A novel FAST feed cabin mechanism structural parameter optimization method

Abstract

This invention discloses a method for optimizing the structural parameters of a novel FAST feed cabin mechanism, comprising: Step 1, establishing a global coordinate system and two local coordinate systems corresponding to the novel feed cabin mechanism, and representing the rotation matrix using quaternions; Step 2, performing static modeling of the novel feed cabin mechanism; Step 3, setting a cable force optimization function; Step 4, setting anti-collision constraints; Step 5, setting the objective function and constraint conditions for optimizing the structural parameters of the novel feed cabin mechanism and solving them. By optimizing the structural parameters of the novel FAST feed cabin mechanism, this invention can increase the observation angle of the feed cabin mechanism to a zenith angle of 50° within the cable force range, thereby enabling FAST to observe the center of the Milky Way.

Description

Technical Field

[0001] This invention relates to the field of astronomical equipment, and in particular to a method for optimizing the structural parameters of a novel feed cabin mechanism for FAST. Background Technology

[0002] The Five-hundred-meter Aperture Spherical radio Telescope (FAST) is currently the world's largest and most sensitive single-aperture radio telescope. FAST mainly consists of an active reflector, a six-cable drive mechanism, and a feed cabin. Although FAST is currently operating normally, its maximum observation angle is limited to 40° due to the weight limitation of its feed cabin, preventing it from observing the center of the Milky Way. To observe the galactic center, the weight of FAST's feed cabin needs to be reduced to increase the maximum observation angle to 50°.

[0003] Chinese patent application CN202022993173.1 discloses a novel FAST feed cabin mechanism, which uses a flexible cable drive to reduce the weight of the feed cabin. While this is a novel feed cabin mechanism, it fails to provide precise structural parameters or optimization methods. Due to the unique operating mode and flexible cable drive characteristics of the novel feed cabin mechanism, structural parameter optimization methods suitable for other types of mechanisms are not applicable to the novel feed cabin mechanism.

[0004] Therefore, optimizing the structural parameters of the new cable-driven feed cabin mechanism based on performance is a problem that urgently needs to be solved.

[0005] In view of this, the present invention is hereby proposed. Summary of the Invention

[0006] Based on the problems existing in the prior art, the purpose of this invention is to provide a method for optimizing the structural parameters of a novel feed cabin mechanism for FAST, which can increase the observation angle of the novel feed cabin mechanism to 50° zenith angle within the cable force range, thus meeting the requirement of FAST to observe the center of the Milky Way.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] This invention provides a method for optimizing the structural parameters of a novel FAST feed cabin mechanism, comprising:

[0009] Step 1: Establish a global coordinate system and two local coordinate systems on the novel feed cabin mechanism whose structural parameters are to be optimized. Among them, the global coordinate system G is established at the center of the bottom surface of the active reflector of FAST.

[0010] The origin is taken as the center point of the external anchoring point plane of FAST's star-shaped frame. Establish the first local coordinate system Tie;

[0011] The origin is taken as the center point of the upper surface of the lower platform of the new feed cabin mechanism. Establish a second local coordinate system Tie;

[0012] Based on the established global coordinate system G and the first local coordinate system System and second local coordinates Determine the rotation matrix of the C system where the star-shaped frame is located relative to the G system and the rotation matrix of the P system where the lower platform is located relative to the C system where the star-shaped frame is located.

[0013] Step 2, establish the static equations of the new feed cabin mechanism:

[0014] Based on the global coordinate system G and the first local coordinate system established in step 1 System, Second Local Coordinates The static equations of the novel feed cabin mechanism are established by taking the rotation matrices of the C system (where the star-shaped frame is located) relative to the G system and the rotation matrices of the P system (where the lower platform is located) relative to the C system (where the star-shaped frame is located).

[0015] Step 3, set the cable force optimization function:

[0016] The cable force optimization function is set to ensure that the cable forces of the nine flexible cables driving the novel feed cabin mechanism are continuously varied, without sharp points, and far from the upper and lower limits of the cable forces:

[0017] (20)

[0018] In the above formula (20), T Smax T Umax These are the upper limits of the cable tension for pulling up and down the three flexible cables, T. Smin T Umin These are the lower limits of the cable force for pulling up and down the three flexible cables, respectively. , These are the average tension values ​​of the upward and downward pulling cables, respectively. , The normalization term is lg(), which is the logarithmic barrier function; k1 and k2 are used to adjust the variance weights. and As weight;

[0019] Step 4, set anti-collision constraints:

[0020] Based on the anti-collision requirements between the components of the new feed cabin mechanism, the anti-collision constraint is set as Distance. ;

[0021] Where Distance=GJK(a,b) means that the pull-down and pull-up cables are modeled as straight lines, the two feed receivers and the lower platform are modeled as cylinders, and the connecting ring is modeled as a cylinder with a height of 1cm. All objects are convex hulls. The GJK algorithm is used to perform collision detection in all directions at a 50° zenith angle. a and b represent two objects being detected. The collision detection includes: collision detection between the pull-down cable and the two feed receivers, collision detection between the pull-down cable and the lower platform, collision detection between the pull-up cable and the connecting ring, collision detection between the pull-up cable and the two feed receivers, and collision detection between the connecting ring and the inner wall of the star-shaped frame.

