Method and device for calculating service safety of steel rail

Abstract

This invention proposes a method and apparatus for calculating the service safety of rails, relating to the field of railway safety operation technology. The calculation method includes: obtaining the maximum dynamic bending stress at the rail base of the rail damage pit under vehicle load, the additional dynamic bending stress at the damage pit caused by tread collapse, and the temperature stress on the rail base at the rail damage pit; calculating the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse based on the maximum dynamic bending stress, the additional dynamic bending stress, and the temperature stress at the rail base; and evaluating the service safety of the rail based on the maximum tensile stress and the fatigue limit under corresponding damage. The method and apparatus for calculating the service safety of rails proposed in this invention can calculate and evaluate the service safety of rails under two damage conditions simultaneously: tread collapse and nearby rail base damage pits.

Description

Technical Field

[0001] This invention relates to the field of railway safety operation technology, and in particular to a method and apparatus for calculating the service safety of rails. Background Technology

[0002] During railway line maintenance, rail tread subsidence has led to numerous track defects, especially with the widespread installation of seamless tracks, where welded joints, due to their lower hardness, commonly exhibit subsidence. Tread subsidence affects rail continuity; when a train passes over a subsidence area, the rail experiences significant additional impact force. According to measured data on wheel unsprung mass acceleration, these additional forces are 2-3 times the normal load, and in severe cases, can reach 4-5 times. For example, for a 1m long subsidence with a maximum diameter of 1mm, a 7-ton train traveling at 200km / h experiences a maximum wheel weight exceeding 200kN, reaching three times the static wheel weight. As joint subsidence progresses, the additional impact force from the wheel on the rail continuously increases, and this enormous impact force accelerates the development of joint defects, causing forced track vibration, accelerating rail deformation, and rapidly deteriorating track conditions.

[0003] Furthermore, rail corrosion is the most common type of damage on railway lines, with rail base corrosion being particularly severe. Deep pits at the rail base create stress concentration effects, resulting in rail failures caused by rail base corrosion accounting for the highest proportion of all rail failures, reaching approximately 49%, posing a significant threat to line safety. For coal transport lines, the rails are constantly exposed to a corrosive environment contaminated by coal dust and antifreeze, making the rail base prone to corrosion and the formation of numerous pits. These pits become stress concentration points, making them highly susceptible to crack initiation.

[0004] In rail failure cases, several rail fracture failures, including those on heavy-haul and conventional railways, shared a common characteristic: cracks originated from damage pits on the underside of the rail, and low-profile collapse was observed at the flash weld joints near these pits. Therefore, the impact of tread collapse on the stress of nearby rail base damage pits and the rail's service condition requires attention. However, current technology lacks relevant research and calculation methods for assessing the service safety of rails under the combined effects of tread collapse and nearby rail base corrosion pits.

[0005] Furthermore, existing theoretical formulas for calculating the additional impact force on rails when there is tread indentation do not consider the influence of the vehicle's own weight, nor do they account for the stress on the damaged area at the rail base. Additionally, existing methods for calculating the additional impact force on rails with tread indentation generally employ finite element simulation, which involves complex modeling and preprocessing, is time-consuming, and requires strong simulation expertise, making it unsuitable for rapid and convenient calculation and analysis by railway maintenance personnel. Moreover, while existing methods for calculating rail stress under uneven conditions consider the vehicle's weight, their quasi-static calculation methods cannot account for situations with significant tread collapse damage, and their empirically based dynamic factor increments cannot accurately calculate the additional impact force on the rail under collapse excitation.

[0006] In view of this, based on years of experience in production and design in this and related fields, the inventor has designed a calculation method and device for the service safety of rails through repeated experiments, in order to solve the problems existing in the prior art. Summary of the Invention

[0007] This invention proposes a method and apparatus for calculating the service safety of rails, which can calculate and evaluate the service safety of rails under two damage conditions: tread collapse and nearby rail bottom damage pits.

[0008] To achieve the above-mentioned objectives, this invention proposes a method for calculating the service safety of rails, wherein the calculation method includes:

[0009] The maximum dynamic bending stress at the bottom of the rail at the rail damage pit under vehicle load, the additional dynamic bending stress at the damage pit caused by the additional impact of tread collapse, and the temperature stress on the bottom of the rail at the rail damage pit are obtained.

[0010] Based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base, calculate the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse.

[0011] The service safety of the rail is evaluated based on the maximum tensile stress and the fatigue limit under corresponding damage.

[0012] This invention also proposes a calculation device for the service safety of rails, wherein the device comprises:

[0013] The maximum dynamic bending stress calculation module at the rail base calculates the maximum dynamic bending stress at the rail base using the static bending moment of the rail section and the rail base end face coefficient.

[0014] The additional dynamic bending stress calculation module calculates the additional dynamic bending stress of the additional impact on the damaged pit based on the additional impact force, the rail foundation parameters, and the horizontal distance coefficient.

[0015] The temperature stress on the rail base is calculated based on the locked rail temperature and the measured rail temperature.

[0016] The maximum tensile stress calculation module calculates the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse, based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base.

[0017] The safety evaluation module evaluates the service safety of the rail based on the maximum tensile stress and the fatigue limit under corresponding damage.

