Structural Flexibility Effect on Spaceborne Solar Observation System’s Micro-Vibration Response

Round 1

Reviewer 1 Report

The paper under review discusses the accurate tracking of the turntable of a spaceborn solar observation system. Previous simulations included the active control and the rigid body motions of the continuous turntable, but not its flexural dynamics. These flexural (micro) vibrations do not have a major influence on the tracking, but decrease the optical performance of the system. The mathematical treatment seems sound and takes into consideration rigid and flexural dynamics, as well as electrical motor, and a simple active controller. The vibrational properties are derived from a finite element model. The dynamics of the turntable are truncated at the third vibration mode. Actual solar observations provided control inputs to simulations. Reduced-scale experiments were performed to validate the results. The effect of control frequency is taken into account. The comparison between experiments and simulations shows large discrepancies with respect to the simulations. However, there is a qualitative correspondence in the appearance of high frequency vibrations. The authors justify the discrepancies only in part with nonlinearity and damping uncertainty. Figures 1 and 2 do not add useful meaning to the paper and should be removed. In conclusion, the publication of the article is recommended although the experiment and conclusion sections could be extended and improved. 

Author Response

Response: Thanks a lot for the the reviewer’s comment. Figure 1 and 2 have been deleted and the experiment section has been revised. The authors agree with the reviewer that study has room for improvement and we will improve the study in further work.

Reviewer 2 Report

Peer review report on Structural Flexibility Effect on Spaceborne Solar Observation System's Micro-Vibration Response

Aerospace

The proposed study introduced a coupling model that integrates mechanical, electrical, and control models to investigate the structural flexibility effect on the micro-vibration response. The influence of flexible features besides studying the dynamic responses was considered. The acceleration responses of the rigid–flexible and rigid models under angle tracking modes were simulated.

The authors introduce a good work and the topic is attractive but some issues are summarized in

the following comments: 

1-     The introduction maybe need to be revised as the challenges, and contributions are more clear.  Also, shall be updated with more papers up to 2024. Authors may highlight the effect of catastrophic resonance in the study.

2-     Strengthening the literature in terms of the percentage of participating frequencies, studying the frequencies using FEM, and damping of vibration of harvesting materials as piezoelectric harvesting may be added, please see the following references may be proper

 “Tailoring the panel inertial and elastic forces for the flutter and stability characteristics enhancement using copper patches” Composite Structures  274  (2021)  114311.

Mechanical modeling and numerical investigation of earthquake-induced structural vibration self-powered sensing device.

Tailoring the panel inertial and elastic forces for the flutter and stability characteristics enhancement using copper patches.

3-     References for model equations may be added, mechanical model based on newtons or Lagrange…

4-     Assumptions of the model in both cases rigid and flexible models

5-     The model in equations 1, 3, and 10 doesn't include the stiffness part, it is required to add the stiffness part, the model only includes the inertia and damping parts.

6-     I think that the 2 degree of freedom model is a very simplified, more real, and complicated model that includes details like the bearing and other moving parts(coupling) that may be appreciated

7-     More details about the 2 DOF model in Fig. 5. Must be added, the dimensions of the model are based on previous work. Properties and dimensions of the model?

8-     The NO elements utilized in the FEM may be added, and a mesh convergence study needs to be conducted to show the model's accuracy.

9-     The basics of selecting the dimensions and materials of the model.

10- What is the importance of determining the natural frequencies in Fig. 5, what about the resonance study to avoid the failure and high vibration effects, information about the source frequency may be added.

11- For the modal participation study, it is commonly known that the first three modes contribute the main value of the vibration

12- In Figure 10, the control frequencies were chosen to be 2-10 hz, while the simulation frequency was from 0-200 Hz, what are the reasons? what about the excitation frequency (source of vibration frequency)

13- More discussions are recommended to be added to the results and discussion section

14- What is base of selection for the control frequencies

15- Figure 11(b) represents a rigid or flexible rigid simulation.

16- A dot in the title of figures must be added to the whole manuscript.

17- What is the type of controller in the experimental section

18- In Figure 10-a, what is the reason for beak acceleration at frequency=180 Hz?

19- the frequency error was approximately 10.3%, what are the reasons for this high error ?

Comments for author File: Comments.pdf

The article may be thoroughly revised.

Author Response

The authors appreciate the reviewer for your great effort and valuable and constructive comments. It is grateful to give the authors suggestions to improve the quality of this paper.

Below are the point-by-point answers to the reviewers’ comments.

Reviewer 2:

• The introduction maybe need to be revised as the challenges, and contributions are more Also, shall be updated with more papers up to 2024. Authors may highlight the effect of catastrophic resonance in the study.

Response: Thanks a lot for the reviewer’s comment. The introduction has been revised according to the reviewer’s suggestion. The challenges and contributions have been more clarified. The effect of catastrophic resonance in the study has been highlight. Some references up to 2024 have been added.

• Strengthening the literature in terms of the percentage of participating frequencies,studying the frequencies using FEM, and damping of vibration of harvesting materials as piezoelectric harvesting may be added, please see the following references may be proper “Tailoring the panel inertial and elastic forces for the flutter and stability characteristics enhancement using copper patches” Composite Structures 274 (2021) 114311. 

Mechanical modeling and numerical investigation of earthquake-induced structural vibration self-powered sensing device.

Tailoring the panel inertial and elastic forces for the flutter and stability characteristics enhancement using copper patches.

Response: Thanks a lot for the reviewer’s comment. The authors have read the recommended literatures which have been referred in the revised manuscript.

• References for model equations may be added, mechanical model based on newtons orLagrange…

Response: Thanks a lot for the reviewer’s comment. The reference for model equations have been added in Section 2.1.

