Optimal Craig–Bampton Mode Selection for Nonlinear Flexible Multibody Analysis

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The research topic in this paper is closely aligned with industrial needs, and the authors focuses on the optimization of Craig-Bampton (CB) superelement mode selection in FMBS. The findings provide a feasible technical solution for efficient simulation of complex flexible multibody systems.The reviewer has the following comments on the manuscript.

1. The rationality of EBR method application needs to be improved. The excitation forces in EBR are set "arbitrarily" in the paper, while the mode selection result of EBR is highly dependent on the frequency and spatial distribution of excitation forces. Arbitrary excitation may lead to a lack of objectivity in method evaluation. It is recommended to supplement the analysis of the correlation between excitation force settings and actual aircraft engine operating conditions, or use typical operating condition excitation data for verification.
2. The analysis of the influence of nonlinear factors is insufficient. Model B introduces the nonlinear characteristics of the planetary gearbox, but the paper does not clearly analyze whether nonlinear factors (such as tooth contact, 3D motion coupling) will change the priority or accuracy performance of mode selection methods. It is recommended to supplement the correlation analysis between nonlinearity degree and mode selection effect, and improve the discussion on the adaptability of the method in strongly nonlinear systems.
3. The error evaluation index is too single. The paper only uses the relative error of bearing load as the accuracy evaluation standard, and does not involve the accuracy verification of key dynamic responses of flexible components (such as displacement, stress, vibration acceleration). It is recommended to expand the error evaluation dimensions to fully reflect the impact of the method on the prediction of the overall dynamic characteristics of the system.
4. Model A verification shows that both are optimal methods, but Model B only verifies the performance of LPF without comparing the performance of EIM in this model. It is recommended to supplement the test data of EIM in Model B to provide a more clear method selection basis for engineering applications.

Publication Suggestion

After supplementing and improving the above deficiencies, the scientificity, completeness, and practicality of the paper will be significantly enhanced, which meets the publication requirements of the journal Vibration.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a valuable and industrially relevant study on improving the efficiency of flexible multibody simulations through optimized Craig-Bampton mode selection. The comparison of multiple mode-ranking techniques on a realistic aircraft engine model is well-motivated and clearly presented. The results demonstrate significant computational savings while maintaining acceptable accuracy, which is of practical importance. However, the paper requires revisions to strengthen the methodological justification, clarify certain implementation choices, and improve the discussion of limitations before it can be accepted for publication.

1. The authors mention that fixed-interface modes are computed up to 5 times the maximum frequency of interest, but this maximum frequency is not explicitly stated. Providing this value (or the range) is essential for reproducibility and for understanding the scope of the modal basis used in the reduction. Without it, it is difficult to assess the generality of the conclusions or to replicate the study.
2. The paper highlights a quadratic relationship between the number of modes and simulation time, which is a key motivation for mode reduction. However, no explanation or hypothesis is provided for why this relationship holds in the specific FMBS context described. A brief discussion—whether it is due to the solver type, matrix operations, or contact handling—would strengthen the argument and help readers understand the scalability of the approach.
3. The Lenoir Participation Factor (LPF) method is applied with the simplification that interface mass matrices are neglected. While this is stated, the authors do not discuss the potential impact of this assumption on accuracy, especially in cases where interface masses are significant. A short commentary on the validity of this assumption in the context of the stator components studied would improve the methodological transparency.
4. The choice of truncation criteria (e.g., 90% or 95% of effective interface mass) appears to be based on literature recommendations or trial and error. However, the paper does not systematically explore the sensitivity of results to these thresholds. A brief discussion on how the selected thresholds align with the desired error tolerance in industrial applications would help readers better interpret the trade-offs between speed and accuracy.
5. The introduction provides a good general background in FMBS and model reduction. However, to better situate the work within the specific scope of the journal Vibration, it would be beneficial to cite and discuss relevant studies on multibody analysis and component mode synthesis that have been published in this journal in recent two years. Incorporating such references would demonstrate a clearer connection to the journal's community and provide a more nuanced context for the present contribution.

Author Response

See attached file

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Please refer to the attached document

Comments for author File: Comments.pdf

Author Response

See attached file

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper compares several approaches to the selection of modes to be used to represent substructures over a range of frequencies. It is generally well written; the problem statement and the goals of the analysis are especially clear. The methods considered are treated in appropriate detail and with adequate context. I believe this paper would be of interest to many readers of the journal, and I am pleased to recommend it be accepted for publication once the following points are addressed.

* At the point where Figure 1 appears in the Introduction, the problem has not been defined completely and so the quantitative results depicted there cannot be appreciated. I recommend this figure be moved to the point in the body where is it discussed in detail.

* Line 301 refers to "black boxes" in Figure 5. I think this should be "red boxes"; there are no black boxes visible in that figure.

* The definitions of the numerical scores on lines 360 and 361 are not clear regarding how they treat intermediate values.

* The conclusion ends with the words "this doctoral study". I would recommend omitting "doctoral" here.

The authors may wish to address the following minor points in the course of preparing their final draft:

* Variations on the word "non-linear" are spelled with and without a hyphen (e.g., on lines 39 and 40).

* l. 138: "considering the accounts for" -> "accounting for"

* The occasional use of "*" to indicate matrix multiplication is needless and potentially confusing.

* l. 154 should not be indented, and "where" should not be capitalized.

* Spaces (blanks) appear before some colons but not others (" :" versus ":").

* l. 191: "pulsation" -> "frequency"

* The term "degree of freedom" is abbreviated both as "dof" and as "DOF".

* l. 266: "bring gather" -> "gather"

* l. 289: "an" -> "and"

* The "scare quotes" appearing on lines 329, 330, and 334 are unnecessary and distracting.

* l. 371: "of was" -> "was"

* l. 400: "satisfying" -> "satisfactory"

* The journal names in References [1] and [2] are capitalized differently from the others.

Author Response

See attached file

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Accept