Parametric design method of fixed frog rail and wing rail profile considering geometric characteristics

Abstract

The application provides a parameterized design method for fixed frog rail and wing rail profile considering geometric characteristics, belongs to the technical field of target identification, and can realize high-precision reconstruction of the profile of the fixed frog rail and the wing rail, so that the profile parameter adjustment of the rail and the wing rail is more targeted and predictable; can automatically execute processes such as drawing, design, modification and output, and compared with a traditional design method, the method has significant advantages in profile fitting accuracy and reconstruction efficiency; with the aid of the parameterized design method, the design rail and wing rail type can be flexibly adjusted, and rapid parameterized reconstruction of the fixed frog rail and wing rail structure is realized.

Description

Technical Field

[0001] This invention relates to the field of railway turnout frog rail profile technology, specifically to a parametric design method for the profiles of fixed frog point rail and wing rail considering geometric characteristics. Background Technology

[0002] Fixed frogs are core components of railway turnout systems and also weak links in the track structure. The structural discontinuity between the center rail and wing rails in the hazardous space causes severe wheel-rail impact and dynamic response when train wheelsets pass. With the rapid development of my country's railways towards high-speed and heavy-haul operation, the service environment of rails in the frog area is becoming increasingly harsh, leading to frequent defects such as wear, peeling, crushing, and fatigue cracks, seriously affecting the safety and stability of train operation.

[0003] Optimizing the rail profile in the frog area is a key means to improve wheel-rail contact, reduce wheel-rail impact load, slow down rail wear, and extend the service life of the frog. However, the current common method for reconstructing the profile of a fixed frog is to first obtain the key cross-sectional profile through standard turnout design drawings or field measurements, modify and adjust the key profile based on experience, and finally use discretization to obtain dense data points of the rail profile, and then use linear interpolation to complete the fitting of other cross-sectional profiles. Existing designs mostly use traditional methods to adjust a single cross-section, lacking a systematic description of the longitudinal variable cross-sectional characteristics of the frog rail and wing rail; it cannot achieve rapid modification driven by parameters such as "rail top slope" or "gauge angle radius". Summary of the Invention

[0004] The purpose of this invention is to provide a parametric design method for the profile of a fixed frog center rail and wing rail that considers geometric features, transforming the structural geometric features of the frog into control parameters, and using NURBS theory to achieve high-precision reconstruction of the profile, thereby solving at least one of the technical problems existing in the background art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides a parametric design method for the profiles of a fixed frog point rail and wing rail considering geometric features, comprising:

[0007] Based on the structural characteristics of the fixed frog, feature parameters describing the geometric morphology of the frog section and the wing section are extracted;

[0008] A coordinate system is established with the center axis of the center track and the track gauge measurement point of the wing track as the reference. Based on the characteristic parameters, a profile control boundary composed of straight line segments and circular arc segments is constructed, and the coordinates of key control points are calculated by analytical geometry method.

[0009] Local profile data points are added between the circular curves of the center rail and the wing rail profiles, and the coordinates of each point are calculated. Then, based on the NURBS curve, a high-precision parametric profile of the center rail and the wing rail cross sections is constructed by combining specific weight vectors and node vector configurations.

[0010] The key control points and local profile data points are used as control vertices of the NURBS curve. Combined with preset weight vectors and node vectors, parameterized profiles of arbitrary cross sections of the center track and the wing track are constructed.

[0011] As a further limitation of the first aspect of the present invention, NURBS curves are used for profile fitting, with the number of control vertices being m+1, the curve order being k, and the total number of nodes being m+k+2; these control points {N} are connected sequentially. j} and {W j} forms the profile control boundary; k represents the order of the B-spline basis function; {Q j} is the control vertex {N j} and {W j The corresponding weighting coefficients, and the weights of each control point on the center rail and wing rail are determined comprehensively based on the changes in the profile curvature.

[0012] As a further limitation of the first aspect of the present invention, the geometric characteristic parameters of the fixed frog point rail and wing rail are determined based on the geometric characteristics of the point rail and wing rail reflected in the standard design drawing of the fixed frog, specifically including the cross slope k of the point rail top. n1 , Track gauge and longitudinal slope k n2 Half width of the top surface of the center track w n The height h of the top rail above the gauge measurement point n , Track gauge angle radius r n Longitudinal slope k of the working side of the wing rail w1 wing rail top cross slope k w2 , longitudinal slope k of non-working side of wing rail w3 Half width of the top surface of the wing rail w w1 The height h of the wing rail above the gauge measurement point w1 The left side arc of the wing rail head w1 The right-side arc of the wing rail head. w2 .

[0013] As a further limitation of the first aspect of the present invention, the method for determining control point coordinates involves the profiles of the center rail and the wing rail. For the center rail profile, utilizing the symmetry characteristic of the center rail's central axis, a single-sided profile is selected for parameterization. The main control points determined include the center rail vertex N1, the control point N2 of the straight section of the rail top, the upper tangent point N3 of the gauge angle arc, the lower tangent point N4 of the side arc, the bottom width control point N5, and the center of the side arc N6. For the wing rail profile, a coordinate system is established with the gauge measurement point as the origin. The main control points determined include the wing rail vertex W5, the gauge measurement point W2, the tangent point W3 of the working edge arc, the left tangent point W4 of the rail top arc, the right tangent point W6 of the rail top arc, the tangent point W7 of the non-working edge arc, the auxiliary measurement point W8, and the centers W9 and W1 of the left and right side arcs. 10 .

[0014] As a further limitation of the first aspect of the present invention, the coordinates of the top N1 of the center track and the bottom width control point N5 of the center track are determined according to the geometric height and width-related characteristic parameters of the center track. The coordinates of the center N6 of the side arc are determined by the point-to-straight-line distance formula. The coordinates of the tangent points N3 and N4 between the arc and the straight lines on both sides are calculated by combining the cross slope of the center track top and the longitudinal slope of the track gauge side. The ordinate of the control point N2 of the straight section of the track top is set as the height of the center track, and the abscissa is determined by the control points N1 and N3 according to the fixed ratio point formula, with a proportionality coefficient of λ, thereby completing the construction of all key control points of the center track.

