A method for designing the alignment of a high-speed maglev turnout and its alignment

Abstract

This invention provides a method and design for the alignment of high-speed maglev turnouts, including determining the angle constraint between adjacent turnout beams based on the geometric relationship constraints of the track; constructing a straight-line approximation curve design using the standard stator unit length as a constraint; constructing a curve-to-straight-broken-line alignment design using circular curve segments; verifying the parameters of the designed transition curve and circular curve using at least the angle constraint between adjacent turnout beams; solving all parameters of the transition-circular-broken-line turnout alignment after verification; verifying the mechanical performance of the turnout alignment using static stress-deformation, dynamic analysis models, and modal analysis models; and selecting the optimal alignment parameters for the optimal turnout alignment while meeting the mechanical performance requirements. This invention solves the problem that existing turnout alignments are insufficient to meet the needs of practical engineering for turnouts with different levels of lateral passing speed.

Description

Technical Field

[0001] This invention relates to the field of rail transit technology, and in particular to a method and alignment design for a high-speed maglev turnout. Background Technology

[0002] Compared with conventional wheel-rail systems, maglev rail transit features low noise, low energy consumption, high speed, and high efficiency, and is considered a promising new mode of transportation. Maglev turnouts, as a key component for track switching in maglev trains, play a vital role in the safe and stable operation of the train.

[0003] The planar alignment design of turnouts is the first step in turnout design, a crucial prerequisite for ensuring the safe passage of vehicles, and an important basis for the structural design of turnouts. The core of the polygonal turnout alignment design method is "approximating a curve with a straight line," forming a polygonal approximation curve on the turnout's side rails. This is achieved by fitting a circular curve using multiple inscribed regular polygons, or by fitting a transition curve using secants. Polygonal turnouts can be categorized based on their lateral throughput capacity into single-circular polygonal turnouts (i.e., transforming a single circle into a straight line using polygonal fitting) and transition curve-circular curve-transition curve polygonal turnouts (i.e., transforming a gradual circle-gradient curve into a straight line using polygonal fitting). Single-circular polygonal turnouts are generally used for turnouts with lower lateral throughput speeds, such as the three-segment type used in medium- and low-speed maglev turnouts. Gradual circle-gradual polygonal turnouts have a smaller impact angle and are smoother than single-circular polygonal turnouts, thus adapting to higher lateral throughput speeds. Polygonal turnouts are also used in superconducting maglev systems because concrete beams cannot achieve lateral elastic bending.

[0004] A search of existing patents related to maglev turnout alignment reveals that existing methods can achieve beam deflection by applying loads to obtain the alignment, but this has low operability in specific alignment design. Furthermore, some solutions do not consider all factors when designing the turnout alignment, resulting in limitations in feasibility and applicability.

[0005] In summary, there are virtually no patents available for specific and feasible design methods for maglev turnout alignments. Furthermore, the "High-Speed ​​Maglev Transportation Design Standard" (CJJ / T310-2021) only specifies turnout alignment parameters for lateral passing speeds of 98 km / h and 196 km / h; the "Medium and Low Speed ​​Maglev Transportation Design Specification" (CJJ / T 262-2017) only specifies turnout alignment parameters for lateral passing speeds of 25 km / h. Neither of these two sets of specifications clearly defines specific turnout alignment design methods, and the two types of turnouts are insufficient to meet the actual engineering requirements for turnouts with different levels of lateral passing speeds.

[0006] To address the above-mentioned technical shortcomings, the technical problem to be solved by this invention is to provide a high-speed maglev turnout alignment design method and alignment. The proposed alignment design method guides the design of a series of turnout alignments to meet different lateral passing speeds, solving the problem that existing turnout alignments cannot meet the actual engineering requirements for turnouts with different levels of lateral passing speeds, and filling the gap in high-speed maglev turnout alignment design methods. Summary of the Invention

[0007] This invention provides a high-speed maglev turnout alignment design method and alignment, which solves the problem that existing turnout alignments cannot meet the actual engineering requirements for turnouts with different levels of lateral passing speed.

[0008] According to one aspect of the present invention, a method for designing the alignment of a high-speed maglev turnout is provided, comprising: Determine the included angle constraint between adjacent turnout beams based on the geometric relationship constraints of the track. Using the standard stator unit length as a constraint, a straight-line substitution curve design is constructed to create a transition curve. Based on the relationship between the length of the broken turnout beam in the transition curve segment and the length of the broken turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, the design of the broken line shape of the circular curve segment is constructed. At least the included angle constraint between adjacent turnout beams should be used to verify the parameters of the designed transition curve and circular curve; After the verification is passed, all parameters of the turnout alignment are solved; and the mechanical performance of the turnout alignment is verified by static stress-deformation, dynamic analysis model and modal analysis model. Under the premise of satisfying mechanical performance, select the optimal alignment parameters of the turnout alignment.

[0009] Optionally, the determination of the included angle constraint between adjacent turnout beams based on the geometric relationship constraints of the track includes: The included angle between adjacent turnout beams is constrained based on the geometric relationship between the vehicle length and the track, as well as the geometric relationship based on the longitudinal gap of the turnout beams, in order to determine the included angle constraint between adjacent turnout beams.

[0010] Optionally, the transition curve is a spiral; the design of constructing the transition curve using a straight line as a curve, constrained by the standard stator unit length, includes: The radius of the spiral and the minimum transition curve length are calculated based on the lateral passing velocity and lateral acceleration. The coordinates of the second endpoint of the transition curve are calculated based on the radius of the spiral curve and the minimum transition curve length; the transition curve is divided into two segments, namely the first curve and the second curve, the first curve including the first endpoint and the second curve including the second endpoint; The length of the first curve and the chord length corresponding to the first curve are determined based on the coordinates of the first endpoint of the transition curve; the lengths of the first curve and the second curve are equal. The actual turnout beam segment length of the transition curve is calculated based on the chord length corresponding to the first curve, and the actual turnout beam segment length is an integer multiple of the standard stator unit length; The actual length of the transition curve is calculated based on the actual length of the turnout beam segment, and the actual coordinates of the first endpoint on the first curve are also calculated. The actual coordinates of the second endpoint are calculated based on the assumed length of the transition curve and the actual coordinates of the first endpoint. Calculate the actual coordinates of the second endpoint based on the actual coordinates of the first endpoint, calculate the initial angle of the transition curve, and the angle between the chord length of the first curve and the chord length of the second curve. Optionally, the step of constructing the curve-to-straight-line broken-line alignment design for the circular curve segment based on the relationship between the length of the broken-line turnout beam of the transition curve segment and the length of the broken-line turnout beam of the circular curve segment, and the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, includes: When the length of the broken turnout beam of the transition curve segment is equal to the length of the broken turnout beam of the circular curve segment, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve is equal to the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve, and both are equal to the included angle of the chord length of the adjacent circular curve, the radius of the turnout circular curve and the included angle of the chord length of the adjacent circular curve are solved based on the lateral passing velocity, lateral acceleration and the chord length of the second curve of the transition curve. The total turn angle is calculated based on the angle between the chord lengths of adjacent circular curves, the angle between the chord lengths of adjacent transition curves, and the initial angle of the transition curve. The lateral offset of the turnout endpoint is calculated based on the length of the turnout beam of the circular curve segment and the coordinates of the second endpoint where the second curve connects with the circular curve. The number of segments of the circular curve turnout beam is then calculated based on the lateral offset of the turnout endpoint.

