering the environmental temperature Tt are k1=-0.0085·T t +1.816 and k2=-0.0035·T t+0.260, the fitting function of the horizontal and vertical coordinates of the intersection point of the two regions I and II is x1 = -0.1054*T t +19.464, y1 = -0.5155*T t +33.711, the wheel wear model considering the ambient temperature Tt is as follows:

[0013] Region I: 0 < Tγ / A < x1, the wear rate is k1*(Tγ / A);

[0014] Region II: x1 < Tγ / A, the wear rate is k2*(Tγ / A) - k2*x1 + y1.

[0015] As preferred, in step 2), the fitting function of the slope of the line segment of the two regions I and II in the wheel wear model considering the material hardness ratio is k3 = 0.3872 + 0.0507*e 4.9177Hv and k4 = 0.0847 + 0.0056*e 4.7672Hv , and the horizontal coordinate x2 of the intersection point of the two regions I and II is the intersection value x2 = 16.657 of the wheel Tγ / A-wear rate function relationship under the ambient temperature 20℃; the wheel wear model considering the material hardness ratio Hv is as follows:

[0016] Region I: 0 < Tγ / A < x2, the wear rate is k3*(Tγ / A);

[0017] Region II: x2 < Tγ / A, the wear rate is k4*(Tγ / A) + 16.657*(k3-k4).

[0018] As preferred, in step 3), the two-dimensional wear map 2DMAP(Tt1) and 2DMAP(Hv1) of the wheel under the same ambient temperature Tt1 and material hardness ratio Hv1 are selected, the interpolation fitting of the slopes of the two regions I and II in the two-dimensional wear maps 2DMAP(Tt1) and 2DMAP(Hv1) of the wheel is carried out by using MATLAB software, and the reference two-dimensional wear map 2DMAP(S) is constructed; the wheel wear model considering the ambient temperature Tt and the wheel wear model considering the material hardness ratio Hv are fitted with the reference two-dimensional wear map 2DMAP(S) through normalization, so as to obtain the wheel wear model considering the ambient temperature and the material hardness ratio at the same time; based on the wheel wear model considering the ambient temperature and the material hardness ratio at the same time, the variable Tt·e 4.9177·Hv is derived, and the three-dimensional wear map 3DMAP(Tt, Hv) of the wheel considering the ambient temperature and the material hardness ratio of the wheel-rail at the same time is constructed with the wear rate, Tγ / A and Tt·e 4.9177·Hv as the coordinate parameters.

[0019] As preferred, in step 3), the same ambient temperature Tt1 and material hardness ratio Hv1 are respectively 20℃ and 1.08; and the wheel wear map I, II two region slopes considering the ambient temperature and the material hardness ratio are respectively 0.6075*k1k3, 5.2604*k2k4, and the two region intersection point abscissa is 1.0394*x1; the wheel wear model of the wheel three-dimensional wear map 3DMAP(Tt, Hv) considering the ambient temperature and the material hardness ratio is as follows:

[0020] I region: 0<Tγ / A<1.0394*x1, the wear rate is 0.6075*k1k3*(Tγ / A);

[0021] II region: 1.0394*x1<Tγ / A, the wear rate is 5.2604*k2k4*(Tγ / A)+0.6314*y1k3-1.0394*y1k2k4 / k1.

[0022] The application provides a wheel wear prediction method, which adopts the three-dimensional wear map constructed by the wheel-rail three-dimensional wear map construction method considering the ambient temperature and the material characteristics, and comprises the following steps:

[0023] a) a vehicle-track coupled multi-body dynamics model is established by using SIMPACK multi-body dynamics simulation software, and wheel-rail contact parameters are obtained by analysis and calculation;

[0024] b) based on the wheel-rail contact parameters, the size of the wheel-rail contact spot, the creep force and the stick-slip region distribution in the service process of the wheel-rail are calculated by using the Hertz contact theory and the FASTSIM theory;

[0025] c) the wear distribution on the contact spot is calculated in combination with the wheel three-dimensional wear map considering the ambient temperature and the material hardness ratio, and finally the wheel wear depth and the wear profile are obtained. The most commonly used Tγ / A wear rate model in the existing research is obtained based on the test data of CL60 wheel and U71Mn rail matching at a certain temperature, and the wheel wear depth and the wear profile can be predicted by substituting the wear model into the above wheel wear prediction process. However, the ambient temperature and the wheel-rail material hardness ratio are inversely proportional to the material wear rate, that is, the wheel wear of different ambient temperatures and different material hardness matching should exist. Therefore, the wear model has two disadvantages: i) it is not suitable for wear prediction of other wheel-rail hardness matching materials. If necessary, friction and wear tests need to be carried out on the remaining hardness matching wheel-rail material pairs to obtain the corresponding Tγ / A wear rate model; ii) when the CL60-U71Mn wheel-rail material is matched, the influence of the ambient temperature on the wheel wear prediction value cannot be reflected;

