Method for calculating rail generated stress

Abstract

To provide a method for calculating rail-generated stress capable of accurately calculating rail-generated stress at an arbitrary position by inputting a floating amount of a floating pillow obtained from track inspection data or the like and an unevenness amount of a top surface of a rail.SOLUTION: There is provided a method for calculating rail-generated stress, which calculates the stress generated in a rail. The method includes steps of in a numerical analysis model of a rail track on which the rail is laid, setting the unevenness wavelength of an unevenness generated on the top surface of the rail S2, setting a plurality of continuous numbers of floating sleepers for each amount of unevenness using the numerical analysis model, and performing the analysis S3, determining a relation between the stress value of the continuous number of floating for which the rail-generated stress is the maximum and the amount of flotation of the floating sleepers for each amount of unevenness from the analysis result, and determining stress estimation means for deriving the rail-generated stress from the amount of flotation and the amount of unevenness based on the relation between the stress values of the plurality of unevenness amounts and the amount of flotation S5.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for calculating rail-generated stress that calculates the stress generated in a rail.

Background Art

[0002] Damage to rails due to corrosion has conventionally accounted for a large portion of the occurrence of rail damage. As a damage factor, a decrease in the fatigue strength of the rail due to corrosion in the rail bottom region is considered the main factor, and research and inspections focusing on the amount of corrosion at the rail bottom have been conducted so far (see Non-Patent Document 1). For this purpose, ultrasonic flaw detection cars, ultrasonic flaw detection devices, etc. are widely used.

[0003] On the other hand, it has been reported that rail damage occurs even with minor corrosion at the rail bottom (see Non-Patent Document 2, etc.). As a factor, at the water leakage locations in tunnels, the top surface of the rail head is locally worn due to repeated train running, and it also leads to the occurrence of a floating sleeper state (a state where a gap is generated between the bottom surface of the sleeper and the roadbed surface), and generally the rail bending stress increases. Until now, because such locations could not be extracted, rail damage has sometimes occurred.

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, in order to obtain the rail generated stress such as rail bending stress, it is a heavy burden to conduct on-site tests each time at an arbitrary position on a continuous operating line. On the other hand, a method has been proposed to grasp the unevenness of the rail head top surface and the crib support state at an arbitrary kilometer by analyzing track inspection data (see Non-Patent Document 3).

[0006] Therefore, an object of the present invention is to provide a method for calculating rail generated stress that can accurately calculate the rail generated stress at an arbitrary position by inputting the floating amount of floating cribs and the unevenness amount of the rail head top surface obtained from track inspection data and the like.

Means for Solving the Problems

[0007] To achieve the above object, the method for calculating rail generated stress of the present invention is a method for calculating rail generated stress for calculating the stress generated in a rail, comprising: setting an uneven wavelength of unevenness generated on the head top surface of the rail in a numerical analysis model of a track on which the rail is laid; using the numerical analysis model to perform analysis by setting a plurality of continuous floating numbers of floating cribs for each unevenness amount of the head top surface of the rail; obtaining, for each unevenness amount, the relationship between the stress value of the continuous floating number at which the rail generated stress is maximized and the floating amount of the floating crib from the results of the analysis; obtaining a stress estimation means for deriving the rail generated stress from the floating amount and the unevenness amount based on the relationships between the stress values and the floating amounts of the plurality of unevenness amounts; and calculating the rail generated stress by inputting the floating amount of the floating crib measured from the rail in the inspection target section and the unevenness amount of the head top surface of the rail into the stress estimation means.

[0008] Here, it is preferable that the stress estimation means is a relational expression between the floating amount, the uneven amount, and the rail generated stress, or a numerical table for deriving the rail generated stress from the floating amount and the uneven amount.

[0009] Further, it is preferable that the analysis is performed by setting the conditions of the track and the conditions of the traveling vehicle in the inspection target section. And the rail generated stress can be the rail bottom generated stress generated at the bottom of the rail.

