A method for correcting the cross section of the reflecting surface of a radio telescope with a large cable-net support system

Abstract

The present invention relates to the field of radio telescope structural analysis and discloses a method for correcting the cross-section of a radio telescope reflector with a large cable-net support system. The method comprises: establishing an initial calculation model of the telescope cable-net reflector; calculating the internal and external forces of particles; performing nonlinear static calculations to obtain an equilibrium model; calculating the spatial coordinate deviation of the main cable nodes between the equilibrium model and the initial calculation model; applying the obtained coordinate deviation inversely to the initial calculation model to update the equilibrium model; repeating steps 3 to 5 to obtain model information under a reference state; calculating the ideal cross-sectional dimensions of each cable element; matching the cable element with the optimal ideal cross-sectional dimensions in a cable element cross-sectional library; and updating the initial calculation model to complete the cable-net cross-sectional correction. This solution utilizes the finite mass method to perform initial morphological analysis of the cable-net reflector, achieving a more uniform cable force distribution by selecting the appropriate cable-net cross-sectional dimensions from a given cross-sectional library.

Description

Technical Field

[0001] The present invention relates to the field of radio telescope structure analysis, and in particular to a method for correcting the cross section of a reflecting surface of a radio telescope with a large cable net support system. Background Art

[0002] Large-scale cable-net support systems for radio telescopes, crucial facilities for modern astronomical observation, feature innovative structural designs that transcend the engineering limitations of traditional rigid supports, achieving high-precision deformation adjustment of the reflector surface through flexible cable nets. Most radio telescopes employing cable-net support technology utilize a triangular main cable net structure. The FAST radio telescope, in particular, innovatively proposes an active displacement strategy for celestial object source search, demonstrating the potential for cable-net systems in large-scale structures and providing an important engineering reference for flexible cable-net support technology for telescopes.

[0003] In engineering practice, cable-net support systems face two key technical challenges: First, precise control of the reference state morphology—that is, precisely positioning thousands of cable-net nodes on the target sphere through pretension and deadweight balance. This type of problem requires the construction of a large-scale nonlinear system of equations for iterative solution, whose computational efficiency and convergence directly impact the feasibility of the design. Second, uniform stress control of the cable-net reflective surface structure. In the reference state system analysis, all main cables and lower-stay cables use the same cross-section, resulting in uneven stress in the cable net. Some cable segments exhibit high stress, exceeding the design strength, while others exhibit low stress, failing to meet the requirements for active displacement. Therefore, an effective cross-section correction method is needed to avoid stress unevenness and improve the overall performance of the structure. Summary of the Invention

[0004] The present invention aims to provide a method for correcting the cross-section of a radio telescope reflector with a large cable net support system, so as to solve the problem of uneven stress in the current reference state cable net reflector structure.

[0005] To achieve the above-mentioned object, the present invention adopts the following technical solution: a method for correcting the cross-section of a reflecting surface of a radio telescope with a large cable net support system, comprising:

[0006] Step 1: Establish the initial calculation model of the telescope cable net reflector surface and discretize the cable net structure into mass points and cable units;

[0007] Step 2: Calculate the internal and external forces of the mass point;

[0008] Step 3: Perform nonlinear static calculations on the cable net structure to obtain an equilibrium model that meets the preset equilibrium conditions;

[0009] Step 4: Calculate the spatial coordinate deviation of the main cable node between the equilibrium model and the initial calculation model;

[0010] Step 5: Apply the obtained coordinate deviation in reverse to the main cable nodes in the initial calculation model to obtain a new initial model, re-perform the overall static calculation, and obtain an updated equilibrium model;

[0011] Step 6: Repeat steps 3 to 5 until the coordinate deviations of all main cable points in the latest equilibrium model compared to the initial calculation model are less than the set threshold. At this point, the model information under the reference state is obtained, which includes the coordinates of the mass points and the stress distribution of the cable elements.