[0026] The three-dimensional wheel-rail wear map (model) considering the environmental temperature and the material hardness ratio can solve the above two problems: i) by inputting the environmental temperature and the material hardness ratio value, the corresponding two-dimensional wear model under the condition of a certain environmental temperature and a certain material hardness ratio can be output, and the wheel wear under the condition can be more accurately predicted; ii) under the same wheel-rail hardness matching condition, the corresponding two-dimensional wear model under different environmental temperatures can be obtained, and the wheel wear depth and wear profile under different environmental temperatures can be more accurately predicted.

[0027] The present application has the advantages that: the present application provides a wheel-rail three-dimensional wear map construction method considering the environmental temperature and the material characteristics, compared with the existing commonly used wheel-rail wear map, the wheel-rail three-dimensional wear map can reflect the influence of the environmental temperature and the material hardness on the wheel-rail wear rate, the wheel Tγ / A wear rate model under the condition of a specific environmental temperature and a specific material characteristic can be directly obtained, and based on the constructed three-dimensional wear map, the wheel-rail wear under the condition of the environmental temperature and the material hardness ratio is predicted by using the wheel-rail wear prediction method, which has important engineering application value and theoretical guiding significance. BRIEF DESCRIPTION OF DRAWINGS

[0028] Fig. 1 is a whole flow chart of a wheel-rail three-dimensional wear map construction method and wear prediction method considering the environmental temperature and the material characteristics;

[0029] Fig. 2 is a structural diagram of a wheel-rail rolling contact friction and wear testing machine;

[0030] Fig. 3 is a low-temperature cavity structure diagram;

[0031] Fig. 4 is a small-scale wheel-rail sample sampling diagram;

[0032] In the figure, 1 is a driving motor, 2 is a torque sensor, 3 is a main shaft, 4 is an upper sample (wheel sample), 5 is a companion shaft servo motor, 6 is a companion shaft, 7 is a vertical load loading device, 8 is a lower sample (rail sample), 9 is a copper pipe, 10 is a low-temperature cavity, 11 is a wheel, and 12 is a rail;

[0033] Fig. 5 is a wheel three-dimensional wear map 3DMAP (Tt) considering the environmental temperature according to experimental data;

[0034] Fig. 6 is a wheel three-dimensional wear map 3DMAP (Hv) considering the material hardness ratio according to experimental data;

[0035] Fig. 7 is a wheel two-dimensional wear map 2DMAP (20℃, 0.8) under the condition of an environmental temperature of 20℃ and a material hardness ratio of 0.8;

[0036] Fig. 8 is a wheel three-dimensional wear map 3DMAP (Tt, Hv) considering the environmental temperature and the material hardness ratio according to experimental data;

[0037] Fig. 9 is a corresponding wear profile diagram obtained according to the most commonly used Tγ / A wear rate model in the prior research;

[0038] Fig. 10 is a wheel wear depth distribution diagram in the range of environmental temperature -40-40℃ and wheel-rail hardness ratio 0.8-1.4 obtained by the wheel three-dimensional wear model for predicting and calculating the environmental temperature and the material hardness ratio;

[0039] Fig. 11 is a wheel wear volume distribution diagram in the range of environmental temperature -40-40℃ and wheel-rail hardness ratio 0.8-1.4 obtained by the wheel three-dimensional wear model for predicting and calculating the environmental temperature and the material hardness ratio. DETAILED DESCRIPTION

[0040] For further understanding of the present application, the present application will be described in detail with reference to the accompanying drawings and examples. It should be understood that the examples are only for the purpose of interpretation of the present application and are not limited.

[0041] Examples

[0042] As shown in Fig. 1, the present embodiment provides a wheel-rail three-dimensional wear map construction method considering environmental temperature and material characteristics, which comprises the following steps:

[0043] Step 1) Based on the wheel-rail rolling friction and wear experiments under different contact parameters, the friction and wear properties of the wheel material under different environmental temperatures and different material characteristics (the material characteristics of the present embodiment are the wheel-rail hardness ratio) are obtained, and a functional relationship between the wheel wear rate and the unit area wheel-rail contact spot dissipation energy under a series of different environmental temperatures and wheel-rail hardness ratios is constructed;

[0044] All wheel-rail rolling contact experiments are completed on the wheel-rail rolling contact tester shown in Fig. 2, which is equipped with a low-temperature environmental chamber and can simulate different environmental temperatures, as shown in Fig. 3. The wheel and rail disc samples are taken from the wheel flange and rail head, respectively, as shown in Fig. 4, and the sample size is processed according to the structure of the tester as a diameter of 60mm, the wheel sample is stepped, and the wheel-rail sample contact width is 5mm.