• Assumptions of the model in both cases rigid and flexible models

Response: Thanks a lot for the reviewer’s comment. Assumptions of the model have been clarified in the revised manuscript.

• The model in equations 1, 3, and 10 doesn't include the stiffness part, it is required to addthe stiffness part, the model only includes the inertia and damping parts.

Response: Thanks a lot for the reviewer’s comment. Equation 1 represents the rotational motion equation of the turntable rotor. As the rotor rotates approximately unconstrained, the stiffness part is not considered in the manuscript, which is a common assumption. Equation 3 and 10 are the same as equation 1. The authors have added some explanations in section 2.1 of the manuscript to make it more readable.

• I think that the 2 degree of freedom model is a very simplified, more real, andcomplicated model that includes details like the bearing and other moving parts(coupling) that may be appreciated

Response: Thanks a lot for the reviewer’s comment. This manuscript mainly focus on the influence of flexibility on the motion of the turntable, so the model is simplified as a two degree of freedom rigid body and flexible body coupling model, and some details like the bearing and other moving parts were not considered. The reviewer's suggestions are very valuable, and we will consider these details in the future research.

• More details about the 2 DOF model in Fig. 5. Must be added, the dimensions of themodel are based on previous work. Properties and dimensions of the model?

Response: Thanks for the reviewer’s comment. The properties and dimensions have been added in the revised manuscript.

• The NO elements utilized in the FEM may be added, and a mesh convergence studyneeds to be conducted to show the model's accuracy.

Response: Thanks for the reviewer’s comment.There are no NO elements in this model. A mesh convergence study has been conducted.

The results of mesh convergence is as follows. It is shown that when the mesh size is less than 10, as the mesh size decreases, the first modal frequency converges to 119.6 Hz. As the calculation speed decreases with the mesh size, the mesh size 10 is adopted. The authors have added some explanations in the manuscript to make it more readable.

• The basics of selecting the dimensions and materials of the model.

Response: The turntable was designed in the previous study, and the material and dimentions of the model are determined by the real turntable’s material and dimentions.

• What is the importance of determining the natural frequencies in Fig. 5, what about theresonance study to avoid the failure and high vibration effects, information about the source frequency may be added.

Response: The natural frequency of the turntable may couple with the frequency of external excitation, resulting in structural resonance. Therefore, it is necessary to calculate the natural frequency of the turntable structure. These external excitations may be caused by the control frequency of the motor, motor noise , and nonlinear factors. The manuscript has added the information about the source frequency in Section 3.

• For the modal participation study, it is commonly known that the first three modescontribute the main value of the vibration

Response: Thanks for the reviewer’s comment. The reviewer is right that the first three modes contribute the main value of the vibration, but the participation proportion of the first three modes is unknown, so it is necessary to determine the truncation frequency by calculating the participation factors of the first n modes.

• In Figure 10, the control frequencies were chosen to be 2-10 hz, while the simulationfrequency was from 0-200 Hz, what are the reasons? what about the excitation frequency (source of vibration frequency)

Response: Thanks for the reviewer’s comment. The manuscript may be not clarified. The control frequency of 0.2-10Hz represents the number of instruction signals per second. But the frequency in horizontal axis represents the excitation frequency. These external excitations may be caused by the control frequency of the motor, motor noise , and nonlinear factors.

• More discussions are recommended to be added to the results and discussion section.

Response: Thanks for the reviewer’s comment. More discussions have been added in the discussion section.

• What is base of selection for the control frequencies

Response:Thanks for the reviewer’s comment. In order to avoid resonance caused by coupling between the control frequency and the natural frequency of the turntable, the manuscript chooses a control frequency lower than 1/10 of the natural frequency of the turntable. In order to choose a better control frequency, several typical control frequencies are selected to calculate the acceleration response and tracking error of the turntable, and optimize the optimal control frequency. In order to make the manuscript more readable, the authors have added some explanations.

• Figure 11(b) represents a rigid or flexible rigid simulation.

Response: Thanks for the reviewer’s comment. Figure 11(b) represents flexible rigid simulation. Explanation has been added to make the manuscript more readable.

• A dot in the title of figures must be added to the whole manuscript.

Response: Thanks for the the reviewer’s comment. All the titles of figures added a dot.

• What is the type of controller in the experimental section

Response: Thanks for the the reviewer’s comment. The controller is adopted a PI controller. The type of the controller is elmo’s BMTWID20SE. The authors have revised the manuscript to make it more clarified.

• In Figure 10-a, what is the reason for beak acceleration at frequency=180 Hz?

Response: Thanks for the the reviewer’s comment. The reason for the peak acceleration at about 180 Hz is that the third-order modal frequency of the turntable is 180.2 Hz, which amplifies the vibration of the turntable, resulting in a peak acceleration at about 180 Hz. The authors added some discussions to make the manuscript more readable.

• the frequency error was approximately 10.3%, what are the reasons for this high error ?

Response: Thanks for the the reviewer’s comment. The reason for the frequency error 10.3% is due to the inaccuracy of material properties and constraints in finite element simulation, which results in errors between the natural frequency of the finite element model and the natural frequency of the actual turntable, further affecting the error of the dynamic simulation of the turntable. The authors think that a 10% error is acceptable without using modal experimental verification. The author will improve the accuracy of finite element simulation in subsequent research to further enhance the accuracy of two-dimensional turntable dynamics simulation.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The quality of Figure 5 needs to be improved. 

The quality of English needs to be improved.

Author Response

1 The quality of Figure 5 needs to be improved.

Response: Thanks for the reviewer's comment. Figure 5 has been changed into a clearer version.

2 The quality of English needs to be improved.