[0018] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor implements any of the methods described above when executing the computer program.

[0019] The present invention also proposes a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described above.

[0020] Compared with existing technologies, the rail service safety calculation method proposed in this invention has the following characteristics and advantages:

[0021] The rail service safety calculation method proposed in this invention considers the superimposed effects of two types of damage: low collapse of the welded joint and nearby rail base damage pit, rather than the single effect of a single type of damage. Furthermore, through the established theoretical formula model, the stress state of the rail base damage pit and the rail service safety under the superimposed effects of the two types of damage are evaluated, which can effectively address the concerns of railway on-site maintenance personnel regarding the rail service safety under such conditions.

[0022] The rail service safety calculation method proposed in this invention can be implemented more simply and conveniently than the finite element simulation method for calculating the stress state of rail base damage pits and rail service safety. It does not require lengthy modeling and calculation time or a high threshold of finite element simulation knowledge and skills, and is more suitable for on-site railway maintenance personnel to conduct rapid assessments.

[0023] The rail service safety calculation method proposed in this invention can analyze the evolution of the stress and fatigue limit of the rail damage pit as the two damages develop by calculating the tread collapse depth and the stress concentration factor of the rail bottom damage pit with different values; and can provide reliable data support for the failure cause analysis of similar rail failure cases in reality by comparing the stress and fatigue limit of the damage pit. Attached Figure Description

[0024] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. Furthermore, the shapes and proportions of the components in the drawings are merely illustrative to aid in understanding the invention and do not specifically limit the shapes and proportions of the components. Those skilled in the art, guided by the teachings of this invention, can select various possible shapes and proportions to implement the invention according to specific circumstances.

[0025] Figure 1 This is a schematic diagram of the stress composition of the damage pit at the bottom of the rail.

[0026] Figure 2 This is a schematic diagram showing the distribution of vehicle loads on the rails.

[0027] Figure 3A Schematic diagram of the low-lying shape of the rail tread (I);

[0028] Figure 3B Schematic diagram of the low-collapse form of rail tread (II);

[0029] Figure 4 Schematic diagram of the damage pit;

[0030] Figure 5 This is a flowchart of the rail service safety calculation method proposed in this invention;

[0031] Figure 6 This is a schematic diagram of the load distribution on the rails caused by vehicles in an embodiment of the present invention;

[0032] Figure 7 This is a schematic diagram of the damage pit on the bottom of the failed rail in an embodiment of the present invention. Detailed Implementation

[0033] The details of the present invention can be more clearly understood by referring to the accompanying drawings and the description of specific embodiments. However, the specific embodiments of the present invention described herein are for illustrative purposes only and should not be construed as limiting the invention in any way. Under the teachings of this invention, those skilled in the art can conceive of any possible modifications based on the invention, and these should all be considered to fall within the scope of the invention.

[0034] In this invention, when an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element.

[0035] A method for calculating the service safety of rails, such as Figures 1 to 5 As shown, the calculation method includes:

[0036] The maximum dynamic bending stress at the rail base of the rail damage pit under vehicle load, the additional dynamic bending stress at the damage pit caused by the additional impact of tread collapse, and the temperature stress on the rail base are obtained.

[0037] Based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base, the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse is calculated.

[0038] The service safety of the rail is evaluated based on the maximum tensile stress and the fatigue limit under corresponding damage.

[0039] The rail service safety calculation method proposed in this invention considers the superimposed effects of two types of damage: low collapse of the welded joint and nearby rail base damage pit, rather than the single effect of a single type of damage. Furthermore, through the established theoretical formula model, the stress state of the rail base damage pit and the rail service safety under the superimposed effects of the two types of damage are evaluated, which can effectively address the concerns of railway on-site maintenance personnel regarding the rail service safety under such conditions.

[0040] The rail service safety calculation method proposed in this invention can be implemented more simply and conveniently than the finite element simulation method for calculating the stress state of rail base damage pits and rail service safety. It does not require lengthy modeling and calculation time or a high threshold of finite element simulation knowledge and skills, and is more suitable for on-site railway maintenance personnel to conduct rapid assessments.

[0041] In an optional embodiment of the present invention, tread collapse includes collapse at welded joints, collapse caused by hidden damage, abrasion, corrugation, etc. on the rail tread, and other collapses that are approximately half-wave sinusoidal in shape.

[0042] In an optional embodiment of the present invention, the rail base damage pit can be a rust pit, or a rail base impact pit caused during the transportation and laying of the rail, as well as a damage pit formed by hot scratches, abrasions, folds, oxide scale indentation, rolling marks, etc. formed during the hot state of rail production, and a damage pit formed by scratches formed in the cold state.

[0043] In an optional embodiment of the present invention, obtaining the maximum dynamic bending stress at the rail base of the rail damage pit under vehicle load includes:

[0044] Obtain the static bending moment of the rail section at the rail damage pit and the rail bottom end face coefficient at the rail damage pit. Calculate the maximum dynamic bending stress at the rail bottom using the static bending moment of the rail section and the rail bottom end face coefficient. Then, we have...

