Simple chain-shaped dropper non-uniform arrangement method based on equal-elasticity space construction

Abstract

The invention discloses a simple chain-shaped dropper non-uniform arrangement method based on equal-elasticity space construction, relates to the technical field of bows, and aims at any cross-catenary, stress analysis is carried out on a positioner through a moment balance formula, a simulation model is constructed to carry out stress analysis on a positioning point, the optimal value of the distance between a first dropper and the positioning point is obtained, and the optimal value of the distance between the first dropper and the positioning point is calculated. The arrangement of the first dropper is completed; after the first droppers are arranged, the remaining droppers in the span area are arranged at equal intervals, a first sub-area and an adjacent second sub-area corresponding to the maximum elasticity of the span center area are analyzed through an equal-elasticity reference curve and an elastic gain, and the maximum elasticity of the two sub-areas is equal by adjusting the positions of the droppers on the left side and the right side of the second sub-area; therefore, an equal-elasticity space is constructed, and non-uniform arrangement of the simple chain-shaped droppers is completed. The problems that in the prior art, when the dynamic performance of the simple chain-shaped bow net system is improved, modeling and simulation are difficult, resources are consumed, and the simulation and actual deviation is large are solved.

Description

Technical Field

[0001] This invention relates to the field of pantograph-catenary technology, and more particularly to a method for non-uniform arrangement of simple chain-shaped droppers based on an isoelastic spatial construction. Background Technology

[0002] In a pantograph-catenary system, the simple catenary is the most basic suspension configuration, consisting of a catenary cable, droppers, and contact wire. Its core feature is that the contact wire is suspended from the catenary cable by the droppers. For the pantograph-catenary system, its dynamic performance refers to the stability, contact quality, and energy transmission efficiency of the pantograph and contact wire during dynamic interaction while the train is running. Its core function is to ensure the safe, efficient, and reliable operation of electrified railways. Therefore, improving the dynamic performance indicators of the pantograph-catenary system is of paramount importance.

[0003] The dynamic performance of the pantograph-catenary system is mainly determined by three factors: the characteristics of the pantograph, the static performance of the catenary, and the wave propagation characteristics under the action of the pantograph and catenary. The elasticity of the catenary is a key static performance indicator; the more uniform the elasticity of the catenary, the smoother the interaction between the pantograph and catenary. In existing technologies, for simple chain-type catenaries, finite element models are often used to simulate the dynamic response of the pantograph and catenary under different working conditions. By adjusting the arrangement of the droppers, the elasticity non-uniformity coefficient of the catenary is made to meet the design target, thereby improving the dynamic performance of the pantograph and catenary. However, this method has the following drawbacks: First, modeling and simulation are difficult; the pantograph-catenary dynamic model based on the dynamic performance evaluation of the pantograph and catenary is extremely complex. Second, multiple simulations are required to adjust the dropper arrangement, consuming a lot of time and resources. Third, the simulation model needs to be updated and maintained irregularly. Fourth, environmental factors can cause deviations between the simulation results and actual working conditions. Summary of the Invention

[0004] In view of this, this application provides a simple method for non-uniform arrangement of chain suspensions based on the construction of an isoelastic space, in order to overcome the shortcomings of the prior art.

[0005] The first aspect of this application provides a method for non-uniform arrangement of simple chain suspension wires based on an isoelastic space, including: For any span of the overhead contact line, the two droppers closest to the two positioning points are designated as the first dropper, and the area within the span between the two positioning points is designated as the area within the span. Based on the torque balance formula, the force analysis of the positioner at the positioning point is performed, and the first analysis result is obtained. A simulation model is constructed, and the force analysis of the positioning point is performed to obtain the second analysis result; Based on the first analysis result and the second analysis result, the optimal value of the distance between the first dropper and the corresponding positioning point is obtained; Based on the optimal spacing value, the corresponding first suspension cable position is determined, and the remaining suspension cables in the span region are arranged at equal intervals to obtain multiple equally spaced span sub-regions; Elastic baseline curves and elastic gain analyses are performed on multiple sub-regions located at the center of the span region, and the sub-region corresponding to the maximum elasticity is denoted as the first sub-region. The adjacent sub-regions within the first sub-region are recorded as the second sub-regions. The suspension strings on the left and right sides of the second sub-regions are moved outward by a preset distance to make the maximum elasticity between all first sub-regions and all second sub-regions equal, thus completing the construction of the equipotential elastic space. Based on the optimal spacing value and the equal elastic space, a non-uniform arrangement of simple chain suspension wires is completed.

