Guiding rope catenary curve solving method and system

Abstract

The invention discloses a guide rope catenary curve solving method and system, and relates to the technical field of guide rope construction, and the method comprises the steps: building a guide rope curve equation through a catenary model; determining independent parameters of a unique catenary curve according to the guide rope curvilinear equation; constructing a solution model of the independent parameters, and calculating the independent parameters by adopting a Newton iteration method; and solving the optimal guide rope catenary curve according to the calculated independent parameters. According to the method, a guide rope curvilinear equation is constructed through a catenary model, and independent parameter calculation is carried out by adopting a Newton iteration method; the optimal guide rope catenary curve is solved according to the independent parameters obtained through calculation, the result deviation and the calculation speed are comprehensively considered, the solving result of the guide rope catenary curve is closer to the actual situation, and the calculation accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of guide rope construction, and more particularly to a method and system for solving a guide rope catenary curve. Background Art

[0002] There are two analytical calculation methods for the guide rope suspension model, namely numerical algorithm and analytical algorithm. The numerical algorithm can comprehensively consider the elasticity, flexibility, uniform load or concentrated load distribution of the guide rope, and has high calculation accuracy, but the calculation speed of the numerical algorithm is slow and is not suitable for calculations in actual on-site construction. The analytical algorithm makes assumptions such as inelasticity and high flexibility for the guide rope, and the calculation results have a certain deviation from the actual situation, but the analytical algorithm has a fast calculation speed and is easy to implement in code. Generally speaking, the deviation of the model calculation results of the analytical algorithm for most actual situations is within an acceptable range.

[0003] Therefore, how to propose a method and system for solving the catenary curve of the guide rope, comprehensively consider the result deviation and calculation speed, make the solution result of the catenary curve of the guide rope closer to the actual situation, and improve the calculation accuracy is an urgent problem that technical personnel in this field need to solve. Summary of the invention

[0004] In view of this, the present invention provides a guide rope catenary curve solution method and system, which comprehensively considers the result deviation and calculation speed, makes the guide rope catenary curve solution result closer to the actual situation, and improves the calculation accuracy. In order to achieve the above purpose, the first aspect of the present invention provides a guide rope catenary curve solution method, comprising:

[0005] S1. Construct the guide rope curve equation through the catenary model;

[0006] S2. Determine the independent parameters of the unique catenary curve according to the guide rope curve equation;

[0007] S3, construct a solution model for independent parameters and use Newton iteration method to calculate independent parameters;

[0008] S4. Solve the optimal guide rope catenary curve based on the calculated independent parameters.

[0009] Optionally, the constraint conditions of the catenary model are: the guide rope is a flexible rope that cannot be stretched and can be bent arbitrarily, the guide rope is only subjected to tension, and the gravity load of the guide rope is evenly distributed along the rope.

[0010] Optionally, the guide rope curve equation is:

[0011] ;

[0012] Among them, the weight per unit length of the guide rope is , the height difference between any points A and B is , the horizontal distance, that is, the gear spacing is , the height difference angle is , the horizontal component of force on the guide rope is , the vertical component and tension at point A are and , the vertical load and tension at point B are and , the angles between the tension at points A and B and the horizontal direction are and , establish a coordinate system with A as the origin, right as the positive direction of the x-axis, and upward as the positive direction of the y-axis, and set a point on the guide rope in the file as P , point P is away from the line segment The vertical distance, that is, the sag is , the maximum sag of segment AB is The lowest point is .

[0013] Optionally, it also includes: calculating according to the guide rope curve equation Length of guide rope in time slot ; The length of the guide rope in the gear, the sag at a point P in the gear, the position and size of the maximum sag in the gear, the position and height of the lowest point in the gear, the tension and vertical component of the guide rope at the two hanging points, and the hanging angle of the guide rope at the two hanging points.

[0014] Optionally, based on the guide rope tension at the two hanging points:

[0015] ; The formula shows that in the guide rope curve equation, the difference in tension at both ends of the guide rope is only related to the specific gravity of the guide rope and the height difference between the two hanging points, and has nothing to do with the horizontal distance between the two hanging points.

[0016] Optionally, the independent parameters of the unique catenary curve include: , height difference and relative horizontal tension .

[0017] Optionally, the independent parameter solution model is constructed and the independent parameter calculation is performed using the Newton iteration method, including: obtaining the length of the guide rope in the gear, the sag or coordinates of a certain point in the gear, the maximum sag or the coordinates of the lowest point in the gear, and the tension and horizontal tension of the guide rope at the hanging point. The relationship model is used to find the roots using Newton's iteration method. Perform calculations.