[0015] As a further limitation of the first aspect of the present invention, the track gauge measurement point W2 is the origin of the coordinate system. The coordinates of the wing rail vertex W5 and the auxiliary measurement point W8 are determined according to the geometric characteristic parameters of the wing rail, the top half-width, and the height, as well as the auxiliary measurement parameters. The centers of the left and right arcs W9 and W8 are determined by the point-to-straight-line distance formula. 10 Coordinates, based on the center W9 and W 10 The coordinates of the tangent points W3, W4 and W6, W7 between the arc and the straight lines on both sides are calculated along the transverse slope of the top of the rail and the longitudinal slope of the sides, thus completing the construction of all key control points of the wing rail.

[0016] As a further definition of the first aspect of the present invention, the two endpoints of the arc on the side of the center track are the tangent points N3 and N4 between the arc and the straight segments on both sides. The tangents passing through the two tangent points pass through the center track vertex N1 and the bottom width control point N5, respectively. The distances from the center N6 to the tangents at the two tangent points are equal, both being the radius of the arc of the center track gauge angle. Based on this, the coordinates of the center N6 of the arc of the center track gauge angle are obtained. Then, based on the principle that the tangents at the two tangent points and the intersecting lines perpendicular to them both pass through the center N5, the coordinates of the tangent points N3 and N4 are determined.

[0017] As a further definition of the first aspect of the invention, the two endpoints of the arc on the left side of the wing rail are the tangent points W3 and W4 between the arc and the straight lines on both sides. The tangent lines passing through the two tangent points pass through the gauge measurement point W2 and the wing rail vertex W5, respectively. The distances from the center W9 to the tangent lines at the two tangent points are equal, both being the radius of the arc on the left side of the wing rail head. Based on this, the circular coordinates W9 of the arc on the left side of the wing rail head are obtained. Then, based on the principle that the tangent lines at the two tangent points and their perpendicular intersecting lines all pass through the center W9, the coordinates of the tangent points W3 and W4 are determined. Similarly, the center W of the arc on the right side of the wing rail can be determined. 10 And the coordinates of the two tangent points W6 and W7.

[0018] As a further limitation of the first aspect of the present invention, based on the advantage of NURBS curves in achieving continuous and smooth curve fitting, weight vectors are preset for key control points and profile data points of the center rail and wing rail, and node vectors are calculated to complete the parametric profile reconstruction of arbitrary cross sections of the center rail and wing rail.

[0019] As a further limitation of the first aspect of the present invention, a comprehensive evaluation index including Pearson coefficient, cosine similarity, and distance similarity is introduced to perform correlation analysis on the standard profile and reconstructed profile of each key section. The evaluation index system adopts a comprehensive correlation coefficient Rcomp, which is composed of Pearson correlation coefficient RPearson, cosine similarity RCosine, and distance similarity RDist, and is used to comprehensively evaluate the matching degree between the parameterized model and the standard profile. When Rcomp ≥ 0.90, it is judged to be extremely strongly correlated, which verifies the feasibility of the parameterization method.

[0020] In a second aspect, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the parameterized design method for the profiles of fixed turnout center rail and wing rail considering geometric features as described in the first aspect.

[0021] Thirdly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the parameterized design method for the profile of the fixed turnout center rail and wing rail considering geometric features as described in the first aspect.

[0022] Fourthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the parametric design method for the profiles of fixed turnout center rail and wing rail considering geometric features as described in the first aspect.

[0023] The beneficial effects of this invention are: it can achieve high-precision reconstruction of the profiles of fixed frog point rails and wing rails, making the adjustment of the profile parameters of the point rails and wing rails more targeted and predictable; it can automatically execute processes such as drawing, designing, modifying, and outputting; compared with traditional design methods, this method has significant advantages in both profile fitting accuracy and reconstruction efficiency; with the help of this parametric design method, the design of the point rails and wing rails can be flexibly adjusted to achieve rapid parametric reconstruction of the fixed frog point rail and wing rail structure.

[0024] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the parametric design method for the profiles of fixed turnout center rail and wing rail, taking into account geometric features, as described in an embodiment of the present invention.

[0027] Figure 2 This is a diagram showing the distribution of cardiac track parameters and key control points according to an embodiment of the present invention.

[0028] Figure 3 This is a diagram showing the distribution of wing rail parameters and key control points according to an embodiment of the present invention.

[0029] Figure 4 This is a comparison diagram of the key cross-sectional contour fitting described in an embodiment of the present invention.

[0030] Figure 5 This is a schematic diagram of the parametric reconstruction of the profiles of the center track and the wing track according to an embodiment of the present invention.

[0031] Figure 6 This is a parameterized fitting curve of the 20mm cross-section of the heart track based on different control parameters, as described in an embodiment of the present invention.

[0032] Figure 7 This is a comparison diagram of the fitted profiles under single-factor variations of key parameters of the 20mm cross-section of the track as described in this embodiment of the invention.

[0033] Figure 8 This is a parameterized fitting curve of the 50mm cross-section of the track based on different control parameters, as described in an embodiment of the present invention.

[0034] Figure 9This is a comparison diagram of the fitted profiles under single-factor variations of key parameters of the 50mm cross-section of the track as described in this embodiment of the invention.

[0035] Figure 10 This is a parameterized fitting curve of the wing-rail section based on different control parameters, as described in an embodiment of the present invention.

[0036] Figure 11 This is a comparison diagram of the fitted profiles of the key parameters of the wing-rail section under single-factor variations as described in the embodiments of the present invention. Detailed Implementation

[0037] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0038] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0039] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0040] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0041] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0042] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0043] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0044] Non-uniform rational B-spline curves (NURBS) have the advantage of reconstructing continuous smooth curves using a small number of characteristic parameters, and are widely used in industrial production. The rail head profiles of the center rail and wing rails in a fixed frog area are both continuous smooth curves composed of straight lines and circular arcs. Therefore, parametric reconstruction of the rail profile in the frog area using NURBS curves has significant advantages, making the optimization design of the rail profile in the frog area more targeted and predictable. Based on this, this invention addresses the problems in traditional frog structure optimization, which relies on repeated trial and error adjustments of local geometric profiles for scheme design, and then reconstructs the profile using dense discrete point data. This process suffers from large reconstruction errors, low efficiency, and the inability to achieve global optimization. Therefore, this invention proposes a parametric design method for the rail profile based on the geometric characteristics of the frog profile. This method includes: first, extracting geometric feature parameters of the frog rail and wing rail based on the standard turnout design drawing, including the rail top cross slope, gauge side longitudinal slope, gauge angle radius, and other key arc radii; second, constructing profile control boundaries based on the geometric feature parameters, and accurately determining the coordinates of key control points of the NURBS curve using analytical geometry methods; third, adding local profile data points in the profile circular curve region and calculating the coordinates of each point; then, combining specific weight vectors and node vector configurations, constructing high-precision parametric profiles of the frog rail and wing rail sections based on the NURBS curve; finally, introducing a comprehensive evaluation index including Pearson coefficient, cosine similarity, and distance similarity, and conducting correlation analysis on the standard profiles and reconstructed profiles of each key section to verify the feasibility and rationality of this parametric design method. This invention enables refined fitting and adjustment of the frog profile, realizing the parametric description of complex rail profiles, and providing a new perspective for optimizing rail profile design in fixed frog areas and optimizing rail grinding profiles. It is of great significance for effectively improving wheel-rail contact relationships and extending the service life of turnouts.

