Method for calculating static horizontal force of catenary locator

Abstract

The application discloses a kind of contact network positioner static horizontal force calculation method, the method includes the following steps: with the positioning point A of positioner as origin O establishes rectangular coordinate system, positioner applies static horizontal force to contact wire, Y axis positive direction is consistent with the direction of horizontal force;Contact wire is compared with the deformation of positioning point corner, and forms flexural curve portion, and flexural curve AB and flexural curve AC are compared with the symmetry of positioning point, and the straight line portion of the outward extension of two points B, C on contact wire;Force analysis is carried out to contact wire flexural curve portion, according to the differential equation of tension beam flexural curve, obtain control differential equation, solve, obtain control differential equation solution;The flexural curve portion of contact wire on the two sides of positioning point A is approximately considered as axial force cantilever beam, and the bending moment of axial force cantilever beam is obtained according to bending moment balance of axial force cantilever beam, so that the horizontal force generated due to the bending stiffness of contact wire at positioning point A is obtained;The application improves the calculation precision of positioning point horizontal force.

Description

Technical Field

[0001] This invention belongs to the field of electrified railway catenary design technology, and particularly relates to a method for calculating the static horizontal force of the catenary positioner. Background Technology

[0002] The calculation of the horizontal force of the catenary positioner is a key professional technology in the design, construction and operation of electrified railways, especially high-speed railways. It is directly related to the stability of the catenary system, the current collection quality of the pantograph, and the safety of train operation.

[0003] Currently, in engineering practice, the contact wire is simplified to a flexible cable model when calculating the static horizontal force of the catenary positioner, and simplified formulas are commonly used, which is based on the ideal assumption of ignoring the bending stiffness of the contact wire. In straight sections or sections with large curve radii, the errors of this simplified calculation method do not cause serious consequences. However, in sections with small radius curves, because the contact wire at the positioning point is actually a deflection curve, simplifying it to a broken line and using trigonometric functions for vector synthesis calculations leads to significant errors in the calculation of the positioner's horizontal force and slope. These errors increase dramatically as the curve radius decreases; this can cause various problems, such as deterioration of the pantograph-catenary contact quality, excessive equipment wear, and even operational safety accidents. Therefore, there is an urgent need for a calculation method that can comprehensively consider multiple factors such as curve radius, contact wire bending stiffness, and contact wire deflection, providing more accurate results that better reflect engineering realities, and solving the problem of accurately calculating the static horizontal force of the catenary positioner at curves. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention combines the bending deformation equation of a tension beam and the bending moment balance equation of an axial force cantilever beam to accurately calculate the static horizontal force at the positioning point;

[0005] This invention provides a method for calculating the static horizontal force of a contact wire positioner, the method comprising the following steps:

[0006] S1. Establish a rectangular coordinate system with the positioning point A of the positioner as the origin O. The positioner applies a static horizontal force to the contact line. Y-axis and horizontal force The Y-axis is aligned with the direction of the horizontal force. The contact line is deformed relative to the positioning point by an angle, forming a deflection curve, namely the deflection curve AB and the deflection curve AC. The deflection curves AB and AC are symmetrical relative to the positioning point. The outward extension of the contact line from points B and C is a straight line.

[0007] S2. Perform a force analysis on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, obtain the governing differential equation for the deflection curve portion of the contact line to the right of positioning point A. Solve the governing differential equation to obtain the form of the solution:

[0008] ;

[0009] ;

[0010] ;

[0011] in, x , y This represents the coordinates of the contact line deflection curve to the right of positioning point A. E represents the Young's modulus of the contact wire, I represents the moment of inertia of the contact wire section, and T represents the tension on both sides of the contact wire. l This represents the length of either the deflection curve AB or the deflection curve AC. The angle between the straight portion of the contact line and the horizontal line;