[0012] Step 7: Set the target stress value of the cable net and calculate the ideal cross-sectional dimensions of each cable element based on the reference state cable element stress;

[0013] Step 8: Set the cable unit cross-section library and match the best ideal cross-section size for the cable unit in the cable unit cross-section library;

[0014] Step 9: Substitute the optimized cable unit cross-sectional dimensions into the initial calculation model and repeat steps 3 to 5 once to complete the cable net cross-sectional correction.

[0015] This scheme discretizes the cable net structure into mass points and cable units, and then uses the finite mass method to perform the initial morphological analysis of the cable net reflection surface. By gradually inversely iterating and calculating the model information under the reference state, the prestress distribution of the cable units that meets the reference surface shape is obtained. The ideal cross-sectional dimensions of each cable unit, namely the ideal cross-sectional diameter and ideal cross-sectional area, are calculated based on the cable net target stress and the reference state cable unit stress. The cable unit cross-sectional library is then used to match the cable unit with the optimal ideal cross-sectional dimensions to complete the cable net cross-sectional optimization.

[0016] Preferably, the step 3 specifically includes:

[0017] Step 31: Iteratively calculate the coordinates of the unconstrained mass point

[0018]

[0019] Where, is the coordinate of the unconstrained mass point i at the n+1th step, c is the damping factor required for structural equilibrium, h is the time step, 、 They represent the coordinates and velocity of the unconstrained particle i at the nth and step, respectively. is the coordinate of the unconstrained particle at step n-1, is the mass assigned to particle i, is the internal force of particle i at step n, is the external force on particle i at step n;

[0020] Step 32: Apply three-dimensional displacement constraints to the constrained mass

[0021]

[0022] Where, 、 They represent the coordinates of the constrained particle j at step n+1 and step 0 (initial step) respectively;

[0023] Step 33: Iterate step by step until the coordinates of the unconstrained particle in two adjacent time steps meet the preset relative error norm requirement, and obtain the equilibrium state model.

[0024] Preferably, the step 1 specifically includes: discretizing the structure into mass points and cable units, and allocating the entire mass of the structure to the mass points, where the mass of the mass points is:

[0025]

[0026] Where, is the mass assigned to mass point i, num is the total number of cable elements connected to mass point i, m is the number of cable elements connected to mass point i, 、 、 represent the initial length, cross-sectional area and density of cable unit m respectively.

[0027] Preferably, the step 2 specifically includes:

[0028] Step 21: Calculate the internal force of the particle. The specific formula is:

[0029]

[0030] Where, is the internal force of particle i at step n, , denote the length and length increment of cable element m in the nth step, is the elastic modulus of cable element m, is the prestress of cable element m, is the direction vector of cable element m, is the cross-sectional area of ​​cable unit m; if , represents the relaxation of cable unit m. Since cable unit cannot bear compressive stress, it is necessary to set ;

[0031] Step 22: Calculate the internal force of the particle. The specific formula is:

[0032]

[0033] Where, is the external force on particle i at step n, and g is the acceleration due to gravity.

[0034] Preferably, the equilibrium condition of the equilibrium state model in step 33 is that the coordinates of all unconstrained particles in two adjacent time steps meet the relative error requirement, that is:

[0035]

[0036] Where, is the preset tolerance.

[0037] Preferably, the main cable node spatial coordinate deviation between the equilibrium state model and the initial calculation model in step 4 is:

[0038]

[0039] Where k is the main cable node number, is the coordinate deviation of the main cable node k, , The coordinates of the main cable node k in the equilibrium step and the initial step.

[0040] Preferably, in step 5

[0041] In the formula is the coordinate of the unconstrained mass point i corresponding to the main cable node k in the new initial model at step 0, is the coordinate of the unconstrained mass point i corresponding to the main cable node k in the original initial model at step 0.

[0042] Preferably, the calculation formula for the ideal cross-sectional size in step 7 is:

[0043]

[0044]

[0045] Where, is the ideal cross-sectional area of ​​cable element m, is the tension of cable m unit in the reference state model (the product of cable unit stress and cross-sectional area), is the target stress of cable element m, is the ideal cross-sectional diameter of cable element m.