[0045]

[0046] In the formula, σ0 is the maximum dynamic bending stress at the rail base, M0 is the static bending moment of the rail section, and W1 is the rail base end face coefficient.

[0047] In an optional example, W1 can be found in the appendix of standard TB 2034—1988.

[0048] It should be noted that, since the wheel-rail dynamic response to the unevenness of the welded joint is calculated separately, the effect of vehicle load on the rail in the above formula (3) does not take into account the influence of the dynamic increase during vehicle travel.

[0049] In an optional example of this implementation, obtaining the static bending moment of the rail section at the rail damage pit includes,

[0050] Determine the most unfavorable wheel position of the vehicle and the load on that most unfavorable wheel position;

[0051] Obtain the rail foundation parameters, as well as the horizontal distance between the rail damage pit and the collapsed area;

[0052] Calculate the static bending moment of the rail section based on the load at the most unfavorable wheel position, the rail foundation parameters, and the horizontal distance.

[0053] In an optional example, the rail foundation parameters include the rail foundation-to-rail stiffness ratio coefficient, the rail foundation elasticity coefficient, and the rail vertical bending stiffness, then we have:

[0054]

[0055] In the formula, M0 is the static bending moment of the rail section, ∑Pμ is the equivalent load of each wheel, P is the load at the most unfavorable wheel position, and μ=e -βx (cosβx-sinβx), where x is the horizontal distance between the damaged pit and the low-lying area, and β is the stiffness ratio coefficient between the rail foundation and the rail. The elastic modulus of the rail foundation, EJ x This refers to the vertical bending stiffness of the rail.

[0056] In this invention, the static bending moment of the rail section at the damaged pit caused by vehicle load is determined using the basic mechanical principles of track strength calculation. The rail is treated as a continuous elastic foundation beam model, and the track's self-weight is ignored. The dynamic bending stress at the rail base is determined through static calculation. The static bending moment M0 of the rail section at the damaged pit is obtained by solving the problem based on the Winkler assumption.

[0057] In one alternative example, the most unfavorable wheel position is the wheel position that generates the maximum load at the damaged pit when the four wheels of the vehicle's front and rear bogies pass over the low-lying area. For example... Figure 2As shown, the four wheel positions (Ⅰ~Ⅳ) of the front bogie and the rear bogie of the rear vehicle form a unit. Considering the influence of the calculation wheel and its adjacent front and rear wheels, and based on the principle of independent action of forces, the forces acting on the calculation section by each wheel are superimposed, that is, the resultant force of the section when each wheel is regarded as a calculation wheel is obtained, thereby determining the most unfavorable wheel position, that is, the wheel position with the largest ∑Pμ.

[0058] In another alternative example, the most unfavorable wheel position is the wheel position in a six-axle or eight-axle vehicle where the wheel generates the maximum load at the pit when each wheel passes over the low-lying area.

[0059] It is particularly important to note that the calculation of the maximum stress and the most unfavorable wheel position that cause the rail bottom damage pit is defined as the maximum ΣPμ value generated at the damage pit rather than at the low collapse point when each wheel passes through the low collapse point, but not directly above the corrosion pit, and the calculated wheel position at which this value is generated.

[0060] In an optional embodiment of the present invention, obtaining the additional dynamic bending stress on the rail bottom caused by the additional impact of tread collapse includes,

[0061] Obtain the vehicle's operating speed and the shape parameters of the tread collapse;

[0062] Based on the shape parameters of the tread collapse and the vehicle's running speed, the additional impact force generated when the vehicle passes over the tread collapse is calculated.

[0063] Obtain the rail foundation parameters and the horizontal distance between the rail damage pit and the collapsed area. Calculate the additional dynamic bending stress of the damage pit based on the additional impact force, rail foundation parameters, and horizontal distance coefficient.

[0064] In an optional example of this implementation, the tread collapse shape is considered as a half-wave sinusoidal curve, such as... Figure 3A , Figure 3B As shown, the shape parameters of tread slump include maximum slump, slump length, and excitation frequency, then we have,

[0065]

[0066] In the formula: λ is the maximum subsidence; L is the subsidence length; ω is the excitation frequency, and ω=2πv / L, v is the train speed; t is the time from the starting point, t=l / v; l is the horizontal distance between the subsidence and the starting point; η is the rail surface irregularity value corresponding to a certain moment t when the wheel passes through the subsidence.

[0067] In an optional example, based on the shape parameters of the tread collapse and the vehicle's operating speed, the additional impact force generated by the tread collapse is calculated, then:

[0068]

[0069] In the formula: y is the dynamic deflection of the rail. Indicates the time it takes for the wheel to pass through the depression. This represents the period of free oscillation of the unsprung mass on the track. Let be the natural circular frequency of the unsprung mass, k be the equivalent stiffness of the track foundation, m be the unsprung mass, and t be the time taken from the starting point.

[0070] It should be noted that for the dynamic response caused by the collapse of the tread, the flexural vibration equation of the rail established by D'Alembert's principle and the boundary conditions (t=0, y=0, dy / dt=0) can be solved to obtain the dynamic deflection y of the rail. In addition, to simplify the calculation, the wheel-rail contact deformation is not considered and the rail mass and friction are neglected. Then, the formula for calculating the dynamic deflection y of the rail is formula (5).

