In this paper, the authors present a methodology for calculation of the probability of failure of a wind turbine pitch bearing due to static overload – specifically based on exceedance of the static safety factor as determine by the recently published pitch bearing design guide (Stammler et al 2024). The presented methodology also includes treatment of a variety of design uncertainties, which is especially interesting, and examines specific wind sites. Having said that, I have a number of technical and editorial comments. My most significant question pertains to the interrelationship of terms R and S as described in the comments. Maybe there is no issue, but I seek clarification and comment from the authors.

Title

• The phrase “reliability design” is applied very broadly in the title and “reliability analysis” similarly in the text. This is a little misleading, as what has been examined is the risk of static overload resulting in plastic deformation damage, which is just one aspect of the design. Obviously, rolling contact fatigue and wear prevention are other essential aspects in the design.
• Other than in the Title, “code calibration” is not used in the manuscript. What did the authors intend with this phrase? I have the feeling it has something to do with comparison of IEC wind classes to actual wind sites, but I would not describe this as “code calibration”. Please reconsider your meaning.

Abstract

• Lines 1-5: The Abstract says the manuscript presents and describes “the reliability analysis” in several places. As commented on the Title, this manuscript examines the risk of static overload resulting in plastic deformation damage. This is one or “a” aspect of the design, not “the” aspect. Additionally, the abstract mentions “probability of failure” very broadly without specifying that it is limited to risk of static overload resulting in plastic deformation damage. In terms of the importance of ball diameter and the conclusion on IEC vs. actual wind sites, please see later comments.
• Lines 3-6: The phrase “sensitivity in the dimension aspect of reliability” is unclear. That is, it is not clear if “dimension” refers to a physical dimension (ball diameter, pitch diameter) assessed in the reliability analysis, or if it refers to one element or an aspect of the analysis. Further, lines 3-6 all say similar things, but in slightly different manners – so, it is not clear if key differences are being communicated or not. My sense is not, so for greater clarity, I recommend lines 3-6 be combined and simplified to something like “The sensitivity of the probability of failure to uncertainties in turbulence intensity, material properties, and bearing dimensions is evaluated. Within the bounds examined, the pitch bearing conformity and ball diameter have the largest effect on the probability of failure.”
• Lines 6-7: Here too the sentence is a bit hard to understand, especially “IEC standards…are studied…”. I recommend more simply and directly “The probability of failure for some example wind sites around the world is assessed and is higher at those sites than for wind conditions described by IEC 61400-1.”

1 Introduction

• Lines 14-15: I believe a more accurate representation of the cost in Stehly et al 2023 is that “Although the entire pitch system assembly costs less than one percent of the wind turbine Stehly et al. (2023), changing a blade bearing is costly due to the need for lowering of the blade with a large crane.” That is, Stehly lists the full system assembly cost (for all 3 blades, including the bearings, motors, controls, batteries, etc.) rather than only the bearing and I recommend emphasizing that an individual bearing is vanishingly cheap but can have a costly failure ramification.
• Lines 17-18: This sentence, especially “perform the calculation of the ultimate limit state” is a bit garbled and incomplete. I believe a better statement of its intent is “As part of the design and certification process, the blade bearing static safety factor must be assessed in the ultimate limit state (ULS) (IEC 61400-1 2019; DNV-ST-0437 2016; Harris et al. 2009; Germanischer Lloyd 2010; Stammler et al. 2024).”
• Line 20: I recommend deleting the sentence “There are numerous studies on the fatigue of the bearings; however, the studies about the blade bearing are not many.” It provides no information, is entirely subjective, and as time moves on, is less and less accurate. My personal opinion is that it is not accurate even today, as I have a library of 6 dozen technical papers and journal articles regarding blade bearings.
• Line 26-27: Although I myself was a co-author on Rezai et al (2023) and the paper does speak to “seed number”, the phrase “…shows the importance of seed number in the turbulence wind model at bearing’s life” is not the best description of the work and likely to confuse many readers. I believe a better description of Rezai et al (2023) is that it “…assessed the variation in blade bearing fatigue with shear power law exponent, turbulence intensity, and even resulting from each individual turbulent wind time series.”
• Line 32-33: I recommend deleting the phrase “…blade bearing reliability is not studied thoroughly…”. Similar to line 20, this phrase provides no information and is entirely subjective. I also recommend the phrase “…it is not clear what level of reliability one can obtain with the current design process” also be revised. Although true to some extent, a more informative statement would be to refer to the statistics in Haus, Sheng, and Pulikollu (2024) at https://app.box.com/s/ktjzjdxn77omu1cjoy9znymbrynlsw0d. The statistics therein from 55+ GW of wind plant data show that pitch bearings installed pre-2016 perform fairly well, only reaching a 10% replacement rate in 15 years. However, pitch bearings installed post-2016 on larger wind turbines are projected to have a 10% replacement rate in only 7.5 years.
• Line 34: It isn’t clear that ISO 19902 and ISO 19904-1 standards for oil and gas industries are relevant to offshore wind. More broadly, it seems like IEC 61400-3-1 and -3-2 are better references here. Additionally, IEC 61400-8, titled “Design of wind turbine structural components”, seems better suited for a general reference than ISO 2394 for general principles on reliability for structures. Do the authors have a particular meaning in mind with the references to oil and gas standards? In what situations would these standards apply to offshore wind?
• Line 39: I think most readers will find the sentences “ISO 76 (2006) stated that experience shows that a total permanent deformation of 0,0001 of the rolling element diameter at the center of the most heavily loaded rolling element/raceway contact can be tolerated in most bearing applications without the subsequent bearing operation being impaired. The bearing static failure corresponds to such a permanent deformation” conflicting. That is, “without operation being impaired” and “corresponds to bearing static failure” are conflicting. I recommend changing the second sentence to “In this work, it is proposed that ball-raceway contact stresses approaching the limits corresponding to ISO 76 increase the probability of failure of the bearing.”
• Line 42: The phrase “and the formation of cavities in the raceways” was curious to me. Does this refer to the core crushing phenomenon described in Harris et al. 2009 and Stammler et al 2024?