[0022] Step 5: Set the objective function and constraints for optimizing the structural parameters of the new feed cabin mechanism and solve them:

[0023] The original point of the lower platform Distance from the origin of the C system Distance z in the z direction p Six pull cables are anchored at the second anchor point of the slide rail. Height H in the C series B Six pull cables are anchored at the first anchor point of the slide rail. Distribution radius r B The distribution radius r of the six upper tension cables at the second anchoring point P[i] on the lower platform P The three pull-down cables are anchored at the third anchor point of the star-shaped frame. Distribution radius r E The three pull-down cables are anchored at the third anchor point of the star-shaped frame. Height H in the C series E The fourth anchor point of the three pull-down flexible cables on the connecting ring. Distribution radius r W The fourth anchor point of the three pull-down flexible cables on the connecting ring. High H in the P-series W These variables serve as structural parameters to be optimized, and the optimization aims to make the azimuth angle... The zenith angle is If the squared difference between the maximum and minimum cable forces of each flexible cable is minimized, then the objective function for setting the constraints is:

[0024] (twenty one)

[0025] st Distance ,

[0026] T s [i]∈[T smin , T smax ], T U[i]∈[T Umin , T Umax ],

[0027] z p ∈[z pmin z pmax ], H B ∈[H Bmin H Bmax ],

[0028] r B ∈[r Bmin r Bmax ], r P ∈[r Pmin r Pmax ],

[0029] r E ∈[r Emin r Emax ], H E ∈[H Emin H Emax ],

[0030] r W ∈[r Wmin r Wmax ] , H W ∈[H Wmin H Wmax ],

[0031] Among them, Soli He Suoli Obtained through the above equation (20), The azimuth angle is Zenith angle is The minimum force of the nine flexible ropes at that time; The azimuth angle is Zenith angle is The maximum force of the nine flexible ropes at that time;

[0032] Solving the above objective function yields the structural parameters that minimize the squared difference between the maximum and minimum cable forces of each flexible cable, which are the optimized structural parameters of the FAST novel feed cabin mechanism.

[0033] Compared with existing technologies, the FAST novel feed cabin mechanism structural parameter optimization method provided by this invention has the following beneficial effects:

[0034] To minimize the range of cable force variation, a function with minimum variance is added to the cable force distribution function. Simultaneously, to keep the cable force away from the boundary, a logarithmic barrier function is added to the cable force distribution function, ensuring continuous cable force variation without cusps and far from the cable force boundary. In structural parameter optimization, the objective function is set to minimize the square of the difference between the maximum and minimum cable forces of the nine flexible cables at a specific location with a 50° zenith angle and an azimuth angle of 0°, rather than the square of the difference between the maximum and minimum cable forces across the entire working space from 0 to 360°. This not only minimizes the cable force variation across the entire working space but also significantly reduces solution time, effectively solving the problem of long solution times due to the nonlinear optimization process of the cable force distribution function. By optimizing the structural parameters of the FAST novel feed cabin mechanism, the observation angle of the feed cabin mechanism can be increased to 50° zenith angle within the cable force range, thus enabling observation of the center of the Milky Way. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 A flowchart illustrating the method for optimizing the structural parameters of the novel FAST feed cabin mechanism provided in this embodiment of the invention.

[0037] Figure 2 This is a schematic diagram of the novel FAST feed cabin mechanism and coordinates provided in an embodiment of the present invention.

[0038] Figure 3 A schematic diagram of the composition of the novel FAST feed cabin mechanism provided in an embodiment of the present invention.

[0039] Figure 4 This invention provides a top view of the novel FAST feed cabin mechanism and a representation of the structural parameters to be optimized for embodiments of the invention.

[0040] Figure 5 This invention provides a side view of the novel FAST feed cabin mechanism and a representation of the structural parameters to be optimized for embodiments of the present invention.

[0041] The component names corresponding to each mark in the diagram are: 1-lower platform; 2-PAF beam receiver; 3-19 beam receiver; 4-connecting ring; 5-upper pull-up cable; 6-lower pull-down cable. Detailed Implementation

[0042] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the specific content of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention. Contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0043] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the specific content of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments, which do not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0044] First, the following explanations are provided for the terms that may be used in this article:

[0045] The term "and / or" means that either or both can be achieved simultaneously. For example, X and / or Y means that it includes both "X" or "Y" as well as the three cases of "X and Y".

[0046] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0047] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0048] Unless otherwise explicitly specified or limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this document according to the specific circumstances.

[0049] The terms “center,” “longitudinal,” “lateral,” “length,” “width,” “thickness,” “upper,” “lower,” “front,” “back,” “left,” “right,” “vertical,” “horizontal,” “top,” “bottom,” “inner,” “outer,” “clockwise,” and “counterclockwise” indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience and simplification of description and do not imply that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this document.

[0050] The following is a detailed description of the method for optimizing the structural parameters of the novel FAST feed cabin mechanism provided by this invention. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Where specific conditions are not specified in the embodiments of this invention, they are performed according to conventional conditions in the art or conditions recommended by the manufacturer. Reagents or instruments used in the embodiments of this invention, unless otherwise specified by the manufacturer, are all commercially available conventional products.

