A method for designing the gradient of turnouts

Abstract

This invention relates to the field of turnout technology, specifically a turnout gradient design method, comprising the following steps: S1. Obtaining the gradient limit of the turnout's straight track based on the track horizontal deviation limit and the track superelevation limit; S2. Setting the gradient of the turnout's straight track based on the gradient limit; S3. Obtaining the gradient of the turnout's side track based on the gradient of the turnout's straight track. This invention provides a turnout gradient design method that solves the problem of quantitatively calculating turnout gradient limits and the challenge of gradient matching design for the straight and side tracks after a turnout with a large gradient, providing a solution for gradient design in turnout areas of mountainous rail transit with large gradients.

Description

Technical Field

[0001] This invention relates to the field of turnout technology, and in particular to a turnout gradient design method. Background Technology

[0002] Currently, to meet the climbing requirements of rugged mountainous areas, mountain rail transit, represented by mountain railways and cogwheel railways, has made significant progress in recent years. For example, the maximum gradient of some existing mountain railways and cogwheel railways in China reaches 120‰, and the maximum design gradient of planned mountain railways and cogwheel railways reaches 250‰.

[0003] However, as a weak link in the track system, the gradient of railway turnouts in China is generally no more than 6‰, which has become a technical bottleneck restricting the climbing ability of mountain rail transit. Whether the turnout gradient can be further increased, and what the maximum gradient that each type of turnout can adapt to, are urgent problems to be solved in the design of mountain rail transit.

[0004] On the other hand, when a turnout is located on a steep gradient, the straight and siding tracks following the turnout lie in the same inclined plane and have an angle between them (frog angle), resulting in a difference in their gradient values. This difference has often been overlooked in previous railway designs, but it becomes increasingly apparent as the gradient increases. How to design gradient matching between the straight and siding tracks following a turnout on steep gradient sections is a crucial issue that cannot be ignored in mountain rail transit design.

[0005] Currently, there is a lack of mature experience in China regarding the determination of extreme gradient values ​​for turnouts and the matching design of gradients for straight and siding tracks after turnouts. The development of mountain rail transit urgently requires a turnout gradient design method that can adapt to tracks with steep gradients. Summary of the Invention

[0006] The purpose of this invention is to provide a turnout slope design method, addressing the lack of mature experience in China regarding the determination of turnout limit slopes and the matching design of slopes for straight and side tracks after turnouts.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for designing the gradient of a turnout includes the following steps:

[0009] S1. Based on the track horizontal deviation limit and the track superelevation limit, the gradient limit of the turnout straight track is obtained;

[0010] S2. Set the gradient of the turnout straight track according to the gradient limit of the turnout straight track;

[0011] S3. Obtain the slope of the turnout side track based on the slope of the straight track of the turnout.

[0012] This invention discloses a turnout slope design method. Based on track horizontal deviation limits and track superelevation limits, the slope limit for the turnout's straight track is obtained. The slope of the turnout's straight track is then set according to this slope limit. Finally, the slope of the turnout's side track is obtained based on the slope of the turnout's straight track. This method solves the problem of quantitatively calculating turnout slope limits and addresses the challenge of slope matching design for the straight and side tracks after a turnout with a large gradient. It provides a solution for slope design in turnout areas of mountainous rail transit with large gradients.

[0013] Preferably, step S1 specifically includes the following steps:

[0014] S11. Calculate the frog angle θ0 based on the turnout number;

[0015] S12. Based on the turnout angle θ0, and the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, the gradient angle limit α for the straight track with turnout is obtained. max ;

[0016] S13. Gradient Angle Limit α for Straight Track with Turnout max Obtain the gradient limit i for turnout straight track. max .

[0017] Preferably, step S12 specifically includes:

[0018] S121. Establish the frog angle θ0 and the maximum overrun / side track horizontal deviation η of the turnout guide curve. max The relationship model between the turnout and the slope angle α of the slope surface is defined as the first relationship model;

[0019] S122. Establish the maximum reverse overshoot / lateral track horizontal deviation η of the turnout guide curve. max The relationship model between the smaller value η0 of the track horizontal deviation limit and the track superelevation limit is defined as the second relationship model;

[0020] S123. Based on the first and second relational models, obtain the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, and the slope angle limit α of the turnout straight track. max The relationship model between them is defined as the third relationship model;

[0021] S124. Input the smaller value η0 among the frog angle θ0, track horizontal deviation limit, and track superelevation limit into the third relational model to obtain the slope angle limit α for the turnout straight track. max .

[0022] By transforming the first and second relational models, a third relational model is obtained. This model allows inputting the smaller of the frog angle θ0, the track horizontal deviation limit, and the track superelevation limit η0 into the third relational model, thus obtaining the slope angle limit α for the turnout straight track. max There is a certain logical relationship between them, so the gradient angle limit α of the turnout straight track can be calculated based on the turnout angle θ0, and the smaller value η0 of the track horizontal deviation limit and the track superelevation limit. max .