[0045] The functional relationship between the wheel wear rate and the unit area wheel-rail contact spot dissipation energy under a series of different environmental temperatures and wheel-rail hardness ratios is Tγ / A-wear rate functional relationship, wherein the wheel wear rate is the wear amount divided by the product of the running distance and the wheel-rail contact area A; the unit area wheel-rail contact spot dissipation energy Tγ / A is the product of the wheel-rail interface tangential force T and the creep rate γ divided by the wheel-rail contact area A.

[0046] To establish a functional relationship (Tγ / A - wear rate) between wheel wear rate and energy dissipation per unit area of ​​wheel-rail contact patch under various ambient temperatures and wheel-rail hardness ratios, different Tγ / A values ​​were obtained by varying the vertical load and slip. The slip γ was controlled by the speed difference between the wheel and rail samples. The tangential force T was calculated by combining the vertical load between the wheel and rail with the friction coefficient values ​​during the experiment. This embodiment is based on Tγ / A ranging from 0 to 60 N / mm. 2 The wear rate statistics of a wide area with a rail / wheel hardness ratio of 0.8 to 1.3 and an ambient temperature of -40 to 20℃ were obtained. The Tγ / A-wear rate function relationship can be divided into two regions, I and II, according to the slope of the curve.

[0047] Step 2) Use MATLAB software to fit the experimental data to obtain the three-dimensional wear map of the wheel considering ambient temperature and the three-dimensional wear map of the wheel considering the hardness ratio of the wheel and rail materials, respectively.

[0048] Using MATLAB software, with ambient temperature as the independent variable, the slopes of the Tγ / A-wear rate curves in regions I and II and the abscissa of the intersection point of regions I and II under different ambient temperatures were fitted to obtain a wheel wear model considering ambient temperature Tt. Based on the wheel wear model considering ambient temperature Tt, a three-dimensional wheel wear map 3DMAP(Tt) considering ambient temperature was constructed with wear rate, Tγ / A and ambient temperature Tt as coordinate parameters.

[0049] By fitting the slopes of the Tγ / A-wear rate curves in regions I and II under different wheel-rail hardness ratios, a wheel wear model considering the material hardness ratio Hv is obtained. Based on the wheel wear model considering the material hardness ratio Hv, a three-dimensional wheel wear map 3DMAP(Hv) is constructed, with wear rate, Tγ / A, and wheel-rail hardness ratio as coordinate parameters. From the three-dimensional wheel wear map 3DMAP(Tt) and the three-dimensional wheel wear map 3DMAP(Hv), two-dimensional wheel wear maps 2DMAP(Tt) and 2DMAP(Hv) under a certain ambient temperature or material hardness ratio condition are obtained.

[0050] Table 1 shows the Tγ / A-wheel wear rate model data under ambient temperatures of -40℃, 0℃, and 20℃. Using MATLAB software, linear regression fitting was performed on the slopes of the Tγ / A-wear rate curves in regions I and II, as well as the abscissa of the intersection point of regions I and II, under different ambient temperatures. The resulting wheel wear model considering ambient temperature Tt is shown in Table 2. The fitting functions for the slopes of the line segments in regions I and II are k1 = -0.0085*T. t +1.816 and k2 = -0.0035*T t +0.260, the fitting functions for the x and y coordinates of the boundary point between regions I and II are x1 = -0.1054·T.t +19.464, y1 = -0.5155*T t +33.711. A wheel three-dimensional wear map 3DMAP(Tt) considering the environmental temperature is constructed based on the wheel wear model considering the environmental temperature Tt, with the wear rate, Tγ / A and the environmental temperature Tt as the coordinate parameters, as shown in FIG. 5;

[0051] Table 1 Wheel wear model experimental data at different environmental temperatures Tt

