A Design Method for the Rack and Pinion Unit of the Curved Section of a Rack Rail Line

Abstract

The present invention discloses a design method for the rack unit of the rack rail on the curve part of a rack rail line, which relates to the field of rack rail railway design and comprises the following steps: S1: Establish a calculation model for the rack rail curve; S2: Establish a spatial coordinate system with the initial end of the rack rail line as the origin of the coordinate system; S3: Substitute the designed transition curve length L', the designed circular curve radius R', and the designed rack unit length l' of the pre-constructed track into the calculation model for the rack rail curve to obtain the endpoint coordinates of all rack units on the pre-constructed track. By establishing a calculation model for the rack rail curve through the preset values of the rack rail superelevation threshold, the transition curve length, and the circular curve length, the present invention realizes the data calculation of the endpoints of all rack units in the rack rail on the curve part, speeds up the preliminary simulation process of the rack rail, and effectively improves the overall design speed of the rack rail track. It has the advantages of being fast and accurate, providing a good theoretical basis for the actual design and construction of the rack rail railway.

Description

Technical Field

[0001] The present invention relates to the field of rack railway design, and particularly to a design method for rack and pinion units in the curved section of a rack railway track. Background Art

[0002] A rack railway is a mountain railway. By setting a special rack on the sleeper in the middle of the ordinary track, a locomotive running on the rack railway is equipped with one or more gears that mesh with the rack to overcome the problem of insufficient adhesion between the locomotive and the track, enabling the locomotive to travel on a steep slope of up to 48 degrees.

[0003] In the construction of a rack railway, it is very important to ensure that the cooperation between the train and the rack meets the requirements. Different from the adhesion design between train wheels and tracks in the prior art, the construction of the rack needs to consider the meshing situation between the running gears and the rack. In the prior art, there is no method or model for rapid virtual design to determine the rack parameters and operating performance. Usually, it is obtained through experimental methods, which have the following disadvantages: 1) It takes a certain amount of time and economic cost to build a test line; 2) The data obtained from the test line can only show the operating performance of the rack train on the test line. In reality, the rack railway track often has a certain slope, includes a curved section and superelevation, and these parameters have a great impact on the actual operating performance of the train. Therefore, the data obtained from the test line is specific and difficult to reflect different line operating conditions; 3) For a 200m railway, about 160 racks are required, and the coordinates, superelevation, inclination and other parameters of each rack are different. If the relevant parameters of a single rack need to be calculated one by one in the actual line construction, or if a model is built in computer software, several gear elements also need to be manually established in the software, which is very time-consuming and error-prone. The length of the test line is short and the curve radius is small. The number of rack rail parameters to be calculated is negligible compared to the number required for the actual line, and it is difficult to play a guiding role in actual design and construction. Therefore, the technology for rapid and batch calculation of rack rail parameters needs to be further studied. Summary of the Invention

[0004] In view of the above deficiencies of the prior art, the present invention provides a design method for rack and pinion units in the curved section of a rack railway track that can quickly calculate the parameters of each rack unit.

[0005] To achieve the above invention objective, the technical solution adopted by the present invention is as follows:

[0006] Provide a design method for rack and pinion units in the curved section of a rack railway track, which includes the following steps:

[0007] S1: Establish a rack curve calculation model;

[0008] S2: Establish a spatial coordinate system with the initial end of the rack rail line as the origin of the coordinate system;

[0009] Among them, the x-axis of the spatial coordinate system is the tangent line of the projection initial end of the pre-constructed rack rail on the horizontal plane, and one side of the pre-constructed rack rail is the positive direction of the x-axis; the y-axis is on the same horizontal plane as the x-axis, and one side of the pre-constructed rack rail is the positive direction of the y-axis; the positive direction of the z-axis is vertically downward;

[0010] The rack rail line includes a front transition curve section, a circular curve section, and a rear transition curve section; the circular curve section is further divided into a front circular curve section and a rear circular curve section with the midpoint as the boundary;

[0011] S21: The calculation model of the front transition curve section is as follows:

[0012]

[0013]

[0014] (x(i + 1) - x(i)) 2 +(y(i + 1) - y(i)) 2 +(z(i + 1) - z(i)) 2 = l sec 2 ;

[0015] z(i + 1) - z(i) = -i(s(i + 1) - s(i));