[0071] because in L is the elastic coefficient of the rail foundation. k The effective equivalent length of the spring, thus the additional force P acting on the rail. c for:

[0072] P c =ky=8EJ x β 3 y (6)

[0073] In the formula, k is the converted stiffness of the rail foundation, y is the dynamic deflection of the rail, and EJ is the dynamic deflection of the rail. x Let β be the vertical bending stiffness of the rail, and β be the ratio of the rail foundation stiffness to the rail stiffness. This is the elastic coefficient of the rail foundation.

[0074] Furthermore, based on the additional impact force, rail foundation parameters, and horizontal distance coefficient, the additional dynamic bending stress on the damaged pit caused by the additional impact is calculated, and thus,

[0075]

[0076] In the formula, σ cd To add dynamic bending stress, P c As additional driving force, μ = e -βx (cosβx-sinβx), where x is the horizontal distance between the damaged pit and the low-lying area, and β is the stiffness ratio coefficient between the rail foundation and the rail. The elastic modulus of the rail foundation, EJ x Let β be the vertical bending stiffness of the rail, and β be the vertical bending stiffness of the rail. and EJ x These are basic rail parameters, with W1 being the rail bottom end face coefficient.

[0077] It should be noted that, based on the additional impact force P generated by the collapse... c Formula (7) can be obtained from the above formula (2) and formula (3).

[0078] In an optional embodiment of the present invention, obtaining the temperature stress on the rail base includes:

[0079] Obtain the locked rail temperature and the measured rail temperature. Calculate the rail base temperature stress based on the locked rail temperature and the measured rail temperature. Then, we have...

[0080] σ T =2.45ΔT (8)

[0081] In the formula, σ T The temperature stress on the rail base is ΔT, which is the difference between the locked rail temperature and the measured rail temperature.

[0082] In an optional embodiment of the present invention, calculating the maximum tensile stress at the bottom of the rail damage pit includes:

[0083] The maximum stress at the rail base under the influence of tread collapse is calculated based on the maximum dynamic bending stress, additional dynamic bending stress and rail base temperature stress at the rail base.

[0084] Obtain the shape parameters of the rail bottom damage pit, and calculate the stress concentration factor of the damage pit based on the shape parameters;

[0085] The maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse is calculated based on the maximum stress at the rail base and the stress concentration factor at the rusted area of ​​the rail.

[0086] In an optional example of this implementation, the maximum stress at the rail base under the influence of tread collapse is calculated based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base. Then, we have:

[0087] σ d =σ0+σ cd +σ T (1)

[0088] In the formula, σ d σ0 is the maximum stress at the rail base, and σ0 is the maximum dynamic bending stress at the rail base. cd To add dynamic bending stress, σ T This refers to the temperature stress experienced by the rail base.

[0089] In this invention, the stress on the rail base of a seamless track rail consists of the dynamic bending stress and temperature stress under the maximum possible load (dynamic load). The maximum possible load is the increase in dynamic force on the rail exceeding the static load, considering the dynamic effects of train movement. For failed rails with severe joint collapse, to accurately calculate the stress state on the rail base near the collapse, the vertical dynamic response of the wheel-rail system under collapse excitation is calculated separately. Therefore, the stress on the rail base caused by vehicle load is obtained through static calculation.

[0090] Therefore, the maximum tensile stress σ at the rail bottom near the damaged pit near the low collapse is... d ,like Figure 1 As shown, this should include the maximum dynamic bending stress σ0 caused by the vehicle's static load on the rail base, and the dynamic bending stress σ0 caused by the additional vertical impact generated when the vehicle passes over a low slab on the rail base. cd and temperature stress σ T .

[0091] Furthermore, if the analysis shows that the rust pit on the bottom of the rail is located near the center line of the bottom of the rail, or the rust pit is far away from the weld at the joint collapse, or it is a collapse of other tread surfaces that is not at the joint collapse, then there is still residual stress inside the rail. In this case, a residual stress term can be added to the right side of the equal sign in formula (1), and the calculation method of the present invention can also be used to analyze the service safety of the rail.

[0092] In an optional example, the shape parameters of the railbed damage crater include the depth of the crater and the radius of the crater root, then,

[0093]

[0094] In the formula, K t ρ is the stress concentration factor, h is the depth of the pit, and ρ is the radius of the pit root.

[0095] In this invention, the shape parameters of the rail base damage pit are determined by defining the shape of the pit as the maximum profile projected onto a cross-section parallel to the rail length direction. The pit depth h and bottom radius ρ are measured on this maximum profile. The stress concentration factor of the rail base corrosion pit is calculated by considering the pit as a notch existing at the edge of the plate. According to fracture mechanics, for an infinitely long plate, such as... Figure 4 As shown, there is a tensile stress at the far end along the length direction and a notch at the edge of the plate. The shape of the notch root can be equivalent to an ellipse, so the stress concentration factor of the damage pit can be calculated by formula (9).