Advantages of the Invention

[0010] In the method for calculating the rail generated stress of the present invention configured as described above, the uneven wavelength of the unevenness generated on the top surface of the rail is set in the numerical analysis model of the track, and for each uneven amount of the top surface of the rail, a plurality of floating continuous numbers of the floating sleeper are set and the analysis is performed. Further, based on the result of the analysis, a stress estimation means for deriving the rail generated stress from the floating amount and the uneven amount is obtained.

[0011] Therefore, by inputting the floating amount of the floating sleeper and the uneven amount of the top surface of the rail obtained from the track measurement data of the inspection target section and the like into the stress estimation means, the rail generated stress at an arbitrary position can be accurately calculated.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Embodiments for Carrying Out the Invention

[0013] Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a flowchart for explaining the processing flow of the method for calculating the rail-generated stress according to this embodiment.

[0014] Rails are known to be damaged due to corrosion. Among the occurrences of rail damage, there are many cases caused by damage. As described above, as a damage factor, a decrease in the fatigue strength of the rail due to corrosion in the rail bottom region is considered.

[0015] Also, it is known that rail damage can occur even due to slight corrosion at the bottom of the rail. As a factor, at leak points in tunnels, etc., due to repeated train running, the top surface of the rail is locally worn, and a rocking state occurs. Also, at the rail welded part, it can be assumed that rail unevenness occurs due to the hardness and swelling of the weld metal, and a rocking state occurs. Therefore, it is desirable to extract such locations early so as to prevent rail damage or to be able to perform early treatment on the damaged locations.

[0016] The method for calculating the rail generated stress of the present embodiment enables the calculation of the stress generated in the rail at an arbitrary rail position (kilometer level) such as on a railway operating line. If the rail generated stress at an arbitrary rail position is accurately obtained, it can also lead to the elucidation of the dominant factors leading to rail deterioration.

[0017] The bending stress generated at the bottom of the rail when a train passes can be estimated from the unevenness amount of the top surface of the rail, the state of rocking, and vehicle conditions such as wheel load. Here, "wheel load" refers to the vertical load acting on the rail from the wheel, which is mainly determined by the weight of the train. In the present embodiment, the track inspection data measured by the track inspection vehicle, the wheel load obtained from on-site measurement at a location without unevenness and rocking of the top surface, the static wheel load, etc. are used as the wheel load that is a vehicle condition. The wheel load can also be set from the specifications of the vehicle.

[0018] The depth of the unevenness existing on the top surface of the rail is defined as the unevenness amount (top surface unevenness amount). Also, the state where a gap is generated between the bottom surface of the sleeper and the roadbed surface is called "rocking", and the amount of the gap is defined as the floating amount (rocking amount).

[0019] In recent years, due to the advancement of track detection technology and the like, the amount of unevenness and the amount of uplift can be used as parameters at each rail position. Regarding the amount of unevenness of the rail, there are methods of estimating it from the axle box acceleration obtained from track detection (for example, "Study on the method for evaluating the unevenness of the rail head top surface using axle box acceleration" (2 authors, Shinyu, Annual Academic Lecture of the Japan Society of Civil Engineers, Vol. 55, VI-269, 1999), etc.), and the method of continuously measuring shown in Non-Patent Document 3, etc.

[0020] In addition, technologies for estimating the floating tie plate are disclosed in Japanese Patent Application Laid-Open No. 2020-16094, "Method for detecting floating tie plate based on track displacement data" (2 authors, Kusuda, Journal of the Japan Society of Civil Engineers, Vol. 59, No. 66, pp. 33-35, 2012), etc.

[0021] Subsequently, with reference to FIG. 2, a wheel load fluctuation simulation with a floating tie plate set will be described. The wheel load fluctuation simulation with a floating tie plate set is a numerical analysis by a numerical analysis model of vehicle running with a floating tie plate set, as shown in FIG. 2.