[0006] In one possible implementation of the first aspect, for any span of the contact wire, the two droppers closest to the two positioning points are designated as the first dropper, and the area within the span between the two positioning points is designated as the area within the span; Based on the torque balance formula, the force analysis of the positioner at the positioning point is performed, and the first analysis result is obtained. A simulation model is constructed, and the force analysis of the positioning point is performed to obtain the second analysis result; Based on the first analysis result and the second analysis result, the optimal value of the distance between the first dropper and the corresponding positioning point is obtained; Based on the optimal spacing value, the corresponding first suspension cable position is determined, and the remaining suspension cables in the span region are arranged at equal intervals to obtain multiple equally spaced span sub-regions; Elastic baseline curves and elastic gain analyses are performed on multiple sub-regions located at the center of the span region, and the sub-region corresponding to the maximum elasticity is denoted as the first sub-region. The adjacent sub-regions within the first sub-region are recorded as the second sub-regions. The suspension strings on the left and right sides of the second sub-regions are moved outward by a preset distance to make the maximum elasticity between all first sub-regions and all second sub-regions equal, thus completing the construction of the equipotential elastic space. Based on the optimal spacing value and the equal elastic space, a non-uniform arrangement of simple chain suspension wires is completed.

[0007] In one possible implementation of the first aspect, the force analysis of the positioner at the positioning point based on the torque balance formula includes: Based on the torque balance formula, the mathematical relationship between the distance between the first dropper and the positioning point and the angle of the positioner is obtained as follows: The distance between the first drop string and the positioning point. For the unit mass of the contact wire, The overall quality of the positioner and its clamps. The horizontal component of the pulling force on the positioner. This is the angle value of the locator.

[0008] One possible implementation of the first aspect also includes: The contact wire is fixed to the positioner, and the positioner and the positioner support are connected by a hook and form an intersection. The positioner rotates around the intersection to adjust the positioner angle. The overall quality of the positioner and its clamp Obtain it using the following formula: For the quality of the positioner, The quality of the wire clamp.

[0009] In one possible implementation of the first aspect, constructing a simulation model and performing a force analysis on the positioning point includes: Built on the location point The radius of the line at that location is Location point The left and right adjacent positioning points are positioning points. and positioning points And the contact line is at the positioning point The point is subjected to pulling forces from the contact lines on both sides. and the pulling force of the locator A simulation model in which the three forces are in equilibrium; Based on the simulation model, the positioning points Force analysis is performed, and the analytical expressions include: When the line radius for At that time, the line is approximately a straight line, and the tangent of the angle formed by the contact wire and the center line of the line is equal to the pull-out value. span between positioning points Interval ratio; When the line radius Not for At that time, the line is a curve, and the line radius is... With each forward stride, the angle difference generated by the track is: When the positioning point When it is inside the curve, in the formula Pick When the positioning point When it is outside the curve, in the formula Pick .

[0010] In one possible implementation of the first aspect, obtaining the optimal distance between the first suspension cable and the corresponding positioning point includes: Based on prior engineering data, the maximum angle limit for the positioner in the overhead contact line was selected as [value missing]. and when the positioning point When the line is inside the curve, the minimum design radius is: ; Minimum design radius of the line Substituting the analytical expression and setting the maximum angle limit of the locator... Substituting into the torque balance formula, the maximum distance between the first hanger and the positioning point is obtained as follows: ; For the maximum limit of the spacing The optimal spacing value is obtained by rounding down.

[0011] One possible implementation of the first aspect also includes: Based on prior engineering data, the maximum allowable spacing between suspension cables in a simple catenary suspension system is obtained. Determine whether the optimal spacing value exceeds the maximum allowable value. If not, no action is taken; if so, the corresponding optimal spacing value is adjusted.

