Detection method for contact position of wheel and rail
Patent Information
- Application Number
- JP2023108112
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-06-30
- Publication Date
- 2025-01-17
Smart Images
Figure 2025007004000001_ABST
Abstract
Description
[Technical field]
[0001] An embodiment of the present invention relates to a method for detecting a contact position between a wheel and a rail. [Background technology]
[0002] To evaluate the running safety of railway vehicles in detail, it is necessary to detect the wheel / rail contact position in the sleeper direction with high accuracy, and also to continuously detect the wheel contact position of a traveling railway vehicle. [Prior art documents] [Patent documents]
[0003] [Patent Document 1] JP 2007-331492 A [Patent Document 2] Patent Publication No. 2021-60381 [Patent Document 3] JP 2022-41349 A [Non-patent literature]
[0004] [Non-Patent Document 1] Hiromichi Kanehara and Takehiko Fujioka: Study on the method of measuring the contact position between rail and wheel of railway vehicles, Transactions of the Japan Society of Mechanical Engineers (Series C), Vol. 67, No. 654 (2001-2), p193-p200 [Non-Patent Document 2] Hiromichi Kanehara: Development of a continuous measuring device for wheel-rail contact position, Railway Technology Union Symposium 2002 (J-RAIL2002), p495-p498 [Non-Patent Document 3] Hiroaki Ishida, Kenji Ueki, Yoshitoshi Fukazawa, Kazuhiko Tezuka, Masaki Matsuo: Development of a continuous measuring device for wheel load, lateral force and derailment coefficient, Railway Technical Research Institute Report Vol.7, No.8, August 1993, p25-p38 Summary of the Invention [Problem to be solved by the invention]
[0005] The following methods have been reported as methods for measuring the wheel / rail contact position. Non-Patent Document 1 reports a method of measuring the contact position between the wheel and the rail by attaching a strain gauge to the inner peripheral surface of a hole provided in the wheel plate. Non-Patent Document 2 reports a method for continuous measurement of contact position by applying Non-Patent Document 1. However, in both cases, the contact position measurement method is constructed while ignoring the influence of the lateral pressure load position and the front and rear tangential forces.
[0006] In Patent Document 1, it is assumed that the output of the strain gauge for measuring contact position is only affected when the contact position changes in the sleeper direction, and an equation for calculating the contact position from the strain output is derived. However, there is no mention of whether the method is applicable to cases where the contact position changes significantly in the wheel radial direction, such as when the flanges come into contact. In addition, since a strain gauge for measuring lateral force is used when continuously measuring the contact position, if the lateral force is to be measured at the same time as the contact position measurement, a new strain gauge for measuring lateral force must be attached.
[0007] Patent Document 2 reports a method that takes into account the respective load positions of the wheel load and lateral force, and can measure the contact position even when the contact position changes significantly in the sleeper direction and the wheel radial direction. However, the contact position could only be measured directly above the through-hole for measuring the wheel load provided in the wheel plate. In addition, the influence of the front and rear tangential forces was not taken into account when calculating the contact position. The contact position measurement method disclosed in Patent Document 3 is characterized by using the shear strain of the wheel. Therefore, the sensitivity of the bridge output to changes in contact position is lower than that using wheel bending.
[0008] An object of the present invention is to provide a method for detecting the contact position between a wheel and a rail, which is capable of continuously detecting the contact position of the wheel with high accuracy. [Means for solving the problem]
[0009] The method for detecting the contact position between a wheel and a rail in this invention includes a finite element analysis process in which a boundary condition of an assumed wheel load is set on a finite element model of the wheel and a finite element analysis is performed, strains around a through hole in the plate portion of the wheel are extracted to calculate a first output of the strain gauge bridge, and the strain extraction position at which the sensitivity change of the first output is greatest with respect to a change in the sleeper direction at the setting position of the assumed wheel load is identified as a first position. In addition, the method includes a load application test process in which a wheel load, a lateral force and a tangential force are applied to a wheel having a strain gauge attached at a first position, a second output of the strain gauge bridge is measured, and a relational expression between the magnitude and position of the load and the second output is calculated. In addition, the method includes a contact position estimation step of measuring a third output of the strain gauge bridge while running the wheel on the rail, calculating the load acting on the wheel, and substituting the third output and the calculated load into an estimation equation derived from the relational expression, to continuously calculate the first contact position between the wheel and the rail in the sleeper direction over the entire circumference of the wheel.
[0010] Since the strain gauge is attached at the first position where the change in sensitivity of the first output is greatest, noise resistance is improved and the wheel contact position can be detected with high accuracy. For the wheel load, lateral force and tangential force, a relational expression is calculated between the magnitude and position of the load and the second output, so that the wheel contact position can be detected with high accuracy over the entire area of the wheel tread.
[0011] The through hole has a first through hole and a second through hole that are out of phase with each other in the circumferential direction of the wheel. The strain gauge bridge has a first strain gauge bridge that uses strain around the first through hole and a second strain gauge bridge that uses strain around the second through hole. In the load application test process, a first estimation equation corresponding to the first strain gauge bridge and a second estimation equation corresponding to the second strain gauge bridge are calculated as estimation equations, and a corrected estimation equation is calculated by adding the first estimation equation multiplied by the first weighting function and the second estimation equation multiplied by the second weighting function.