[0011] Optionally, the step of constructing the curve-to-straight-line broken-line alignment design for the circular curve segment based on the relationship between the length of the broken-line turnout beam of the transition curve segment and the length of the broken-line turnout beam of the circular curve segment, and the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, includes: When the length of the broken turnout beam of the transition curve segment is equal to the length of the broken turnout beam of the circular curve segment, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve is also equal to the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve and is equal to the first angle, the radius of the turnout circular curve and the included angle of the chord length of the adjacent circular curve are solved based on the lateral passing velocity, lateral acceleration and the chord length of the second curve of the transition curve. The total turn angle is determined based on the angle between the chord lengths of adjacent circular curves, the angle between the chord lengths of adjacent transition curves, and the first angle. The lateral offset of the turnout endpoint is calculated based on the angle between the chord lengths of adjacent circular curves, the angle between the chord lengths of adjacent transition curves, the initial angle of the transition curve, the length of the broken turnout beam of the transition curve segment, and the coordinates of the second endpoint where the second curve connects to the circular curve. The first angle is calculated based on the lateral offset of the turnout endpoint, and then all parameters of the turnout alignment are determined.

[0012] Optionally, the step of constructing the curve-to-straight-line broken-line alignment design for the circular curve segment based on the relationship between the length of the broken-line turnout beam of the transition curve segment and the length of the broken-line turnout beam of the circular curve segment, and the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, includes: When the length of the broken turnout beam of the transition curve segment is equal to the length of the broken turnout beam of the circular curve segment, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve is not equal to the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve, and one of the included angles of the straight segment of the turnout beam connecting the transition curve to the circular curve and the straight segment of the turnout beam connecting the circular curve to the transition curve is equal to the included angle of the chord length of the adjacent circular curve, the radius of the turnout circular curve and the included angle of the chord length of the adjacent circular curve are solved based on the lateral passing velocity, lateral acceleration and the chord length of the second curve of the transition curve; Establish the relationship between the included angle of the chord lengths of adjacent circular curves, the included angle of the straight segments of the turnout beams connecting the transition curves to circular curves, the included angle of the straight segments of the turnout beams connecting the circular curves to transition curves, and the number of segments of the circular curve turnout beams and the total turnout angle; the included angle of the straight segments of the turnout beams connecting the transition curves to circular curves or the included angle of the straight segments of the turnout beams connecting the circular curves to transition curves is equal to the included angle of the chord lengths of adjacent circular curves; Establish the relationships between the angle between adjacent circular curve chords, the angle between adjacent chords of the transition curve, the initial angle of the transition curve, the length of the broken-line turnout beam of the transition curve segment, the coordinates of the second endpoint where the second curve connects to the circular curve, the angle between the straight segments of the turnout beams connecting the transition curve to the circular curve, the angle between the straight segments of the turnout beams connecting the circular curve to the transition curve, and the number of segments of the circular curve turnout beam and the lateral offset of the turnout endpoint. Then, solve for the angle between the straight segments of the turnout beams connecting the transition curve to the circular curve, the angle between the straight segments of the turnout beams connecting the circular curve to the transition curve, and the number of segments of the circular curve turnout beam.

[0013] Optionally, the step of constructing the curve-to-straight-line broken-line alignment design for the circular curve segment based on the relationship between the length of the broken-line turnout beam of the transition curve segment and the length of the broken-line turnout beam of the circular curve segment, and the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, includes: The length of the turnout beam in the transition curve segment is equal to the length of the turnout beam in the circular curve segment, and the angle between the straight sections of the turnout beams transitioning from the transition curve to the circular curve is not equal to the angle between the straight sections of the turnout beams transitioning from the circular curve to the transition curve; the radius of the turnout circular curve and the angle between the chords of adjacent circular curves are calculated based on the lateral passing velocity, lateral acceleration, and the chord length of the second curve of the transition curve. The total turn angle is calculated based on the angle between the chord lengths of adjacent circular curves, the radius of the fork curve, and the chord length of the second curve of the transition curve. Establish the following relationships: the angle between adjacent circular curve chord lengths, the angle between adjacent chord lengths of transition curves, the initial angle of transition curves, the length of the broken-line turnout beam of the transition curve segment, the coordinates of the second endpoint where the second curve connects to the circular curve, the angle between the straight segments of the turnout beams where the transition curve transitions to the circular curve, the angle between the straight segments of the turnout beams where the circular curve transitions to the transition curve, and the relationship between the number of segments of the circular curve turnout beam and the lateral offset of the turnout endpoint. The angle between the straight segments of the turnout beams where the transition curve transitions to the circular curve and the angle between the straight segments of the turnout beams where the circular curve transitions to the transition curve are respectively the angles between the turnout beams of the two transition curves and the turnout beams of the circular curve. Based on the lateral offset of the turnout endpoint, the angle between the straight segments of the connecting turnout beams when transitioning from a transition curve to a circular curve, the angle between the straight segments of the connecting turnout beams when transitioning from a circular curve to a transition curve, and the number of segments of the circular curve turnout beam are calculated.

[0014] Optionally, the verification of the parameters of the designed transition curve and circular curve by at least using the included angle constraint of adjacent turnout beams includes: Based on the constraint of the included angle between adjacent turnout beams, the included angle of the chord length of adjacent circular curves in the transition curve and circular curve, the included angle of adjacent chord lengths of the transition curve, the initial included angle of the transition curve, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve and the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve are verified. The kinetic energy loss is calculated based on the included angle constraint between adjacent turnout beams, the included angle between adjacent chord lengths of the transition curve and the circular curve, the included angle between adjacent chord lengths of the transition curve, the initial included angle of the transition curve, and the included angle between the straight segment of the turnout beam connecting the transition curve to the circular curve and the straight segment of the turnout beam connecting the circular curve to the transition curve. The calculated kinetic energy loss is verified based on the preset maximum kinetic energy loss. The lateral acceleration and lateral acceleration rate of change in the designed transition curve and circular curve are verified based on the preset maximum lateral acceleration and maximum rate of change of acceleration. The lengths of transition curves and circular curves are verified based on preset vehicle length constraints.

[0015] Optionally, the verification of the mechanical performance of the turnout alignment using static stress-deformation, dynamic analysis models, and modal analysis models includes: establishing a refined static analysis model of the turnout beam, a magnetic buoyancy coupling analysis model of the vehicle-turnout-subfoundation system, and a modal analysis model; calculating whether the stress-deformation of the turnout, the dynamic performance of the vehicle-turnout system, the deflection of the turnout beam, the turnout's passing performance, and its natural frequency meet the specifications.

[0016] According to another aspect of the present invention, a high-speed maglev turnout alignment is provided, which is constructed by the high-speed maglev turnout alignment design method described in any embodiment of the present invention.

[0017] The technical solution of this invention determines the angle constraint between adjacent turnout beams based on the geometric relationship constraint of the track; constructs a straight-to-curve shape design for the transition curve using the standard stator unit length as a constraint; constructs a straight-to-curve shape design for the circular curve segment based on the relationship between the length of the broken-line turnout beam in the transition curve segment and the length of the broken-line turnout beam in the circular curve segment, as well as the relationship between the angle between the straight-line segments of the connecting turnout beams from the transition curve to the circular curve and the angle between the straight-line segments of the connecting turnout beams from the circular curve to the transition curve; verifies the parameters of the designed transition curve and circular curve using at least the angle constraint between adjacent turnout beams; after verification, solves all parameters of the transition-circle-transition-broken-line turnout shape; and verifies the mechanical performance of the turnout shape using static stress-deformation, dynamic analysis models, and modal analysis models; and selects the optimal shape parameters of the optimal turnout shape while satisfying the mechanical performance requirements. This invention transforms abstract linear design into a quantifiable and reproducible engineering method, clarifying the specific calculation logic for two-segment fitting of transition curves and four adaptation scenarios of circular curves. It addresses the shortcomings of existing standards (CJJ / T 310-2021, CJJ / T 262-2017) that only specify specific lateral speed parameters and do not clarify the design method. It can realize the design of a series of turnouts with different levels of lateral passing speed, and can flexibly adapt to the engineering requirements of medium and high-speed lateral passing. It solves the problem that existing turnouts cannot cover diverse speed scenarios and improves the engineering adaptability of the technical solution.

