Dynamic Study on a Passive Damping Scheme for Permanent Magnet Electrodynamic Suspension Vehicle Utilizing Onboard Magnets End Effects

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper considers the passive damping solution for the magnetic levitation system (maglev). The authors optimize several parameters of the system in order to achieve maximum damping.

However, the optimization problem is not clearly formulated. In Figs. 2a and 2c, we see that the thickness and width of the magnets should be as large as possible, while the length of the magnet has a maximum effect on the damping force. This means that the maximum damping is limited by the geometric constraints of the magnets. Similar monotonic functions are also observed in Figs. 9, 11, and 12, but how can these be used for optimization remains unclear.

Regarding speed, the calculations were performed only for speeds ranging from 0 to 15 meters/second (Figs. 6, 7, and 9), which is very low compared to the actual speed of a maglev train. Moreover, the damping force decreases as the speed increases, suggesting that damping may be low at higher speeds. However, Figs. 15 through 19 show even higher speeds, which contradicts the results presented in Section 3.

Formula (5) is unclear. Why is the 10th order used when the 2nd order is typically used for band components?

The model's description in Section 4 is inadequate. It is difficult to understand the model's details.

The vibration reduction shown in Figs. 15, 16, and 18 seems to be insignificant, using dB values that are close to zero. The optimization seems unreasonable.

In conclusion, I must state that the submitted manuscript is not a scientific research paper. The model and optimization methods are not described in sufficient detail. The found effect seems too weak to be considered significant. I believe the paper will not be useful to readers of the "Actuators" journal.

Author Response

Comments 1: the optimization problem is not clearly formulated. In Figs. 2a and 2c, we see that the thickness and width of the magnets should be as large as possible, while the length of the magnet has a maximum effect on the damping force. This means that the maximum damping is limited by the geometric constraints of the magnets. Similar monotonic functions are also observed in Figs. 9, 11, and 12, but how can these be used for optimization remains unclear.

Response 1: Thank you for pointing this out. We agree with this comment. The optimization logic of this study follows a systematic approach: (1) Establishing the permissible dimensional range for permanent magnets based on prescribed train load standards and levitation capacity requirements; (2)Employing the levitation-to-damping force ratio as the primary optimization metric; (3) Analyzing electromagnetic force variations with respect to magnet length (l₀), width (w₀), and thickness (d₀); (4) Determining the optimal magnet configuration under these triple constraints. As detailed in Equation 2 (updated), we have supplemented the objective function formulation, and the final optimized magnet dimensions were derived through comprehensive analysis of the target function combined with the levitation-to-damping force ratio influence results presented in Figure 4.

Comments 2: Regarding speed, the calculations were performed only for speeds ranging from 0 to 15 meters/second (Figs. 6, 7, and 9), which is very low compared to the actual speed of a maglev train. Moreover, the damping force decreases as the speed increases, suggesting that damping may be low at higher speeds. However, Figs. 15 through 19 show even higher speeds, which contradicts the results presented in Section 3.

Response 2: We deeply appreciate the reviewers' insightful observations regarding the vibration damping mechanism. As clarified below,The Halbach permanent magnet array generates a strong magnetic field at both ends, where flux lines originate from the enhanced side, traverse the end regions, and terminate at the suppressed side to form closed loops - this constitutes the end leakage field. Based on this principle, our design utilizes the Halbach array's end leakage field for vertical vibration damping. In Figures 6, 7, and 9, the velocity range of 0-15 m/s refers to the PM array's lateral motion relative to the conductive plate. This low-speed regime is intentionally selected to exploit the larger magnetic drag forces for effective vibration suppression. We clarify that this differs from the maglev train's operational (longitudinal) speed, which was not the focus of these particular analyses.

Comments 3:. Formula (5) is unclear. Why is the 10th order used when the 2nd order is typically used for band components?

Response 3: We deeply appreciate the reviewers' time and effort in reviewing our work.  Equation (5) presents the Sperling index evaluation parameter formula. In rail transportation applications, the Sperling index implementation follows two distinct international standard systems: The UIC 513/UIC 518 standards from the International Union of Railways utilize 2nd-order filtering primarily for conventional frequency band analysis, while the Chinese National Standard GB/T 5599-2019 and German DIN 45669 specifications recommend 10th-order Butterworth filtering to better accommodate the wide-band vibration characteristics inherent in high-speed maglev systems.

Comments 4: The model's description in Section 4 is inadequate. It is difficult to understand the model's details.

Response 4: We sincerely apologize for the insufficient clarity in our initial explanation. Figure 13 presents both the 3D SIMPACK multibody dynamics model and the 2D topological diagram of articulated connections, with detailed structural and parametric specifications primarily shown in Figure13(a). To ensure full reproducibility, we have provided the complete SIMPACK model package (including all boundary condition settings and parameter configurations) as supplementary material.

