Dynamic Vibration Absorbing Performance of 5-DoF Magnetically Suspended Momentum Wheel Based on Damping Regulation
Round 1
Reviewer 1 Report
This paper presents a method to enhance the performance of a five degrees of freedom (5-DoF) magnetically suspended flywheel (MSMW) system subject to translational and torsional vibration effects. In the manuscript a detailed evaluation is presented. Laboratory and simulation results are interesting for this kind of system. However, I have some comments for the authors:
The presented model is based on transfer functions. Thus, how the nonlinear phenomena are considered in the model, or physically they are not present. Saturation effect?
What about severe perturbations, which conduct to the state variables far from the current steady state conditions? How is the desired performance guaranteed?
Please can you clarify the scope of the proposed method. Physical restrictions of system variables.
The laboratory results are attained under a controlled environment. Can you give more details about considerations to obtain the presented results?
The figures' quality must be enhanced.
Author Response
Ref: actuators-2304257 (Dynamic Vibration Absorbing Performance of 5-DoF Magnetically Suspended Momentum Wheel Based on Damping Regulation)
Authors reply to Reviewer 1 The authors thank the reviewer for the valuable comments on the manuscript. The manuscript is revised according to the reviewer’s suggestions. Moreover, it seems that the reviewer submitted the wrong comments. In this article, the nonlinear phenomena and the state variable are not mentioned in the submission.
Reviewers' comments:
Original comment:
Concern #1: Thus, how the nonlinear phenomena are considered in the model, or physically they are not present. Saturation effect?
Authors’ response: Thank you for your valuable comment! The nonlinear characteristics about the magnetic forces in the MSWM are not considered in this submission, and the magnetic forces are considered to a linear function about the control current and the rotor displacement. Moreover, the research focus of this article is about the damping regulation based on the feedback model.
On page 5 of revised manuscript:
The attractive magnetic forces generated by the axial 3-DoF AMB and the radial 2-DoF AMB could be approximately expressed as the linear functions about the displacement term and the control current
Concern #2: What about severe perturbations, which conduct to the state variables far from the current steady state conditions? How is the desired performance guaranteed?
Authors’ response: Thank you for your valuable comment! During the operation of the MSWM by regulating the rotating speed, the displacement variation of the flywheel rotor and the vibration at the high-rating speed could affect the stability of the MSMW, and then the damping coefficient is regulated to suppress the displacement variation of the MSMW.
On page 6 of revised manuscript:
During the operation process of the 5-DoF MSMW by regulating the rotating speed of the momentum wheel, the vibration displacement of the momentum wheel could affect the stability of the 5-DoF MSMW, and the vibration model should be established.
Concern #3: Please can you clarify the scope of the proposed method. Physical restrictions of system variables.
Authors’ response: Thank you for your valuable comment! The nonlinear characteristics about the magnetic forces in the MSWM are not considered in this submission, and the magnetic forces are considered to a linear function about the control current and the rotor displacement. Moreover, the research focus of this article is about the damping regulation based on the feedback model.
On page 6 of revised manuscript:
The attractive magnetic forces generated by the axial 3-DoF AMB and the radial 2-DoF AMB could be approximately expressed as the linear functions about the displacement term and the control current
Concern #4: The laboratory results are attained under a controlled environment. Can you give more details about considerations to obtain the presented results?
Authors’ response: Thank you for your valuable comment! The 5-DoF MSMW is located on the shock table, and then the disturbance could be imposed on the MSMW. In order to make the momentum wheel stable suspended at the equilibrium position, the damping and stiffness are regulated.
Concern #5: The figures' quality must be enhanced.
Authors’ response: Thank you for your valuable comment! The size and quality of figures had been revised in the submission.
Reviewer 2 Report
attached
Comments for author File: 
Comments.pdf
Author Response
Ref: actuators-2304257 (Dynamic Vibration Absorbing Performance of 5-DoF Magnetically Suspended Momentum Wheel Based on Damping Regulation)
Authors reply to Reviewer 2 The authors thank the reviewer for the valuable comments on the manuscript. The manuscript is revised according to the reviewer’s suggestions.