[0045] Example 1

[0046] In this embodiment 1, a parametric design system for the profiles of the fixed frog's point rail and wing rail, considering geometric features, is first provided. This system includes: an extraction module, used to extract feature parameters describing the geometric morphology of the point rail and wing rail cross-sections based on the structural characteristics of the fixed frog; an analysis module, used to establish coordinate systems based on the point rail's central axis and the wing rail gauge measurement points, construct profile control boundaries composed of straight line segments and circular arc segments based on the feature parameters, and calculate the coordinates of key control points using analytical geometry methods; a calculation module, used to add local profile data points within the circular curve intervals of the point rail and wing rail profiles, and calculate the coordinates of each point; then, combining specific weight vectors and node vector configurations, a high-precision parametric profile of the point rail and wing rail cross-sections is constructed based on NURBS curves; and a construction module, used to use the key control points and local profile data points as control vertices of the NURBS curves, and combine preset weight vectors and node vectors to construct parametric profiles of arbitrary point rail and wing rail cross-sections.

[0047] In this embodiment, the above-described system is used to implement a parametric design method for the profiles of the fixed frog's point rail and wing rail, considering geometric features. The method first extracts feature parameters. That is, based on the structural characteristics of the fixed frog, feature parameters describing the geometric morphology of the point rail and wing rail cross sections are extracted; the point rail feature parameters include at least the point rail top cross slope (k). n1 ), track gauge and longitudinal slope (k) n2 ) and the radius of the arc of the center track gauge angle (r) n The characteristic parameters of the wing rail include at least the longitudinal slope of the working side of the wing rail (k). w1 ), wing rail top cross slope (k) w2 ), longitudinal slope of non-working side of wing track (k) w3 ) and the left-side arc of the wing rail head (r w1 ), right-side arc of the wing rail head (r) w2 Next, the control point coordinates are calculated. Specifically: coordinate systems are established with the center axis of the center track and the track gauge measurement points of the wing track as references; a profile control boundary composed of straight line segments and circular arc segments is constructed based on the aforementioned characteristic parameters; and key control points (N) are calculated using analytical geometry methods. i W j ,) coordinates; secondly, add local profile data points (N) within the circular curve range of the center track and wing track profiles. pi W pj And complete the coordinate calculation; then, use the key control points and local profile data points as the control vertices of the NURBS curve, and combine them with the preset weight vector (M) and node vector (U) to construct the parameterized profile curve function Prof{N} for arbitrary cross-sections of the center track and the wing track. i , N pi}, Prof{W j W pjFinally, correlation analysis was performed on the standard profiles of the center track and wing track with the parametric reconstructed profiles to evaluate and verify the feasibility and rationality of the parametric fitting method.

[0048] NURBS curves were used for profile fitting, with m+1 control vertices, k curve order, and m+k+2 total nodes. These control points {Q} were then connected sequentially. j} forms the profile control boundary; k represents the order of the B-spline basis function; {Q j} is the control vertex {N j} and {W j The corresponding weighting coefficients, and the weights of each control point on the center rail and wing rail are determined comprehensively based on the changes in the profile curvature.

[0049] The geometric characteristic parameters of the fixed frog point rail and wing rail are determined based on the geometric characteristics of the point rail and wing rail as reflected in the standard design drawings of the fixed frog, specifically including the cross slope k of the point rail top. n1 , Track gauge and longitudinal slope k n2 Half width of the top surface of the center track w n The height h of the top rail above the gauge measurement point n , Track gauge angle radius r n Longitudinal slope k of the working side of the wing rail w1 wing rail top cross slope k w2 , longitudinal slope k of non-working side of wing rail w3 Half width of the top surface of the wing rail w w1 The height h of the wing rail above the gauge measurement point w1 The left side arc of the wing rail head w1 The right-side arc of the wing rail head. w2 .

[0050] The method for determining control point coordinates involves the profiles of the center rail and the wing rail. For the center rail profile, utilizing the symmetry of the center rail's central axis, a single-sided profile is selected for parameterization. The main control points determined include the center rail vertex N1, the control point N2 of the straight section at the rail top, the upper tangent point N3 of the gauge angle arc, the lower tangent point N4 of the side arc, the bottom width control point N5, and the center of the side arc N6. For the wing rail profile, a coordinate system is established with the gauge measurement point as the origin. The main control points determined include the wing rail vertex W5, the gauge measurement point W2, the tangent point W3 of the working edge arc, the left tangent point W4 of the rail top arc, the right tangent point W6 of the rail top arc, the tangent point W7 of the non-working edge arc, the auxiliary measurement point W8, and the centers W9 and W1 of the left and right side arcs. 10The coordinates of the key control points are obtained by simultaneously solving the system of equations for the straight lines and the system of equations for the normal equidistant lines determined by the geometric feature parameters. The coordinates of the top N1 and bottom width control point N5 of the center track are determined based on the geometric height and width-related feature parameters of the center track. The coordinates of the center N6 of the side arc are determined by the point-to-straight-line distance formula. The coordinates of the tangent points N3 and N4 between the arc and the straight lines on both sides are calculated by combining the cross slope of the center track top and the longitudinal slope of the track gauge side. The ordinate of the control point N2 of the straight section at the top of the track is set as the height of the center track, and the abscissa is determined by the control points N1 and N3 according to the formula of a fixed ratio, with a proportionality coefficient of λ, thereby completing the construction of all key control points of the center track.

[0051] The track gauge measurement point W2 is the origin of the coordinate system. The coordinates of the wing rail vertex W5 and the auxiliary measurement point W8 are determined based on the wing rail's geometric characteristic parameters (top surface half-width, height) and auxiliary measurement parameters. The centers of the left and right arcs W9 and W8 are determined using the point-to-straight-line distance formula. 10 Coordinates, based on the center W9 and W 10 The coordinates of the tangent points W3, W4 and W6, W7 between the arc and the straight lines on both sides are calculated along the transverse slope of the top of the rail and the longitudinal slope of the sides, thus completing the construction of all key control points of the wing rail.