Comments 5: The vibration reduction shown in Figs. 15, 16, and 18 seems to be insignificant, using dB values that are close to zero. The optimization seems unreasonable.

Response 5:. We sincerely appreciate your attention to the vibration damping performance. The key innovation of this work lies in developing a novel auxiliary damping approach utilizing the end leakage magnetic field of Halbach permanent magnet arrays. Although the absolute damping improvement (in dB scale) appears relatively modest, this method holds significant value as it systematically exploits this traditionally neglected magnetic field for vertical vibration suppression - requiring no additional magnetic field assistance or excitation devices, thereby offering distinct advantages in structural simplification. Importantly, this approach serves as an effective complementary solution that can be integrated with conventional passive damping plates or damping magnets to enhance overall system performance.

 

Reviewer 2 Report

Comments and Suggestions for Authors

The research presented in this article is highly applied, they use techniques that are far from original, but the intended application is of great interest. The scientific approach is rigorous. The methodology is based on parametric optimization which, while not very effective, does have the merit of producing easily interpretable results. The influence of the various dimensional parameters of the damper system is very well analyzed. The negative point that needs to be emphasized is the relative poverty of the bibliography, which does not go beyond the railway framework and pays little heed to the great diversity of research carried out internationally on dynamic eddy current damping systems.

The curves showing the influence of a parameter on a characteristic must imperatively recall at what values the other parameters are fixed; most of the parametric variation curves are concerned.

Author Response

Comments 1: The negative point that needs to be emphasized is the relative poverty of the bibliography, which does not go beyond the railway framework and pays little heed to the great diversity of research carried out internationally on dynamic eddy current damping systems.

Response 1: We sincerely appreciate your constructive critique of the reference section. Comprehensive international literature on dynamic eddy current damping systems has been incorporated in the revised manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

The study presents issues related to modeling vertical damping in the suspension of PMEDS vehicles. Magnetic levitation vehicles (PMEDS), like all vehicles interacting with the track/surface on which they move, interact with the road and require damping of this interaction in the suspension system.
The SIMPACK software selected by the authors is a recognized software for performing MBD (Multibody Dynamics) analyses. The authors correctly presented the vehicle parameters and the vehicle model structure used during the dynamic tests. The measurable result of simulating the dynamics of a vehicle suspended on a magnetic cushion was the presentation of the damping forces in the suspension and the levitation forces of the vehicle as a function of the gap between the magnetically interacting elements.
The study focused on presenting the results of vehicle bogie vibrations, expressed as changes in acceleration while driving at different speeds on a straight track. The authors presented the results of tests in the speed range of 40-120 m/s. The selected range corresponds to the operating speeds of the vehicle in question.
In Figure 16 of the study, the authors present the results relating to the original and optimal bogie design. In the submitted research, the distinction between the optimal and original versions is not clear; the work would benefit from greater clarity if the authors were to specify or elaborate on the differences between the optimal and original designs.
The conclusions presented in the chapter are very concise but sufficient. In a few sentences, the authors presented the most critical issues discussed in the article and the resulting changes in vehicle behavior in the context of geometric and structural changes in the vehicle's magnetic suspension.
The literature sources used are accurate, and all graphics used by the authors are sourced from internal sources.

Author Response

We sincerely appreciate the reviewer for their insightful comments and constructive suggestions. Their professional perspective has helped us identify several important limitations that we had initially overlooked in our study. By carefully addressing these valuable concerns through additional experiments and refined analyses, we have significantly strengthened the methodological rigor and improved the overall quality of the research. The manuscript has been substantially enhanced through this revision process.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper has not been significantly revised. There are only two minor additions to the text.
Despite these additions, the paper remains unclear and I do not believe it is suitable for publication.

Author Response

Comments 1: the optimization problem is not clearly formulated. In Figs. 2a and 2c, we see that the thickness and width of the magnets should be as large as possible, while the length of the magnet has a maximum effect on the damping force. This means that the maximum damping is limited by the geometric constraints of the magnets. Similar monotonic functions are also observed in Figs. 9, 11, and 12, but how can these be used for optimization remains unclear.

Response 1:

We sincerely apologize for the lack of clarity in our initial optimization approach that solely relied on the levitation-to-damping force ratio Rc as a single performance metric. This paper will elucidate the optimized methodology through three key aspects:

1)Principle: Regarding the damping analysis of permanent magnet electrodynamic suspension (PMEDS) systems, conventional approaches typically fall into two categories: active control and passive damping. Both methods require additional magnets/coils or damper plates to enhance system damping. In contrast, this study innovatively utilizes the end leakage magnetic field of permanent magnets—a traditionally overlooked aspect in PMEDS systems—to provide inherent damping through the longitudinal edge effects of the magnets themselves. Figure 1 illustrates the working principle of these longitudinal edge effects.    Note: Figure 1 is provided in the supplementary materials.