[0051] like Figure 1 As shown, this embodiment of the invention provides a method for optimizing the structural parameters of a novel FAST feed cabin mechanism, including:

[0052] Step 1: Establish a global coordinate system and two local coordinate systems on the novel feed cabin mechanism whose structural parameters are to be optimized. Among them, the global coordinate system G is established at the center of the bottom surface of the active reflector of FAST.

[0053] The origin is taken as the center point of the external anchoring point plane of FAST's star-shaped frame. Establish the first local coordinate system Tie;

[0054] The origin is taken as the center point of the upper surface of the lower platform of the new feed cabin mechanism. Establish a second local coordinate system Tie;

[0055] Based on the established global coordinate system G and the first local coordinate system System and second local coordinates Determine the rotation matrix of the C system where the star-shaped frame is located relative to the G system and the rotation matrix of the P system where the lower platform is located relative to the C system where the star-shaped frame is located.

[0056] Step 2, establish the static equations of the new feed cabin mechanism:

[0057] Based on the global coordinate system G and the first local coordinate system established in step 1 System, Second Local Coordinates The static equations of the novel feed cabin mechanism are established by taking the rotation matrices of the C system (where the star-shaped frame is located) relative to the G system and the rotation matrices of the P system (where the lower platform is located) relative to the C system (where the star-shaped frame is located).

[0058] Step 3: Based on the force and moment balance equations in the static equations of Step 2, the expression for the cable force is obtained. Since the cable force is not unique, the cable force optimization function is set to ensure that the cable forces of the nine flexible cables driven by the flexible cables of the new feed cabin mechanism change continuously, have no sharp points, and are far from the upper and lower limits of the cable force:

[0059] (20)

[0060] In the above formula (20), T Smax T Smax These are the upper limits of the cable tension for pulling up and down the three flexible cables, T. Smin T Umin These are the lower limits of the cable force for pulling up and down the three flexible cables, respectively. , These are the average tension values ​​of the upward and downward pulling cables, respectively. , The normalization term is lg(), which is the logarithmic barrier function; k1 and k2 are used to adjust the variance weights. and As weight;

[0061] Step 4, set anti-collision constraints:

[0062] Based on the anti-collision requirements between the components of the new feed cabin mechanism, the anti-collision constraint is set as Distance. ;

[0063] Where Distance=GJK(a,b) means that the pull-down and pull-up cables are modeled as straight lines, the two feed receivers and the lower platform are modeled as cylinders, and the connecting ring is modeled as a cylinder with a height of 1cm. All objects are convex hulls. The GJK algorithm is used to perform collision detection in all directions at a 50° zenith angle. a and b represent two objects being detected. The collision detection includes: collision detection between the pull-down cable and the two feed receivers, collision detection between the pull-down cable and the lower platform, collision detection between the pull-up cable and the connecting ring, collision detection between the pull-up cable and the two feed receivers, and collision detection between the connecting ring and the inner wall of the star-shaped frame.

[0064] Step 5: Set the objective function and constraints for optimizing the structural parameters of the new feed cabin mechanism and solve them:

[0065] The original point of the lower platform Distance from the origin of the C system Distance z in the z direction p Six pull cables are anchored at the first anchor point of the slide rail. Height H in the C series B The first anchoring point of the six pull cables on the slide rail Distribution radius r B The distribution radius r of the six upper tension cables at the second anchoring point P[i] on the lower platform P The three pull-down cables are anchored at the third anchor point of the star-shaped frame. Distribution radius r E The three pull-down cables are anchored at the third anchor point of the star-shaped frame. Height H in the C series E The three pull-down flexible cables are anchored at the fourth anchor point of the connecting ring. Distribution radius r W And three pull-down flexible cables at the fourth anchor point of the connecting ring High H in the P-series W These variables serve as structural parameters to be optimized, and the optimization aims to make the azimuth angle... The zenith angle is If the squared difference between the maximum and minimum cable forces of each flexible cable is minimized, then the objective function for setting the constraints is:

[0066] (twenty one)

[0067] st Distance ,

[0068] T s [i]∈[T smin , T smax ], T U [i]∈[T Umin , TUmax ],

[0069] z p ∈[z pmin z pmax ], H B ∈[H Bmin H Bmax ],

[0070] r B ∈[r Bmin r Bmax ], r P ∈[r Pmin r Pmax ],

[0071] r E ∈[r Emin r Emax ], H E ∈[H Emin H Emax ],

[0072] r W ∈[r Wmin r Wmax ] , H W ∈[H Wmin H Wmax ],

[0073] Among them, Soli He Suoli Obtained through the above equation (20), The azimuth angle is Zenith angle is The minimum force of the nine flexible ropes at that time; The azimuth angle is Zenith angle is The maximum force of the nine flexible ropes at that time.

[0074] Solving the above objective function yields the structural parameters that minimize the squared difference between the maximum and minimum cable forces of each flexible cable, which are the optimized structural parameters of the FAST novel feed cabin mechanism.

[0075] In step 1 of the above method, the novel feed cabin mechanism is installed inside the star-shaped frame of FAST.

