A method for calculating a rail head profile of a switch rail based on a switch line type

Abstract

The present application belongs to the field of rail transit technology, and proposes a method for calculating the rail head profile of a switch rail based on the line type of a turnout: a rectangular coordinate system Y1O1Z1 is established, the complete rail head profile of the curved switch rail is discretized based on the coordinate system to obtain coordinate points of potential wheel-rail contact positions; the structural size parameters of the switch rail are obtained according to the design of the line type based on the theory of the turnout plane; a planar rectangular coordinate system X1O1Y1 is established, the guide curve equation and tangent line equation are calculated based on the coordinate system, and the working edge equation of the curved switch rail is determined; the rail head width of the switch rail at different longitudinal positions is calculated according to the working edge equation of the curved switch rail, and the height drop value of the switch rail at different longitudinal positions is obtained by using the linear interpolation method; the horizontal displacement and vertical displacement are calculated; the complete rail head profile of the curved switch rail is first horizontally displaced by the horizontal displacement and then vertically displaced by the vertical displacement by using the coordinate linear transformation strategy of 'horizontal displacement first and then vertical displacement', the intersection of the transformed profile and the oblique tangent line of the basic rail is obtained to obtain the actual profile of the switch rail.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit technology, in particular to a method for calculating a rail head profile of a switch rail based on a switch line type. BACKGROUND

[0002] Switches are key equipment for realizing the change of a high-speed train from one track to another, and in a switch area, a switch rail forms a passage by abutting against a basic rail to realize the change of a switch. The cross-sectional profile of the switch rail changes along the direction of train advancement, which affects the position of wheel-rail contact points and the vibration characteristics of a vehicle. Accurate acquisition of the rail head profile of the switch rail is a prerequisite for ensuring the effectiveness of vehicle-switch coupling dynamics simulation, and can also assist in the design of the profile of the switch rail.

[0003] The traditional profile generation method is to obtain the profiles at other positions through linear interpolation of several key profiles, for example, the profile of the switch rail at a top width of 20mm can be generated through linear interpolation according to the key cross sections at top widths of 15mm and 25mm. This method requires that the two profiles used for interpolation have the same number of discrete points, and the operation is complex and the precision is very limited. SUMMARY

[0004] The present application aims to provide a method for calculating a rail head profile of a switch rail based on a switch line type, which can ensure the precision and smoothness of the generated profile compared to the traditional method of obtaining the remaining profiles through interpolation of several key profiles.

[0005] The present application solves the technical problem by adopting the technical solution of:

[0006] A method for calculating a rail head profile of a switch rail based on a switch line type, comprising the following steps:

[0007] According to the direction specification of the standard track system coordinate system, the direction of train advancement is determined as the positive direction of the X axis, the right side of the direction of train advancement is the positive direction of the Y axis, and the vertical downward direction is the positive direction of the Z axis;

[0008] A rectangular coordinate system Y1O1Z1 is established with O1(0, 0) as the origin, and the complete rail head profile of the curved switch rail is discretized based on the coordinate system to obtain the coordinate points of the potential wheel-rail contact positions;

[0009] According to the theoretical design line type of the switch plane, the geometric structure size parameters of the switch rail area are obtained;

[0010] A plane rectangular coordinate system X1O1Y1 is established, the equation of the guide curve and the tangent line are calculated based on the coordinate system, and the equation of the working edge of the curved switch rail is determined;

[0011] The rail head width of the switch rail at different longitudinal positions is calculated according to the equation of the working edge of the curved switch rail, and the height drop value of the switch rail at different longitudinal positions is obtained by using the linear interpolation method;

[0012] According to the geometric structure size parameters of the frog area, the rail head width at different longitudinal positions of the frog, and the height drop value at different longitudinal positions of the frog, the lateral displacement and the vertical displacement are calculated;

[0013] By using the "first lateral displacement and then vertical displacement" coordinate linear transformation strategy, the complete rail head profile of the curved frog is first laterally displaced by the lateral displacement, and then vertically displaced by the vertical displacement. The intersection of the transformed profile and the tangent line of the basic rail is obtained to obtain the actual frog profile.

[0014] As a further optimization, the origin O1(0, 0) is located 16 mm below the rail head of the basic rail, which is a reference point for measuring the track gauge.

[0015] As a further optimization, the obtained coordinate points of the potential wheel-rail contact positions, i.e., the coordinate values of each point above 16 mm below the rail head on the rail cross section.

[0016] As a further optimization, the geometric structure size parameters of the frog area include the curved frog radius , the standard track gauge , the total length of the curved frog tip , the distance from the frog tangent point to the actual tip , the separation value from the theoretical tip to the basic rail , the distance from the actual tip to the theoretical tip , and the complete frog rail head width .