[0012] In one possible implementation of the first aspect, arranging the remaining suspension cables at equal intervals in the inner span region includes: Once the position of the first dropper is determined, the spacing between the remaining droppers in the span region is determined using the following formula: The remaining suspension strings in the inner span region are evenly spaced. Arrangement, The number of all hangers in the span region.

[0013] In one possible implementation of the first aspect, performing elastic reference curve and elastic gain analysis on multiple intra-span sub-regions located at the center of the intra-span region includes: Obtain the elastic curves corresponding to multiple sub-regions within the span at the center of the span region. The elastic curves include an elastic reference curve and an elastic gain, and the elastic gain is proportional to the distance between the suspension wires. When the number of all suspension strings in the span region is even, the span sub-region with the highest elasticity curve is selected as the maximum elastic span sub-region, and is denoted as the first sub-region. When the number of all suspension strings in the span region is odd, the two span sub-regions with the highest elasticity curves are selected as the maximum elastic span sub-regions, and are also referred to as the first sub-region.

[0014] In one possible implementation of the first aspect, obtaining the adjacent sub-regions within the first sub-region as the second sub-region, and moving the suspension cables on the left and right sides of the second sub-region outward by a preset distance includes: The preset distance is calculated using the following formula: For the preset distance, To maximize the elasticity between the suspension strings in a simple chain suspension, For a simple chain suspension, the elasticity at any position within the span region is considered. are positive integers and .

[0015] In one possible implementation of the first aspect, the non-uniform arrangement of a simple chain suspension wire, based on the optimal spacing value and the isoelastic space, includes: Based on the optimal distance between the positioning point and the first dropper, the two first droppers are arranged; based on the arranged first droppers and the constructed equal elastic space, all droppers in the span region are arranged at equal intervals, and the droppers at the center of the span region are adjusted to make the elasticity of the corresponding mid-span region equal, thus completing the non-uniform arrangement of the simple chain droppers.

[0016] Its beneficial effects are as follows: This invention discloses a method for non-uniform arrangement of simple chain-type droppers based on the construction of an isoelastic space. Specifically, for any span of the contact network, the force analysis of the positioner is performed using the torque balance formula, and a simulation model is constructed to analyze the force at the positioning point. The optimal distance between the first dropper and the positioning point is obtained, and the arrangement of the first dropper is completed. After the first dropper is arranged, the remaining droppers in the span area are arranged at equal intervals. The first sub-region and the adjacent second sub-region corresponding to the maximum elasticity in the central region of the span are analyzed using the isoelastic reference curve and elastic gain. By adjusting the dropper positions on the left and right sides of the second sub-region, the maximum elasticity of the two types of sub-regions is made equal, thereby constructing an isoelastic space. Finally, based on the optimal spacing value and the constructed isoelastic space, the non-uniform arrangement of simple chain-type droppers is completed. This invention solves the problems of difficult modeling and simulation, high resource consumption, and large deviation between simulation and reality in the existing technology when improving the dynamic performance of simple chain-type pantograph-catenary systems. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic flowchart of a simple chain-shaped suspension wire non-uniform arrangement method based on the construction of an isoelastic void, provided in an embodiment of this application. Figure 2 This is a schematic diagram of the force analysis of the positioner in an embodiment of this application; Figure 3 This is a schematic diagram of the force analysis at the positioning point in the embodiments of this application; Figure 4 This is a schematic diagram of the contact wire elasticity curves before and after the optimization of the dropper arrangement in the embodiments of this application; Figure 5 This is a schematic diagram comparing the distribution and elastic characteristics of the suspension wires in the simple chain suspension non-uniform arrangement and the traditional uniform arrangement proposed in the embodiments of this application. Figure 6 This is a visualization of the contact force and a schematic diagram of the support data showing the improvement of the pantograph-catenary dynamic performance by the arrangement method in the embodiments of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0021] Example In existing technologies, for simple catenary systems, finite element models are often used to simulate the dynamic response of the pantograph and catenary under different working conditions. By adjusting the arrangement of droppers, the elastic non-uniformity coefficient of the catenary is made to meet the design target, thereby improving the dynamic performance of the pantograph and catenary. However, this method has the following drawbacks: First, modeling and simulation are difficult, and the pantograph-catenary dynamic model based on the dynamic performance evaluation of the pantograph and catenary is extremely complex; second, multiple simulations are required to adjust the dropper arrangement, which consumes a lot of time and resources; third, the simulation model needs to be updated and maintained irregularly; and fourth, environmental factors cause deviations between the simulation results and the actual working conditions.