[0052] The two endpoints of the arc on the side of the track are the tangent points N3 and N4 between the arc and the straight segments on both sides. The tangents passing through the two tangent points pass through the top N1 and the bottom width control point N5 of the track, respectively. The distance from the center N6 to the tangents at the two tangent points is equal, which is the radius of the track gauge angle arc. Based on this, the coordinates of the center N6 of the track gauge angle arc can be obtained. Then, based on the principle that the tangents at the two tangent points and the intersecting lines perpendicular to them all pass through the center N5, the coordinates of the tangent points N3 and N4 are determined.

[0053] The two endpoints of the arc on the left side of the wing rail are the tangent points W3 and W4 between the arc and the straight lines on both sides. The tangent lines passing through the two tangent points pass through the gauge measurement point W2 and the wing rail vertex W5, respectively. The distances from the center W9 to the tangent lines at the two tangent points are equal, both being the radius of the arc on the left side of the wing rail head. Based on this, the circular coordinates W9 of the arc on the left side of the wing rail head can be obtained. Then, based on the principle that the tangent lines at the two tangent points and their perpendicular intersecting lines all pass through the center W9, the coordinates of the tangent points W3 and W4 can be determined. Similarly, the center W of the arc on the right side of the wing rail can be determined. 10 And the coordinates of the two tangent points W6 and W7.

[0054] In this embodiment, to improve the profile fitting accuracy, local profile data points {N} are added to the circular curve region of the center rail and wing rail profiles. pi}, { W pj The coordinates of each profile data point are determined based on the relevant key control points and profile geometric features.

[0055] In this embodiment, taking advantage of the NURBS curve's ability to achieve continuous and smooth curve fitting using a small number of points, a weight vector (Q) is preset for the key control points and profile data points of the center track and wing track, and a node vector (U) is calculated to complete the parametric profile reconstruction of any cross-section of the center track and the wing track. The profile curve functions of the center track and the wing track are respectively represented as Prof{N i, N pi} and Prof{W j W pj}

[0056] In this embodiment, the evaluation index system adopts the comprehensive correlation coefficient R. comp This coefficient is derived from the Pearson correlation coefficient R. Pearson Cosine similarity R Cosine and distance similarity R Dist Weighted composition is used to comprehensively evaluate the degree of matching between the parametric model and the standard profile; when R comp When the correlation coefficient is ≥0.90, it is determined to be extremely strong, which verifies the feasibility of the parameterization method.

[0057] Example 2

[0058] This embodiment proposes a parametric design method for the profiles of fixed frog point rails and wing rails that considers geometric features. This method transforms the structural geometric features of the frog into control parameters and utilizes NURBS theory to achieve high-precision reconstruction and flexible design of the profiles. Based on Non-Uniform Rational B-Spline Curves (NURBS), this method proposes geometric feature parameters for the point rail and wing rails by defining their profiles, determining key control points, and reconstructing their profiles. By adjusting the geometric feature parameters of the point rail and wing rail profiles, multiple design schemes for the key cross-sectional profiles of the point rail and wing rails are implemented. Correlation analysis with standard profiles verifies the feasibility of this design method, ultimately achieving parametric design of the fixed frog point rail and wing rail profiles.

[0059] In this embodiment, the specific geometric characteristic parameters of the heart track include the cross slope k of the heart track top. n1 , Track gauge and longitudinal slope k n2 Half width of the top surface of the center track w n The height h of the top rail above the gauge measurement point n , Track gauge angle radius r n The geometric characteristic parameter of the wing track profile is the longitudinal slope k of the working side of the wing track. w1 wing rail top cross slope k w2 , longitudinal slope k of non-working side of wing rail w3 Half width of the top surface of the wing rail w w1 wing rail height h w1 Radius r of the left side arc of the wing rail head w1 The radius r of the right arc of the wing rail headw2 , Wing rail auxiliary measurement width w w2 wing rail-assisted height measurement h w2 .

[0060] The key control points of the frog profile in this invention are determined as follows: First, based on the axisymmetric characteristics of the frog of the fixed turnout, the profile on one side of the frog's central axis is selected for parametric design. The frog's central axis is taken as the vertical axis, and the horizontal axis where the gauge measurement point is located is taken as the horizontal axis. Combined with the geometric feature parameters of the frog, the cross slope of the frog top and the longitudinal slope of the frog gauge side intersecting the vertical and horizontal axes can be determined. The two straight lines, the vertical and horizontal axes, and the gauge angle arc form the control boundary of the frog profile. The intersection of the two straight lines with the vertical and horizontal axes and the endpoint of the gauge angle arc are the key control points, which are used to realize the parametric reconstruction of the frog's profile of any cross section.

[0061] In this embodiment, the key control points of the wing rail profile are determined as follows: First, a coordinate system is established with the wing rail gauge measurement point as the origin. Combining the geometric characteristic parameters of the wing rail, the longitudinal slope of the working side of the wing rail, the transverse slope of the top of the wing rail, and the longitudinal slope of the non-working side of the wing rail can be determined. The longitudinal slope of the working side of the wing rail and the transverse slope of the top of the wing rail form a left arc, and the transverse slope of the top of the wing rail and the longitudinal slope of the non-working side of the wing rail form a right arc. The three straight lines and the two arcs on both sides form the control boundary of the wing rail profile. The intersection of the longitudinal slope of the working side of the wing rail with the horizontal coordinate axis, the half-width point of the top surface of the wing rail, the auxiliary measurement of the right wing rail, and the endpoints of the arcs on both sides of the rail head are the key control points, which are used to realize the parametric reconstruction of the wing rail cross-sectional profile.

[0062] In this embodiment, the Non-Uniform Rational B-Spline Curve (NURBS) is essentially a segment of rational polynomial vector functions defined by m+1 control points. Its local support is reflected in the fact that any point on the NURBS curve is only related to its corresponding control vertex and the weight factor influencing that control vertex; its strong convex hull property is reflected in the fact that the control vertices in the NURBS curve form a convex hull containing all the nodes of the curve corresponding to the control vertex; its weight factor characteristic is reflected in the fact that the shape of the curve can be adjusted, and increasing or decreasing the weight factor will cause the curve to move closer to or further away from the control points.

