CN107491594B - Cable net antenna shape surface precision calculation method - Google Patents
Cable net antenna shape surface precision calculation method Download PDFInfo
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Abstract
The method overcomes the defects of the existing calculation method of the shape and surface precision of the cable net antenna, considers the influence of the cable net antenna on the shape and surface precision of the cable net antenna after the cable net antenna is unfolded in the track, and the provided calculation process can effectively supplement the defects of the cable net antenna ground unfolding test caused by the influence of the earth gravity and the atmosphere, and can accurately predict the shape and surface precision and the working performance of the cable net antenna in the space in-track working state. Meanwhile, the error root mean square value is calculated according to the minimum distance between the node and the whole paraboloid, and the smoothness of the cable net surface of the antenna can be reflected more accurately by the method; a pointing error calculation method is provided, and the method can reflect the electric signal reflection accuracy of the antenna cable net surface more intuitively.
Description
Technical Field
The invention belongs to the technical field of radar antennas, and particularly relates to a cable network antenna shape surface precision calculation method.
Background
The cable net antenna refers to a radar antenna using a flexible cable net as a reflecting surface (the reflecting surface of the flexible cable net is hereinafter referred to as a flexible cable net surface). The cable net antenna mainly comprises an expandable truss structure and a reflecting net. The reflecting net is generally in a paraboloid shape, and the edge of the reflecting net is connected with the expandable truss structure at a plurality of positions. By taking the peripheral truss type cable net antenna widely applied at home and abroad at present as an example, the structure comprises an expandable peripheral truss, a flexible tension cable net for supporting and forming and a reflection net, wherein the flexible tension cable net is mostly a three-way grid cable net, the unit of the flexible tension cable net is triangular, and the metal reflection net is attached to the back of the front cable net to realize the reflection of a feed source signal. Compared with the conventional rigid reflector antenna, the cable net antenna has the advantages of large aspect ratio, light weight, good folding performance, high rigidity of a main structure after being unfolded and the like, and is widely applied to the aerospace fields of communication satellites, remote sensing satellites, reconnaissance satellites and the like at home and abroad at present. For example, the American Turaya (Thuraya-1) satellite weighs 78 kg, has a diameter of 1.3 m in a folded launching state, has a diameter of 12.25 m after in-orbit unfolding, and has an aspect ratio of 10: 1.
for the mechanism which is composed of the flexible cable net surface and the rod piece expandable structure, such as the cable net antenna, because the flexible cables which form the flexible cable net surface are in a loose state when not being subjected to axial tension, the axial rigidity is only realized under the action of stress after the flexible cables are expanded and tensioned, and the geometric shape of the cable net reflecting surface which is composed of the flexible cables before the flexible cables are tensioned has uncertainty. The design and analysis of the flexible cable net itself is therefore a common problem for cable net antennas of different deployable truss structures. A key problem of the design of the cable net antenna and the in-orbit application is to ensure the surface accuracy of the flexible cable net surface after the expansion of the in-orbit. The shape precision refers to the consistency of the shape of the flexible cable net surface after the expansion on the rail and the design shape, and the condition that the shape is completely consistent with the shape of the design shape is the highest precision. The shape precision directly influences the electrical property of the flexible cable net surface. Modeling and calculating the shape and accuracy of the wire mesh surface after the wire mesh antenna is expanded on the rail is generally called shaping or forming design. In practical engineering, a paraboloid is approximated by a series of nodes and a triangular unit with a certain area in the forming design, and the shape surface deviation between a forming result and an ideal paraboloid is generally measured by the root mean square of the distances between all corresponding nodes of a net surface. And when the antenna is designed, the best fitting paraboloid where the antenna is located is determined by solving the minimum root mean square, and then the minimum number of flexible cables or the simplest grid division meeting the requirement of the precision index is obtained.