[0018] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0020] Figure 1 This is a flowchart of a high-speed maglev turnout alignment design method according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram illustrating the calculation of the vehicle length requirement for the turnout angle in a high-speed maglev turnout alignment design method of the present invention. Figure 3 This is a schematic diagram illustrating the calculation of the longitudinal clearance of the turnout beam for the turnout angle in a high-speed maglev turnout alignment design method according to the present invention. Figure 4This is a schematic diagram of the alignment calculation when the transition curve of the high-speed maglev turnout alignment design method of the present invention is divided into two segments; Figure 5 This is a schematic diagram of the overall calculation of the gradual circular curve of the high-speed maglev turnout alignment design method of the present invention; Figure 6 The present invention provides a high-speed maglev turnout alignment design method, which calculates the optimal turnout alignment design parameters in the second case, taking a lateral passing speed of 100 km / h as an example. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0023] Example 1 Figure 1 This is a flowchart illustrating a high-speed maglev turnout alignment design method provided in Embodiment 1 of the present invention. Figure 1 As shown, the method includes: S101. Determine the included angle constraint between adjacent turnout beams based on the geometric relationship constraints of the track.

[0024] In this embodiment, the included angle constraint between adjacent turnout beams can be determined based on the geometric relationship constraint between the vehicle and the track. Specifically, the included angle between adjacent turnout beams can be constrained based on the geometric relationship between the vehicle length and the track, as well as the geometric relationship based on the longitudinal gap of the turnout beams, in order to determine the included angle constraint between adjacent turnout beams.

[0025] Among them, such as Figure 2 As shown, the geometric relationship between the vehicle length and the track requires the following for the switch angle:

[0026] In the formula, θ is the turning angle between adjacent turnout beams; H is the width of the maglev vehicle, which is taken as 3.7m according to CJT 367-2011 General Technical Conditions for High-Speed ​​Maglev Transportation Vehicles; h is the beam width, which is taken as 2.8m; lc is the length of the maglev vehicle, which is taken as 28m (24.768m and 27.211m are taken as the larger value). Substituting these values ​​into the calculation, the maximum turning angle does not exceed 7.569°.

[0027] like Figure 3 As shown, in the turnout section, due to the need for lateral movement and rotation of the turnout beams, the gap between adjacent beams is wider than in the mainline section, set to 0.06m. Therefore, to ensure that adjacent beams do not interfere with each other during the turnout, a maximum turnout angle limit should be set, as illustrated in the geometric diagram below. During the turnout, the gap at the center of the beam remains at μ=0.06m, with the outer gap increasing and the inner gap decreasing. Therefore, it is necessary to ensure that the inner sides of the beams do not interfere with each other.

[0028] The geometric relationship of the longitudinal clearance between turnout beams constrains the included angle between adjacent turnout beams as follows:

[0029] In the formula, θ is the turning angle between adjacent turnout beams; h is the beam width, taken as 2.8m; substituting into the calculation, the maximum turning angle is 2.4557°.

[0030] Based on the two constraints, the minimum θ value calculated by the two formulas must be taken, meaning θ cannot exceed 2.4557°, or 0.04286 radians. The calculated angle θ between adjacent turnout beams will be used as a verification condition for subsequent design.

[0031] S102. Using the standard stator unit length as a constraint, construct a straight-line substitution curve design for the transition curve.

[0032] The transition curve can be constrained by the length of the standard stator unit, meaning it should be an integer multiple of the length of the standard stator unit (generally 1.032m), i.e., composed of an integer number of turnout beams.

[0033] It should be noted that the high-speed maglev turnout alignment in this embodiment consists of three segments: the first segment is a transition curve, the second segment is a circular curve, and the third segment is also a transition curve, namely, the fitted polyline of the first transition curve ls1, the fitted polyline of the circular curve ly, and the fitted polyline of the second transition curve ls2. The parameters of the first transition curve should be the same as those of the second transition curve, ls1=ls2. The transition curve is a spiral curve, which can shorten the turnout length as much as possible, improving economy and adaptability. In this embodiment, the transition curve is fitted using two straight lines, that is, using two spans to fit the transition curve segments. This means that the first and second transition curves can be divided into equal-length first and second curve segments. After completing the transition curve design, the circular curve segment is then designed with segmented polyline fitting, and the circular curve is the circumcircle of the corresponding polyline.

[0034] like Figure 4 As shown in the figure, after the transition curve ls1 is divided into two segments OA and AB, it can be known that the length of the broken turnout beam of the first curve OA of the transition curve ls1 is l. 01 The length l of the broken-line turnout beam equal to the second curve AB 01 .

[0035] Specifically, the process of constructing a transition curve by substituting a straight line for a curved shape includes: S1021. Calculate the spiral radius and minimum transition curve length based on lateral passing speed and lateral acceleration.

[0036] Specifically, the lateral passing speed v (km / h) is used as the input value; the lateral acceleration ay ∈ [1.9999, 0.0001], ay iterates from 1.9999 to 0.0001 in steps of 0.0001, ay is the built-in input iterative value; the spiral radius R and the minimum transition curve length lsmin are calculated using v and ay, and the corresponding initial spiral parameter A2 is determined:

[0037] The initial equation of the spiral is:

[0038] S1022. Calculate the coordinates of the second endpoint of the transition curve based on the radius of the spiral curve and the minimum transition curve length; the transition curve is divided into two segments, namely the first curve and the second curve, the first curve including the first endpoint and the second curve including the second endpoint.

[0039] like Figure 2 As shown, OA can be considered the first curve, AB the second curve, and point O the origin. Then, the first endpoint is A, the second endpoint is B, and the line segment l... OA =l AB =l01 The coordinates of point B can then be calculated based on the radius R of the spiral curve and the minimum transition curve length lsmin.

[0040] Simplified to:

[0041]

[0042] Simplified to:

[0043] S1023. Based on the coordinates of the first endpoint of the transition curve, solve for the length of the first curve of the initial spiral and the chord length corresponding to the first curve; the lengths of the first curve and the second curve are equal.

[0044] We can set A(x) ap y ap The coordinates of point A can be represented by the length of the transition curve ls1p of segment OA, which is the only unknown. Points O, A, and B lie on the same spiral curve, then:

[0045]

[0046] Simplified to:

[0047]

[0048] Simplified to:

[0049] Let line segment l OA =l AB =l 01p ,but:

[0050] Simplified to:

[0051] In the above formula, x bp y bp Given; x ap y ap Each equation can be represented by a single unknown, ls1p. One equation, one unknown; ls1p can then be solved. Once ls1p is solved, the corresponding coordinates A(x) are determined. ap y ap It can be calculated by ) straight segment lOA =l AB =l 01 x ap y ap Given, and thus the corresponding l 01p The answer can then be determined.

[0052] or

[0053] S1024. Calculate the actual turnout beam segment length of the transition curve based on the chord length corresponding to the first curve. The actual turnout beam segment length is an integer multiple of the standard stator unit length.

[0054] Calculate the chord length l corresponding to the first curve. 01p Then, divide by 1.032 and round up, then multiply by 1.032 again to obtain the actual length l of the turnout beam segment. 01 This ensures the actual l 01 It is an integer multiple of 1.032.

[0055] S1025. Calculate the actual length of the transition curve and the actual coordinates of the first endpoint on the first curve based on the actual length of the turnout beam segment of the transition curve.

