A highly adaptive reverse curve connection method for railway yard design

Abstract

The application discloses a high-adaptability reverse curve connection method for railway station design and relates to the field of railway plane design, and comprises the following steps: S1, specifying the front and rear straight lines and turnout parameters of the reverse curve connection; S2, specifying the reverse curve connection parameters; S3, calculating two feasible center positions of the front curve; S4, calculating eight feasible center positions of the rear curve; S5, calculating the center angle of each of the front curve and the rear curve; S6, calculating the reverse curve with the shortest length; S7, connecting the two reverse curves with the clamping straight line; and S8, modifying the terminal straight line section to complete the reverse curve connection. The application is applicable to the special scene that a large-angle included angle exists between a starting straight line section and a terminal straight line section, the center angle of the reverse curve exceeds 180 degrees, the easement curves in the reverse curve are not equal in length, and the length of the turnout connected with the starting and terminal ends and the straight line after the turnout is fixed, has high practicability, high universality and high popularization and application value.

Description

Technical Field

[0001] This invention relates to the field of railway plan design, and in particular to a highly adaptable reverse curve connection method for railway station design. Background Technology

[0002] A reverse curve is a type of alignment where two curves with opposite directions are connected by a straight line. It is a common alignment type in linear engineering surveying and design. In railway plan design, it is generally used for adjusting track spacing, shortening line terminal connections, and reverse crossover connections. Existing reverse curve connection algorithms are suitable for general connection scenarios where the starting and ending straight segments are parallel, there is a small angle between them (less than 90 degrees), both central angles of the reverse curve are less than 180 degrees, the reverse curve does not contain transition curves, and the transition curves are of equal length. However, it does not support special scenarios where the starting and ending straight segments have a large angle between them (greater than 90 degrees), the central angle of the reverse curve exceeds 180 degrees, the transition curves in the reverse curve are of unequal length, and the starting and ending points connect to turnouts with fixed post-turnout straight lengths. Designers need to experiment repeatedly to draw reverse curves that meet these special requirements, severely impacting design efficiency. A more adaptable reverse curve connection algorithm needs to be developed to meet the needs of different connection scenarios. Summary of the Invention

[0003] The purpose of this invention is to provide a highly adaptable reverse curve connection method for railway station design, in order to solve the technical problems in the existing reverse curve connection algorithm that does not support special scenarios such as large angles (greater than 90 degrees) between the starting and ending straight segments, the central angle of the reverse curve exceeding 180 degrees, unequal lengths of transition curves in the reverse curve, and fixed lengths of turnouts and straight lines after the turnouts at the starting and ending ends.

[0004] This invention provides a highly adaptable reverse curve connection method for railway station design, comprising the following steps:

[0005] S1: Specifies the parameters of the preceding and following straight lines and turnouts for the reverse curve connection;

[0006] This includes specifying the starting straight segment l1 and the ending straight segment l2 of the reverse curve connection; when the terminal connection is a turnout, specifying the turnout frog angle β, the distance b from the turnout center to the rail gap behind the frog, and the length c of the straight segment after the turnout.

[0007] S2: Specifies the parameters for connecting the reverse curve;

[0008] This includes specifying the length la1 of the preceding transition curve a1 of the preceding curve C1, the type ta1 of the preceding transition curve C1, the length lb1 of the following transition curve b1 of the preceding curve C1, the type tb1 of the following transition curve C1, the radius r1 of the arc A1 of the preceding curve C1, the length la2 of the preceding transition curve a2 of the following curve C2, the type ta2 of the preceding transition curve of the following curve C2, the length lb2 of the following transition curve b2 of the following curve C2, the type tb2 of the following transition curve C2, the radius r2 of the arc A2 of the following curve C2, and the length f of the clamping line.

[0009] S3: Calculate the two feasible center positions of the previous curve;

[0010] This refers to calculating the center C11 when A1 rotates clockwise and the center C12 when A1 rotates counterclockwise.