The traditional calculation method of the net surface precision of the cable network antenna mainly adopts a dynamic relaxation method, a force density method and a finite element-based method. The basic idea of the dynamic relaxation method is to regard the shape-finding process of the structure as a process from dynamic to static balance, and in the dynamic attenuation process, the position of the maximum kinetic energy is the balance position of the structure, so that the position of the structure when the kinetic energy is maximum is determined, namely the shape-finding result. The force density method is the main method for shape finding analysis of tension structure, and its basic idea is to disperse the cable structure into node and rod network model, and according to the topological relation between the structure unit and the node, at the same time, set the force density value or stress density value to establish the balance equation set related to the node, so as to obtain the coordinate of each node, i.e. the corresponding curved surface form. The finite element method has the main ideas that the displacement mode of the cable unit is deduced by assuming the geometric shape of the cable unit, the cable length change before and after deformation is calculated, a rigidity matrix is deduced according to a balance equation or an energy principle, the relationship between the end node force and the end node displacement of the cable unit is calculated, and an integrated structure overall balance equation is subjected to iterative calculation.
The common property of the methods is that the surface of the flexible cable net surface in the unfolding state is directly considered, the tension of each unit (or among nodes) with the highest surface precision and the corresponding geometric position coordinates of each node of the flexible cable net surface are found by using an iterative optimization method, and a new flexible cable net surface meeting the design requirement is obtained by calculation.
The first method is to calculate the vertical distance between a sampling node of a new flexible cable mesh surface and a sampling node corresponding to a nominal mesh surface, and then calculate the root mean square value of the whole mesh surface; the second method is to calculate the distance between the sampling node of the new flexible cable mesh surface and the single reflecting surface unit of the nominal mesh surface containing the node, and then calculate the root mean square value of the whole mesh surface.
The cable net antenna is transmitted in a folded state in practical engineering application, and the antenna is unfolded and locked in an on-orbit mode after the spacecraft is in orbit. Therefore, the method for simply establishing the flexible cable mesh surface unfolding state model as shape finding and surface precision calculation has limitation, the calculation result is only a special solution in all the balance states, and the influence of the in-orbit unfolding process cannot be considered. Meanwhile, the results obtained by adopting the two shape surface precision error calculation methods are greatly influenced by local unit deformation of the flexible cable mesh surface, the shape surface precision of the whole flexible cable mesh surface is limited, the error obtained by the two methods has a larger relation with the smoothness of the mesh surface, and the method is limited in the capability of evaluating the electrical property of the cable mesh antenna after being unfolded and is necessary for further improvement.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the defects of the prior art are overcome, and the calculation method of the shape and surface precision of the cable network antenna is provided. The method solves the problems that the existing calculation method for the shape and surface precision of the cable net antenna cannot consider the on-orbit expansion influence and cannot comprehensively reflect the shape surface smoothness and the pointing precision.
The technical scheme adopted by the invention is as follows: a method for calculating the shape and surface precision of a cable network antenna comprises the following steps:
dividing cable net grids on a surface paraboloid of a flexible cable net surface, and calculating according to a static shape finding method to obtain a flexible cable tension value between each node and a nominal length of each expanded flexible cable section to obtain a static shape finding net surface;
step two, establishing a truss mechanism dynamic model of the cable network antenna by adopting a multi-body system dynamic method, wherein the truss mechanism dynamic model comprises a rod, a hinge, a rotating joint and an unfolding driving coil spring dynamic model;
step three, based on the static shape-finding net surface obtained by calculation in the step one, establishing a closed state dynamic model of the flexible cable net surface by adopting a bead type model, wherein the model comprises a concentrated mass point model and a flexible cable tension model between nodes;
step four, assembling the two models in the step two and the step three into a dynamic model through the connecting nodes of the flexible cable mesh surface and the truss mechanism, and performing dynamic calculation of the unfolding process for one time, wherein the calculation result comprises the geometric positions of all the nodes of the flexible cable mesh surface after unfolding and the tension value of each flexible cable section to obtain the unfolded and calculated flexible cable mesh surface;
step five, calculating and expanding the surface precision error s of the flexible cable net surface based on the calculation result of the step four;
step six, calculating and expanding a pointing accuracy error α of the flexible cable mesh surface based on the calculation result of the step four;
and step seven, if the surface precision error s and the pointing precision error α in the step five and the step six meet the set threshold, finishing the method, and if the surface precision error s and the pointing precision error α do not meet the set threshold, adjusting the initial node positions and the initial tension of each unit of the flexible cable mesh surface, and returning to the step one.