[0022] Therefore, this application provides a simple method for non-uniform arrangement of chain suspensions based on an isoelastic spatial construction, such as... Figure 1 As shown, it includes: For any span of the overhead contact line, the two droppers closest to the two positioning points are designated as the first dropper, and the area within the span between the two positioning points is designated as the area within the span. Based on the torque balance formula, the force analysis of the positioner at the positioning point is performed, and the first analysis result is obtained. A simulation model is constructed, and the force analysis of the positioning point is performed to obtain the second analysis result; Based on the first analysis result and the second analysis result, the optimal value of the distance between the first dropper and the corresponding positioning point is obtained; Based on the optimal spacing value, the corresponding first suspension cable position is determined, and the remaining suspension cables in the span region are arranged at equal intervals to obtain multiple equally spaced span sub-regions; Elastic baseline curves and elastic gain analyses are performed on multiple sub-regions located at the center of the span region, and the sub-region corresponding to the maximum elasticity is denoted as the first sub-region. The adjacent sub-regions within the first sub-region are recorded as the second sub-regions. The suspension strings on the left and right sides of the second sub-regions are moved outward by a preset distance to make the maximum elasticity between all first sub-regions and all second sub-regions equal, thus completing the construction of the equipotential elastic space. Based on the optimal spacing value and the equal elastic space, a non-uniform arrangement of simple chain suspension wires is completed.

[0023] In this embodiment, the position calculation for the first suspension wire is as follows: In a simple catenary suspension system, the position of the first suspension string is constrained by the static installation angle of the positioner, and the angle of the positioner is determined by the resultant forces received by the positioner from multiple directions, such as... Figure 2 As shown, the contact wire is fixed to the positioner, which is connected to its support via a hook. The intersection of the two is equivalent to a rotation axis, around which the positioner rotates. The positioner's angle is related to the lateral and longitudinal tensile forces of the contact wire, as well as the positioner's length and weight. The vertical force acting on the positioning point... Equal to length is Based on the contact wire mass and the torque balance formula, the distance between the first suspension string (or elastic cable suspension string) and the positioning point is obtained. Angle with locator The mathematical relationship is as follows: The distance between the first drop string and the positioning point. For the unit mass of the contact wire, The overall quality of the positioner and its clamps. The horizontal component of the pulling force on the positioner. The angle value of the locator, and It equals the sum of half the mass of the positioner and the mass of the clamp, that is... .

[0024] and Then by establishing such Figure 3 The simulation model shown is used for solving, with the contact line at the positioning point. Pulling force of contact lines on both sides and the pulling force of the locator When the three forces are in equilibrium, and the line is straight, due to the large aspect ratio of the line, the tangent of the angle formed by the contact line and the center line of the line is considered to be... It equals the ratio of the pull-out value to the span; when the line is curved, the line radius is... The difference in turning angle produced by the line for each forward stride is calculated as follows: Then, by solving based on trigonometric functions, we finally obtain... The analytical expression is: When the line radius for At that time, the line is approximately a straight line, and the tangent of the angle formed by the contact wire and the center line of the line is equal to the pull-out value. span between positioning points Interval ratio; When the line radius Not for At that time, the line is a curve, and the line radius is... With each forward stride, the angle difference generated by the track is: When the positioning point When it is inside the curve, in the formula Pick When the positioning point When it is outside the curve, in the formula Pick .

[0025] In this embodiment, in order to reduce the elastic non-uniformity coefficient of the contact wire, and as can be seen from formula (1), the static angle of the positioner is... The upper limit determines The upper limit of the positioner's angle setting should ensure sufficient lifting space. However, a larger positioner angle does not necessarily mean better system performance; it needs to be considered in conjunction with the pantograph-catenary dynamic performance and the positioner's own wear. The specific limit needs to be selected based on prior engineering data, denoted as [insert limit here]. .