[0076] The first local coordinate system was established. Department The axis is perpendicular to the plane of the outer anchor point of the star-shaped frame and faces upward;

[0077] Established second local coordinates The origin of the system The center of rotation of the lower platform. The axis is from the origin point to direction, The axis is perpendicular to the first anchoring point of the new feed cabin mechanism. Plane upwards, Axis perpendicular to flat;

[0078] When the platform is kept horizontal relative to the feed cabin, System and The systems are completely parallel;

[0079] Based on the established global coordinate system G, the rotation matrix expressed using quaternions is as follows:

[0080] (1)

[0081] in, It is a quaternion, in which , , , , Let be the equivalent rotation axis vector in the G system; This is the equivalent rotation angle;

[0082] As FAST tracks electromagnetic waves, the star-shaped frame rotates at the zenith angle. The lower platform then rotates the zenith angle relative to the star-shaped frame. Therefore, in the global coordinate system G, the total zenith angle of the lower platform's rotation is... Based on the established global coordinate system G and the first local coordinate system System and second local coordinates The system determines the azimuth angle when the star-shaped frame and the lower platform are located. At that time, the equivalent axes of rotation are: The different rotation angles are: , ;

[0083] The rotation matrix of the C-frame relative to the G-frame, where the star-shaped frame is located, is then:

[0084] (2)

[0085] The rotation matrix of the P-frame relative to the C-frame of the star-shaped frame is:

[0086] (3).

[0087] In step 1 of the above method, the novel feed cabin mechanism includes: a lower platform, a 19-beam receiver, a PAF beam receiver, six upward pull cables, six slide rails, three downward pull cables, and a connecting ring.

[0088] The 19-beam receiver and the PAF beam receiver are mounted on the lower platform, with one end of each of the six pull cables extending from the first anchor point located on the slide rail. The six upper tension cables, i=1,…,6, are drawn out, with their other ends passing through the second anchor point. i=1,…,6 are fixed on the lower platform, the first anchor point The height can vary within the slide rail travel range; second anchor point The distribution radius is First anchor point The distribution radius is Six first anchor points The height is the same in the C series. ;

[0089] One end of each of the three pull-down cables is anchored at the third anchor point fixed to the star-shaped frame. The three pull-down cables, with j=1, 2, and 3, are connected at their other ends via the fourth anchor point. j=1, 2, 3, fixed on the connecting ring; third anchor point The distribution radius is Fourth anchor point The distribution radius is Six third anchor points The height is the same in the C series. Fourth anchor point In the P-series, the height is ;

[0090] Lower platform origin Located at the origin of the C series Directly below, distance The distance in the z-direction is .

[0091] In step 2 of the above method, the global coordinate system G and the first local coordinate system established in step 1 are used in the following manner. System, Second Local Coordinates Based on the rotation matrices of the C-frame (where the star-shaped frame is located) relative to the G-frame and the P-frame (where the lower platform is located) relative to the C-frame (where the star-shaped frame is located), the static equations of the novel feed cabin mechanism are established, including:

[0092] In the C-frame, the coordinates of the anchor points are as follows:

[0093] (4)

[0094] (5)

[0095] (6)

[0096] (7)

[0097] (8)

[0098] (9)

[0099] In the above formula (8), For the anchoring point of the lower platform of the P series The coordinates; The origin of the C-frame. To the origin of the P series Distance vector; define vector and for:

[0100] (10)

[0101] (11)

[0102] Then vector and The unit vectors are as follows:

[0103] (12)

[0104] (13)

[0105] If the new feed cabin mechanism has an upward and downward flexible cable (the upward cable is the first and second anchor points) , The steel cables in between, and the pull-down flexible cables serve as the third and fourth anchor points. , The magnitudes of the cable forces (between the steel cables) are respectively and Then the vector forces provided by the upward and downward tension cables in the G system are respectively:

[0106] (14)

[0107] (15)

[0108] The equilibrium equations for the lower platform based on the vector forces provided by the upper and lower tension cables are as follows:

[0109] (16)

[0110] The torque about the center of mass of the lower platform is:

[0111] (17)

[0112] In equations (16) and (17) above, For the lower platform mass; g = [0 0 -9.8] T m / s 2 It is the acceleration due to gravity; In the P-system, the distance from the center of mass of the lower platform to the origin of the P-system is... If the position vector is given, then equations (16) and (17) above can be expressed as:

[0113] (18)

[0114] In the above formula (18), ;

[0115] ;

[0116] The first to sixth columns of N above are ( );

[0117] Columns 7 to 9 of N above are ( ).

[0118] In step 4 of the above method, the collision avoidance requirements between the components of the novel feed cabin mechanism include:

[0119] 41) Collision prevention between the pull-down flexible cable and the two feed receivers;

[0120] 42) Collision prevention between the pull-down flexible cable and the lower platform;

[0121] 43) Collision prevention between the pull-up flexible cable and the connecting ring;

[0122] 44) Collision prevention between the pull-up flexible cable and the two feed receivers;

[0123] 45) Collision prevention between the connecting ring and the inner wall of the star-shaped frame.

[0124] In step 5 of the above method, any one of the particle swarm optimization algorithm, genetic algorithm, or simulated annealing algorithm is used to solve the above objective function to obtain the structural parameters that minimize the range of cable force variation for each flexible cable.

[0125] In summary, the optimization method of the present invention has at least the following advantages:

[0126] (1) Adding the function with the smallest variance to the cable force optimization function can make the cable force change range smaller; adding the logarithmic barrier function to the cable force optimization function can make the cable force move away from the boundary, and the cable force changes continuously without cusps and is far away from the cable force boundary.

