JP7711029B2 - Calculation method for rail stress - Google Patents

Description

The present invention relates to a method for calculating rail stress, which calculates the stress generated in a rail.

Rail damage due to corrosion has traditionally accounted for a large proportion of rail damage occurrences. The main cause of damage is thought to be a decrease in rail fatigue strength due to corrosion in the rail bottom area, and research and inspections have focused on the amount of corrosion in the rail bottom area (see Non-Patent Document 1). For this purpose, ultrasonic flaw detection vehicles and ultrasonic flaw detection devices are widely used.

On the other hand, it has been reported that even minor corrosion at the bottom of the rail can cause rail damage (see, for example, Non-Patent Document 2). One of the causes of this is that at water leak points in tunnels, repeated train travel causes localized wear of the rail head surface and can also lead to a floating sleeper condition (a condition in which a gap occurs between the bottom of the sleeper and the ballast surface), which generally increases rail bending stress. Until now, it has been impossible to identify such points, which has resulted in rail damage.

Hosoda et al., "Remaining life evaluation of rails in corrosive and electrolytic corrosion environments", Railway Technical Research Institute Report, Railway Technical Research Institute, Vol. 27, No. 04, pp. 5-11, April 2013. Taizan et al., "Rail breakage incidents in tunnels and strengthening management of corroded rails," Journal of the Japan Railway Construction Association, Vol. 59, No. 5, pp. 345-348, May 1, 2021 Tanaka et al., "Development of a continuous rail unevenness measurement device using the eccentric arrow method and its application to rail corrugation wear measurement," Transactions of the Japan Society of Mechanical Engineers, Vol. 85, No. 880, 2019, p.19-00235, 2019

However, conducting on-site tests at any position on a continuous operating line each time in order to obtain rail-induced stress, known as rail bending stress, is a heavy burden. On the other hand, a method has been proposed for determining the unevenness of the rail head surface and the sleeper support condition at any kilometer by analyzing track inspection data (see Non-Patent Document 3).

The present invention aims to provide a method for calculating rail stress that can accurately calculate rail stress at any position by inputting the amount of floating of a floating sleeper obtained from track inspection data, etc., and the amount of unevenness on the top surface of the rail.

In order to achieve the above object, the rail stress calculation method of the present invention is a method for calculating the stress generated in a rail, and is characterized by comprising the steps of: setting the unevenness wavelength of the unevenness generated on the top surface of the rail in a numerical analysis model of the track on which the rail is laid; performing an analysis by setting multiple consecutive numbers of floating sleepers for each amount of unevenness on the top surface of the rail using the numerical analysis model; determining, for each amount of unevenness, the relationship between the stress value of the consecutive number of floating sleepers at which the rail stress is maximized and the amount of floating sleepers from the results of the analysis; determining a stress estimation means for deriving the rail stress from the amount of floating and the amount of unevenness based on the relationship between the stress value of the multiple amounts of unevenness and the amount of floating; and calculating the rail stress by inputting the amount of floating sleepers measured from the rail in the inspection target section and the amount of unevenness on the top surface of the rail to the stress estimation means.

Here, the stress estimation means is preferably a relational expression between the amount of lift and the amount of unevenness and the stress generated in the rail, or a numerical table that derives the stress generated in the rail from the amount of lift and the amount of unevenness.

The analysis is preferably performed by setting the track conditions of the inspection target section and the conditions of the running vehicles. The rail stress can be rail bottom stress that occurs at the bottom of the rail.

In the method for calculating rail stress of the present invention, which is configured in this way, the wavelength of the unevenness occurring on the top surface of the rail is set in the numerical analysis model of the track, and the analysis is performed by setting multiple numbers of consecutive floating sleepers for each amount of unevenness on the top surface of the rail. Furthermore, based on the results of the analysis, a stress estimation means is found that derives rail stress from the amount of floating and the amount of unevenness.

Therefore, by inputting the amount of floating of the floating sleeper and the amount of unevenness of the rail top surface obtained from track inspection data for the inspection target section into the stress estimation means, it becomes possible to accurately calculate the stress generated in the rail at any position.