[0016] Among them, L is the length of the front transition curve or the rear transition curve; L2 is the length of the circular curve; R is the radius of the circular curve; l sec is the length of the rack and pinion unit of the rack rail;

[0017] (x(i), y(i), z(i)) are the spatial coordinates of the first end point of the i-th rack and pinion unit on the front transition curve section; (x(i + 1), y(i + 1), z(i + 1)) are the spatial coordinates of the end point of the i-th rack and pinion unit on the front transition curve section; i ∈ [1, m], is the number of rack and pinion units on the front transition curve section. When i = 1, the spatial coordinates of the first end point of the first rack and pinion unit on the front transition curve section are (0, 0, 0);

[0018] Iteratively calculate the coordinates of the first end point and the end point of each rack and pinion unit on the front transition curve section, and integrate the information K i (Z i (sh), Z i (mo), s(i)) and incorporate them into the same set to obtain the first data set P1{K1, K2, K3...K i ...Km}; Among them, Z i (sh) is the spatial coordinate of the starting point of the i-th rack and pinion unit; Z i (mo) is the spatial coordinate of the end point of the i-th rack and pinion unit; s(i) is the length from the horizontal projection point of the starting point of the i-th rack and pinion unit to the origin of the spatial coordinate system;

[0019] S22: The calculation model of the front circular curve segment includes the following:

[0020] (x(r) - x R ) 2 +(y(r) - y R ) 2 = R 2 ;

[0021] z(r) = -is(r);

[0022] (x(r + 1) - x(r)) 2 +(y(r + 1) - y(r)) 2 +(z(r + 1) - z(r)) 2 = l sec 2 ;

[0023] z(r + 1) - z(r) = z sec ;

[0024] (x(r), y(r), z(r)) is the spatial coordinate of the starting point of the r-th rack and pinion unit on the front circular curve segment; (x(r + 1), y(r + 1), z(r + 1)) is the spatial coordinate of the end point of the r-th rack and pinion unit on the front transition curve segment; r ∈ [1, k], is the number of rack and pinion units on the front transition curve segment. When r = 1, the spatial coordinates of the starting point of the rack and pinion unit on the first front circular curve segment are x(m + 1), y(m + 1), z(m + 1); z sec The difference in the z coordinates between the start and end of each rack and pinion unit on the front circular curve segment;

[0025] The starting point coordinates and end point coordinates of k rack and pinion units are obtained through iterative calculation, and the information K' of k rack and pinion units on the front transition curve segment is integrated r (Z' r (sh), Z' r (mo), s'(r)) and incorporated into the same set to obtain the second data set P2{K'1, K'2, K'3...K' r ...K' k}; Among them, Z' r (sh) is the spatial coordinate of the starting point of the r-th rack and pinion unit; Z'r (m_o) is the spatial coordinate of the end point of the r-th rack and pinion unit; s'(r) is the length from the horizontal projection point of the starting point of the r-th rack and pinion unit to the origin of the spatial coordinate system;

[0026] S23: With the line connecting the midpoint of the circular curve segment in the xy plane and the center of the circular curve segment in the xy plane as the axis of symmetry, the front transition curve segment and the front circular curve segment are axially symmetric to the rear circular curve segment and the rear transition curve segment in the xy plane projection;

[0027] The front circular curve segment and the front transition curve segment are collectively referred to as the front half of the rack and pinion, and the rear circular curve segment and the rear transition curve segment are collectively referred to as the rear half of the rack and pinion. The rear circular curve segment and the rear transition curve segment adopt the same calculation model. The calculation model of the rear half of the rack and pinion includes the following:

[0028] Let point S f be the starting point of any rack and pinion unit in the front half of the rack and pinion; (x(f), y(f), z(f)) is the spatial coordinate of point S f ; s(f) is the length from point S f to the origin of the coordinate system in the horizontal projection;

[0029] S 4f is the symmetric point of point S f on the rear half of the rack and pinion. (x(4f), y(4f), z(4f)) is the spatial coordinate of point S 4f ; s(4f) is the length from point S 4f to the origin of the coordinate system in the horizontal projection; 4f ∈ [1, p], is the number of rack and pinion units in the rear half of the rack and pinion; when 4f = 1, that is, the spatial coordinates of the starting point of the rack and pinion unit on the first rear half of the rack and pinion are x(k + 1), y(k + 1), z(k + 1);

[0030]

