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• The tooth compliance is corrected by a modified cantilever beam model. • It takes into consideration the coupling effect between tooth slices. • Deformation compatibility equation with the slice coupling is derived. • It does not require compliance correction coefficients. The meshing characteristics (MCs) including time-varying meshing stiffness (TVMS), loaded transmission error (LTE) and contact stress are the key indexes of spiral bevel gears (SBGs). Traditional analytical methods for SBGs have some limitations in MCs calculation, including the utilization of finite element (FE) method-based correction coefficients to compute tooth compliance and the oversight of coupling effects between slices, thus leading to a lack of overall model applicability. To fill those gaps, an accurate and widely applicable analytical model for computing MCs of SBGs is proposed. The tooth compliance is corrected by a modified cantilever beam model derived from the energy method. Additionally, the deformation compatibility equation (DCE) for SBGs contact after considering the slice coupling is rederived. Finally, the correctness and generalization of the proposed method are verified through comparisons with references and FE results. The findings reveal that the maximum LTE errors of the proposed model are 2.35 % and 2.67 %, and 3.59 % and 4.42 %, respectively, when compared with the references and FE results. This research offers theoretical support for optimal design and meshing quality evaluation of SBGs. [ABSTRACT FROM AUTHOR]

• A numerical method for TVMS calculation of spiral bevel gear with spalling is developed. • A finite element model is established to check the correctness of the proposed method. • Some differences between proposed method and finite element method are explained. • The effect of spalling length, width, location and shape are discussed. Spiral bevel gears often operate at high speeds and under heavy loads, which can easily lead to the occurrence of spalling faults on the tooth surfaces, particularly in cases of inadequate lubrication. In this study, we introduce an efficient and accurate numerical calculation method to determine the time-varying meshing stiffness (TVMS) of a spiral bevel gear pair with actual spalling faults, taking into consideration the effects of multi-tooth meshing and the flexibility of the gear flank. In parallel, a finite element model is established to verify the accuracy of the proposed method across various spalling parameters. We delve into the impact of spalling length, width, location, and shape. The results demonstrate that the TVMS values obtained from our proposed method align closely with those obtained using the finite element method. The range of TVMS reduction caused by the spalling fault is primarily determined by the spalling location and width. Moreover, the magnitude of TVMS decline is strongly associated with the spalling length. Furthermore, the clearances between two conjugated tooth surfaces change due to the presence of the spalling fault, resulting in a redistribution of contact forces on the same contact surface and other meshing tooth surfaces. [ABSTRACT FROM AUTHOR]

• An integrated coupling model of the wind turbine drivetrain is established. • Wind-speed variations, flexibilities of blade and gear shafts are considered. • The coupling model is verified by comparing with the finite element model and previous literature. • Dynamic characteristics of the wind turbine drivetrain under different non-torque loads are studied and compared. With the increase of the rotor diameter and the deterioration of operating conditions, modern wind turbines suffer from more and more significant time-varying non-torque loads, which increases the burden of turbine structures especially the gearbox. Based on an aeroelastic loose coupling approach and assembly of the finite element method, an integrated drivetrain coupling analysis model including blade module, aerodynamic module, and gearbox module is established in this study. This proposed model is validated by comparing the calculation results with previous literature. Taking National Renewable Energy Laboratory 5-MW wind turbine as the research object, the gearbox vibration responses, gear meshing forces and bearing forces under non-torque loads caused by blade gravity, wind shear (WS), tower shadow (TS) and yawed inflow are studied in detail. Results show that the y -direction displacements of the gearbox, sun gear 1, sun gear 2 and gear are larger than those in x -direction because F y or M x generated by blade gravity, WS and TS dominates the non-torque loads. The non-torque loads lead to a non-uniform planet load sharing especially for the planetary gear stage 1. Because of the fluctuations of non-torque loads, not only the rotation frequencies of the corresponding carrier but also the multiple frequencies of the carrier 1 are observed in the frequency spectrums. The non-torque loads are mainly borne by carrier 1 bearings. Except for the blade gravity, the bearing forces caused by other unsteady inflows have obvious fluctuations. [ABSTRACT FROM AUTHOR]