[0011] S4: The eight feasible center positions of the curve after calculation;

[0012] This refers to calculating the feasible center positions of A2 (C21, C22, C23, C24) when the center of A1 is C11; and calculating the feasible center positions of A2 (C21′, C22′, C23′, C24′) when the center of A1 is C12.

[0013] S5: Calculate the central angles of the front and back curves respectively;

[0014] This refers to calculating the central angles corresponding to A1 and A2 for different combinations of circle centers.

[0015] S6: Calculate the shortest reverse curve;

[0016] This refers to finding the center of the front and back curves {minC1, minC2} and the central angle {minβc1, minβc2} corresponding to the shortest reverse curve in the solutions of S4 and S5.

[0017] S7: Connect two opposite curves with a straight line.

[0018] S8: Modify the terminating straight line segment to complete the reverse curve connection;

[0019] This means that when β is 0, l2 is modified so that its starting point coincides with the ending point of the reverse curve, and l1, the reverse curve, and l2 are connected in sequence to obtain the final result; when β is not 0, the ending point of C2 is used as the starting point, and a straight line l2′ is drawn along the tangent direction of the ending point of C2. l2′ intersects l2 at point p, which is the bifurcation position. l2′ is modified so that its ending point coincides with p, and l1, the reverse curve, and l2′ are connected in sequence to obtain the final result.

[0020] Furthermore, the calculation of the eight feasible center positions of the curve in S4 specifically includes the following steps:

[0021] S4-1. Calculate the length of the pseudo-clamping line between the front and back curves;

[0022] bf = mb1 + f + ma2;

[0023] Where: mb1 is the tangent growth value of b1, and ma2 is the tangent growth value of a2.

[0024] S4-2, Calculate the pseudo radius of the curve before and after;

[0025] br1 = r1 + pb1;

[0026] br2 = r2 + pa2;

[0027] Where: pb1 is the inner shift value of b1, and pa2 is the inner shift value of a2.

[0028] S4-3. Calculate the circle containing the center of the curve.

[0029] C3 = C11;

[0030]

[0031] Where: C3 is the center of the circle, r c Let be the radius of the circle.

[0032] S4-4. Calculate the two straight lines containing the center of the curve after calculation;

[0033] l3 = Trans(l2, -v, d);

[0034] l4 = Trans(l2,v,d);

[0035] d=(r2+pb2+(b+c+mb2)*tan(β))*cos(β));

[0036] Where: Trans(l,v,d) is a line translation operation, which moves line l a distance d along the direction v; v is the unit vector pointing from the endpoint p1 of l1 to p′1, p′1 is the vertical projection point of p1 on l2; pb2 is the inward shift value of b2.

[0037] S4-5. Calculate the feasible center positions of the curve after the curve is centered.

[0038] Calculate the intersection points of the two straight lines containing the center of circle S4-3 and the center of circle S4-4. The intersection points are the feasible center positions of circle A2: C21, C22, C23, and C24.

[0039] S4-6. Calculate the remaining feasible center positions of the curve after calculation;

[0040] Replace C11 with C12 and repeat steps S4-3 to S4-5; calculate C21′, C22′, C23′, and C24′ in sequence.

[0041] Furthermore, the calculation of the central angles of the front and back curves in S5 includes the following steps:

[0042] S5-1. Calculate the perpendicular vectors of the front and back lines.

[0043] S5-2. Calculate the direction vector from the center of the front curve to the center of the back curve.

[0044] S5-3. Calculate the pseudo-central angles corresponding to the curves before and after;

[0045] δc1 = Angle(v1,v3);

[0046] When C1 rotates clockwise, δc2 = Angle(v2, -v3) + β;

[0047] When C1 rotates counterclockwise, δc2 = Angle(v2,-v3) - β;

[0048] Among them: Angle(v a ,v b The operation is the angle between vectors, i.e., the angle between vectors v. a Rotate to v b The angle through which it rotates is the same as the rotation direction of C1; v1 and v2 are the vertical vectors of the front and back straight lines, and v3 is the direction vector from the center of the front curve to the center of the back curve.