[0127] (2) In the structural parameter optimization, the objective function is set to minimize the square of the difference between the maximum and minimum cable forces of the nine flexible cables at a specific position of 50° zenith angle and 0 azimuth angle, rather than the square of the difference between the maximum and minimum cable forces in the entire workspace from 0 to 360°. This not only minimizes the change in cable forces in the entire workspace, but also greatly saves the solution time, solving the problem that the solution of the cable force optimization function is a nonlinear optimization process with a long solution time.

[0128] (3) By optimizing the structural parameters of the new FAST feed cabin mechanism in this invention, the observation angle of the new feed cabin mechanism can be increased to 50° zenith angle within the cable force range, thereby enabling the observation of the center of the Milky Way.

[0129] To more clearly demonstrate the technical solution and its effects provided by the present invention, the following detailed description of the method for optimizing the structural parameters of the FAST novel feed cabin mechanism provided by the present invention is based on specific embodiments.

[0130] Example 1

[0131] This embodiment provides a method for optimizing the structural parameters of a novel FAST feed cabin mechanism, such as... Figure 2 As shown, the novel feed cabin mechanism in this method mainly includes: a lower platform, a 19-beam receiver, a PAF beam receiver, six upward pull-up flexible cables (referred to as six upward pull-up cables), six slide rails, three downward pull-up flexible cables (referred to as three downward pull-up cables), and a connecting ring;

[0132] The new feed cabin mechanism is installed inside the star-shaped frame;

[0133] Establish a global coordinate system G at the center of the bottom surface of the active reflecting surface of FAST;

[0134] Taking the center of the external anchoring point plane of FAST's star-shaped frame as the origin Establish the first local coordinate system Tie, The axis is perpendicular to the plane and points upward;

[0135] Taking the center of the upper surface of the lower platform of the new feed cabin mechanism as the origin Establish a second local coordinate system System, the origin It is also the rotation center of the lower platform. The axis is from the origin point to direction, The axis is perpendicular to the feed cabin anchor point. Plane upwards, Axis perpendicular to flat;

[0136] When the current platform remains horizontal relative to the star-shaped framework, System and systems are completely parallel.

[0137] The 19-beam receiver and the PAF beam receiver are mounted on the lower platform, with one end of each of the six pull cables extending from the first anchor point located on the slide rail. The six upper tension cables, i=1,…,6, are drawn out, with their other ends passing through the second anchor point. i=1,…,6 are fixed on the lower platform, the first anchor point The height can vary within the travel range of the slide rail;

[0138] One end of each of the three pull-down cables is anchored at the third anchor point fixed to the star-shaped frame. The three pull-down cables, with j=1, 2, and 3, are connected at their other ends via the fourth anchor point. j=1, 2, 3, fixed on the connecting ring.

[0139] like Figure 3 As shown, the origin of the lower platform Located at the origin of the C series Directly below, distance The distance in the z-direction is First anchor point The distribution radius is Second anchor point The distribution radius is Third anchor point The distribution radius is Fourth anchor point The distribution radius is First anchor point Height in the C series (default 6) (same height) Third anchor point Height in the C series (default 6) (same height) Fourth anchor point The height of the (connecting ring) in the P-system is When tracking electromagnetic waves, the star-shaped frame rotates at the zenith angle. The lower platform rotates at a zenith angle relative to the star-shaped frame. Therefore, in the G system, the total zenith angle of the lower platform's rotation is... .

[0140] This method is performed in the following steps (see Figure 1 ):

[0141] Step 1: Establish a global coordinate system G and two local coordinate systems C and P, and represent the rotation matrix using quaternions. Assume that in the global coordinate system... The equivalent rotation axis vector of the system is The equivalent rotation angle is Then quaternion ,

[0142] in,

[0143]

[0144] The rotation matrix is ​​represented as

[0145] (1)

[0146] As FAST tracks electromagnetic waves, the star-shaped frame rotates at the zenith angle. The lower platform then rotates the zenith angle relative to the star-shaped frame. Therefore, in the G system, the total zenith angle of the lower platform's rotation is... When the star-shaped frame and the lower platform are located at the azimuth angle At the same time, they have the same equivalent axis of rotation: Different rotation angles: , Therefore, the rotation matrix of the C-frame relative to the G-frame, where the star-shaped frame is located, is:

[0147] (2)

[0148] The rotation matrix of the P-frame relative to the G-frame where the lower platform is located is expressed as follows:

[0149] (3)

[0150] Step 2, establish the static equations of the new feed cabin mechanism: in local coordinates Under this system, the coordinates of these anchor points are:

[0151] (4)

[0152] (5)

[0153] (6)

[0154] (7)

[0155] (8)

[0156] (9)

[0157] In the above formula (8) For the anchoring point of the lower platform of the P series coordinates The origin of the C-frame. To the origin of the P series The distance vector. Define the vector. and Represented as:

[0158] (10)

[0159] (11)

[0160] Then vector and The unit vectors are as follows:

[0161] (12)

[0162] (13)

[0163] Assume the magnitudes of the tensions in the upper and lower cables are respectively... , global coordinates The vector forces provided by each flexible cable are:

[0164] (14)

[0165] (15)

[0166] The equilibrium equations for the lower platform are as follows:

[0167] (16)

[0168] The torque about the center of mass of the lower platform is:

[0169] (17)