[0046] Preferably, in step 8, the cable element is matched with an ideal cross-sectional size closest to the ideal cross-sectional size obtained in step 8 in the cable element cross-sectional library.

[0047] Advantages of this solution:

[0048] 1. This invention analyzes the initial morphology of the telescope's reflective surface in a large cable-net support system by using the spatial coordinate deviation of the main cable nodes between the equilibrium model and the initial calculation model. The offset distance is then reversely applied to the main cable nodes. By repeatedly applying forced displacement and performing static equilibrium calculations, the main cable nodes are continuously brought closer to the spherical position, ultimately meeting the accuracy requirements.

[0049] 2. The present invention adopts the finite particle method to perform the initial morphological analysis of the reflecting surface, avoiding the problems of singular stiffness matrix and non-convergence of iteration in traditional finite element method when performing complex structure analysis;

[0050] 3. By analyzing the initial morphology of the reflective surface, a baseline equilibrium model is derived. The cross-section of the cable net reflective surface is modified based on the baseline prestress in the model information to avoid stress unevenness and improve the overall performance of the structure. The initial morphology of the cable net reflective surface is analyzed using the finite mass method, and a more uniform cable force distribution is achieved by selecting the appropriate cable net cross-section size from a given cross-section library.

[0051] 4. The present invention proposes for the first time a cross-section correction method for the reflective surface of a cable net, ensuring that the tension of each cable segment remains unchanged and achieving uniform stress distribution by adjusting the cross-sectional area of ​​the cable segment. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of a flow chart of an embodiment of the present invention.

[0053] Figure 2 Schematic diagram of a numerical model of an embodiment of the present invention.

[0054] Figure 3 For the embodiment of the present invention Figure 2 A partial enlarged view of point A in the middle.

[0055] Figure 4 2 is a comparison diagram of the cable net before and after deformation according to an embodiment of the present invention.

[0056] Figure 5 This is a displacement cloud diagram of the main cable node according to an embodiment of the present invention.

[0057] Figure 6 Statistical comparison diagram of the main cable net stress before and after correction according to an embodiment of the present invention.

[0058] Figure 7 This is a stress cloud diagram of the main cable net before correction according to an embodiment of the present invention.

[0059] Figure 8 This is a modified main cable net stress cloud diagram according to an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The following is further described in detail through specific implementation methods:

[0061] Example:

[0062] A method for correcting the cross section of the reflecting surface of a large cable-net-supported radio telescope. Figure 1 Shown, including:

[0063] Step 1: Establish the initial calculation model of the telescope cable net reflector

[0064] In this proposal, the initial computational model is established using the design sphere as a benchmark. The computational model in this proposal refers to the corresponding numerical model. Based on the actual structural topology of the cable net structure, this proposal discretizes the triangular cable net structure into a series of mass points and cable units. The cable net connecting adjacent nodes is discretized into cable units, and the nodes are discretized into corresponding mass points. Boundary constraints are set based on the actual structural layout. Specifically, fixed support constraints are set at the lower ends of the lower cables and at the mass points around the main cable net. The equivalent mass of the main cable net, back frame, and reflective panels is concentrated at the mass points.

[0065] In this scheme, masses include constrained and unconstrained masses. Constrained masses are masses whose translational degrees of freedom in the X / Y / Z directions are completely restricted in the numerical model, preventing free movement. Unconstrained masses are masses that are not geometrically constrained in the numerical model and are allowed to move freely based on the forces acting on them. Main cable net nodes are key geometric points where two or more main cables intersect in a real physical cable net model. The masses in the numerical model correspond one-to-one with the nodes in the physical model.

[0066] In this step, the structure is discretized into mass points and cable elements, and the mass of the structure is all allocated to the mass points. for:

[0067] (1)

[0068] Where, is the mass assigned to mass point i, num is the total number of cable elements connected to mass point i, m is the number of cable elements connected to mass point i, 、 、 represent the initial length, cross-sectional area and density of cable unit m respectively.

