the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jan 2024
Load case selection for finite element simulations of wind turbine pitch bearings and hubs
Abstract. Finite element simulations of large rolling bearings and structural parts are an indispensable tool in the design of wind turbines. Unlike simpler structures or smaller bearings in rigid environments where analytical formulas suffice, wind turbine components require a more comprehensive approach. This is because analytical formulas often fall short in predicting load distributions and stresses, leading to inadequate designs. However, due to the size of the finite element models and operational loads involved, it’s necessary to strike a balance between achieving realistic results and keeping computational times manageable. This study focuses on the selection of load cases for simulations of pitch bearings and hubs of wind turbines. The models for these contain the hub, the pitch bearings, the inner parts of three blades, and any necessary interfaces parts. The simulation results allow the calculation of static and fatigue strength. Given the complexity of the problem, with each rotor blade having six degrees of freedom, five types of loads, and the pitch angle, the potential combinations of loads would result in an unmanageably high number of required simulations. The present work exploits relationships between load components and the rotor position to reduce the number of load cases needed for fatigue calculations. The IWT 7.5-164 reference turbine and three commercial turbines serve as the basis for case studies which include bin counts and exemplary finite element simulations. The blade’s azimuth angle and bending moments of one blade allow determining the loads at all three blade roots with a reasonable degree of confidence.
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RC1: 'Comment on wes-2023-163', Jonathan Keller, 31 Jan 2024
In this paper, the authors present a methodology for selection (or really, downselection) of load cases related to finite element analyses of a pitch bearing design. In general, the paper is well written and structured and presents a nice contribution on the topic of pitch bearing design.
Lines 4-5: I believe this sentence could be written a bit better, as I’m not sure the “size” of the model or the (magnitude) of the operational loads matters. I think the sentiment being expressed is something like “However, due to the number of contacting bodies and operational load cases involved, it’s necessary to…” Then again, in the case of a structure such as a pitch bearing, it’s more like the small size and large number of contact patches compared to the large overall size of the bearing itself that is what we mean by “size” of the model. But, I think the provided sentence gives the proper gist of things.
I will admit the large number of very short paragraphs typically of 1-3 sentences in Sections 1 through 2.1 make things a bit hard to read. I recommend a little effort to group like paragraphs together. For example, the paragraphs in lines 16-43 and then separately 44-56 can all be combined into a single paragraph. Sections 2.2 through 4 are much better.
Figures 1 and 2: If possible, I believe it would be helpful for the reader to label each box that corresponds to the descriptions in the text. For example, in Figure 1 it might be “Load time-series”, “Rainflow counts”, “Rotor model”, “Finite element analysis”, and “Stress calculations”.
Lines 72-74: I think the second version of the sentence is written more clearly than the first, honestly, as I don’t think we’re talking about “signals”. It is most easily cleared up by changing the first sentence to “…to which the loads on a pitch bearing are affected by not only the loads on the blade to which it is connected, but also the loads from the other blades as transmitted through the hub.” I’m not sure if the second sentence is then needed, or maybe the first can be deleted and just the second kept.
Although nice to have, I believe Figures 3-5 could be placed side-by-side or otherwise condensed a bit more, as 3 independent figures here seem a bit overkill. I suppose that’s just a preference thing though. I would label the primary and secondary blades in Figure 5 (or some version of it) though.
Lines 103-106: I am curious as to the message intended here. Everything is pretty cut-and-dry to this point, but these sentences beg as may questions as they answer, or maybe they don’t answer anything at all? It almost feels like it’s a description of future work that might be included in a conclusions section. I don’t have any more specific comment here, but rather I’m just generally a bit puzzled as to what to make of these sentences.
Section 2.3: I’m also a bit confused by the title of this section and the description of “missing” pitch angles. I believe what lines 111-115 is saying is that the pitch angles of the secondary blades can simply be assumed the same as the primary blade. In that respect, it’s not missing, so it feels like this statement is better suited in the previous section. Similarly with the hub moments, as these are best derived from the blade root moments. I guess I also don’t understand how the blade azimuth angle would be “missing” from a simulation. Overall, I believe some additional context would be helpful here, or my other suggestion would be to just combine this with Section 2.2. I really must be missing something, as later on I also don’t seem to understand the value of Figure 12.
Table 1: I will admit I only “sorta” get what is being described here, but also sorta not. I was also puzzled by the statement “The results are arbitrarily chosen”. It feels like a better use of some text would be to maybe show an example real result for the IWT7.5 in an Appendix, if such a result would be too long in the main body.
Figure 8: It’s a bit hard to interpret as is. I see in the second row that the moments are thick lines and the forces thin ones. But I don’t see any thick lines in the first row? It also looks like there are two sets of thin lines in the first row, one solid and one dashed, but the text says only one force? It also feels like 30 seconds is more than needed, something like 20 seconds (or 3 revolutions) is probably sufficient. I might also suggest expanding the plot vertically, or plotting on a 2x2 grid rather than a 4x1 grid to make the plots more visible.
Figure 9: What do the vertical yellow lines indicate?
Figure 11: Is currently quite small and should be increased in size, especially the font size.
Minor typos:
Line 7: I think it should be “…interface parts” or “…interfacing parts”.
Line 34: I believe the citation style here should look like “Chen and Wen (2012) simulated…”
Line 313: I believe the volume, issue, page numbers and doi are missing from Chen and Wen. 134 (4): 041105, https://doi.org/10.1115/1.4007349.
Line 134: Missing space between sentences.
Line 186: I think what is being described here is the “bolt holes”, instead of “bore holes”. Similar in line 187. Maybe this is just me though, and “bore hole” is common in the pitch bearing community.
Line 191: I’m not sure what the “As axial location” here indicates.