The sixth step comprises the following specific steps:
step 6.1, setting that the electric signals are incident in parallel along the irradiation direction of the feed source of the flexible cable mesh surface, and calculating α included angles between the reflection direction vectors and the vector pointing to the feed source from the incident point after the M sampling reflection surface units in the M reflection surface units receive the electric signalsξWherein ξ is 1,2,3, M is a positive integer;
step 6.2, calculating the pointing accuracy error of the flexible cable net surface
In the fifth step, a calculation formula of the surface precision error s of the flexible cable mesh surface is as follows:
wherein N is the number of sampling nodes of the flexible cable mesh surface and is a positive integer;λin the process of the cable mesh antenna from the folded state to the unfolded state, the shortest distance between the sampling node of the flexible cable mesh surface and the surface paraboloid of the flexible cable mesh surface is 1,2,3.
Compared with the prior art, the invention has the advantages that:
(1) the method considers the influence of the on-orbit expansion of the antenna, and can accurately predict the shape surface precision and the working performance of the cable net antenna in the on-orbit working state of the outer space.
(2) The invention provides an error root mean square value calculated according to the minimum distance between the node and the whole paraboloid, and the smoothness of the cable net surface of the antenna can be more accurately reflected.
(3) The pointing error calculation method provided by the invention can more visually reflect the electric signal reflection precision of the cable net surface of the antenna.
(4) The calculation process provided by the invention has good universality, can effectively supplement the defects of earth gravity and atmospheric influence in the ground expansion test of the cable net antenna, and can improve the on-track surface precision of the cable net antenna by combining with the ground test.
Drawings
Fig. 1 is a structural diagram of a flexible cable mesh of a cable mesh antenna according to the present invention.
Fig. 2 is a flowchart of a method for calculating the accuracy of the profile of the cable network antenna according to the present invention.
Fig. 3 is a schematic diagram of coordinate system definition and pointing accuracy calculation of a cable network antenna according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of a three-way grid cable network type according to an embodiment of the present invention.
FIG. 5 is a schematic diagram of a cabled bead model according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The embodiment of the invention relates to a peripheral annular truss type cable network antenna, which has an expansion caliber of 30m and an expansion-contraction ratio of 11.4: 1. the truss mechanism of the cable net antenna is composed of 30-span parallelogram truss units with the same structure. After the truss is unfolded in place, the front and rear cable nets and the vertical tension cables reach the balance position under the action of internal tension, and an antenna paraboloid is formed. The configuration of the wire mesh surface is shown in figure 1.
As shown in fig. 2, a method for calculating the shape and surface accuracy of a cable network antenna includes the following steps:
step one, a shape surface paraboloid of a flexible cable net surface is obtained according to the on-orbit working mode and the electrical performance design requirement of the cable net antenna, a Cartesian reference coordinate system is created and is shown in FIG. 3, and the equation of the paraboloid is as follows:
wherein f is the focal length of the parabolic antenna. (X, Y and Z) are coordinates of any point on the paraboloid of the flexible cable net surface.
And step two, performing grid division on the paraboloid in the step one according to the three-way grid cable net type shown in fig. 4, wherein the divided cable net comprises n nodes, m reflecting surface units and k sections of flexible cables. And calculating according to a force density method by using a static shape finding method to obtain the tension value of the flexible cables among all nodes and the nominal length of each flexible cable section after expansion to obtain a static shape finding net surface, wherein the shape finding result is the force density of all cable sections in the expansion and tensioning state of the cable net. The process is to find a set of pretension forces for the cable net structure so that the entire cable net is force balanced under the constraint of the perimeter truss and the ratio of the maximum and minimum flexible cable tensions is satisfied to be as small as possible. n, m and k are positive integers.
The cable net surface after grid division comprises k sections of flexible cables. Force density q of each segment of flexible cableiComprises the following steps:
qi＝ti/li(i＝1,2,3...,k) (2)
wherein, tiIs the tension of the i-th section of flexible cable in the state that the net surface is unfolded,/iThe length of the i-th section of the flexible cable in the expanded state of the net surface is shown. The static equilibrium equation of the node j (j ═ 1,2,3 …, n) in the cable net surface in the X direction is as follows:
in the formula (3), CjSet of nodes connected to node j, qμIs node j and adjacent node mu (mu ∈ C)jFinger node μ belongs to set Cj) Force density of the flexible cable segments between, /)μxIs the component of the length of the flexible cable segment between the node j and the adjacent node mu in the X direction, fgxIs a component of the constraint reaction force of the truss to the node j in the X direction.