[0012] S3. Approximate the deflection curves of the contact lines on both sides of positioning point A as an axially loaded cantilever beam, with points B and C as the free ends. The free ends of the cantilever beam are subjected to axial force and vertical load. Based on the moment equilibrium of the axially loaded cantilever beam, the moment equilibrium equation of the axially loaded cantilever beam to the right of positioning point A is obtained as follows:

[0013] ;

[0014] Formula Substitute into the formula The bending moment of the contact line deflection curve to the right of point A is obtained. :

[0015] ;

[0016] S4. Following the method in step S2, perform a force analysis on the deflection curve portion of the contact line to the left of positioning point A to obtain the governing differential equation and the form of the equation solution for the deflection curve portion of the contact line to the left of positioning point A. Following the method in step S3, obtain the bending moment equilibrium equation of the axial force cantilever beam to the left of positioning point A, and then obtain the bending moment of the deflection curve portion of the contact line to the left of point A. :

[0017] ;

[0018] in, The x-coordinate of the contact line deflection curve to the left of positioning point A;

[0019] S5. According to the expression for the bending moment of the contact line deflection curve, the horizontal force exerted at point A on the end of the right cantilever beam is... The horizontal force applied at point A to the end of the left cantilever beam is Therefore, the horizontal force at location point A due to the bending stiffness of the contact wire is obtained. :

[0020] .

[0021] Furthermore, the calculation method is applied to deflection curve sections with a radius of less than 3000 meters, and the angular deformation of the positioning point does not exceed 2 degrees.

[0022] Furthermore, in step S2, a force analysis is performed on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, the governing differential equation of the deflection curve portion of the contact line to the right of positioning point A is obtained. The method for solving the governing differential equation and obtaining the form of the solution is as follows:

[0023] Force analysis is performed on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, the governing differential equation of the deflection curve portion of the contact line to the right of positioning point A is obtained:

[0024] ;

[0025] make The form of the solution to the governing differential equation is obtained as follows:

[0026] ;

[0027] ;

[0028] ;

[0029] Based on the constraints at location point A:

[0030] ,have to: ;

[0031] ,have to: ;

[0032] ,have to: ;

[0033] therefore: ;

[0034] Where x and y represent the coordinates of the contact line deflection curve to the right of positioning point A, E represents the Young's modulus of the contact line, and I represents the moment of inertia of the contact line section. These represent the undetermined parameters of the general solution of the control differential equation for the contact line deflection curve to the right of positioning point A.

[0035] Furthermore, the method for solving the governing differential equation in step S2 to obtain the form of the solution to the governing differential equation also includes:

[0036] Assume that the angle between the straight portions of the contact lines on both sides and the horizontal line is 1. The lengths of the deflection curves AB and AC are l m, where the absolute value of the x-coordinate of point B or C is considered the length of the deflection curve AB or AC. l Therefore, for the contact line deflection curve to the right of positioning point A, we have:

[0037] Substitute it into the formula We can obtain:

[0038] ;

[0039] in, This represents the x-coordinate of point C;

[0040] Formula Substitute into the formula : ;

[0041] Therefore, we get:

[0042] ;

[0043] ;

[0044] Therefore, we get:

[0045] ;

[0046] ;

[0047] .

[0048] The beneficial technical effects of this invention are as follows:

[0049] 1. This invention significantly improves the calculation accuracy of the horizontal force at the positioning point by introducing the straight section and the deflection curve section of the contact line at the positioning point with a small curve radius, and by using the tension beam model and the axial force cantilever beam model. This avoids safety hazards such as underestimating the horizontal force and causing the equipment selection to be too small. At the same time, it provides a more accurate simulation calculation method for the dynamic simulation calculation of the pantograph-catenary system of high-speed railway, and further improves the reliability of the simulation calculation.

