Switch rail railhead profile calculation method based on turnout line type

Abstract

The invention belongs to the technical field of rail traffic, and provides a point rail railhead profile calculation method based on a turnout line type, which comprises the following steps of: establishing a rectangular coordinate system Y1O1Z1, discretizing a complete railhead profile of a curved point rail based on the coordinate system, and obtaining coordinate points of potential contact positions of wheel rails; designing a line type according to a turnout plane theory, and obtaining structural size parameters of the switch rail; establishing a rectangular plane coordinate system X1O1Y1, calculating a lead curve equation and a tangent equation based on the coordinate system, and determining a curved switch rail working edge equation; rail head widths of the switch rail at different positions in the longitudinal direction are calculated according to a curved switch rail working edge equation, and height decline values of the switch rail at the different positions in the longitudinal direction are obtained through a linear interpolation method; calculating a transverse movement amount and a vertical movement amount; and by utilizing a coordinate linear transformation strategy of transverse movement first and vertical movement second, transversely moving the complete rail head profile of the curved switch rail by the transverse movement amount and then downwards moving the complete rail head profile of the curved switch rail by the vertical movement amount, and solving an intersection point of the transformed profile and a stock rail oblique tangent to obtain an actual switch rail profile.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit, and particularly relates to a method for calculating the profile of the switch rail head based on the turnout alignment. Background Art

[0002] The turnout is a key device for realizing the transformation of a high-speed train from one track to another. In the switch area, the switch rail forms a path by leaning against the stock rail to achieve the function of changing the track of the turnout. The cross-sectional profile of the switch rail changes continuously along the advancing direction of the train, affecting the position of the wheel-rail contact point and the vibration characteristics of the vehicle. Accurately obtaining the profile of the switch rail head is a prerequisite for ensuring the effectiveness of the vehicle-turnout coupling dynamics simulation, and can also assist in the profile design of the switch rail.

[0003] The traditional profile generation method is to obtain the profiles at other positions by linearly interpolating several key profiles. For example, according to the key cross-sections at the top widths of 15 mm and 25 mm, the profile of the switch rail at the top width of 20 mm can be linearly interpolated. This method requires that the two profiles used for interpolation have the same number of discrete points, and the operation is complex and the accuracy is very limited. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating the profile of the switch rail head based on the turnout alignment. Compared with the traditional method of obtaining the remaining profiles by interpolating several key profiles, the present invention can ensure the accuracy and smoothness of the generated profile.

[0005] To solve its technical problems, the present invention adopts the following technical solutions: A method for calculating the profile of the switch rail head based on the turnout alignment includes the following steps: According to the direction regulations of the standard track system coordinate system, determine that the advancing direction of the train is the positive direction of the X-axis, the right side of the advancing 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, establish a rectangular coordinate system Y1O1Z1, and discretize the complete profile of the curved switch rail based on this coordinate system to obtain the coordinate points of the potential wheel-rail contact positions; According to the turnout plane theory design alignment, obtain the geometric structure dimension parameters of the switch rail area; Establish a plane rectangular coordinate system X1O1Y1, calculate the guide curve equation and the tangent equation based on this coordinate system, and determine the working edge equation of the curved switch rail; Calculate the rail head widths at different longitudinal positions of the switch rail according to the working edge equation of the curved switch rail, and use the linear interpolation method to obtain the height drop values at different longitudinal positions of the switch rail; Calculate the lateral displacement and the vertical displacement according to the geometric structure dimension parameters of the switch rail area, the rail head widths at different longitudinal positions of the switch rail, and the height drop values at different longitudinal positions of the switch rail; Using the "horizontal translation first and then vertical translation" coordinate linear transformation strategy, first horizontally translate the complete rail head profile of the curved switch rail by the horizontal translation amount, and then vertically translate it by the vertical translation amount, and solve the intersection point of the transformed profile and the inclined tangent line of the stock rail to obtain the actual switch rail profile.

[0006] As a further optimization, the origin O1(0, 0) is located 16 mm below the stock rail head and is the reference point for measuring the gauge.

[0007] As a further optimization, the coordinate points of the potential wheel-rail contact positions obtained, that is, the coordinate values of the points above 16 mm below the rail head on the cross-section of the rail.

[0008] As a further optimization, the geometric structure dimension parameters of the switch rail area include the radius of the curved switch rail , the standard gauge , the total length of the tip of the curved switch rail , the distance from the tangent point of the switch rail to the actual tip , the separation value from the theoretical tip to the stock rail , the distance from the actual tip to the theoretical tip and the width of the complete switch rail head .

