Designing of composite reticulated shell mounting for reflectors of satellite antennas enhanced ribs

. The growth in the number of communication satellites and the increase in antenna signal frequencies places higher demands on the accuracy and mass of reflectors. The accuracy of the reflector depends not only on its structure and materials but is also influenced by its mounting. In this paper, based on the rib-reinforced reflector designed by Bauman


Introduction
A growing number of countries and regions are researching and developing communication satellites to ensure the transmission of various types of information [1][2][3]. With an increase in the number of communication satellites, the signal frequency increases to 60 GHz and higher to provide the necessary amount of transmitted information [4,5]. Therefore, the requirements for the reflective surface precision of satellite mirror antennas are getting higher. The research shows that the deformation of the reflector should not exceed onefiftieth of the wavelength of the antenna's reflected signal throughout the operation [6]. The deformation of the satellite mirror antennas' reflective surface is primarily generated by temperature uneven distribution due to the solar radiation and the reaction radiation from the Earth [7,8].
To suppress the thermal deformation of reflective surfaces, new-type composite materials and structures were invented and created to fabricate satellite mirror antennas, in particular with the epoxy resin/carbon fiber, not merely because of its high specific modulus [9], but also because of its coefficient of thermal expansion in the direction along the fiber less than one, therefore, through special design, the use of this material can achieve zero thermal expansion of the structure [10][11]. A more typical composite structure is the honeycomb interlayer structure, since the hexagonal honeycomb structure [12][13][14], which is perpendicular to the reflective surface, can effectively suppress the thermal deformation of the surface. For purpose of decreasing the mass of the satellite antennas, researchers designed and exploited a composite structure with enhanced ribs [15][16][17][18][19][20][21]. Although the principle of this structure is similar to the honeycomb interlayer structure, its manufacturing process is easier, the manufacturing cycle is shorter, and the weight is lighter.
The thermal deformation of the reflector depends not only on its material and structure but is also affected by its mounting. Currently, dual-gridded reflector design with reinforced stiffeners has become widespread [22]. The upper shell works as the reflective surface, and the lower shell links to the upper shell and the satellite. Another way is to use specially designed small brackets to connect the reflective surface back enhancement ribs to the satellite's main body [23]. Researchers at Bauman Moscow State Technical University designed a reticulated structure for connecting the satellite antenna to the satellite body, which can effectively reduce the thermal deformation of the reflective surface while controlling its mass [24]. However, the study has not fully discussed the reasons for the design of geometric parameters of the structure. Therefore, it is necessary to investigate the effect of the geometric parameters of the reticulated shell mounting on the performance of the mirror space antenna reflector.

Objects and materials
A reflector developed at the Bauman Moscow State Technical University was taken as a basic variant [1,13,25]. It was a paraboloid of rotation with an aperture of 1200 mm, a construction height of 180 mm and a focal length of 500 mm, reinforced with stiffeners according to the "six-pointed star" scheme ( Fig 1). The expected frequency of the satellite antenna signal is at least 60 GHz, so the deflections of the reflector surface profile should not exceed 0.1 mm (Table 1).  As a kind of reinforced composite structure, reticulated shell structure has been widely used in the aerospace field and has relatively mature manufacturing technology. However, it has not been used as a mounting for a satellite antenna. Therefore, the reticulated shell mounting with a height of 300 mm, a bottom radius of 320 mm, and a top radius of 150 mm was designed. The ring ribs are located in the middle of the intersection of the interlacing ribs. The baseline of the interlacing ribs that make up the grid is the geodesic line of that circular truncated cone.
It was assumed that the upper base of the mount is rigidly connected to the mate of the spacecraft with the help of fasteners, and the lower one is glued into the hexagon formed by the stiffening ribs of the reflector. The mesh mounting structure consists of annular and interlacing ribs. To increase the contact area and reduce the risk of rupture during the adhesive connection, special inserts are provided to increase the bonding area (Fig. 2).

Fig. 2. Reflector mounting scheme
At the first stage of the design, the task was to determine the number of interlacing ribs at which the deformation of the surface profile is of the least importance. In the manufacture of mesh fastening, the width of the ribs is determined by the width of the prepreg used for winding and the width of the groove in the shape and is not subject to change at will. On the other hand, the thickness of the ribs can be changed depending on the number of layers of laying.
It was assumed that the mass of the considered mounting options, the number of ring elements and the width of the ribs had fixed values. Only the number and thickness of interlacing ribs varied. As a result, five variants of structures with different numbers of ribs were designed, as shown in Figure 3, and their specific parameters are shown in Table 2.  The thickness of the ribs , mm 8.0 6.9 5.2 4.4 It was assumed that the reflector was made of quasi-isotropic carbon fiber reinforced plastic with a density of 1500 kg/m 3 . The mounting material is isotropic. The parameters of the mechanical and thermophysical characteristics of the materials are given in Table 3. Bending modulus G, GPa: G12=G13=G23 6.9 6.9

Simulation
Simcenter 3D Space Systems Thermal solver in Siemens NX software was used to simulate the stress-strain state of the structure in geosynchronous orbit. It was assumed that the reflecting surface of the reflector is always directed at the Earth, and the direction of its movement is shown in Figure 5. The parameters of the environment in orbit are given in Table 4.  Eight sampling points equally distributed in the orbit are taken for the study, as shown in Fig. 6. The orbital times corresponding to the sampling points are shown in Table 5.   The simulation results are shown in Table 6, including the maximum temperature difference and the moment when they occurred.  Figure 7 shows the characteristic temperature deformations of the reflecting and lateral surfaces of the reflector. The greatest deformations are observed on the lateral surface, but it does not participate in the reflection of the signal. Therefore, in the further analysis, only the reflecting parabolic surface of the reflector will be considered. By counting the obtained thermal deformation data, the maximum deformation at different periods was obtained as shown in Table 7. Table 7. Thermal deformation calculation results of the structures It can be concluded from the table that the maximum deformation tends to occur in the spring and autumn equinox. It is assumed that the design retains dimensional stability if the maximum thermal deformation of the reflecting surface of the reflector does not exceed the permissible values. For modern reflectors, the maximum profile deviations should not exceed 0.1 mm. With the number of spiral ribs 30, the maximum deformation is no more than 0.083 mm, which satisfies this requirement. Figure 8 shows the relationship between the root-mean-square (RMS) value of the displacements of the reflecting surface and the orbital time. The greatest profile deviations Of the options considered, the most rational is a mount with 30 interlacing ribs (Fig. 9).

Fig. 2. Relationship between thermal deformation and the number of interlacing ribs
The mass of the mounting can be reduced by reducing the cross-sectional area of the ribs. At the second stage, the effect of the size of the ribs on the deformation of the reflecting surface of the reflector is investigated. For a structure with 30 interlacing ribs, options are considered in which the width and thickness of the ribs are reduced by two times, respectively, relative to the base dimensions. Reducing the thickness of the ribs has a less active effect on the deformation of the reflecting surface of the reflector ( Fig. 10 and Table 8). From the graphs and tables, the thickness-reducing variation results in a smaller maximum thermal deformation and a smaller RMS value of the reflective surface. Therefore, for the weight reduction design, it is reasonable to reduce the thickness of the ribs.

Conclusions
Variants of the shell mounting of the satellite antenna reflector in the form of a truncated cone of interlacing and annular ribs with high dimensional stability are proposed. The most rational is a mount with 30 spiral stiffeners, which ensures temperature movements of the reflecting surface of the reflector in a geostationary orbit of no more than 0.1 mm. It was found that in order to reduce the weight of the mount, it is advisable to reduce the thickness of the mesh shell ribs.