[0023] Preferably, the gradient angle limit α of the turnout straight track is obtained based on the turnout angle θ0, and the smaller value η0 between the track horizontal deviation limit and the track superelevation limit. max Specifically:

[0024] α max =arcsin(η0 / (s*sinθ0))

[0025] In the formula, α max —Slope angle limit for turnout straight track; η0—The smaller of the track horizontal deviation limit and track superelevation limit; s—Center distance of rails, i.e., the sum of track gauge and rail head width. For 60kg / m standard gauge railways, s = 1508mm; for 50kg / m meter gauge railways, s = 1070mm; θ0—Frog angle.

[0026] Preferably, step S13 specifically includes: i max =tanα max

[0027] Where: i max —Gradient limit for turnout straight track; α max —Slope angle limit for turnout straight track.

[0028] Preferably, step S2 specifically involves: based on the gradient limit i of the turnout straight track. max The actual gradient of the turnout straight track is i, where i ≤ i max .

[0029] Step S3 is as follows:

[0030] S31. Obtain the corresponding actual slope angle α of the turnout straight track based on the actual slope i of the turnout straight track.

[0031] S32. The slope angle α of the side track of the turnout is obtained from the frog angle θ0 and the actual slope angle α of the straight track of the turnout. c ;

[0032] S33. Based on the gradient angle α of the track side of the turnout c Obtain the corresponding turnout side track gradient i c .

[0033] Preferably, step S31 specifically involves: α = arctan(i)

[0034] Where: i—actual gradient of the turnout straight track; α—actual gradient angle of the turnout straight track;

[0035] Preferably, step S32 specifically includes: α c =arcsin(cosθ0·sinα)

[0036] Where: α c — Gradient angle of the turnout side track; θ0 — Fault angle; α — Actual gradient angle of the turnout straight track;

[0037] Preferably, step S33 specifically includes: i c =tanα c

[0038] Where: i c —Slope of the track on the turnout side; α c —Slope angle of the track on the turnout side.

[0039] This application also discloses another method for designing turnout gradients, comprising the following steps:

[0040] A1. Establish a relationship model between track horizontal deviation / guide curve superelevation η, the angle θ between the center lines of the turnout straight track and the side track, and the slope angle α of the slope where the turnout is located, and define it as the fourth relationship model;

[0041] A2. Input the slope angle α of the slope where the turnout is located and the angle θ between the center lines of the straight and side tracks of the turnout into the fourth relational model to obtain the turnout track horizontal deviation / guide curve superelevation η.

[0042] This invention provides a turnout slope design method, which obtains the turnout track horizontal deviation / guide curve superelevation η based on the slope angle α of the slope surface where the turnout is located and the angle θ between the center lines of the straight and side tracks of the turnout; thus solving the problem of quantitative calculation of turnout track horizontal deviation / guide curve superelevation η.

[0043] Preferably, the fourth relational model is: η = s·sinθ·sinα

[0044] Where: s—the center distance of the rails, i.e., the sum of the track gauge and the width of the rail head; θ—the angle between the center lines of the straight track and the side track of the turnout; within the guide curve range, 0≤θ≤θ0, and at the end of the guide curve, θ=θ0; the straight section of the side track of the turnout after the guide curve, θ=θ0. Where θ0 is the turnout frog angle; α—the slope angle α of the slope where the turnout is located. α=arctan(i), where i is the slope of the straight track of the turnout.

[0045] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0046] 1. This invention provides a turnout slope design method. Based on the track horizontal deviation limit and the track superelevation limit, the slope limit of the turnout straight track is obtained; the slope of the turnout straight track is set according to the slope limit of the turnout straight track; and the slope of the turnout side track is obtained according to the slope of the turnout straight track. This solves the problem of quantitative calculation of turnout slope limit and the slope matching design problem of the straight and side tracks after the turnout of a turnout with a large gradient, providing a solution for the slope design of the turnout area in the steep gradient section of mountain rail transit.

[0047] 2. This invention provides a turnout slope design method, which obtains the turnout track horizontal deviation / guide curve superelevation η based on the slope angle α of the slope surface where the turnout is located and the angle θ between the center lines of the straight and side tracks of the turnout; thus solving the problem of quantitative calculation of the turnout track horizontal deviation / guide curve superelevation η. Attached Figure Description

[0048] Figure 1 This is the main flowchart of a turnout gradient design method.

[0049] Figure 2 This is a schematic diagram of the horizontal deviation of the track.

[0050] Figure 3 This is a schematic diagram of the horizontal deviation of the turnout side track on a steep slope.

[0051] Figure 4 This is a schematic diagram of the turnout guide curve for reverse superelevation on a steep slope.

[0052] Figure 5 This is the overall diagram for calculating the horizontal deviation of the turnout side track on a steep slope.

[0053] Figure 6 This is a detailed diagram showing the calculation of the horizontal deviation of the turnout side track on a steep slope.