[0009] As a further optimization, after establishing the plane rectangular coordinate system X1O1Y1 and before calculating the guide curve equation and the tangent equation based on this coordinate system, it further includes: Determine the positions of each key point in this coordinate system according to the geometric structure dimension parameters of the switch rail area.

[0010] As a further optimization, the calculation of the guide curve equation and the tangent equation based on the plane rectangular coordinate system X1O1Y1 and the determination of the working edge equation of the curved switch rail means: Calculate the guide curve equation according to the radius of the curved switch rail and the center coordinate ; Solve the tangent equation according to the tangent point ( , ) and the actual tip of the switch rail (0, 0); Determine the working edge equation of the curved switch rail according to the guide curve equation and the tangent equation.

[0011] As a further optimization, the rail head width at different longitudinal positions of the switch rail is expressed as , and the height drop value at different longitudinal positions of the switch rail is expressed as .

[0012] As a further optimization, the calculated horizontal translation amount is , and the vertical translation amount is .

[0013] 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 switch rail coordinate system by using the coordinate transformation equation, and is used for the switch rail profile design or as the rail profile input for vehicle-switch coupling dynamics.

[0014] The beneficial effects of the present invention are as follows: First, the present invention abandons the traditional method of interpolating other switch rail profiles by using 4-5 key sections, but uses the complete switch rail profile to perform translation transformation based on the turnout line type, improving the generation accuracy of the switch rail profile. Second, in the present invention, only the complete rail head profile and the turnout line type parameters are needed to generate the switch rail profiles at different positions, and the switch rail head reduction value and the rail head width at any position can be further optimized, which can assist in the switch rail profile design. Finally, the present invention can provide a sufficient amount of accurate switch rail profile samples, which can be used as the rail profile input for vehicle-switch coupling dynamics modeling and can meet the requirements of dynamic calculation accuracy. Description of the Drawings

[0015] Figure 1 is a flowchart of a method for calculating the switch rail head profile based on the turnout line type in an embodiment of the present invention; Figure 2 is a cross-sectional view at the end point C of the switch rail in an embodiment of the present invention; Figure 3 is a schematic diagram of the switch rail line type of the No. 18 high-speed turnout in an embodiment of the present invention; Figure 4 is the lead curve and the tangent BD equation in an embodiment of the present invention; Figure 5 is a cross-sectional view at a certain point E of the switch rail in an embodiment of the present invention; Figure 6 is the longitudinal position mm of the basic rail and the switch rail profiles calculated according to this embodiment; Figure 7 is a schematic diagram of coordinate transformation by applying the embodiment of the present invention. Detailed Embodiments

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0017] Embodiment This embodiment provides a method for calculating the profile of the switch rail head based on the turnout line type. For its flowchart, see Figure 1 , where the method includes the following steps: S1. According to the direction regulations of the standard track system coordinate system, determine that the train traveling direction is the positive direction of the X-axis, the right side of the traveling direction is the positive direction of the Y-axis, and the vertical downward direction is the positive direction of the Z-axis; S2. Taking O1(0, 0) as the origin, establish a rectangular coordinate system Y1O1Z1. Based on this coordinate system, discretize the complete profile of the curved switch rail head to obtain the coordinate points of the potential wheel-rail contact positions; S3. According to the turnout plane theory design line type, obtain the geometric structure dimension parameters of the switch rail area; S4. Establish a plane rectangular coordinate system X1O1Y1. Based on this coordinate system, calculate the guide curve equation and the tangent equation, and determine the working edge equation of the curved switch rail; S5. According to the working edge equation of the curved switch rail, calculate the rail head width at different longitudinal positions of the switch rail, and use the linear interpolation method to obtain the height drop values at different longitudinal positions of the switch rail; S6. According to the geometric structure dimension parameters of the switch rail area, the rail head width at different longitudinal positions of the switch rail, and the height drop values at different longitudinal positions of the switch rail, calculate the lateral displacement and the vertical displacement; S7. Using the "lateral displacement first and then vertical displacement" coordinate linear transformation strategy, first laterally displace the complete profile of the curved switch rail by the lateral displacement amount, and then vertically displace it by the vertical displacement amount, and solve the intersection point of the transformed profile and the inclined tangent line of the stock rail to obtain the actual switch rail profile.