[0170] In equations (16) and (17) above, For the quality of the lower platform, g = [0 0 -9.8] T m / s 2 It is the acceleration due to gravity. In the P-system, the distance from the center of mass of the lower platform to the origin of the P-system is... The position vector, =[0.0771666, -0.0519681, -0.0612656] T Then, the above equations (16) and (17) can be expressed as:

[0171] (18)

[0172] In the above formula (18),

[0173] ,

[0174] ,

[0175] The first to sixth columns of N above are ( ),

[0176] The 7th to 9th columns of N above are ( )

[0177] Step 3, Set the cable force optimization function: To ensure that the cable forces of the nine flexible cables change continuously without sharp points and are far from the upper and lower limits of cable force, the cable force optimization function is set as follows:

[0178] (20)

[0179] In the above formula (20), T Smax = 0.8mg and T Smax = 0.8mg are the upper limits of the cable force for the pull-up and pull-down three cables, respectively, T Smin = 0.1mg and T Umin = 0.1mg represents the lower limit of the cable force for pulling up and down the three cables, respectively; , Let be the average cable forces of the upward and downward pulling cables, respectively. We consider the upward and downward pulling cables separately. To minimize the difference in cable forces between the cables, we add the minimum variance parameter to equation (20) above, and use... , Normalization is performed, and k1 and k2 are used to adjust the variance weights. Simultaneously, to keep the cable force away from the boundary, a logarithmic barrier function lg is added. and As weight, and The larger the value, the further the cable force is from the boundary. To make the range of cable force variation between the six-cable pull-up and the three-cable pull-down cables comparable, set... , , ;

[0180] Step 4, Set Anti-Collision Constraints: The main anti-collision measures include: 1) Collision prevention between the pull-down flexible cable and the two feed receivers; 2) Collision prevention between the pull-down flexible cable and the lower platform; 3) Collision prevention between the pull-up flexible cable and the connecting ring; 4) Collision prevention between the pull-up flexible cable and the two feed receivers; 5) Collision prevention between the connecting ring and the inner wall of the star-shaped frame. The flexible cable is modeled as a straight line, the two feed receivers and the lower platform are modeled as cylinders, and the connecting ring is modeled as a 1cm high cylinder. All of these objects are convex hulls. The GJK algorithm is used to detect the above four types of collisions. At the zenith angle... At that time, interference was quite severe, so the following optimizations were performed at a 50° zenith angle, covering all angles. The collision detection is performed by assuming the convex hulls of two objects are a and b, respectively. The collision detection function is represented as gjk(a,b), which returns the distance between the two detected objects a and b, i.e., distance=gjk(a,b). Considering that the new feed cabin mechanism may have errors during actual movement, a certain collision threshold is set. If distance < If the collision detection fails, it is considered that a collision has occurred between the two objects. All collision detection can be written as Distance = GJK(a, b), and the collision avoidance constraint is Distance. ;

[0181] Step 5: Set the objective function and constraints for optimizing the structural parameters of the novel feed cabin mechanism and solve them. At a zenith angle of 50°, the force range of the nine flexible cables in all directions from 0 to 360° is not significantly different from the force range at 0° azimuth. Therefore, to save solution time, the azimuth angle is selected as... The zenith angle is The cable tension is optimized, and the minimum value of the cable tension of the 9 flexible cables is recorded. Let the maximum force of the 9 flexible cables be denoted as . , and This can be obtained through the above equation (20). Let z... p H B r B r P r E H E r W H W These eight variables serve as the structural parameters to be optimized, and the objective function and constraints can be set as follows:

[0182] (twenty one)

[0183] st Distance ,

[0184] T s [i] ∈ [T smin , T smax , T U [i] ∈ [T Umin , T Umax ,

[0185] z p ∈ [z pmin , z pmax , H B ∈ [H Bmin , H Bmax ,

[0186] r B ∈ [r Bmin , r Bmax , r P ∈ [r Pmin , r Pmax ,

[0187] r E ∈ [r Emin , r Emax , H E ∈ [H Emin , H Emax [[ID=​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​The above objective function is solved by using particle swarm optimization or other heuristic algorithms, such as genetic algorithms or simulated annealing, and finally the structural parameters that minimize the range of cable force variation are obtained.

[0191] In summary, the method of the present invention has at least the following beneficial effects compared with the prior art:

[0192] (1) By optimizing the structural parameters of the new feed cabin mechanism of FAST, the observation angle of the feed cabin mechanism can be increased to 50° zenith angle within the cable force range, thereby enabling FAST to observe the center of the Milky Way.

[0193] (2) In order to make the range of cable force variation small, the function with the smallest variance is added to the cable force optimization function. At the same time, in order to make the cable force far away from the boundary, a logarithmic barrier function is added to the cable force optimization function, so that the cable force changes continuously without cusps and is far away from the cable force boundary.

[0194] (3) Since the solution of the cable force optimization function is a nonlinear optimization process, the solution time is relatively long. The objective function is set to minimize the square of the difference between the maximum and minimum cable forces of the nine flexible cables at a specific position of 50° zenith angle and 0 azimuth angle, rather than the square of the difference between the maximum and minimum cable forces in the entire workspace from 0 to 360°. This can not only minimize the cable force change in the entire workspace, but also greatly save the solution time.