[0049] S5-4. Calculate the combination of central angles corresponding to the arcs in the curves before and after the curves;

[0050] βc1=δc1-β a1 -β b1 -sin -1 (bf / r c );

[0051] βc2=δc2-β a2 -β b2 -sin -1 (bf / r c );

[0052] Where: β a1 Let β be the deflection angle of a1. b1 Let β be the deflection angle of b1. a2 Let β be the deflection angle of a2. b2 Let b2 be the deflection angle.

[0053] S5-5. Calculate the remaining combinations of central angles;

[0054] Replace C21 with C22, C23, and C24 in sequence, and repeat steps S5-1 to S5-4 to calculate the corresponding central angle combinations when the center of circle A2 is C22, C23, and C24. Replace C11 with C12, and replace C21 with C21′, C22′, C23′, and C24′ in sequence, and repeat steps S5-1 to S5-4 to calculate the corresponding central angle combinations when the center of circle A2 is C12 and when the center of circle A2 is C21′, C22′, C23′, and C24′.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] The reverse curve connection method proposed in this invention is applicable not only to general connection scenarios where the starting and ending straight segments are parallel, have a small angle (less than 90 degrees), both central angles of the reverse curve are less than 180 degrees, the reverse curve does not contain transition curves, and the transition curves are of equal length; it is also applicable to special scenarios where the starting and ending straight segments have a large angle (greater than 90 degrees), the central angle of the reverse curve exceeds 180 degrees, the transition curves in the reverse curve are of unequal length, and the starting and ending ends connect to turnouts and the length of the straight lines after the turnouts is fixed. It provides a highly adaptable solution for reverse curve connections. The method is simple in steps, logically rigorous, and can be quickly implemented using computer programming. In the field of railway station design, it can significantly improve the design efficiency of planar reverse curve alignments, is highly practical and versatile, and has high application value. Attached Figure Description

[0057] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0058] Figure 1 A flowchart of a highly adaptable reverse curve connection method for railway station design;

[0059] Figure 2 Flowchart showing the eight feasible center positions of the curve after calculation;

[0060] Figure 3 Flowchart for calculating the central angles of the front and back curves. Detailed Implementation

[0061] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0062] The components of the embodiments of the invention described and shown in the accompanying drawings can typically be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0063] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] The following is combined Figures 1 to 3 As shown, this embodiment of the invention provides a highly adaptable reverse curve connection method for railway station design, comprising the following steps:

[0065] S1: Specifies the parameters of the preceding and following straight lines and turnouts for the reverse curve connection;

[0066] This step is used to obtain the user-input reverse curve connection scenario, including the starting straight segment l1 and the ending straight segment l2 of the reverse curve connection. When the terminal connection is a turnout, the frog angle β, the distance b from the turnout center to the rail gap behind the frog, and the length c of the straight segment after the turnout are specified. When the terminal connection is a straight line, β, b, and c are all zero.

[0067] S2: Specifies the parameters for connecting the reverse curve;

[0068] This step is to obtain the connection parameters input by the user, including the length la1 of the preceding transition curve a1 of the preceding curve C1, the type ta1 of the preceding transition curve ta1 of the preceding curve C1, the length lb1 of the following transition curve b1 of the preceding curve C1, the type tb1 of the following transition curve tb1 of the preceding curve C1, the radius r1 of the arc A1 of the preceding curve C1, the length la2 of the preceding transition curve a2 of the following curve C2, the type ta2 of the preceding transition curve ta2 of the following curve C2, the length lb2 of the following transition curve b2 of the following curve C2, the type tb2 of the following transition curve tb2 of the following curve C2, the radius r2 of the arc A2 of the following curve C2, and the length f of the clamping line. When no transition curve is needed, the length of the transition curve is zero.