The static balance equation of nodes j (j ═ 1,2,3 …, n) in the plane of the cable net in the Y and Z directions is the same as the form of the equation (3).
The optimization model is as follows: setting initial force density and network surface initial node coordinates, and searching q1,q2,…,qkA set of solutions of, let tmax/tminObtaining a minimum value;
the constraint equation is:
0<qi≤[q](7)
in the constraint equation, the equations (4) to (6) are balance equations of the surface force and density of the flexible cable mesh, wherein CjSet of nodes connected to node j, qμIs node j and adjacent node mu (mu ∈ C)jFinger node μ belongs to set Cj) Force density of the flexible cable segments between, /)μx,lμy,lμzIs a component of the length of the flexible cable segment between the node j and the adjacent node mu in the direction X, Y, Z, fgx,fgy,ffzThe constraint reaction force applied to the nodes for the truss attachment is a component in the direction X, Y, Z.
Equation (7) is the force density maximum constraint, where [ q ] is the maximum design allowable value for the force density of the cable segment.
The formula (8) is the space position (x) of the node on the cable net surface under the Cartesian reference coordinate systemj,yj,zj) Dependence, where f is the focal length of the parabolic antenna. Q is obtained by optimization calculationi,ti,liK and a restraining reaction force f applied to the truss fixed connection nodegThe value of (c).
And step three, establishing a cross rod, a vertical rod, an inter-rod hinge and a driving moment of the unfolded truss by adopting a multi-body system dynamics method to obtain a truss mechanism dynamics model.
And step four, establishing a dynamic model of the furled state of the flexible cable mesh surface by adopting a bead model based on the static shape-finding mesh surface obtained by calculation in the step two. Specifically, the mass of the flexible cable is equivalent to each node, and the tension of the flexible cable between the nodes of the cable net is established as a tension model between concentrated mass points. The vertical tension cable was built as a force model, as shown in fig. 5. In order to improve the calculation speed, the rear cable net nodes are symmetrical to the front cable net nodes, and the vertical tension cables between the front cable net and the rear cable net are parallel to the Z axis.
Function of tension of flexible cable between nodes of cable netiComprises the following steps:
wherein K is the stiffness coefficient of the flexible cable, c is the damping coefficient of the flexible cable, diIs the length of the i-th segment of the flexible cable, liThe length of the i-th section of the flexible cable in the expanded state of the net surface, and k is the number of the flexible cables.
Vertical tensile force cable force function FzjComprises the following steps:
wherein g is the stiffness coefficient, hjThe displacement of the nodes of the cable network is shown, a is the judgment condition of the force function, e is an index, b is a damping coefficient, and n is the number of the nodes.
And step five, assembling the model in the step three and the model in the step four into a dynamic model through the connecting nodes of the flexible cable mesh surface and the truss mechanism, and performing dynamic calculation of the unfolding process once to obtain the geometric coordinates of each node of the flexible cable mesh surface, the flexible cable length and the flexible cable tension of the flexible cable mesh surface, and the vertical tension cable tension of the flexible cable.
And step six, calculating and expanding the surface precision error of the flexible cable net surface based on the analysis result of the step five: after the cable net antenna is unfolded, calculating the root mean square s of the shortest distance between the sampling node of the flexible cable net surface and the surface paraboloid of the flexible cable net surface, wherein the calculation formula is as follows:
wherein N is the number of sampling nodes of the flexible cable mesh surface and is a positive integer;λand (λ 1., N) is the shortest distance between the sampling node and the surface parabolic curve (formula (1)). Compared with the traditional method of only calculating the root mean square of the difference between the Z-axis coordinate of the sampling node and the Z-axis coordinate of the position corresponding to the surface paraboloidThe surface precision error calculation method can reflect the smoothness of the expanded flexible cable net surface and the surface consistency;
and step seven, analyzing and unfolding the calculated pointing accuracy error α of the flexible cable mesh surface based on the analysis result of the step five.
The parabolic surface of the cable net is shown in FIG. 3, and the incident signal vector is parallel to the Z axis of the antenna reference coordinate system
The nominal orientation vector after reflection by a curved surface element is
Pointing to the focus F with a normal vector of
It can be known that
The vector pointing accuracy error is 0. And simultaneously obtaining the coordinates of three nodes of the curved surface unit based on the fifth step, wherein the plane unit formed by the three nodes is E.