[0052] Table 2 Wheel wear model considering the environmental temperature Tt

[0053] The Tγ / A-wheel wear rate model data under different wheel-rail material hardness matching conditions involved in the existing literature are shown in Table 3. The Tγ / A-wear rate curve I and II region slopes under different wheel-rail hardness ratio conditions are least square fitted, and the wheel wear model considering the material hardness ratio Hv is shown in Table 4, wherein the I and II region line segment slope fitting functions are and k4 = 0.0847 + 0.0056*e 4.7672Hv The I and II region intersection point abscissa x2 is the intersection point value x2 = 16.657 of the wheel Tγ / A-wear rate function relationship at the environmental temperature 20°C in Table 1 (all existing hardness ratio data are experimental results at the environmental temperature 20°C). A wheel three-dimensional wear map 3DMAP(Hv) considering the wheel-rail material hardness ratio is constructed based on the wheel wear model considering the material hardness ratio Hv, with the wear rate, Tγ / A and the wheel-rail hardness ratio as the coordinate parameters, as shown in FIG. 6;

[0054] Table 3 Wheel wear model experimental data at different wheel-rail hardness ratios Hv

[0055] Table 4 Wheel wear model considering the environmental temperature Tt

[0056] A wheel two-dimensional wear map 2DMAP(Tt, Hv) under a certain environmental temperature and a certain material hardness ratio condition can be obtained from the wheel three-dimensional wear map 3DMAP(Tt) and the wheel three-dimensional wear map 3DMAP(Hv), and FIG. 7 shows a wheel two-dimensional wear map 2DMAP(20°C, 0.8) at the environmental temperature 20°C and the material hardness ratio 0.8.

[0057] Step 3) Select a two-dimensional reference wear map and construct a wheel three-dimensional wear map considering the environmental temperature and the material hardness ratio through normalization processing.

[0058] The wheel two-dimensional wear map 2DMAP(Tt1) and 2DMAP(Hv1) under the same environmental temperature (Tt1) and material hardness ratio (Hv1) are selected, and the slopes of the two regions I and II in the two wheel two-dimensional wear maps 2DMAP(Tt1) and 2DMAP(Hv1) are interpolated and fitted by using MATLAB software to construct a reference two-dimensional wear map 2DMAP(S); the wheel wear model considering the environmental temperature Tt and the wheel wear model considering the material hardness ratio Hv are fitted with the reference two-dimensional wear map 2DMAP(S) by normalization to obtain a wheel wear model considering both the environmental temperature and the material hardness ratio; based on the wheel wear model considering both the environmental temperature and the material hardness ratio, a variable Tt·e 4.9177·Hv is derived, and a wheel three-dimensional wear map 3DMAP(Tt, Hv) considering both the environmental temperature and the material hardness ratio of the wheel rail is constructed with the wear rate, Tγ / A and Tt·e 4.9177·Hv as coordinate parameters, as shown in FIG. 8.

[0059] The same environmental temperature Tt1 and material hardness ratio Hv1 are 20℃ and 1.08 respectively; the slopes of the two regions I and II of the wheel wear map considering both the environmental temperature and the material hardness ratio are 0.6075*k1k3 and 5.2604*k2k4 respectively, and the horizontal coordinate of the intersection point of the two regions is 1.0394*x1; the wheel wear model of the wheel three-dimensional wear map 3DMAP(Tt, Hv) considering both the environmental temperature and the material hardness ratio is shown in Table 5.

[0060] Table 5 Wheel wear model considering both the environmental temperature Tt and the material hardness ratio Hv

[0061] Further, the small-scale test adopts a Hertz contact simulation criterion, that is, the ratio of the major and minor axes of the elliptical spot of the contact area between the wheel and rail and the maximum contact stress under laboratory conditions are the same as those in the field, so as to approximately simulate the actual working conditions of the wheel-rail friction pair in the field, and the Tγ / A wear model established based on the material friction and wear data obtained by the test can further accurately and effectively predict the full-size wheel wear in the field. The Hertz contact simulation criterion needs to satisfy the following formula 1:

[0062] In formula (1), σ max is the maximum contact stress; F is the vertical force applied to the wheel-rail interface; μ1 and μ2 are the Poisson's ratios of the wheel and rail materials; E1 and E2 are the elastic moduli of the wheel and rail materials; L is the contact width of the wheel and rail samples (the contact width L of the samples in the two test machines is 5mm); ρ is the curvature at the contact between the wheel sample and the rail sample; and Σρ is the sum of the principal curvatures of the wheel sample and the rail sample.

[0063] R in formula (2) 11 , R 21 is the lateral curve radius of the wheel-rail sample, and in the embodiment, R 11 , R 21 is ∞; R 12 , R 22 is the longitudinal curve radius of the wheel-rail sample.

