Deployment analysis of deployable antennas considering cable net and truss flexibility

https://doi.org/10.1016/j.ast.2018.09.038Get rights and content

Abstract

Dynamic analysis of antennas during the deployment is very important. Several successful methods have been demonstrated. However, few studies have been conducted on the deployment analysis of antennas with cable net and flexible truss. This paper presents an analysis method of the deployment of antennas consisting of cable net and flexible truss. First, a beam element is used to model the flexible truss and a cable element with a transition function is used to model the cable net from slack to tension state. Then, the deployment of the antenna is planned and the corresponding variation of the length of the driving cable is obtained. Due to the fact that antennas deploy very slowly in space, the mechanism analysis problem for the antenna during deployment is discretized to several quasi-static configuration analysis problems. By using the principle of minimum potential energy, the equilibrium state of the quasi-static configuration at an instant of the deployment is computed. Numerical simulation of 2 m aperture mesh reflector antenna was performed. The numerical results are compared with previous works, and the validity of the method is demonstrated.

Introduction

The development of space technology has led to an increasing requirement for large space structures. For example, the high-precision Earth observation system utilizes a large-aperture spaceborne antenna to improve the resolution. Due to the limit of the loading weight and volume of the vehicle, spaceborne antennas are moving towards the deployable structures. Among the various forms of deployable antennas, mesh reflector antennas are receiving more attention on its advantages of large foldable ratio, light weight and high accuracy [1], [2]. As showed in Fig. 1, AstroMesh series loop antenna used on SMAP Soil Test Satellite, which is mainly composed of a deployable truss, a wire mesh and a cable net (including the front net, rear net and vertical cables). Deployable antenna has to deploy in-orbit from the folded state where the cable net is slack, and it is gradually tensioned by the truss at the middle and late stages of the deployment [3].

At present, much work has been done on the deployment of deployable truss [4], [5], however, few studies have been done on the deployment of antenna including cable net and flexible truss. Li [3] studied the deployment of the truss based on Lagrange equation of the second kind, where the cable net can be equivalent to the spring and the equivalent stiffness coefficient is given, but this assumption does not accurately reflect the complex topological structure of the cable net and the stress state of each cable. Mitsugi [6] established a flexible multi-body dynamics model of the overall structure of the mesh reflector antenna where cables are treated with bar elements. The driving force during the deployment was analyzed and the peak of the driving force was reduced by implementing a translational spring in the center standoff. However, the current overall modeling method for the cable net is a bit simple and difficult to describe its dynamic characteristics. Li et al. [7] studied the deployment of the mesh reflector antenna and performed a detailed analysis of the asynchronous phenomenon. Since the driving force in the antenna deployment has been planned in advance, the study does not reflect its relationships with cable tension. Nei et al. [8] analyzed the deployment of the spatial cable net with geometrical nonlinearity and topological diversity. The spring-damping element was used to model the cable and the tension state of the cable was described by updating the stiffness matrix. The expression of the elastic potential energy was obtained by fitting the elastic potential energy of the cable net with a polynomial, and the kinetic energy of the truss structure was obtained with the assumption of rigid truss, and then the deployment of the antenna was described by Lagrange's equation [9]. Zhang et al. [10] described the cable net based on the elastic catenary elements. First, the instantaneous shape and the tension distribution of the cable net were obtained, then all the instantaneous analysis results were integrated and added to the dynamic model in order to get the cable tension during the deployment. From the energy point of view, the dynamic model of elastic catenary element is deduced by Lagrange equation of the second kind, and then the cable net model is constructed. Combined with truss modeling, the whole antenna model was established [11]. All of these studies [8], [9], [10], [11] have successfully analyzed the deployment of antenna with cable net, but ignored the flexible deformation of the truss. Therefore, the interaction between the deformation of truss and tension of cable net during the deployment is not obtained.

Mesh reflector antenna consists of flexible truss and cable net, the large deformation of the flexible truss has to be taken into account in the deployment. Several finite element formulations have been proposed for the large displacement analysis of flexible multibody systems, such as the floating frame of reference method [12], the incremental methods [13], [14], and large rotation vector formulations [15]. Currently, absolute nodal coordinate formulation (ANCF) is a widely used modeling method for multi-body dynamics which can accurately describe the dynamics of flexible bodies [7], [16], [17]. In the ANCF, the absolute displacements and global slopes are used as the element nodal coordinates. When such a formulation is used, some of the fundamental problems encountered when using the other finite element formulations can be avoided. Such as no infinitesimal or finite rotation parameters are used as the nodal coordinates [13], [14], the locations and deformations of the material points on the element are defined in the global coordinate system, using the element shape function and nodal coordinates, the mass matrix in the system governing equations remains constant instead of nonlinear [15], the centrifugal and Coriolis forces are all zero, and no limited to small deformation problems [12].

In this paper, the ANCF is used to study the deployment of the mesh reflector antenna. The deployment is divided into many quasi-static configurations at the independent time. The equilibrium state of a quasi-static configuration is studied by using the principle of minimum potential energy, and the antenna deployment is analyzed with the integration of all the configurations.

The remainder of this paper is as follows: In Section 2, using the ANCF, the beam and cable element is developed to model the flexible truss and the slack/tensioned cables, respectively. In Section 3, using the principle of minimum potential energy, the equilibrium equation of the antenna under quasi-static configuration is established. In Section 4, numerical example of 2 m aperture antenna is presented and compared with the results from other literatures. In Section 5, some useful conclusions are obtained.

Section snippets

Molding of truss

Based on Euler–Bernoulli beam, Gerstmayr et al. [18] proposed a low-order beam element which is suitable for large deformation, nonlinear dynamic model of flexible beams. It is assumed that the element is isotropic and its shear deformation and torsion deformation can be ignored. This space beam element is employed for the antenna truss structure.

The deformed three-dimensional two-noded beam element is shown in Fig. 2, and the position vector of any point on the element is:r=Sxa where S is the

Antenna deployment planning

The mesh reflector antenna mainly has two parts, the deployable truss and the cable net, as shown in Fig. 5.

The deployable truss is assembled with a number of geometrically identical parallelograms, assumed the number of parallelograms to be 6, as shown in Fig. 6. Each of the parallelogram consists of two three-dimensional hinges (such as node A2 and B3), two five-dimensional hinges (such as node B2 and A3, the interior of the five-dimensional hinge contains a pulley and a torsion spring), two

Numerical example

In this section, numerical simulation is conducted for a 2 m aperture mesh reflector antenna. As shown in Fig. 5, the deployable truss consists of 6 parallelograms. The length of the horizontal and vertical links is R2=1 m and R1=0.6 m, respectively, and each link is discretized with 5 beam elements. The cross-section of the link is an annulus with the outer diameter 18 mm and thickness 1.2 mm. Horizontal and vertical links are of the same material parameters: the density 1.8×103 kg/m3 and the

Conclusions

In this paper, the quasi-static equilibrium equation of deployable antenna considering cable net and flexible truss is deduced with the ANCF. The method of this paper is demonstrated by the deployment of the 2 m deployable antenna.

In general, the research on deployable antennas often neglects the flexible deformation of the truss. In fact, this deformation has a great influence on the tension state of the cable net. From the results, it can be seen that the flexible deformation of the truss

Conflict of interest statement

The authors declared that they have no conflicts of interest to this work.

Acknowledgements

The authors would like to thank the National Natural Sciences Foundation of China under Grants 51675398 and 51775401 for their financial support.

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