[0031]

[0032] z(4f) = -is(4f);

[0033] s(4f) = 2s rend - s(f);

[0034] where, x rend is the x coordinate of the midpoint of the circular curve segment; y rend is the y coordinate of the midpoint of the circular curve segment; s rend is the length from the midpoint of the circular curve segment to the origin of the coordinate system in the horizontal projection;

[0035] The elements in the first data set P1 and the second data set P2 are respectively brought into the calculation model of the second half of the rack rail to calculate the coordinates of the starting point and the ending point of the rack rail unit on the second half of the rack rail. After integration, the information K” of p rack rail units on the circular curve section and the second transition curve section is obtained. 4f (Z” 4f (sh), Z” 4f (mo), s”(4f)) and incorporated into the same collection to obtain the third data set P3{K”1, K”2, K”3...K” 4f ...K” p}; where Z” 4f (sh) is the spatial coordinate of the starting point of the pth rack rail unit; Z” 4f (mo) is the spatial coordinate of the ending point of the pth rack rail unit; s”(4f) is the length from the horizontal projection point of the starting point of the pth rack rail unit to the origin of the spatial coordinate system.

[0036] S3: Substitute the designed transition curve length L', designed circular curve length L2', designed circular curve radius R' and designed rack rail unit length l' of the pre-constructed track into the rack rail curve calculation model to obtain the endpoint coordinates of all rack rail units on the pre-constructed track.

[0037] Furthermore, the calculation model of the center coordinates (x R , y R ) of the circular curve section in the xy plane is as follows:

[0038]

[0039]

[0040] (y R -y(m+1)) 2 +(x R -x(m+1)) 2 =R 2 ;

[0041] where k h is the tangent slope value at the end of the projection of the first transition curve section on the xy plane.

[0042] Furthermore, the calculation method of the difference z sec between the head and tail end z coordinates of each section of the rack rail unit on the first circular curve section is as follows:

[0043] Establish a coordinate system O-x'y' with the plane where the circular curve section is located. Take the starting point of the circular curve as the origin of the coordinate system O-x'y'. Then the starting end of the first rack rail unit on the circular curve section is located at the origin.

[0044] Let the end of the first rack unit on the circular curve segment be located at the point (a, b) on the coordinate system O-x'y', and the projected length of the first rack unit on the circular curve segment on the coordinate system O-x'y' be l sec1 , and the difference between the head and tail ends s of the first rack unit on the circular curve segment is s sec ;

[0045]

[0046] z sec =-is sec ;

[0047]

[0048] a 2 +(b - R) 2 =R 2 ;

[0049] By solving the above four equations simultaneously, z sec and s sec can be obtained.

[0050] Furthermore, the rack curve calculation model further includes a superelevation value calculation model, and the superelevation value calculation model is as follows:

[0051] The superelevation value of any point S1 on the previous transition curve segment where H is the rack superelevation threshold, and s1 is the length of point S1 from the origin of the coordinate system in the horizontal projection;

[0052] The superelevation value of any point S2 on the circular curve segment u2 = H;

[0053] The superelevation value of any point S3 on the subsequent transition curve segment where s3 is the length of point S3 from the origin of the coordinate system in the horizontal projection.

[0054] The beneficial effects of the present invention are as follows:

[0055] By presetting the rack superelevation threshold, the transition curve length, and the circular curve length, the present invention establishes a rack curve calculation model, realizes the data calculation of the endpoints of all rack units in the curved part of the rack, speeds up the preliminary simulation process of the rack, and effectively improves the overall design speed of the rack track. It has the advantages of being fast and accurate, providing a good theoretical basis for the actual design and construction of the rack railway. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a schematic flow chart of the present invention;

[0057] Figure 2 is a coordinate schematic diagram of the established coordinate system O-x'y'. Detailed implementation manners

[0058] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of this technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art of this technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0059] As Figure 1 shown, a design method for the rack and pinion unit of the curve part of a rack rail line includes the following steps:

[0060] S1: Establish a calculation model for the rack rail curve;

[0061] S2: Establish a space coordinate system with the initial end of the rack rail line as the origin of the coordinate system;

[0062] Among them, the x-axis of the space coordinate system is the tangent line of the projection of the pre-constructed rack rail at the initial end on the horizontal plane, and one side of the pre-constructed rack rail is the positive direction of the x-axis; the y-axis is on the same horizontal plane as the x-axis, and one side of the pre-constructed rack rail is the positive direction of the y-axis; the positive direction of the z-axis is vertically downward;

