the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Oct 2025
Validation of a finite-element model of a 5 m three-row roller wind turbine blade bearing
Abstract. Large rolling bearings with complex interfaces need reliable finite-element models to determine the load distribution and deformation behavior. To ensure the accuracy of the results, it is important to validate the models against experimental data. Several works on models with different approaches are published but rarely is this validated. The present work now firstly validates a finite-element model of an original size three-row roller wind turbine blade bearing. For the validation, strain gauges are used to compare the deformation behavior of the bearing rings against experimental results. A characteristic of three-row roller bearings is the segmentation of one of the rings for manufacturing purposes. In this work, the authors investigate the influence of different coefficients of friction between the segmented outer ring and different bolt preloads on the occurring strain on the bearing rings. Two different sets of bolt preloads were considered: One to represent operational behavior with no relative movement between the segments of the split ring and one with gap opening and sliding to investigate nonlinear behavior of the bearing. The result of this work is a validated finite-element bearing and test rig model for different parameter sets and loads.
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Status: final response (author comments only)
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RC1: 'Comment on wes-2025-203', Anonymous Referee #1, 06 Nov 2025
- AC1: 'Reply on RC1', Matthis Grassmann, 18 Nov 2025
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RC2: 'Comment on wes-2025-203', Anonymous Referee #2, 25 Nov 2025
In this article, the authors present the experimental validation of a finite element (FE) model for a three-row roller bearing with an outer diameter of 5 meters designed for a wind turbine—an aspect that, as the author rightly points out, has been scarcely documented in the literature to date.
To validate the model, the experimental results are compared with those obtained through FE analysis, which includes modelling the actual test bench (Fraunhofer IWES BEAT 6.1) under representative conditions.
The study also examines the influence of various critical parameters, such as the friction coefficient, bolt preload, and nonlinear effects, on the validation results.
Regarding validation criteria, the author proposes two distinct approaches: first, the maximum deviation must be less than 10%, and second, the trend must match. These criteria are highly relevant, and although each author may define their own validation criteria, in my opinion, a minimum standardized criterion should be established.
The reviewer suggests addressing the following comments:General suggestions:
- In the context of wind turbines, although both terminologies are accepted, I would recommend using the term pitch bearing in this article instead of blade bearing. The author should consider this as a suggestion; however, I believe it is important to standardize the terminology.
- Please improve the resolution of Figure 7.
Specific comments:
- As mentioned earlier, the author defines two criteria for accepting the validation of the model. On what assumptions has the author based the definition of these criteria?
- In the FE model of the three-row roller bearing, the axial rollers are represented by five springs and the radial rollers by three. Could the author clarify which guideline was followed to determine this number of springs? Additionally, was a sensitivity analysis performed to evaluate the influence of the number of springs? Finally, was this choice supported by references in the literature?
- According to Figure 2, and as I understand it, the contact between the spring and the raceway appears to be defined over a larger area than the actual contact between the roller and the raceway. The entire raceway is divided into green segments, which suggests that there are no areas without contact. Is this interpretation correct? If so, the contact between the spring and the raceway would be greater than in reality. Has the potential impact of this on the results been analysed?
- The non-linear behaviour of the spring elements is controlled by a force–deformation curve derived from analytical calculations. As I understand it, this force–deformation curve is obtained for a cylindrical roller, whereas the actual roller used in the bearing is logarithmic. Could the author clarify how the formulation was modified to account for this difference?
- In the finite element model, frictional contacts between the flanges are defined with coefficients of friction of 0.2 and 0.5. Furthermore, the flanges of the bearings toward the surrounding structures are coated to increase the coefficient of friction to 0.67. Could the author explain the assumptions made to define these values? Additionally, was a sensitivity analysis performed regarding these coefficients?
- In line 141, the author states that the reaction frame is the bottom white steel structure that connects the rig to the foundation. Could the author clarify how this connection is modelled? What boundary condition has been defined for this connection?
- In line 149, the author states that in the first step gravitational loads and bolt forces are applied. Has the influence of the pretensioning sequence on the results been analysed?
- In line 170, it is stated that the measurement uncertainty is less than 2%, but its potential impact on the results is not analysed. I suggest adding a paragraph discussing the effect on the outcomes.
- In general, for the experimental measurements using strain gauges (figures 8-12), the scatter appears to be very low; the difference between maximum and minimum values across different points is minimal, although in some points the difference is noticeable. Could the author explain the reason for such low variation? Or what typical deviation do we observe across the different points?
- The results presented in Table 3 correspond to strain gauges. Although it may extend the length of the paper, in my opinion, it would be valuable to also include the results from the other sensors.
I would like to the authors for their work. This is a very interesting and neccesary contribution, as there are currently no references in the literature addressing this topic. By incorporating the suggested changes, I sincerely believe the manuscript will become a much more comprehensive and robust piece of work. Therefore, once the comments have been addressed and clarified, the reviewer considers that the manuscript is suitable for publication.