[0017] As a further optimization, after establishing the plane rectangular coordinate system X1O1Y1, and before calculating the tangent equation and the tangent equation based on the coordinate system, it further includes:

[0018] According to the geometric structure size parameters of the frog area, the positions of the key points in the coordinate system are determined.

[0019] As a further optimization, the calculation of the tangent equation and the tangent equation based on the plane rectangular coordinate system X1O1Y1, and the determination of the curved frog working edge equation, means that:

[0020] According to the curved frog radius and the center coordinates , the tangent equation is calculated;

[0021] According to the tangent point ( , ) and the actual frog tip (0, 0), the tangent equation is solved;

[0022] According to the tangent equation and the tangent equation, the curved frog working edge equation is determined.

[0023] As a further optimization, the rail head width at different longitudinal positions of the frog is represented as , and the height drop value of the frog at different longitudinal positions is represented as .

[0024] As a further optimization, the calculated lateral displacement is , and the vertical displacement is .

[0025] As a further optimization, after obtaining the rail head profile data in the rectangular coordinate system Y1O1Z1, the rail head profile data in the rectangular coordinate system Y1O1Z1 is translated into the basic rail coordinate system or the frog coordinate system using a coordinate transformation equation, for frog profile design or as a rail profile input for vehicle-frog coupling dynamics.

[0026] The beneficial effects of the present application are: first, the present application discards the traditional method of obtaining other frog profiles by interpolating 4-5 key sections, and instead uses the complete frog profile based on the turnout alignment for translation transformation, improving the generation accuracy of the frog profile, second, in the present application, only the complete rail head profile and the turnout alignment parameters are needed to generate the frog profile at different positions, which can further optimize the frog head drop value and the rail head width at any position, and can assist in the profile design of the frog, finally, the present application can provide sufficient and accurate frog profile samples, which can be used as a rail profile input for vehicle-frog coupling dynamics modeling, and can meet the accuracy requirements of dynamic calculation. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a flowchart of a frog rail head profile calculation method based on turnout alignment in an embodiment of the present application;

[0028] Figure 2 is a cross-sectional view of the end point C of the frog in an embodiment of the present application;

[0029] Figure 3 is a schematic diagram of the No. 18 high-speed turnout frog alignment in an embodiment of the present application;

[0030] Figure 4 is the equation of the guide curve and the tangent BD in an embodiment of the present application;

[0031] Figure 5 is a cross-sectional view of a certain point E of the frog in an embodiment of the present application;

[0032] Figure 6 is the basic rail and frog profile at a longitudinal position of mm calculated according to the present embodiment;

[0033] Figure 7A schematic diagram for applying the embodiment of the present application to coordinate transformation is shown. DETAILED DESCRIPTION

[0034] To make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0035] EMBODIMENT

[0036] The embodiment provides a calculation method of a point rail head profile based on a turnout line type, and a flowchart is shown in the figure. Figure 1 The method comprises the following steps.

[0037] S1, according to the direction specification of the standard track system coordinate system, determining that the train running direction is the positive direction of the X axis, the right side of the running direction is the positive direction of the Y axis, and the vertical downward direction is the positive direction of the Z axis.

[0038] S2, establishing a rectangular coordinate system Y1O1Z1 with O1(0, 0) as the origin, discretizing the complete point rail head profile based on the coordinate system, and obtaining the coordinate points of the potential wheel-rail contact positions.

[0039] S3, obtaining the geometric structure size parameters of the point rail region according to the turnout plane theoretical design line type.

[0040] S4, establishing a plane rectangular coordinate system X1O1Y1, calculating the tangent curve equation and tangent line equation based on the coordinate system, and determining the working edge equation of the point rail.

[0041] S5, calculating the head width of the point rail at different longitudinal positions according to the working edge equation of the point rail, and obtaining the height drop value of the point rail at different longitudinal positions by using the linear interpolation method.

[0042] S6, calculating the horizontal displacement and vertical displacement according to the geometric structure size parameters of the point rail region, the head width of the point rail at different longitudinal positions, and the height drop value of the point rail at different longitudinal positions.

[0043] S7, using the "horizontal displacement first and then vertical displacement" coordinate linear transformation strategy, horizontally displacing the complete point rail head profile by the horizontal displacement first, and then vertically displacing the complete point rail head profile by the vertical displacement, solving the intersection points of the transformed profile and the tangent line of the basic rail, and obtaining the actual point rail profile.