[0063] The rack rail line includes a front transition curve section, a circular curve section, and a rear transition curve section; the circular curve section is further divided into a front circular curve section and a rear circular curve section with the midpoint as the boundary;

[0064] S21: The calculation model of the front transition curve section includes the following:

[0065]

[0066]

[0067] (x(i + 1)-x(i)) 2 +(y(i + 1)-y(i)) 2 +(z(i + 1)-z(i)) 2 = l sec 2 ;

[0068] z(i + 1)-z(i)= -i(s(i + 1)-s(i));

[0069] Among them, L is the length of the front transition curve or the rear transition curve; L2 is the length of the circular curve; R is the radius of the circular curve; l sec is the length of the rack and pinion unit;

[0070] (x(i), y(i), z(i)) are the spatial coordinates of the starting point of the i-th tooth-rail rack unit on the front transition curve section; (x(i + 1), y(i + 1), z(i + 1)) are the spatial coordinates of the ending point of the i-th tooth-rail rack unit on the front transition curve section; i ∈ [1, m], is the number of tooth-rail rack units on the front transition curve section. When i = 1, the spatial coordinates of the starting point of the tooth-rail rack unit on the first front transition curve section are (0, 0, 0);

[0071] The starting point coordinates and ending point coordinates of each tooth-rail rack unit on the front transition curve section are obtained through iterative calculation, and the information K of the m tooth-rail rack units on the front transition curve section is integrated i (Z i (sh), Z i (mo), s(i)) and incorporated into the same collection to obtain the first data set P1{K1, K2, K3...K i ...K m}; where Z i (sh) are the spatial coordinates of the starting point of the i-th tooth-rail rack unit; Z i (mo) are the spatial coordinates of the ending point of the i-th tooth-rail rack unit; s(i) is the length from the horizontal projection point of the starting point of the i-th tooth-rail rack unit to the origin of the spatial coordinate system;

[0072] S22: The calculation model of the front circular curve section includes the following:

[0073] (x(r) - x R ) 2 +(y(r) - y R ) 2 = R 2 ;

[0074] z(r) = -is(r);

[0075] (x(r + 1) - x(r)) 2 +(y(r + 1) - y(r)) 2 +(z(r + 1) - z(r)) 2 = l sec 2 ;

[0076] z(r + 1) - z(r) = z sec ;

[0077] (x(r), y(r), z(r)) are the spatial coordinates of the starting point of the r-th tooth-rail rack unit on the front circular curve section; (x(r + 1), y(r + 1), z(r + 1)) are the spatial coordinates of the ending point of the r-th tooth-rail rack unit on the front transition curve section; r ∈ [1, k], is the number of the toothed rail and rack units in the front transition curve section. When r = 1, that is, the spatial coordinates of the starting point of the toothed rail and rack unit on the first front circular curve section are x(m + 1), y(m + 1), z(m + 1); z sec The difference in the z coordinates between the starting and ending points of each toothed rail and rack unit on the front circular curve section;

[0078] Through iterative calculation, the coordinates of the starting points and the ending points of k toothed rail and rack units are obtained, and the information K' of the k toothed rail and rack units on the front transition curve section is integrated r (Z' r (sh), Z' r (mo), s'(r)) and incorporated into the same collection to obtain the second data set P2{K'1, K'2, K'3...K' r ...K' k}; where Z' r (sh) is the spatial coordinates of the starting point of the rth toothed rail and rack unit; Z' r (mo) is the spatial coordinates of the ending point of the rth toothed rail and rack unit; s'(r) is the length from the starting point of the rth toothed rail and rack unit in the horizontal projection point to the origin of the spatial coordinate system;

[0079] S23: Taking the line connecting the midpoint of the circular curve section in the xy plane and the center of the circular curve section in the xy plane as the axis of symmetry, the front transition curve section and the front circular curve section are axisymmetric with the rear circular curve section and the rear transition curve section in the xy plane projection;

[0080] The front circular curve section and the front transition curve section are collectively referred to as the front half of the toothed rail, and the rear circular curve section and the rear transition curve section are collectively referred to as the rear half of the toothed rail. The rear circular curve section and the rear transition curve section adopt the same calculation model. The calculation model of the rear half of the toothed rail includes the following:

[0081] Let point S f be the starting point of any toothed rail and rack unit on the front half of the toothed rail; (x(f), y(f), z(f)) are the spatial coordinates of point S f ; s(f) is the length from point S f to the origin of the coordinate system in the horizontal projection;

[0082] S 4f is the symmetric point of point S f on the rear half of the toothed rail. (x(4f), y(4f), z(4f)) are the spatial coordinates of point S 4f ; s(4f) is the length from point S 4f to the origin of the coordinate system in the horizontal projection; 4f ∈ [1, p], is the number of the rack and pinion units in the second half of the rack rail; when 4f = 1, that is, the spatial coordinates of the starting point of the rack and pinion unit on the first second half of the rack rail are x(k + 1), y(k + 1), z(k + 1);

[0083]

[0084]

[0085] z(4f) = -is(4f);

[0086] s(4f) = 2s rend -s(f);

[0087] where x rend is the x coordinate of the midpoint of the circular curve segment; y rend is the y coordinate of the midpoint of the circular curve segment; s rend is the length from the midpoint of the circular curve segment to the origin of the coordinate system in the horizontal projection;

[0088] Substitute the elements in the first data set P1 and the second data set P2 into the calculation model of the second half of the rack rail to calculate the starting point coordinates and the ending point coordinates of the rack and pinion units on the second half of the rack rail, and integrate the information K” 4f (Z” 4f (sh), Z” 4f (mo), s”(4f)) of p rack and pinion units on the circular curve segment and the second transition curve segment and incorporate them into the same set to obtain the third data set P3{K”1, K”2, K”3...K” 4f ...K” p}; where Z” 4f (sh) is the spatial coordinates of the starting point of the p-th rack and pinion unit; Z” 4f (mo) is the spatial coordinates of the ending point of the p-th rack and pinion unit; s”(4f) is the length from the horizontal projection point of the starting point of the p-th rack and pinion unit to the origin of the space coordinate system;

[0089] S3: Substitute the designed transition curve length L', designed circular curve length L2', designed circular curve radius R' and designed rack and pinion unit length l' of the pre-constructed track into the rack rail curve calculation model to obtain the endpoint coordinates of all rack and pinion units on the pre-constructed track.

[0090] Furthermore, the calculation model of the center coordinates (x R , y R ) of the circular curve segment in the xy plane includes the following:

[0091]

[0092]

[0093] (y R -y(m + 1)) 2 +(x R -x(m + 1)) 2 =R 2 ;

[0094] where k h is the tangent slope value at the end of the projection of the front transition curve segment on the xy plane.

[0095] Furthermore, the difference z sec in the z - coordinates of the head and tail ends of each tooth - rail rack unit on the front circular curve segment is calculated as follows:

[0096] As Figure 2 shown, establish a coordinate system O - x'y' in the plane where the circular curve segment is located. Take the starting point of the circular curve as the origin of the coordinate system O - x'y'. Then the head end of the first tooth - rail rack unit on the circular curve segment is located at the origin;

[0097] Let the end of the first tooth - rail rack unit on the circular curve segment be located at the point (a, b) in the coordinate system O - x'y'. The projected length of the first tooth - rail rack unit on the circular curve segment in the coordinate system O - x'y' is l sec1 , and the difference s sec in the s - coordinates of the head and tail ends of the first tooth - rail rack unit on the circular curve segment is s;

[0098]

[0099] z sec = - is sec ;

[0100]

[0101] a 2 +(b - R) 2 =R 2 ;

[0102] By simultaneously solving the above four equations, z sec and s sec can be solved.

[0103] Furthermore, the tooth - rail curve calculation model also includes a superelevation value calculation model, and the superelevation value calculation model is as follows:

[0104] The superelevation value of any point S1 on the front transition curve segment, where H is the tooth - rail superelevation threshold, and s1 is the length of point S1 from the origin of the coordinate system in the horizontal projection;

[0105] The superelevation value u2 of any point S2 on the circular curve segment is u2 = H;

[0106] Superelevation value of any point S3 on the rear transition curve section Where s3 is the length from point S3 to the origin of the coordinate system in the horizontal projection.