[0050] 2. The method of the present invention is compatible with various working conditions, tensions and wires, simplifies the design process, improves the accuracy of calculations, and the calculation results can provide more reliable input for cantilever structure optimization, support capacity verification, etc., thereby improving the economy and safety of the entire catenary system and providing more accurate guidance for the construction of new railway construction projects and major overhaul projects. Attached Figure Description

[0051] Figure 1This is a plan view of the contact wire positioning point in an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of the positioning A-pillar of turnout No. 18 at the construction site in an embodiment of the present invention. Detailed Implementation

[0053] The following description, in conjunction with the accompanying drawings, provides a clearer and more complete explanation of the method for calculating the static horizontal force of a contact wire positioner provided by the present invention:

[0054] like Figure 1 As shown, Figure 1 This is a plan view of the contact wire positioning point. The contact wire is positioned by a positioner. The force and angular deformation of the contact wire on both sides of the positioner are symmetrical with respect to the positioning point A. The contact wire is subjected to tension T on both sides, and the positioner applies a horizontal force to the contact wire. Establish a rectangular coordinate system with the positioning point A of the locator as the origin O, and the Y-axis is perpendicular to the horizontal force. Coincident, positive Y-axis direction is The directions are consistent; the contact line deforms relative to the positioning point at an angle, forming deflection curves AB and AC, which are symmetrical relative to the positioning point. The outward extensions of the contact line from points B and C are straight sections. In practical engineering, the forces and angle deformations on both sides of the positioning point are symmetrical, and the angle deformation is small, generally not exceeding 2 degrees. To simplify analysis and calculation, the locator in the figure is considered as a fixed hinge support.

[0055] Considering tension T and horizontal force Under these conditions, a force analysis is performed on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, the governing differential equation can be obtained:

[0056] ;

[0057] make The form of the solution to the governing differential equation is obtained as follows:

[0058] ;

[0059] ;

[0060] ;

[0061] Based on the constraints at location point A:

[0062] We can obtain: ;

[0063] We can obtain:

[0064] ;

[0065] We can obtain:

[0066] ;

[0067] therefore: ;

[0068] Where x and y represent the coordinates of the contact line deflection curve to the right of positioning point A, E represents the Young's modulus of the contact line, and I represents the moment of inertia of the contact line section. These represent the undetermined parameters of the general solution of the control differential equation for the contact line deflection curve to the right of positioning point A;

[0069] In practical engineering, the forces and angular deformations on both sides of the positioning point are symmetrical with respect to positioning point A. Assume that the angle between the straight portions of the contact lines on both sides and the horizontal line is... The lengths of the deflection curves AB and AC are l Since the angular deformation at point A is small, the absolute value of the x-coordinate of point B or C is considered as the length of the deflection curve AB or AC. l Therefore, for the contact line deflection curve to the right of positioning point A, we have:

[0070] Substitute it into the formula We can obtain:

[0071] ;

[0072] in, This represents the x-coordinate of point C;

[0073] Formula Substitute into the formula : ;

[0074] Therefore, we get:

[0075] ;

[0076] ;

[0077] Therefore, we get:

[0078] ;

[0079] ;

[0080] ;

[0081] It should be noted that the obtained , , The form of the solution to the differential equation governing the contact line deflection curve to the right of positioning point A;

[0082] Considering tension T and horizontal force Under these conditions, a force analysis is performed on the deflection curve portion of the contact line to the left of positioning point A. Based on the differential equation of the deflection curve of the tension beam, the governing differential equation can be obtained:

[0083] ;

[0084] make The form of the solution to the governing differential equation can be obtained as follows:

[0085] ;

[0086] ;

[0087] ;

[0088] Based on the constraints at location point A:

[0089] We can obtain: ;

[0090] We can obtain:

[0091] ;

[0092] We can obtain:

[0093] ;

[0094] therefore: ;

[0095] in, , E represents the coordinates of the contact line deflection curve to the left of positioning point A, E represents the Young's modulus of the contact line, and I represents the moment of inertia of the contact line section. These represent the undetermined parameters of the general solution of the control differential equation for the contact line deflection curve to the left of positioning point A;

[0096] In practical engineering, the forces and angular deformations on both sides of the positioning point are symmetrical with respect to positioning point A. Assume that the angle between the straight portions of the contact lines on both sides and the horizontal line is... The lengths of the deflection curves AB and AC are l Since the angular deformation at point A is small, the absolute value of the x-coordinate of point B or C is considered as the length of the deflection curve AB or AC. l Therefore, for the contact line deflection curve to the left of positioning point A, we have:

[0097] Substitute it into the formula We can obtain:

[0098] ;

[0099] in, This represents the x-coordinate of point B;

[0100] Formula Substitute into the formula : ;

[0101] Therefore, we get:

[0102] ;

[0103] ;

[0104] Therefore, we get:

[0105] ;

[0106] ;

[0107] ;

[0108] It should be noted that the obtained , , The form of the solution to the differential equation governing the contact line deflection curve to the left of positioning point A;

[0109] Considering the constraints at positioning point A and the small angular deformation, the deflection curves of the contact lines on both sides of positioning point A are approximated as axially loaded cantilever beams, with points B and C as the free ends of the cantilever beams; the free ends of the cantilever beams are subjected to axial force and vertical load. N Based on the bending moment equilibrium of the axial force cantilever beam, the equilibrium equation to the right of positioning point A is obtained as follows:

[0110] ;

[0111] Formula , Substitute into the formula The axial force cantilever beam bending moment is obtained, which is the bending moment of the contact line deflection curve to the right of point A. : ;

[0112] Based on the bending moment equilibrium of the axial force cantilever beam, the equilibrium equation to the left of positioning point A is obtained as follows:

[0113] ;

[0114] Formula , Substitute into the formula The axial force cantilever beam bending moment is obtained, which is the bending moment of the contact line deflection curve to the left of point A. : ;

[0115] According to the expression for the bending moment of an axially loaded cantilever beam, the horizontal force exerted at point A on the right end of the cantilever beam is... The horizontal force applied at point A to the end of the left cantilever beam is Therefore, the horizontal force at location point A due to the bending stiffness of the contact wire is obtained. :

[0116] (11);

[0117] As an example, in this embodiment, such as Figure 2 As shown, taking the positioning A-post of turnout No. 18 at the construction site as an example, that is, for Figure 2 Calculate the horizontal force of the positioner on the rightmost support curved carpal arm; the contact wire cross-sectional area is known to be 150 mm². 2 ,tension T =15000N, based on the properties of the No. 18 turnout curve and the mileage and pull-out value of the A-pillar (i.e., through geometric calculation), the angle between the straight part of the contact line on both sides and the horizontal line is obtained. ;

[0118] First, the horizontal force is calculated using a simplified formula. The simplified algorithm reduces the contact line to a flexible cable model, where the contact lines on both sides of positioning point A are straight lines and form an angle with the horizontal line. Therefore, the horizontal force generated at point A by the contact lines on both sides is The horizontal force of the positioner is 925N.

[0119] Then, the horizontal force is calculated using the method of this embodiment: contact wire cross-sectional area 150mm². 2 ,tension T =15000N, Young's modulus E=120GPa, moment of inertia of section m 4 Bending stiffness EI = 214.859 N*m 2 ; m -1 On-site measured deflection curves AB and AC lengths l =0.13m, therefore we can obtain kl =1.086; Substituting into formula (11), we get P1=1424N;

[0120] Finally, the horizontal force of the locator was measured on-site, and the actual value of the horizontal force of the locator was 1360N.

[0121] Therefore, it can be seen that the simplified formula results in a deviation. The calculation results of the method of the present invention have a deviation. .

[0122] Therefore, using a simplified algorithm to calculate the horizontal force of the positioner will result in a large deviation. If no manual adjustment is made after on-site installation, problems such as excessively high contact wire height and insufficient positioner slope may occur. This may lead to deterioration of the pantograph-catenary contact quality, excessive wear of equipment, or even operational safety accidents. However, using this method can avoid this error.