[0018] In this embodiment, on the one hand, this embodiment can obtain the true switch rail profiles at other longitudinal positions by translating and cutting the complete profile of the switch rail. Compared with the traditional method of interpolating the remaining profiles relying on several key profiles, the method of profile translation can ensure the accuracy and smoothness of the generated profiles; on the other hand, this embodiment can establish a rectangular coordinate system according to the turnout line type, calculate the working edge equation of the switch rail, and determine the translation amounts of the complete profiles of the switch rail at different longitudinal positions, including the lateral displacement and the vertical displacement of , and this parametric translation method can quickly generate a sufficient number of profile samples, thereby meeting the accuracy requirements of dynamic calculations.

[0019] It should be noted that the method of this embodiment is not only applicable to the switch rail of the separated half-cut type turnout, but also applicable to other line type turnouts such as the tangent type, the secant type, and the semi-secant type. At the same time, the method of this embodiment is not only applicable to the calculation of the switch rail profile of the No. 18 turnout, but also applicable to the switch rails of other models such as No. 9, No. 12, No. 42, and No. 60 turnouts.

[0020] In the specific application process, the above method of this embodiment is implemented through the following specific steps: Step 1: Establish a Y1O1Z1 rectangular coordinate system, discretize the complete rail head profile of the curved switch rail, and obtain the coordinate values of each point on the cross-section. Figure 2 is a schematic cross-section at the end point C of the switch rail. In the coordinate system Y1O1Z1, the origin O1(0, 0) and the point F( , 0) are located 16 mm below the rail head, and the width of the complete switch rail head is . Discretize the complete rail head profile (curve ) to obtain the coordinates of each point. Part of the results are shown in Table 1; Table 1. Discrete points of the complete rail head cross-section of the curved switch rail (partial data)

[0021] Step 2: According to the plane theory design line type of the turnout, confirm the geometric structure dimension parameters of the switch rail area. As Figure 3 shows, taking the curved switch rail of the No. 18 turnout on the passenger dedicated line as an example, the geometric structure dimension parameters of its switch rail area include the radius of the curved switch rail , the standard gauge , the total length of the tip of the curved switch rail , the distance from the tangent point of the switch rail to the actual tip , the separation value from the theoretical tip to the stock rail , the distance from the actual tip to the theoretical tip and the width of the complete switch rail head .

[0022] Step 3: Establish a plane rectangular coordinate system, calculate the equation of the lead curve and the tangent equation, determine the working edge equation of the curved switch rail, and calculate the rail head width at different positions along the longitudinal direction (X1 direction) of the switch rail. As Figure 4 shows, establish the coordinate system X1O1Y1, and the point O1 is the origin (0, 0) of the coordinate system, which coincides with the actual tip B of the switch rail. Combining 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 lead curve where the theoretical tip A and the tangent point D are located is an arc, and it satisfies the equation: (1) Among them, the abscissa of the tangent point D , and its ordinate . Determine the tangent BD equation from the actual tip B point and the tangent point D: (2) Determine the working edge equation of the curved switch rail according to the tangent equation and the derivative curve equation: (3) The coordinates of any point E on the working edge of the curved switch rail can be determined from this equation ( x , y ), where y is the rail head width, and its measurement point is usually below the top surface of the rail head.

[0023] Step 4: According to the design scheme of the switch rail, use the linear interpolation method to obtain the height drop values of the switch rail at different longitudinal positions (in the X1 direction). Taking the 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 drops of the curved switch rail with respect to the stock rail are 18.5 mm, 9.9 mm, 1.7 mm, 1.2 mm, and 0 mm respectively. Use linear interpolation to obtain the height drop values at other longitudinal positions , and the results are shown in Table 2; Table 2. Relative height drop of the curved switch rail with respect to the stock rail

[0024]

[0025] Step 5: Use the "transverse translation first and then vertical translation" coordinate linear transformation strategy to find the intersection point of the rail head profile and the oblique tangent of the stock rail, and obtain the rail head profiles at each longitudinal position of the switch rail. As shown in Figure 5 , in the coordinate system Y1O1Z1, the rail head profile is first translated to the left by , and then translated downward by . Taking the point F ( , 0) as an example, after translation, the point F1 ( , 0) is obtained. This point coincides with the midpoint E of Figure 4 . Calculate the intersection point H of the rail head profile and the line O1G. Then, the combination of O1H and the curve is the rail head profile of the switch rail at the E section. Among them, the line O1H satisfies the following equation: (4) For example, to solve the switch rail profile at x = 5000 mm, according to formula (3), the rail head width y = 25.9 mm is solved. According to the interpolation result of the rail top height, is obtained. The result of the calculated rail head profile in the coordinate system Y1O1Z1 is as shown in Figure 6As shown, the horizontal and vertical coordinates respectively represent the horizontal and vertical distances from a certain point to the origin O1 in the coordinate system Y1O1Z1.