4 is a flowchart illustrating a process flow of a method for calculating a rail-generated stress according to the present embodiment. FIG. 13 is an explanatory diagram of a numerical analysis model for a simulation in which floating sleepers are installed. 11 is a diagram illustrating the amount of lifting and the amount of unevenness, which are actual measured values. 1A and 1B are diagrams for comparing stress time history waveforms obtained by numerical analysis and field testing, in which FIG. 1A illustrates the results of numerical analysis, and FIG. 1B illustrates the measurement results of field testing. 1A and 1B are diagrams summarizing the relative error of the numerical analysis results with respect to the field test results, where FIG. 1A is a diagram when the vehicle travel direction is direction A, and FIG. 1B is a diagram when the vehicle travel direction is direction B. This is a graph with the horizontal axis representing the amplitude of unevenness and the vertical axis representing the stress generated at the rail bottom, in which approximate values of rail top surface unevenness approximated by a sine wave and amounts of unevenness measured by on-site measurements are plotted in relationship to the stress generated at the rail bottom. FIG. 11 is a diagram illustrating deformation of a track when a floating sleeper is present, where (a) is a schematic diagram illustrating a case in which stress generated at the bottom of the rail is not maximum, and (b) is a schematic diagram illustrating a case in which stress generated at the bottom of the rail is maximum. FIG. 1 is an explanatory diagram illustrating an example of stress generated at the bottom of a rail according to the amount of floating and the number of consecutive floating for a certain amount of unevenness. FIG. 1 is an explanatory diagram illustrating an example of the relationship between the amount of unevenness and lift of a rail top surface and the stress generated at the rail bottom. FIG. 11 is an explanatory diagram illustrating an example of a numerical table for calculating stress generated at the rail bottom.

The following describes an embodiment of the present invention with reference to the drawings. Figure 1 is a flowchart illustrating the process flow of the rail stress calculation method of this embodiment.

It is known that rails are damaged due to corrosion. Many rail damage cases are caused by damage. As mentioned above, it is believed that the cause of the damage is a decrease in fatigue strength of the rail due to corrosion in the bottom area of the rail.

It is also known that even minor corrosion at the bottom of the rail can cause rail damage. One of the causes of this is said to be localized wear on the top surface of the rail due to repeated train travel at water leak points in tunnels, resulting in a floating sleeper. It is also possible that at rail welds, the hardness and swelling of the weld metal can cause rail unevenness, resulting in a floating sleeper. It is therefore desirable to be able to identify such areas at an early stage and prevent rail damage or take early action on damaged areas.

The rail stress calculation method of this embodiment makes it possible to calculate the stress generated in the rail at any rail position (kilometers) on a railway operating line, etc. If the rail stress at any rail position can be obtained with high accuracy, it can also lead to elucidation of the dominant factors that lead to rail deterioration.

The bending stress generated at the bottom of the rail when a train passes can be estimated from vehicle conditions such as the amount of unevenness on the top surface of the rail, the state of the floating sleepers, and wheel load. Here, "wheel load" refers to the vertical load acting on the rail from the wheels, which is determined mainly by the weight of the train. In this embodiment, the wheel load, which is a condition of the vehicle, is determined by track inspection data measured with a track inspection car, wheel load obtained by on-site measurement of a location without unevenness on the top surface or floating sleepers, static wheel load, etc. Wheel load can also be set from the vehicle specifications.

The depth of the unevenness on the top surface of the rail is the amount of unevenness (top surface unevenness). Also, a gap between the bottom of the sleeper and the ballast surface is called a "floating sleeper," and the amount of this gap is the amount of floating (floating sleeper amount).

In recent years, with the advancement of track inspection technology, it has become possible to treat the amount of unevenness and the amount of floating as parameters at each rail position. Regarding the amount of rail unevenness, there are methods to estimate it from the axle box acceleration obtained from track inspection (for example, "Study on a method for evaluating rail top surface unevenness using axle box acceleration" (Susumu Gani, 2nd Annual Academic Lecture Meeting of the Japan Society of Civil Engineers, Vol. 55, VI-269, 1999)) and a continuous measurement method as shown in Non-Patent Document 3.

In addition, technology for estimating floating sleepers is disclosed in JP 2020-16094 A and in "Method for detecting floating sleepers based on track displacement data" (Kusuda et al., Journal of the Japan Society of Civil Engineers, Vol. 59, No. 66, pp. 33-35, 2012).

Next, we will explain the wheel load fluctuation simulation with floating sleepers, with reference to Figure 2. The wheel load fluctuation simulation with floating sleepers is a numerical analysis using a numerical analysis model of vehicle travel with floating sleepers, as shown in Figure 2.

In this numerical analysis model, each component of the railway track and vehicle is represented as a mass point and a spring, making it possible to calculate the dynamic movement when the vehicle is running. Displacement simulating unevenness (top surface unevenness) can be input to the rail, and spring characteristics simulating the amount of lift can be input to the springs under the sleepers.