[0018] Optionally, the parameters include maximum sag , lowest point height , tension at the hanging point or , the horizontal tension is obtained by using Newton's iteration method , according to the gear spacing , height difference and horizontal tension Determine the optimal guide rope catenary curve.

[0019] A second aspect of the present invention provides a system, which is used in the guide rope catenary curve solving method provided in the first aspect, comprising:

[0020] Guide rope curve equation construction module: used to construct the guide rope curve equation through the catenary model;

[0021] Parameter determination module: used to determine the independent parameters of the unique catenary curve according to the guide rope curve equation;

[0022] Parameter calculation module: used to build a solution model for independent parameters and use Newton iteration method to calculate independent parameters;

[0023] Solution module: used to solve the optimal guide rope catenary curve based on the calculated independent parameters.

[0024] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method and system for solving the catenary curve of a guide rope, which has the following beneficial effects:

[0025] The present invention proposes a method for solving a guide rope catenary curve, comprising: constructing a guide rope curve equation through a catenary model; determining independent parameters of a unique catenary curve according to the guide rope curve equation; constructing a solution model for independent parameters, and using Newton's iteration method to calculate independent parameters; solving the optimal guide rope catenary curve according to the calculated independent parameters. The present invention constructs a guide rope curve equation through a catenary model, and uses Newton's iteration method to calculate independent parameters; solving the optimal guide rope catenary curve according to the calculated independent parameters, comprehensively considering the result deviation and calculation speed, making the solution result of the guide rope catenary curve closer to the actual situation, and improving the accuracy of the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0027] Figure 1 A schematic flow chart of a method for solving a guide rope catenary curve provided by the present invention.

[0028] Figure 2 A schematic diagram of a guide rope catenary curve solution method provided by the present invention.

[0029] Figure 3 The present invention provides a relationship diagram between the maximum sag in the gear and the horizontal tension in the gear.

[0030] Figure 4 The present invention provides a relationship diagram between the lowest point height in the gear and the horizontal tension in the gear.

[0031] Figure 5 A diagram showing the relationship between the tension at the hanging point and the horizontal tension in the gear provided by the present invention.

[0032] Figure 6 The catenary curve shapes under different tension levels provided by the present invention. DETAILED DESCRIPTION

[0033] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0034] The embodiment of the present invention discloses a method for solving a guide rope catenary curve. Figure 1 As shown, including:

[0035] S1. Construct the guide rope curve equation through the catenary model;

[0036] S2. Determine the independent parameters of the unique catenary curve according to the guide rope curve equation;

[0037] S3, construct a solution model for independent parameters and use Newton iteration method to calculate independent parameters;

[0038] S4. Solve the optimal guide rope catenary curve based on the calculated independent parameters.

[0039] The constraint conditions of the catenary model are as follows: the guide rope is a flexible rope that cannot be stretched and can be bent arbitrarily, the guide rope is only subjected to tension, and the gravity load of the guide rope is evenly distributed along the rope.

[0040] In the construction of the guide rope for UAV deployment, the bending coefficient of the Dyneema rope used as the guide rope is very small, and the elastic coefficient (the ratio of unit force to unit deformation) is very large. It can be assumed that the guide rope is not subjected to bending force, but only to tension in the tensile direction, and the length of the guide rope is not extended due to the tension on the rope, so the analytical algorithm is applicable. Therefore, considering the deviation of the calculation results and the calculation speed, the analytical algorithm is used for analysis in the guide rope suspension model. At present, there are two main models for the suspension of the guide rope between two hanging points, namely the oblique parabola model and the catenary model. Both models assume that the guide rope is an inextensible and arbitrarily bendable flexible rope. The difference is that the oblique parabola model assumes that the gravity load of the guide rope is evenly distributed along the line between the two hanging points, while the catenary model assumes that the gravity load of the guide rope is evenly distributed along the rope. Both models can be used to calculate the guide rope suspension model. The catenary model is closer to the actual situation and the calculation results are more accurate, so the catenary model is used for calculation.

[0041] In a specific embodiment, Figure 2 As shown, the guide rope curve equation is:

[0042] ;

[0043] Among them, the weight per unit length of the guide rope is , the height difference between any points A and B is , the horizontal distance, that is, the gear spacing is , the height difference angle is , the horizontal component of force on the guide rope is , the vertical component and tension at point A are and , the vertical load and tension at point B are and , the angles between the tension at points A and B and the horizontal direction are and , establish a coordinate system with A as the origin, right as the positive direction of the x-axis, and upward as the positive direction of the y-axis, and set a point on the guide rope in the file as P , point P is away from the line segment The vertical distance, that is, the sag is , the maximum sag of segment AB is The lowest point is .