Reviewers' comments:
Original comment:
Concern #1: Abstract: the displacement reductions due to the anti-vibration measure shall be given in % comparing the vibrations without and with anti-vibration measure.
Authors’ response: Thank you for your valuable comment! The reduction is presented by the percentage in the abstract.
On page 1 of revised manuscript:
The results indicate that the displacement deflection of the translational vibration is reduced by 68.8% and the angle deflection of the torsional vibration is mitigated by 71.2% by regulating the damping coefficient.
Concern #2: Title of section 6: Experimental verification (or validation).
Authors’ response: Thank you for your valuable comment! The title of section 6 is revised to Experimental Validation.
On page 14 of revised manuscript:
Experimental Validation
Concern #3: Conclusion: the authors conclude that increasing the damping of the feedback controller reduces the translational and torsional displacements which seems to be an obvious result. Usually, there is an optimum damping gain which minimizes the target displacements (in this case translational and torsional). If the damping gain is further increased the resulting vibrations are increased again. Does this also apply to the system described here? In other words: could the authors perform tests with far greater damping gains to demonstrate that, first, an optimum damping gain exists, and, second, to determine this optimum damping gain?
Authors’ response: Thank you for your valuable comment! The damping coefficient could be optimized to obtain the better performance on the translational and torsional displacements considering the comprehensive performance of the MSMW. In this article, the relationship between the damping regulation and the displacement variation is developed, but the optimization of the damping coefficient is not considered. In the future work, the optimization about the damping coefficient could be considered.
On page 17 of revised manuscript:
To further regulate the translational and torsional displacements of the MSMW, the optimization methods about the stiffness and damping coefficients could be considered in the future work.
Concern #4: Conclusion: increasing the damping gain usually shows a negative impact on the band width of the feedback controller, i.e., on how fast the feedback controller can track the desired input, e.g., a step input. Is this the case here as well? Please discuss this issue.
Authors’ response: Thank you for your valuable comment! The band width of the feedback controller is 10 kHz, and this band width is far wider than the frequency of the translational and torsional vibration. Therefore, the influences on the band width caused by the damping regulation are not analyzed and considered in this article.
On page 5 of revised manuscript:
The bandwidth of the AMB is 10 kHz, and the damping regulation based on the feedback control causes a little influence on the bandwidth of the AMB.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper studied the dynamic vibration absorbing performance of 5-DoF magnetically suspended momentum wheel based on damping regulation. The characteristics of the torsional vibration and the translational vibration are investigated, the numerical simulations and experiments are conducted to verify the vibration characteristics of the magnetically momentum flywheel. Generally, this paper was well organized and presented. It could be accepted to future publication if the authors can address some concerns as listed below:
(1) This paper mainly discussed the dynamic vibration absorbing performance, and discussed the translational vibration and the torsional vibration respectively. Is there a coupling between the translational vibration and the torsional vibration? Please consider and state it.
(2) From the research results of this paper, the frequency of the response magnitude for the translational vibration is at about 85 Hz, the frequency of the response magnitude for the torsional vibration is at about 475 Hz. The rotating speed is 2000 rpm, which keep away from the torsional vibration frequency. What is the contribution of the torsional vibration to rotor vibration.
(3) The object of study is a disc rotor with gyro effect. How did the author consider it? It is recommended to elaborate further.
(4) This paper mainly focuses on theoretical analysis, numerical simulation, and experimental verification, but the description of how to carry out vibration control methods is not clear enough.
Author Response
Ref: actuators-2304257 (Dynamic Vibration Absorbing Performance of 5-DoF Magnetically Suspended Momentum Wheel Based on Damping Regulation)
Authors reply to Reviewer 3 The authors thank the reviewer for the valuable comments on the manuscript. The manuscript is revised according to the reviewer’s suggestions.