[0064] When the Poisson's ratio and the elastic modulus of the wheel-rail sample are respectively 0.3 and 2.06×10 5 MPa, the maximum stress σ max of the line contact can be calculated according to the following formula (3):

[0065] As shown in FIG. 1, the embodiment provides a wheel wear prediction method, which adopts the three-dimensional wear map constructed by the wheel-rail three-dimensional wear map construction method considering the environmental temperature and the material characteristics, and includes the following steps:

[0066] a) a vehicle-track coupled multi-body dynamics model is established by using the SIMPACK multi-body dynamics simulation software, and wheel-rail contact parameters are obtained by analysis and calculation;

[0067] b) based on the wheel-rail contact parameters, the Hertz contact theory and the FASTSIM theory are used to calculate the wheel-rail contact spot, the creep force and the stick-slip area distribution at each moment during the service of the wheel-rail;

[0068] The shape of the contact spot and the distribution of the contact pressure are calculated by using the Hertz contact theory, the obtained elliptical contact spot is discretized into units, and the elliptical contact spot is divided into square units with a side length of 0.1 mm, the x direction is the longitudinal direction (the rolling direction of the wheel), and the y direction is the lateral direction (perpendicular to the rolling direction of the wheel). The specific calculation formula of the normal force f z (x,y) is as follows:

[0069] In formula 4, N is the normal load, and a and b are the major and minor semi-axes of the wheel-rail elliptical contact spot.

[0070] The FASTSIM algorithm of the Kalker simplified theory is used to solve the wheel-rail tangential contact problem, the linear relationship between the force and the displacement based on the generalized elasticity theory is used, and the elastic force on the contact area is integrated to determine the linear functions of the wheel-rail creep forces f x , f y and the creep moment M in the x and y directions.

[0071] In formula (5), C 11 is the longitudinal creep coefficient (quantitative unit of the tangential force generated by the longitudinal creep), and C 22C is the lateral creep coefficient (quantifies the tangential force generated by a unit of lateral creep), 23 C is the lateral-rotational creep coefficient (quantifies the coupling effect of lateral creep and rotational creep), 33 G is the rotational creep coefficient (quantifies the moment generated by a unit of rotational creep), G = G x , γ y , respectively represent the longitudinal, lateral and spin creep rates. By using the longitudinal and lateral compliance coefficients (L x , L y ), the complex expressions derived from the general elasticity theory are simplified. Where the compliance coefficients depend on the creep rates and spin coefficients of the linear theory. The relationship of the wheel creep force f x , the rail creep force f y and the wheel-rail contact patch displacement u wr is as formula (6): u wr = u w - u r = [L x f x L y f y ] T (6)

[0072] In formula (6): u w , u r are the final position and initial position of the contact patch respectively.

[0073] The wheel-rail creep forces f x , f y in the contact patch can be obtained by integrating the whole wheel-rail contact patch area as:

[0074] In formula (7): f Tx is the longitudinal tangential force, f Ty is the lateral tangential force, L x is the longitudinal compliance coefficient, L y1 is the lateral compliance coefficient, L y2 is the rotational compliance coefficient.

[0075] The formula for calculating the compliance coefficient L is:

[0076] c) Calculate the wear distribution on the contact patch by combining the three-dimensional wheel wear map considering the ambient temperature and material hardness ratio at the same time, and finally obtain the wheel wear depth and wear profile.

[0077] Based on the calculation of the wheel-rail contact patch, creep force and stick-slip region distribution at each time by using the Hertz contact theory and FASTSIM theory, the wear distribution (i.e., the contact patch wear depth distribution) on the contact patch is calculated by combining the three-dimensional wheel wear model, and finally the wheel wear depth and wear profile are obtained. The specific wear prediction calculation formula is as follows:

[0078] In the FASTSIM algorithm, the displacement μ is assumed to be related to the surface stress p and the flexibility coefficient L, that is:

[0079] In formula (10), v x is the longitudinal slip speed between the wheel and the rail at the unit, v y is the transverse slip speed between the wheel and the rail at the unit, v v is the linear speed of the wheel, γ x is the longitudinal creep rate, γ y is the transverse creep rate, is the longitudinal spin creep rate, is the transverse spin creep rate, μ x is the longitudinal elastic displacement, μ y is the transverse elastic displacement, is the longitudinal elastic slip vector, is the transverse elastic slip vector.

[0080] Rewrite formula (10) into a vector form and perform dimensionless processing, that is:

[0081] In formula (11), w is the total slip vector, s is the rigid slip vector, is the elastic slip vector.