Figure 3 shows the amount of floating and unevenness, which are the actual measured values at the points where on-site measurements of the track were conducted. This figure shows the number of the measurement point at the on-site measurement and the direction of travel of the vehicle (direction A, direction B). Among these actual measurements, the amount of floating and unevenness is greatest at measurement point (4).

These measured values were then input into a numerical analysis model, and the stress generated at the bottom of the rail was calculated as rail generated stress (stress generated at the bottom of the rail) using the local track and vehicle conditions as parameters.

Figure 4 is a diagram for comparing the stress time history waveforms of numerical analysis and field testing, where Figure 4(a) shows the numerical analysis results and Figure 4(b) shows the measurement results of the field testing. Here, even if the track conditions are the same, the stress time history waveform will show different results if the conditions of the running vehicle (running direction, running speed, wheel load, etc.) change.

On-site testing and numerical analysis were performed on a certain track using multiple test numbers with different vehicle conditions, and Figure 4 shows an example. For the test number shown in this figure, it can be seen that the on-site test results and numerical analysis results are in good agreement at all measurement points. Similar results were also obtained for other test numbers.

Figure 5 shows the relative error of the numerical analysis results compared to the field test results. Figure 5(a) shows the case where the vehicle travels in direction A, and Figure 5(b) shows the case where the vehicle travels in direction B.

Figure 5 shows the relative error of the numerical analysis results against the field test results for peak stress at measurement point (4). The calculation results of the numerical analysis model have a relative error of within 20%, except for test number 5 in the A direction (Figure 5(a)). For this reason, it is believed that the above-mentioned numerical analysis model is able to accurately calculate the stress generated in the rail of a track with floating sleepers and rail irregularities. Therefore, in the following, this numerical analysis model will be used to simulate the stress generated at the bottom of the rail.

When simulating stress generated at the rail bottom, as mentioned above, it is necessary to set the amount of unevenness on the rail top surface of the numerical analysis model. There are thought to be various distributions of rail unevenness, but we will examine the characteristics of rail unevenness that contribute to stress generated at the rail bottom.

As an example, we will look at rail unevenness at a tunnel water leak location. Figure 6 shows the results of calculating the stress generated at the bottom of the rail by setting the sinusoidal rail head surface depression with various wavelengths under the condition that the amount of lift is 0.

In detail, Figure 6 is a graph with the horizontal axis representing the amplitude of unevenness and the vertical axis representing the stress generated at the bottom of the rail, which plots the amount of unevenness on the rail top surface approximated by sine waves of multiple wavelengths (wavelength 0.256 m (legend: ◯), wavelength 0.512 m (legend: □), wavelength 0.768 m (legend: △)) as well as the amount of unevenness measured at the on-site measurement location (legend: ×) and at the fracture site (fracture example 1, fracture example 2) in relation to the stress generated at the bottom of the rail.

It is known that the smaller the wavelength of rail irregularities (wavelength 0.256 m (legend: circle)), the greater the stress generated at the bottom of the rail, and this tendency can be seen in Figure 6. On the other hand, when the amount of rail irregularity obtained at the on-site measurement point and the fracture site was input into the numerical analysis model, the calculated stress generated at the bottom of the rail was plotted on top of the calculation results when a sinusoidal rail irregularity with a wavelength of approximately 0.512 m (legend: square) was input.

Therefore, it can be said that by setting the rail irregularity in the numerical analysis model to a sine wave with a wavelength of 0.5 m at the tunnel leakage location, it is possible to take into account the amount of rail irregularity that is related to the stress generated at the bottom of the rail.

In this example, the target was rail unevenness at the tunnel water leakage point, but for example, at rail welds, the wavelength of rail unevenness is expected to vary depending on the hardness and bulge of the weld metal. Therefore, for rail welds and other rail unevenness, the wavelength of rail unevenness for applying this calculation method can be set by comparing the on-site rail unevenness with the analysis results in which sinusoidal rail unevenness is input.

Next, we will explain the characteristics of floating sleepers that contribute to stress generated at the bottom of the rail. The amount of floating of a floating sleeper and the number of consecutive floating sleepers (number of consecutive floating sleepers) are related to the stress generated at the bottom of the rail. Stress generated at the bottom of the rail due to floating sleepers is caused by deformation of the track when a vehicle passes over the floating part, which creates a curvature in the rail.

The condition for the curvature of the rail to be at its maximum is when the rail, which acts as a beam, is simply supported between the support sleepers, and the underside of the sleeper does not come into contact with the top surface of the ballast when the vehicle is running. In other words, even if the amount of floating is large, if the number of consecutive sleepers is large, it is possible to imagine a case where the underside of the sleeper comes into contact with the top surface of the ballast and stress does not become large. Figure 7 is a diagram explaining the deformation of the track when there are floating sleepers, with Figure 7(a) being a schematic diagram when the stress generated at the bottom of the rail is not at its maximum, and Figure 7(b) being a schematic diagram when the stress generated at the bottom of the rail is at its maximum.