[0056] l 01 It is known that, through A 2 Given that the corresponding ls1 can be calculated using the following formula, the coordinates (x, y) of the assumed point A can then be calculated. a y a );

[0057]

[0058]

[0059] S1026. Calculate the actual coordinates of the second endpoint based on the assumed length of the transition curve and the actual coordinates of the first endpoint.

[0060] Furthermore, through A 2 Given that l 01 Given that x a y a Given that the equation has only one unknown parameter ls, the length ls of the transition curve corresponding to OB can be calculated by inverse calculation, and then the actual B(x) can be obtained through ls. b y b Point coordinates;

[0061]

[0062] Let A be the control parameter of the spiral curve equation, and let ls correspond one-to-one with R. Then:

[0063] It should be noted that at this point, ls is definitely not less than lsmin, which corresponds to R. s If R is less than lsmin, then ls has increased, and a yp It is definitely less than the limit of 2m / s 3 Because of rounding up, the numerical change will not be too large, therefore at 2m / s 3 The design principle is also reflected in the surrounding area, which is to minimize the value of the turnout while meeting the limit requirements.

[0064] The above operations transform lsmin into ls, and both are on the same spiral line, while A2 remains unchanged; R consists of two input values ​​v and a. y The decision is made, therefore R remains unchanged, i.e., R s As the value increases to R, the curve becomes flatter overall, and the equation of the spiral changes from to . If A1 > A, then the calculated value of a is... yp It must also meet the requirement of being less than 2.

[0065] S1027. Calculate the actual coordinates of the second endpoint based on the actual coordinates of the first endpoint, calculate the initial angle of the transition curve, and the angle between the chord length of the first curve and the chord length of the second curve. The calculation yielded the actual l that satisfies an integer multiple of 1.032. 01 R, let A(x) be an actual value. a y a ) and B(x b y b The coordinates, the actual length of the fitted transition curve ls, and the equation of the fitted spiral curve are given. ; By setting the coordinates of points A and B, the initial angle α1 of the transition curve and the angle θ1 between adjacent chords of the transition curve can be calculated: , .

[0066] In this embodiment, the four parameters of the calculated transition curve can also be verified, including the time-varying rate of lateral acceleration α. yp Kinetic energy loss ω, turnout beam angle θ maxThe transition curve ls (not less than the length lc of one car section) is used. When selecting the impact angle ω, the more unfavorable conditions are considered, and the larger value of α1 and θ1 is chosen. Transition rails or angle bisector devices are not considered because the on-site structure may not be able to implement transition rails or angle bisector devices at the joint position; or ω1 (corresponding to the impact angle α1) and ω2 (corresponding to the impact angle θ1) are calculated simultaneously, and compared with the limit value ω. max Make a judgment.

[0067] , , θ max ≤0.04286 radians.

[0068] Since the turn angle of a transition curve is generally small, it can be approximated by a straight line segment. 01p When taking a value, take l. 01p ≈lsmin / 2, lsmin is known, then l 01p Given that l 01p Divide by 1.032 and round up to get l 01 , l 01 It is known that the transition curve can be transformed into a straight line through fitting; in practical implementation, the most accurate method is preferred.

[0069] The linear parameter ls2 of the second transition curve is the same as that of the first transition curve ls1. For the special case where the transition curve is divided into n segments and straightened, the calculation method is the same as above. The key point is to select the length of the transition curve ls1 as the only variable, and then solve for all variables in this way.

[0070] S103. Based on the relationship between the length of the broken-line turnout beam in the transition curve segment and the length of the broken-line turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, construct the broken-line shape design of the circular curve segment.

[0071] It should be noted that, since the angle θ1 between the fitted straight lines of the transition curve segment and the angle θ between the fitted straight lines of the circular curve segment are not necessarily equal, the broken-line turnout beam l at the transition from the transition curve to the circular curve... 01 The angle between the straight segment connecting to the chord length l0 of the circular curve and the straight segment is γ1. The broken turnout beam l0, which transitions from the circular curve to the transition curve, is l... 01 Given an included angle of γ2, there are four possibilities: whether γ1 equals γ2, whether γ1 equals θ, and so on. That is: ①l 01 =l0, γ1=γ2=θ: chord length of the transition curve l 01 = chord length of the circular curve l0, chord length of the first transition curve l 01The angle γ1 between adjacent chord lengths l0 that connect to the circular curve is equal to the angle θ between the chord lengths of the circular curve; the chord length l0 of the circular curve that connects to the second transition curve is l 01 The included angle γ2 is equal to the included angle θ of the chord length of the circular curve.

[0072] ②l 01 =l0, γ1=γ2=γ≠θ: chord length of the transition curve l 01 = chord length of the circular curve l0, chord length of the first transition curve l 01 The angle γ1 between adjacent chord lengths l0 that connect to the circular curve is equal to the chord length l0 that connects the circular curve chord length l to the second transition curve. 01 The included angle is γ2, but it is not equal to the included angle θ of the chord length of the circular curve.

[0073] ③l 01 =l0, γ1=θ≠γ2 or γ2=θ≠γ1: chord length of the transition curve l 01 = chord length of the circular curve l0, chord length of the first transition curve l 01 The angle γ1 between adjacent chord lengths l0 that connect to the circular curve is equal to the angle θ between the chord lengths of the circular curve, but not equal to the chord length l0 between the circular curve chord length l0 and the second transition curve. 01 Angle γ2; or the chord length l0 of the circular curve where it meets the second transition curve. 01 The included angle γ2 is equal to the included angle θ of the chord length of the circular curve, but not equal to the chord length l of the first transition curve. 01 The angle γ1 between adjacent chord lengths l0 that connect with the circular curve.

[0074] ④l 01 =l0, γ1≠γ2≠θ: chord length of the transition curve l 01 = chord length of the circular curve l0, chord length of the first transition curve l 01 The angle γ1 between the chord length l0 and the circular curve is not equal to the angle θ between the chord lengths of the circular curve and the second transition curve, nor is it equal to the chord length l0 between the circular curve chord length l0 and the second transition curve. 01 Angle γ2.

[0075] like Figure 5 As shown, Figure 5 The turnout alignment shown in the diagram includes a transition curve OAB, circular curves B1B2B3B4, and a transition curve B4CN, with the radius of the circular curve being R.

[0076] In the first case, the length l of the broken turnout beam of the transition curve segment is given. 01 When the length l0 of the turnout beam is equal to that of the broken line of the circular curve segment, and the included angle γ1 of the straight segment of the turnout beam connecting the transition curve to the circular curve is equal to the included angle γ2 of the straight segment of the turnout beam connecting the circular curve to the transition curve, and both are equal to the included angle of the chord length of the adjacent circular curve, that is, l 01=l0, γ1=γ2=θ. The turnout radius and the angle between adjacent circular curve chords can be calculated based on the lateral passing velocity, lateral acceleration, and the chord length of the second curve of the transition curve; the total turnout angle τ can be calculated based on the angle θ between adjacent circular curve chords, the angle θ1 between adjacent chords of the transition curve, and the initial angle α1 of the transition curve; the turnout beam length l0 of the circular curve segment, and the second endpoint (x) where the second curve connects to the circular curve... B1 y B1 Solve for the lateral offset y at the end point of the turnout using the coordinates of the turnout. n =3.65, based on the lateral offset y at the turnout endpoint n =3.65 Calculate the number of segments n of the circular curve turnout beam.