3.2 Safety factor and failure function

• Lines 76-84: Although somewhat relevant, I don’t believe the ISO 76 static safety factor S0 = C0a/P0a mentioned here or shown in Step 5 of Figure 1 is used in the remainder of the manuscript. If this is the case, I recommend deleting these lines as not to distract the reader.
• Equations 6-8: I am curious how it is handled and might be worth discussing in the manuscript that the contact area parameters a and b in Equation 6 and within the variable R in Equation 8 are dependent on the maximum ball load Qmax in Equation 6 which is the variable S in Equation 8. That is, R = R(S). Is this automatically accounted for in the described methodology? If so, how? This appears to me acknowledged to some extent in line 135.
• Line 102: It appears the text here has the opposite sense of Equation 8. Shouldn’t the text here say “If the failure function value is less than or equal to the static safety ratio, the bearing is safe; otherwise, the bearing is in a failure state”?
• Lines 107 – 115: Although I don’t disagree, the math here seems a little longer than necessary. I think one can simply take the cube root of Equation 9 and get to Equation 12 quite directly.
• Line 126: Here R and S are described as resistance and stress. Hearkening back to Equation 6, these are meant to be R = 4200*pi*a*b/1.5 and S = Qmax I believe. I don’t disagree that the load S = Qmax partially represents the stress, but so do the terms pi*a*b (contact ellipse area) which is part of what is called R (resistance) if I understand correctly. As commented earlier, a and b are dependent on Qmax, that is, R = R(S). I do agree that the stress of 4200 MPa can be thought of as resistance here.
• Figure 2: Two boxes here are “Uncertainty on aerodynamic” and “Uncertainty on wind”. I’m not entirely sure I understand the distinction.

3.2.1 Uncertainty in material

• In addition to the given citations, I recommend the authors consider adding Lai, J. 2011. “A New Model for the Static Load Rating of Surface-Induction Hardened Bearings.” Evolution 2:27– 32 and Lai, J., P. Ovize, H. Kuijpers, A. Bacchetto, and S. Ioannides. 2009. “Case Depth and Static Capacity of Surface Induction-Hardened Rings.” Journal of ASTM International 6 (10): 1–16. http://doi.org/10.1520/JAI102630.

3.2.3 Uncertainty in loads

• Lines 174-176: Here again, the focus on “seed number” still feels odd to me, as though this number has a much more important meaning than it really does. It seems much more straightforward to say that “Different realizations of the turbulence produce a Gaussian distribution of TI in the longitudinal wind component due to spatial coherence (Jonkman 2009)” and “Each simulation leads to a time series of distributions… Different simulations result in a series of…” Similarly in lines 193 to 197, different numbers simulations are considered.

4.2 Sensitivity analysis and Conclusions

• Lines 237-239: I’m not sure I understand why this discussion of raceway conformity is here compared to Section 4.2.3?
• Comparing sections 4.2.1 through 4.2.4 and Figures 5a-d, the discussion here feels like it is missing the major point: That changes in failure probability for groove conformity are 10^3 greater than those for ball diameter, pitch diameter, and contact angle. Isn’t this a very important part of the discussion, or am I missing something? That is, the Pf for a groove conformity of 0.545 is like 10-3 and rapidly decreases to 10-5 for 0.525 – a similar level for ball diameter, pitch diameter, and contact angle. Or maybe that’s the point of the vertical lines – that outside this range these conformities aren’t realistic? In the Abstract and Conclusions, is it then fair to compare that “Ball diameter and raceway conformity in this aspect have the highest contribution to the reliability of the blade bearing”? From the plots in 5a-d all with different y-scales, it is really hard for a reader to really see this. Why can’t all 4 be put on the same plot? It still feels to me that the effect of the groove conformity is far larger effect than the ball diameter, even within the range of vertical lines in Figure 5c.

4.2.1 Ball diameter

• In this section, how are the differences in ball diameter applied? Are all balls equal in diameter and a range of diameters studied, or are these differences in diameter present in the bearing for a given simulation? I wonder what inspection methods might be applied by suppliers during assembly – I believe it is typical to make an effort to select balls of similar diameter.