[0044] Also includes: Calculation based on the guide rope curve equation Length of guide rope in time slot ; The length of the guide rope in the gear, the sag at a point P in the gear, the position and size of the maximum sag in the gear, the position and height of the lowest point in the gear, the tension and vertical component of the guide rope at the two hanging points, and the hanging angle of the guide rope at the two hanging points.

[0045] In a specific implementation, the guide rope curve equation is used to calculate Length of guide rope in time slot ; The length of the guide rope in the gear, the sag at a point P in the gear, the position and size of the maximum sag in the gear, the position and height of the lowest point in the gear, the tension and vertical force of the guide rope at the two hanging points, and the sag angle of the guide rope at the two hanging points specifically include:

[0046] for Length of guide rope in time slot:

[0047] ;

[0048] The length of the guide rope in the file is:

[0049] ;

[0050] The sag at a point P in the profile is:

[0051] ;

[0052] Position and size of maximum sag within the file:

[0053] ;

[0054] ;

[0055] The position and height of the lowest point in the file:

[0056] ;

[0057] ;

[0058] ;

[0059] The guide rope tension and vertical force at the two hanging points are:

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] The hanging angles of the guide rope at the two hanging points are:

[0065] ;

[0066] ;

[0067] According to the guide rope tension at the two hanging points:

[0068] ; The formula shows that in the guide rope curve equation, the difference in tension at both ends of the guide rope is only related to the specific gravity of the guide rope and the height difference between the two hanging points, and has nothing to do with the horizontal distance between the two hanging points.

[0069] The independent parameters of the unique catenary curve include: , height difference and relative horizontal tension .

[0070] The independent parameter solution model is constructed and the independent parameter calculation is performed using the Newton iteration method, including: obtaining the length of the guide rope in the gear, the sag or coordinates of a certain point in the gear, the maximum sag or the coordinates of the lowest point in the gear, and the tension and horizontal tension of the guide rope at the hanging point. The relationship model is used to find the roots using Newton's iteration method. Perform calculations.

[0071] The parameters include maximum sag , lowest point height , tension at the hanging point or , the horizontal tension is obtained by using Newton's iteration method , according to the gear spacing , height difference and horizontal tension Determine the optimal guide rope catenary curve.

[0072] In a specific implementation, it can be known from the guide rope curve equation that in order to obtain a unique catenary curve, three independent parameters need to be obtained, namely, the pitch , height difference and relative horizontal tension Among them, the gear spacing , height difference and the weight per unit length of the guide rope These are easy-to-measure parameters and can be directly obtained in actual engineering design and construction. The measurement of the horizontal tension is difficult and not easy to obtain in actual engineering. Therefore, it is necessary to obtain the length of the guide rope in the gear, the sag or coordinates of a certain point in the gear, the maximum sag or the coordinates of the lowest point in the gear, the tension of the guide rope at the hanging point, etc., and establish these parameters and the horizontal tension The relationship between the horizontal tension and the horizontal tension is obtained by using Newton's iteration method. Perform calculations.

[0073] According to the above derivation, in order to calculate the horizontal tension , as long as you get ,θA 或 θ B Any one (or a group of) of the conditions will do.

[0074] To this end, we can substitute it into the corresponding formula above and use Newton's iteration method to solve the problem containing The transcendental equation of , and then determine the curve equation of the guide rope, and then Substitute into other formulas and calculate the values ​​of other parameters. When using Newton's iteration method to solve, the nonlinear equation is linearized. Specifically, for the nonlinear equation f(x) = 0, first expand f(x) into a Taylor series near a certain point x0, and take its linear part, that is, f(x) ≈ f(x0) + f'(x0)(x - x0). Then let f(x) = 0, and solve x1 = x0 - f(x0) / f'(x0). This process can be iterated continuously to obtain a more accurate solution. The iterative formula is: x(n+1) = x(n) - f(x(n)) / f'(x(n)), where n represents the number of iterations. ‌ ‌In actual engineering, for the proposed engineering problems, the commonly used Relationships include maximum sag , lowest point height , tension at the hanging point or wait.

[0075] In the embodiment, the following are given for a specific construction condition (spacing , height difference , guide rope specific gravity )Maximum sag , lowest point height , tension at the hanging point or With horizontal tension The relationship between the two. Based on this, the shape of the catenary is drawn. Figure 3-Figure 6 It can be seen that the horizontal tension The larger it is, the smaller the guide rope sag is, the more compact the shape is, and the more accurate the result is.