[0096] Meanwhile, since the size of the rail base damage pit is very small relative to the rail, the stress near the rail base damage pit can be regarded as tensile stress uniformly distributed along the longitudinal direction of the rail, with the direction of tensile stress being the length direction of the rail. The damage pit that serves as the crack source on the target damage pit or fracture surface is obtained by the maximum profile projected parallel to the length direction of the rail. The depth h and bottom radius ρ of the maximum profile of the damage pit are measured, and then the stress concentration factor K of the damage pit can be calculated according to formula (9). t .

[0097] Furthermore, given the maximum stress and stress concentration factor at the rail base where the rail is corroded, the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse is:

[0098] σ pit =K t ·σ d (10)

[0099] In the formula, σ pit K represents the maximum tensile stress at the bottom of the damage pit. t σ is the stress concentration factor. d This represents the maximum stress at the bottom of the rail at the damaged pit.

[0100] In an optional embodiment of the present invention, the service safety of the rail is evaluated based on the maximum tensile stress and the fatigue limit under corresponding damage, including:

[0101] Confirm whether the maximum tensile stress at the bottom of the rail damage pit and the fatigue limit of the rail under the corresponding damage meet the judgment standard formula. If they meet the judgment standard formula, the rail is judged to be in a safe service state; if they do not meet the judgment standard formula, the rail is judged to be in an unsafe service state.

[0102] In an optional example of this implementation, the determination criterion formula is:

[0103] σ pit ≤σ r ·K t (13)

[0104] In the formula, σ pit K represents the maximum tensile stress at the bottom of the damage pit. t σ is the stress concentration factor. r This represents the fatigue limit under the corresponding damage.

[0105] Specifically, during the service life of rails, the combined effects of tread collapse at the welded joint and nearby rail base damage pits reduce the rail's fatigue life. When these two damages reach a certain level, and the stress at the damage pit exceeds the fatigue limit, the rail will be in an unsafe service state. Therefore, the maximum stress σ at the rail base damage pit is... pit and the fatigue limit σ under corresponding damage r The comparison is used to determine the safety of the rails in service.

[0106] In an optional example of this implementation, the fatigue limit under the corresponding damage is the rail fatigue limit including the effects of tread and rail bottom damage pits, then we have:

[0107] σ r =aσ y +bE+c (11)

[0108] and,

[0109]

[0110] c = 12.0K t R+28.2K t -82.8R-191,

[0111] Where: σ y R is the yield strength of the rail; E is the elastic modulus of the rail; R is the stress ratio of the cyclic tensile stress at the damaged pit.

[0112] For in service rails, each wheel of a vehicle will roll over the rail when it passes by, and the bottom of the rail will be subjected to cyclic dynamic bending stress. At the damage pit at the bottom of the rail, cyclic tensile stress will be generated. Therefore, the fatigue limit of the rail, including the damage pit at the bottom of the rail and the low tread, is evaluated by the multi-parameter empirical formula (11).

[0113] Furthermore, the stress ratio R of the cyclic tensile stress at the damaged pit is related to the tread collapse, therefore,

[0114]

[0115] In the formula, σ max σ is the maximum force at the damaged pit when the wheel passes over the collapsed tread. min For the stress at the damaged pit under the rail base, which is subjected only to temperature stress and without collapse or the weight of the vehicle, σ T The temperature stress on the rail base, σ d This represents the maximum stress at the bottom of the rail.

[0116] Soon σ max Defined as the maximum stress σ generated at the rust pit when the wheel passes over the tread. d ;σ min Defined as the temperature stress σ experienced by the rail T The stress ratio R of the cyclic tensile stress at the damaged pit is a parameter related to the tread collapse λ.

[0117] The present invention also proposes a calculation device for the service safety of rails, wherein the device comprises:

[0118] The module for calculating the maximum dynamic bending stress at the rail base calculates the maximum dynamic bending stress at the rail base using the static bending moment of the rail section and the rail base end face coefficient.

[0119] The additional dynamic bending stress calculation module calculates the additional dynamic bending stress of the damage pit based on the additional impact force, rail foundation parameters, and horizontal distance coefficient.

[0120] The temperature stress on the rail base is calculated based on the locked rail temperature and the measured rail temperature.

[0121] The maximum tensile stress calculation module calculates the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse, based on the maximum dynamic bending stress, additional dynamic bending stress and rail bottom temperature stress.

[0122] The safety evaluation module assesses the service safety of rails based on the maximum tensile stress.

[0123] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements any of the methods described above.

[0124] The present invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0125] The following is a detailed description of the implementation process of the calculation method and device for rail service safety proposed in this invention, with reference to an embodiment:

[0126] In this embodiment, the failed rail is a 75kg / m rail, made of a certain type of rail steel, in a heat-treated state, and the fracture is located on a straight section of the track. Figure 5 As shown, a fatigue crack perpendicular to the length of the rail originates from the underside of the rail. A moving flash weld joint is located 60 mm (x) from the crack. The tread surface of this joint has collapsed, with a maximum collapse λ of 0.7 mm and a collapse range L of 90 mm. The crack initiation point on the underside of the rail is 15 mm off from the centerline of the rail web.

[0127] Step 1: Calculate the maximum dynamic bending stress σ0 at the rail bottom of the damaged pit under vehicle load.