[0077] Specifically, the lateral passing velocity v and the lateral acceleration a y As design input conditions; where To ensure design accuracy, a y Retain 5 decimal places when inputting; a y When inputting, the value is gradually reduced from the maximum value of 1.99999 to the minimum value of 0.00001 in increments of 0.00001. l 01 Given that l 01 =l0, then l0 is known. R and θ are calculated by the following formula, where the radius R of the turnout circular curve refers to the radius of the circumcircle of the broken line formed by the center lines of each section of track on the turnout.

[0078] ,

[0079] Given α1, θ1, and θ, τ is a function of n, and the unknown n∈[2, 15]. Solve for the total turn angle τ:

[0080] Using the lateral offset y at the end of the turnout n =3.65 Calculate the number of segments n of the circular curve turnout beam: y n The calculation formula is shown below, l0, x B1 y B1 Given that y n Let y be a function of n. n There is only one unknown n; through y n =3.65 can be used to find n. Since n is a positive integer in the range [2, 15], the calculated value of n needs to be filtered, with an error range of 1e. -6 ;

[0081]

[0082] a y Starting from the maximum value of 1.99999, gradually decreasing to the minimum value of 0.00001 in steps of 0.00001, there will always be a value 'a'. y The value ensures that the calculated n is a positive integer greater than or equal to 2 (with an error of 1e). -6 Assume there are a total of m0 a's. y To ensure that the calculated n is a positive integer greater than or equal to 2, there are m0 possible n values. At this point, all the key parameters of the turnout alignment are known; It should be noted that y can also be calculated by starting with n from 2 and gradually increasing the value by a step size of 1. n -3.65, to make the error value from 3.65 less than 1e -6 If so, then the requirement is met.

[0083] The first scenario is through a y → Solve for n, and filter the results according to requirements. During the solution process, a needs to be considered. y A single-level traversal is performed to obtain all key parameters of the turnout alignment.

[0084] In the second case, the length l of the broken turnout beam of the transition curve segment is used as a reference. 01 When the length l0 of the turnout beam is equal to that of the broken line of the circular curve segment, and the included angle γ1 of the straight segment of the turnout beam connecting the transition curve to the circular curve is equal to the included angle γ2 of the straight segment of the turnout beam connecting the circular curve to the transition curve and is equal to the first angle l, 01 =l0, γ1=γ2=γ, γ is not necessarily equal to θ (γ is unknown). Based on lateral passing velocity v and lateral acceleration a y And the chord length l of the second curve of the transition curve 01 Solve for the radius R of the turnout circular curve and the angle θ between the chords of adjacent circular curves; determine the total turnout angle based on the angle θ between the chords of adjacent circular curves, the angle θ1 between the chords of adjacent transition curves, and the first angle γ; determine the turnout beam length l of the broken line segment based on the angle θ between the chords of adjacent circular curves, the angle θ1 between the chords of adjacent transition curves, the initial angle α1 of the transition curve, and the broken line turnout beam length l of the transition curve segment. 01 And the coordinates (x, y) of the second endpoint where the second curve meets the circular curve. B1 y B1 Solve for the lateral offset y at the end of the turnout. n =3.65; based on the lateral offset y at the fork endpoint n =3.65 Calculate the first angle γ, and then determine all parameters of the turnout alignment.

[0085] Specifically, the lateral passing velocity v and the lateral acceleration a yAs design input conditions; where To ensure design accuracy, a y Retain 5 decimal places when inputting; a y When inputting, the value is gradually reduced from the maximum value of 1.99999 to the minimum value of 0.00001 in increments of 0.00001. l 01 Given that l 01 =l0, then l0 is known. R and θ are calculated by the following formula, where the radius R of the turnout circular curve refers to the radius of the circumcircle of the broken line formed by the center lines of each section of track on the turnout.

[0086] ,

[0087] Given α1 and θ1, and γ and n unknown; τ is a function of γ and n; then solve for the total turn angle τ:

[0088] Using the lateral offset y at the end of the turnout n =3.65 Calculate the angle γ between the transition curve turnout beam and the circular curve turnout beam: y n The calculation formula is shown below, x B1 y B1 α1, θ1, l0, and θ are known; γ and n are unknown; y n Let be a function of γ and n;

[0089]

[0090] In a y Starting with a certain value, let n gradually increase from small to large, initially at 2, with a step size of 1, until it reaches 15; through y n Solve for each a y The value of γ corresponding to the value of n.

[0091] The second scenario is through a y →n→ To solve for γ, we need to consider a y The values ​​are obtained by traversing the n-level loop to determine all parameters of the turnout alignment.

[0092] For the third case, the length l of the broken turnout beam in the transition curve segment should be considered. 01The length l0 of the turnout beam is equal to that of the broken line of the circular curve segment. Furthermore, the included angle γ1 of the straight segment of the turnout beam transitioning from the transition curve to the circular curve is not equal to the included angle γ2 of the straight segment of the turnout beam transitioning from the circular curve to the transition curve. The value of one of the included angles γ1 and γ2 is equal to the included angle θ of the chord lengths of the adjacent circular curves, i.e., l 01 =l0, γ1=θ≠γ2 or γ2=θ≠γ1; based on lateral passing velocity v and lateral acceleration a y And the chord length l of the second curve of the transition curve 01 Solve for the radius R of the turnout circular curve and the angle θ between the chord lengths of adjacent circular curves; establish the relationship between the angle θ between the chord lengths of adjacent circular curves, the angle γ1 between the straight segments of the turnout beams transitioning from the transition curve to the circular curve, the angle γ2 between the straight segments of the turnout beams transitioning from the circular curve to the transition curve, and the number of segments n of the circular curve turnout beam with respect to the total turnout angle τ; the angle between the straight segments of the turnout beams transitioning from the transition curve to the circular curve or the angle between the straight segments of the turnout beams transitioning from the circular curve to the transition curve is equal to the angle θ between the chord lengths of adjacent circular curves; establish the angle θ between the chord lengths of adjacent circular curves, the angle θ1 between the adjacent chord lengths of the transition curve, the initial angle α1 of the transition curve, and the length l of the broken-line turnout beam of the transition curve segment. 01 The coordinates (x, y) of the second endpoint where the second curve intersects the circular curve. B1 y B1 The angle γ1 of the straight segments of the turnout beams transitioning from the transition curve to the circular curve, the angle γ2 of the straight segments of the turnout beams transitioning from the circular curve to the transition curve, and the number of segments n of the circular curve turnout beam and the lateral offset y at the end of the turnout. n The relationship between 3.65 is used to solve for the included angle γ1 of the straight segments of the turnout beams connecting the transition curve to the circular curve, the included angle γ2 of the straight segments of the turnout beams connecting the circular curve to the transition curve, and the number of segments n of the circular curve turnout beam.

[0093] Specifically, the lateral passing velocity v and the lateral acceleration a y As design input conditions; where To ensure design accuracy, a y Retain 5 decimal places when inputting; a y When inputting, the value is gradually reduced from the maximum value of 1.99999 to the minimum value of 0.00001 in increments of 0.00001. l 01 Given that l 01 =l0, then l0 is known. R and θ are calculated by the following formula, where the radius R of the turnout circular curve refers to the radius of the circumcircle of the broken line formed by the center lines of each section of track on the turnout.

[0094] ,

[0095] Let τ be a function of θ, n, γ1, and γ2. Given l0 and R, θ is known. Let γ1 or γ2 equal to θ; then τ is a function of n, γ2, or γ1. Solve for the total turn angle τ:

[0096] Using the lateral offset y at the end of the turnout n =3.65 Calculate the angle γ2 or γ1 between the transition curve turnout beam and the circular curve turnout beam: y n The calculation formula is shown below, x B1 y B1 α1 and θ1 are known; l0 and θ are known, γ2 or γ1 are unknown, and n is unknown; y n It is a function of n, γ2, or γ1;

[0097]

[0098] In a y Based on a certain value, let n gradually increase from small to large with an initial value of 2 and a step size of 1, until it reaches 15; solve for γ2 or γ1 corresponding to each value of n.