[0063] The characteristics of the NURBS curves described above meet the requirements for fitting the profiles of the center track and the wing track, solving the problem that the profiles of the center track and the wing track cannot be reasonably represented. At the same time, it is convenient to adjust the profiles of the center track and the wing track, and facilitates the comparison of schemes.

[0064] Non-uniform rational B-spline curves (NURBS) are represented as follows:

[0065] ;

[0066] In the formula, {W j} represents the control vertices of the NURBS curve, with a total of m+1 control points. These control points are connected sequentially by {W}.j} forms the profile control boundary; k represents the order of the B-spline basis function; {Q j} is the control vertex {W j The corresponding weighting coefficients; N j,k (u) is a k-th degree non-uniform rational B-spline basis function defined by a recursive formula.

[0067] In this embodiment, based on the characteristic of the central axis symmetry of the heart track profile, a single-sided profile control boundary of the heart track profile is determined by the geometric feature parameters of the heart track profile, such as... Figure 2 As shown.

[0068] The geometric characteristic parameters of the above-mentioned track profile are the cross slope k of the track top. n1 , Track gauge and longitudinal slope k n2 Half width of the top surface of the center track w n The height h of the top rail above the gauge measurement point n , track gauge angle radius r n .

[0069] Based on the aforementioned control boundaries for the cardiac track profile, the key control points {N} for fitting the cardiac track profile can be determined. i = (x i y i )}(i=1,2,…,5,6).

[0070] Six key control points are defined: N1, N2, N3, N4, N5, and N6.

[0071] According to the half-width w of the top surface of the track n Track gauge measurement points and the height h of the track ball. n Parameters are used to determine the coordinates of the top N1 and bottom width control point N5 of the track. Based on analytical geometry, a system of equations for the distance from a point to a line is established to calculate the distances that simultaneously satisfy the conditions: the distance to the top cross slope and the longitudinal slope of the track gauge side are equal and equal to the radius r of the track gauge angle arc. n The coordinates of the center N6 of the circle.

[0072] Based on the position of the center N6, the distance of the arc radius is translated in the opposite direction of the normal vector of the transverse slope of the rail top and the longitudinal slope of the center rail gauge side, and the upper tangent point N3 and the lower tangent point N4 of the gauge angle arc are accurately calculated.

[0073] Based on this, the control point N2 for the straight section of the rail top is determined, and its ordinate is set as the height h of the frog rail. nThe horizontal coordinate is determined by the control points N1 and N3 according to the constant ratio point formula, with a scaling factor of λ. To improve the fitting accuracy of the track profile, in the circular curve region of the track profile, a certain number of local profile data points, denoted as N, are added at equal intervals based on the coordinates of the key control points. pi Based on NURBS curves, weights are set according to the influence of each control point on the profile. Combined with the control point coordinates, the parameterized reconstruction of the profile of any cross-section of the frog's frog is completed. The frog profile curve function is represented as Prof{N}. i , N pi}

[0074] The coordinates of the key control points are as follows:

[0075] ;

[0076] In this embodiment, the profile control boundary of a fixed frog wing rail profile is determined by the geometric feature parameters of the wing rail profile, such as... Figure 3 As shown.

[0077] The geometric characteristic parameters of the above-mentioned wing rail profile are the longitudinal slope k of the working side of the wing rail. w1 wing rail top cross slope k w2 , longitudinal slope k of non-working side of wing rail w3 , half width of the top surface of the wing rail w w1 wing rail height h w1 Radius r of the left side arc of the wing rail head w1 The radius r of the right arc of the wing rail head w2 , Wing rail auxiliary measurement width w w2 1. Wing rail auxiliary measurement of height h w2 .

[0078] Based on the aforementioned profile control boundaries, the key control points {W} for wing track profile fitting can be determined. j = (x j y j )} ( j =1, 2, ..., 9, 10).

[0079] Nine key control points are defined: W5 (the apex of the wing rail), W2 (the gauge measurement point), W3 (the tangent point of the working edge arc), W4 (the tangent point of the left side of the rail top arc), W6 (the tangent point of the right side of the rail top arc), W7 (the tangent point of the non-working edge arc), W8 (the auxiliary measurement point), and W9 and W1 (the centers of the left and right side arcs). 10 .

[0080] Based on the geometric characteristics of the wing rail, a coordinate system is established with the gauge measurement point W2 as the origin. The coordinates of the wing rail apex W5 and the auxiliary measurement point W8 are directly determined based on the wing rail top surface half-width, height, and auxiliary measurement parameters. For the left-side arc of the wing rail, based on analytical geometry, the vertical distances between the longitudinal slope of the working edge and the transverse slope of the rail top are calculated to be equal and both are radii r. w1 The center of the left arc is W9.

[0081] Based on the position of the center W9, the distance of the left arc radius is translated in the opposite direction of the normal vector of the longitudinal slope of the working side of the wing rail and the transverse slope of the top of the wing rail, and the tangent point W3 of the working side arc and the tangent point W4 of the left arc of the top of the rail are calculated.

[0082] For the circular arc on the right side of the wing rail, using the point-to-straight-line distance formula, the radius r is calculated as follows: [Formula missing in original text]. w2 The center of the right arc W 10 Based on the center W 10 The location is determined by translating the arc radius in the opposite direction of the normal vectors of the transverse slope of the rail top and the longitudinal slope of the non-working side, and calculating the tangent point W6 of the arc on the right side of the rail top and the tangent point W7 of the arc on the non-working side.

[0083] In this embodiment, to improve the fitting accuracy of the airfoil profile, a certain number of local profile data points, denoted as W, are added at equal intervals in the circular curve region of the airfoil profile, based on the coordinates of the key control points. pj Based on NURBS curves, weights are assigned according to the influence of each control point on the profile. Combined with the control point coordinates, the profile of any cross-section of the frog wing rail is reconstructed. The wing rail profile curve function is represented as Prof{W}. j, W pj The coordinates of the key control points of the wing track are as follows:

[0084] ;

[0085] Pearson correlation coefficient focuses on linear trends and is insensitive to changes in position and amplitude; cosine similarity measures directional consistency, ignoring position but focusing on shape; distance similarity provides an intuitive point-to-point proximity assessment, comprehensively perceiving differences in position, amplitude, and shape; the comprehensive correlation coefficient, by weightedly integrating the advantages of the first three, forms an evaluation index that can comprehensively assess the accuracy of contour reconstruction. In summary, while each individual method has its own emphasis, the comprehensive correlation coefficient, through an integration strategy, balances the three dimensions of trend, direction, and distance, providing the most reliable overall assessment for curve similarity analysis.