[0022] In this numerical analysis model, the railway track and each member of the vehicle are represented by mass points and springs, and the dynamic motion when the vehicle runs can be calculated. A displacement simulating the amount of unevenness (the amount of unevenness of the head top surface) can be input to the rail, and spring characteristics simulating the amount of uplift can be input to the spring under the tie plate.

[0023] Therefore, FIG. 3 shows the measured values of the amount of uplift and the amount of unevenness at the location where the in-situ measurement of the track was performed. This figure shows the numbers of the measurement points in the in-situ measurement and the running directions (A direction, B direction) of the vehicle. Among these measured values, the amount of uplift and the amount of unevenness are the largest at the measurement point (4).

[0024] Therefore, these measured values were input into the numerical analysis model, and the stress generated at the bottom of the rail was calculated as the rail generated stress (the stress generated at the bottom of the rail) with the in-situ track and vehicle conditions as parameters.

[0025] Figure 4 is a diagram for comparing the stress time history waveforms of numerical analysis and in-situ tests. Figure 4(a) shows the numerical analysis results, and Figure 4(b) shows the measurement results of the in-situ tests. Here, even if the track conditions are the same, the stress time history waveforms will show different results when the conditions of the running vehicle (such as running direction, running speed, wheel load, etc.) change.

[0026] The in-situ tests and numerical analysis were carried out for a certain track in multiple test numbers with different vehicle conditions, and Figure 4 shows an example of this. It can be seen that in the test numbers shown in this figure, the in-situ test results and the numerical analysis results are in good agreement at all measurement points. Also, similar results were shown in other test numbers.

[0027] Therefore, Figure 5 summarizes the relative errors of the numerical analysis results with respect to the in-situ test results. Figure 5(a) shows the case where the running direction of the vehicle is in the A direction, and Figure 5(b) shows the case where the running direction of the vehicle is in the B direction.

[0028] This Figure 5 shows the relative error of the numerical analysis results with respect to the in-situ test results of the peak stress at the measurement point (4). The calculation results of the numerical analysis model have a relative error within 20% except for Test No. 5 in the A direction (Figure 5(a)). Therefore, it is considered that the above-mentioned numerical analysis model can accurately calculate the rail generated stress of the track with floating sleepers and rail unevenness. Therefore, hereinafter, this numerical analysis model will be used for the simulation of the rail bottom generated stress.

[0029] When performing the simulation of the rail bottom generated stress, as described above, it is necessary to set the unevenness amount on the top surface of the rail in the numerical analysis model. Although various distributions are considered to exist in the rail unevenness, the characteristics of the rail unevenness that contribute to the rail bottom generated stress will be examined.

[0030] Here, as an example, the rail unevenness at the tunnel leakage location is targeted. With the condition that the floating amount is 0, the depression of the sinusoidal rail top surface is set with various wavelengths, and the results of calculating the rail bottom generated stress are shown in Figure 6.

[0031] Specifically, Fig. 6 is a graph with the horizontal axis representing the unevenness amplitude and the vertical axis representing the stress generated at the bottom of the rail. In this graph, the approximated values of the unevenness amount on the top surface of the rail head by sine waves of multiple wavelengths (wavelength 0.256 m (legend: 〇), wavelength 0.512 m (legend: □), wavelength 0.768 m (legend: △)), the unevenness amounts measured at the in-situ measurement locations (legend: ×) and the fracture sites (fracture example 1, fracture example 2) are plotted in relation to the stress generated at the bottom of the rail.

[0032] It is known that the smaller the wavelength of the rail unevenness (wavelength 0.256 m (legend: 〇)), the greater the stress generated at the bottom of the rail, and this tendency can also be confirmed in Fig. 6. On the other hand, when the unevenness amounts of the rails obtained at the in-situ measurement locations and the fracture sites are input into the numerical analysis model, the calculated stress generated at the bottom of the rail is plotted above the calculation result when sine-wave-shaped rail unevenness with a wavelength of approximately 0.512 m (legend: □) is input.