Line 222: I believe it should be “Both moments had positive effects…”
Line 292: I believe the citation style here should look like “…based on in Becker and Jorgensen (2023).”
Citation: https://doi.org/10.5194/wes-2023-163-RC1 -
CC1: 'Comment on wes-2023-163', Patrick Müller, 10 Oct 2024
Please find a version of this document commented by thyssenkrupp rothe erde Germany GmbH Bearing Calculation Department in the attachment.
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer. -
RC2: 'Comment on wes-2023-163', Anonymous Referee #2, 05 Dec 2024
General Comments:
- The abstract could be improved by summarizing the methodology for reducing the number of load cases and stating the main results of the case study.
- The authors use many short paragraphs. Readability could be improved by rearrangement of paragraphs
- At times, the authors refer to results/findings of previous studies and assume knowledge about these findings from the reader. I suggest checking references throughout the manuscript and considering elaborating on explanations.
- At times, the manuscript reads like a project report, where prior knowledge about methodologies, procedures, and data sets can be assumed. I suggest checking the manuscript for understandability from the perspective of an uninformed reader and adding context where needed.
Specific Comments:
- Line 12: It is unclear what bin counts refer to here.
- Line 13: It is not clear what a reasonable degree of confidence means here. Can the accuracy and confidence of in the method be quantified?
- Line 27: Do the authors mean at each time step of the aeroelastic simulation?
- Line 29: A short explanation/estimation of the required computational time would be helpful for context.
- Line 32: Is it assumed that pitch-bearing loads are influenced by each other or that they are correlated?
- Section 2.2: In this section, the authors explain the signals used but do not explain the input data sets used. A clear overview of the used data sets and their origin would be helpful.
- Line 99: Input data to FE-Simulations?
- Line 103-106: The meaning of this section is not clear. Are additional signals included or not? Why?
- Line 138: The paragraph lacks clarity and should be revised. What is time series file duration, to which simulations is it referring? The weighting procedure and statements about dependencies are not clear.
- Table 1: It should be clearly explained what the columns of the tables are referring to and what can be seen from the given numbers. Please also revise the caption.
- Line 145-150. To what data set is the table referring? The bin counting procedure is unclear for the uninformed reader, and explanations should be revised.
- Section 2.5: This section could benefit from a brief explanation of the mentioned models to give the uninformed reader some context.
- Line 157: I'm unsure what “different scenarios” refer to here. A more detailed explanation would be helpful.
- Line 163: Does this mean the above calculation for “missing signals” is not used in this case? Please clarify.
- Line 164, Figure 7: What can be seen from the figure?
- Figure 8: Please add legends to the plot. In the top row, which lines are moments and which are forces? A more detailed caption could also be helpful for interpretation of the figure. Are there specific findings the authors want to highlight showing the figure?
- Line 175: More context on the two commercial turbines data sets would be useful. Is it simulated data or measurements? What are the differences in design, rating, onshore/offshore, and the implications for the present study? It is mentioned that the data sets contain different load cases (production vs. extreme loads). What is the implication of that?
- Figure 9: Please add legends.
- Line 189: Is this an assumption, or is it known? Can a reference support this?
- Figure 11 and explanation: It is hard to visualize which situation is shown here. Could a second plot showing the mentioned axis help?
- Line 201: This statement needs more explanation.
- Section 3.3: I believe this section will become clearer with an elaborate methodology explanation in section 2.4. I suggest carefully revising it, considering an overview of investigated cases, scenarios, and turbines /data sets.
- Section 3.5: I think the azimuth angle calculation could be included in section 2.3, while the results can be shown in the results section. This would also allow a direct comparison between the results in Table 9/6.
Citation: https://doi.org/10.5194/wes-2023-163-RC2 -
EC1: 'Comment on wes-2023-163', Nikolay Dimitrov, 05 Dec 2024
I would like to complement the existing reviews of the paper by several additional comments (so-called review by editor):
General comments
- It is positive that the authors consider the potential interaction between multiple blades. However, I believe in their current setup the authors have omitted the discussion of a potentially important part of the problem, which is the way the hub is modelled in the aeroelastic simulations. This model is very often simplistic with little or no flexibility in the hub assembly. Please discuss the way hub deformation is modelled in the aeroelastic simulations and if that may have an effect on your calculations and conclusions.
- It seems to me that with their selection algorithm, the authors are doing a sort of ad-hoc analysis of variance or variance sensitivity analysis (i.e., considering how much the variance of a given input variable contributes to the variance of the target value). Maybe this can be formalized by linking the theory with some sort of statistical test (F-test may be relevant?) or with variance-based sensitivity analysis?
Specific comments
- Page 4, line 83: The authors state that “the pitch angle is positive in a mathematically negative sense”. This is unclear. Maybe the authors mean that the angle convention is opposite to the typical right-hand rule, or opposite to the trigonometric convention (anti-clockwise positive)?
- Page 4, line 85: Authors point out that the flapwise/edgewise coordinate system rotates with the pitch angle. One way to refer to the moments which do not rotate with the pitch angle is by calling them an “in-plane blade bending moment” and “out-of-plane blade bending moment” with reference to the rotor plane. I can see the authors use the in- and out-of-plane notation later in the paper, so why not already here?
- Page 7, line 135: Multipliers: this is normally referred to as probability weights?
- Page 8, section 2.5: It does not get clear what part of the structure is modelled by FE simulations. Is it only the bearing, or also the hub/blade? The reference Graßmann et al. (2023) only considers bearing modelled in a test rig. This brings the discussion back to my general comment on how and if hub deformation plays a role, and if the modelling approaches used in the paper can capture that.
- Page 11, line 191: Unfinished (or redundant) sentence: “As axial location”.
Citation: https://doi.org/10.5194/wes-2023-163-EC1
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