[0012] The range in which the sensitivity change of the first estimation equation is large and the range in which the sensitivity change of the second estimation equation is large can be combined to calculate a corrected estimation equation, which makes it possible to detect the wheel contact position continuously and with high accuracy over the entire circumference of the wheel.
[0013] The first weighting function and the second weighting function are functions that exhibit a rectangular wave shape with respect to the second contact position between the wheel and the rail in the circumferential direction. The first weighting function and the second weighting function are set so that the corrected estimation equation monotonically increases and decreases with respect to the first touch position. Since the modified estimation equation increases and decreases monotonically, the solution of the modified estimation equation can be obtained by numerical calculation.
[0014] In the load application test step, a first relational expression corresponding to the first strain gauge bridge and a second relational expression corresponding to the second strain gauge bridge are calculated as relational expressions. In the contact position estimation step, a wheel load and a tangential force are calculated as loads. The calculated wheel load, tangential force, and first contact position are substituted into the first relational expression to calculate a first corrected lateral force, and the calculated wheel load, tangential force, and first contact position are substituted into the second relational expression to calculate a second corrected lateral force. The first corrected lateral force multiplied by the first weighting function and the second corrected lateral force multiplied by the second weighting function are added together to calculate a corrected lateral force. The corrected lateral force, the calculated tangential force, and first contact position are substituted into the first relational expression to calculate the first corrected wheel load, and the corrected lateral force, the calculated tangential force, and first contact position are substituted into the second relational expression to calculate the second corrected wheel load. The corrected wheel load is calculated by adding the first corrected wheel load multiplied by the first weighting function and the second corrected wheel load multiplied by the second weighting function. The corrected lateral force and the corrected wheel load are substituted into the modified estimation formula to calculate the corrected first contact position, which is a corrected value of the first contact position.
[0015] The corrected lateral force and corrected wheel load are calculated taking into account the first contact position, and the corrected first contact position is calculated. This makes it possible to continuously detect the wheel contact position with high accuracy. Effect of the Invention
[0016] According to the present invention, since the strain gauge is attached to the first position where the change in sensitivity of the first output is greatest, noise resistance is improved and the wheel contact position can be detected with high accuracy. For the wheel load, lateral force and longitudinal tangential force, the relationship between the magnitude and position of the load and the second output is calculated, so that the wheel contact position can be detected with high accuracy over the entire area of the wheel tread. [Brief description of the drawings]
[0017] [Figure 1] FIG. 1(a) is a side view of the wheel to be analyzed, and FIG. 1(b) is a front cross-sectional view taken along line II in FIG. 1(a). [Diagram 2] FIG. [Diagram 3] FIG. 2 is an explanatory diagram showing the positions and names of strain gauges. [Figure 4] FIG. 1 is a bridge circuit diagram of a strain gauge for measuring wheel load. [Diagram 5] FIG. 1 is a bridge circuit diagram of a strain gauge for measuring lateral pressure. [Figure 6] FIG. 1 is a bridge circuit diagram of a strain gauge for measuring contact position. [Figure 7] 13 is a graph showing the change in the slope of the contact position bridge output when the attachment position of the contact position strain gauge is changed in the radial direction. [Figure 8] 13 is a graph showing the change in the slope of the contact position bridge output when the attachment position of the contact position strain gauge is changed in the circumferential direction. [Figure 9] FIG. 9(a) shows the target load application position, and FIG. 9(b) is an image of the load application position. [Figure 10] 13 is a graph showing a contact variable of a bridge output when a wheel load is applied. [Figure 11] 13 is a graph showing contact parameters of bridge output when a lateral pressure is applied. [Figure 12] 13 is a graph showing the contact parameters of the bridge output when a tangential force is applied. [Figure 13]FIG. 13(a) is a graph of the first estimation equation of the first system, and FIG. 13(b) is a graph of the derivative of the first estimation equation. [Figure 14] FIG. 14(a) is a graph of the second estimation equation of the second system, and FIG. 14(b) is a graph of the derivative of the second estimation equation. [Figure 15] 1 is a graph of a weighting function of an estimation formula. [Figure 16] FIG. 16(a) is a graph of the modified estimation equation, and FIG. 16(b) is a graph of the derivative of the modified estimation equation. [Figure 17] 1 is a graph of the wheel load calculated using the new continuous method. [Figure 18] 1 is a graph of lateral pressure and corrected lateral pressure calculated using the new continuous method. [Figure 19] 1 is a graph of tangential force calculated by the new continuation method. [Figure 20] 13 is a graph of an estimated contact position. [Figure 21] 1 is a graph showing the wheel load and corrected wheel load calculated using the new continuous method. [Figure 22] 13 is a graph of an estimated touch position and a corrected estimated touch position. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0018] Hereinafter, a method for detecting a contact position between a wheel and a rail according to an embodiment will be described with reference to the drawings. FIG. 1(a) is a side view of the wheel to be analyzed, and FIG. 1(b) is a front cross-sectional view taken along line II in FIG. 1(a).
