CN-121765979-B - Calculation method of static horizontal force of overhead line system positioner

CN121765979BCN 121765979 BCN121765979 BCN 121765979BCN-121765979-B

Abstract

The invention discloses a calculation method of static horizontal force of a contact net positioner, which comprises the following steps of establishing a rectangular coordinate system by taking a positioning point A of the positioner as an origin O, applying static horizontal force to a contact line by the positioner, enabling a Y-axis positive direction to be consistent with the horizontal force direction, enabling a contact line to be deformed relative to a positioning point corner to form a deflection line part, enabling two outwards extending parts of the deflection line AB and the deflection line AC to be linear parts relative to the positioning point, carrying out stress analysis on the deflection line part of the contact line, obtaining a control differential equation according to a deflection line differential equation of a tension beam, solving the control differential equation, enabling the deflection line parts of the contact line at two sides of the positioning point A to be approximately an axial force cantilever beam, and balancing the axial force cantilever arm Liang Wanju according to the axial force cantilever Liang Wanju, so as to obtain the horizontal force generated at the positioning point A due to bending rigidity of the contact line.

Inventors

LUO JIAN
ZHANG XUE
TAN XIN
YANG JIACHEN
GUO XIAOXU
CUI RUILIN
YAN HAN
WANG HUISHENG
JIA ZHENGANG
BAI YIFENG
CHEN WEI
GU XIAODONG
LIU GUOFU
WANG YATING
LIU MENGKAI
WANG GUOLIANG
CHEN CHEN

Assignees

中国铁路设计集团有限公司

Dates

Publication Date: 20260508
Application Date: 20260228

Claims (4)

1. A method for calculating a static horizontal force of a contact net positioner, the method comprising the steps of: S1, establishing a rectangular coordinate system by taking a positioning point A of a positioner as an original point O, and applying static horizontal force to a contact line by the positioner Y-axis and horizontal force The contact line is deformed at the corner of the positioning point to form a flexible line part which is a flexible line AB and a flexible line AC respectively, the flexible line AB and the flexible line AC are symmetrical with each other compared with the positioning point, and the outward extending parts of the two points B, C on the contact line are straight line parts; S2, carrying out stress analysis on the contact line deflection line part on the right side of the positioning point A, obtaining a control differential equation of the contact line deflection line part on the right side of the positioning point A according to a deflection line differential equation of the tension beam, and solving the control differential equation to obtain a form of a control differential equation solution: ; ; ; wherein x and y represent the coordinates of the flexible line of the contact line on the right side of the positioning point A, E represents the Young's modulus of the contact wire, I represents the section moment of inertia of the contact wire, T represents the tension applied to both sides of the contact wire, l represents the length of the flexible line AB or AC, An included angle between the linear part of the contact line and the horizontal line; S3, approximating the bending line parts of the contact lines at the two sides of the positioning point A to axial force cantilever beams, wherein the free ends of the cantilever beams are the point B and the point C, the free ends of the cantilever beams are subjected to axial force and vertical load, and the axial force cantilever Liang Wanju balance equation at the right side of the positioning point A is obtained according to the balance of the axial force cantilever Liang Wanju: ; The formula is given by Substitution formula To the right of point A bending moment of bending line part of contact line : ; S4, carrying out stress analysis on the contact line deflection line part at the left side of the positioning point A according to the method of the step S2 to obtain a control differential equation and an equation solution form of the contact line deflection line part at the left side of the positioning point A, and obtaining an axial force cantilever Liang Wanju balance equation at the left side of the positioning point A according to the method of the step S3 to further obtain the bending moment of the contact line deflection line part at the left side of the point A : ; Wherein, the The abscissa of the contact line deflection line on the left side of the positioning point A; s5, according to the expression of the bending moment of the bending line part of the contact line bending line, the horizontal force applied to the end head of the right cantilever beam at the A position is The horizontal force applied to the left cantilever beam end at A is Therefore, a horizontal force at the positioning point A due to the bending rigidity of the contact line is obtained : (11)。
2. A method of calculating the static horizontal force of a catenary positioner according to claim 1, wherein the calculation method is applied to flexible line sections having a radius of less than 3000 meters and the setpoint rotational angle deformation is no more than 2 degrees.
3. The method for calculating the static horizontal force of the contact net positioner according to claim 1, wherein in the step S2, the stress analysis is performed on the contact line deflection line portion on the right side of the positioning point a, the control differential equation of the contact line deflection line portion on the right side of the positioning point a is obtained according to the deflection line differential equation of the tension beam, the control differential equation is solved, and the method for obtaining the form of the control differential equation solution is as follows: Carrying out stress analysis on the contact line deflection line part on the right side of the positioning point A, and obtaining a control differential equation of the contact line deflection line part on the right side of the positioning point A according to the deflection line differential equation of the tension beam: ; Order the The form of the control differential equation solution is obtained: ; ; ; According to the constraint condition at the positioning point A: Obtaining: ; Obtaining: ; Obtaining: ; thus: ; Wherein x and y represent the coordinates of the flexible line of the contact line on the right side of the positioning point A, E represents the Young's modulus of the contact line, I represents the section moment of inertia of the contact line, And represent undetermined parameters of the differential equation general solution of the contact line flexible line control on the right side of the locating point A respectively.
4. A method for calculating a static horizontal force of a catenary positioner according to claim 3, wherein the method for solving the control differential equation in step S2 to obtain a solution form of the control differential equation further comprises: straight line part with contact lines on two sides included angles with horizontal line The absolute value of the abscissa of the flexible line AB and AC length l m, point B or point C is regarded as the flexible line AB or AC length l, and therefore, for the contact line flexible line on the right side of the anchor point A, there are: Substituting it into formula The method can obtain: ; Wherein, the The abscissa representing point C; The formula is given by Carry-over formula : ; Thereby obtaining the following steps: ; ; Thus, there is obtained: ; ; 。