[0195] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0196] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing the structural parameters of a novel FAST feed cabin mechanism, characterized in that, include: Step 1: Establish a global coordinate system and two local coordinate systems on the novel feed cabin mechanism whose structural parameters are to be optimized. Among them, the global coordinate system G is established at the center of the bottom surface of the active reflector of FAST. The origin is taken as the center point of the external anchoring point plane of FAST's star-shaped frame. Establish the first local coordinate system Tie; The origin is taken as the center point of the upper surface of the lower platform of the new feed cabin mechanism. Establish a second local coordinate system Tie; Based on the established global coordinate system G and the first local coordinate system System and second local coordinates Determine the rotation matrix of the C system where the star-shaped frame is located relative to the G system and the rotation matrix of the P system where the lower platform is located relative to the C system where the star-shaped frame is located. Step 2, establish the static equations of the new feed cabin mechanism: Based on the global coordinate system G and the first local coordinate system established in step 1... System, Second Local Coordinates The static equations of the novel feed cabin mechanism are established by taking the rotation matrices of the C system (where the star-shaped frame is located) relative to the G system and the rotation matrices of the P system (where the lower platform is located) relative to the C system (where the star-shaped frame is located). Step 3: Based on the force and moment balance equations in the static equations of Step 2, the expression for the cable force is obtained. Since the cable force is not unique, the cable force optimization function is set to ensure that the cable forces of the nine flexible cables driven by the new feed cabin mechanism change continuously, without sharp points, and far from the upper and lower limits of the cable force: （20） In the above formula (20), T Smax T Smax These are the upper limits of the tension on the uplift and downlift cables, respectively, T. Smin T Umin These are the lower limits of the cable tension for the upward and downward pulling ropes, respectively. , These are the average tension values ​​of the upward and downward pulling cables, respectively. , The normalization term is lg(), which is the logarithmic barrier function; k1 and k2 are used to adjust the variance weights. and As weight; Step 4, set anti-collision constraints: Based on the anti-collision requirements between the components of the new feed cabin mechanism, the anti-collision constraint is set as Distance. ; Where Distance=GJK(a,b) means that the pull-down and pull-up cables are modeled as straight lines, the two feed receivers and the lower platform are modeled as cylinders, and the connecting ring is modeled as a cylinder with a height of 1cm. All objects are convex hulls. The GJK algorithm is used to perform collision detection in all directions at a 50° zenith angle. a and b represent two objects being detected. The collision detection includes: collision detection between the pull-down cable and the two feed receivers, collision detection between the pull-down cable and the lower platform, collision detection between the pull-up cable and the connecting ring, collision detection between the pull-up cable and the two feed receivers, and collision detection between the connecting ring and the inner wall of the star-shaped frame. Step 5: Set the objective function and constraints for optimizing the structural parameters of the new feed cabin mechanism and solve them: The original point of the lower platform Distance from the origin of the C system Distance z in the z direction p The first anchoring point of the six pull cables on the slide rail Height H in the C series B The first anchoring point of the six pull cables on the slide rail Distribution radius r B The distribution radius r of the second anchoring point P[i] of the six upper tension cables on the lower platform P The three pull-down cables are anchored at the third anchor point of the star-shaped frame. Distribution radius r E The three pull-down cables are anchored at the third anchor point of the star-shaped frame. Height H in the C series E The fourth anchor point of the three pull-down flexible cables on the connecting ring. Distribution radius r W And three pull-down flexible cables at the fourth anchor point of the connecting ring High H in the P-series W These variables serve as structural parameters to be optimized, and the optimization aims to make the azimuth angle... The zenith angle is The squared difference between the maximum and minimum cable forces of each flexible cable is minimized at that time. This represents the zenith angle of the star-shaped frame rotation as FAST tracks electromagnetic waves. To determine the zenith angle at which the platform rotates relative to the star-shaped frame when FAST tracks electromagnetic waves, the objective function with constraints is set as follows: （21） s.t. Distance , T s [i]∈[T Smin , T Smax ],T U [i]∈[T Umin , T Umax ], z p ∈[z pmin , z pmax ],H B ∈[H Bmin , H Bmax ], r B ∈[r Bmin ，r Bmax ]，r P ∈[r Pmin ，r Pmax ]， r E ∈[r Emin ,r Emax ],H E ∈[H Emin , H Emax ], r W ∈[r Wmin ,r Wmax ] ,H W ∈[H Wmin , H Wmax ], Among them, Soli He Suoli Obtained through the above equation (20), The azimuth angle is zenith angle is The minimum force of the nine flexible ropes at that time; The azimuth angle is zenith angle is The maximum value of the tension of the nine flexible ropes; in the above formula (21), , z pmin = -1.5m, z pmax = -2.5m, H Bmin = -0.5m, H Bmax = 1m, r Bmin = 3m, r Bmax =3.5m, r Pmin = 2.15m, r Pmax = 2.6m, r Emin = 3m, r Emax = 3.5m, H Emin = -2m, H Emax =-1.5m, r Wmin =1m, r Wmax = 2m, H Wmin = 1.74m, H Wmax = 3m; Solve the above objective function to obtain the structural parameters that minimize the range of cable force variation of each flexible cable, which are the optimized structural parameters of the FAST new feed cabin mechanism.