[0128] The vehicles operating on the failed rail line were 27t axle load C80E freight cars. Considering the loads on the rear bogies of the preceding and following cars, identify the most unfavorable wheelset causing the maximum bending moment. Figure 6As shown in Table 1, the ΣPμ values ​​at the pit locations were calculated for wheels I through IV when they passed through the low-lying area, thus determining the most unfavorable wheelset that would cause the maximum bending moment at the pit.

[0129] Table 1 Calculation of ΣPμ for each wheel position

[0130]

[0131] It can be seen that when wheel III passes through the low collapse, the value of ΣPμ is the largest, which is 100.8kN, so it is the most unfavorable wheel position. According to formulas (2) to (3), the maximum dynamic bending stress σ0 at the bottom of the rail at the damaged pit is 35.9MPa.

[0132] In contrast, when there is no tread collapse (λ = 0 mm), the rail base stress reaches its maximum when the wheel passes directly above the pit. The ΣPμ values ​​for each wheel position when passing above the pit are calculated according to Table 1. The results show that the ΣPμ value is maximum when wheel II (III) passes the tread collapse, at which point the maximum dynamic bending stress σ at the rail base is also highest. 0(λ＝0) =43.1MPa.

[0133] Step 2: Calculate the dynamic bending stress σ at the rail base caused by the additional impact of tread collapse excitation. cd

[0134] Based on formulas (4) to (7), the additional impact force P of the low-collapse excitation can be obtained. c The additional dynamic bending stress σ at the rail base of the damaged pit is 144.6 kN. cd =43.4MPa.

[0135] Step 3, calculate the temperature stress σ at the rail base. T

[0136] The locked rail temperature of the failed rail was 28℃, and the rail temperature was measured at 7℃ when cracks were found in the rail. The temperature stress σ experienced by the failed rail at that temperature was calculated using formula (8). T =51.5MPa.

[0137] Step 4: Calculate the maximum stress σ at the rail bottom of the damaged pit. d

[0138] From formula (1) and the calculation results above, it can be seen that when the wheel passes through a low-lying area, the stress at the rail bottom near the pit is the greatest, σ d =130.8MPa.

[0139] When there is no tread collapse at the joint (λ=0mm), the stress at the rail bottom stress location when the wheel passes over the pit only includes σ. 0(λ＝0) and σ T At this time, the maximum stress σ at the bottom of the rail d(λ＝0) =94.6MPa.

[0140] Step 5: Calculate the stress concentration factor K of the rail base damage crater. t and maximum stress σ pit

[0141] After measurement, such as Figure 7 As shown, the depth h of the damage pit at the initiation point of the rail bottom crack is 0.43 mm, and the bottom radius ρ is 0.20 mm.

[0142] Based on formulas (9) to (10), the stress concentration factor K of the damage pit can be obtained. t The maximum stress σ at the bottom of the rail erosion pit is 3.92. pit =511.8MPa. Without subsidence, the σ at the bottom of the pit when the wheel passes over it is... pit(λ＝0) =370.3MPa.

[0143] Step 6: Calculate the rail fatigue limit σ, which includes the effects of tread collapse and rail bottom damage pits. r

[0144] Based on formulas (11) to (12), calculate the fatigue limit σ of the rail with the damaged pit. r The results are shown in Table 2.

[0145] Table 2. Fatigue limit σ of rail base with damaged pits under different tread conditions. r

[0146]

[0147] Step 7, Safety assessment of rail service

[0148] Compare σ under the same damage condition pit and σ r ·K t To assess the service safety of the rails. Table 2 shows that, under the existing damage pits and 0.7mm tread subsidence conditions, σ pit Greater than σ r ·K t The rail does not meet the criteria of formula (13), therefore the rail is in an unsafe state during service, and fatigue cracks are prone to start from the stress concentration point at the bottom of the rail, i.e. the bottom of the damage pit.

[0149] In contrast, when there is no tread subsidence, σ pit Less than σ r ·K t The rail meets the criteria of formula (13), therefore the rail is in a safe service condition. By comparison, it can be seen that the deep tread collapse near the rail bottom damage pit will also have a significant impact on the stress at the damage pit, thus leading to a decrease in the service safety of the rail.

[0150] The proposed method for calculating rail service safety considers the combined effects of two types of damage: welded joint collapse and nearby rail base damage pits (rust pits), rather than the single effect of any one type of damage. Through an established theoretical model, the stress state of the rail base rust pits and the rail service safety under the combined effects of these two types of damage are evaluated, effectively addressing the concerns of railway maintenance personnel regarding the service safety of rails in such conditions.

[0151] The calculation method for rail service safety proposed in this invention is simple and convenient to implement compared with the finite element simulation method, which can be used to calculate the stress state of rust pits on the rail base and the service safety of rails. It does not require a long modeling and calculation time or a high knowledge and skill threshold of finite element simulation. Therefore, it is more suitable for on-site railway maintenance personnel to conduct rapid assessment.