[0054] Figure 7 This is a schematic diagram showing the relationship between the angle θ between AB and CD and the turn angle θ0.

[0055] Figure 8 This is a schematic diagram showing the relationship between the gradient angle of the straight track and the gradient angle of the side track.

[0056] Attached diagram descriptions: 1-Left rail; 2-Right rail; 3-Turnout; 4-Center line of turnout side rail; 5-Center line of turnout straight rail. Detailed Implementation

[0057] The present invention will now be described in detail with reference to the accompanying drawings.

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0059] Example 1

[0060] like Figure 1-8 As shown in this embodiment, a turnout slope design method is described. Figure 1 This is the main flowchart of the technical solution of this invention. For example... Figure 1 As shown, a turnout gradient design method includes the following steps:

[0061] S1: Based on the track horizontal deviation limit and the track anti-over-height limit, the gradient limit of the turnout straight track is obtained.

[0062] S2: Set the gradient of the turnout straight track according to the gradient limit of the turnout straight track.

[0063] S3: Obtain the slope of the side track of the turnout based on the slope of the straight track of the turnout.

[0064] Step S1: Calculate the gradient limit for the turnout straight track based on the track horizontal deviation limit and the track superelevation limit. The specific procedure is as follows:

[0065] 1. First, based on the turnout number, the frog angle θ0 is calculated using the following formula:

[0066] θ0=arctan(1 / n) Equation (1)

[0067] Where: θ0—frog angle; n—turnout number, such as turnouts No. 7, No. 9, No. 12, and No. 18, with n taking values ​​of 7, 9, 12, and 18 respectively.

[0068] 2. Then, according to relevant design specifications, take the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, and calculate the gradient angle limit α of the turnout straight track using the following formula. max :

[0069] α max =arcsin(η0 / (s·sinθ0) ) Formula (2)

[0070] Where: α max —The slope angle limit for straight track turnouts; η0—The smaller of the track horizontal deviation limit and the track superelevation limit; s—The center distance of the rails, i.e., the sum of the track gauge and the width of the rail head. For 60kg / m standard gauge railways, s=1508mm; for 50kg / m meter gauge railways, s=1070mm; θ0—The frog angle, which is obtained from equation (1).

[0071] 3. The corresponding gradient limit for the straight track of the turnout is:

[0072] i max =tanα max Equation (3)

[0073] Where: i max —Gradient limit for turnout straight track; α max —The gradient angle limit for the straight track of the turnout is obtained from equation (2).

[0074] II. Step S2: Set the gradient of the turnout straight track according to the gradient limit of the turnout straight track and the actual engineering requirements. The specific procedure is as follows:

[0075] 1. Within the gradient limit i of the turnout straight track. max Under the premise of actual engineering needs, the actual gradient i of the turnout straight track is set;

[0076] 3. Step S3: Calculate the slope of the turnout side track based on the slope of the straight track of the turnout.

[0077] The specific steps are as follows:

[0078] 1. Based on the actual gradient i of the turnout straight track, the corresponding actual gradient angle of the turnout straight track is:

[0079] α = arctan(i) Equation (4)

[0080] Where: i—actual gradient of the turnout straight track, determined by step (1) in S2; α—actual gradient angle of the turnout straight track.

[0081] 2. Based on the turnout frog angle and the actual gradient angle of the straight track, the gradient angle of the track on the turnout side is calculated:

[0082] α c =arcsin(cosθ0·sinα) Formula (5)

[0083] Where: α c —Slope angle of the turnout side track; θ0—Frog angle, obtained from equation (1); α—Slope angle of the turnout straight track, obtained from equation (4).

[0084] 3. The corresponding gradient of the turnout side track is:

[0085] i c =tanα c Equation (6)

[0086] Where: i c —Slope of the track on the turnout side; α c —The gradient angle of the track on the turnout side is obtained from equation (5).

[0087] Equation (2) "α max The derivation of “=arcsin(η / (s·sinθ0))”:

[0088] Track horizontal deviation refers to the relative height difference between the top surfaces of the left and right rails. Figure 2 As shown, track horizontal deviation is the relative height difference between the top surfaces of the left rail (1) and the right rail (2). To maintain stable train operation and uniform stress on both rails, the top surfaces of the two rails on a straight track should theoretically be at the same level, meaning the track horizontal deviation should be as close to zero as possible. However, in actual engineering projects, due to construction errors, turnout construction, and other reasons, a certain level of track horizontal deviation always exists. my country's "Railway Track Design Code (TB10082-2017)" and "Railway Dedicated Line Design Code (Trial) (TB10638-2019)" both specify limits for track horizontal deviation.