[0033] Therefore, it can be said that by setting the rail unevenness in the numerical analysis model as a sine wave with a wavelength of 0.5 m at the tunnel water leakage location, it becomes possible to consider the unevenness amount of the rail related to the stress generated at the bottom of the rail.

[0034] In this example, the rail unevenness at the tunnel water leakage location is targeted. However, for example, at the rail welding part, it is expected that the wavelength of the rail unevenness will vary depending on the hardness and bulge of the welding metal. Therefore, for other rail unevenness such as the rail welding part, by comparing the on-site rail unevenness with the analysis results when sine-wave-shaped rail unevenness is input, the wavelength of the rail unevenness for applying this calculation method will be set.

[0035] Subsequently, the characteristics of the floating fasteners that contribute to the stress generated at the bottom of the rail will be described. The floating amount and the continuous number of floating fasteners (floating continuous number) of the floating fasteners are related to the stress generated at the bottom of the rail. The stress generated at the bottom of the rail associated with the floating fasteners is caused by the deformation of the track when the vehicle passes through the floating part, resulting in curvature in the rail.

[0036] The condition for the curvature generated in the rail to be maximized is when the rail acting as a beam is simply supported between the sleepers and the lower surface of the sleeper does not contact the upper surface of the ballast during vehicle running. That is, even if the floating amount is large or the number of continuous floating is large, a case where the lower surface of the sleeper contacts the upper surface of the ballast and the stress does not increase can be assumed. Fig. 7 is a diagram for explaining the deformation of the track in the floating sleeper state. Fig. 7(a) is a schematic diagram when the stress generated at the bottom of the rail does not reach the maximum, and Fig. 7(b) is a schematic diagram when the stress generated at the bottom of the rail reaches the maximum.

[0037] In short, the relationship between the floating amount and the number of continuous floating that satisfies the condition for the curvature generated in the rail to be maximized varies depending on the superposition with the wheel load (the force loaded from the vehicle to the rail), the unevenness amount, the running conditions (running direction, running speed), etc. Therefore, for the floating sleeper, two parameters, namely the floating amount and the number of continuous floating sleepers, will be used.

[0038] Subsequently, an explanation will be given regarding the parametric study with the state of the floating sleeper (floating amount, number of continuous floating) and the unevenness amount as variables. As described above, regarding the rail unevenness, its unevenness amount, and regarding the floating sleeper, the floating amount and the number of continuous floating are set as variables in the numerical analysis model, and these rail unevenness and floating sleeper are set to conduct a parametric study.

[0039] The wavelength of the rail unevenness is 0.5 m at the tunnel leakage location as described above. Fig. 8 is a relationship diagram for explaining the stress generated at the bottom of the rail according to the floating amount and the number of continuous floating for a certain unevenness amount. In Fig. 8, the case where the unevenness amount is 4 mm is exemplified.

[0040] As can be seen from this Fig. 8, for a certain unevenness amount (4 mm in this figure) and the floating amount, the number of continuous floating at which the stress generated at the bottom of the rail becomes the maximum is different. For example, when the unevenness amount is 4 mm and the floating amount is 11 mm, the number of continuous floating at which the stress generated at the bottom of the rail becomes the maximum is 5 (refer to the plot with an arrow marked with the legend of △).

[0041] Here, when finally calculating the stress generated at the rail bottom, it is assumed that two variables, the floating amount and the unevenness amount, are used as input values. However, as described above, for the floating sleepers, the floating amount and the number of continuous floating are variables. Therefore, among the results of the parametric study, for a certain unevenness amount and floating amount, the stress value of the number of continuous floating at which the stress generated at the rail bottom becomes maximum is adopted as the representative value of the stress generated at the rail bottom.

[0042] The results of extracting the stress values of the number of continuous floating at which the stress generated at the rail bottom becomes maximum for the floating amounts with various unevenness amounts are shown in Fig. 9. For example, the plotted point (× mark) with an arrow in Fig. 9 has the same value as the stress value of the plotted point (△ mark) with 5 continuous floating and a floating amount of 11 mm at the unevenness amount of 4 mm with an arrow in Fig. 8. In short, the number of continuous floating does not appear in Fig. 9.