2) Optimization methodology: The longitudinal edge effects of permanent magnets are closely related to their dimensions. While stronger edge effects theoretically improve vibration suppression, they must be carefully balanced with levitation performance, as excessive edge effects can compromise suspension stability. Our team's prior research has established a robust design methodology through extensive optimization work. Building on this foundation, the current study further explores enhanced damping characteristics by supplementing the existing lift-to-drag ratio optimization with dedicated damping structure optimization.

3) Improvement: To systematically improve the research methodology, we have made the following essential additions in Section 3.2 "Damper Structure Optimization": first, we established the optimal damping force objective function in Equation 4 considering the effects of speed (0-15 m/s) and damping plate thickness (2-40 mm), and determined the optimal damping plate thickness meeting levitation requirements through parametric scanning analysis (Figure 7); simultaneously, we supplemented the objective function in Equation 6 accounting for speed and gap (8-20 mm) influences, and identified the optimal gap based on parametric scanning results (Figure 12).

 

Comments 2: The vibration reduction shown in Figs. 15, 16, and 18 seems to be insignificant, using dB values that are close to zero. The optimization seems unreasonable.

Response 2:

We sincerely apologize for the insufficient clarity in our previous explanation regarding the relatively modest vibration reduction effects observed in Figures 15, 16, and 18. To better elucidate the damping performance of this method, we provide the following comprehensive analysis:

1) Optimized damping performance analysis: Current damping optimization in PMEDS systems has inherent limitations. As shown in Figures 15-18, while the vibration reduction appears modest, comparative analysis with Reference [17]'s passive damper plate method reveals critical advantages: conventional passive dampers lose effectiveness at high speeds due to their dependence on gap magnetic fields that diminish with velocity. In contrast, our method utilizes the magnets' longitudinal edge effects, achieving velocity-independent damping that actually improves with transverse vibration speed without compromising levitation gap. This provides a viable solution for PMEDS systems, as validated through system dynamics analysis.

2)Optimal damping approach: Although active control theoretically offers superior damping, its implementation in PMEDS systems introduces intractable challenges - including control complexity, thermal issues, and time-delay problems at ultra-high speeds (e.g., the 1040 km/h system developed by the Institute of Electrical Engineering, CAS ultimately adopted passive damping due to these constraints). Our passive method demonstrates clear advantages over conventional passive damper plates in both principle and performance.

We sincerely apologize once again for these limitations, and we will continue to refine and deepen our research on vibration damping to develop more effective solutions that advance PMEDS technology.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

There have been no significant changes to the revised paper, and the issues remain the same. Therefore, I cannot recommend publication of the paper at this time.

Author Response

Comments:There have been no significant changes to the revised paper, and the issues remain the same.

Response:

In response to the relatively modest vibration reduction effects observed in Figures 15-18, this study introduces new dynamic analyses of an individual levitation unit (comprising one permanent magnet array set with damping structure) in Section 4. The investigation specifically examines the dynamic responses of the magnetic and damping components without bogie involvement, thereby validating the structure's effectiveness under conditions requiring neither additional magnetic field assistance nor excitation devices.

Thinking: The research methodology progresses systematically through four key phases: initially constructing a single-degree-of-freedom levitation model in SIMPACK based on the optimized magnet and damping structure from Section 3; subsequently applying time-varying external excitations converted from measured track vertical irregularities to the permanent magnets to examine system responses under complex disturbances; then quantitatively analyzing vibration accelerations and peak displacements of both the equivalent vehicle body and permanent magnets in an individual levitation unit (one PM array with damping structure) under these excitations; and ultimately conducting comparative dynamics analysis between damped and undamped configurations to validate the solution's effectiveness without requiring supplementary magnetic field assistance or excitation devices. The research methodology progresses systematically through four key phases (all implemented in Section 4.1, It is indicated in red font).

Improvement: Passive vibration damping in PMEDS systems has long remained a significant technical challenge. While the damping structure presented in this study shows relatively modest performance compared to active control or bogie-mounted air spring systems, it offers distinct advantages by maintaining consistent effectiveness regardless of longitudinal operating speed or gap magnetic field variations. Notably, this solution demonstrates clearly superior damping capability compared to conventional PMEDS damping plate configurations as documented in Ref. [17], indicating strong potential for real-world implementation. The design's speed-independent operation and reliable performance under variable gap conditions represent meaningful progress in passive vibration control for PMEDS applications.

We sincerely appreciate the experts' valuable guidance and suggestions, and we will continue to enhance our research capabilities, further refining and deepening our investigations into PMEDS vibration damping to develop superior solutions that advance PMEDS technology.

Author Response File: Author Response.pdf