[0026] According to equation (1) The smaller, The smaller, therefore The determination needs to meet the following conditions. The minimum positioner angle requirement is determined by equation (2) when the positioning point is inside the curve and the curve radius is... Take the minimum value hour, The minimum value is when the calculated locator angle is at its minimum.

[0027] In conclusion, The positioner angle should be less than [value missing] under all line operating conditions. The maximum angle limit of the contact wire positioner and the minimum design radius of the line Substituting into equations (1) and (2) respectively, the maximum distance between the first dropper and the positioning point can be calculated. And the maximum spacing limit The optimal spacing value is obtained by rounding down.

[0028] Furthermore, an excessively large spacing between the first droppers will cause significant differences in the static and dynamic loads of the first dropper compared to adjacent droppers, resulting in differences in dropper lifespan and negatively impacting system reliability. Therefore, the dropper spacing of the first dropper should be comprehensively selected by the designer based on factors such as the dropper's dynamic load and fatigue characteristics, and taken as the maximum allowable value. Only when the calculated optimal spacing value does not exceed this maximum allowable value should it be used as a parameter for arranging the position of the first dropper. If the optimal spacing value exceeds the maximum allowable value, an adaptive adjustment (adjusting it to be less than the maximum allowable value) is required.

[0029] Construction across medium-elasticity spaces: The elasticity curve of the overhead contact line is a linear combination of an elastic reference curve and an elastic gain. The elastic reference curve is unaffected by the arrangement of the droppers, while the elastic gain is proportional to the distance between the droppers. Figure 4In the case where the droppers are evenly spaced in the middle of the span, the elastic reference curve of dropper spacing A is higher than that of dropper spacing B, while the elastic gain of the two is the same. Therefore, the maximum elasticity of the contact network is in the middle of spacing A. In order to make the maximum elasticity of spacing A and B equal, the dropper spacing of B needs to be significantly larger than that of A, so that the difference in elastic gain between the two at the position of maximum elasticity is exactly equal to the difference in reference elasticity, thus achieving the equality of maximum elasticity. It should be noted that the above dropper spacing refers to the sub-region within the span, and is only used for better explanation.

[0030] like Figure 4 As shown in the upper part, the mid-span dropper spacing is first calculated when using an equal-spacing arrangement. When a simple chain suspension has a certain number of suspension wires within one span When the value is greater than or equal to 4, the maximum elasticity between A and B is made equal by increasing the string spacing B and decreasing the string spacing A. Specifically, the string spacings on the left and right sides of the string spacing B are moved outward by a preset distance. ,like Figure 4 The lower half is shown.

[0031] Therefore, the problem of constructing a mid-span flexible space is transformed into the problem of the spacing between the suspension cables at mid-span. Solve below The problem is, firstly, after determining the position of the first dropper, we obtain... The analytical expression is: For a simple chain suspension, based on the parity of the number of suspension strings, we obtain: For the preset distance, To maximize the elasticity between the suspension strings in a simple chain suspension, For a simple chain suspension, the elasticity at any position within the span region is considered. are positive integers and .

[0032] It should be noted that the maximum elasticity between the suspension strings in a simple chain suspension is... And elasticity at any location within the span of the region The acquisition of these values ​​is based on existing technologies. This embodiment provides the following formula to better understand the solution for the preset distance in this embodiment, specifically: Maximum elasticity between simple chain suspension wires formula: The elasticity of a simple chain suspension at any position within the span region formula: Calculate based on equations (3) and (4) and Then, follow the steps as follows Figure 4 The optimized arrangement of the droppers shown can be used to construct an isoelastic space.

[0033] This embodiment reduces the elastic non-uniformity coefficient by determining the position of the first dropper and constructing an equal elastic space. The principle is as follows: the positioning point is the core support node of the contact network, and the elastic stability near it directly determines the reference accuracy of the elasticity within the span. If the position of the first dropper is unreasonable, it will cause abrupt changes in the contact line elasticity at the positioning point, becoming a hidden danger of increasing the elastic non-uniformity coefficient. This embodiment determines the optimal distance between the first dropper and the positioning point through torque balance formulas, simulation models, and prior engineering data. Essentially, it avoids this area becoming a break in elasticity by precisely controlling the elasticity near the positioning point. The central area within the span is the main working area for pantograph sliding, and the elastic uniformity of this area directly determines the dynamic performance of the pantograph-catenary system. This embodiment constructs an equal elastic space through initial equal spacing → elasticity analysis of the central area → fine-tuning of the dropper position. Essentially, it eliminates elastic fluctuations in this area by precisely matching the elasticity of the core area within the span.