Claims

1. A design method for the rack unit of a rack-rail line in the curved section, characterized in that, Including the following steps: S1: Establish a calculation model for the rack curve; S2: Establish a spatial coordinate system with the initial end of the rack line as the origin of the coordinate system; Among them, the x-axis of the spatial coordinate system is the tangent line at the initial end of the projection of the pre-constructed rack on the horizontal plane, and one side of the pre-constructed rack is the positive direction of the x-axis; the y-axis is in the same horizontal plane as the x-axis, and one side of the pre-constructed rack is the positive direction of the y-axis; the positive direction of the z-axis is vertically downward; The rack line includes a front transition curve section, a circular curve section, and a rear transition curve section; the circular curve section is further divided into a front circular curve section and a rear circular curve section with the midpoint as the boundary; S21: The calculation model of the front transition curve section is as follows: (x(i + 1)-x(i)) 2 +(y(i + 1)-y(i)) 2 +(z(i + 1)-z(i)) 2 =l sec 2 ; z(i + 1) - z(i) = -i(s(i + 1) - s(i)); wherein, L is the length of the front transition curve or the rear transition curve; L2 is the length of the circular curve; R is the radius of the circular curve; l sec is the length of the rack and pinion unit; (x(i), y(i), z(i)) are the spatial coordinates of the first endpoint of the i-th tooth-rail rack unit on the front transition curve segment; (x(i + 1), y(i + 1), z(i + 1)) are the spatial coordinates of the end point of the i-th tooth-rail rack unit on the front transition curve segment; i ∈ [1, m], is the number of tooth-rail rack units on the front transition curve segment. When i = 1, the spatial coordinates of the first endpoint of the tooth-rail rack unit on the first front transition curve segment are (0, 0, 0); Iteratively calculate the coordinates of the starting point and the ending point of each rack and pinion unit on the pre-transition curve segment, and integrate the information K of m rack and pinion units on the pre-transition curve segment i (Z i (sh), Z i (mo), s(i)) and incorporate them into the same collection to obtain the first data set P1{K1, K2, K3...K i ...K m}; where Z i (sh) is the spatial coordinate of the starting point of the i-th rack and pinion unit; Z i (mo) is the spatial coordinate of the ending point of the i-th rack and pinion unit; s(i) is the length from the horizontal projection point of the starting point of the i-th rack and pinion unit to the origin of the spatial coordinate system; S22: The calculation model of the front circular curve section is as follows: (x(r) - x R ) 2 +(y(r) - y R ) 2 = R 2 ; z(r) = -is(r); (x(r + 1)-x(r)) 2 +(y(r + 1)-y(r)) 2 +(z(r + 1)-z(r)) 2 =l sec 2 ; z(r + 1)-z(r)=z sec ; (x(r), y(r), z(r)) is the spatial coordinate of the starting point of the r-th tooth-rail unit on the front circular curve segment; (x(r + 1), y(r + 1), z(r + 1)) is the spatial coordinate of the end point of the r-th tooth-rail unit on the front transition curve segment; r ∈ [1, k], is the number of tooth-rail units on the front transition curve segment. When r = 1, the spatial coordinate of the starting point of the tooth-rail unit on the first front circular curve segment is x(m + 1), y(m + 1), z(m + 1); z sec The difference in the z coordinates between the start and end of each tooth-rail unit on the front circular curve segment; Iteratively calculate the coordinates of the starting points and the ending points of k rack and pinion units, and integrate the information K' of the k rack and pinion units on the pre-transition curve section r (Z' r (sh), Z' r (mo), s'(r)) and incorporate them into the same collection to obtain the second data set P2{K'1, K'2, K'3...K' r ...K' k}; where, Z' r (sh) is the spatial coordinate of the starting point of the r-th rack and pinion unit; Z' r (mo) is the spatial coordinate of the ending point of the r-th rack and pinion unit; s'(r) is the length from the horizontal projection point of the starting point of the r-th rack and pinion unit to the origin of the spatial coordinate system; Taking the line connecting the midpoint of the circular curve section in the xy plane and the center of the circular curve section in the xy plane as the axis of symmetry, the projections of the front transition curve section and the front circular curve section on the xy plane are axisymmetric with the projections of the rear circular curve section and the rear transition curve section; The front circular curve section and the front transition curve section are collectively referred to as the front half of the rack, and the rear circular curve section and the rear transition curve section are collectively referred to as the rear half of the rack. The rear circular curve section and the rear transition curve section adopt the same calculation model. The calculation model of the rear half of the rack is as follows: Set point S f as the leading end point of any rack unit on the first half of the toothed rail; (x(f), y(f), z(f)) is the spatial coordinate of point S f ; s(f) is the length from point S f to the origin of the coordinate system on the horizontal projection; S 4f is the symmetric point on the latter half of the tooth rail, and (x(4f), y(4f), z(4f)) are the spatial coordinates of point S f on the latter half of the tooth rail, and s(4f) is the length from point S 4f to the origin of the coordinate system in the horizontal projection; 4f ∈ [1, p], 4f where p is the number of tooth rail rack units in the latter half of the tooth rail; when 4f = 1, that is, the spatial coordinates of the starting point of the tooth rail rack unit on the first latter half of the tooth rail are x(k + 1), y(k + 1), z(k + 1); p is the number of tooth rail rack units in the latter half of the tooth rail; when 4f = 1, that is, the spatial coordinates of the starting point of the tooth rail rack unit on the first latter half of the tooth rail are x(k + 1), y(k + 1), z(k + 1); z(4f) = -is(4f); s(4f) = 2s rend -s(f); where x rend is the x - coordinate of the mid - point of the circular curve segment; y rend is the y - coordinate of the mid - point of the circular curve segment; s rend is the length from the mid - point of the circular curve segment to the origin of the coordinate system on the horizontal projection; The elements in the first data set P1 and the second data set P2 are respectively brought into the calculation model of the latter half of the rack rail to calculate the coordinates of the starting point and the ending point of the rack and pinion unit on the latter half of the rack rail. After integration, the information K” of p rack and pinion units on the circular curve segment and the latter transition curve segment is obtained. 4f (Z” 4f (sh), Z” 4f (mo), s”(4f)) and incorporated into the same collection to obtain the third data set P3 {K”1, K”2, K”3... K” 4f ... K” p}; where Z” 4f (sh) is the spatial coordinate of the starting point of the p-th rack and pinion unit; Z” 4f (mo) is the spatial coordinate of the ending point of the p-th rack and pinion unit; s”(4f) is the length from the horizontal projection point of the starting point of the p-th rack and pinion unit to the origin of the spatial coordinate system. S3: Substitute the designed transition curve length L', designed circular curve length L2', designed circular curve radius R', and designed rack and pinion unit length l' of the pre-constructed track into the rack curve calculation model to obtain the endpoint coordinates of all rack and pinion units on the pre-constructed track.