4.3 IEC wind conditions and 5 Conclusions

• In this section, I’m not sure a “fair” comparison is being made between results from say 15 seeds to many, many seeds. The design guideline suggests using load factors as described in Section 7.6.2.2 of IEC 61400-1. Although it is buried in the Appendix A of the design guideline, a safety factor of 1.35 and a partial load factor of 1.25 are applied to the average of the highest loads from each of the DLC turbulent seed time series to determine the maximum stress and static safety factor. Can the authors comment on this? That is, these load factors are purposefully applied knowing that only a few simulations aren’t enough to represent the maximum loads and thus the maximum stress and risk of exceeding 4200 MPa. Greater importance is placed on this matter in the Conclusions, where it is stated “It is observed that by considering 15 seed numbers, as proposed in the standards and guidelines, the effect of different turbulence conditions cannot be achieved.”

Table 3, Section 4.4 Wind sites and Conclusions

• I am both interested in and curious about the wind site characteristics of the real sites presented in this study compared to IEC classes. I don’t think I saw it anywhere: what are Vave and TI for the real sites compared to the IEC classes? Are they appreciably different? If so, how? Is TI much higher? If they’re appreciably different, then it should be no surprise that putting a turbine with a pitch bearing designed even for say IEC 1A is a bad idea. Isn’t that an important part of the discussion? Without this information, is it really fair to say “The probability of failure for the selected onshore and offshore wind sites are mostly worse than those of IEC sites”?

References

• The citation for Harris, Rumbarger, and Butterfield 2009 leaves Butterfield’s name incomplete. That is, it is only “C.P. B.”.
• The doi for Stehly et al 2023 actually takes one to Harris, Rumbarger, and Butterfield 2009. Since I stumbled on this, I also recommend that this citation be updated to the Stehly 2024 edition at doi 10.2172/2479271.

Minor grammatical comments:

• Line 14: Please ensure consistency in citation style throughout the manuscript, here “Stehly et al. (2023)”, in line 17, “(Andreasaen et al., 2022)” (parenthesis w/ comma), and line 42 “[Harris and Kotzalas (2006)]” (square-bracketed w/out comma). Each citation is used in the same manner and thus should have the same style, which in Latex would be \citep for example.
• Line 27: Should be “…wind turbine and showed the…”
• Lines 28-29, 169, and 310: I recommend that “fatigue life” be used here instead of just simply “life” (4 places).
• Line 40: Change “…can cause possibly stress…” to more simply “…can cause stress…” or “…can possibly cause stress…”, although “can possibly” is redundant.
• Line 42: Please add “also” to “can also lead to” to help distinguish the risk of static failure from surface-initiated fatigue failure.
• Line 43: Single sentences rarely constitute a paragraph. Please combine with the previous paragraph. Additionally, this sentence refers to “main parameter” (singular), when multiple parameters (plural) are examined.
• Line 85: I don’t believe the acronym SF is used elsewhere in the manuscript. If so, please replace with variable S0.
• Line 86 and 90: MPa is used in 86 while megapascals is used in 90. Please define on first use.
• Line 94: Please italicize parameters a and b in the text.
• Line 96: The number of balls is listed previously as z, whereas in equation 7 the variable Z is used.
• Line 98: Variables Dpw, z, and alpha are previously defined in Table 2, so do not need to be defined here.
• Line 161: I’m not sure I understand “spherical roller bearings” and “ball diameter”. Shouldn’t this be roller diameter?
• Line 163: Should be “sensitivity”.
• Line 168: I think simply “turbulence” or “atmospheric turbulence” makes more sense than “turbulence of the wind turbine”. I suppose one could say “turbulence acting on the wind turbine” here.
• Lines 216 and 236: here this should be “IEC 61400-1”.
• Line 239: Should be “0.5%”
• Line 306: Should be “Pf”.
• Line 310: “if are used” should be simply “if used”.

This article builds upon previous studies on pitch bearing design guide (ISO 76, DG03) and extended the life calculation from a classic deterministic approach to probabilistic one. The latter approach takes into account the uncertainties in wind turbulence, bearing geometry, material hardness level, et al, which can qualitatively rank the most sensitive parameters for its probability of failure

Specific comments are as follows:

1. The life calculation did not root from rolling contact fatigue assumption, instead, it derives from contact stress safety factor. How realistic is to assume structural reliability as the driving failure mode for pitch bearings? Is there evidence from field observations to support this assumption?
2. Included in the introduction, the failure modes are mentioned as “rolling contact fatigue, core crushing, edging loading, ring fracture, fretting, false brinelling”. Is there any connection of the present study with the top failure modes?
3. Degradation criteria G should get close to the failure modes as much as possible. The proposed one based on safety factor only appears an oversimplification. As shown in the results, probability of failure is less than 0.1% for most of the cases. This estimate is much lower than what has been reported in public domain.
4. The studied bearing is 3.6m size. Is there any plan to address the structural flexibility as the uncertainty in the study?
5. Please correct typos in the paper.