Flexible Surface Reflector Antenna for Small Satellites

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The innovation of the work is to design, fabricate, and experimentally validate a novel deployable reflector antenna for small satellites. A doubly curved flexible surface reflector is manufactured using a triaxially woven fabric-reinforced silicone (TWFS) composite. To demonstrate the feasibility of this deployable reflector antenna, a reflector prototype is designed, fabricated, and tested. Before the manuscript is considered for publication, the authors are requested to clarify and revise the following issues:   

1. The strain is measured using a 3D strain measurement system known as ARAMIS. The measured strain field for the tensile specimen using ARAMIS is required to visualize the specimen's large deformation. The authors need to clarify how to experimentally determine the macroscopic equivalent modulus of the composite material.
2. The authors proposed that for TWF composites with stiff matrix materials, multiple modeling options (coupling, rigid beam) were used for tow-to-tow connections. The authors would benefit from being more explicit in detailing the method used in the current study to model tow-to-tow connections.
3. The authors should revise Fig. 3(a). The geometric dimensions and boundary conditions of the numerical model depicted in Fig. 3(a) in the current manuscript are unclear. For example, the unit cell must satisfy periodic boundary conditions. Once the periodic boundary conditions are properly set, the calculated macroscopic equivalent modulus should exhibit properties that are independent of the specimen's aspect ratio.
4. Figure 6 compares the deformation of the tensile test and simulation, but the physical quantities represented by the distribution contour and their physical meaning are missing and must be added.
5. The author must clearly explain the physical meaning of the physical quantities listed in Eq. (1).
6. The authors should revise Fig. 11 to better quantify the distribution of surface errors, specifically the surface error due to gravitational effects relative to the ideal parabolic shape. Figure 11 of the current manuscript does not show the distribution or magnitude of the error.
7. The introduction of the manuscript proposes that deployable reflector antennas must maintain precise surface accuracy, particularly for high-frequency applications such as Ka-band communications. Surface errors must be within λ/50 to λ/100 to ensure optimal performance. The authors report that the antenna surface has a current RMS error of 0.17 mm. However, the authors need to clarify whether this RMS error meets the requirements for optimal communication performance.

Comments for author File: Comments.pdf

Author Response

Comment #1.

The strain is measured using a 3D strain measurement system known as ARAMIS. The measured strain field for the tensile specimen using ARAMIS is required to visualize the specimen's large deformation. The authors need to clarify how to experimentally determine the macroscopic equivalent modulus of the composite material.

Response #1.

The strain was calculated using the ARAMIS software, based on the measured deformation data and the initial specimen length obtained through the ARAMIS system. The stress data were acquired from the tensile testing machine. Accordingly, the effective modulus of the TWFS specimen was determined from the linear region of the stress–strain curve. These details have been clarified and highlighted in blue in the revised manuscript.

 

Comment #2.

The authors proposed that for TWF composites with stiff matrix materials, multiple modeling options (coupling, rigid beam) were used for tow-to-tow connections. The authors would benefit from being more explicit in detailing the method used in the current study to model tow-to-tow connections.

Response #2

For the TWFS composite, accurate modeling of both the tow and the connection elements is critical for reliable prediction of mechanical properties. With precise representation of the connection, the beam finite element (FE) model offers the advantage of efficiently analyzing relatively large samples compared to 3D solid FE models. The simulation results show good agreement with the tensile test data, as presented in Figures 4 and 7. We have provided a more detailed description of the modeling methodology and its advantages in the revised manuscript.

 

Comment #3.

The authors should revise Fig. 3(a). The geometric dimensions and boundary conditions of the numerical model depicted in Fig. 3(a) in the current manuscript are unclear. For example, the unit cell must satisfy periodic boundary conditions. Once the periodic boundary conditions are properly set, the calculated macroscopic equivalent modulus should exhibit properties that are independent of the specimen's aspect ratio.

