Wheel-rail contact point calculation method

Abstract

The present disclosure provides a wheel-rail contact point calculation method, comprising the following steps: S1, wheel-rail local coordinate system and global coordinate system selection; S2, wheelset posture description mode selection; S3, wheel and rail profile segmentation fitting; S4, wheel-rail profile penetration amount calculation; S5, obtaining wheel-rail contact point position, wherein step S2 adopts Euler parameters. The method adopts the technical route of the trace method based on profile fitting, and adopts Euler parameters instead of Euler angles in the wheelset posture description mode selection link, thereby improving the universality of the posture description of the wheel-rail contact point solving algorithm, solving the singular problem of Euler angles, and enabling the algorithm to be conveniently integrated into multi-body dynamics solving.

Description

Technical Field

[0001] This disclosure relates to the field of wheel-rail contact analysis for rail vehicles, and in particular to a method for calculating wheel-rail contact points. Background Technology

[0002] Wheel-rail contact point calculation is a crucial and indispensable part of locomotive and rolling stock dynamics calculations. Currently, contact point calculation methods are mainly divided into two categories: mesh-based enumeration methods and profile-fitting-based trajectory methods. Mesh-based enumeration methods are relatively slower, but have a wider range of applications for complex profiles after wear; profile-fitting-based trajectory methods are faster and suitable for real-time calculations, but their applicability to different profiles is limited.

[0003] In existing technologies, the trajectory method based on profile fitting uses Euler angles in the wheelset attitude description stage, which can lead to Euler angle singularities. In the calculation of the maximum wheel-rail profile penetration, the interpolation method is used, which can result in errors in the obtained contact points.

[0004] Therefore, existing technologies still urgently need improvement. Summary of the Invention

[0005] One of the technical problems to be solved by this disclosure is to provide a method for calculating wheel-rail contact points. It adopts the technical route of the trajectory method based on profile fitting. By replacing Euler angles with Euler parameters in the selection of wheelset attitude description method, the versatility of the attitude description of the wheel-rail contact point solution algorithm is improved, the Euler angle singularity problem is solved, and it can be easily integrated into multibody dynamics solution.

[0006] To solve the above-mentioned technical problems, this disclosure provides a method for calculating wheel-rail contact points, including the following steps: S1, selection of wheel-rail local coordinate system and global coordinate system; S2, selection of wheelset attitude description method; S3, segmented fitting of wheel and rail profiles; S4, calculation of wheel-rail profile penetration; S5, obtaining the wheel-rail contact point position, wherein step S2 uses Euler parameters.

[0007] In some embodiments, step S4 employs the iterative method based on the derivative information of the profile fitting curve.

[0008] In some embodiments, step S2 adopts a 3-1-3 rotation sequence, where the rotation sequence is first head shaking followed by side rolling.

[0009] In some embodiments, the Euler parameter calculation formula in step S2 is as follows:

[0010]

[0011] Where θ0, θ1, θ2 and θ3 are Euler parameters, φ is the roll angle and ψ is the head-up angle.

[0012] In some embodiments, the coordinate transformation matrix in step S2 is:

[0013]

[0014] In some embodiments, step S4 includes the following sub-steps:

[0015] S4.1 Calculation of piecewise matching point pairs for wheel-rail profile function;

[0016] S4.2 Calculation of the maximum penetration amount of wheel-rail profile.

[0017] In some embodiments,

[0018] In step S4.1, the potential contact point of the wheelset is C(h) w (yw)sinα,yw,h w (yw)cosα), where: α is the leading angle or lagging angle, h w Let y be the rolling circle radius at different positions of the vehicle profile, and yw be the lateral coordinate of the wheelset's local coordinate system.

[0019] In some embodiments, the formula for calculating the leading angle or lagging angle α is:

[0020]

[0021] In some embodiments, the coordinates C of the points on the wheelset profile in step S4.1 in the global coordinate system are... wg for:

[0022] C wg =T T C+{0,Y wg Z wg}

[0023] Where: Y wg and Z wg These represent the lateral and vertical displacements of the wheelset in global coordinates, respectively.