[0043] From the relationship between the floating amount and the stress generated at the rail bottom for a plurality of unevenness amounts (in this figure, 5 cases with unevenness amounts from 1 mm to 5 mm) arranged as shown in this Fig. 9, the relationship formula for estimating the stress σ m generated at the rail bottom is obtained.

[0044] In short, using the data shown in Fig. 9, multiple regression analysis is performed with the floating amount d and the unevenness amount z as variables to obtain the following relational expression. σ m = az + bd + c Here, the coefficient a is 16.4, the coefficient b is 6.5, and the coefficient c is 31.4. The multiple correlation coefficient of this multiple regression equation is R 2 = 0.844, and for the t-value and p-value, results indicating significance were obtained.

[0045] On the other hand, Fig. 10 is an explanatory diagram exemplifying a numerical table for calculating the stress generated at the rail bottom. To calculate the stress σ m generated at the rail bottom, it can be obtained by inputting the floating amount d and the unevenness amount z into the above relational expression and performing calculations, but a numerical table as shown in Fig. 10 can also be created in advance.

[0046] In short, when the floating amount and unevenness amount of the floating tie are obtained by measuring the rails in the inspection target section, by applying these measured values to the matrix of the numerical table in Fig. 10 and simply reading the stress values described in the intersecting columns, the stress generated at the bottom of the rail can be easily calculated.

[0047] Next, the method for calculating the stress generated in the rail according to the present embodiment will be described in order with reference to the flowchart shown in Fig. 1. First, in step S1, a numerical analysis model as described with reference to Fig. 2 is created.

[0048] In the numerical analysis model, in step S2, the uneven wavelength of the unevenness generated on the top surface of the rail is set. Regarding the setting of this uneven wavelength, as described above with reference to Fig. 6, it can be set after performing an analysis using the measured values obtained from the track in the inspection target section.

[0049] Also, when the situation in the inspection target section is clear, such as the water leakage location in the tunnel or the rail welding part, the uneven wavelength set in other sections with similar situations can be directly used. For example, if the inspection target section is the water leakage location in the tunnel, the uneven wavelength of the rail unevenness can be set to 0.5 m.

[0050] In step S2, the range of the amplitude (unevenness amount) of the unevenness that needs to be considered is also set. On the other hand, in step S3, the range to be considered in the inspection target section is set for the floating amount indicating the state of the floating tie and the number of consecutive floating ties (floating consecutive number).

[0051] Furthermore, in step S4, the conditions of the track and the vehicle are set. The conditions of the track include the number of years elapsed since laying, the size of the rail, information on the curved section, etc. Also, the conditions of the vehicle are information regarding the vehicles of the train running on the track in the inspection target section, and include the weight of the train, wheel load, etc.

[0052] Then, within the range of the set amplitude (amount of unevenness) of the unevenness, numerical analysis is performed using a numerical analysis model. At this time, for the floating sleepers, the floating amount and the number of consecutive floating sleepers are set to arbitrary values within the range set in step S3.

[0053] In step S5, from the numerical analysis results, for the floating amount and the amount of unevenness, the relational expression of the multiple regression analysis as described above, the numerical table as shown in FIG. 10, or both are created as stress estimation means. On the other hand, in the inspection target section, the floating amount and the amount of unevenness associated with the rail position are acquired by running an orbital inspection vehicle or having a worker measure them, etc. When running the orbital inspection vehicle, the wheel load can also be measured.

[0054] Also, by running the orbital inspection vehicle at a constant speed and associating the measurement time with the measured value, it can be converted into position information indicating the rail position. In addition, position information based on GPS (Global Positioning System) can also be associated with the measured value.

[0055] When the floating amount and the amount of unevenness associated with the rail position in the inspection target section are acquired, the rail bottom generated stress generated at that rail position can be calculated by the above relational expression or numerical table.