[0069] In this scheme, the cable element in the model adopts a linear elastic constitutive relation, and the input parameters include material elastic modulus, density, cross-sectional specifications, and cable net prestress.

[0070] Step 21: Calculate the internal force of the particle, specifically:

[0071] (2)

[0072] Where, is the internal force of particle i at step n, , denote the length and length increment of cable element m in the nth step, is the elastic modulus of cable element m, is the prestress of cable element m, is the direction vector of cable element m. , represents the relaxation of cable unit m. Since cable unit cannot bear compressive stress, it is necessary to set .

[0073] The internal force of the particle is expressed as the superposition of the internal force generated by the unit length increment and the internal force generated by the prestress.

[0074] Step 22: Calculate the external force on the particle, specifically:

[0075] (3)

[0076] Where, is the external force on particle i at step n, and g is the acceleration due to gravity.

[0077] The external force of the particle is represented by the deadweight of the structure. The cable net structure produces displacement deformation under the combined action of internal and external forces.

[0078] Step 31: Calculate the coordinates of the unconstrained mass point by iteratively calculating the displayed time step, specifically:

[0079] (4)

[0080] Where, is the coordinate of the unconstrained mass point i at the n+1th step, c is the damping factor required for structural equilibrium, h is the time step, 、 They represent the coordinates and velocity of the unconstrained particle i at the nth and step, respectively. are the coordinates of the unconstrained particle at step n-1.

[0081] Step 32: Apply three-dimensional displacement constraints to the constrained mass:

[0082] (5)

[0083] Where, 、 They represent the coordinates of the constrained particle j at step n+1 and step 0 (initial step) respectively.

[0084] Step 33: Iterate step by step until the equilibrium condition is met (the coordinates of all unconstrained particles in two adjacent time steps meet the relative error norm requirement) to obtain the equilibrium state model.

[0085] The specific equilibrium conditions are:

[0086] (6)

[0087] Where, It is the preset tolerance, usually set to 10 -4 ~10 -6 within the range.

[0088] In this step, nonlinear static calculation is performed on the cable net structure to obtain an equilibrium model that meets the force balance conditions.

[0089] Step 4: Calculate the spatial coordinate deviation of the main cable node between the equilibrium model and the initial calculation model;

[0090] (7)

[0091] Where k is the main cable node number, is the coordinate deviation of the main cable node k, , The coordinates of the main cable node k in the equilibrium step and the initial step.

[0092] Step 5: Apply the coordinate deviation obtained in step 3 in reverse to the main cable nodes in the initial model to obtain a new initial model, re-perform the overall static calculation, and obtain an updated equilibrium model;

[0093] (8)

[0094] In the formula is the coordinate of the unconstrained mass point i corresponding to the main cable node k in the new initial model at step 0, is the coordinate of the unconstrained mass point i corresponding to the main cable node k in the original initial model at step 0.

[0095] Step 6: Repeat steps 3 to 5 until the coordinate deviations of all main cable nodes in the latest equilibrium model compared to the initial calculation model are less than the set threshold. At this point, the model information under the reference state is obtained. The reference state is the equilibrium state of the reflective surface structure under the action of its own weight that satisfies the coordinate deviation. The model information includes the coordinates of the particle points and the stress distribution of the cable unit.

[0096] This application uses the finite particle method of steps 2 to 6 to perform an initial morphological analysis of the cable net reflection surface to solve the stress distribution of the cable unit that meets the reference surface shape, and then solves the ideal cross-sectional size of the cable unit based on the stress distribution of the cable unit, and achieves uniform stress distribution by adjusting the cross-sectional area.

[0097] Step 7: Given the target stress level of the cable net, calculate the ideal cross-sectional dimensions of each cable element;

[0098] (9)

[0099] (10)

[0100] Where, is the ideal cross-sectional area of ​​cable element m, is the tension of cable m unit in the reference state model (the product of cable unit stress and cross-sectional area), is the target stress of cable element m, is the ideal cross-sectional diameter of cable element m.