2. The design method of the rack and pinion unit for the curved section of the rack rail line according to claim 1, characterized in that The calculation model of the center coordinates (x R , y R ) of the circular curve segment in the xy plane includes the following: (y R -y(m + 1)) 2 +(x R -x(m + 1)) 2 =R 2 ; where k h is the tangent slope value at the end of the projection of the previous transition curve segment on the xy plane.

3. The method for designing the rack unit of the rack-rail line curve part according to claim 1, characterized in that The difference z in the z - coordinate between the head and the tail of each tooth - rail and rack unit on the front circular curve section sec is calculated as follows: Establish a coordinate system O-x'y' with the plane where the circular curve section is located. Taking the starting point of the circular curve as the origin of the coordinate system O-x'y', the starting end of the first rack and pinion unit on the circular curve section is located at the origin; Let the end of the first rack and pinion unit on the circular curve segment be located at the point (a, b) on the coordinate system O-x'y', and the projected length of the first rack and pinion unit on the circular curve segment on the coordinate system O-x'y' be l sec1 , and the difference between the head and tail ends s of the first rack and pinion unit on the circular curve segment be s sec ; z sec =-is sec ; a 2 +(b - R) 2 = R 2 ; By simultaneously solving the above four equations, z can be obtained sec and s sec .

4. The design method of the rack and pinion unit for the curved section of the rack-rail line according to claim 1, characterized in that, The rack curve calculation model also includes a superelevation value calculation model. The superelevation value calculation model is as follows: Superelevation value of any point S1 on the previous transition curve section Where H is the superelevation threshold of the rack rail, and s1 is the length from point S1 to the origin of the coordinate system in the horizontal projection; The superelevation value u2 at any point S2 on the circular curve section = H; Superelevation value of any point S3 on the rear transition curve section Where s3 is the length from point S3 to the origin of the coordinate system in the horizontal projection.

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