[0082] Integrate formula (11), and the tangential stress P(x, y) of each unit in the contact patch can be calculated. Assuming that the FASTSIM algorithm satisfies the Coulomb friction law, the limit tangential force P L (x, y) of the unit in the contact patch can be obtained as:

[0083] When the tangential force is less than the limit value of the tangential force, that is, P(x, y)≤P L (x, y), the unit is in the stick region and has no slip; when P(x, y) > P L (x, y), the wheel is in the slip region, and the corrected tangential force P S (x, y) is:

[0084] In formula (13), P x (x, y) is the longitudinal tangential stress in the unit, P y(x, y) is the tangential stress in the unit.

[0085] Because the rigid sliding amount in the contact patch is much larger than the elastic deformation amount, the influence of elastic sliding can be ignored in calculation. Thus, the sliding velocity in the contact patch can be simplified as:

[0086] The creep rate of each unit in the contact patch can be expressed as:

[0087] The Tγ / A of the unit in the sliding area is equal to the product of the tangential resultant stress of the unit and the total creep rate of the unit, which is taken as the input of the wear model:

[0088] The wear depth δz(x, y) of each sliding unit in the contact patch is:

[0089] In equation (18), K is the wear rate, which is calculated by the Tγ / A wear model, ρ1 is the density of the wheel material, and Δx is the relative sliding displacement of the unit on the contact patch.

[0090] After the wear depth of each unit is calculated, the wear depth of the contact patch is superimposed in the longitudinal direction, and the wear amount of a single section can be obtained by using the integral method:

[0091] According to the lateral position of the wheel contact point, the wear amount of the contact patch is superimposed to obtain the wheel wear amount W(y) under the working condition:

[0092] In equation (20), R is the nominal rolling circle radius of the wheel, L s and L e are the start and end positions of the calculation, s1 is the sampling point interval, and l is the lateral contact length.

[0093] In the actual train operation process, the shape of the wheel will continuously change as the train mileage increases. However, in numerical simulation, it is difficult to accurately simulate the continuous change of the profile. Therefore, the profile of the wheel is assumed to remain unchanged during the single calculation process, and the profile of the wheel is updated according to the pre-set update scheme after each iteration process is completed. In this way, the simulation process can be simplified, and the change of the wheel profile can be reflected to some extent. In this embodiment, the profile update is based on the vehicle mileage reaching a threshold. The tread data is processed by 5-point 3-time smoothing to obtain the worn wheel tread and perform the next simulation.

[0094] Further, through the wheel wear prediction calculation, the applicability of the wheel three-dimensional wear model considering the temperature and material hardness ratio is simulated and verified, specifically:

[0095] The most commonly used Tγ / A wear rate model in existing research is based on the matching test data of CL60 wheel and U71Mn rail at a certain temperature. By substituting the wear model into the above wheel wear prediction method, the corresponding wear profile can be predicted as shown in FIG. 9, and the wear depth and wear volume are 0.02972 mm and 3158.4906·10 -9 mm 3 However, the environmental temperature and the wheel-rail material hardness ratio are inversely proportional to the material wear rate, that is, the wheel wear of different environmental temperatures and different material hardness matching should exist differences. Therefore, the applicability of this wear model has two disadvantages: i) it is not suitable for wear prediction of other wheel-rail hardness matching materials. If necessary, friction and wear tests of the remaining wheel-rail material pairs are required to obtain the corresponding Tγ / A wear rate model; ii) when CL60-U71Mn wheel-rail material is matched, the influence of environmental temperature on the predicted value of wheel wear cannot be reflected;

[0096] The wheel three-dimensional wear model considering the environmental temperature and the material hardness ratio in this embodiment can solve the above two disadvantages: i) by inputting the environmental temperature and the material hardness ratio value, the corresponding two-dimensional wear model under a certain environmental temperature and a certain material hardness ratio condition can be output, and the wheel wear under this condition can be more accurately predicted; ii) under the same wheel-rail hardness matching condition, the corresponding two-dimensional wear model under different environmental temperatures can be obtained, and the wheel wear depth and wear profile under different environmental temperatures can be more accurately predicted.

[0097] In addition to the wheel three-dimensional wear map construction and wheel wear prediction considering the environmental temperature and the material hardness ratio, the wheel-rail three-dimensional wear map construction method considering the environmental temperature and the material characteristics can also be used for the three-dimensional wear map construction of the wheel pair (rail) and the rail wear prediction in the wheel-rail rolling contact experiment. The rail three-dimensional wear map construction method and the rail wear prediction method are consistent with the wheel three-dimensional wear map construction method and the wheel wear prediction method, and the only difference is that in step 1), the friction and wear properties of the rail material under different environmental temperatures and different wheel-rail hardness ratios are obtained based on the wheel-rail rolling friction and wear experiment under different contact parameters, and a series of function relationships between the rail wear rate and the unit area wheel-rail contact spot dissipation energy under different environmental temperatures and wheel-rail hardness ratios are constructed. The construction of the related rail wear model and the rail wear prediction in the subsequent steps are all based on the function relationship between the rail wear rate and the unit area wheel-rail contact spot dissipation energy under different environmental temperatures and wheel-rail hardness ratios.