[0019] In this application, the XYZ Cartesian coordinate system is defined as follows: The X direction is the width direction (sleeper direction) of the wheel W. The +X direction is the inside of the railway vehicle. The +X direction is sometimes referred to as the flange side, and the -X direction is the rim side. The Y direction is the horizontal direction (longitudinal direction of the rail). The Z direction is the vertical direction, and the +Z direction is the upward direction. The radial direction of the wheel W is sometimes referred to as the Z direction. On the other hand, the circumferential direction of the wheel W is defined as the θ direction. The +θ direction is the rotation direction of a right-handed screw progressing in the -X direction.
[0020] The state in which a railway vehicle is stopped on a straight rail is called the standard state. In the standard state, wheel W contacts the rail near reference position R, which is 65 mm in the -X direction from the end in the +X direction. The X coordinate of reference position R is set to 0. The diameter of wheel W is represented by the diameter at reference position R. The diameter of wheel W at reference position R is 804 mm.
[0021] As shown in FIG. 1(a), the wheel W has a boss portion 4, a plate portion 5, and a rim portion 6. An axle (not shown) is inserted into the boss portion 4. The plate portion 5 extends from the outer periphery of the boss portion 4 to the outside in the radial direction of the wheel W. The rim portion 6 is disposed radially outside the plate portion 5. As shown in FIG. 1(b), the thickness of the rim portion 6 in the X direction is greater than the thickness of the plate portion 5 in the X direction. A flange 8 that protrudes radially outward is formed at the end of the rim portion 6 in the +X direction. A tread surface 9 is formed on the outer periphery of the rim portion 6 in the -X direction of the flange 8. The tread surface 9 is formed in a tapered shape that narrows toward the -X direction.
[0022] A plurality of through holes h for measuring wheel load are formed in the plate portion 5. The diameter of the through holes h is 50 mm. The through holes h are formed at a position 285.5 mm away from the center of the wheel in the radial direction. In the example of FIG. 1(a), eight through holes h are formed at equal intervals in the circumferential direction. The through holes h1 to h8 are defined clockwise from the through hole h1 at the 12 o'clock position in FIG. 1(a). The through holes h1 to h8 include a first system of through holes (first through holes) h1, h2, h5, and h6 and a second system of through holes (second through holes) h3, h4, h7, and h8 that are out of phase with each other in the θ direction by 90 degrees.
[0023] At the contact point between wheel W and the rail, the weight of the railway vehicle acts from wheel W to the rail in the Z direction. The reaction force acts from the rail to wheel W as a wheel load in the Z direction. Meanwhile, forces such as centrifugal force when a railway vehicle runs on a curved rail act from wheel W to the rail in the X direction. The reaction force acts from the rail to wheel W as a lateral pressure in the X direction. In addition, the propulsive force of the railway vehicle acts from wheel W to the rail in the Y direction. The reaction force acts from the rail to wheel W as a tangential force in the Y direction.
[0024] When a railway vehicle runs on a curved rail, the wheel W may come into contact with the rail at a point other than the reference position R. In order to evaluate the running safety of the railway vehicle, it is important to detect the contact position (first contact position) between the wheel W and the rail in the sleeper direction with high accuracy. A method for detecting the contact position between the wheel W and the rail will be described below.
[0025] When a wheel load acts on the tread 9 of the wheel W, a strain in the Z direction is generated in the plate portion 5. When the contact position of the wheel W in the X direction changes, the strain in the plate portion 5 changes. If strain is extracted at a position where a small change in the contact position causes a large change in the strain gauge bridge output, the contact position can be detected with high accuracy. A finite element method analysis is performed to find the position (first position) of the plate portion 5 where the sensitivity change in the strain gauge bridge output is the largest.
[0026] (Finite element method analysis) A finite element model of the wheel W was created. The material properties were assumed to be those of ordinary steel, with a density of 80,000 kg / m3, Young's modulus of 206 GPa, and Poisson's ratio of 0.3. Hexagonal elements were used for mesh division. As a boundary condition, the fitting part with the axle was fixed.
[0027] FIG. 2 is an explanatory diagram of the load application conditions. The boundary conditions of the wheel load and the assumed lateral load (hereinafter referred to as the wheel load and the lateral force) were set. The wheel load and the lateral force were set to 50 kN. From the finite element method analysis results and the load application test results in Patent Document 2, it is known that the relationship between the load application position in the sleeper direction (X direction) and the wheel radial direction (Z direction) and the bridge output is linear. Therefore, assuming the load application test described later, the wheel load was applied at positions X=15 mm and -10 mm on the wheel tread. The lateral force was applied at the same Z coordinate position as the reference position R on the wheel back side (flange side) and at a position -15 mm from there. Each load was applied at intervals of 11.25 deg in the wheel circumferential direction (θ direction).
[0028] FIG. 3 is an explanatory diagram of the positions and names of strain gauges. FIG. 3(a) is a side view, and FIG. 3(b) is a front cross-sectional view taken along line III-III in FIG. 3(a). FIG. 4 is a bridge circuit diagram of a strain gauge for measuring wheel load (hereinafter referred to as a wheel load strain gauge). FIG. 5 is a bridge circuit diagram of a strain gauge for measuring lateral pressure (hereinafter referred to as a lateral pressure strain gauge). FIG. 6 is a bridge circuit diagram of a strain gauge for measuring contact position (hereinafter referred to as a contact position strain gauge). In a load test to be described later, a strain gauge is attached at the position shown in FIG. 3, and the output of the bridge circuit in FIGS. 4 to 6 is evaluated. In a finite element method analysis, the output of the bridge circuit is calculated and evaluated from the strain at the position where the strain gauge is attached.