[0026] Step Six: If necessary, the rail head profile data can be translated into other coordinate systems by using plane coordinate transformation. For example, Figure 7 As shown, 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 between the coordinate system Y1O1Z1 and the coordinate system Y2O2Z2 is: (5) Where: represents the horizontal distance from the center O2 of the basic rail head to the origin O1.

[0027] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, various changes and modifications can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the profile of a switch rail head based on a turnout line shape, characterized in that: The steps include: According to the direction regulations of the standard track system coordinate system, the train travel direction is determined to be the positive direction of the X axis, the right side of the travel direction is the positive direction of the Y axis, and vertically downward is the positive direction of the Z axis; With O1 (0, 0) as the origin, a rectangular coordinate system Y1O1Z1 is established. Based on this coordinate system, the complete rail head profile of the curved rail is discretized to obtain the coordinate points of the potential wheel-rail contact position. Design the line shape according to the turnout plane theory and obtain the geometric structure size parameters of the point rail area; Establish a plane rectangular coordinate system X1O1Y1, calculate the guide curve equation and tangent equation based on the coordinate system, and determine the working edge equation of the curved rail; The rail head width at different longitudinal positions of the point rail is calculated according to the working edge equation of the curved point rail, and the height drop value at different longitudinal positions of the point rail is obtained by linear interpolation method; The lateral displacement and the vertical displacement are calculated according to the geometric structure dimension parameters of the point rail area, the rail head width at different positions along the longitudinal direction of the point rail, and the height drop values ​​at different positions along the longitudinal direction of the point rail; The coordinate linear transformation strategy of "first lateral shift and then vertical shift" is used to first transversely shift the complete rail head profile of the curved point rail by the lateral shift amount and then move it downward by the vertical shift amount. The intersection of the transformed profile and the basic rail tangent line is solved to obtain the actual point rail profile.

2. The method for calculating the profile of the switch rail head based on the turnout line shape according to claim 1, characterized in that: The origin O1 (0, 0) is located 16 mm below the rail head of the stock rail and is the reference point for measuring the track gauge.

3. The method for calculating the profile of the switch rail head based on the turnout line shape according to claim 1, characterized in that: The coordinate points of the potential wheel-rail contact positions obtained are the coordinate values ​​of each point on the rail cross section that is more than 16 mm below the rail head.

4. The method for calculating the rail head profile of a switch rail based on the turnout line shape according to claim 1, characterized in that: The geometrical dimension parameters of the point rail area include the radius of the curved point rail , Standard track gauge , Total length of the curved point rail tip , the distance from the point of intersection of the pointed rail to the actual tip , the separation value from the theoretical tip to the basic orbit , the distance from the actual tip to the theoretical tip and full point rail head width .

5. The method for calculating the rail head profile of a switch rail based on the turnout line shape according to claim 4, characterized in that: After establishing the plane rectangular coordinate system X1O1Y1 and before calculating the derivative curve equation and the tangent line equation based on the coordinate system, it also includes: The positions of the key points in the coordinate system are determined according to the geometric structure size parameters of the point rail area.

6. The method for calculating the rail head profile of a switch rail based on the turnout line shape according to claim 4, characterized in that: The calculation of the guide curve equation and the tangent equation based on the plane rectangular coordinate system X1O1Y1 and the determination of the working edge equation of the curved rail refers to: According to the radius of the curved rail and the center coordinates Calculate the guide curve equation; According to the cut point ( , ) and the actual tip of the point rail (0, 0) to solve the tangent equation; The working edge equation of the curved rail is determined based on the guide curve equation and the tangent equation.

7. The method for calculating the profile of the switch rail head based on the turnout line shape according to claim 4, characterized in that: The rail head width of the point rail at different longitudinal positions is expressed as , the height drop value of the point rail at different longitudinal positions is expressed as .

8. The method for calculating the profile of the switch rail head based on the turnout line shape according to claim 7, characterized in that: The calculated lateral displacement is , the vertical displacement is .

9. A method for calculating the profile of a switch rail head based on a turnout line shape according to any one of claims 1 to 8, characterized in that: After obtaining the rail head profile data in the rectangular coordinate system Y1O1Z1, the coordinate transformation equation is used to translate the rail head profile data in the rectangular coordinate system Y1O1Z1 to the basic rail coordinate system or the point rail coordinate system for point rail profile design or as rail profile input for vehicle-turnout coupling dynamics.

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