[0152] The proposed method for calculating rail service safety analyzes the evolution of stress and fatigue limit in rail rust pits as damage progresses by calculating different values ​​of tread collapse depth and stress concentration factor of rail bottom rust pits. Furthermore, by comparing the stress and fatigue limit of the rust pits, reliable data support can be provided for analyzing the failure causes of similar rail failure cases in reality.

[0153] The detailed explanations of the above embodiments are intended only to explain the present invention so as to facilitate a better understanding of the present invention. However, these descriptions should not be construed as limiting the present invention for any reason. In particular, the various features described in different embodiments can be arbitrarily combined with each other to form other embodiments. Unless there is an explicit description to the contrary, these features should be understood to be applicable to any embodiment, and not limited to the described embodiments.

Claims

1. A method for calculating the service safety of rails, characterized in that, The calculation method includes: Determine the most unfavorable wheel position of the vehicle and the load at that position; obtain the rail foundation parameters and the horizontal distance between the rail damage pit and the low-lying area; Calculate the static bending moment of the rail section based on the load of the most unfavorable wheel position, the rail foundation parameters, and the horizontal distance; Obtain the rail bottom end face coefficient at the rail damage pit, and calculate the maximum dynamic bending stress at the rail bottom of the rail damage pit under vehicle load based on the rail bottom end face coefficient and the static bending moment of the rail section. The additional dynamic bending stress at the damaged pit caused by the additional impact of the tread collapse, as well as the temperature stress on the rail bottom, are obtained. Based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base, calculate the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse. The service safety of the rail is evaluated based on the maximum tensile stress and the fatigue limit under corresponding damage.

2. The method for calculating the service safety of rails as described in claim 1, characterized in that, The maximum dynamic bending stress at the rail base is calculated using the static bending moment of the rail section and the rail base end face coefficient. Then, we have... (3) In the formula, σ0 is the maximum dynamic bending stress at the rail base, M0 is the static bending moment of the rail section, and W1 is the rail base end face coefficient.

3. The method for calculating the service safety of rails as described in claim 1, characterized in that, The rail foundation parameters include the rail foundation-to-rail stiffness ratio coefficient, the rail foundation elasticity coefficient, and the rail vertical bending stiffness. Therefore, (2) In the formula, M0 is the static bending moment of the rail section. Let P be the equivalent load of each wheel, and P be the load at the most unfavorable wheel position, μ = x is the horizontal distance between the damaged pit and the low-lying area, and β is the stiffness ratio coefficient between the rail foundation and the rail. , The elastic modulus of the rail foundation, EJ x This refers to the vertical bending stiffness of the rail.

4. The method for calculating the service safety of rails as described in claim 1, characterized in that, The most unfavorable wheel position is the wheel position at which the maximum load is generated at the damaged pit when the four wheel positions of the vehicle, including the rear bogie of the front vehicle and the front bogie of the rear vehicle, pass through the low-lying area.

5. The method for calculating the service safety of rails as described in claim 1, characterized in that, The additional dynamic bending stress at the rail base caused by the additional impact of tread collapse is obtained. include, Obtain the vehicle's operating speed and the shape parameters of the tread collapse; Based on the shape parameters of the tread collapse and the vehicle's operating speed, calculate the additional impact force generated when the vehicle passes over the tread collapse; Obtain the rail foundation parameters and the horizontal distance between the rail damage pit and the low-lying area, and calculate the additional dynamic bending stress of the additional impact on the damage pit based on the additional impact force, the rail foundation parameters, and the horizontal distance.

6. The method for calculating the service safety of rails as described in claim 5, characterized in that, The shape parameters of the tread collapse include the maximum collapse amount, collapse length, and excitation frequency. Therefore, (4) In the formula: λ is the maximum subsidence; L is the subsidence length; ω is the excitation frequency, and ω = 2πv / L, v is the vehicle speed; t is the time from the starting point, t = l / v; l is the horizontal distance from the subsidence to the starting point; η is the rail surface irregularity value corresponding to a certain moment t when the wheel passes through the subsidence.

7. The method for calculating the service safety of rails as described in claim 6, characterized in that, Based on the shape parameters of the tread collapse and the vehicle's operating speed, the additional impact force generated by the tread collapse is calculated, and thus, (5) In the formula: y is the dynamic deflection of the rail. Indicates the time it takes for the wheel to pass through the depression. This represents the period of free oscillation of the unsprung mass on the track. Let be the natural circular frequency of the unsprung mass, k be the equivalent stiffness of the track foundation, m be the unsprung mass, and t be the time taken from the starting point. because ,in The elastic coefficient of the rail foundation. The effective equivalent length of the spring, thus the additional force P acting on the rail. c for: (6) In the formula, k is the converted stiffness of the rail foundation, y is the dynamic deflection of the rail, and EJ is the dynamic deflection of the rail. x Let β be the vertical bending stiffness of the rail, and β be the ratio of the rail foundation stiffness to the rail stiffness. , This is the elastic coefficient of the rail foundation.