[0029] As shown in Fig. 3, the attachment positions of the wheel load strain gauges (1A, 1B, etc.) are the inner circumferential surfaces of the through holes h1 to h8, the center positions of the through holes h1 to h8 in the radial direction, and both sides of the through holes h1 to h8 in the θ direction. The attachment positions of the lateral pressure strain gauges (1a, 1b, etc.) are on both the front and back sides of the plate portion 5, the same positions as the through holes h1, h3, h5, h7 in the θ direction, and closer to the center of the wheel than the through holes h1, h3, h5, h7 in the radial direction. The attachment positions of the contact position strain gauges (1T1, 1T2, 1F1, 1F2, etc.) are on both the front and back sides of the plate portion 5, the both sides of the through holes h1 to h8 in the θ direction, and near the through holes h1 to h8 in the radial direction. The name of the contact position strain gauge is based on the first letter indicating the number of the through hole h, the second letter indicating the front and back of the wheel (T for the rim side, F for the flange side), and the third letter indicating the left and right of the through hole h (1 for the -θ direction, 2 for the +θ direction). Each strain gauge detects radial strain of the wheel.
[0030] The wire connections of the strain gauge bridge for measuring wheel load (hereinafter referred to as wheel load bridge) shown in FIG. 4 and the strain gauge bridge for measuring lateral pressure (hereinafter referred to as lateral pressure bridge) shown in FIG. 5 are the same as the new continuous method described in Non-Patent Document 3. Strains around four through holes are used for one bridge. The bridge using the strain around the first through holes h1, h2, h5, and h6 is the first system (first strain gauge bridge), and the bridge using the second through holes h3, h4, h7, and h8 is the second system (second strain gauge bridge). Regarding the output of the wheel load bridge shown in FIG. 4, the output of the first system is F1, and the output of the second system is F2. Regarding the output of the lateral pressure bridge shown in FIG. 5, the output of the first system is G1, and the output of the second system is G2.
[0031] The contact position measuring strain gauge bridge (hereinafter referred to as the contact position bridge) shown in Figure 6 has eight circuits (4 circuits x 2 systems) per wheel. The output H1 of the first system is calculated using the following formula 1. The output H2 of the second system is calculated using the following formula 2.
[0032]
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[0033]
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[0034] When the wheel load P (kN), lateral force Q (kN) and tangential force T (kN) are simultaneously acting on a single point on the wheel tread, the wheel load bridge output F i (με), lateral pressure bridge output G i (με) and contact position bridge output H i The relationship between (με) and the magnitude and position of the load can be expressed as Equations 3 to 5.
[0035]
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[0036]
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[0037]
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[0038] where j P and k P are the slope (με / 10kN / mm) and intercept (με / 10kN) (hereafter referred to as contact variable) of the regression line between the load position (in the sleeper direction when the wheel load P and tangential force T are applied, and in the wheel radial direction when the lateral force Q is applied) and the bridge outputs F, G, and H (με / 10kN, second output) in the relationship between the two. The contact variables are functions of the circumferential position θ of the wheel. The subscript irepresents the system (i=1,2). x (mm) and z (mm) are the load application positions (contact positions) in the sleeper direction and radial direction on the wheel tread, respectively, and are defined in a coordinate system with the reference position R of the wheel tread as the origin (see Fig. 9(b)). When the wheel tread shape is known, z can be regarded as a function of x.
[0039] Figures 7 and 8 show the relationship between the contact position bridge output (first output) H i The slope m P 7 is a graph showing the change in strain gauge attachment position. FIG. 7 shows the case where the attachment position of the contact position strain gauge is set to 4 mm from the edge of the through hole h in the circumferential direction and is changed every 10 mm in the radial direction. FIG. 7(a) is an overall view, and FIG. 7(b) is an enlarged view of part VII in FIG. 7(a). FIG. 8 shows the case where the attachment position of the contact position strain gauge is set to 275.5 mm in the radial direction and is changed every 2 mm in the circumferential direction. FIG. 8(a) is an overall view, and FIG. 8(b) is an enlarged view of part VIII in FIG. 8(a).
[0040] From Fig. 7, the maximum radial inclination m P The larger the inclination m is, the closer the contact strain gauge is to the edge of the through hole h. P The same tendency was obtained when a lateral force Q was applied (not shown), so the attachment position of the contact position strain gauge can be determined based on the results when a wheel load P was applied. Based on the above results, the attachment position of the contact position strain gauge was determined to be 275.5 mm in the radial direction (10 mm below the center of the through hole h) and 4 mm from the edge of the through hole h at Z = 275.5 mm (Y = 27 mm in the case of the through hole h1 shown in Figure 1 (a)) so that it could be attached without difficulty in the circumferential direction.