[0089] When a train passes through a curve, it generates a centrifugal force outward along the curve's normal. Generally, a certain superelevation is required on the outer rail of the curve to balance this centrifugal force using the horizontal component of the train's weight. However, due to the shorter length of the guide curve within a turnout and the presence of complex structures such as switch rails and frogs before and after it, superelevation cannot be implemented. In the actual installation of turnouts, reverse superelevation should be avoided as much as possible to prevent potential safety hazards. my country's "Rules for Repairing Conventional Speed ​​Railway Lines (TG / GW102-2019)" and other standards stipulate limits for reverse superelevation on guide curves.

[0090] When a turnout is installed on a steep gradient, the entire frame of the turnout lies on an inclined plane, such as... Figure 3 As shown. Figure 3 Plane P1 is the plane where turnout 3 is located, and plane P2 is the horizontal plane passing through any point B on the rail on the turnout side. On plane P1, draw a straight line perpendicular to the other rail through point B, intersecting the rail at point A. Then AB is the normal to the centerline of the track on the turnout side. According to the definition of track horizontal deviation mentioned above, the height difference between points A and B is the track horizontal deviation value at that point. Figure 3 As can be seen, point A is significantly higher than point B, therefore there is a track level deviation on the turnout side track.

[0091] Specifically, when points A and B are located within the turnout guide curve, such as Figure 4 As shown. Since point A is located in the lower strand of the guide curve (i.e., the inner strand of the curve) and point B is located in the upper strand of the guide curve (i.e., the outer strand of the curve), and point A is higher than point B, it means that there is a superelevation of the guide curve. The value of the superelevation is the height difference between points A and B.

[0092] The following calculations, based on the principles of solid geometry, examine the horizontal deviation of the side track and the superelevation of the guide curve of a turnout on a steep gradient.

[0093] Let CD be the intersection of plane P1 and plane P2. Figure 3 (or Figure 4 Add the following auxiliary lines to the diagram:

[0094] Draw a perpendicular line from point A to plane P2, intersecting plane P2 at point O. Then AO⊥plane P2. Draw a line from point O perpendicular to CD, intersecting CD at point F. Then OF⊥CD. Connect points A and F, as shown below. Figure 5 As shown. The local details near points A and B are as follows: Figure 6 As shown.

[0095] from Figure 5 and Figure 6 As can be seen from this, the length of line segment AB is the center distance s between the left and right rails, which is the sum of the rail gauge and the width of the rail head.

[0096] like Figure 5 As shown, since plane P1 is the slope surface where the turnout is located and plane P2 is a horizontal plane, the angle between plane P1 and plane P2 is the slope angle α of the slope surface where the turnout is located (i.e., the slope angle of the straight track of the turnout). Slope angle α = arctan(i), where i is the slope of the straight track of the turnout.

[0097] like Figure 6 As shown, since line AO⊥plane P2, AO is perpendicular to any line on plane P2, therefore AO⊥CD. Also, since OF⊥CD, CD⊥plane AOF, therefore CD⊥AF. Lines AF and OF are located in planes P1 and P2 respectively, and are both perpendicular to the intersection line CD of the two planes. Therefore, the angle between AF and OF is the angle α between the two planes (i.e., the gradient angle of the turnout straight track).

[0098] like Figure 5 and Figure 7 As shown, in plane P1, since line AB is the normal to the center line of the turnout side track and line CD is the normal to the center line of the turnout straight track, the angle θ between line AB and line CD is the angle between the center lines of the turnout straight track and side track.

[0099] like Figure 7 As shown, within the guide curve range, θ gradually increases from front to back along the guide curve, reaching its maximum value θ0 at the end of the guide curve; on the straight segment after the end of the guide curve, θ = θ0. Where θ0 is the turnout frog angle, and its conversion relationship with the turnout number n is: θ0 = arctan(1 / n).

[0100] Based on the turnout angle θ0, and the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, the gradient angle limit α for the straight track with turnout is obtained. max Specifically as follows:

[0101] Establish the frog angle θ0 and the maximum reverse overshoot / side track horizontal deviation η of the turnout guide curve. max The relationship model between the turnout and the slope angle α of the slope surface is defined as the first relationship model;

[0102] Establish the maximum reverse overrun / side track horizontal deviation η of the turnout guide curve max The relationship model between the smaller value η0 of the track horizontal deviation limit and the track superelevation limit is defined as the second relationship model;

[0103] Based on the first and second relational models, the smaller value η0 between the track horizontal deviation limit and the track superelevation limit is obtained, along with the slope angle limit α for the turnout straight track. max The relationship model between them is defined as the third relationship model;

[0104] By inputting the smaller value η0 from the turnout angle θ0, the track horizontal deviation limit, and the track superelevation limit into the third relational model, the gradient angle limit α for the turnout straight track is obtained. max .

[0105] By transforming the first and second relational models, a third relational model is obtained. This model allows inputting the smaller of the frog angle θ0, the track horizontal deviation limit, and the track superelevation limit η0 into the third relational model, thus obtaining the slope angle limit α for the turnout straight track. max There is a certain logical relationship between them, so the gradient angle limit α of the turnout straight track can be calculated based on the turnout angle θ0, and the smaller value η0 of the track horizontal deviation limit and the track superelevation limit. max .