In short, the relationship between the amount of floating and the number of consecutive floating sleepers that meets the condition for maximizing the curvature of the rail varies depending on the wheel load (the force applied to the rail by the vehicle), the amount of unevenness, and the running conditions (running direction and running speed). Therefore, for floating sleepers, the two parameters are the amount of floating and the number of consecutive floating sleepers.

Next, we will explain the parametric study that uses the state of the floating sleepers (amount of floating, number of consecutive floating sleepers) and the amount of unevenness as variables. As mentioned above, the amount of unevenness was used as a variable for rail unevenness, and the amount of floating and number of consecutive floating sleepers were used as variables for the floating sleepers. These rail unevenness and floating sleepers were set in the numerical analysis model, and a parametric study was performed.

As mentioned above, the wavelength of rail irregularities is 0.5 m at the tunnel leakage point. Figure 8 is a relationship diagram that explains the stress generated at the bottom of the rail depending on the amount of floating and the number of consecutive floating for a certain amount of unevenness. Figure 8 shows an example where the amount of unevenness is 4 mm.

As can be seen from Figure 8, the number of consecutive floatings at which the stress generated at the rail bottom is maximum varies depending on the amount of unevenness (4 mm in this figure) and the amount of floating. For example, when the amount of unevenness is 4 mm and the amount of floating is 11 mm, the number of consecutive floatings at which the stress generated at the rail bottom is maximum is 5 (see the plot with the arrow in the △ legend).

Here, we assume that two variables, the amount of lift and the amount of unevenness, will be used as input values when finally calculating the stress generated at the bottom of the rail. However, as mentioned above, for a lifted sleeper, the variables are the amount of lift and the number of consecutive lifts. Therefore, from the results of the parametric study, for a certain amount of unevenness and amount of lift, the stress value of the number of consecutive lifts that maximizes the stress generated at the bottom of the rail is adopted as the representative value of the stress generated at the bottom of the rail.

Figure 9 shows the results of extracting the stress value for the number of consecutive floats that maximizes the stress generated at the rail bottom for various amounts of float with various unevenness. For example, the plot with an arrow in Figure 9 (marked with an x) is the same stress value as the plot with an arrow in Figure 8 (marked with a triangle) where the unevenness is 4 mm, there are 5 consecutive floats, and the amount of float is 11 mm. In other words, the number of consecutive floats does not appear in Figure 9.

From the relationship between the amount of uplift for multiple amounts of unevenness (in this figure, five cases with amounts of unevenness ranging from 1 mm to 5 mm) and the stress generated at the rail bottom, organized as shown in Fig. 9, a relational equation for estimating the stress generated at the rail bottom, σ _m, is obtained.

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, coefficient a was 16.4, coefficient b was 6.5, and coefficient c was 31.4. The multiple correlation coefficient of this multiple regression equation was ^R2 = 0.844, and the t-value and p-value also showed significant results.

On the other hand, Fig. 10 is an explanatory diagram illustrating an example of a numerical table for calculating the stress generated at the rail bottom. The stress generated at the rail bottom _σm can be calculated by inputting the floating amount d and the unevenness amount z into the above relational expression, but it is also possible to prepare a numerical table such as that shown in Fig. 10 in advance.

In short, when the amount of lift and unevenness of the loose sleeper are obtained by measuring the rail in the section to be inspected, the stress generated at the bottom of the rail can be easily calculated by simply applying these measurements to the matrix in the table in Figure 10 and reading the stress values recorded in the intersecting columns.

Next, a method for calculating rail stress according to this embodiment will be described in detail with reference to the flow chart shown in FIG.
First, in step S1, a numerical analysis model such as that described with reference to FIG. 2 is created.

In step S2, the wavelength of the irregularities occurring on the top surface of the rail is set in the numerical analysis model. This wavelength of irregularities can be set after performing an analysis using the measured values obtained from the track of the section to be inspected, as described above with reference to Figure 6.

In addition, if the condition of the section to be inspected is clear, such as a tunnel leak or rail welds, the irregularity wavelength set in other sections with similar conditions can be used as is. For example, if the section to be inspected is a tunnel leak, the irregularity wavelength of the rail irregularities can be set to 0.5 m.