[0041] (Load Loading Test) A load test was carried out on the wheels with contact position strain gauges attached at the above-mentioned positions using a wheel load / lateral force testing device to investigate the relationship between the load application position and the second output. The wheel load P was changed from 0 to 20 to 40 to 60 to 40 to 20 to 0kN while changing the load position in the sleeper direction, and the lateral force Q was changed from 0 to 10 to 30 to 50 to 30 to 10 to 0kN while changing the load position in the wheel radial direction. The tangential force T was changed from 0 to 1 to 3 to 5 to 3 to 1 to 0kN while changing the load position in the sleeper direction, with a wheel load P of 40kN.
[0042] Fig. 9(a) shows the target load application positions, and Fig. 9(b) is an image of the load application positions. With the reference position R as the origin, the wheel load P and tangential force T were applied at the target positions of X = 15, 0, -10, and -25 mm. The lateral force Q was applied at the target positions of Z = 0, 8, 13, and 18 mm. The contact variables (slope and intercept) of the relational expressions 3 to 5 were obtained through the load application tests.
[0043] Figure 10 shows the bridge output F when the wheel load P is applied. i ,G i ,H i FIG. 10(a) shows the contact parameters of the P ,s P ,m P and Fig. 10(b) shows the intercept k P ,t P ,n P It is. Figure 11 shows the bridge output F when a lateral force Q is applied. i ,G i ,H i FIG. 11(a) shows the contact parameters of the Q ,s Q ,m Q and Fig. 11(b) shows the intercept k Q ,t Q ,n Q It is. Figure 12 shows the bridge output F when a tangential force T is applied. i ,G i ,H i FIG. 12(a) is a graph showing the contact parameters of the T ,sT ,m T and Fig. 12(b) shows the intercept k T ,t T ,n T It is. Subscripts on bridge output, slope and intercept i represents the bridge system (i=1,2). The relational equation for the first system is the first relational equation, and the relational equation for the second system is the second relational equation.
[0044] In the above-mentioned finite element method analysis, the contact variables of the relational expressions 3 to 5 were obtained. The contact variables obtained by the load test were roughly consistent with the contact variables obtained by the finite element method analysis. Therefore, the contact position (attachment position of the strain gauge) can be determined by the finite element method analysis. According to Fig. 12, the wheel load P and lateral pressure Q as well as the tangential force T are i ,G i ,H i It has been confirmed that it has an effect on
[0045] (Contact position estimation) When the contact position (second contact position) θ between the wheel and rail in the wheel circumferential direction is known, and P, Q, T and bridge outputs F, G, H (με, third output) are obtained, the contact position x in the sleeper direction can be obtained by solving any of Equations 3 to 5 for x. The new continuous method described in Non-Patent Document 3 is an example of a method for continuously obtaining P, Q, and T acting on a rotating wheel. However, when the contact position moves from the center of the tread, such as when the flange makes contact, the lateral force Q obtained by the new continuous method is superimposed with the apparent lateral force due to the wheel load P. In addition, the bridge output F is less sensitive than the bridge outputs G and H, and is therefore easily affected by noise. Therefore, Equation 4 is solved for Q to obtain Equation 7. By shifting the right side of Equation 5 to the left side, f i (x, θ). Formula 7 is expressed as f i Substituting (x, θ), we obtain Equation 6 (hereinafter referred to as the estimation equation).
[0046]
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[0047]
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[0048] In Equation 6, f1(x,θ) is the first estimation equation of the first system, and f2(x,θ) is the second estimation equation of the second system. The loads P and T obtained by the new continuation method using the outputs F and G of the third output, the outputs G and H, and the contact variable at the circumferential position θ are substituted into the estimation equation shown in Equation 6. Then, f i By solving (x, θ) = 0, the contact position x between the wheel and the rail in the sleeper direction can be obtained. θ is obtained from the encoder pulse attached to the end of the axle.
[0049] FIG. 13(a) is a graph of the first estimated equation f1 of the first system, and FIG. 13(b) is a graph of the derivative f1' of the first estimated equation f1. FIG. 14(a) is a graph of the second estimated equation f2 of the second system, and FIG. 14(b) is a graph of the derivative f2' of the second estimated equation f2. Note that FIG. 13 and FIG. 14 are graphs in the case where P=40kN, Q=0kN, and T=0kN are loaded at x=0mm. Also, due to the symmetry of the contact variables, only the representative circumferential position θ between 0 and 180deg is shown. Each bridge has two systems, but the contact position can be calculated by the estimated equation using either system. However, the following points must be noted.
[0050] In the first system shown in Figure 13, the sign of f1' is constant when θ=0, 45, 67.5, 135, 157.5, and 180 deg. Therefore, f1 increases and decreases monotonically, and there is one intersection with the x-axis. However, when θ=90 deg, the sign of f1' changes at x=25 mm, and there are two intersections between f1 and the x-axis. Also, when θ=0, 45, and 180 deg, the absolute value of f1' in the vicinity of x=0 is approximately 5 με / mm, but at θ=135 deg, it is small, less than 1 με / mm.
[0051] In the second system shown in Figure 14, the sign of f2' is constant and the absolute value is large when θ = 90 and 135 deg. The sign is constant and the absolute value is small when θ = 45 deg. The sign changes when θ = 0 and 180 deg. In this way, the second system shows a tendency for the phase to be shifted by 90 deg from the first system.