Response #3

We have revised Figure 3 to improve clarity and provided a more detailed description of the geometric dimensions and boundary conditions in the manuscript. These updates have been clarified and highlighted in blue in the revised version.

 

Comment #4.

Figure 6 compares the deformation of the tensile test and simulation, but the physical quantities represented by the distribution contour and their physical meaning are missing and must be added.

Response #4

The mechanical properties of the specimen in the 0° direction are not significantly influenced by the specimen size. In contrast, the properties in the 90° direction are highly dependent on the specimen dimensions. When loading is applied along the 90° direction, the load is primarily distributed along the ±60° fiber orientations. As a result, stiff regions develop near the fixed boundaries, while the effects of weaknesses at the free edges become more pronounced, as illustrated in the figure. Furthermore, the accuracy of the numerical model is validated through comparison with experimental results. Distribution contours have been added to the figure, and their physical significance is described in greater detail in the revised manuscript.

 

Comment #5.

The author must clearly explain the physical meaning of the physical quantities listed in Eq. (1).

Response #5

The revised manuscript provides detailed descriptions of the physical quantities defined in Equation (1).

 

Comment #6.

The authors should revise Fig. 11 to better quantify the distribution of surface errors, specifically the surface error due to gravitational effects relative to the ideal parabolic shape. Figure 11 of the current manuscript does not show the distribution or magnitude of the error.

Response #6

We have revised the figure to more clearly illustrate the distribution of surface errors caused by gravity.

 

Comment #7.

The introduction of the manuscript proposes that deployable reflector antennas must maintain precise surface accuracy, particularly for high-frequency applications such as Ka-band communications. Surface errors must be within λ/50 to λ/100 to ensure optimal performance. The authors report that the antenna surface has a current RMS error of 0.17 mm. However, the authors need to clarify whether this RMS error meets the requirements for optimal communication performance.

Response #7

It is well known that, for Ka-band applications, surface errors should be within λ/50 to λ/100. In this study, we evaluated the reflector performance through a near-field test for the X-band. Based on the critical values for the X-band, the surface error should be within 0.6 mm to 0.3 mm. The measured surface error of 0.17 mm, accounting for the effects of gravity, satisfies this criterion. It is further estimated that, without the influence of gravity, the surface error would be less than 0.1 mm. The near-field test also shows very good agreement between the experimental and simulation results. However, for Ka-band communication applications, further improvement of the surface accuracy will be necessary. These updates have been clarified and highlighted in blue in the revised version.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents the results of the development of a new deployable reflector antenna for small satellites. Experimental studies and results of numerical modeling were conducted. A deployment mechanism providing high surface accuracy during deployment was proposed. The manuscript is well structured and the results and methods are correctly described. Several comments arose during review.

1. Figure 3a, the scale is poorly visible. Please increase the size of the numbers.
2. Section 2.2b, line 127. The description of S₁₁ is not defined. Please write the physical meaning of S₁₁.
3. Figure 13. Please explain the formation of experimental drops at angles of +/-19

Author Response

Comment #1.

Figure 3a, the scale is poorly visible. Please increase the size of the numbers.

Response #1

The figure has been revised to enhance clarity.

 

Comment #2.

Section 2.2b, line 127. The description of S₁₁ is not defined. Please write the physical meaning of S₁₁.

Response #2.

In the revised manuscript, detailed explanations of the physical quantities, including S₁₁ ​, have been provided.

 

Comment #3.

Figure 13. Please explain the formation of experimental drops at angles of +/-19

Response #3.

The observed experimental gain drops at approximately ±19° are consistent with the theoretically expected antenna radiation pattern, which typically exhibits nulls due to the sinc-function characteristics of an idealized reflector antenna. These nulls arise naturally at predictable angles as a fundamental consequence of diffraction from the finite antenna aperture, rather than from structural imperfections or measurement errors. Minor discrepancies between the measured and simulated null positions or depths may be attributed to slight deviations in the deployed antenna surface or minor asymmetries. Nevertheless, the primary cause of the gain drops at ±19° is a natural and theoretically predictable phenomenon, not an anomaly or defect. These details have been clarified and highlighted in blue in the revised manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

I would like to begin my review by commending the authors for the substantial effort invested in this study. The article is well-structured, and the presented data is relevant.