[0106] Specifically, such as Figure 6 As shown, in right triangle AFB, |AF|=|AB|·sinθ=s·sinθ; in right triangle AOF, |AO|=|AF|·sinα=s·sinθ·sinα.

[0107] Since points O and B are located on the same horizontal plane P2, their elevations are the same. Therefore, the elevation difference between points A and B is |AO|. Thus, the track horizontal deviation / superelevation η of the guide curve is:

[0108] η = s·sinθ·sinα (Equation 7)

[0109] Where: s—the center distance of the rails, i.e., the sum of the track gauge and the width of the rail head. For 60kg / m standard gauge railways, s = 1508mm; for 50kg / m meter gauge railways, s = 1070mm; θ—the angle between the center lines of the turnout's straight track and side track. Within the guide curve range, 0 ≤ θ ≤ θ0; at the end of the guide curve, θ = θ0; the straight section of the turnout's side track after the guide curve, θ = θ0. Where θ0 is the turnout frog angle; α—the slope angle α of the slope where the turnout is located. α = arctan(i), where i is the slope of the turnout's straight track.

[0110] For a given set of turnouts, the rail center distance *s* and frog angle *θ0* are fixed values. According to equation (7), within the turnout guide curve range, due to the gradual change of the angle *θ* between the center lines of the straight and side rails, the superelevation of the guide curve gradually increases from front to back along the guide curve. At the end of the guide curve, *θ* = *θ0*, and the superelevation reaches its maximum value *s·sinθ0·sinα*. After the end of the guide curve, the angle *θ* between the center lines of the straight and side rails is a fixed value *θ0*, so the horizontal deviation of the side rail track is also *s·sinθ0·sinα*. Therefore, in a given set of turnouts, the maximum superelevation of the turnout guide curve / horizontal deviation of the side rail track is:

[0111] η max =s·sinθ0·sinα Equation (8)

[0112] Where: η max — Maximum reverse superelevation / side track horizontal deviation of turnout guide curve; s — Rail center distance; θ0 — Fault angle; α — Slope angle α of the slope where the turnout is located, i.e., the slope angle of the straight track of the turnout.

[0113] Maximum reverse overrun / side track horizontal deviation η of turnout guide curve max It should not exceed the track horizontal deviation limit and the track superelevation limit. Let η0 be the smaller value between the track horizontal deviation limit and the track superelevation limit. Then it should satisfy:

[0114] η max ≤η0 Equation (9)

[0115] Substituting equation (8) into equation (9), we get:

[0116] s·sinθ0·sinα≤η0 Formula (10)

[0117] By transforming equation (10), we can obtain:

[0118] α≤arcsin(η0 / (s·sinθ0) ) Formula (11)

[0119] Right now:

[0120] α max=arcsin(η0 / (s·sinθ0))

[0121] Where: α max —Slope angle limit for turnout straight track; η0—The smaller of the track horizontal deviation limit and track superelevation limit; s—Center-to-center distance of rails, i.e., the sum of track gauge and rail head width. For 60kg / m standard gauge railways, s = 1508mm; for 50kg / m meter gauge railways, s = 1070mm; θ0—Frog angle.

[0122] In formula (5), the formula "α" c The derivation of “ =arcsin(cosθ0·sinα)”:

[0123] Figure 8 Plane P1 is the plane containing turnout 3, and plane P3 is the horizontal plane passing through point M on the center line of the turnout's straight track. Plane P3 intersects the center line 4 of the turnout's side track at point N. Let H be the intersection point of the center line 5 of the turnout's straight track and the center line 4 of the side track. Then the angle between straight lines HM and HN is the turnout frog angle θ0. Draw a perpendicular line from point H to the horizontal plane P3, intersecting plane P3 at point G. Connect GM and GN, then HG⊥GM and HG⊥GN. Therefore, the angle between straight lines HM and GM is the actual slope angle α of the turnout's straight track, and the angle between straight lines HN and GN is the slope angle α of the turnout's side track. c In addition, since the turnout sleepers on the straight track must be installed horizontally, MN⊥HM.

[0124] In right triangle HGM:

[0125] sinα=|HG| / |HM| Equation (12)

[0126] In right triangle HGN:

[0127] sinα c =|HG| / |HN| Equation (13)

[0128] In right triangle HMN:

[0129] cosθ0=|HM| / |HN| Equation (14)

[0130] By combining equations (12), (13), and (14) and eliminating |HG|, |HM|, and |HN|, we can obtain:

[0131] sinα c =cosθ0 ·sinα Equation (15)

[0132] Right now:

[0133] α c=arcsin(cosθ0·sinα)

[0134] Where: α c —Slope angle of the turnout side track; θ0—Frog angle; α—Actual slope angle of the turnout straight track.

[0135] The following uses an actual test line as an example to illustrate the application of the turnout slope design method of the present invention in actual engineering.

