the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Jul 2024
Identification of operational deflection shapes of a wind turbine gearbox using fiber-optic strain sensors on a serial production end-of-line test bench
Abstract. Wind energy has witnessed a staggering development race, resulting in higher torque density demands for the drivetrain in general and the gearbox in particular. Accurate knowledge of the input torque and suitable models are essential to ensure reliability, but neither of them are currently available in commercial wind turbines. The present study explores how a subspace identification framework, using distributed fiber-optic strain sensors on a four-stage gearbox, can provide input torque measurements through the use of operational deflection shapes. Compared to conventional gear tooth root strain gauge measurements, an innovative measurement setup with 129 fiber-optic strain sensors has been installed on the outer surface of the ring gears to research the deformations caused by the gear mesh events. Consistent estimates of the deflection shapes have been found by applying the Multivariable Output-Error State-sPace (MOESP) subspace identification method to strain signals measured on a serial production end-of-line test bench. These operational deflection shapes, driven by periodic excitations, account for almost all the energy in the measured strain signals. Their contribution is controlled by the torque applied to the gearbox. From this contribution, a torque estimate has been derived for dynamic operating conditions. Accurate knowledge of the input torque throughout the entire service life allows future improvements in assessing the remaining useful life of wind turbine gearboxes. Additionally, tracking the operational deflection shapes over time is proposed to enhance condition monitoring in planetary gear stages.
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RC1: 'Comment on wes-2024-83', Anonymous Referee #1, 16 Sep 2024
In this paper, the authors present a system to measure the operational deflection shapes (ODSs) of the ring gear of a gearbox using fiber optic strain sensors. The shapes then have application to the measurement of mechanical torque in the gearbox, currently not typically available, for the purposes of remaining useful life estimation or even gearbox condition monitoring. In general, the article is interesting and well-written. I have provided the following comments and some grammatical suggestions at the end.
In the Abstract, gear tooth root strain gauge measurements are described in comparison to the fiber optic ODS and torque measurements. Although I generally understand the comparison, I think most readers might be a bit confused here as Abstract speaks to torque measurement up to this point. It might be simpler just to delete “Compared to conventional gear tooth root strain gauge measurements,” as the deflections measured by them relate to the sun-planet and/or planet-ring tooth load distributions rather than the deflection of the ring gear from torque. Nothing is lost from the sentence by deleting this and it is much simpler and direct. Additionally, I might recommend changing “research the deformations caused by gear mesh events” to “measure the deformations caused by planet gear passage events”. The primary content measured by the fiber optics is the planet passage, as evidenced by Figure 8, not the gear meshing that occurs at a much higher frequency.
Introduction, line 50: A small point, but I recommend deleting “substantial” and just saying “impact on the main frame, tower, and foundation”. The implication is that tower-top mass (and especially from the drivetrain) substantially impacts these costs – unless a reference can be given, we have found that the rotor loads are the main driver. Reducing drivetrain mass was not a particularly strong driver as described in https://www.sciencedirect.com/science/article/pii/S0306261923006360.
Introduction, line 62: Another minor suggestion - an additional reference might be nice at the end of this paragraph. I recommend https://doi.org/10.5194/wes-7-387-2022.
Introduction, line 70: Unmentioned here is that estimating mechanical torque from electrical currents also contains inherent uncertainties in the converter, generator, and gearbox efficiencies. I can’t think of a reference that quantifies this, but I believe this to be generally accepted. It would be nice to add this point here. In terms of the impact of load on at least bearing fatigue, since the fatigue is roughly proportional to the cube of the load, then even a 10% error results in a 33% error in fatigue – this even in normal operating conditions. I will admit I don’t know whether this uncertainty or the omission of torque fluctuations in dynamic events is more important, but I wonder.
Introduction, lines 109-111: Initially, when I read the stated third contribution of the paper it, at least to me, read as the most important contribution. So much so that I was going to suggest it is important enough to merit being “elevated” as part of the Title. After reading the remainder of the article; however, it feels like this bullet point is a bit of an overstatement. Certainly such measurements could be used in a framework, but the framework itself is only mentioned rather than being proposed (and certainly described) in this paper. I’m not quite sure what I’d recommend here – to leave this as a third contribution and “soften” the contribution, or put this in text as the usefulness of such a system and analysis. I simply ask the authors to reconsider how this third bullet is written with respect to how the article itself is written.
Section 2, line 150: Could you add a short mention of what Ab is? I take it that the periodic and structural modes are Aper and Asys, but I don’t see mention of what Ab represents.