[0034] This embodiment reduces the elasticity non-uniformity coefficient by determining the elasticity benchmark of the key node of the control positioning point by determining the position of the first dropper (avoiding abrupt elastic changes at both ends) and by constructing an equal elasticity space to control the elasticity uniformity of the core area within the span (eliminating intermediate elastic fluctuations). The elasticity uniformity coefficient is a core static indicator of pantograph-catenary dynamic performance. Its improvement directly translates into optimization of the smoothness of pantograph-catenary interaction, contact quality, and energy transmission efficiency, ultimately achieving an improvement in pantograph-catenary dynamic performance.

[0035] This embodiment addresses the shortcomings of existing technologies and forms four core advantages in technology implementation and practical application, specifically: Existing methods require the construction of extremely complex pantograph-catenary dynamics models, while this invention can complete the force analysis of the positioning point simply by using "torque balance formula + simulation model", without the need for complex modeling; Existing methods require multiple simulations to adjust the arrangement of the droppers, which is time-consuming and labor-intensive. This embodiment can complete the arrangement by determining the position of the first dropper and constructing an equally flexible space, without the need for repeated simulations, thus saving time and resources significantly. Existing methods require periodic updates and maintenance of simulation models to adapt to changes in operating conditions, while this implementation does not rely on complex simulation models and can be applied simply by combining prior engineering data, with no model maintenance costs. Existing methods suffer from deviations between simulation results and actual working conditions due to environmental factors. This embodiment uses prior engineering data and on-site adjustments based on equal elastic space to make the dropper arrangement more closely match the actual contact network working conditions, reducing the deviation between theory and practice and improving the stability and reliability of the pantograph-catenary system's dynamic performance.

[0036] In some embodiments, the force analysis of the positioner at the positioning point based on the torque balance formula includes: Based on the torque balance formula, the mathematical relationship between the distance between the first dropper and the positioning point and the angle of the positioner is obtained as follows: The distance between the first drop string and the positioning point. For the unit mass of the contact wire, The overall quality of the positioner and its clamps. The horizontal component of the pulling force on the positioner. This is the angle value of the locator.

[0037] In some embodiments, it also includes: The contact wire is fixed to the positioner, and the positioner and the positioner support are connected by a hook and form an intersection. The positioner rotates around the intersection to adjust the positioner angle. The overall quality of the positioner and its clamp Obtain it using the following formula: For the quality of the positioner, The quality of the wire clamp.

[0038] In some embodiments, constructing a simulation model and performing force analysis on the positioning point includes: Built on the location point The radius of the line at that location is Location point The left and right adjacent positioning points are positioning points. and positioning points And the contact line is at the positioning point The point is subjected to pulling forces from the contact lines on both sides. and the pulling force of the locator A simulation model in which the three forces are in equilibrium; Based on the simulation model, the positioning points Force analysis is performed, and the analytical expressions include: When the line radius for At that time, the line is approximately a straight line, and the tangent of the angle formed by the contact wire and the center line of the line is equal to the pull-out value. span between positioning points Interval ratio; When the line radius Not for At that time, the line is a curve, and the line radius is... With each forward stride, the angle difference generated by the track is: When the positioning point When it is inside the curve, in the formula Pick When the positioning point When it is outside the curve, in the formula Pick .

[0039] In some embodiments, obtaining the optimal distance between the first dropper and the corresponding positioning point includes: Based on prior engineering data, the maximum angle limit for the positioner in the overhead contact line was selected as [value missing]. and when the positioning point When the line is inside the curve, the minimum design radius is: ; Minimum design radius of the line Substituting the analytical expression and setting the maximum angle limit of the locator... Substituting into the torque balance formula, the maximum distance between the first hanger and the positioning point is obtained as follows: ; For the maximum limit of the spacing The optimal spacing value is obtained by rounding down.