Description

Calculation method of static horizontal force of overhead line system positioner Technical Field The invention belongs to the technical field of design of overhead contact systems of electrified railways, and particularly relates to a calculation method of static horizontal force of a overhead contact system positioner. Background The calculation of the horizontal force of the overhead line system locator is a key professional technology in the design, construction and operation and maintenance of electrified railways, in particular high-speed railways, and is directly related to the stability of overhead line systems, the current taking quality of pantographs and the driving safety. At present, the contact line is simplified into a flexible rope model when the static horizontal force of the contact line positioner is calculated in engineering, a simplified formula is generally adopted for calculation, and the method belongs to an ideal assumption that the bending stiffness of the contact line is ignored. In straight line sections or large curve radius sections, errors in this simplified calculation method do not have serious consequences. However, in the small-radius curve section, since the contact line at the locating point is actually a flexible line, vector synthesis calculation is simplified to be carried out by using a trigonometric function, so that larger errors are generated in the calculation of the horizontal force and the gradient of the positioner, and the errors are greatly increased along with the decrease of the radius of the curve, and various problems such as the degradation of the contact quality of the bow net, excessive wear of equipment and even running safety accidents can be generated. Therefore, the method is urgently needed to comprehensively consider multidimensional factors such as curve radius, bending rigidity of the contact line, deformation of the contact line flexible line and the like, has more accurate calculation results, is more in line with an actual calculation method of engineering, and solves the problem of accurate calculation of static horizontal force of the contact line positioner at the curve. Disclosure of Invention In order to solve the problems in the background technology, the invention combines the bending deformation equation of the tension beam and the balance equation of the axial force cantilever Liang Wanju to accurately calculate the static horizontal force at the positioning point; The invention provides a calculation method of static horizontal force of a contact net positioner, which comprises the following steps: S1, establishing a rectangular coordinate system by taking a positioning point A of a positioner as an original point O, and applying static horizontal force to a contact line by the positioner Y-axis and horizontal forceThe contact line is deformed at the corner of the positioning point to form a flexible line part which is a flexible line AB and a flexible line AC respectively, the flexible line AB and the flexible line AC are symmetrical with each other compared with the positioning point, and the outward extending parts of the two points B, C on the contact line are straight line parts; S2, carrying out stress analysis on the contact line deflection line part on the right side of the positioning point A, obtaining a control differential equation of the contact line deflection line part on the right side of the positioning point A according to a deflection line differential equation of the tension beam, and solving the control differential equation to obtain a form of a control differential equation solution: ; ; ; Wherein x and y represent the coordinates of the flexible line of the contact line on the right side of the positioning point A, E represents the Young's modulus of the contact wire, I represents the section moment of inertia of the contact wire, T represents the tension applied to both sides of the contact wire, l represents the length of the flexible line AB or AC,An included angle between the linear part of the contact line and the horizontal line; S3, approximating the bending line parts of the contact lines at the two sides of the positioning point A to axial force cantilever beams, wherein the free ends of the cantilever beams are the point B and the point C, the free ends of the cantilever beams are subjected to axial force and vertical load, and the axial force cantilever Liang Wanju balance equation at the right side of the positioning point A is obtained according to the balance of the axial force cantilever Liang Wanju: ; The formula is given by Substitution formulaTo the right of point A bending moment of bending line part of contact line: ; S4, carrying out stress analysis on the contact line deflection line part at the left side of the positioning point A according to the method of the step S2 to obtain a control differential equation and an equation solution form of the contact line deflection line part at th