Structural Design and Modeling Analysis of an Active Magnetic Levitation Vibration Isolation System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents a novel five-degree-of-freedom active magnetic levitation vibration isolation system designed for high-precision applications. Its contributions include an electromagnetic-structure co-design method based on the equal magnetic reluctance principle for optimized force density, an explicit dynamic model that incorporates base kinematic excitation to clarify vibration transmission paths, and a coordinate reconstruction approach to resolve spatial mismatch between sensors and actuators. The theoretical development is systematic and rigorous. However, the study remains largely analytical and lacks FEM and experimental validation. Critical practical aspects such as magnetic saturation, flux leakage, and thermal effects are not sufficiently addressed. To meet publication standards, the authors should supplement the work with simulation results or experimental data to verify the performance and feasibility of the proposed design and models.

Revision Suggestions

1. The paper is currently confined to design and modeling. It is strongly recommended to include experimental data from a prototype or, at the very least, high-fidelity finite element analysis comparisons to validate the accuracy of the analytical force models.
2. Eq. (1) assumes an ideal air-gap magnetic field. In precision systems, flux leakage and fringe effects significantly impact output force. Please discuss how these non-ideal factors affect the linearization of the model under varying gap widths.
3. Some system parameters are scattered throughout the text. A dedicated system parameter table should be added to list the mass, inertia, stiffness coefficients, and electrical parameters of the physical prototype.
4. Magnetic levitation systems are inherently nonlinear. Since the model is linearized in Eqs. (29) and (32), please provide the displacement range within which the linearized model maintains sufficient accuracy.
5. Eq. (20) employs a small-angle approximation. While precision isolation systems have small displacements, large angular motions may occur during extreme disturbances or startup. Please specify the applicable boundaries of this model.
6. You introduce matrices and . Please verify and explicitly state that these matrices are non-singular given the specific geometric parameters of your design, ensuring the system is fully observable/controllable. The matrix notation in the equations is inconsistent with that used in the main text of the article.
7. Regarding the 12-tooth lateral structure, the main and auxiliary teeth share a common winding. Please provide a detailed analysis of whether this structure generates unwanted radial coupling forces when producing tilting moments.
8. The open-loop control block diagram in Figure 15 is overly dense with overlapping symbols. It is recommended to optimize the layout to clearly distinguish between sensor feedback paths and disturbance input paths.
9. What is the purpose of presenting the open-loop control block diagram for the lateral magnetic levitation system at the end of the article, given that no corresponding analysis is provided?

Author Response

We are very honored to receive the constructive comments from the editors and the reviewers regarding this paper. The comments provided by the four reviewers will help us further improve our research work and have clarified directions for our future studies. We also sincerely appreciate the editor for giving us the opportunity to revise our manuscript.

In the revised manuscript, we have rewritten the introduction and improved the description of the research motivation and innovation of this paper; modified the disturbance assumptions and stability analysis; discussed the performance of the observer; revised all figures and tables; conducted an in-depth analysis of the comparative experimental results. Below are our responses to the reviewers’ comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents an innovative structural design, electromagnetic force analysis, and control system modeling for an active magnetic levitation vibration isolation system. The logic of the manuscript is clear, and the figures and tables are generally well-presented. The work in this paper is solid, and it is recommended for acceptance after revision. However, there are a few areas where the manuscript could be improved or clarified:

1.  The phrase "Five-Degree-of-Freedom" appears frequently throughout the text. It is recommended to define the standard abbreviation "5-DOF" at the first mention and use the abbreviation consistently thereafter to improve readability and conciseness.
2. The dynamic modeling in Section 4.1 assumes the floater is a rigid body. However, for high-precision isolation platforms, structural flexibility might influence performance. It is suggested that the authors briefly discuss the validity of this rigid body assumption. For instance, is the first natural frequency of the floater significantly higher than the targeted isolation bandwidth?
3. In Section 4.2, the base vibration $z_{mr}$ is introduced as a disturbance input. To provide better context for the application, could the authors specify what kind of base vibration spectrum this system is primarily designed to suppress (e.g., low-frequency road noise, onboard machinery harmonic vibration, or broadband random vibration)?
4. Following Equation (32), regarding the linearization description, it is suggested to use the approximation symbol "$\approx$" instead of the equality sign to strictly represent the linearized relationship and distinguish it from the exact nonlinear model.
5. There are several minor formatting errors that need to be addressed. For example, there are missing citation placeholders represented as [?] or [[?]] in the text (e.g., Page 15, Line 412; Page 18, Line 504). Please carefully proofread the manuscript to ensure all references are correctly cited and formatted according to the journal's guidelines.
6. Figure 15 (referred to as Figure 2.15 in your note) depicts the open-loop control block diagram. As the variables ($x_a, x_b$) indicate this is specifically for the X-axis dynamics, it is suggested to explicitly state this in the figure caption or the main text to avoid confusion (e.g., "Open-loop control block diagram of the lateral magnetic levitation system (X-axis)").
7. The paper mentions the design of the electromagnetic actuator. In practical continuous operation, the temperature of the coils may rise, leading to resistance changes. Although a current loop is mentioned in Section 4.2, it would be beneficial to explicitly state that the closed-loop current control effectively mitigates the impact of resistance variations caused by thermal effects.

 

Author Response

We are very honored to receive the constructive comments from the editors and the reviewers regarding this paper. The comments provided by the four reviewers will help us further improve our research work and have clarified directions for our future studies. We also sincerely appreciate the editor for giving us the opportunity to revise our manuscript.

In the revised manuscript, we have rewritten the introduction and improved the description of the research motivation and innovation of this paper; modified the disturbance assumptions and stability analysis; discussed the performance of the observer; revised all figures and tables; conducted an in-depth analysis of the comparative experimental results. Below are our responses to the reviewers’ comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. The study is applied to an active magnetic levitation isolation system for high-precision equipment. To simplify the design and control, several idealized assumptions are adopted, including the absence of magnetic flux leakage and hysteresis, a uniform magnetic field within the air gap, a rigid floater, lateral symmetry of the system, a static payload, and no lateral base motion. However, these assumptions are difficult to realize in practical implementations and are highly sensitive to real-world uncertainties because of nonlinear magnetic behavior. As a result, the applicability and contribution of the manuscript to realistic engineering systems are limited.
2. The manuscript places substantial emphasis on structural design and modeling analysis under these idealized assumptions. But, it lacks comparative simulation results or experimental validation, which are necessary to substantiate the proposed design, modeling approach, and control strategy for real-world applications.
3. The authors are strongly encouraged to include experimental  by using a physical prototype to validate the accuracy and practicality of the proposed dynamic models.
4. Although the manuscript establishs a model that incorporates explicit base kinematic excitation inputs, the analysis is limited to vertical vibration suppression. Incorporating active rejection of complex, simultaneous multi-axis disturbances—both in simulation and experimental studies would demonstrate the overall capabilities and robustness of the proposed active magnetic levitation isolation system.

Author Response

We are very honored to receive the constructive comments from the editors and the reviewers regarding this paper. The comments provided by the four reviewers will help us further improve our research work and have clarified directions for our future studies. We also sincerely appreciate the editor for giving us the opportunity to revise our manuscript.

In the revised manuscript, we have rewritten the introduction and improved the description of the research motivation and innovation of this paper; modified the disturbance assumptions and stability analysis; discussed the performance of the observer; revised all figures and tables; conducted an in-depth analysis of the comparative experimental results. Below are our responses to the reviewers’ comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have fully addressed my comments on the manuscript. I believe it is suitable for publication in its present form.