The authors have done an excellent job in crafting a well-written paper. The introduction provides sufficient background information and includes appropriate references. The research design is well-conceived, with scientifically sound models that are adequately described. Additionally, the paper presents a validation of the numerical simulation, alongside a comparison between experimental and numerical results. The findings are clearly presented, and the conclusions are well-supported by the results.

Suggestions

As a recommendation, the authors may consider incorporating a discussion on the calibration procedures and potential sources of measurement error associated with the 3D strain measurement system (ARAMIS) and the digital image correlation (DIC) technique, particularly in the context of surface error measurement and 3D strain measurement. Addressing these factors could provide valuable insight into any discrepancies observed between the numerical simulations and the experimental results

Improvements

In Figure 7, the authors present the experimental layout, with the location of the tested material indicated by a red square. However, it would strengthen the manuscript if the authors included an actual photograph from the real testing setup to complement the representation.

Comments for author File: Comments.pdf

Author Response

Suggestions

As a recommendation, the authors may consider incorporating a discussion on the calibration procedures and potential sources of measurement error associated with the 3D strain measurement system (ARAMIS) and the digital image correlation (DIC) technique, particularly in the context of surface error measurement and 3D strain measurement. Addressing these factors could provide valuable insight into any discrepancies observed between the numerical simulations and the experimental results

Response

The calibration process requires a light source and a calibration panel, the size of which is determined by the dimensions of the object to be measured. The procedure is conducted as follows: first, the distance between the camera and the calibration panel is adjusted; second, the camera focus is fine-tuned, followed by adjustment of the aperture; and finally, three-dimensional calibration is performed by varying the position and orientation of the calibration panel. Measurement errors are closely linked to the quality of the calibration results, which can be influenced by inadequate lighting conditions and improper positioning or orientation of the calibration panel during the 3D calibration process. These details have been clarified and highlighted in blue in the revised manuscript.

 

 

Improvements

In Figure 7, the authors present the experimental layout, with the location of the tested material indicated by a red square. However, it would strengthen the manuscript if the authors included an actual photograph from the real testing setup to complement the representation.

 

Response

The figure was intended to illustrate the test setup; however, the actual measurements were conducted using the setup shown in the updated figure in the revised manuscript. This method is well known for its high reliability and minimal measurement error and has been adopted in previous studies [19]. In response to the reviewer’s suggestion, the figure has been revised to include the specimen used during the measurement.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors propose a novel deployable reflector antenna using TWFS composite as shell-membrane material. The paper is interesting and scientifically sound.

Minor comments:

• A more detailed comparison with similar deployment technologies would be recommended.
• In Section 2.1. (Fabrication of the TWFS Composite), the analysis of the specimen's aspect ratio could be illustrated by a figure.
• Have you characterized the electrical properties of the TWFS for different orientations to check the isotropy?
• The WR90 standard wave-guides employed for S-parameter measurements operate from 8.20 to 12.40 GHz. How have you measured from 2 to 22 GHz?
• The measured surface accuracy of 0.17 mm RMS should be given in terms of the wavelength.

Author Response

Comment #1.

A more detailed comparison with similar deployment technologies would be recommended.

Response #1

More detailed comparisons have been provided and clarified in the revised manuscript, with the updates highlighted in blue.

 

Comment #2.

In Section 2.1. (Fabrication of the TWFS Composite), the analysis of the specimen's aspect ratio could be illustrated by a figure.

Response #2

The aspect ratio of the specimen is illustrated in the revised manuscript.

 

Comment #3.

Have you characterized the electrical properties of the TWFS for different orientations to check the isotropy?

Response #3

Yes, the electrical properties of the TWFS have been characterized at different sample orientations, and the isotropic characteristics of the specimen have been clearly confirmed.