[0044] In this embodiment, on the one hand, the actual switch rail profile at other longitudinal positions can be obtained by translating and cutting the complete switch rail profile. Compared with the traditional method of obtaining the remaining profiles by interpolating a few key profiles, the profile translation method can ensure the accuracy and smoothness of the generated profile. On the other hand, this embodiment can establish a rectangular coordinate system according to the turnout alignment, calculate the working side equation of the switch rail, and determine the translation amount of the complete switch rail profile at different longitudinal positions, including the lateral translation amount. and vertical displacement are This parametric translation method can quickly generate a sufficient number of profile samples, thereby meeting the accuracy requirements of dynamic calculations.

[0045] It should be noted that the method of this embodiment is not only applicable to the switch rails of the separated half-cut type turnout, but also to other line types such as tangent type, secant type, and half-secant type turnouts. Furthermore, the method of this embodiment is not only applicable to the calculation of the switch rail profile of No. 18 turnout, but also to the switch rails of other types such as No. 9, No. 12, No. 42, and No. 60 turnouts.

[0046] In practical applications, the above method of this embodiment is implemented through the following specific steps:

[0047] Step 1: Establish a Y1O1Z1 rectangular coordinate system, discretize the complete rail head profile of the curved point rail, and obtain the coordinate values ​​of each point on the cross section. Figure 2 This is a schematic diagram of the cross-section at the end point C of the switch rail. In the coordinate system Y1O1Z1, the origin O1 (0, 0) and point F ( ,0) Located 16 mm below the rail head, the width of the complete switch rail head is Discrete complete track head profile (curve) The coordinates of each point were obtained, and some results are shown in Table 1.

[0048] Table 1. Discrete points of the complete railhead section of the curved-point rail (partial data)

[0049]

[0050] Step 2: Design the track alignment based on the turnout's planar theoretical design, and confirm the geometric dimensions of the switch rail area. For example... Figure 3 As shown, taking the curved switch rail of the No. 18 turnout on the passenger dedicated line as an example, the geometric dimensional parameters of its switch rail area include the radius of the curved switch rail. Standard gauge Total length of the tip of the curved switch rail The distance from the point of contact of the switch rail to the actual tip Phase separation value from theoretical tip to basic orbit The distance between the actual tip and the theoretical tip and the width of the complete switch rail head .

[0051] Step three, establish a plane rectangular coordinate system, calculate the tangent curve equation and tangent equation, determine the curve rail working edge equation, calculate the rail head width at different positions along the longitudinal direction (X1 direction) of the rail. As shown in Figure 4 , the coordinate system X1O1Y1 is established, and the point O1 is the origin (0, 0) of the coordinate system, which coincides with the actual tip B of the rail. Combined with Figure 3 , the coordinates of each key point are obtained, the theoretical tip A ( , ), the actual tip B (0, 0), and the tip end point C ( , 0). The tangent curve on which the theoretical tip A and the tangent point D are located is a circular arc, which satisfies the equation:

[0052] (1)

[0053] The abscissa of the tangent point D is , and the ordinate is . The tangent BD equation is determined by the actual tip B point and the tangent point D:

[0054] (2)

[0055] According to the tangent equation and the tangent curve equation, the curve rail working edge equation is determined:

[0056] (3)

[0057] The coordinates of any point E on the curve rail working edge can be determined by the equation x , y , where y is the rail head width, and the measurement point is usually below the top surface of the rail head.

[0058] Step four, according to the design scheme of the rail, the linear interpolation method is used to obtain the height drop value of the rail at different positions along the longitudinal direction (X1 direction). Taking No. 18 turnout as an example, at the longitudinal positions x = 0, 964 mm, 3855 mm, 6574 mm, 8604 mm, 10970 mm, the relative height drop of the curve rail to the basic rail is 18.5 mm, 9.9 mm, 1.7 mm, 1.2 mm and 0 mm respectively, and the height drop value at other longitudinal positions is obtained by linear interpolation , and the results are shown in Table 2.

[0059] Table 2. Relative height drop of curve rail to basic rail

[0060]

[0061] Step five, find the intersection of the rail head profile and the basic rail tangent line by using the "first horizontal translation and then vertical translation" coordinate linear transformation strategy, and obtain the rail head profile at each position of the switch rail. As shown in the figure, Figure 5 , the rail head profile is first translated horizontally , and then translated vertically . Taking point F ( , 0) as an example, the translated point F1 ( , 0) is obtained, which coincides with the midpoint E. The intersection H of the rail head profile and the straight line O1G is calculated, and the combination of O1H and the curve Figure 4 is the rail head profile of the switch rail at the E section, wherein the straight line O1H satisfies the following equation:

[0062] (4)

[0063] For example, to solve the switch rail profile at x = 5000 mm, the rail head width y = 25.9 mm is obtained according to formula (3), and is obtained according to the rail top height interpolation result. The calculated rail head profile in the coordinate system Y1O1Z1 is shown in the figure, Figure 6 , wherein the horizontal and vertical coordinates represent the horizontal and vertical distances of a point in the coordinate system Y1O1Z1 to the origin O1.

