the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Jun 2026
Fatigue-constrained gradient-based design optimization of main bearing–shaft systems for floating wind turbine drivetrains
Abstract. Floating offshore wind turbines have significant potential for economical and environmentally-efficient solutions for energy production. However, current state-of-the-art witnesses a lack of integrated analysis and optimization of these large, dynamically-coupled complex engineering machines and their critical sub-systems, such as the drivetrain, with research and experience still in their infancy. The aim of the paper is to facilitate efficient and holistic gradient-based multi-disciplinary constraint optimization of drivetrains by exploiting numerical models with varied fidelity-levels. This is illustrated through a constraint optimization of the main-shaft assembly, which includes critical fatigue-limit constraints of main-bearings, bridging design load case-based load spectra reduction with analytically-differentiable damage equivalent loads in contrast to conventional non-smooth bin-counting. The importance of fatigue as a design driver is shown by comparison to only static structural design. The proposed methodology is implemented as a modular extension within the open-source WISDEM-WEIS framework based on OpenMDAO, enabling efficient integration into existing multidisciplinary system-level wind turbine design workflows.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
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RC1: 'Comment on wes-2026-105', Anonymous Referee #1, 20 Jul 2026
- AC2: 'Reply on RC1', Vasudev Gupta, 26 Aug 2026
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RC2: 'Comment on wes-2026-105', Anonymous Referee #2, 20 Jul 2026
Comments
Technical comments
- Although the paper discusses coupled and system-level optimization, the hub loads are kept fixed, and the optimized design is not fed back into OpenFAST to calculate updated loads. The authors should clarify how coupled the presented method actually is.
- The main bearing configurations chosen for the paper needs more justification/discussion. In terms of both why these specific bearing types are used in these positions and why a double main bearing configuration is used instead of a single main bearing configuration.
- The rotational stiffness of the bearing is quite important in determining the results obtained. A discussion of how such a value was obtained is missing. Especially important would be its change with respect to differing bearing dimensions.
- Section 2.3.3 onwards: Inconsistency between LRD and LDD: LRD has been discussed but some amount of discussion and a figure is made while discussing LDDs.
- “The model enhances design accuracy and setup validity, matching real drivetrain physics better compared to the low-fidelity analytical equations.” This statement is to be further justified.
- Section 4.1: Results are presented but not discussed.
Structural comments:
- Add a list of abbreviations to improve comprehensibility of the paper.
- Not all figures, equations and tables in the paper are referred to within the text.
- When multiple sub-figures are part of a figure, please label each of them individually.
- Overall, derivations and formulas need to be explained in more detail and with each variable described for comprehensibility.
- Please make the citations consistent. Some appear to, for example, have important details, like the year of publication missing.
Citation: https://doi.org/10.5194/wes-2026-105-RC2 - AC1: 'Reply on RC2', Vasudev Gupta, 26 Aug 2026
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This paper achieves an multidisciplinary constrained mass optimization method for floating wind turbine drivetrains by introducing Damage Equivalent Loads (DEL) into a gradient-based optimization framework and proposing a main bearing analytical model that accounts for moment-reacting characteristics. Few comments are listed below:
1. The introduction repeatedly emphasizes the limitations of sequential optimization methods in industry and calls for fully coupled, system-level optimization. However, the experimental setup uses a traditional "two-step global-local decoupled approach," assuming fixed hub loads throughout the drivetrain optimization process. When system mass undergoes drastic changes of up to 48%, the structural frequencies will inevitably shift, subsequently altering the aeroelastic loads. Assuming constant loads weakens the credibility of the "coupled MDAO" core contribution.
2. The optimization process relies entirely on the analytical DEL surrogate model. After obtaining the optimal design (e.g., the converged design in Tab. 9), the paper fails to feed this design back into OpenFAST for full-time-series IEC DLC simulations. This step is crucial to verify whether the bearing fatigue life optimized using smooth DEL still strictly meets the standards in true transient time-domain conditions.
3. The authors criticize current research for "utilizing expensive genetic algorithms for drivetrain component design" in the background section. However, in the results section, they only compare the convergence of different gradient calculation methods. There is no direct quantitative comparison of computational time or global optimal solution quality against the criticized gradient-free/heuristic algorithms (like GAs, PSO), leaving the argument for its computational superiority insufficiently supported.