[0099] The third scenario is through a y →n→ To solve for γ2 or γ1, we need to consider a y The values ​​of n are obtained by performing two-level traversal, thereby determining all parameters of the turnout alignment.

[0100] For the fourth case, the length l of the broken turnout beam in the transition curve segment should be considered. 01 The length l0 of the turnout beam is equal to that of the broken line of the circular curve segment, and the included angle γ1 of the straight segment of the turnout beam connecting the transition curve to the circular curve is not equal to the included angle γ2 of the straight segment of the turnout beam connecting the circular curve to the transition curve, that is, l 01 =l0, γ1≠γ2, and are independent of θ; based on lateral passing velocity v and lateral acceleration a y And the chord length l of the second curve of the transition curve 01 Solve for the radius R of the turnout circular curve and the angle θ between the chords of adjacent circular curves; based on the angle θ between the chords of adjacent circular curves, the radius R of the circular curve, and the chord length l of the second curve of the transition curve. 01 Solve for the total turnout angle; establish the angle θ between the chord lengths of adjacent circular curves, the angle θ1 between the chord lengths of adjacent transition curves, the initial angle α1 of the transition curve, and the length l of the broken turnout beam of the transition curve segment. 01 The coordinates (x, y) of the second endpoint where the second curve intersects the circular curve.B1 y B1 The relationships between the straight segment angle γ1 of the turnout beam transitioning from the transition curve to the circular curve, the straight segment angle γ2 of the turnout beam transitioning from the circular curve to the transition curve, and the number of segments n of the circular curve turnout beam and the lateral offset of the turnout endpoint are defined as follows: the straight segment angles γ1 and γ2 of the turnout beam transitioning from the transition curve to the circular curve are the angles between the turnout beams at both ends of the transition curve and the circular curve turnout beam, respectively; based on the lateral offset γ of the turnout endpoint... n =3.65 Solve for the included angle γ1 of the straight segments of the turnout beams connecting the transition curve to the circular curve, the included angle γ2 of the straight segments of the turnout beams connecting the circular curve to the transition curve, and the number of segments n of the circular curve turnout beam.

[0101] Specifically, the lateral passing velocity v and the lateral acceleration a y As design input conditions; where To ensure design accuracy, a y Retain 5 decimal places when inputting; a y When inputting, the value is gradually reduced from the maximum value of 1.99999 to the minimum value of 0.00001 in increments of 0.00001. l 01 Given that l 01 =l0, then l0 is known. R and θ are calculated by the following formula, where the radius R of the turnout circular curve refers to the radius of the circumcircle of the broken line formed by the center lines of each section of track on the turnout.

[0102] ,

[0103] Given l0 and R, then θ is known; τ is a function of n, γ1, and γ2;

[0104] ③ Utilizing the lateral offset y at the end of the turnout n =3.65 Calculate the angle γ2 or γ1 between the transition curve turnout beam and the circular curve turnout beam: y n The calculation formula is shown below, x B1 y B1 α1 and θ1 are known; l0 and θ are known; γ1 and γ2 are unknown; n is unknown; y n Let be a function of n, γ1, and γ2;

[0105]

[0106] In a yStarting with a given value, let n gradually increase from small to large, starting with an initial value of 2 and a step size of 1, until it reaches 15. Then, within the allowed range, iterate through γ1 or γ2 with an initial value of 0.0001 and a step size of 0.0001 to find the other included angle γ2 or γ1. For example, if we iterate through γ1 to find γ2, then γ1∈(0, min(θmax=0.04286, ...). )).

[0107] The fourth case involves solving for γ2 or γ1 using ay→n→γ1 or γ2→, which requires a y The values ​​of γ1 or γ2 are obtained by performing a three-level traversal, thereby determining all parameters of the turnout alignment.

[0108] S104. At least the included angle constraint between adjacent turnout beams shall be used to verify the parameters of the designed transition curve and circular curve.

[0109] It should be noted that the following indicators need to be checked during the design of turnout alignment: The gradual curve and straight line shape are used to adapt to turnouts with high lateral passing speeds. The limits for lateral acceleration and the time-varying rate of lateral acceleration are set at 2 m / s². 2 and 2m / s 3 Meanwhile, since the curve is straightened, the kinetic energy loss ω, the maximum included angle θmax (the included angle between adjacent turnout beams must meet the geometric constraint relationship of the train track), the length of the transition curve ls, and the length of the circular curve ly (not less than the length of a single car lc=24.768m) must be checked, for a total of 6 parameters.

[0110] ① Lateral acceleration a y ≤2m / s 2 ; ②Rate of change of lateral acceleration a - ≤2m / s 3 ; ③ Kinetic energy loss ωmax≤0.65km 2 / h 2 ; ④ The maximum included angle θmax of the turnout beam ≤ 0.04286 radians; ⑤ The length of the transition curve is ls ≥ lc = 24.768m; ⑥ The length of the circular curve ly ≥ lc = 24.768 m; After meeting the above-mentioned linear parameter limit requirements, the final alignment of the turnout must also meet the mechanical performance requirements. The turnout alignment is checked from the perspectives of static strength, dynamic performance and natural frequency.

[0111] In one embodiment, the process includes verifying the angles between adjacent circular curve chords, adjacent chord lengths, initial angles, and straight segments of the transition beams from the transition curve to the circular curve, based on the angle constraints between adjacent turnout beams; calculating the kinetic energy loss based on the angle constraints between adjacent turnout beams, and verifying the calculated kinetic energy loss based on a preset maximum kinetic energy loss; verifying the lateral acceleration and lateral acceleration rate of change in the designed transition curves and circular curves based on a preset maximum lateral acceleration and maximum acceleration rate of change; and verifying the lengths of the transition curves and circular curves based on a preset vehicle length constraint.

[0112] Specifically, the key linear parameter l is calculated by converting the transition curve and circular curve into straight lines. 01 α1, θ1, a y The values ​​of α1, θ1, θ2, γ1, and θ are verified, and each angle must satisfy the geometric constraints of the vehicle line, that is, α1, θ1, θ, γ1, and γ2 cannot exceed θmax ≤ 0.04286 radians. Calculate kinetic energy loss using formula (J corresponds to α1, θ1, θ, γ1, γ2 respectively, and five kinetic energy loss check indicators are calculated), ω≤ωmax=0.65km 2 / h 2 ; lateral acceleration lateral acceleration rate of change ; The transition curves ls1 and ls2, and the length of the circular curve ly, must not be less than the length of one car section lc = 24.768m. This is to avoid a single car section simultaneously crossing three different types of alignments, which could cause an uneven transition in the vehicle's trajectory and potentially lead to a derailment. In challenging situations, the length of the entire wheelbase (distance between the centers of two bogies + the fixed wheelbase of one bogie) of one car section must be met.

[0113] When multiple indicators under the above conditions meet the limit requirements, the corresponding key parameters of the turnout alignment are output; otherwise, no output is output. The l that meets the limit requirements is obtained by calculation. 01 α1, θ1, a y By calculating the values ​​of γ, n, γ1, γ2, γ, and θ, all parameters of the turnout alignment of the gradual circular and gradually broken line can be obtained.

[0114] S105. After the verification is passed, solve all the parameters of the turnout alignment of the gradual curve and the gradual break line; and use static stress-deformation, dynamic analysis model and modal analysis model to verify the mechanical performance of the turnout alignment.