[0101] Step 8: Given a cable element cross-section library, replace each cable element in the cross-section library with a specification closest to the ideal area;

[0102] The cable element cross-sectional library contains commercially available cross-sectional diameters of 20mm, 24mm, 28mm, and 32mm. Based on the calculation results in Step 7, the relevant cross-sectional specifications are matched in the cross-sectional library. For example, if the ideal cross-sectional diameter of a cable element is 22.5mm, the diameter with the smallest absolute difference from 22.5mm is matched, which is 24mm. If the ideal cross-sectional diameter of a cable element is 21.5mm, the diameter with the smallest absolute difference from 21.5mm is matched, which is 20mm.

[0103] Step 9: Substitute the optimized cross-sectional specifications into the initial calculation model and repeat steps 3 to 5 once.

[0104] Taking the FAST radio telescope as an example, a FAST finite particle numerical model is established, such as Figure 2 As shown; Figure 3 for Figure 2 A partial enlarged view of point A in the middle. There are 6980 main cables, 2275 lower cables, and 2590 main cable nodes in the FAST finite mass numerical model. The main cable diameter is 25mm, the lower cable diameter is 10mm, and the elastic modulus is 205GPa. A prestress of 300MPa is applied to the main cable segment, and the main cable node coordinate deviation threshold is set to 5mm. The initial morphological analysis is performed according to steps 2 to 6 to obtain the benchmark state model. The cable net deformation and main cable node displacement are shown in Figure 2. Figure 4 、 Figure 5 As shown, Figure 4 This is a comparison diagram of the cable net before and after deformation. Figure 5 is the displacement cloud diagram of the main cable node, Figure 4 The vertical coordinate unit m represents the displacement value.

[0105] Set the target stress level of the main cable to 350MPa, the cross-section library specifications of the main cable segment are 20mm, 24mm, 28mm, and 32mm, and the cross-section library specifications of the lower cable segment are 8mm, 12mm, 16mm, and 20mm. Follow steps 7 to 9 to perform cross-section correction and morphological analysis to obtain the corrected baseline model. The main cable network stress comparison before and after cross-section correction is as follows: Figure 6 、 Figure 7 、 Figure 8 As shown, Figure 6 The statistical comparison chart before and after the main cable net stress correction is shown. Figure 7 To correct the stress cloud diagram of the main cable net, Figure 8 This is the stress contour of the main cable net after correction. The main cable stress before correction was 79.49~609.50MPa, and after correction it was 305.25~416.73MPa.

[0106] The present invention provides a detailed introduction to the initial morphological analysis process of the reflecting surface of a telescope with a large cable-net support system. The offset distance is reversely applied to the main cable nodes. By repeatedly applying forced displacement and static equilibrium calculations, the main cable nodes are continuously approached to the spherical position and ultimately meet the accuracy requirements. The present invention innovatively uses the finite particle method to perform the initial morphological analysis of the reflecting surface, avoiding the problems of singular stiffness matrix and non-convergence of iterations in traditional finite element methods when performing complex structural analysis. This scheme achieves uniform stress distribution by gradually adjusting the cross-sectional area of ​​the cable segments without changing the tension of each cable segment.