In step S2, the range of the amplitude of unevenness (amount of unevenness) that needs to be taken into consideration is also set. Meanwhile, in step S3, the range of the amount of floating, which indicates the state of the floating sleeper, and the number of consecutive floating sleepers (number of consecutive floating sleepers) that should be taken into consideration in the inspection target section are set.

Furthermore, in step S4, the track conditions and vehicle conditions are set. The track conditions include the number of years since installation, the size of the rails, and information about the curved section. The vehicle conditions include information about the train cars that will run on the track in the section being inspected, such as the train's weight and wheel load.

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

In step S5, from the results of the numerical analysis, the above-mentioned multiple regression analysis relational equation, a numerical table as shown in FIG. 10, or both are created as stress estimation means for the amount of lift and the amount of unevenness. Meanwhile, in the section to be inspected, the amount of lift and the amount of unevenness linked to the rail position are obtained by running a track inspection car or by having workers measure. The wheel load can also be measured when running the track inspection car.

In addition, by running a track inspection vehicle at a constant speed and linking the measurement time to the measurement value, it is possible to convert the data into location information indicating the rail position. In addition, location information based on the Global Positioning System (GPS) can also be linked to the measurement value.

Once the amount of lift and unevenness associated with the rail position in the inspected section is obtained, the rail bottom stress occurring at that rail position can be calculated using the above-mentioned relational equation or table.

This calculation of the stress generated at the bottom of the rail can be performed for the entire length of the track for which measurements were obtained, but to reduce the computational load, it can also be performed only for the kilometers where one or both of the parameters, such as the amount of unevenness or the amount of lift, exceed a threshold value.

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

Furthermore, based on the results of the analysis, the above-mentioned relational expressions and numerical tables (see Figure 10) are obtained as stress estimation means, which can calculate rail stresses such as rail bottom stresses from the amount of lift and unevenness.

Therefore, by inputting the amount of floating of the floating sleeper and the amount of unevenness of the rail top surface obtained from track inspection data for the inspection section into a relational equation or a mathematical table, it becomes possible to accurately calculate the stress generated in the rail at any position.

In other words, it will be possible to easily obtain rail stresses that contribute to elucidating the dominant factors that lead to rail deterioration, without the costly and time-consuming burden of conducting on-site tests at any location on a continuous operating line each time.

Furthermore, if it is possible to calculate rail stress associated with rail position, rail positions where rail damage may occur can be identified at an early stage, making it possible to prevent rail damage or take early action on damaged areas.

The embodiment of the present invention has been described in detail above with reference to the drawings, but 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.

For example, in the above embodiment, the stress occurring at the bottom of the rail was described as the rail stress, but this is not limited to this, and the stress may occur in another part of the rail as long as it is a stress that indicates the condition of the rail.

In addition, in the above embodiment, a case where a relational equation or a numerical table is newly created in the section to be inspected is described, but this is not limited to this, and if a relational equation or a numerical table that has already been created can be applied, the effort of creating a relational equation or a numerical table in the section to be inspected can be eliminated.

Claims (4)

A method for calculating stress generated in a rail, comprising the steps of:
setting an irregularity wavelength corresponding to irregularities occurring on a top surface of the rail in a numerical analysis model of the track on which the rails are laid;
a step of performing an analysis by using the numerical analysis model while setting a plurality of numbers of consecutive floating sleepers for each unevenness amount of the rail head surface;
determining, for each of the irregularities, a relationship between the stress value of the number of consecutive lifts at which the rail stress is maximized and the amount of lift of the lifted sleeper from the results of the analysis;
determining a stress estimation means for deriving the rail generated stress from the amount of lift and the amount of unevenness based on a relationship between the stress value of a plurality of the amounts of unevenness and the amount of lift;
a step of calculating stress generated in the rail by inputting the amount of lift of the lifted sleeper and the amount of unevenness of the rail head surface measured by track inspection from the rail in the inspection target section to the stress estimation means ,
A method for calculating stress generated in a rail, characterized in that the unevenness wavelength is set by determining the wavelength of a sine wave based on the relationship between the amount of unevenness obtained by a previous actual measurement and the stress generated in the rail. The method for calculating rail stress according to claim 1, characterized in that the stress estimation means is a relational expression between the amount of lift and the amount of unevenness and the rail stress, or a numerical table for deriving the rail stress from the amount of lift and the amount of unevenness. The method for calculating rail stress according to claim 1 or 2, characterized in that the analysis is performed by setting track conditions and running vehicle conditions for the section to be inspected. The method for calculating rail stress according to claim 1 or 2, characterized in that the rail stress is rail bottom stress that occurs at the bottom of the rail.