[0052] f i If there are multiple solutions to the estimation equation that satisfy =0, it is difficult to selectively obtain a solution using numerical calculations. i If the absolute value of ´ is small, a slight f i Since the contact position x varies greatly with the change in f, the calculation error of the contact position x increases. i It is necessary that the sign of ´ is constant and its absolute value is large.
[0053] Therefore, the estimation formula for each system f i By weighting (x, θ) according to the circumferential position and adding them up, an equation g(x, θ) (hereinafter referred to as a corrected estimation equation) is set as shown in the following Equation 8. Then, by solving g=0, the contact position (hereinafter referred to as an estimated contact position) x is calculated.
[0054]
number
[0055] In Equation 8, w1 and w2 are functions that determine the weights of f1 and f2 (hereinafter, referred to as weighting functions of the estimation equation). w1 is the first weighting function of the first system, and w2 is the second weighting function of the second system.
[0056] Figure 15 is a graph of the weighting functions w1 and w2 of the estimation formula. The weighting functions w1 and w2 of the estimation formula are rectangular waves in order to use different systems depending on the circumferential position θ. The angle required for the rise of the rectangular wave is 6 deg, and they are connected by a straight line.
[0057] FIG. 16(a) is a graph of the corrected estimation equation g, and FIG. 16(b) is a graph of the derivative g' of the corrected estimation equation g. Note that FIG. 16 is a graph in the case where P=40kN, Q=0kN, and T=0kN are loaded at x=0mm, similar to FIG. 13 and FIG. 14. As shown in FIG. 16(b), the absolute value of g' in the vicinity of x=0mm is large, about 4 to 5με / mm at any θ. In addition, the sign of g' is constant, and as shown in FIG. 16(a), g increases and decreases monotonically, and there is one intersection with the x-axis. Therefore, by using the corrected estimation equation g(x,θ), the estimated contact position x can be calculated with high accuracy over the entire circumference of the wheel.
[0058] Using the calculated estimated contact position x, the lateral force Q can be calculated by correcting the influence of the contact position x using the relational expression in Equation 7. This operation obtains the lateral forces Q1 and Q2 of two systems. That is, by substituting the wheel load P, tangential force T, and estimated contact position x into Equation 7 (first relational expression) of the first system, the first corrected lateral force Q1 of the first system is obtained. By substituting the wheel load P, tangential force T, and estimated contact position x into Equation 7 (second relational expression) of the second system, the second corrected lateral force Q2 of the second system is obtained. However, the calculation error increases at the circumferential positions where the sensitivity of each contact variable is low. Therefore, the weighting functions w1 and w2 of the corrected estimation formula are applied mutatis mutandis, and the first corrected lateral force Q1 and the second corrected lateral force Q2 are combined into one by the operation of Equation 9 below. Hereinafter, this lateral force will be called the corrected lateral force Qcorr.
[0059]
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[0060] (Verification of accuracy of estimated contact position) To verify the validity of the proposed method, we conducted a desk study using the following procedure. (1) As the initial condition, P=40kN, Q=10kN, and T=10kN were applied at the position x=30mm. This condition corresponds to a state in which the wheel is running on a curved rail, the throat of the wheel flange (the flange base end) is in contact with the rail, and the wheel is subjected to the above load. Then, using formulas 3 to 5, the provisional bridge outputs F, G, and H are calculated for 600 points around the wheel circumference. (2) Calculate P and T using the new continuation method described in Non-Patent Document 3. Then, solve the non-linear equation expressed by Equation 8 to obtain the estimated contact position x.
[0061] Fig. 17 is a graph of the wheel load P calculated by the new continuation method. Fig. 18 is a graph of the lateral force Q and corrected lateral force Qcorr calculated by the new continuation method. Fig. 19 is a graph of the tangential force T calculated by the new continuation method. Fig. 20 is a graph of the estimated contact position x. Hereinafter, the difference between the initial condition and the calculation result will be referred to as the calculation error.
[0062] As shown in Fig. 17, a calculation error of up to about 2 kN was found for the wheel load P. As shown in Fig. 18, a steady calculation error of about 4 kN was found for the lateral force Q. These calculation errors were found because the contact position x moved to the throat of the flange, whereas the new continuation method did not take into account the change in the contact position x. However, the corrected lateral force Qcorr was almost consistent with the initial conditions. As shown in Fig. 19, the calculation error of the tangential force T was small, at a maximum of about 1 kN. As shown in Fig. 20, the calculation error of the estimated contact position x was generally about ±1 mm.
[0063] From the above results, it was confirmed that the contact position x can be calculated continuously using the proposed method, although calculation errors in the wheel load P calculated using the new continuation method may result in calculation errors of about ±1 mm in the estimated contact position. It was also found that the effect of changes in the contact position x on the tangential force T calculated using the new continuation method is smaller than that on the wheel load P and lateral force Q. It was also found that the effect of calculation errors in the wheel load P and estimated contact position x on the corrected lateral force Qcorr is small.
[0064] (Recalculation of estimated contact position) From the above verification results, it was found that the new continuous method cannot take into account the effects of movement of the contact position x, and therefore the calculation error of the wheel load P using the new continuous method affects the accuracy of the estimated contact position x. Therefore, we will consider a method of recalculating the wheel load P using the estimated contact position x, and then recalculating the estimated contact position x using the recalculated wheel load P (hereinafter referred to as the corrected wheel load Pcorr).