[0136] A rack railway was selected, with a total length of 698m, including a main line of 525m and a siding of 173m. A set of meter-gauge No. 7 turnouts needs to be installed at the junction of the main line and the siding. The design process for the turnout gradient is as follows:

[0137] Step S1: Calculate the gradient limit for the turnout straight track based on the track horizontal deviation limit and the track superelevation limit. The specific procedure is as follows:

[0138] (1) First, the frog angle is calculated using the following formula based on the turnout number:

[0139] θ0 = arctan(1 / n)

[0140] For turnout No. 7, n = 7, then θ0 = arctan(1 / 7) = 8.13°.

[0141] (2) Then, according to the relevant design specifications, take the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, and calculate the gradient angle limit of the turnout straight track using the following formula:

[0142] α max =arcsin(η0 / (s·sinθ0))

[0143] According to the "Railway Track Design Code (TB10082-2017)," the limit for track horizontal deviation is 4mm; according to the "Rules for Repairing Conventional Speed ​​Railway Lines (TG / GW 102-2019)," the limit for guide curve superelevation is 2mm; therefore, η0 = 2mm is taken. The rack railway is a 50kg / m meter gauge railway, so s = 1070mm is taken. Therefore, the limit for the gradient angle of the turnout straight track is:

[0144] α max =arcsin(2 / (1070*sin(8.13°)))=0.757°

[0145] (3) The corresponding gradient limit for the turnout straight track is:

[0146] i max =tanα max =tan(0.757°) = 13.218‰

[0147] Step S2: Set the gradient of the turnout straight track according to the gradient limit and actual engineering requirements. The specific procedure is as follows:

[0148] (1) Within the gradient limit i of the turnout straight track. max Under the premise of actual engineering needs, the actual gradient i of the turnout straight track is set;

[0149] Provided that the gradient does not exceed the limit of 13.218‰ for the straight track of the turnout, and based on the track gradient requirements at the junction of the main line and the side line of the Ziyang rack test line, the actual gradient of the straight track of the turnout is set at i = 8.52‰.

[0150] (2) The actual gradient angle of the corresponding turnout straight track is:

[0151] α=arctan(i)=arctan(8.52‰)=0.488°

[0152] Step S3: Calculate the gradient of the track beside the turnout based on the gradient of the straight track. The specific procedure is as follows:

[0153] (1) The slope angle of the track on the turnout side is calculated based on the turnout frog angle and the actual slope angle of the straight track:

[0154] α c =arcsin(cosθ0·sinα)=arcsin(cos(8.13°)·sin(0.488°))=0.483°

[0155] (2) The gradient of the corresponding turnout side track is:

[0156] i c =tanα c =tan(0.483°) = 8.43‰

[0157] In summary, the turnout gradient design method of this invention first calculates the gradient limit for the straight track of the No. 7 meter gauge turnout on the rack test line to be 13.218‰ based on the track horizontal deviation limit and track superelevation limit specified in the specifications. Then, based on the turnout straight track gradient limit and actual engineering requirements, the turnout straight track gradient is set to 8.52‰. Finally, based on the turnout straight track gradient, the gradient of the turnout side track is calculated to be 8.43‰. The rack test line designed using this invention's turnout gradient design method underwent actual operation testing, and the test train performed well, proving the correctness and practicality of this invention's turnout gradient design method.

[0158] Example 2

[0159] This embodiment also discloses another method for designing turnout gradients, comprising the following steps:

[0160] A1. Establish a relationship model between track horizontal deviation / guide curve superelevation η, the angle θ between the center lines of the turnout straight track and the side track, and the slope angle α of the slope where the turnout is located, and define it as the fourth relationship model;

[0161] A2. Input the slope angle α of the slope where the turnout is located and the angle θ between the center lines of the straight and side tracks of the turnout into the fourth relational model to obtain the turnout track horizontal deviation / guide curve superelevation η.

[0162] Preferably, the fourth relational model is: η = s·sinθ·sinα

[0163] Where: s—the center distance of the rails, i.e., the sum of the track gauge and the width of the rail head. For 60kg / m standard gauge railways, s = 1508mm; for 50kg / m meter gauge railways, s = 1070mm; θ—the angle between the center lines of the turnout's straight track and side track. Within the guide curve range, 0 ≤ θ ≤ θ0. At the end of the guide curve, θ = θ0; the straight section of the turnout's side track after the guide curve, θ = θ0. Where θ0 is the turnout frog angle; α—the slope angle α of the slope where the turnout is located. α = arctan(i), where i is the slope of the turnout's straight track.

[0164] Specifically, track horizontal deviation refers to the relative height difference between the top surfaces of the left and right rails, such as... Figure 2 As shown, track horizontal deviation is the relative height difference between the top surfaces of the left rail (1) and the right rail (2). To maintain stable train operation and uniform stress on both rails, the top surfaces of the two rails on a straight track should theoretically be at the same level, meaning the track horizontal deviation should be as close to zero as possible. However, in actual engineering projects, due to construction errors, turnout construction, and other reasons, a certain level of track horizontal deviation always exists. my country's "Railway Track Design Code (TB10082-2017)" and "Railway Dedicated Line Design Code (Trial) (TB10638-2019)" both specify limits for track horizontal deviation.