[0076] A system, using the above-mentioned guide rope catenary curve solving method, comprises:

[0077] The guide rope curve equation construction module uses the S1 method of constructing the guide rope curve equation through a known catenary model, and is used to construct the guide rope curve equation through a catenary model.

[0078] The parameter determination module uses the method of S2 for determining the independent parameters of the unique catenary curve according to the guide rope curve equation, and is used to determine the independent parameters of the unique catenary curve according to the guide rope curve equation.

[0079] The parameter calculation module uses S3's method of building an independent parameter solution model and adopting Newton's iteration method to calculate independent parameters.

[0080] The solution module uses the method of S4 for solving the optimal guide rope catenary curve according to the calculated independent parameters, and is used to solve the optimal guide rope catenary curve according to the calculated independent parameters.

[0081] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0082] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for solving a guide rope catenary curve, characterized in that: include: S1. Construct the guide rope curve equation through the known catenary model; S2. Determine the independent parameters of the unique catenary curve according to the guide rope curve equation; S3, construct a solution model for independent parameters and use Newton iteration method to calculate independent parameters; S4. Solve the optimal guide rope catenary curve based on the calculated independent parameters.

2. A method for solving a guide rope catenary curve according to claim 1, characterized in that: The constraint conditions of the catenary model are as follows: the guide rope is a flexible rope that cannot be stretched and can be bent arbitrarily, the guide rope is only subjected to tension, and the gravity load of the guide rope is evenly distributed along the rope.

3. A method for solving a guide rope catenary curve according to claim 1, characterized in that: The guide rope curve equation is: ； Among them, the weight per unit length of the guide rope is , the height difference between any points A and B is , the horizontal distance, that is, the gear spacing is , the height difference angle is , the horizontal component of force on the guide rope is , the vertical component and tension at point A are and , the vertical load and tension at point B are and , the angles between the tension at points A and B and the horizontal direction are and , establish a coordinate system with A as the origin, right as the positive direction of the x-axis, and upward as the positive direction of the y-axis, and set a point on the guide rope in the file as P , point P is away from the line segment The vertical distance, that is, the sag is , the maximum sag of segment AB is The lowest point is .

4. A method for solving a guide rope catenary curve according to claim 3, characterized in that: Also includes: Calculation based on the guide rope curve equation Length of guide rope in time slot ; The length of the guide rope in the gear, the sag at a point P in the gear, the position and size of the maximum sag in the gear, the position and height of the lowest point in the gear, the tension and vertical component of the guide rope at the two hanging points, and the hanging angle of the guide rope at the two hanging points.

5. A method for solving a guide rope catenary curve according to claim 4, characterized in that: According to the guide rope tension at the two hanging points: ; The formula shows that in the guide rope curve equation, the difference in tension at both ends of the guide rope is only related to the specific gravity of the guide rope and the height difference between the two hanging points, and has nothing to do with the horizontal distance between the two hanging points.

6. A method for solving a guide rope catenary curve according to claim 1, characterized in that: The independent parameters of the unique catenary curve include: span l, height difference h and relative horizontal tension H / w.

7. A method for solving a guide rope catenary curve according to claim 1, characterized in that: The independent parameter solution model is constructed, and the independent parameter calculation is performed by using the Newton iteration method which linearizes the nonlinear equation, including: obtaining the length of the guide rope in the gear, the sag or coordinates of a certain point in the gear, the maximum sag or the coordinates of the lowest point in the gear, and the tension and horizontal tension of the guide rope at the hanging point. The relationship model is used to find the roots using Newton's iteration method. Perform calculations.

8. A method for solving a guide rope catenary curve according to claim 7, characterized in that: The parameters include maximum sag , lowest point height , tension at the hanging point or , the horizontal tension is obtained by using Newton's iteration method , according to the gear spacing , height difference and horizontal tension Determine the optimal guide rope catenary curve.

9. A system, characterized in that: A method for solving the catenary curve of a guide rope applied to any one of claims 1-8.

10. The system according to claim 9, characterized in that include: Guide rope curve equation construction module: used to construct the guide rope curve equation through the catenary model; Parameter determination module: used to determine the independent parameters of the unique catenary curve according to the guide rope curve equation; Parameter calculation module: used to build a solution model for independent parameters and use Newton iteration method to calculate independent parameters; Solution module: used to solve the optimal guide rope catenary curve based on the calculated independent parameters.

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