[0098] The wheel three-dimensional wear model considering the environment temperature and the material hardness ratio simultaneously is used to respectively predict and calculate the wear depth and the wear volume under the condition of the wheel-rail hardness ratio of 0.8 (CL60 wheel-U71Mn rail) and the environment temperature of -40, -20, 0, 10 and 20 ℃, which are shown in Table 6. It can be seen that the wear depth and the wear volume under the environment temperature of 10 ℃ are approximate to the wheel wear data calculated by using the common Tγ / A wear rate model, that is, the common Tγ / A wear rate model is based on the test results under the environment temperature of about 10 ℃ and is only applicable to predict the wheel wear behavior under the environment temperature of 10 ℃. Meanwhile, it can be seen that the wheel wear presents an upward trend with the decrease of the environment temperature, that is, the different environment temperatures have an influence on the wheel wear prediction results. Therefore, it is crucial to consider the environment temperature in the wheel Tγ / A wear map.

[0099] Table 6 Wheel wear prediction results under different environment temperatures

[0100] The wheel three-dimensional wear model considering the environment temperature and the material hardness ratio simultaneously is used to respectively predict and calculate the wear depth and the wear volume under the condition of the environment temperature of 20 ℃ and the material hardness ratio of 0.8, 1.12, 1.4 and 1.6, which are shown in Table 7. It can be seen that the wheel wear presents an upward trend with the increase of the hardness ratio under the certain environment temperature, that is, the different wheel-rail material hardness ratios have an influence on the wheel wear prediction results. Therefore, it is crucial to consider the material hardness ratio in the wheel Tγ / A wear map.

[0101] Table 7 Wheel wear prediction results under different hardness ratios

[0102] Fig. 10 and Fig. 11 are the distribution diagrams of the wheel wear depth and the wear volume under the environment temperature of -40-40 ℃ and the wheel-rail hardness ratio of 0.8-1.4, which are calculated by using the wheel three-dimensional wear model considering the environment temperature and the material hardness ratio simultaneously. It can be seen that the wheel wear behavior can be further more accurately predicted by simultaneously considering the environment temperature and the wheel-rail material hardness ratio in the wheel wear model.

[0103] The above description of the present application and its embodiments is illustrative and not restrictive, and the embodiments shown in the drawings are only one of the embodiments of the present application, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it, without departing from the purpose of the present application, similar structure and embodiments can be designed without creativity, which should belong to the protection scope of the present application.

Claims

1. A method for constructing a three-dimensional wheel-rail wear map considering environmental temperature and material properties, characterized in that: Comprise the following steps: 1) Based on the wheel rail rolling friction and wear experiment under different contact parameters, the friction and wear properties of wheel material under different environmental temperature and different wheel rail hardness ratio conditions are obtained, and the function relationship between the wheel wear rate and the unit area wheel rail contact spot dissipation energy under a series of different environmental temperature and wheel rail hardness ratio conditions is constructed; In step 1), the function relationship between the wheel wear rate and the unit area wheel rail contact spot dissipation energy under a series of different environmental temperature and wheel rail hardness ratio conditions is Tγ / A-wear rate function relationship, wherein the wheel wear rate is the wear amount divided by the product of running distance and wheel rail contact area A; The unit area wheel rail contact spot dissipation energy Tγ / A is the product of wheel rail interface tangential force T and creep rate γ divided by wheel rail contact area A; The Tγ / A-wear rate function relationship is divided into two regions I and II according to the curve change slope; 2) The experimental data is fitted by MATLAB software, and the wheel three-dimensional wear map considering environmental temperature and the wheel three-dimensional wear map considering wheel rail material hardness ratio are obtained respectively; 3) Select two-dimensional reference wear map and construct wheel three-dimensional wear map considering environmental temperature and material hardness ratio through normalization processing; In step 3), the wheel two-dimensional wear maps 2DMAP(Tt1) and 2DMAP(Hv1) under the same environmental temperature Tt1 and material hardness ratio Hv1 are selected, and the slopes of the two regions I and II in the two wheel two-dimensional wear maps 2DMAP(Tt1) and 2DMAP(Hv1) are interpolated and fitted by using MATLAB software to construct a reference two-dimensional wear map 2DMAP(S); the wheel wear model considering the environmental temperature Tt and the wheel wear model considering the material hardness ratio Hv are normalized and fitted with the reference two-dimensional wear map 2DMAP(S) to obtain a wheel wear model considering both the environmental temperature and the material hardness ratio; based on the wheel wear model considering both the environmental temperature and the material hardness ratio, a variable Tt·e 4.9177·Hv that simultaneously involves the environmental temperature and the material hardness ratio is derived, and a wheel three-dimensional wear map 3DMAP(Tt, Hv) considering both the environmental temperature and the material hardness ratio of the wheel-rail is constructed with the wear rate, Tγ / A and Tt·e 4.9177·Hv as coordinate parameters.