[0069] S3: Calculate the two feasible center positions of the previous curve;

[0070] This refers to calculating the center C11 when A1 rotates clockwise and the center C12 when A1 rotates counterclockwise;

[0071] C11 = pa1 + va1 × vz * r1;

[0072] C12 = pa1′ - va1′ × vz * r1;

[0073] Where pa1 is the endpoint of a1 when rotated clockwise, va1 is the tangential unit vector of the endpoint of a1 when rotated clockwise, and vz is the Z-axis (0,0,1). pa1′ is the endpoint of a1 when rotated counterclockwise, and va1′ is the tangential unit vector of the endpoint of a1 when rotated counterclockwise.

[0074] S4: The eight feasible center positions of the curve after calculation;

[0075] The purpose of this step is to calculate the centers of the preceding and following curves corresponding to all feasible reverse curves. That is, when the center of A1 is C11, calculate the feasible center positions of A2: C21, C22, C23, and C24; when the center of A1 is C12, calculate the feasible center positions of A2: C21′, C22′, C23′, and C24′.

[0076] Specifically, it includes the following steps:

[0077] S4-1. Calculate the length of the pseudo-clamping line between the front and back curves;

[0078] bf = mb1 + f + ma2;

[0079] Where: mb1 is the tangent growth value of b1, and ma2 is the tangent growth value of a2.

[0080] S4-2, Calculate the pseudo radius of the curve before and after;

[0081] br1 = r1 + pb1;

[0082] br2 = r2 + pa2;

[0083] Where: pb1 is the inner shift value of b1, and pa2 is the inner shift value of a2.

[0084] S4-3. Calculate the circle containing the center of the curve.

[0085] C3 = C11;

[0086]

[0087] Where: C3 is the center of the circle, r c Let be the radius of the circle.

[0088] S4-4. Calculate the two straight lines containing the center of the curve after calculation;

[0089] l3 = Trans(l2, -v, d);

[0090] l4 = Trans(l2,v,d);

[0091] d=(r2+pb2+(b+c+mb2)*tan(β))*cos(β));

[0092] Where: Trans(l,v,d) is a line translation operation, which moves line l a distance d along the direction v; v is the unit vector pointing from the endpoint p1 of l1 to p′1, p′1 is the vertical projection point of p1 on l2; pb2 is the inward shift value of b2.

[0093] S4-5. Calculate the feasible center positions of the curve after the curve is centered.

[0094] Calculate the intersection points of the two straight lines containing the center of circle S4-3 and the center of circle S4-4. The intersection points are the feasible center positions of circle A2: C21, C22, C23, and C24.

[0095] S4-6. Calculate the remaining feasible center positions of the curve after calculation;

[0096] Replace C11 with C12 and repeat steps S4-3 to S4-5; calculate C21′, C22′, C23′, and C24′ in sequence.

[0097] S5: Calculate the central angles of the front and back curves respectively;

[0098] The purpose of this step is to calculate the central angles of the preceding and following curves for all feasible reverse curves. That is, to calculate the central angles of A1 and A2 for different combinations of center points.

[0099] Specifically, it includes the following steps:

[0100] S5-1. Calculate the perpendicular vectors of the front and back lines;

[0101] When C1 rotates clockwise, the direction vector of the front line v1 (the direction vector of l1) rotates 90 degrees counterclockwise, and the direction vector of the rear line v2 (the direction vector of l2) rotates 90 degrees clockwise; when C1 rotates counterclockwise, the direction vector of v1 (the direction vector of l1) rotates 90 degrees clockwise, and the direction vector of v2 (the direction vector of l2) rotates 90 degrees counterclockwise.

[0102] S5-2. Calculate the direction vector from the center of the first curve circle to the center of the second curve circle;

[0103] v3 = C21 - C11.

[0104] S5-3. Calculate the pseudo-central angles corresponding to the curves before and after;

[0105] δc1 = Angle(v1,v3);

[0106] When C1 rotates clockwise, δc2 = Angle(v2, -v3) + β;

[0107] When C1 rotates counterclockwise, δc2 = Angle(v2,-v3) - β;

[0108] Among them: Angle(v a ,v b The operation is the angle between vectors, i.e., the angle between vectors v. a Rotate to v b The angle through which it rotates and the direction of rotation are the same as the direction of rotation of C1.