[0040] In some embodiments, it also includes: Based on prior engineering data, the maximum allowable spacing between suspension cables in a simple catenary suspension system is obtained. Determine whether the optimal spacing value exceeds the maximum allowable value. If not, no action is taken; if so, the corresponding optimal spacing value is adjusted.

[0041] In some embodiments, arranging the remaining suspension cables at equal intervals in the span region includes: Once the position of the first dropper is determined, the spacing between the remaining droppers in the span region is determined using the following formula: The remaining suspension strings in the inner span region are evenly spaced. Arrangement, The number of all hangers in the span region.

[0042] In some embodiments, performing elastic baseline curve and elastic gain analysis on multiple intra-span sub-regions located at the center of the intra-span region includes: Obtain the elastic curves corresponding to multiple sub-regions within the span at the center of the span region. The elastic curves include an elastic reference curve and an elastic gain, and the elastic gain is proportional to the distance between the suspension wires. When the number of all suspension strings in the span region is even, the span sub-region with the highest elasticity curve is selected as the maximum elastic span sub-region, and is denoted as the first sub-region. When the number of all suspension strings in the span region is odd, the two span sub-regions with the highest elasticity curves are selected as the maximum elastic span sub-regions, and are also referred to as the first sub-region.

[0043] In some embodiments, obtaining the adjacent sub-regions within the first sub-region as the second sub-region, and moving the suspension cables on the left and right sides of the second sub-region outward by a preset distance includes: The preset distance is calculated using the following formula: For the preset distance, To maximize the elasticity between the suspension strings in a simple chain suspension, For a simple chain suspension, the elasticity at any position within the span region is considered. are positive integers and .

[0044] In some embodiments, based on the optimal spacing value and the isoelastic space, completing the non-uniform arrangement of a simple chain suspension includes: Based on the optimal distance between the positioning point and the first dropper, the two first droppers are arranged; based on the arranged first droppers and the constructed equal elastic space, all droppers in the span region are arranged at equal intervals, and the droppers at the center of the span region are adjusted to make the elasticity of the corresponding mid-span region equal, thus completing the non-uniform arrangement of the simple chain droppers.

[0045] The arrangement effect of this embodiment is as follows: Figure 5 As shown, it significantly improves the uniformity of elastic distribution by optimizing the structure in a simple chain suspension.

[0046] After the improvements in this embodiment, the dynamic performance of the pantograph-catenary system is effectively enhanced, and the system's operational quality is significantly improved. For example... Figure 6 As shown, taking the typical simple catenary suspension system of the Beijing-Tianjin Intercity Railway as an example, the key performance indicators of the pantograph-catenary system have been positively improved after optimization using this method. Specifically, the maximum value of the contact force has decreased, the minimum value has increased, and the standard deviation has decreased.

[0047] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computing software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0048] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0049] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for non-uniform arrangement of simple chain-shaped suspension wires based on isoelastic spatial construction, characterized in that, include: For any span of the overhead contact line, the two droppers closest to the two positioning points are designated as the first dropper, and the area within the span between the two positioning points is designated as the area within the span. Based on the torque balance formula, the force analysis of the positioner at the positioning point is performed, and the first analysis result is obtained. A simulation model is constructed, and the force analysis of the positioning point is performed to obtain the second analysis result; Based on the first analysis result and the second analysis result, the optimal value of the distance between the first dropper and the corresponding positioning point is obtained; Based on the optimal spacing value, the corresponding first suspension cable position is determined, and the remaining suspension cables in the span region are arranged at equal intervals to obtain multiple equally spaced span sub-regions; Elastic baseline curves and elastic gain analyses are performed on multiple sub-regions located at the center of the span region, and the sub-region corresponding to the maximum elasticity is denoted as the first sub-region. The adjacent sub-regions within the first sub-region are recorded as the second sub-regions. The suspension strings on the left and right sides of the second sub-regions are moved outward by a preset distance to make the maximum elasticity between all first sub-regions and all second sub-regions equal, thus completing the construction of the equipotential elastic space. Based on the optimal spacing value and the equal elastic space, a non-uniform arrangement of simple chain suspension wires is completed.

2. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 1, characterized in that, Based on the torque balance formula, the force analysis of the positioner at the positioning point includes: Based on the torque balance formula, the mathematical relationship between the distance between the first dropper and the positioning point and the angle of the positioner is obtained as follows: The distance between the first dropper and the positioning point. For the unit mass of the contact wire, The overall quality of the positioner and its clamps. The horizontal component of the pulling force on the positioner. This is the angle value of the locator.

3. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 2, characterized in that, Also includes: The contact wire is fixed to the positioner, and the positioner and the positioner support are connected by a hook and form an intersection. The positioner rotates around the intersection to adjust the positioner angle. The overall quality of the positioner and its clamp Obtain it using the following formula: For the quality of the positioner, The quality of the wire clamp.

4. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 2, characterized in that, Constructing a simulation model and performing force analysis on the positioning points includes: Built on location points The radius of the line at that location is Location point The left and right adjacent positioning points are positioning points. and positioning points And the contact line is at the positioning point The point is subjected to pulling forces from the contact lines on both sides. and the pulling force of the locator A simulation model in which the three forces are in equilibrium; Based on the simulation model, the positioning points Force analysis is performed, and the analytical expressions include: When the line radius for At that time, the line is approximately a straight line, and the tangent of the angle formed by the contact wire and the center line of the line is equal to the pull-out value. span between positioning points Interval ratio; When the line radius Not for At that time, the line is a curve, and the line radius is... With each forward stride, the angle difference generated by the track is: When the positioning point When it is inside the curve, in the formula Pick When the positioning point When it is outside the curve, in the formula Pick .

5. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 4, characterized in that, Obtaining the optimal distance between the first suspension cable and the corresponding positioning point includes: Based on prior engineering data, the maximum angle limit for the positioner in the overhead contact line was selected as [value missing]. and when the positioning point When the line is inside the curve, the minimum design radius is: ; Minimum design radius of the line Substituting the analytical expression and setting the maximum angle limit of the locator... Substituting into the torque balance formula, the maximum distance between the first hanger and the positioning point is obtained as follows: ; For the maximum limit of the spacing The optimal spacing value is obtained by rounding down.

6. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 5, characterized in that, Also includes: Based on prior engineering data, the maximum allowable spacing between suspension cables in a simple catenary suspension system is obtained. Determine whether the optimal spacing value exceeds the maximum allowable value. If not, no action is taken; if so, the corresponding optimal spacing value is adjusted.

7. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 4, characterized in that, The remaining hangers in the inner span region are arranged at equal intervals, including: Once the position of the first dropper is determined, the spacing between the remaining droppers in the span region is determined using the following formula: The remaining suspension strings in the inner span region are evenly spaced. Arrangement, The number of all hangers in the span region.

8. The method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 1, characterized in that, Elastic baseline curve and elastic gain analysis were performed on multiple sub-regions located at the center of the said intra-span region, including: Obtain the elastic curves corresponding to multiple sub-regions within the span at the center of the span region. The elastic curves include an elastic reference curve and an elastic gain, and the elastic gain is proportional to the distance between the suspension wires. When the number of all suspension strings in the span region is even, the span sub-region with the highest elasticity curve is selected as the maximum elastic span sub-region, and is denoted as the first sub-region. When the number of all suspension strings in the span region is odd, the two span sub-regions with the highest elasticity curves are selected as the maximum elastic span sub-regions, and are also referred to as the first sub-region.

9. A method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 7, characterized in that, The adjacent sub-regions within the first sub-region are designated as the second sub-region, and the suspension cables on the left and right sides of the second sub-region are moved outward by a preset distance, including: The preset distance is calculated using the following formula: For the preset distance, To maximize the elasticity between the suspension strings in a simple chain suspension, For a simple chain suspension, the elasticity at any position within the span region is considered. are positive integers and .

10. A method for non-uniform arrangement of simple chain suspension wires based on isoelastic space construction according to claim 1, characterized in that, Based on the optimal spacing value and the equal elastic space, the non-uniform arrangement of a simple chain suspension includes: Based on the optimal distance between the positioning point and the first dropper, the two first droppers are arranged; based on the arranged first droppers and the constructed equal elastic space, all droppers in the span region are arranged at equal intervals, and the droppers at the center of the span region are adjusted to make the elasticity of the corresponding mid-span region equal, thus completing the non-uniform arrangement of the simple chain droppers.

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