2. The method according to claim 1, wherein the method is characterized by: In step 2), the MATLAB software is used to fit the line segment slope of Tγ / A-wear rate curve I and II regions and the horizontal coordinate of I and II regions intersection point under different environmental temperature with environmental temperature as independent variable, to obtain the wheel wear model considering environmental temperature Tt, and to construct the wheel three-dimensional wear map considering environmental temperature 3DMAP(Tt) with wear rate, Tγ / A and environmental temperature Tt as coordinate parameters based on the wheel wear model considering environmental temperature Tt; The slopes of Tγ / A-wear rate curve I and II regions under different wheel rail hardness ratio conditions are fitted to obtain the wheel wear model considering material hardness ratio Hv, and the wheel three-dimensional wear map considering wheel rail material hardness ratio 3DMAP(Hv) is constructed with wear rate, Tγ / A and wheel rail hardness ratio as coordinate parameters based on the wheel wear model considering material hardness ratio Hv; The wheel two-dimensional wear map 2DMAP(Tt) and 2DMAP(Hv) under certain environmental temperature or material hardness ratio conditions are obtained from the wheel three-dimensional wear map 3DMAP(Tt) and the wheel three-dimensional wear map 3DMAP(Hv).

3. The method according to claim 2, wherein the method is characterized by: In step 2), the fitting functions of the slopes of the line segments in the two regions I and II in the wheel wear model considering the ambient temperature Tt are k1 = -0.0085*T t +1.816 and k2 = -0.0035*T t +0.260, and the fitting functions of the horizontal and vertical coordinates of the intersection point of the two regions I and II are x1 = -0.1054*T t +19.464 and y1 = -0.5155*T t +33.711, and the wheel wear model considering the ambient temperature Tt is as follows: Region I: 0 < Tγ / A < x1, wear rate is k1*(Tγ / A); Region II: x1 < Tγ / A, wear rate is k2*(Tγ / A)-k2*x1+y1.

4. The method of claim 3, wherein the method further comprises: determining the three-dimensional wheel-rail wear map based on the environmental temperature and the material properties. In step 2), the fitting functions of the slopes of the line segments in the two regions I and II in the wheel wear model considering the material hardness ratio are k3 = 0.3872 + 0.0507 * e 4.9177Hv and k4 = 0.0847 + 0.0056 * e 4.7672Hv , and the abscissa x2 of the intersection point of the two regions I and II is the intersection value x2 = 16.657 of the wheel Tγ / A wear rate function relationship at the ambient temperature 20℃; the wheel wear model considering the material hardness ratio Hv is as follows: Region I: 0 < Tγ / A < x2, wear rate is k3*(Tγ / A); Region II: x2 < Tγ / A, wear rate is k4*(Tγ / A)+16.657*(k3-k4).

5. The method of constructing a three-dimensional wheel-rail wear map taking into account the ambient temperature and material properties according to claim 4, characterized in that: In step 3), the same environment temperature Tt1 and material hardness ratio Hv1 are taken as 20℃ and 1.08 respectively; the wheel wear map I and II two area slopes of the environment temperature and material hardness ratio are taken as 0.6075*k1k3 and 5.2604*k2k4 respectively, and the two area intersection point horizontal coordinate is taken as 1.0394*x1; the wheel wear model of the wheel three-dimensional wear map 3DMAP(Tt, Hv) considering the environment temperature and material hardness ratio is as follows: Region I: 0 < Tγ / A < 1.0394 x1 The wear rate is 0.6075 * k1k3 * (Tγ / A). Region II: 1.0394 x1 Tγ / A, wear rate = 5.2604 * k2k4 * (Tγ / A) + 0.6314 * y1k3 - 1.0394 * y1k2k4 / k1.

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