[0123] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for calculating the static horizontal force of a contact wire positioner, characterized in that, The method includes the following steps: S1. Establish a rectangular coordinate system with the positioning point A of the positioner as the origin O. The positioner applies a static horizontal force to the contact line. Y-axis and horizontal force The Y-axis is aligned with the direction of the horizontal force. The contact line is deformed relative to the positioning point by an angle, forming a deflection curve, namely the deflection curve AB and the deflection curve AC. The deflection curves AB and AC are symmetrical relative to the positioning point. The outward extension of the contact line from points B and C is a straight line. S2. Perform a force analysis on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, obtain the governing differential equation for the deflection curve portion of the contact line to the right of positioning point A. Solve the governing differential equation to obtain the form of the solution: ； ； ； Where x and y represent the contact line deflection curve coordinates to the right of positioning point A, E represents the Young's modulus of the contact wire, I represents the moment of inertia of the contact wire section, T represents the tension on both sides of the contact wire, and l represents the length of the deflection curve AB or AC. The angle between the straight portion of the contact line and the horizontal line; S3. Approximate the deflection curves of the contact lines on both sides of positioning point A as an axially loaded cantilever beam, with points B and C as the free ends. The free ends of the cantilever beam are subjected to axial force and vertical load. Based on the moment equilibrium of the axially loaded cantilever beam, the moment equilibrium equation of the axially loaded cantilever beam to the right of positioning point A is obtained as follows: ； Formula Substitute into the formula The bending moment of the contact line deflection curve to the right of point A is obtained. : ； S4. Following the method in step S2, perform a force analysis on the deflection curve portion of the contact line to the left of positioning point A to obtain the governing differential equation and the form of the equation solution for the deflection curve portion of the contact line to the left of positioning point A. Following the method in step S3, obtain the bending moment equilibrium equation of the axial force cantilever beam to the left of positioning point A, and then obtain the bending moment of the deflection curve portion of the contact line to the left of point A. : ； in, The x-coordinate of the contact line deflection curve to the left of positioning point A; S5. According to the expression for the bending moment of the contact line deflection curve, the horizontal force exerted at point A on the end of the right cantilever beam is... The horizontal force applied at point A to the end of the left cantilever beam is Therefore, the horizontal force at location point A due to the bending stiffness of the contact wire is obtained. : (11)。 2. The method for calculating the static horizontal force of a contact wire positioner according to claim 1, characterized in that, The calculation method is applied to deflection curve sections with a radius of less than 3000 meters, and the angular deformation of the positioning point does not exceed 2 degrees.

3. The method for calculating the static horizontal force of a contact wire positioner according to claim 1, characterized in that, In step S2, a force analysis is performed on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, the governing differential equation of the deflection curve portion of the contact line to the right of positioning point A is obtained. The method for solving the governing differential equation and obtaining the form of the solution is as follows: Force analysis is performed on the deflection curve portion of the contact line to the right of positioning point A. Based on the differential equation of the deflection curve of the tension beam, the governing differential equation of the deflection curve portion of the contact line to the right of positioning point A is obtained: ； make The form of the solution to the governing differential equation is obtained as follows: ； ； ； Based on the constraints at location point A: ,have to: ; ,have to: ; ,have to: ; therefore: ; Where x and y represent the coordinates of the contact line deflection curve to the right of positioning point A, E represents the Young's modulus of the contact line, and I represents the moment of inertia of the contact line section. These represent the undetermined parameters of the general solution of the control differential equation for the contact line deflection curve to the right of positioning point A.

4. The method for calculating the static horizontal force of a contact wire positioner according to claim 3, characterized in that, The method for solving the governing differential equation in step S2 to obtain the form of the solution to the governing differential equation also includes: Assume that the angle between the straight portions of the contact lines on both sides and the horizontal line is 1. The lengths of the deflection curves AB and AC are 1m. The absolute value of the x-coordinate of point B or C is considered as the length l of the deflection curve AB or AC. Therefore, for the contact line deflection curve to the right of positioning point A, we have: Substitute it into the formula We can obtain: ； in, This represents the x-coordinate of point C; Formula Substitute into the formula : ; Therefore, we get: ； ； Therefore, we get: ； ； 。

Images