[0065] The corrected wheel load Pcorr is calculated using Equation 10 and Equation 11, which are modifications of Equation 3.
[0066]
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[0067]
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[0068] The wheel loads P1 and P2 of the two systems are obtained by using Equation 10. That is, by substituting the corrected lateral force Qcorr, tangential force T, and estimated contact position x into Equation 10 (first relational expression) of the first system, the first corrected wheel load P1 of the first system is obtained. By substituting the corrected lateral force Qcorr, tangential force T, and estimated contact position x into Equation 10 (second relational expression) of the second system, the second corrected wheel load P2 of the second system is obtained. In Equation 11, the weighting functions w1 and w2 of the modified estimation formula are applied mutatis mutandis, and the first corrected wheel load P1 and the second corrected wheel load P2 are combined into one to obtain the corrected wheel load Pcorr.
[0069] In addition, the wheel load P in formula 7 used when calculating the corrected lateral force Qcorr is the wheel load P calculated using the new continuation method. Additionally, both tangential forces T are values calculated using the new continuation method. The corrected wheel load Pcorr and the corrected lateral force Qcorr are substituted into the estimation formula shown in formula 12 below, weighted using formula 8, and then x is solved. Below, x calculated in this way is referred to as the corrected estimated contact position (corrected first contact position) xcorr.
[0070]
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[0071] Figure 21 is a graph of the wheel load P and corrected wheel load Pcorr calculated by the new continuous method. It was confirmed that the calculation error of the corrected wheel load Pcorr was reduced compared to the wheel load P calculated by the new continuous method. 22 is a graph of the estimated contact position x and the corrected estimated contact position xcorr. It was confirmed that the calculation error of the corrected estimated contact position xcorr is reduced compared to the estimated contact position x. As described above, by using the proposed method, the wheel contact position can be detected continuously and with high accuracy.
[0072] As described in detail above, the method of detecting the contact position between a wheel W and a rail in this invention includes a finite element analysis process in which a boundary condition of the wheel load P assumed load is set on a finite element model of the wheel W and a finite element analysis is performed, strains around the through hole h in the plate portion 5 of the wheel W are extracted to calculate a first output H of the strain gauge bridge, and the strain extraction position at which the sensitivity change of the first output H is greatest with respect to changes in the sleeper direction at the setting position of the wheel load P assumed load is identified as the first position. In addition, the method includes a load application test process in which a wheel load P, a lateral force Q and a tangential force T are applied to a wheel W having a strain gauge attached at a first position to measure the second outputs F, G, H of the strain gauge bridge, and the contact variables in equations 3 to 5, which are equations relating the magnitude of the loads P, Q, T and the load positions x, z to the second outputs F, G, H, are calculated. In addition, the method includes a contact position estimation process in which the wheel W is made to run on the rail to measure the third output of the strain gauge bridge, the loads P and T acting on the wheel W are calculated, and the third output and the calculated loads P and T are substituted into the estimation equation of Equation 6 derived from the relational equations of Equations 4 and 5 to continuously calculate the contact position x between the wheel W and the rail in the sleeper direction over the entire circumference of the wheel W.
[0073] Since the strain gauge is attached at the first position where the change in sensitivity of the first output H is greatest, noise resistance is improved and the contact position x of the wheel W can be detected with high accuracy. For the wheel load P, lateral force Q and tangential force T, the contact variables in equations 3 to 5, which are the relational expressions between the magnitude of the loads P, Q, T and the load positions x, z and the second outputs F, G, H, are calculated, so that the contact position x of the wheel W can be detected with high accuracy over the entire area of the tread 9 of the wheel W.
[0074] The through holes h have first through holes h1, h2, h5, h6 and second through holes h3, h4, h7, h8 that are out of phase with each other in the circumferential direction θ of the wheel W. The strain gauge bridge has a first strain gauge bridge that uses strains around the first through holes h1, h2, h5, h6 and a second strain gauge bridge that uses strains around the second through holes h3, h4, h7, h8. In the contact position estimation step, a first estimation formula f1 corresponding to the first strain gauge bridge and a second estimation formula f2 corresponding to the second strain gauge bridge are calculated as estimation formulas, and the first estimation formula f1 multiplied by the first weighting function w1 and the second estimation formula f2 multiplied by the second weighting function w2 are added together to calculate a corrected estimation formula g.
[0075] The range in which the sensitivity change of the first estimation formula f1 is large and the range in which the sensitivity change of the second estimation formula f2 is large can be combined to calculate the corrected estimation formula g. This makes it possible to obtain the estimated contact position x of the wheel W continuously and with high accuracy over the entire circumference of the wheel W.