Citation: https://doi.org/10.5194/wes-2025-203-RC2
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In this manuscript, the authors present a detailed FE model to simulate the static response of a large three-row roller bearing intended for wind turbine applications. The ultimate goal of the study is the validation of this model, which is achieved by comparing experimental results with those obtained from the FEM, which includes the structure of the test rig itself.
The topic addressed is undoubtedly of great relevance to the wind energy industry, since such models are widely used both in the development and in the certification process of pitch bearings. The scarcity of references on the subject—mainly due to the confidentiality with which manufacturers protect their know-how—fully justifies the interest of this work for researchers and engineers working in the field. The manuscript is also well written and well organized, making it easy to follow and understand.
However, considering that the main objective of the paper is the validation of the FE model, this reviewer thinks that it is not described in sufficient detail for the work to be reproducible and, consequently, for its contribution to be significant enough. In addition, the considerable effort invested by the authors in developing the model, along with the undoubtedly expensive experimental campaign, could be further leveraged to draw more relevant conclusions that would help structural analysts of such components to develop reliable and efficient models.
For these reasons, this reviewer raises the following comments, grouped into two sections.
* General comments regarding the scope of the work:
- It would be highly valuable to provide a modelling guideline, offering a more detailed description of the model used and giving recommendations on aspects such as mesh size selection, contact configuration (beyond simply differentiating bonded/frictional types), and other modelling details discussed below.
- Only strain results are compared, although it seems it would have been quite straightforward to also measure displacements, which would allow assessing the model’s capability to predict bearing stiffness. While strains are undoubtedly an essential parameter for model validation, the relative deformation between the inner and outer rings is not considered, even though it is strongly influenced by some of the modelling aspects discussed later. A comparison between experimental and simulated displacements would represent a meaningful contribution, without complicating the experimental setup (for instance, this could be easily done using dial gauges). Is there any specific reason why this comparison was not made? Am I missing something?
* Comments regarding the model description:
- For the simplified modelling of the ball-raceway contact, it is indeed common to use a mechanism similar to the one proposed in this paper, where springs connect the curvature centres of the raceways. However, in the case of rollers, it is more typical to use a spring bed connecting the raceways directly (Golbach 1999) or even a single spring per roller (Kania 2006), without the need for the V-shaped mechanisms shown in Figure 2. Why was this mechanism chosen instead of a spring bed or a single-spring approach? Have different modelling options been tested and compared? It would be very interesting to evaluate different alternatives in terms of accuracy and computational cost, especially in a bearing with such a large number of rollers. Furthermore, why are used 5 or 3 springs per roller, and not more or fewer? Have simulations been carried out in this regard? What conclusions were drawn? Could any guideline be derived on the number of springs to use depending on the roller length or other parameters?
- Regarding the formulation of the roller–raceway contact, there are several alternatives to the one cited in the paper (Palmgren 1964). More recent formulations, such as those by Puttock (1969), Norden (1973), Tripp (1985), Johnson (1989), Hamrock (1991), or the more recent one by Houpert (2001), could also be considered. Is the Palmgren formulation the most suitable for simulating roller–raceway contact in the case of logarithmic profiles, as studied here? Were other formulations tested?
- Concerning the implementation of the FDC formulation, and if I understood correctly, each spring is connected to the whole raceway sector that corresponds to each roller. More details on this modelling choice would be required. Why was the spring connected to the whole surface instead of only to the area where the contact is expected (which would be much smaller)? Why not use a rigid-type (MPC/RBE2) spring-raceway connection? Have comparisons been made? Such tests could lead to useful conclusions in terms of accuracy and computational cost.
- Regarding the other contacts in the model, key details are missing, such as the formulation used in each case, the penetration tolerance or the normal contact stiffness (for penalty-based contacts), and other parameters that may significantly influence the model’s behaviour and displacements/stiffness results.
- As for the mesh, was a mesh sensitivity analysis performed? Were quadratic elements used throughout the model? Could any recommendations be provided regarding mesh size and element type?
- It is essential to describe the different load steps. Given the nonlinear nature of the model, the order in which loads are applied will influence the results.
- Concerning the simulation of the test rig, figures showing the mesh and model details are missing. The description of the test rig model—beyond that of the bearing itself—is rather brief.
Most of the above aspects might not have a major impact on the strain results reported in the paper, but they could significantly affect the relative deformations between the rings, i.e. the bearing stiffness, which is a relevant parameter to consider.
Many thanks to the authors for their work. I am sorry for being so meticulous regarding the modelling aspects, but I sincerely believe that the work carried out by the authors is of great value and that the manuscript could be significantly improved by addressing these. I am also confident that the authors will be able to respond to all of them, so I have no doubt that the paper could be published (at least from this reviewer’s perspective) once these comments have been taken into consideration.