[0109] S5-4. Calculate the combination of central angles corresponding to the arcs in the curves before and after the curves;

[0110] βc1=δc1-β a1 -β b1 -sin -1 (bf / r c );

[0111] βc2=δc2-β a2 -β b2 -sin -1 (bf / r c );

[0112] Where: β a1 Let β be the deflection angle of a1. b1 Let β be the deflection angle of b1. a2 Let β be the deflection angle of a2. b2 Let b2 be the deflection angle.

[0113] S5-5. Calculate the remaining combinations of central angles;

[0114] Replace C21 with C22, C23, and C24 in sequence, and repeat steps S5-1 to S5-4 to calculate the corresponding central angle combinations when the center of circle A2 is C22, C23, and C24. Replace C11 with C12, and replace C21 with C21′, C22′, C23′, and C24′ in sequence, and repeat steps S5-1 to S5-4 to calculate the corresponding central angle combinations when the center of circle A2 is C12 and when the center of circle A2 is C21′, C22′, C23′, and C24′.

[0115] S6: Calculate the shortest reverse curve;

[0116] The purpose of this step is to find the shortest reverse curve among all feasible reverse curves, that is, to find the center of the front and back curves {minC1,minC2} and the central angle {minβc1,minβc2} corresponding to the shortest reverse curve in the solution results of S4 and S5.

[0117] Summing up the central angles of the feasible front and back curves for CA1 and CA2 one by one, the combination of central angles corresponding to the minimum value is {minβc1,minβc2}, and the corresponding front and back curve centers are {minC1,minC2}.

[0118] S7: Connect two opposite curves with a straight line.

[0119] The purpose of this step is to connect the two curve segments with a straight line to form a complete reverse curve. Based on the calculation results of S6, draw C1 and C2, and connect the end point of C1 and the starting point of C2 with a straight line segment.

[0120] S8: Modify the terminating straight line segment to complete the reverse curve connection.

[0121] The purpose of this step is to connect the reverse curve with the preceding and following straight line segments to form a continuous whole.

[0122] When β is 0, modify l2 so that its starting point coincides with the ending point of the reverse curve, and connect l1, the reverse curve, and l2 in sequence to obtain the final result; when β is not 0, take the ending point of C2 as the starting point and draw a straight line l2′ along the tangential direction of the ending point of C2. l2′ intersects l2 at point p, which is the bifurcation point. Modify l2′ so that its ending point coincides with p, and connect l1, the reverse curve, and l2′ in sequence to obtain the final result.

[0123] When specifying the reverse curve connection parameters in S2, there is no need to specifically specify the rotation direction of C1 and C2. S3-S8 will automatically calculate the shortest transition curve.