[0064] Step six, the rail head profile data can be translated into other coordinate systems as needed by using plane coordinate transformation. As shown in the figure, Figure 7 , after obtaining the profile data in the coordinate system Y1O1Z1, the rail head profile in the basic rail coordinate system Y2O2Z2 or in the switch rail coordinate system Y3O3Z3 can be obtained by using coordinate transformation. The transformation equation of the coordinate system Y1O1Z1 and the coordinate system Y2O2Z2 is:

[0065] (5)

[0066] wherein: represents the horizontal distance from the basic rail head center O2 to the origin O1.

[0067] The above is only a preferred embodiment of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.​

Claims

1. A method for calculating a rail head profile of a switch rail based on a turnout line type, characterized in that, It comprises the following steps: According to the direction specification of the standard track system coordinate system, the train running direction is determined as the positive direction of the X axis, the right side of the running direction is the positive direction of the Y axis, and the vertical downward direction is the positive direction of the Z axis; Taking O1(0, 0) as the origin, a rectangular coordinate system Y1O1Z1 is established, and the coordinates of the potential wheel-rail contact positions are obtained by discretizing the complete rail head profile of the curve rail based on the coordinate system; According to the theoretical design line of the turnout plane, the geometric structure size parameters of the switch region are obtained; A plane rectangular coordinate system X1O1Y1 is established, the guide curve equation and tangent line equation are calculated based on the coordinate system, and the working edge equation of the curve rail is determined; According to the working edge equation of the curve rail, the rail head width at different longitudinal positions of the rail is calculated, and the height drop value at different longitudinal positions of the rail is obtained by using the linear interpolation method; According to the geometric structure size parameters of the switch region, the rail head width at different longitudinal positions of the rail, and the height drop value at different longitudinal positions of the rail, the horizontal displacement and vertical displacement are calculated; By using the "horizontal displacement first and vertical displacement second" coordinate linear transformation strategy, the complete rail head profile of the curve rail is first horizontally displaced by the horizontal displacement, and then vertically displaced by the vertical displacement, and the intersection of the transformed profile and the oblique tangent line of the basic rail is calculated to obtain the actual rail profile.

2. The method according to claim 1, wherein, The origin O1(0, 0) is located 16 mm below the rail head and is the reference point for measuring the track gauge.

3. The method according to claim 1, wherein, The obtained coordinate points of the potential wheel-rail contact positions are the coordinate values of each point above 16 mm below the rail head on the rail cross section.

4. The switch rail head profile calculation method based on the turnout line type according to claim 1, characterized in that, Geometric dimension parameters of the said switch region include curve switch radius , standard gauge , total length of curve switch tip , distance from switch point to actual tip , separation value from theoretical tip to basic rail , distance from actual tip to theoretical tip and complete switch nose width .

5. The method according to claim 4, wherein, After the plane rectangular coordinate system X1O1Y1 is established, and before the guide curve equation and tangent line equation are calculated based on the coordinate system, it further comprises: According to the geometric structure size parameters of the switch region, the positions of the key points in the coordinate system are determined.

6. The method according to claim 4, wherein, The guide curve equation and tangent line equation are calculated based on the plane rectangular coordinate system X1O1Y1, and the working edge equation of the curve rail is determined, which means: According to the curve rail radius and the center coordinates Calculate the guide curve equation; According to the tangent point ( , Solve the tangent equation using the actual tip of the switch rail (0, 0); The working edge equation of the curve rail is determined according to the guide curve equation and tangent line equation.

7. The method according to claim 4, wherein, The rail head width at different longitudinal positions of the point rail is denoted by The height drop at different longitudinal positions of the point rail is denoted by .

8. The method according to claim 7, wherein, The calculated lateral shift amount is , and the vertical shift amount is .

9. The method according to any one of claims 1-8, wherein, After obtaining the rail head profile data in the rectangular coordinate system Y1O1Z1, the rail head profile data in the rectangular coordinate system Y1O1Z1 is translated into the basic rail coordinate system or the switch rail coordinate system by using the coordinate transformation equation, which is used for switch rail profile design or as the input of the rail profile for vehicle-turnout coupling dynamics.

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