[0086] In this embodiment, based on the comprehensive correlation coefficient, combined with, for example Figure 4As shown, correlation analysis was performed on the parametrically reconstructed profiles of the center rail and wing rail at each key section of the fixed frog and their corresponding standard profiles to evaluate the effectiveness of the method. The correlation coefficients of the profiles of each key section are shown in Table 1.

[0087] Table 1 Evaluation Index of Key Section Profile Fitting Accuracy

[0088]

[0089] In summary, the parametric design method of this embodiment can achieve high-precision reconstruction of the profiles of fixed frog point rails and wing rails, making the adjustment of the rail and wing rail profile parameters more targeted and predictable. This parametric design method can automatically execute processes such as drawing, designing, modifying, and outputting. Compared with traditional design methods, this method has significant advantages in both profile fitting accuracy and reconstruction efficiency. Using this parametric design method, the design of the point rail and wing rail types can be flexibly adjusted, achieving rapid parametric reconstruction of the fixed frog point rail and wing rail structure. Figure 5 As shown. This method is applicable to the parametric design of the profiles of fixed frog point rails and wing rails.

[0090] Example 3

[0091] In this embodiment, addressing the problem of the difficulty in automatically designing and adjusting the profiles of the existing fixed frog point rails and wing rails using parametric methods, a parametric design method for the fixed frog point rails and wing rails considering geometric features is proposed. The basic process of this method is as follows: First, based on the existing standard design drawings of fixed frogs, the morphological features and dimensional parameters of the standard profiles of the point rails and wing rails are analyzed, and the geometric feature parameters in the profile design are thoroughly explored; then, based on the geometric feature parameters of the profiles, the profile control boundaries and profile control points are determined; finally, a corresponding profile reconstruction algorithm is written, and through the input and setting of various parameter variables, the profiles of the fixed frog point rails and wing rails are automatically generated, thereby completing the parametric design process of the point rails and wing rails.

[0092] Based on the geometric characteristic parameters of the standard center rail and wing rail profiles and the geometric control boundary of the profiles, the geometric characteristic parameters required for profile reconstruction are determined. Combined with the coordinates of key control points, curve fitting of the center rail and wing rail profiles is completed based on NURBS curve theory.

[0093] This example, based on the severe wear observed on the top surface of the rail head, the gauge angle arc, and the left arc portion of the wing rail head in operational practice, selects the cross slope k of the center rail head. n1 , Track gauge and longitudinal slope k n2 , Track gauge angle radius r n Longitudinal slope k of the working side of the wing rail w1 wing rail top cross slope k w2 Radius r of the left side arc of the wing rail head w1As the main influencing parameter, a parametric scheme design is carried out for the profile of the fixed frog rail.

[0094] For the 20mm and 50mm cross sections of the frog rail, the cross slope k of the frog rail head was investigated. n1 , Track gauge and longitudinal slope k n2 and the radius r of the track gauge angle. n A three-factor, three-level full-factor experimental design was conducted, resulting in various design schemes (see Tables 2 and 6). The longitudinal slope k of the working side of the wing rail section was then investigated. w1 wing rail top cross slope k w2 and the radius r of the left arc of the wing rail head w1 A three-factor, three-level full-factor experimental design was conducted, and the various design schemes were obtained (see Table 10).

[0095] Table 2. Three-factor, three-level, full-factor experimental design scheme for the 20mm cross-section of the track.

[0096]

[0097] The parameters were fitted using the data in Table 2, and the fitting results are as follows: Figure 6 As shown. To evaluate the influence of various parameters on the cross-sectional profile of the frog rail at 20mm, the data from the following schemes were selected for comparison, as shown in Tables 3, 4, and 5. Table 3 shows the frog rail head cross slope k for each scheme. n1 Changes, track gauge, and longitudinal slope k n2 And the center track gauge angle radius r n constant.

[0098] Table 3 Cross slope k of the center rail head n1 Changed design scheme

[0099]

[0100] Table 4 shows the longitudinal slope k of the track gauge for each scheme. n2 Changes, cross slope of the track head k n1 And the center track gauge angle radius r n constant.

[0101] Table 4. Track gauge and lateral longitudinal slope k of the center track n2 Changed design scheme

[0102]

[0103] Table 5 shows the radius r of the center track gauge angle arc in each scheme. n Changes, cross slope of the track head k n1 And the track gauge and side longitudinal slope k n2 constant.

[0104] Table 5. Track gauge, angle, and radius r of the center track.n Changed design scheme

[0105]

[0106] The parameters were fitted using the data in Tables 3, 4, and 5. The fitting results are as follows: Figure 7 As shown.

[0107] according to Figure 7 And the profile results shown in Tables 3, 4, and 5, the cross slope k of the center track head. n1 An increase in the height of the track profile will cause the top of the track to shift inward and reduce the cross-sectional height; the longitudinal slope k of the track gauge of the track will also affect the track profile. n2 Increasing the angle will significantly improve the steepness of the sidewalls and reduce the robustness of the center rail head; the radius r of the center rail gauge angle arc n The increase in radius causes the overall profile of the track center to converge inward. Through comprehensive comparative analysis, the radius r of the track center gauge angle arc... n The impact on the profile is most significant, as it directly determines the robustness of the profile and the width of the straight section of the rail head, and has a large impact on the wheel-rail contact area.

[0108] Table 6. Three-factor, three-level, full-factor experimental design scheme for the 50mm cross-section of the track.

[0109]

[0110] The parameters were fitted using the data in Table 6, and the fitting results are as follows: Figure 8 As shown. To evaluate the influence of various parameters on the cross-sectional profile of the frog rail at 50mm, the following data were selected for comparison, as shown in Tables 7, 8, and 9. Table 7 shows the frog rail head cross slope k for each scheme. n1 Changes, track gauge, and longitudinal slope k n2 And the center track gauge angle radius r n constant.

[0111] Table 7 Cross slope k of the track head n1 Changed design scheme

[0112]

[0113] Table 8 shows the longitudinal slope k of the track gauge for each scheme. n2 Changes, cross slope of the track head k n1 And the center track gauge angle radius r n constant.

[0114] Table 8 Track gauge and lateral longitudinal slope k of the center track n2 Changed design scheme

[0115]

[0116] Table 9 shows the radius r of the center track gauge angle arc in each scheme.n Changes, cross slope of the track head k n1 And the track gauge and side longitudinal slope k n2 constant.