 

Comment #4.

The WR90 standard wave-guides employed for S-parameter measurements operate from 8.20 to 12.40 GHz. How have you measured from 2 to 22 GHz?

Response #4

The specific waveguides used in the measurement have been added to Figure 8(b) in the revised manuscript.

 

Comment #5.

The measured surface accuracy of 0.17 mm RMS should be given in terms of the wavelength.

Response #5

In this study, we evaluated the reflector performance through a near-field test for the X-band. Based on the critical values for the X-band, the surface error should be within 0.6 mm to 0.3 mm. The measured surface error of 0.17 mm, accounting for the effects of gravity, satisfies this criterion. It is further estimated that, without the influence of gravity, the surface error would be less than 0.1 mm. The near-field test also shows very good agreement between the experimental and simulation results. However, for Ka-band communication applications, further improvement of the surface accuracy will be necessary. The wavelength corresponding to the target operating frequency of 10 GHz has been added as a reference in the revised manuscript. These updates have been clarified and highlighted in blue in the revised version.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1. The authors use beam elements to model tow for the numerical model of the TWF unit cell. It is recommended that the authors provide the mechanical properties and geometric parameters of the beam elements.
2. Regarding the boundary conditions of the numerical model, the author has clarified the boundary conditions of the two nodes of each connection beam element, but the boundary conditions of the free end of the beam in the unit cell of Fig. 3(a) are unclear. Is it a free boundary condition, or does it need to be given a periodic boundary condition? Generally, triaxial woven fabrics are expected to exhibit quasi-isotropic mechanical properties due to their repetitive geometric pattern. The reviewer believes that if the periodic boundary conditions of the unit cell are given correctly, the equivalent mechanical properties of the unit cell should also satisfy the quasi-isotropic condition.
   
3. The labeling of “week edge” in Figure 6(b) is incorrect.

Author Response

Comment #1.

The authors use beam elements to model tow for the numerical model of the TWF unit cell. It is recommended that the authors provide the mechanical properties and geometric parameters of the beam elements.

 

Response #1.

The geometric parameters and mechanical properties of the beam are explicitly provided. These revisions have been clearly addressed and are highlighted in blue in the updated manuscript.

 

Comment #2.

Regarding the boundary conditions of the numerical model, the author has clarified the boundary conditions of the two nodes of each connection beam element, but the boundary conditions of the free end of the beam in the unit cell of Fig. 3(a) are unclear. Is it a free boundary condition, or does it need to be given a periodic boundary condition? Generally, triaxial woven fabrics are expected to exhibit quasi-isotropic mechanical properties due to their repetitive geometric pattern. The reviewer believes that if the periodic boundary conditions of the unit cell are given correctly, the equivalent mechanical properties of the unit cell should also satisfy the quasi-isotropic condition.

 

Response #2.

The unit cell model with periodic boundary conditions is commonly employed to evaluate the mechanical properties of triaxially woven fabric (TWF) composites, typically under the assumption of an infinitely large specimen. Under such conditions, the mechanical response of the TWF exhibits quasi-isotropic behavior. However, in this study, we further investigate the influence of the aspect ratio on the mechanical properties of a triaxially woven fabric reinforced silicone (TWFS) composite by considering the finite dimensions of the specimen. To this end, the finite-size specimens are modeled by periodically expanding the unit cell in the 0° and 90° directions, with each unit sharing nodal points with adjacent cells to maintain structural continuity, as illustrated in Figure 3(b). The lateral (left and right) edges are treated as free boundaries, while the upper and lower edges—where external loads are applied—are constrained using rigid body elements, each defined with a single independent node to impose uniform displacement. It is important to note that periodic boundary conditions are not applied in this analysis. These modeling details have been clarified and are highlighted in blue in the revised manuscript.

 

Comment #3

The labeling of “week edge” in Figure 6(b) is incorrect.

 

Response #3

Figure 6(b) has been corrected and updated in the revised manuscript.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

It can be accepted.