CN-120633059-B - Calculation method for tension distribution of traction rope on curved annular rope grooved pulley

CN120633059BCN 120633059 BCN120633059 BCN 120633059BCN-120633059-B

Abstract

The invention discloses a calculation method of tension distribution of traction ropes on curved annular rope sheaves, belongs to the field of rope sheaves, solves the problem that the traditional calculation method of friction distribution cannot effectively calculate the friction distribution of the rope sheaves, and adopts the technical proposal that a parameterized model is established for the curved annular rope sheaves to parameterize the curved paths of the curved sheaves, and (3) carrying out stress analysis on the traction rope by adopting a microcell method, and analyzing resultant force of the traction rope in the circumferential direction, the radial direction and the axial direction of the curved annular rope grooved pulley, so that a tension attenuation formula of the micro arc section can be deduced, a tension value can be calculated by iterating the tension attenuation according to the tension attenuation of the micro arc section, and a tension distribution formula can be obtained after fitting the tension value. The method is mainly used for precisely calculating the tension distribution of the traction rope on the curved annular rope grooved pulley.

Inventors

ZHANG LITIAN
ZHANG WENYAO

Assignees

浙江诺和机电股份有限公司

Dates

Publication Date: 20260512
Application Date: 20250508

Claims (9)

1. The method for calculating the tension distribution of the traction rope on the curved annular rope grooved pulley is characterized in that a curved surface groove for winding the traction rope is formed in the outer peripheral side of the curved annular rope grooved pulley, the curved surface groove comprises two annular wall surfaces with wavy curves, and the method for calculating the stress of the curved surface groove on the traction rope comprises the following steps: S1, parameterizing a curved annular rope sheave and establishing a model parameter equation of the curved annular rope sheave; S2, calibrating a plurality of nodes on the traction rope, calculating the pulling force F of each node on the traction rope, and calculating the included angle between the tangent line of the corresponding traction rope at each node and the radial cross section of the curved annular rope grooved wheel Calculating the included angle between the tangent line of the corresponding hauling rope at each node and the central axis of the curved annular rope sheave ; S3, correspondingly selecting micro-arc segments at each node of the traction rope by adopting a micro-element method, carrying out stress analysis on the micro-arc segments in the circumferential direction, the radial direction and the axial direction of the curved annular rope grooved pulley based on Newton' S third law and coulomb law, and obtaining the tension attenuation of the micro-arc segments through the stress analysis ; S4, attenuating according to the tension of the micro-arc section Carrying out iterative calculation on the tension force F of each node of the traction rope through an iterative program, thereby obtaining a tension value T of each node on the traction rope; S5, carrying out exponential fitting on the tension values T of all the nodes so as to obtain a distribution formula of the tension of the nodes of the haulage rope 。
2. The method for calculating the tension distribution of the traction rope on the curved annular rope sheave according to claim 1, wherein the parameter equation in S1 is used for completely expressing the curved path of the traction rope, and the specific expression of the parameter equation is as follows: ; wherein R represents the radius of the curved annular rope grooved wheel, the curved path of the hauling rope is a trigonometric function waveform, A represents the amplitude of the trigonometric function waveform path, and N represents the number of waveforms on the curved groove.
3. The method for calculating the tension distribution of a traction rope on a curved annular rope sheave according to claim 2, wherein the included angle in S2 is And For determining the direction and angle of the pulling force And The calculation method of (2) is as follows: ; ; Wherein the method comprises the steps of The tangent vector of the micro-arc segment is shown, The tangential vector of the corresponding node of the curved annular rope groove wheel is represented, and x, y and z are respectively the radial coordinate, the axial coordinate and the vertical coordinate of the curved groove path node in a three-dimensional coordinate system.
4. The method for calculating the tension distribution of the traction rope on the curved annular rope sheave according to claim 3, wherein the resultant force of the traction rope in the circumferential, radial and axial directions of the curved annular rope sheave in S3 is represented by the following formula: in the circumferential direction of the curved annular rope sheave: ; in the radial direction of the curved annular rope sheave: ; in the axial direction of the curved annular rope sheave: ; wherein F represents the tensile force exerted by the traction rope; 、 Showing the supporting force of the two annular walls against the traction rope; the coefficient of friction is shown; The central angle of the curved annular rope grooved wheel corresponding to the micro arc section is shown; the central angle of the curved surface groove corresponding to the micro arc section is shown; The included angle between the annular wall surface and the radial cross section is shown; the location of the micro-arc segment is indicated; the equivalent friction coefficient correction is shown; Solving the equation set to obtain the tension attenuation of the micro-arc section The specific formula is as follows: 。
5. The method for calculating the tension distribution of a traction rope on a curved annular rope sheave according to claim 4, wherein the central angle of the curved annular rope sheave corresponding to the micro-arc segment Central angle of curved surface groove corresponding to micro arc section The calculation formula of (2) is as follows: ; ; Wherein the method comprises the steps of Is the number of the discrete nodes, 、 The curvature and the arc length of the waveform corresponding to the micro-arc segment of the node are respectively corresponding.
6. The method for calculating the tension distribution of a traction rope on a curved endless rope sheave according to claim 4, wherein the following steps are performed The method is used for judging the arc line position of the force analysis node, and the calculation method is as follows: 。
7. The method for calculating the tension distribution of a traction rope on a curved endless rope sheave according to claim 4, wherein the equivalent friction coefficient is corrected The friction experiment is carried out on the curved annular rope grooved pulley, a section of traction rope contacted with the curved annular rope grooved pulley is obtained, and the tension at two ends of the traction rope is utilized under the wrap angle delta of the section of traction rope And The calculation is carried out, and the calculation formula is as follows: 。
8. The method for calculating the tension distribution of the traction rope on the curved endless rope sheave according to claim 1, wherein the traction rope of each node in S4 is subjected to tension By tension applied to the traction rope at the last node And pull force attenuation The calculation is performed as follows: 。
9. The method for calculating the tension distribution of the traction rope on the curved annular rope sheave according to claim 1, wherein the tension formula of each node of the traction rope is obtained by exponential fitting in S5: ; Wherein the method comprises the steps of The tension value of the initial node point is shown, The attenuation coefficient is shown as such, The index value of the node is represented, and the index value of the initial node is 0.