2. The method for optimizing the structural parameters of the FAST novel feed cabin mechanism according to claim 1, characterized in that, In step 1, The new feed cabin mechanism is installed inside the star-shaped frame of FAST; The first local coordinate system was established. Department The axis is perpendicular to the plane of the outer anchor point of the star-shaped frame and faces upward; Established second local coordinates The origin of the system The center of rotation of the lower platform. The axis is from the origin point to direction, The axis is perpendicular to the second anchoring point of the new feed cabin mechanism. Plane upwards, Axis perpendicular to flat; When the platform is kept horizontal relative to the feed cabin, System and The systems are completely parallel; Based on the established global coordinate system G, the rotation matrix represented by quaternions is determined as follows: （1） in, It is a quaternion, in which , , , , Let be the equivalent rotation axis vector in the G system; This is the equivalent rotation angle; In the global coordinate system G, the total zenith angle of the lower platform's rotation is... , This represents the zenith angle of the star-shaped frame rotation as FAST tracks electromagnetic waves. This is the zenith angle at which the platform rotates relative to the star-shaped frame when FAST tracks electromagnetic waves; based on the established global coordinate system G and the first local coordinate system. System and second local coordinates The system determines the azimuth angle when the star-shaped frame and the lower platform are located. At that time, the equivalent axes of rotation are: The different rotation angles are: , ; The rotation matrix of the C-frame relative to the G-frame, where the star-shaped frame is located, is then: （2） The rotation matrix of the P-frame relative to the C-frame of the star-shaped frame is: （3）。 3. The method for optimizing the structural parameters of the FAST novel feed cabin mechanism according to claim 1, characterized in that, In step 1, the novel feed cabin mechanism includes: a lower platform, a 19-beam receiver, a PAF beam receiver, six upward pull cables, six slide rails, three downward pull cables, and a connecting ring. The 19-beam receiver and the PAF beam receiver are mounted on the lower platform, with one end of each of the six pull cables extending from the first anchor point located on the slide rail. The six upward-pulling flexible cables, i=1,…,6, are led out, with the other ends passing through the second anchor point. i=1,…,6 are fixed on the lower platform, the first anchor point The height can vary within the slide rail travel range; second anchor point The distribution radius is First anchor point The distribution radius is Six first anchor points The height is the same in the C series. ; One end of each of the three pull-down cables is anchored at the third anchor point fixed to the star-shaped frame. The three pull-down cables, with j=1, 2, 3, are extended to the fourth anchor point. j=1, 2, 3, fixed on the connecting ring; third anchor point The distribution radius is Fourth anchor point The distribution radius is Six third anchor points The height is the same in the C series. Fourth anchor point In the P-series, the height is ; Lower platform origin Located at the origin of the C series Directly below, distance The distance in the z-direction is .

4. The method for optimizing the structural parameters of the FAST novel feed cabin mechanism according to claim 1, characterized in that, In step 2, the global coordinate system G and the first local coordinate system established in step 1 are used in the following manner. System, Second Local Coordinates Based on the rotation matrices of the C-frame (where the star-shaped frame is located) relative to the G-frame and the P-frame (where the lower platform is located) relative to the C-frame (where the star-shaped frame is located), the static equations of the novel feed cabin mechanism are established, including: In the C-frame, the coordinates of the first, second, third, and fourth anchorage points are as follows: （4） （5） （6） （7） （8） （9） In the above formula (8), For the anchoring point of the lower platform of the P series The coordinates; The origin of the C-frame. To the origin of the P series Distance vector; Define vector and They are respectively: （10） （11） Then vector and The unit vectors are as follows: （12） （13） If the tensions of the upper and lower flexible cables of the new feed cabin mechanism are respectively and Then the vector forces provided by the upward and downward tension cables in the G system are respectively: （14） （15） in, Let be the rotation matrix of the C-frame relative to the G-frame in which the star-shaped frame is located; The equilibrium equations for the lower platform based on the vector forces provided by the upper and lower tension cables are as follows: （16） The torque about the center of mass of the lower platform is: （17） In equations (16) and (17) above, For the lower platform mass; g = [0 0 -9.8] T m / s 2 It is the acceleration due to gravity; In the P-system, the distance from the center of mass of the lower platform to the origin of the P-system is... If the position vector is given, then equations (16) and (17) above can be expressed as: （18） In the above formula (18), ; ； The first to sixth columns of N above are ( ); Columns 7 to 9 of N above are ( ).

5. The method for optimizing the structural parameters of the novel FAST feed cabin mechanism according to any one of claims 1-4, characterized in that, In step 4, the anti-collision requirements between the components of the novel feed cabin mechanism include: 41) Collision prevention between the pull-down flexible cable and the two feed receivers; 42) Collision prevention between the pull-down flexible cable and the lower platform; 43) Collision prevention between the pull-up flexible cable and the connecting ring; 44) Collision prevention between the pull-up flexible cable and the two feed receivers; 45) Collision prevention between the connecting ring and the inner wall of the star-shaped frame.

6. The method for optimizing the structural parameters of the FAST novel feed cabin mechanism according to any one of claims 1-4, characterized in that, In step 5, any one of the particle swarm optimization algorithm, genetic algorithm, or simulated annealing algorithm is used to solve the above objective function to obtain the structural parameters that minimize the squared difference between the maximum and minimum cable forces of each flexible cable.

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