[0024] In some embodiments, step S4.2 includes the following sub-steps:

[0025] The piecewise fitting function for the wheel-rail profile is obtained through step S3, and the wheel-rail profile penetration is d(y). w Its derivative is d′(y). w ), where: y w The x-coordinate of the wheelset's local coordinate system;

[0026] The Newton-Raphson iteration method is used to select the key point Y0 within the penetration range, calculate its d′(Y0), and calculate its horizontal coordinate increment Δ0, then calculate Y1 = Y0 + Δ0; then calculate its d′(Y1), and calculate its horizontal coordinate increment Δ1, then calculate Y2 = Y1 + Δ1, and repeat this process until the tolerance is met, obtaining the maximum value d(Y0). N and the x-coordinate Y of the wheelset profile in local coordinate system N .

[0027] According to the above technical solution, this disclosure provides a method for calculating wheel-rail contact points. The method adopts the technical route of the trajectory method based on profile fitting. By replacing Euler angles with Euler parameters in the selection of wheelset attitude description method, the versatility of the attitude description of the wheel-rail contact point solution algorithm is improved, the Euler angle singularity problem is solved, and it can be easily integrated into multibody dynamics solution. By using the iterative method of the derivative information of the profile fitting curve to calculate the maximum value of wheel-rail profile penetration, the maximum penetration and contact point position can be obtained more accurately. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of this disclosure or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a block diagram of the novel wheel-rail contact point calculation method disclosed herein;

[0030] Figure 2 This is a flowchart of the sub-process for calculating the penetration amount of the wheel-rail profile disclosed herein;

[0031] Figure 3 This is a model diagram of the method for iteratively calculating the maximum horizontal coordinate of the wheel-rail profile penetration amount disclosed in this paper. Detailed Implementation

[0032] The embodiments of this disclosure will be further described in detail below with reference to the accompanying drawings and examples. The detailed description of the embodiments and the accompanying drawings are used to illustrate the principles of this disclosure by way of example, but should not be used to limit the scope of this disclosure. This disclosure can be implemented in many different forms and is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

[0033] These embodiments are provided to make the disclosure thorough and complete, and to fully express the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specifically stated, the relative arrangement of components and steps, material composition, numerical expressions, and values ​​set forth in these embodiments should be interpreted as exemplary only and not as limiting.

[0034] It should be noted that, in the description of this disclosure, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," and "outer," etc., indicating orientation or positional relationship, are only for the convenience of describing this disclosure and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this disclosure. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0035] Furthermore, the terms "first," "second," and similar terms used in this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different parts. "Vertical" is not strictly vertical, but within the permissible margin of error. "Parallel" is not strictly parallel, but within the permissible margin of error. Terms such as "including" or "contains" mean that the element preceding the word encompasses the element listed after the word, and do not exclude the possibility of encompassing other elements as well.

[0036] It should also be noted that, in the description of this disclosure, unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this disclosure depending on the specific circumstances. When a particular device is described as being located between a first device and a second device, an intermediary device may or may not be present between the particular device and the first or second device.

[0037] All terms used in this disclosure have the same meaning as understood by one of ordinary skill in the art to which this disclosure pertains, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries should be interpreted as having meanings consistent with their meanings in the context of the relevant art, and not as idealized or highly formalized, unless expressly defined herein.

[0038] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification.

[0039] This invention discloses a method for calculating wheel-rail contact points, such as... Figure 1 As shown, the method includes the following steps: S1, selection of wheel-rail local coordinate system and global coordinate system; S2, selection of wheelset attitude description method; S3, segmented fitting of wheel and rail profiles; S4, calculation of wheel-rail profile penetration; S5, obtaining the wheel-rail contact point position, wherein step S2 uses Euler parameters.

[0040] In some embodiments, step S4 employs the iterative method based on the derivative information of the profile fitting curve.

[0041] In some embodiments, step S2 adopts a 3-1-3 rotation sequence, where the rotation sequence is first head shaking followed by side rolling.

[0042] In some embodiments, the Euler parameter calculation formula in step S2 is as follows:

[0043]

[0044] Where θ0, θ1, θ2 and θ3 are Euler parameters, φ is the roll angle and ψ is the head-up angle.

[0045] In some embodiments, the coordinate transformation matrix in step S2 is:

[0046]

[0047] In some embodiments, such as Figure 2 As shown, step S4 includes the following sub-steps:

[0048] S4.1 Calculation of piecewise matching point pairs for wheel-rail profile function;

[0049] S4.2 Calculation of the maximum penetration amount of wheel-rail profile.