[0115] After determining all design parameters for different turnout alignments in this embodiment, a refined static analysis model of the turnout beam, a magnetic buoyancy coupling analysis model of the vehicle-turnout-subfoundation system, and a modal analysis model can be established to calculate the stress and deformation of the turnout, the dynamic performance of the vehicle-turnout system, the deflection of the turnout beam, the turnout's throughput performance, and whether its natural frequency meets the specifications. The first-order natural frequency f1 > 1.1V. max / L n V max L is the maximum lateral passing speed of the turnout. n This refers to the span of a single-span turnout beam.

[0116] S106. Under the condition of satisfying mechanical performance, select the optimal alignment parameters of the optimal turnout alignment.

[0117] Under the premise of meeting the above requirements, in order to improve the economy and applicability of turnouts, the alignment corresponding to the minimum turnout length is determined as the optimal turnout alignment. The turnout length should be minimized as much as possible, thereby determining the optimal alignment parameters of the turnout.

[0118] The above method can be used to achieve the alignment design of a single turnout. For other types of turnouts derived from the single turnout, such as three-way turnouts, five-way turnouts, and single crossover turnouts, the same method can be used to achieve the alignment design.

[0119] By changing the requirements for the single span length of the turnout beam (e.g., the length of the superconducting maglev turnout beam is 9+1.8m, where m is a non-negative integer), the lateral acceleration, the time-varying rate of lateral acceleration, and other limit requirements, the above method can also realize the design of the gradual circular and gradual broken line turnout shape of superconducting maglev turnouts and straddle-type monorail turnouts. The design principle, method, and process are the same.

[0120] In a specific application example, taking a lateral passing speed of v = 100 km / h as an example, in the second case (l 01 =l0, γ1=γ2=γ), and through the above process and calculation, the optimal turnout shape is obtained as follows: Figure 6 As shown in Table 1, the main technical parameters of the turnout with a lateral passing speed of v=100km / h are as follows.

[0121] Table 1 Main Technical Parameters of Turnouts

[0122] The technical solution of this invention transforms abstract linear design into a quantifiable and reproducible engineering method. It clarifies the specific calculation logic for two-segment fitting of transition curves and four adaptation scenarios of circular curves, solving the deficiency of existing specifications (CJJ / T310-2021, CJJ / T 262-2017) that only specify specific lateral speed parameters and do not clarify the design method. It can realize the design of a series of turnouts with different levels of lateral passing speed, and can flexibly adapt to the engineering requirements of medium and high-speed lateral passing. It solves the problem that existing turnouts cannot cover multiple speed scenarios and improves the engineering adaptability of the technical solution.

[0123] Furthermore, the key parameters of this invention are designed to strictly adhere to actual engineering and specification requirements. The length of the turnout beams is adjusted to integer multiples of 1.032m, the standard stator unit length for maglev tracks, reducing the error risks in turnout beam manufacturing and on-site installation, and improving the feasibility of the design. By flexibly adjusting parameters such as turnout beam length constraints (1.032m multiples for conventional maglev, and 9+1.8m for superconducting maglev) and mechanical performance limits, it can be directly applied to superconducting maglev and straddle-type monorail turnout designs without reconstructing the core logic, adapting to different maglev technology routes. In terms of parameter verification, the maximum turning angle of adjacent turnout beams is clearly defined through vehicle-track geometric constraints to avoid vehicle-track interference and collisions between adjacent beams; at the same time, the length of transition curves / circular curves is required to be no less than the length of a single car section to prevent sudden trajectory changes caused by the vehicle simultaneously crossing multiple types of alignments, reducing the risk of derailment. By verifying core indicators such as lateral acceleration, rate of change of lateral acceleration, and kinetic energy loss, and combining static deformation, train-turnout-foundation dynamic coupling analysis, and modal calculations, the system ensures minimal impact and low vibration when trains pass through turnouts, improving ride comfort and track structure durability. By setting two transition curves with identical parameters and symmetrical fitting, the system ensures consistent dynamic response when trains pass through turnouts in both forward and reverse directions, avoiding performance imbalances in unidirectional turnout passage. Finally, under all constraints, the optimal alignment with the minimum total turnout length is selected, effectively reducing the amount of turnout beam material used, shortening track space occupation, and lowering turnout manufacturing, transportation, and construction costs, thus balancing technological advancement and economic rationality.

[0124] Example 2 Figure 2 The high-speed maglev turnout alignment provided in Embodiment 2 of the present invention is constructed by the high-speed maglev turnout alignment design method described in any embodiment of the present invention.

[0125] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0126] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for designing the turnout alignment of a high-speed maglev train, characterized in that, include: Determine the included angle constraint between adjacent turnout beams based on the geometric relationship constraints of the track. Using the standard stator unit length as a constraint, a straight-line substitution curve design is constructed to create a transition curve. Based on the relationship between the length of the broken turnout beam in the transition curve segment and the length of the broken turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight segments of the connecting turnout beams from the transition curve to the circular curve and the included angle of the straight segments of the connecting turnout beams from the circular curve to the transition curve, the design of the broken line shape of the circular curve segment is constructed. At least the included angle constraint between adjacent turnout beams should be used to verify the parameters of the designed transition curve and circular curve; After the verification is passed, all parameters of the turnout alignment are solved; and the mechanical performance of the turnout alignment is verified by static stress-deformation, dynamic analysis model and modal analysis model. Under the premise of satisfying mechanical performance, select the optimal alignment parameters of the turnout alignment.

2. The high-speed maglev turnout alignment design method according to claim 1, characterized in that, The determination of the included angle constraint between adjacent turnout beams based on the geometric relationship constraints of the vehicle track includes: The included angle between adjacent turnout beams is constrained based on the geometric relationship between the vehicle length and the track, as well as the geometric relationship based on the longitudinal gap of the turnout beams, in order to determine the included angle constraint between adjacent turnout beams.

3. The high-speed maglev turnout alignment design method according to claim 1, characterized in that, The transition curve is a spiral; the design of constructing the transition curve using a straight line as a substitute for a curve, constrained by the standard stator unit length, includes: The radius of the spiral and the minimum transition curve length are calculated based on the lateral passing velocity and lateral acceleration. The coordinates of the second endpoint of the transition curve are calculated based on the radius of the spiral curve and the minimum transition curve length; the transition curve is divided into two segments, namely the first curve and the second curve, the first curve including the first endpoint and the second curve including the second endpoint; The length of the first curve and the chord length corresponding to the first curve are determined based on the coordinates of the first endpoint of the transition curve; the lengths of the first curve and the second curve are equal. The actual turnout beam segment length of the transition curve is calculated based on the chord length corresponding to the first curve, and the actual turnout beam segment length is an integer multiple of the standard stator unit length; The actual length of the transition curve is calculated based on the actual length of the turnout beam segment, and the actual coordinates of the first endpoint on the first curve are also calculated. The actual coordinates of the second endpoint are calculated based on the assumed length of the transition curve and the actual coordinates of the first endpoint. Calculate the actual coordinates of the second endpoint based on the actual coordinates of the first endpoint, calculate the initial angle of the transition curve, and the angle between the chord length of the first curve and the chord length of the second curve.

4. The high-speed maglev turnout alignment design method according to claim 3, characterized in that, The design for transforming a circular curve segment into a straight-line broken curve is constructed based on the relationship between the length of the broken-line turnout beam in the transition curve segment and the length of the broken-line turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the circular curve and the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the transition curve. This includes: When the length of the broken turnout beam of the transition curve segment is equal to the length of the broken turnout beam of the circular curve segment, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve is equal to the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve, and both are equal to the included angle of the chord length of the adjacent circular curve, the radius of the turnout circular curve and the included angle of the chord length of the adjacent circular curve are solved based on the lateral passing velocity, lateral acceleration and the chord length of the second curve of the transition curve. The total turn angle is calculated based on the angle between the chord lengths of adjacent circular curves, the angle between the chord lengths of adjacent transition curves, and the initial angle of the transition curve. The lateral offset of the turnout endpoint is calculated based on the length of the turnout beam of the circular curve segment and the coordinates of the second endpoint where the second curve connects with the circular curve. The number of segments of the circular curve turnout beam is then calculated based on the lateral offset of the turnout endpoint.