Reviewers' comments:
Original comment:
Concern #1: This paper mainly discussed the dynamic vibration absorbing performance, and discussed the translational vibration and the torsional vibration respectively. Is there a coupling between the translational vibration and the torsional vibration? Please consider and state it.
Authors’ response: Thank you for your valuable comment! In the practice, there are coupling terms between the translational displacements and the torsional displacements in the 5-DoF MSMW, but the research focus is tried to regulate the damping coefficient to suppress the vibration displacement, so the coupling terms are not considered in the article. Therefore, authors had added more texts to descript this point.
On page 3 of revised manuscript:
For the 5-DoF displacements of the MSWM, there are coupling terms caused by the dynamics coupling and the gyroscopic effect, but the coupling effect among 5-DoF displacements are not considered and analyzed in this article.
Concern #2: From the research results of this paper, the frequency of the response magnitude for the translational vibration is at about 85 Hz, the frequency of the response magnitude for the torsional vibration is at about 475 Hz. The rotating speed is 2000 rpm, which keep away from the torsional vibration frequency. What is the contribution of the torsional vibration to rotor vibration.
Authors’ response: Thank you for your valuable comment! According to equation (31), the frequency of the torsional vibration is determined by the stiffness coefficient, and the frequency of the torsional vibration could be increased with the stiffness coefficient. Moreover, the vibration frequency of the MSMW could be regulated to be far away from the resonance frequency of the torsional vibration, and then the resonant vibration of the torsional vibration could be avoidable. To clearly state this point, the more texts are added in the manuscript.
On page 13 of revised manuscript:
The frequency of the torsional vibration could also be regulated by the stiffness coefficient, and the resonant vibration of the torsion could be avoidable.
Concern #3: The object of study is a disc rotor with gyro effect. How did the author consider it? It is recommended to elaborate further.
Authors’ response: Thank you for your valuable comment! The coupling terms caused by the gyro effect are the main factors of affecting the stability of the MSMW. Especially, the displacement vibration of the MSMW could be serious when the momentum wheel works at the high rotating speed. In the final part of the manuscript, authors had added more discussion.
On page 17 of revised manuscript:
Moreover, the stability control of the 5-DoF MSMW could be investigated considering the gyro effect at high rotating speed.
Concern #4: This paper mainly focuses on theoretical analysis, numerical simulation, and experimental verification, but the description of how to carry out vibration control methods is not clear enough.
Authors’ response: Thank you for your valuable comment! The more details about the experiment are added in the manuscript.
On page 5 of revised manuscript:
Finally, based on the dynamic models of the 5-DoF MSMW and the feedback control loop, the suspension displacements of the rotor could be actively controlled. The bandwidth of the AMB is 10 kHz, and the damping regulation based on the feedback control causes a little influence on the bandwidth of the AMB.
On page 14 of revised manuscript:
In the experiment, the 5-DoF MSMW is located on the shock table along z-axis, and then the impulse and random disturbances generated by the shock table could be imposed on the MSMW. In order to make the momentum wheel stably suspended at the equilibrium position, the stiffness and damping coefficients could be regulated to generate the magnetic forces according to equation (10) and (11), and then the disturbance imposed on the MSMW could be actively suppressed.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The author has made modifications according to the suggestions and the currently submitted manuscript is acceptable. In addition, it is recommended to supplement the research on the impact of lateral and torsional vibrations.
Author Response
Authors’ response: Thank you for your valuable comment! When the disturbance is imposed on the lateral side of the MSWM, the radial displacement would varied with the disturbance force. This vibration characteristics are similar to the vibration of the momentum wheel along the axial direction.
On page 14 of revised manuscript:
For the translational vibration of the 5-DoF MSMW, the vibration characteristics along the radial axes are similar to the vibration along the axial axis, so the vibration characteristics of the MSMW along the axial axis is chosen as the example in the experiment.
Author Response File: Author Response.pdf