[0050] In some embodiments,

[0051] In step S4.1, the potential contact point of the wheelset is C(h) w (yw)sinα,yw,h w (yw)cosα), where: α is the leading angle or lagging angle, h w Let y be the rolling circle radius at different positions of the vehicle profile, and yw be the lateral coordinate of the wheelset's local coordinate system.

[0052] In some embodiments, the formula for calculating the leading angle or lagging angle α is:

[0053]

[0054] In some embodiments, the coordinates C of the points on the wheelset profile in step S4.1 in the global coordinate system are...wg for:

[0055] C wg =T T C+{0,Y wg, Z wg}

[0056] Where: Y wg and Z wg These represent the lateral and vertical displacements of the wheelset in global coordinates, respectively.

[0057] In some embodiments, step S4.2 includes the following sub-steps:

[0058] The piecewise fitting function for the wheel-rail profile is obtained through step S3, and the wheel-rail profile penetration is d(y). w Its derivative is d′(y). w ), where: y w The x-coordinate of the wheelset's local coordinate system;

[0059] like Figure 3 As shown, the key point Y0 of the penetration range is selected using Newton's iteration method, its d′(Y0) is calculated, and its horizontal coordinate increment Δ0 is calculated, and Y1 = Y0 + Δ0 is calculated; then its d′(Y1) is calculated, and its horizontal coordinate increment Δ1 is calculated, and Y2 = Y1 + Δ1 is calculated. This process is repeated until the tolerance is met, and the maximum value d(Y0) is obtained. N and the x-coordinate Y of the wheelset profile in local coordinate system N ...

[0060] The embodiments of this disclosure have now been described in detail. To avoid obscuring the concept of this disclosure, some details known in the art have not been described. Those skilled in the art can fully understand how to implement the technical solutions disclosed herein based on the above description.

[0061] While specific embodiments of this disclosure have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of this disclosure. Those skilled in the art should understand that modifications can be made to the above embodiments or equivalent substitutions can be made to some technical features without departing from the scope and spirit of this disclosure. In particular, as long as there is no structural conflict, the technical features mentioned in the various embodiments can be combined in any manner.

Claims

1. A method for calculating wheel-rail contact points, characterized in that, Includes the following steps: S1. Selection of local and global coordinate systems for wheel-rail systems; S2. Selection of wheelset attitude description method; S3, segmented fitting of wheel and rail profiles; S4. The wheel-rail profile penetration amount is calculated by using the derivative information iteration method of profile fitting curve; S5. Obtain the position of the wheel-rail contact point. In step S2, Euler parameters are used; Step S4 includes the following sub-steps: S4.1 Calculation of piecewise matching point pairs for wheel-rail profile function; S4.2 Calculation of the maximum penetration amount of wheel-rail profile; In step S4.1, the potential contact point of the wheelset is ,in: Leading angle or lagging angle The rolling circle radius at different positions of the vehicle profile. The horizontal coordinate of the wheelset's local coordinate system; Step S4.2 includes the following sub-steps: The piecewise fitting function for the wheel-rail profile is obtained through step S3, and the wheel-rail profile penetration is... Its derivative is ; The key point Y0 of the penetration range is selected using Newton's iteration method, and its value is calculated. And calculate its x-axis increment. ,calculate Then calculate its And calculate its x-axis increment. ,calculate This process is repeated until the tolerance is met and the maximum value is obtained. and the x-coordinate of the wheelset profile in local coordinate system .

2. The method for calculating wheel-rail contact points according to claim 1, characterized in that, Step S2 adopts a 3-1-3 rotation sequence, which is to first shake the head and then roll to the side.

3. The method for calculating wheel-rail contact points according to claim 2, characterized in that, The formula for calculating the Euler parameters in step S2 is as follows: Where: θ0 is the first Euler parameter, θ1 is the second Euler parameter, θ2 is the third Euler parameter, and θ3 is the fourth Euler parameter. For roll angle, It is the head-shaking angle.

4. The method for calculating wheel-rail contact points according to claim 3, characterized in that, The coordinate transformation matrix in step S2 is: 。 5. The method for calculating wheel-rail contact points according to claim 4, characterized in that, The leading angle or lagging angle The calculation formula is: 。 6. The method for calculating wheel-rail contact points according to claim 5, characterized in that, The coordinates of the points on the wheelset profile in the global coordinate system in step S4.1 for: in These represent the lateral and vertical displacements of the wheelset in global coordinates, respectively.

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