Section 4.1, line 265: A similar comment as before regarding “mesh events” versus “planet passage events”. Here in this line I believe the phenomenon being described is better represented as “mesh forces as each planet passes the measurement point on the ring gear occur at different times”. That is, in Figure 8a, one only really sees 7P content, not 83P content.
Section 4.1, line 279: Similar to the Abstract, I recommend “gear mesh events” be changed to “planet passage events”.
Figure 10: In an earlier figure, red and blue were used as 2 different sensors, but here the two colors are not labeled. Could a legend be added here, or other description? I don’t think the colors have the same meaning.
Figure 13 and associated text: I’ll admit I don’t see much point in this figure, but maybe I’m really missing it? Maybe just say that the modules were not found to be time variant. Or maybe the relative magnitudes of each mode could be listed in Table 5 – I think the main point is that mode 2 representing 7P has the highest magnitude, just reinforcing that the signals are primarily comprised of this as Figure 8a already shows.
Minor grammatical comments:
Line 44: I believe the year for “Stehly et al.” is missing. It would typically look like “Stehly et al. (2016)” or “Stehly et al. (2021)”.
Line 86: A comma is needed here “…or a shaker, EMA relies…”. Similarly on line 90: “…with OMA, because in OMA…”
Line 115: I might suggest “described” instead of “shown” here.
Line 158: I believe this inline citation style should be “Verhaegen and Verdult (2007)”.
Line 174: I believe “it” is missing and should read, “it has a sustained oscillation”.
Line 176: I believe the “i” in “ith” should be italicized.
Line 243: “barking” torque should be “braking” torque.
In the References, Veers et al. 2022 can be updated from https://doi.org/10.5194/wes-2022-32 to https://doi.org/10.5194/wes-8-1071-2023.
Citation: https://doi.org/10.5194/wes-2024-83-RC1 - AC1: 'Reply on RC1', Unai Gutierrez Santiago, 28 Oct 2024
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RC2: 'Comment on wes-2024-83', Anonymous Referee #2, 30 Sep 2024
This study introduced a methodology for input torque estimates based on identification of operational deflection shapes of a wind turbine gearbox using fiber-optic strain sensors and Multivariable Output-Error State-sPace (MOESP) subspace identification. A brief literature was given to motivate the current research. Needed theoretical discussions were provided along with a description of the test gearbox, which is composed of three planetary stages and one parallel stage. Experimental data was collected from an end-of-line test bench and used in the development and assessment of the proposed methodology. The reviewer has some comments as detailed below. The few critical for the authors to address are bolded. The manuscript is recommended to be revised before it can be considered for publication by the journal.
1. Abstract:
- line 5: "framework" may be better replaced by "method"; input torque "measurements" may be better expressed as "estimates".
- line 8: "consistent" might mean agreement with expectations here. Please reword to make it clear.
- line 14: statement on "operational deflection shapes over time" being proposed to enhance condition monitoring appears not substantiated in the manuscript but only briefly discussed as one of future benefits. Please consider removing or rewording.
2. Introduction:
- line 37: please elaborate on "the influence of surface friction" .
- lines 38-39: in the sentence, "more power ... enhancing reliability", it appears the first two phrases apply to a plant and the next two phrases apply to individual turbines. Please clarify.
- line 40: "a substantial cost reduction in costs" appears not having a direct causal relationship with "large rotors", which appears directly leading to improved energy production or revenue.
- line 68: please double check whether the torque is estimated by using generator currents.
- lines 75: please consider adding the technology from AeroTorque (https://www.pttech.com/aerotorque-torsional-dampers/).
- lines 109-111: the statement appears not substantiated in the manuscript. Please consider removing.
3. Subspace system identification framework
- It appears this section is on the methodology not a framework, please rename the section title accordingly.
- line 121: is "estate" a typo? Please double check.
- line 127: is "innovation signal" supposed to be "excitation signal"?
- line 150: please define variables in Eq. (6).
4. Experimental Setup:
- line 222: is the proposed sensing technology supposed to be robust and easier to be commercialized?
5. Identification of operational deflection shapes
- line 317: please add a brief explanation on model validation not considering Kalman filter.
- page 24, Figure 17: please consider adding a comparison against torque estimated using SCADA data.
6. Conclusions
- Please add a brief discussion on the potential impact, in terms of both commercial and R&D, of the presented methodology.
Citation: https://doi.org/10.5194/wes-2024-83-RC2 - AC2: 'Reply on RC2', Unai Gutierrez Santiago, 28 Oct 2024
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