[0124] In S4, when calculating the eight feasible center positions of the curve, non-existent centers are allowed in the calculation results. In this case, when calculating the central angles of the curve and the curve respectively in S5, the calculation process of the central angle combination corresponding to the non-existent center is skipped. In S6, when calculating the parameters of the shortest reverse curve, the comparison of the size of the central angle combination corresponding to the non-existent center is also skipped.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A highly adaptable reverse curve connection method for railway station design, characterized in that: Includes the following steps: S1: Specifies the parameters of the preceding and following straight lines and turnouts for the reverse curve connection; S2: Specifies the parameters for connecting the reverse curve; S3: Calculate the two feasible center positions of the previous curve; S4: The eight feasible center positions of the curve after calculation; S5: Calculate the central angles of the front and back curves respectively; S6: Calculate the shortest reverse curve; S7: Connect two opposite curves with a straight line; S8: Modify the terminating straight line segment to complete the reverse curve connection; The parameters for the preceding and following straight sections and turnouts specified in S1 for the reverse curve connection include the starting straight section of the specified reverse curve connection. Terminating straight segment When the terminal is connected to a turnout, specify the frog angle of the turnout. The distance from the fork to the rear rail gap of the frog Length of the straight section after the fork ; The specified reverse curve connection parameters in S2 include the specified front curve. The preceding term easing curve length Front curve Anterior easing curve type Front curve The subsequent easing curve length , front curve Type of subsequent easing curve , front curve arc radius , back curve The preceding term easing curve length , back curve Pre-gradient curve type , back curve Post-gradualization curve length , back curve Post-gradualization curve type ,curve arc radius Length of the straight line ; In S3, the two feasible center positions of the curve before calculation refer to the calculated... The center of the circle when rotating clockwise , The center of the circle when rotating counterclockwise ; The eight feasible center positions of the calculated curve in S4 refer to... The center is At that time, calculate Feasible center position , , , ; The center is At that time, calculate Feasible center position , , , ; The calculation of the eight feasible center positions of the curve in S4 specifically includes the following steps: S4-1. Calculate the length of the pseudo-clamping line between the front and back curves; ； in: for The tangent growth value, for tangent growth value; S4-2, Calculate the pseudo radius of the curve before and after; ； ； in: for The inner shift value, for internal shift value; S4-3. Calculate the circle containing the center of the curve. ； ； in: Let be the center of the circle. Let be the radius of the circle; S4-4. Calculate the two straight lines containing the center of the curve after calculation; ； ； ； in: For the line translation operation, the line is... Along Directional movement distance; for end point to unit vector, for exist Upper vertical projection point; for The inner shift value; S4-5. Calculate the feasible center positions of the curve after the curve is centered. Calculate the intersection point of the two lines containing the centers of circles S4-3 and S4-4. The intersection point is the intersection point of these two lines. Feasible center position , , , ; S4-6. Calculate the remaining feasible center positions of the curve after calculation; Will Replace with Repeat steps S4-3 to S4-5 above; calculate sequentially. , , , .

2. The highly adaptable reverse curve connection method for railway station design according to claim 1, characterized in that: In S5, calculating the central angles of the front and back curves refers to calculating different combinations of center angles. , The corresponding central angle.

3. The highly adaptable reverse curve connection method for railway station design according to claim 1, characterized in that: The shortest reverse curve calculated in S6 refers to the center of the preceding and following curves corresponding to the shortest reverse curve found in the solutions of S4 and S5. and central angle .

4. The highly adaptable reverse curve connection method for railway station design according to claim 1, characterized in that: In S8, modifying the terminating straight line segment to complete the reverse curve connection means that when... When the value is 0, modify Make its starting point coincide with the ending point of the reverse curve, and connect them sequentially. Reverse curve To obtain the final result; when When it is not 0, with Starting from the end point, along Draw a straight line in the tangential direction of the endpoint. , and Intersect at point ,point This refers to the location of the fork in the road; modifications are needed. Make its endpoint and Overlap, connect in sequence Reverse curve The final result is obtained.

5. A highly adaptable reverse curve connection method for railway station design according to claim 1, characterized in that: The calculation of the central angles of the front and back curves in step S5 includes the following steps: S5-1. Calculate the perpendicular vectors of the front and back lines; S5-2. Calculate the direction vector from the center of the first curve circle to the center of the second curve circle; S5-3. Calculate the pseudo-central angles corresponding to the curves before and after; ； when When rotating clockwise, ; when When rotating counterclockwise, ; in: The operation is the angle between vectors, that is, the operation between vectors. Rotate to The angle rotated, the direction of rotation and The rotation direction is the same; , Let be the perpendicular vectors of the front and back lines. This is the direction vector from the center of the front curve circle to the center of the back curve circle; S5-4. Calculate the combination of central angles corresponding to the arcs in the curves before and after the curves; ； ； in: for The deflection angle, for The deflection angle, for The deflection angle, for The deflection angle; S5-5. Calculate the remaining combinations of central angles; Will Replace with in sequence , , Repeat steps S5-1 to S5-4 to calculate The center is , , When, the corresponding combination of central angles; Replace with ,Will Replace with in sequence , , , Repeat steps S5-1 to S5-4 to calculate The center is , The center is , , , When, the corresponding combination of central angles.

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