[0117] Table 9. Track gauge, angle, and radius of the arc r of the center track. n Changed design scheme

[0118]

[0119] The parameters were fitted using the data in Tables 7, 8, and 9. The fitting results are as follows: Figure 9 As shown. According to Figure 9 And the profile results shown in Tables 7, 8, and 9, the cross slope k of the center track head. n1 An increase in the angle will cause the rail top profile to shift inward, reducing the smooth section of the rail top profile; the longitudinal slope k of the center rail gauge side. n2 The increase in size slightly reduces the width of the side rail, which has a certain impact on the robustness of the profile; the radius r of the rail gauge angle arc. n The increase in the angle causes the profile of the heart track to converge inward, reducing its robustness. Through comprehensive comparative analysis, the cross slope k of the heart track head... n1 The impact on the profile is most significant, directly affecting the robustness of the rail head and the profile of the rail top, and has a considerable impact on the wheel-rail contact area.

[0120] Table 10. Three-factor, three-level full-factor experimental design scheme for wing track section

[0121]

[0122] The parameters were fitted using the data in Table 10, and the fitting results are as follows: Figure 10 As shown.

[0123] To evaluate the impact of single factors on the profile of the airfoil rail section, the following data were selected for comparison, as shown in Tables 11, 12, and 13.

[0124] Table 11 shows the longitudinal slope k of the working side of the wing rail in each scheme. w1 Changes, cross slope k at the top of the wing rail w2 The radius r of the left arc of the wing rail head w1 constant.

[0125] Table 11 Longitudinal slope k of the working side of the wing rail w1 Changed design scheme

[0126]

[0127] Table 12 shows the cross slope k of the wing rail top in each scheme. w2 Changes, longitudinal slope k of the working side of the wing rail w1 The radius r of the left arc of the wing rail head w1 constant.

[0128] Table 12 Cross slope k of wing rail top w2 Changed design scheme

[0129]

[0130] Table 13 shows the radius r of the arc on the left side of the wing rail head in each scheme. w1 Changes, longitudinal slope k of the working side of the wing rail w1 and wing track top cross slope k w2 constant.

[0131] Table 13 Radius r of the left side arc of the wing rail head w1 Changed design scheme

[0132]

[0133] The parameters were fitted using the data in Tables 11, 12, and 13. The fitting results are as follows: Figure 11 As shown.

[0134] according to Figure 11 And the experimental data shown in Tables 11, 12, and 13, the longitudinal slope k of the working side of the wing rail. w1 The slope of the inner working edge is affected; its increase causes the side profile to converge inward and changes the contact position of the working edge; the cross slope k at the top of the wing rail. w2 The inclination of the rail top surface affects the vertical height of the rail top profile and the geometry of the contact surface. The radius r of the left arc of the wing rail head. w1 Increasing the slope will enhance the smoothness of the rail head transition area, making the profile more rounded. Through comprehensive comparative analysis, the cross slope k at the top of the wing rail... w2 It has a significant impact on the profile because the numerical changes cause the greatest geometric deviations in the vertical and lateral dimensions, which directly determine the wheel-rail contact distribution characteristics on the top surface of the airfoil.

[0135] In summary, this embodiment, through the construction of a rigorous NURBS mathematical model and in-depth parameter sensitivity orthogonal experimental analysis, realizes an efficient, accurate, and highly controllable method for designing the profile of fixed frog point rails and wing rails. It enables rapid iteration of key parameters and has advantages such as high automation and good repeatability, making it suitable for the design and optimization of fixed frog point rail and wing rail profiles.

[0136] Example 4

[0137] This embodiment 4 provides a non-transitory computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, they implement the parametric design method for the profiles of the fixed frog point rail and wing rail, considering geometric features, as described above. The method includes:

[0138] Based on the structural characteristics of the fixed frog, feature parameters describing the geometric morphology of the frog section and the wing section are extracted;

[0139] A coordinate system is established with the center axis of the center track and the track gauge measurement point of the wing track as the reference. Based on the characteristic parameters, a profile control boundary composed of straight line segments and circular arc segments is constructed, and the coordinates of key control points are calculated by analytical geometry method.

[0140] Add profile data points to the circular curve region of the center rail and wing rail profiles and calculate the coordinates of each point; then, combine specific weight vectors and node vector configurations to construct high-precision parametric profiles of the center rail and wing rail sections based on NURBS curves.

[0141] The key control points and local profile data points are used as control vertices of the NURBS curve. Combined with preset weight vectors and node vectors, parameterized profiles of arbitrary cross sections of the center track and the wing track are constructed.

[0142] Example 5

[0143] This embodiment 5 provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, and the memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the parametric design method for the profiles of a fixed frog point rail and wing rail considering geometric features as described above. The method includes:

[0144] Based on the structural characteristics of the fixed frog, feature parameters describing the geometric morphology of the frog section and the wing section are extracted;

[0145] A coordinate system is established with the center axis of the center track and the track gauge measurement point of the wing track as the reference. Based on the characteristic parameters, a profile control boundary composed of straight line segments and circular arc segments is constructed, and the coordinates of key control points are calculated by analytical geometry method.

[0146] Add profile data points in the circular curve section of the center rail and wing rail profiles and calculate the coordinates of each point; then, combine specific weight vectors and node vector configurations to construct high-precision parametric profiles of the center rail and wing rail sections based on NURBS curves.

[0147] The key control points and local profile data points are used as control vertices of the NURBS curve. Combined with preset weight vectors and node vectors, parameterized profiles of arbitrary cross sections of the center track and the wing track are constructed.

[0148] Example 6

[0149] This embodiment 6 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features as described above. The method includes:

[0150] Based on the structural characteristics of the fixed frog, feature parameters describing the geometric morphology of the frog section and the wing section are extracted;

[0151] A coordinate system is established with the center axis of the center track and the track gauge measurement point of the wing track as the reference. Based on the characteristic parameters, a profile control boundary composed of straight line segments and circular arc segments is constructed, and the coordinates of key control points are calculated by analytical geometry method.

[0152] Add profile data points to the circular curve region of the center rail and wing rail profiles and calculate the coordinates of each point; then, combine specific weight vectors and node vector configurations to construct high-precision parametric profiles of the center rail and wing rail sections based on NURBS curves.

[0153] The key control points and local profile data points are used as control vertices of the NURBS curve. Combined with preset weight vectors and node vectors, parameterized profiles of arbitrary cross sections of the center track and the wing track are constructed.