[0107] The above is only an embodiment of the present invention, and the common knowledge such as the specific technical solutions and / or characteristics in the solution are not described in detail here. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the technical solution of the present invention. In the present invention, unless otherwise clearly specified and limited, the terms "install", "connect", "connect", "fix" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected, or indirectly connected through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. The scope of protection claimed by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for correcting the cross section of a reflecting surface of a radio telescope with a large cable net support system, characterized in that: include: Step 1: Establish the initial calculation model of the telescope cable net reflector surface and discretize the cable net structure into mass points and cable units; Step 2: Calculate the internal and external forces of the mass point; Step 3: Perform nonlinear static calculations on the cable net structure to obtain an equilibrium model that meets the preset equilibrium conditions; Step 4: Calculate the spatial coordinate deviation of the main cable node between the equilibrium model and the initial calculation model; Step 5: Apply the obtained coordinate deviation in reverse to the main cable nodes in the initial calculation model to obtain a new initial model, re-perform the overall static calculation, and obtain an updated equilibrium model; Step 6: Repeat steps 3 to 5 until the coordinate deviations of all main cable points in the latest equilibrium model compared to the initial calculation model are less than the set threshold. At this point, the model information under the reference state is obtained, which includes the coordinates of the mass points and the stress distribution of the cable elements. Step 7: Set the target stress value of the cable net and calculate the ideal cross-sectional dimensions of each cable element based on the reference state cable element stress; Step 8: Set the cable unit cross-section library and match the best ideal cross-section size for the cable unit in the cable unit cross-section library; Step 9: Substitute the optimized cable unit cross-sectional dimensions into the initial calculation model and repeat steps 3 to 5 once to complete the cable net cross-sectional modification. The step 3 specifically includes: Step 31: Iteratively calculate the coordinates of the unconstrained mass point Where, is the coordinate of the unconstrained mass point i at the n+1th step, c is the damping factor required for structural equilibrium, h is the time step, 、 They represent the coordinates and velocity of the unconstrained particle i at the nth and step, respectively. is the coordinate of the unconstrained particle at step n-1, is the mass assigned to particle i, is the internal force of particle i at step n, is the external force on particle i at step n; Step 32: Apply three-dimensional displacement constraints to the constrained mass Where, 、 Represent the coordinates of the constrained particle j at step n+1 and step 0 respectively; Step 33: Iterate step by step until the coordinates of the unconstrained particle in two adjacent time steps meet the preset relative error norm requirement, and obtain the equilibrium state model.

2. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 1, characterized in that: The step 1 specifically includes: discretizing the structure into mass points and cable elements, and allocating the entire mass of the structure to the mass points. The mass of the mass points is: Where, is the mass assigned to mass point i, num is the total number of cable elements connected to mass point i, m is the number of cable elements connected to mass point i, 、 、 represent the initial length, cross-sectional area and density of cable unit m respectively.

3. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 1, characterized in that: The step 2 specifically includes: Step 21: Calculate the internal force of the particle. The specific formula is: Where, is the internal force of particle i at step n, , They represent the length increment and length of cable element m in the nth step, is the elastic modulus of cable element m, is the prestress of cable element m, is the direction vector of cable element m, is the cross-sectional area of ​​cable unit m; if , represents the relaxation of cable unit m. Since cable unit cannot bear compressive stress, it is necessary to set ; Step 22: Calculate the external force of the particle. The specific formula is: Where, is the external force on particle i at step n, and g is the acceleration due to gravity.

4. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 1, characterized in that: The equilibrium condition of the equilibrium state model in step 33 is that the coordinates of all unconstrained particles in two adjacent time steps meet the relative error requirement, that is: Where, is the preset tolerance.

5. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 1, characterized in that: The main cable node spatial coordinate deviation between the equilibrium model and the initial calculation model in step 4 is: Where k is the main cable node number, is the coordinate deviation of the main cable node k, , The coordinates of the main cable node k in the equilibrium step and the initial step.

6. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 5, characterized in that: In step 5 In the formula is the coordinate of the unconstrained mass point i corresponding to the main cable node k in the new initial model at step 0, is the coordinate of the unconstrained mass point i corresponding to the main cable node k in the original initial model at step 0.

7. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 1, characterized in that: The calculation formula for the ideal cross-sectional size in step 7 is: Where, is the ideal cross-sectional area of ​​cable element m, is the tension of cable m unit in the reference state model, is the target stress of cable element m, is the ideal cross-sectional diameter of cable element m.

8. The method for correcting the cross-section of a reflecting surface of a large-scale cable-net support system radio telescope according to claim 1, characterized in that: In step 8, the cable element is matched with an ideal cross-sectional size closest to the ideal cross-sectional size obtained in step 8 in the cable element cross-sectional library.

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