[0165] When a train passes through a curve, it generates a centrifugal force outward along the curve's normal. Generally, a certain superelevation is required on the outer rail of the curve to balance this centrifugal force using the horizontal component of the train's weight. However, due to the shorter length of the guide curve within a turnout and the presence of complex structures such as switch rails and frogs before and after it, superelevation cannot be implemented. In the actual installation of turnouts, reverse superelevation should be avoided as much as possible to prevent potential safety hazards. my country's "Rules for Repairing Conventional Speed ​​Railway Lines (TG / GW102-2019)" and other standards stipulate limits for reverse superelevation on guide curves.

[0166] When a turnout is installed on a steep gradient, the entire frame of the turnout lies on an inclined plane, such as... Figure 3 As shown. Figure 3Plane P1 is the plane where turnout 3 is located, and plane P2 is the horizontal plane passing through any point B on the rail on the turnout side. On plane P1, draw a straight line perpendicular to the other rail through point B, intersecting the rail at point A. Then AB is the normal to the centerline of the track on the turnout side. According to the definition of track horizontal deviation mentioned above, the height difference between points A and B is the track horizontal deviation value at that point. Figure 3 As can be seen, point A is significantly higher than point B, therefore there is a track level deviation on the turnout side track.

[0167] Specifically, when points A and B are located within the turnout guide curve, such as Figure 4 As shown. Since point A is located in the lower strand of the guide curve (i.e., the inner strand of the curve) and point B is located in the upper strand of the guide curve (i.e., the outer strand of the curve), and point A is higher than point B, it means that there is a superelevation of the guide curve. The value of the superelevation is the height difference between points A and B.

[0168] The following calculations, based on the principles of solid geometry, examine the horizontal deviation of the side track and the superelevation of the guide curve of a turnout on a steep gradient.

[0169] Let CD be the intersection of plane P1 and plane P2. Figure 3 (or Figure 4 Add the following auxiliary lines to the diagram:

[0170] Draw a perpendicular line from point A to plane P2, intersecting plane P2 at point O. Then AO⊥plane P2. Draw a line from point O perpendicular to CD, intersecting CD at point F. Then OF⊥CD. Connect points A and F, as shown below. Figure 5 As shown. The local details near points A and B are as follows: Figure 6 As shown.

[0171] from Figure 5 and Figure 6 As can be seen from this, the length of line segment AB is the center distance s between the left and right rails, which is the sum of the rail gauge and the width of the rail head.

[0172] like Figure 5 As shown, since plane P1 is the slope surface where the turnout is located and plane P2 is a horizontal plane, the angle between plane P1 and plane P2 is the slope angle α of the slope surface where the turnout is located (i.e., the slope angle of the straight track of the turnout). Slope angle α = arctan(i), where i is the slope of the straight track of the turnout.

[0173] like Figure 6As shown, since line AO⊥plane P2, AO is perpendicular to any line on plane P2, therefore AO⊥CD. Also, since OF⊥CD, CD⊥plane AOF, therefore CD⊥AF. Lines AF and OF are located in planes P1 and P2 respectively, and are both perpendicular to the intersection line CD of the two planes. Therefore, the angle between AF and OF is the angle α between the two planes (i.e., the gradient angle of the turnout straight track).

[0174] like Figure 5 and Figure 7 As shown, in plane P1, since line AB is the normal to the center line of the turnout side track and line CD is the normal to the center line of the turnout straight track, the angle θ between line AB and line CD is the angle between the center lines of the turnout straight track and side track.

[0175] like Figure 7 As shown, within the guide curve range, θ gradually increases from front to back along the guide curve, reaching its maximum value θ0 at the end of the guide curve; on the straight segment after the end of the guide curve, θ = θ0. Where θ0 is the turnout frog angle, and its conversion relationship with the turnout number n is: θ0 = arctan(1 / n).

[0176] like Figure 6 As shown, in right triangle AFB, |AF|=|AB|·sinθ=s·sinθ; in right triangle AOF, |AO|=|AF|·sinα=s·sinθ·sinα.

[0177] Since points O and B are located on the same horizontal plane P2, their elevations are the same. Therefore, the elevation difference between points A and B is |AO|. Thus, the track horizontal deviation / guide curve superelevation η is:

[0178] η=s·sinθ·sinα

[0179] Where: s—the center distance of the rails, i.e., the sum of the track gauge and the width of the rail head. For 60kg / m standard gauge railways, s = 1508mm; for 50kg / m meter gauge railways, s = 1070mm; θ—the angle between the center lines of the turnout's straight track and side track. Within the guide curve range, 0 ≤ θ ≤ θ0; at the end of the guide curve, θ = θ0; the straight section of the turnout's side track after the guide curve, θ = θ0. Where θ0 is the turnout frog angle; α—the slope angle α of the slope where the turnout is located. α = arctan(i), where i is the slope of the turnout's straight track.