[0154] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0156] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0157] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0158] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A parametric design method for the profiles of a fixed frog point rail and wing rail considering geometric features, characterized in that, include: Based on the structural characteristics of the fixed frog, feature parameters describing the geometric morphology of the frog section and the wing section are extracted; A coordinate system is established with the center axis of the center track and the track gauge measurement point of the wing track as the reference. Based on the characteristic parameters, a profile control boundary composed of straight line segments and circular arc segments is constructed, and the coordinates of key control points are calculated by analytical geometry method. Local profile data points are added to the circular curve region of the center rail and wing rail head, and the coordinates of each point are calculated. Then, based on the NURBS curve, a high-precision parametric profile of the center rail and wing rail cross section is constructed by combining specific weight vectors and node vector configurations. The key control points and local profile data points are used as control vertices of the NURBS curve. Combined with preset weight vectors and node vectors, parameterized profiles of arbitrary cross sections of the center track and the wing track are constructed.

2. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 1, characterized in that, NURBS curves are used for profile fitting, with a control vertex count of m+1, a curve order of k, and a total number of nodes of m+k+2; these control points {N} are connected sequentially. i } and {W j } forms the profile control boundary; k represents the order of the B-spline basis function; {Q j } is the control vertex {N i } and {W j The corresponding weighting coefficients, and the weights of each control point on the center rail and wing rail are determined comprehensively based on the changes in the profile curvature.

3. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 1, characterized in that, The geometric characteristic parameters of the fixed frog point rail and wing rail are determined based on the geometric characteristics of the point rail and wing rail as reflected in the standard design drawings of the fixed frog, specifically including the cross slope k of the point rail top. n1 , Track gauge and longitudinal slope k n2 Half width of the top surface of the center track w n The height h of the top rail above the gauge measurement point n , Track gauge angle radius r n Longitudinal slope k of the working side of the wing rail w1 wing rail top cross slope k w2 , longitudinal slope k of non-working side of wing rail w3 Half width of the top surface of the wing rail w w1 The height h of the wing rail above the gauge measurement point w1 The left side arc of the wing rail head w1 The right-side arc of the wing rail head. w2 .

4. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 1, characterized in that, The method for determining control point coordinates involves the profiles of the center rail and the wing rail. For the center rail profile, utilizing the symmetry of the center rail's central axis, a single-sided profile is selected for parameterization. The main control points determined include the center rail vertex N1, the control point N2 of the straight section at the rail top, the upper tangent point of the gauge angle arc N3, the lower tangent point of the side arc N4, the bottom width control point N5, and the center of the side arc N6. For the wing rail profile, a coordinate system is established with the gauge measurement point as the origin. The main control points determined include the wing rail vertex W5, the gauge measurement point W2, the tangent point of the working edge arc W3, the left tangent point of the rail top arc W4, the right tangent point of the rail top arc W6, the tangent point of the non-working edge arc W7, the auxiliary measurement point W8, and the centers of the left and right side arcs W9 and W1. 10 .

5. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 4, characterized in that, The coordinates of the top N1 and bottom width control point N5 of the center track are determined based on the geometric height and width-related characteristic parameters of the center track. The coordinates of the center N6 of the side arc are determined by the point-to-straight-line distance formula. The coordinates of the tangent points N3 and N4 between the arc and the straight lines on both sides are calculated by combining the cross slope of the center track top and the longitudinal slope of the track gauge side. The ordinate of the control point N2 of the straight section at the top of the track is set as the height of the center track, and the abscissa is determined by the control points N1 and N3 according to the fixed ratio point formula, with a proportionality coefficient of λ, thereby completing the construction of all key control points of the center track.

6. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 4, characterized in that, The track gauge measurement point W2 is the origin of the coordinate system. The coordinates of the wing rail vertex W5 and the auxiliary measurement point W8 are determined based on the wing rail's geometric characteristic parameters (top surface half-width, height) and auxiliary measurement parameters. The centers of the left and right arcs W9 and W8 are determined using the point-to-straight-line distance formula. 10 Coordinates, based on the center W9 and W 10 The coordinates of the tangent points W3, W4 and W6, W7 between the arc and the straight lines on both sides are calculated along the transverse slope of the top of the rail and the longitudinal slope of the sides, thus completing the construction of all key control points of the wing rail.

7. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 5, characterized in that, The two endpoints of the arc on the side of the track are the tangent points N3 and N4 between the arc and the straight segments on both sides. The tangents passing through the two tangent points pass through the top N1 and the bottom width control point N5 of the track, respectively. The distance from the center N6 to the tangents at the two tangent points is equal, which is the radius of the track gauge angle arc. Based on this, the coordinates of the center N6 of the track gauge angle arc are obtained. Then, based on the principle that the tangents at the two tangent points and the intersecting lines perpendicular to them all pass through the center N5, the coordinates of the tangent points N3 and N4 are determined.

8. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 6, characterized in that, The two endpoints of the arc on the left side of the wing rail are the tangent points W3 and W4 between the arc and the straight lines on both sides. The tangent lines passing through the two tangent points pass through the gauge measurement point W2 and the wing rail vertex W5, respectively. The distances from the center W9 to the tangent lines at the two tangent points are equal, both being the radius of the arc on the left side of the wing rail head. Based on this, the circular coordinates W9 of the arc on the left side of the wing rail head are obtained. Then, based on the principle that the tangent lines at the two tangent points and their perpendicular intersecting lines all pass through the center W9, the coordinates of the tangent points W3 and W4 are determined. Similarly, the center W of the arc on the right side of the wing rail can be determined. 10 And the coordinates of the two tangent points W6 and W7.

9. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 1, characterized in that, Based on the advantage of NURBS curves in achieving continuous and smooth curve fitting, weight vectors are preset for key control points and profile data points of the center rail and wing rail, and node vectors are calculated to complete the parametric profile reconstruction of arbitrary cross-sections of the center rail and wing rail.

10. The parametric design method for the profiles of fixed frog point rails and wing rails considering geometric features according to claim 1, characterized in that, A comprehensive evaluation index, including Pearson correlation coefficient, cosine similarity, and distance similarity, is introduced to conduct correlation analysis on the standard profile and reconstructed profile of each key section. The evaluation index system adopts a comprehensive correlation coefficient Rcomp, which is composed of Pearson correlation coefficient RPearson, cosine similarity coefficient RCosine, and distance similarity coefficient RDistance coefficient RDistance, and is used to comprehensively evaluate the matching degree between the parameterized model and the standard profile. When Rcomp ≥ 0.90, it is judged as extremely strong correlation, which verifies the feasibility of the parameterization method.

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