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It is necessary to decrease the weight of space satellites, while maintaining their stiffness. To achieve this weight reduction, many structures, such as honeycomb and isogrid, have been reported in the literature. In this paper, the diamond rib method, a mechanical design method for improving the stiffness of structures, is introduced. By applying this method to a small space satellite, we propose a new structure called the “Diamond Rib Structure”. This structure significantly improves the ability to withstand the vibrational disturbances in a rocket fairing.

ChubuSat [

The rocket launch is shown in

other hand, the low natural frequency of the satellite depends on the satellite structure and the connection parts between the rocket fairing and the satellite. In particular, the low natural frequency of a small space satellite occurs around 100 Hz. The disturbance vibration frequency attributable to vibrations such as combustion vibration is close to the low natural frequency of the satellite. Induced by two disturbances with different frequencies, the total disturbance tends to resonate. Because of resonance, the entire satellite vibrates severely. The resonance may cause some damage to the observation equipment located on the sidewall of the satellite structure. Some damage may occur in the form of connection failures in electrical and electronic devices mounted on the observation system. Because of such damage, the satellite may fail to observe natural phenomenon such as natural disasters or severe weather events even if it can successfully position itself into orbit. The stiffness of the structure of a satellite should be increased so that the low-order natural frequency is just above 100 Hz. To avoid resonance and to increase the stiffness, the structures are generally reinforced by adding new mechanical elements such as ribs. Due to the weight limitation of a space satellite mounted on a launch rocket, this approach of reinforcing the satellite by adding mechanical elements is not acceptable because it increases the launch weight.

Previous studies have indicated that to maintain the reliability of satellite structures and to reduce the vibrations, sheet panels can be added on the surface of the structures. The weight of the sheet panels can be considered almost zero (See Ref. [

weight, it is necessary to optimize the arrangement of the ribs. To maximize the objective function, an optimum design method was applied to the shape of the structure. Optimum design methods generally consist of sizing optimization, shape optimization and topology optimization [

In this paper, the diamond rib method is described. This method is a type of sizing optimization. Using the method, the optimal panel, the diamond rib structure, was created. Aiming to develop a robust satellite, the diamond rib structure is applied to a 50-kg small satellite in

To estimate the natural frequency of a satellite structure, ω, the following equation can be used:

The variables m and k represent the mass and spring constant, respectively. In the case of a plate, the natural frequency, ω, can be obtained based on material properties such as the Young’s modulus and the second moment of the area. The natural mode of a panel in a 50-kg class small satellite is shown in

Various natural modes exist for each plate. By visualizing natural modes through simulation results, we can confirm the occurrence of antinodes or nodes at local areas for each plate. Deformation patterns of the natural vibration mode can be predicted by using the simulation technology. In general, the ribs of the structure were cut out from one plate so that the ribs were set with respect to the antinode of natural modes. However, if inserting ribs as shown in

The algorithm based on this method is shown in

A primary diamond arrangement was rotated from 0˚ to 45˚. The secondary diamond arrangement was created

by rotating the primary diamond arrangement. As inscribed in the primary diamond rib arrangement, the secondary diamond arrangement was obtained. As mentioned above, the procedure of diamond rib arrangement was repeated in the same way. Therefore, the diamond rib arrangements consisted of the primary diamond rib arrangement, the secondary diamond rib arrangement, the tertiary diamond rib arrangement, etc. Using the results of vibration analysis, we can find that some diamond arrangements cannot contribute to the increase in the natural frequency of the structure. The algorithm is terminated after removing a diamond arrangement that does not contribute to the increase in the natural frequency. In this method, the initial structure achieves to the optimal structure. In the paper, the optimal structure is referred to as the diamond rib structure.

As stated above, although this is a computer simulation method, it is possible to create a real panel. Using one flat plate, the diamond rib structure can be cut out using a cutting machine. The diamond rib structure does not require the use of special techniques such as welding technologies. A small space satellite can easily be manufactured with bolted panels. With the aim of developing a commercialized satellite, the diamond rib method can also contribute to cost reduction.

The algorithm of the diamond rib method is shown in

(Step 1) The 3D model of one panel in a space satellite is created using a software.

(Step 2) To calculate the 3D model by the finite element method, the 3D model is divided into meshes. The material properties, boundary conditions, and initial condition are inputted into the 3D model.

(Step 3) The natural frequency and natural mode are calculated using a CAE software.

(Step 4) The location of the antinode is confirmed by visualizing the natural frequency.

(Step 5) The antinode of the natural mode is surrounded by diamond ribs. The diamond rib arrangement is referred to as the primary diamond rib arrangement.

(Step 6) Using the 3D model with the primary diamond rib arrangement, natural frequencies and natural modes are again calculated using a CAE software.

(Step 7) As inscribed in the primary diamond rib arrangement, the secondary diamond arrangement is obtained. Using the modified 3D model, the natural frequency and mode are again calculated. Steps 5 to 7 are repeated until the natural frequency increases.

(Step 8) Based on the calculation results, if the n^{th} diamond rib arrangements do not contribute to the increase in the natural frequency, these ribs are removed from the panel.

(Step 9) The panels based on the n-1^{th} diamond rib arrangements are implemented in the space satellite.

(Step 10) Using the space satellite 3D model, the natural frequency and mode are calculated. We confirm that the natural frequency is over 100 Hz.

(Step 11) If the natural frequency is not more than 100 Hz, the high and the width of the ribs are varied by increasing the second moment of area or decreasing the weight.

(Step 12) The algorithm is terminated.

The optimal panel, based on the diamond rib method, is shown in

frequency and mass are 412 Hz and 1906 g, respectively. Compared with the mass of the flat panel, the mass of the optimal panel can be reduced by about 25%. On the other hand, the natural frequency (479 Hz) of the flat panel in

The reinforced panel with ribs is shown in

Using the optimal panel, the natural vibration and mode of a small satellite model are calculated. The natural mode of a small space satellite is shown in

In this paper, the diamond rib method was introduced and described. After checking the antinode pattern of the natural mode, the ribs pattern on the flat panel was arranged based on the antinode pattern. The ribs pattern was called the diamond rib structure. The diamond rib structure was applied to a small space satellite.

The conclusions are summarized as follows:

・ Compared with satellite structures with a flat plate, the mass of a small space satellite is reduced by about 25%, while the natural frequency of the optimal satellite almost matches the original design value for the small space satellite.

・ Special techniques, such as a welding technology, are not needed in the approach based on the diamond rib method. Therefore, it is possible to reduce the manufacturing cost of the small space satellite.

The diamond rib method was applied to the flat panel. The diamond rib method can also be applied to various other complex structures, only if the antinode of natural frequencies can be obtained by using a CAE software.

As the final goal, the diamond rib structure will be implemented in the 50-kg class satellite: ChubuSat.

Kazunori Shinohara,Masanobu Mizoguchi,Shintatsu Suzuki,Yasutaka Narusawa, (2016) Diamond Rib: A Mechanical Design Method for Improving the Stiffness of a Structure. Engineering,08,308-319. doi: 10.4236/eng.2016.86028