8. The method for calculating the service safety of rails as described in claim 7, characterized in that, Based on the additional impact force, the rail foundation parameters, and the horizontal distance, the additional dynamic bending stress caused by the additional impact on the damaged pit is calculated. Therefore, (7) In the formula, σ cd To add dynamic bending stress, P c For additional power, μ = x is the horizontal distance between the damaged pit and the low-lying area, and β is the stiffness ratio coefficient between the rail foundation and the rail. , The elastic modulus of the rail foundation, EJ x Let β be the vertical bending stiffness of the rail, and β be the vertical bending stiffness of the rail. and EJ x These are basic rail parameters, with W1 being the rail bottom end face coefficient.

9. The method for calculating the service safety of rails as described in claim 1, characterized in that, Obtain the temperature stress on the rail base, including: Obtain the locked rail temperature and the measured rail temperature. Calculate the rail base temperature stress based on the locked rail temperature and the measured rail temperature. Then, we have... (8) In the formula, σ T The temperature stress on the rail base is ΔT, which is the difference between the locked rail temperature and the measured rail temperature.

10. The method for calculating the service safety of rails as described in claim 1, characterized in that, Calculate the maximum tensile stress at the bottom of the rail damage crater, including: The maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base are used to calculate the maximum stress at the rail base at the rusted area under the influence of tread collapse. Obtain the shape parameters of the rail bottom damage pit, and calculate the stress concentration factor of the damage pit based on the shape parameters; The maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse is calculated based on the maximum stress at the rail base where the rail is corroded and the stress concentration factor.

11. The method for calculating the service safety of rails as described in claim 10, characterized in that, Based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base, the maximum stress at the rail base at the rusted area under the influence of tread collapse is calculated. Therefore, s d = σ0+ σ cd + s T (1) In the formula, σ d σ0 is the maximum stress at the rail base, and σ0 is the maximum dynamic bending stress at the rail base. cd To add dynamic bending stress, σ T This refers to the temperature stress experienced by the rail base.

12. The method for calculating the service safety of rails as described in claim 10, characterized in that, The shape parameters of the railbed damage pit include the depth of the pit and the radius of the pit root. Therefore, (9) In the formula, K t ρ is the stress concentration factor, h is the depth of the pit, and ρ is the radius of the pit root.

13. The method for calculating the service safety of rails as described in claim 12, characterized in that, Based on the maximum stress at the rail base of the rusted area and the stress concentration factor, the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse is calculated. Then, we have... (10) In the formula, σ pit K represents the maximum tensile stress at the bottom of the damage pit. t σ is the stress concentration factor. d This represents the maximum stress at the bottom of the rail at the damaged pit.

14. The method for calculating the service safety of rails as described in claim 1, characterized in that, The service safety of rails is evaluated based on the maximum tensile stress and the fatigue limit under corresponding damage, including: Confirm whether the maximum tensile stress at the bottom of the rail damage pit and the fatigue limit of the rail under the corresponding damage meet the judgment standard formula. If they meet the judgment standard formula, the rail is judged to be in a safe service state; if they do not meet the judgment standard formula, the rail is judged to be in an unsafe service state.

15. The method for calculating the service safety of rails as described in claim 14, characterized in that, The formula for the judgment criterion is as follows: (13) In the formula, σ pit K represents the maximum tensile stress at the bottom of the damage pit. t σ is the stress concentration factor. r This represents the fatigue limit under the corresponding damage.

16. The method for calculating the service safety of rails as described in claim 15, characterized in that, The fatigue limit under the corresponding damage is the rail fatigue limit including the effects of tread and rail bottom damage pits, then we have: (11) and, , ， ， In the formula: σ y R is the yield strength of the rail; E is the elastic modulus of the rail; R is the stress ratio of the cyclic tensile stress at the damaged pit.

17. The method for calculating the service safety of rails as described in claim 16, characterized in that, The stress ratio R of the cyclic tensile stress at the damaged pit is related to the tread collapse, therefore, (12) In the formula, σ max σ is the maximum force at the damaged pit when the wheel passes over the collapsed tread. min For the stress at the damaged pit under the rail base, which is subjected only to temperature stress and without collapse or the weight of the vehicle, σ T The temperature stress on the rail base, σ d This represents the maximum stress at the bottom of the rail.

18. A calculation device for the service safety of rails, characterized in that, The device includes: The pre-analysis module determines the most unfavorable wheel position of the vehicle and the load on that wheel position; it also obtains the rail foundation parameters and the horizontal distance between the rail damage pit and the low collapse. The maximum dynamic bending stress calculation module at the rail base calculates the static bending moment of the rail section based on the load of the most unfavorable wheel position, rail foundation parameters, and horizontal distance; and calculates the maximum dynamic bending stress at the rail base using the static bending moment of the rail section and the rail base end face coefficient. The additional dynamic bending stress calculation module calculates the additional dynamic bending stress of the damage pit based on the additional impact force, rail foundation parameters, and horizontal distance. The rail base temperature stress module calculates the rail base temperature stress based on the locked rail temperature and the measured rail temperature. The maximum tensile stress calculation module calculates the maximum tensile stress at the bottom of the rail damage pit under the influence of tread collapse, based on the maximum dynamic bending stress at the rail base, the additional dynamic bending stress, and the temperature stress at the rail base. The safety evaluation module evaluates the service safety of the rail based on the maximum tensile stress and the fatigue limit under corresponding damage.

19. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 17.

20. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 17.

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