[0056] The calculation of this rail bottom generated stress can be performed over the entire line of the track where the measured values are obtained, but in order to reduce the calculation load, it can also be performed only for about every kilometer where any one or both of the parameters such as the amount of unevenness and the floating amount exceed the threshold value.

[0057] Next, the operation of the method for calculating the rail generated stress according to this embodiment will be described. In the method for calculating the rail generated stress according to this embodiment configured as described above, the unevenness wavelength of the unevenness generated on the top surface of the rail is set in the numerical analysis model of the track, and for each amount of unevenness on the top surface of the rail, a plurality of numbers of consecutive floating sleepers of the floating sleepers are set and analyzed.

[0058] Furthermore, based on the results of the analysis, a relational expression or numerical table (see FIG. 10) that can calculate rail generated stress such as the stress generated at the bottom of the rail from the floating amount and the unevenness amount is obtained as stress estimation means.

[0059] Therefore, by inputting the floating amount of the floating sleeper and the unevenness amount of the top surface of the rail obtained from the track measurement data of the inspection target section into the relational expression, numerical table, etc., the rail generated stress at an arbitrary position can be accurately calculated.

[0060] That is, at any position on the continuous operating line, the rail generated stress that contributes to elucidating the dominant factors leading to rail deterioration can be easily obtained, eliminating the cost and time-consuming burden of conducting on-site tests each time.

[0061] In addition, if the rail generated stress associated with the rail position can be calculated, the rail positions where rail damage may occur can be extracted at an early stage, preventing rail damage or enabling early treatment of the damaged parts.

[0062] As described above, the embodiments of the present invention have been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and design changes that do not deviate from the gist of the present invention are included in the present invention.

[0063] For example, in the above embodiment, the stress generated at the bottom of the rail is described as the rail generated stress. However, the present invention is not limited to this, and any stress that indicates the state of the rail and is generated at another part of the rail may be used.

[0064] In addition, in the above embodiment, the case of creating a relational expression or numerical table again in the inspection target section has been described. However, the present invention is not limited to this, and if an existing relational expression or numerical table can be applied, the labor of creating a relational expression or numerical table in the inspection target section can be omitted.

Claims

1. A method for calculating the rail-generated stress that calculates the stress generated in a rail, comprising: a step of setting a concavo-convex wavelength corresponding to the concavo-convexity generated on the top surface of the rail in a numerical analysis model of a track on which the rail is laid; a step of using the numerical analysis model to perform analysis by setting a plurality of floating continuity numbers of floating sleepers for each concavo-convex amount on the top surface of the rail; a step of obtaining, for each concavo-convex amount, the relationship between the stress value of the floating continuity number at which the rail-generated stress is maximized and the floating amount of the floating sleeper from the results of the analysis; a step of obtaining a stress estimation means for deriving the rail-generated stress from the floating amount and the concavo-convex amount based on the relationships between the stress values and the floating amounts of the plurality of concavo-convex amounts; a step of calculating the rail-generated stress by inputting the floating amount of the floating sleeper measured by track inspection and the concavo-convex amount of the top surface of the rail from the rail in the inspection target section into the stress estimation means; The method for calculating the rail-generated stress, wherein the concavo-convex wavelength is set by obtaining the wavelength of a sine wave based on the relationship between the concavo-convex amount obtained by actual measurement in advance and the rail-generated stress.

2. The method for calculating the rail-generated stress according to claim 1, wherein the stress estimation means is an expression of the relationship between the floating amount, the concavo-convex amount, and the rail-generated stress, or a numerical table for deriving the rail-generated stress from the floating amount and the concavo-convex amount.

3. The method for calculating the rail-generated stress according to claim 1 or 2, wherein the analysis is performed by setting the conditions of the track in the inspection target section and the conditions of the running vehicle.

4. The method for calculating the rail-generated stress according to claim 1 or 2, wherein the rail-generated stress is the rail bottom-generated stress generated at the bottom of the rail.

Images