[0076] In the load application test step, a first relational expression corresponding to the first strain gauge bridge and a second relational expression corresponding to the second strain gauge bridge are calculated as relational expressions. In the contact position estimation step, a wheel load P and a tangential force T are calculated as loads. The calculated wheel load P and tangential force T and the estimated contact position x are substituted into the first relational expression to calculate a first corrected lateral force Q1, and the calculated wheel load P and tangential force T and the estimated contact position x are substituted into the second relational expression to calculate a second corrected lateral force Q2. The first corrected lateral force Q1 multiplied by the first weighting function w1 and the second corrected lateral force Q2 multiplied by the second weighting function w2 are added together to calculate a corrected lateral force Qcorr. The corrected lateral force Qcorr, the calculated tangential force T and the estimated contact position x are substituted into the first relational expression to calculate a first corrected wheel load P1, and the corrected lateral force Qcorr, the calculated tangential force T and the estimated contact position x are substituted into the second relational expression to calculate a second corrected wheel load P2. The corrected wheel load Pcorr is calculated by adding the first corrected wheel load P1 multiplied by the first weighting function w1 and the second corrected wheel load P2 multiplied by the second weighting function w2. The corrected lateral force Qcorr and the corrected wheel load Pcorr are substituted into the modified estimation formula g to calculate the corrected estimated contact position xcorr, which is the corrected value of the estimated contact position x.
[0077] The corrected lateral force Qcorr and the corrected wheel load Pcorr are calculated taking into account the contact position x, and the corrected estimated contact position xcorr is calculated. This makes it possible to continuously detect the contact position of the wheel W with high accuracy.
[0078] Although one embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and changes, combinations, deletions, etc. of the configuration are also included within the scope that does not deviate from the gist of the present invention. [Explanation of symbols]
[0079] f...estimation formula, f1...first estimation formula, f2...second estimation formula, g...corrected estimation formula, h...through hole, h1,h2,h5,h6...first through hole, h3,h4,h7,h8...second through hole, P...wheel load (load), P1...first corrected wheel load, P2...second corrected wheel load, Pcorr...corrected wheel load, Q...lateral force (load), Q1...first corrected lateral force, Q2...second corrected lateral force, Qcorr...corrected lateral force, T...tangential force (load), W...wheel, w1...first weighting function, w2...second weighting function, x...contact position, estimated contact position (first contact position), xcorr...corrected estimated contact position (corrected first contact position), 5...plate portion.
Claims
1. a finite element analysis process for performing a finite element analysis by setting a boundary condition of an assumed wheel load on a finite element model of a wheel, extracting strain around a through hole in a plate portion of the wheel to calculate a first output of a strain gauge bridge, and identifying, as a first position, a position from which the strain is extracted at which a change in sensitivity of the first output to a change in the sleeper direction of the setting position of the assumed wheel load is the largest; a load application test process for applying loads of a wheel load, a lateral force, and a tangential force to the wheel having the strain gauge attached at the first position, measuring a second output of the strain gauge bridge, and calculating a relational expression between the magnitude and position of the load and the second output; a contact position estimation step of measuring a third output of the strain gauge bridge while the wheel is running on a rail, calculating the load acting on the wheel, and substituting the third output and the calculated load into an estimation equation derived from the relational expression, to continuously calculate a first contact position between the wheel and the rail in the sleeper direction over an entire circumference of the wheel. A method for detecting the contact position between the wheel and the rail.
2. The through hole includes a first through hole and a second through hole that are out of phase with each other in a circumferential direction of the wheel, the strain gauge bridge includes a first strain gauge bridge using strain around the first through hole and a second strain gauge bridge using strain around the second through hole; In the contact position estimation step, a first estimation equation corresponding to the first strain gauge bridge and a second estimation equation corresponding to the second strain gauge bridge are calculated as the estimation equation, and a corrected estimation equation is calculated by adding the first estimation equation multiplied by a first weighting function and the second estimation equation multiplied by a second weighting function.
2. A method for detecting a contact position between a wheel and a rail according to claim 1.
3. the first weighting function and the second weighting function are functions that exhibit a rectangular wave shape with respect to a second contact position between the wheel and the rail in the circumferential direction; 3. The method for detecting a contact position between a wheel and a rail according to claim 2.
4. the first weighting function and the second weighting function are set such that the corrected estimation equation monotonically increases and decreases with respect to the first contact position.
3. The method for detecting a contact position between a wheel and a rail according to claim 2.
5. In the load application test step, a first relational expression corresponding to the first strain gauge bridge and a second relational expression corresponding to the second strain gauge bridge are calculated as the relational expressions; In the contact position estimation step, The wheel load and tangential force are calculated as the load. calculating a first corrected lateral force by substituting the calculated wheel load, the tangential force, and the first contact position into the first relational expression, and calculating a second corrected lateral force by substituting the calculated wheel load, the tangential force, and the first contact position into the second relational expression; Calculating a corrected lateral force by adding the first corrected lateral force multiplied by the first weighting function and the second corrected lateral force multiplied by the second weighting function; calculating a first corrected wheel load by substituting the corrected lateral force, the calculated tangential force, and the first contact position into the first relational expression, and calculating a second corrected wheel load by substituting the corrected lateral force, the calculated tangential force, and the first contact position into the second relational expression; Calculating a corrected wheel load by adding the first corrected wheel load multiplied by the first weighting function and the second corrected wheel load multiplied by the second weighting function; Substituting the corrected lateral force and the corrected wheel load into the modified estimation equation to calculate a corrected first contact position which is a corrected value of the first contact position.
3. The method for detecting a contact position between a wheel and a rail according to claim 2.