5. The high-speed maglev turnout alignment design method according to claim 3, characterized in that, The design for transforming a circular curve segment into a straight-line broken curve is constructed based on the relationship between the length of the broken-line turnout beam in the transition curve segment and the length of the broken-line turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the circular curve and the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the transition curve. This includes: When the length of the broken turnout beam of the transition curve segment is equal to the length of the broken turnout beam of the circular curve segment, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve is also equal to the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve and is equal to the first angle, the radius of the turnout circular curve and the included angle of the chord length of the adjacent circular curve are solved based on the lateral passing velocity, lateral acceleration and the chord length of the second curve of the transition curve. The total turn angle is determined based on the angle between the chord lengths of adjacent circular curves, the angle between the chord lengths of adjacent transition curves, and the first angle. The lateral offset of the turnout endpoint is calculated based on the angle between the chord lengths of adjacent circular curves, the angle between the chord lengths of adjacent transition curves, the initial angle of the transition curve, the length of the broken turnout beam of the transition curve segment, and the coordinates of the second endpoint where the second curve connects to the circular curve. The first angle is calculated based on the lateral offset of the turnout endpoint, and then all parameters of the turnout alignment are determined.

6. The high-speed maglev turnout alignment design method according to claim 3, characterized in that, The design for transforming a circular curve segment into a straight-line broken curve is constructed based on the relationship between the length of the broken-line turnout beam in the transition curve segment and the length of the broken-line turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the circular curve and the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the transition curve. This includes: When the length of the broken turnout beam of the transition curve segment is equal to the length of the broken turnout beam of the circular curve segment, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve is not equal to the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve, and one of the included angles of the straight segment of the turnout beam connecting the transition curve to the circular curve and the straight segment of the turnout beam connecting the circular curve to the transition curve is equal to the included angle of the chord length of the adjacent circular curve, the radius of the turnout circular curve and the included angle of the chord length of the adjacent circular curve are solved based on the lateral passing velocity, lateral acceleration and the chord length of the second curve of the transition curve; Establish the relationship between the included angle of the chord lengths of adjacent circular curves, the included angle of the straight segments of the turnout beams connecting the transition curves to circular curves, the included angle of the straight segments of the turnout beams connecting the circular curves to transition curves, and the number of segments of the circular curve turnout beams and the total turnout angle; the included angle of the straight segments of the turnout beams connecting the transition curves to circular curves or the included angle of the straight segments of the turnout beams connecting the circular curves to transition curves is equal to the included angle of the chord lengths of adjacent circular curves; Establish the relationships between the angle between adjacent circular curve chords, the angle between adjacent chords of the transition curve, the initial angle of the transition curve, the length of the broken-line turnout beam of the transition curve segment, the coordinates of the second endpoint where the second curve connects to the circular curve, the angle between the straight segments of the turnout beams connecting the transition curve to the circular curve, the angle between the straight segments of the turnout beams connecting the circular curve to the transition curve, and the number of segments of the circular curve turnout beam and the lateral offset of the turnout endpoint. Then, solve for the angle between the straight segments of the turnout beams connecting the transition curve to the circular curve, the angle between the straight segments of the turnout beams connecting the circular curve to the transition curve, and the number of segments of the circular curve turnout beam.

7. The high-speed maglev turnout alignment design method according to claim 3, characterized in that, The design for transforming a circular curve segment into a straight-line broken curve is constructed based on the relationship between the length of the broken-line turnout beam in the transition curve segment and the length of the broken-line turnout beam in the circular curve segment, as well as the relationship between the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the circular curve and the included angle of the straight-line segment of the connecting turnout beams at the transition curve to the transition curve. This includes: The length of the turnout beam in the transition curve segment is equal to the length of the turnout beam in the circular curve segment, and the angle between the straight sections of the turnout beams transitioning from the transition curve to the circular curve is not equal to the angle between the straight sections of the turnout beams transitioning from the circular curve to the transition curve; the radius of the turnout circular curve and the angle between the chords of adjacent circular curves are calculated based on the lateral passing velocity, lateral acceleration, and the chord length of the second curve of the transition curve. The total turn angle is calculated based on the angle between the chord lengths of adjacent circular curves, the radius of the fork curve, and the chord length of the second curve of the transition curve. Establish the following relationships: the angle between adjacent circular curve chord lengths, the angle between adjacent chord lengths of transition curves, the initial angle of transition curves, the length of the broken-line turnout beam of the transition curve segment, the coordinates of the second endpoint where the second curve connects to the circular curve, the angle between the straight segments of the turnout beams where the transition curve transitions to the circular curve, the angle between the straight segments of the turnout beams where the circular curve transitions to the transition curve, and the relationship between the number of segments of the circular curve turnout beam and the lateral offset of the turnout endpoint. The angle between the straight segments of the turnout beams where the transition curve transitions to the circular curve and the angle between the straight segments of the turnout beams where the circular curve transitions to the transition curve are respectively the angles between the turnout beams of the two transition curves and the turnout beams of the circular curve. Based on the lateral offset of the turnout endpoint, the angle between the straight segments of the connecting turnout beams when transitioning from a transition curve to a circular curve, the angle between the straight segments of the connecting turnout beams when transitioning from a circular curve to a transition curve, and the number of segments of the circular curve turnout beam are calculated.

8. The high-speed maglev turnout alignment design method according to claim 1, characterized in that, The verification of the parameters of the designed transition curve and circular curve by at least the included angle constraint of adjacent turnout beams includes: Based on the constraint of the included angle between adjacent turnout beams, the included angle of the chord length of adjacent circular curves in the transition curve and circular curve, the included angle of adjacent chord lengths of the transition curve, the initial included angle of the transition curve, and the included angle of the straight segment of the turnout beam connecting the transition curve to the circular curve and the included angle of the straight segment of the turnout beam connecting the circular curve to the transition curve are verified. The kinetic energy loss is calculated based on the included angle constraint between adjacent turnout beams, the included angle between adjacent chord lengths of the transition curve and the circular curve, the included angle between adjacent chord lengths of the transition curve, the initial included angle of the transition curve, and the included angle between the straight segment of the turnout beam connecting the transition curve to the circular curve and the straight segment of the turnout beam connecting the circular curve to the transition curve. The calculated kinetic energy loss is verified based on the preset maximum kinetic energy loss. The lateral acceleration and lateral acceleration rate of change in the designed transition curve and circular curve are verified based on the preset maximum lateral acceleration and maximum rate of change of acceleration. The lengths of transition curves and circular curves are verified based on preset vehicle length constraints.

9. The high-speed maglev turnout alignment design method according to claim 1, characterized in that, The verification of the mechanical performance of the turnout alignment using static stress-deformation, dynamic analysis models, and modal analysis models includes: establishing a refined static analysis model of the turnout beam, a magnetic buoyancy coupling analysis model of the vehicle-turnout-subfoundation system, and a modal analysis model; calculating the stress-deformation of the turnout, the dynamic performance of the vehicle-turnout system, the deflection of the turnout beam, the turnout's passing performance, and whether its natural frequency meet the specifications.

10. A high-speed maglev turnout alignment, characterized in that, The high-speed maglev turnout alignment is constructed by the high-speed maglev turnout alignment design method according to any one of claims 1-9.

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