Description

Calculation method for tension distribution of traction rope on curved annular rope grooved pulley Technical Field The invention discloses a tension distribution calculation method of a traction rope on a curved annular rope sheave, and belongs to the technical field of rope sheave wheels. Background The electric traction device is hoisting equipment integrating a current collector and a rope groove wheel, wherein the traction rope is wound in the rope groove of the rope groove wheel in the use process of the electric traction device, the traction rope is kept tensioned through friction force between the traction rope and the rope groove wheel, so that the purpose of traction of heavy objects is achieved, friction force between the rope groove wheel and the traction rope is a decisive factor for hoisting and traction efficiency and stability in the operation process of the electric traction device, a rope groove path of a traditional rope groove wheel is generally a circular track surrounding a wheel main body, the operation capacity of a rope wheel system is greatly limited due to insufficient friction force, and based on the rope groove wheel of the curved path, a larger friction driving force and a higher safety factor can be provided by arranging the curved annular groove in the circumferential direction of the rope groove wheel main body, so that more reliable selection is provided for related operation. The existing calculation method for the friction force distribution of the traditional rope groove wheel is mainly a traditional Euler formula, and ignores the comprehensive influence of an axial bending path and a groove shape on rope stress, so that the method is not suitable for a curved annular rope sheave, and in addition, the existing calculation method lacks effective theoretical basis and calculation means when solving the traction rope tension distribution rule, and cannot provide powerful support for the structural design of the curved annular rope sheave. Disclosure of Invention The invention aims to solve the problem that the traditional friction force distribution calculation method cannot effectively calculate the friction force distribution of a rope sheave, and provides the tension distribution calculation method of the traction rope on the curved annular rope sheave, which can accurately calculate the friction force distribution of the surface of the curved annular rope sheave. The technical problems are solved, and the invention adopts the following technical scheme: The method for calculating the tension distribution of the traction rope on the curved annular rope grooved pulley comprises the steps that a curved groove for winding the traction rope is formed in the outer peripheral side of the curved annular rope grooved pulley, the curved groove comprises two annular wall surfaces with wavy curves, and the curved groove is used for calculating the stress of the traction rope, and the method comprises the following steps: S1, parameterizing a curved annular rope sheave and establishing a model parameter equation of the curved annular raw sheave; S2, calibrating a plurality of nodes on the traction rope, calculating the pulling force F of each node on the traction rope, calculating the included angle theta between the tangent line of the corresponding traction rope at each node and the radial cross section of the curved annular rope sheave, and calculating the included angle between the tangent line of the corresponding traction rope at each node and the central axis of the curved annular rope sheave S3, correspondingly selecting micro-arc segments at each node of the traction rope by adopting a infinitesimal method, carrying out stress analysis on the micro-arc segments in the circumferential direction, the radial direction and the axial direction of the curved annular rope grooved pulley based on Newton' S third law and coulomb law, and obtaining the tension attenuation dF of the micro-arc segments through the stress analysis, wherein the tension attenuation dF of each micro-arc segment of the traction rope contacted with the curved annular rope grooved pulley is the friction force born by the micro-arc segments. S4, carrying out iterative calculation on the tension F of each node of the traction rope through an iterative program according to the tension attenuation dF of the micro-arc section, so as to obtain a tension value T of each node on the traction rope; And S5, carrying out exponential fitting on the tension values T of all the nodes, so as to obtain a distribution formula T (T) of the tension of the nodes of the haulage rope. Preferably, the parameter equation in S1 is used for completely expressing the curved path of the traction rope, and the specific expression of the parameter equation is as follows: wherein R represents the radius of the curved annular rope grooved wheel, the curved path of the hauling rope is a trigonometric function waveform, A represents the amplit