The direction vector after reflection by the plane unit E is
Normal vector of
Is provided with
And
angle β2Error angle of pointing accuracy for this unit β2Can be directly calculated and can also be calculated according to the formula (11).
β2＝2β1(11)
β therein1Is composed of
And
the included angle of (a).
Setting M reflecting surface units on the flexible cable net surface, wherein the number of samples is M, and M is a positive integer, and calculating the pointing accuracy error angle α of the M sampled reflecting surface unitsξ(ξ ═ 1,2,3.., M), then the wire mesh pointing accuracy error α is calculated according to equation (12).
The method can visually reflect the directional accuracy of the expanded flexible cable net surface. The directional accuracy can directly reflect the electric reflection performance of the cable network antenna, and the defect that the surface accuracy cannot reflect the local translation error of the network surface is overcome.
Step eight, comparing the calculation results of the profile precision error s and the pointing precision error α in the step six and the step seven with the design index, if the calculation results meet the set threshold index, indicating that the design meets the requirements, if the calculation results do not meet the set threshold index, correcting the initial force density and the coordinate value of the initial node of the mesh surface, and repeating the step two to the step seven for iterative calculation.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (3)
1. A method for calculating the shape and surface precision of a cable network antenna is characterized by comprising the following steps:
dividing cable net grids on a surface paraboloid of a flexible cable net surface, and calculating according to a static shape finding method to obtain a flexible cable tension value between each node and a nominal length of each expanded flexible cable section to obtain a static shape finding net surface;
step two, establishing a truss mechanism dynamic model of the cable network antenna by adopting a multi-body system dynamic method, wherein the truss mechanism dynamic model comprises a rod, a hinge, a rotating joint and an unfolding driving coil spring dynamic model;
step three, based on the static shape-finding net surface obtained by calculation in the step one, establishing a closed state dynamic model of the flexible cable net surface by adopting a bead type model, wherein the model comprises a concentrated mass point model and a flexible cable tension model between nodes;
step four, assembling the two models in the step two and the step three into a dynamic model through the connecting nodes of the flexible cable mesh surface and the truss mechanism, and performing dynamic calculation of the unfolding process for one time, wherein the calculation result comprises the geometric positions of all the nodes of the flexible cable mesh surface after unfolding and the tension value of each flexible cable section to obtain the unfolded and calculated flexible cable mesh surface;
step five, calculating and expanding the surface precision error s of the flexible cable net surface based on the calculation result of the step four;
step six, calculating and expanding a pointing accuracy error α of the flexible cable mesh surface based on the calculation result of the step four;
and step seven, if the surface precision error s and the pointing precision error α in the step five and the step six meet the set threshold, finishing the method, and if the surface precision error s and the pointing precision error α do not meet the set threshold, adjusting the initial node positions and the initial tension of each unit of the flexible cable mesh surface, and returning to the step one.
2. The method for calculating the surface accuracy of the cable network antenna according to claim 1, wherein the method comprises the following steps: the sixth step comprises the following specific steps:
step 6.1, setting that the electric signals are incident in parallel along the irradiation direction of the feed source of the flexible cable mesh surface, and calculating α included angles between the reflection direction vectors and the vector pointing to the feed source from the incident point after the M sampling reflection surface units in the M reflection surface units receive the electric signalsξWherein ξ is 1,2,3, M is a positive integer;
step 6.2, calculating the pointing accuracy error of the flexible cable net surface
3. The method for calculating the accuracy of the shape and surface of the cable network antenna according to claim 1 or 2, wherein: in the fifth step, a calculation formula of the surface precision error s of the flexible cable mesh surface is as follows:
wherein N is the number of sampling nodes of the flexible cable mesh surface and is a positive integer;λin the process of the cable mesh antenna from the folded state to the unfolded state, the shortest distance between the sampling node of the flexible cable mesh surface and the surface paraboloid of the flexible cable mesh surface is 1,2,3.
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| CN114156651B (en) * | 2021-11-12 | 2023-03-24 | 西北工业大学 | Satellite-borne mesh-shaped reflector antenna beam forming method based on memory alloy actuator |
| CN115292989B (en) * | 2022-07-15 | 2023-07-25 | 西安电子科技大学 | Space-ground consistency-oriented cable network antenna profile prediction adjustment method |
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