[0180] The above formula: η=s·sinθ·sinα is defined as the fourth relational model. In the construction design calculation, the slope angle α of the slope where the turnout is located and the angle θ between the center lines of the straight and side strands of the turnout are input into the fourth relational model to obtain the turnout track horizontal deviation / guide curve superelevation η at each point on the track.

[0181] This embodiment describes a turnout slope design method that, based on the slope angle α of the slope where the turnout is located and the angle θ between the centerlines of the straight and side tracks of the turnout, obtains the turnout track horizontal deviation / guide curve superelevation η; thus solving the quantitative calculation problem of turnout track horizontal deviation / guide curve superelevation η. The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing the gradient of a turnout, characterized in that, Includes the following steps: S1. Based on the track horizontal deviation limit and the track superelevation limit, the gradient limit for the turnout straight track is obtained: S11. Calculate the frog angle θ0 based on the turnout number; S12. Based on the turnout angle θ0, and the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, the gradient angle limit α for the straight track with turnout is obtained. max ; Step S12 is as follows: S121. Establish the frog angle θ0 and the maximum overrun / side track horizontal deviation η of the turnout guide curve. max The relationship model between the turnout and the slope angle α of the slope surface is defined as the first relationship model; S122. Establish the maximum reverse overshoot / lateral track horizontal deviation η of the turnout guide curve. max The relationship model between the smaller value η0 of the track horizontal deviation limit and the track superelevation limit is defined as the second relationship model; S123. Based on the first and second relational models, obtain the smaller value η0 between the track horizontal deviation limit and the track superelevation limit, and the slope angle limit α of the turnout straight track. max The relationship model between them is defined as the third relationship model; S124. Input the smaller value η0 among the frog angle θ0, track horizontal deviation limit, and track superelevation limit into the third relational model to obtain the slope angle limit α for the turnout straight track. max ; S1 3. Gradient angle limit α for straight track with turnout max Obtain the gradient limit i for turnout straight track. max ; S2. Set the gradient of the turnout straight track according to the gradient limit of the turnout straight track; S3. Obtain the slope of the turnout side track based on the slope of the straight track of the turnout.

2. The turnout gradient design method according to claim 1, characterized in that: Step S13 is as follows: imax=tanαmax Where: i max —Gradient limit for turnout straight track; α max —Slope angle limit for turnout straight track.

3. The turnout gradient design method according to claim 1, characterized in that: Step S2 specifically involves: based on the gradient limit i of the turnout straight track. max The actual gradient of the turnout straight track is i, where i ≤ i max .

4. The turnout gradient design method according to claim 1, characterized in that: Step S3 is as follows: S31. Obtain the corresponding actual slope angle α of the turnout straight track based on the actual slope i of the turnout straight track. S32. The slope angle α of the side track of the turnout is obtained from the frog angle θ0 and the actual slope angle α of the straight track of the turnout. c ; S33. Based on the gradient angle α of the track side of the turnout c Obtain the corresponding turnout side track gradient i c .

5. The turnout gradient design method according to claim 4, characterized in that: Step S31 is as follows: α = arctan(i) Where: i—actual gradient of the turnout straight track; α—actual gradient angle of the turnout straight track; And / or, Step S32 specifically involves: α c =arcsin(cosθ0 sinα) Where: α c — Gradient angle of the turnout side track; θ0 — Frog angle; α — Actual gradient angle of the turnout straight track; And / or, Step S33 specifically refers to: i c =tanα c Where: i c —Slope of the track on the turnout side; α c —Slope angle of the track on the turnout side.

6. The turnout gradient design method according to claim 1, characterized in that: The quantitative calculation of turnout track horizontal deviation / guide curve superelevation η includes the following steps: A1. Establish a relationship model between track horizontal deviation / guide curve superelevation η, the angle θ between the center lines of the turnout straight track and the side track, and the slope angle α of the slope where the turnout is located, and define it as the fourth relationship model; A2. Input the slope angle α of the slope where the turnout is located and the angle θ between the center lines of the straight and side tracks of the turnout into the fourth relational model to obtain the turnout track horizontal deviation / guide curve superelevation η.

7. The turnout gradient design method according to claim 6, characterized in that: The fourth relational model is specifically: η=s sinθ sinα Where: s—the center distance of the rails, i.e., the sum of the rail gauge and the width of the rail head; θ—the angle between the center lines of the turnout straight track and the side track, 0≤θ≤θ0 within the guide curve range, and θ=θ0 at the end of the guide curve; θ=θ0 for the straight section of the turnout side track after the guide curve, where θ0 is the turnout frog angle; α—the slope angle of the slope where the turnout is located, α=arctan(i), where i is the slope of the turnout straight track.

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