Drive train has a significant influence on the reliability of wind turbines. As for the Offshore Floating Wind Turbine (OFWT), the importance of the drive train is even more prominent due to the more complex operating conditions at the ocean. In this study, dynamic characteristics of the OFWT drive train are investigated based on flexible dynamic model. First, this paper presents a flexible dynamic model of the drive train, which includes not only the full coupling of gear meshing but also the flexibilities of planet carrier and ring gear. Then, a corresponding finite element model is established to verify the reliability of the proposed model by comparing natural frequencies and vibration responses. Afterwards, dynamic characteristics of the drive train are analyzed under different excitations, including the time-varying mesh stiffness, wind turbulence, tower shadow, wind shear and platform motions. Results show that resonant peaks of the system are more likely to appear when the mesh frequency or its multiplication of the gear pair 1–2 is equal to the natural frequency. In addition, it is revealed that the tower shadow is the most significant excitation source for OFWT drive train, followed by platform pitch and surge motions. • A flexible dynamic model of the drive train is established. • Flexibilities of the planet carrier, ring gear and gear shafts are considered. • The flexible model is verified by a finite element model. • Dynamic characteristics of the drive train under different excitations are studied. [ABSTRACT FROM AUTHOR]

The effects of three different gear crack types such as, for example, the crack along tooth width uniformly and the crack propagating in the depth direction (crack type 1, CT1), the crack along tooth width non-uniformly and the crack propagating in both the depth and the tooth width directions (crack type 2, CT2), and the spatial crack propagating in the depth, the tooth width and the tooth profile directions (crack type 3, CT3) on the time-varying mesh stiffness (TVMS) of spur gear pairs are investigated in this study. Firstly, an analytical model for studying these three types of cracks is established based on potential energy method. A finite element (FE) model of the cracked spur gear pair is also built in the ANSYS software as well. In order to verify the analytical method, the TVMS obtained from analytical method is compared with that obtained from FE method under different crack types. Moreover, the effects of the depth, the length and the height of crack are discussed. The equivalent stress, contact pressure and displacement of tooth are also analyzed under different crack types by using the FE method. The results show that the effect of crack depth on TVMS is the largest, while that of the crack height is the smallest, and the non-penetrating crack for CT2 and CT3 will generate the non-uniform load distribution along tooth width. [ABSTRACT FROM AUTHOR]

Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness under double-tooth engagement region, nonlinear contact stiffness and tooth spalling defect, an analytical model for time-varying mesh stiffness (TVMS) calculation of spur gears is established. In addition, the analytical model is also verified by comparing the TVMS under different spalling widths, lengths and locations with that obtained from finite element method. The results show that gear mesh stiffness decreases sharply with the increase of spalling width, especially during the single-tooth engagement; the spalling length only has an effect on the beginning and ending of gear mesh stiffness reduction; the spalling location can affect the range of gear mesh stiffness reduction, and the range will reduce when the spalling location is close to the addendum. This study can provide a theoretical basis for spalling defect diagnosis. [ABSTRACT FROM AUTHOR]

Using Neural Networks, this paper present a method of generating virtual images under virtual lighting conditions. The relationship between the lighting conditions and the color of image is non-linear, several neural networks technologies are introduced to make curve fitting. As a result, virtual images of same scene under different lighting conditions can be deduced from known real scene image, and the inherent relations of image color and outside lighting conditions are discovered. Combining techniques of IBMR or panoramic image, the model of scene is recovered. Further, combining the dynamic virtual images obtained by our method, time-sequence dynamic virtual scene can be reconstructed and revisited in virtual reality. [Copyright &y& Elsevier]

Blade pitch control (BPC) is an indispensable part of a variable speed wind turbine, which maintains a stable power output by adjusting the blade pitch angle to adapt to the changing inflow speed introduced by the platform pitching motion (PPM). An integrated aeroelastic-servo transmission system of a floating offshore wind turbine (FOWT) is established and validated. Comparing with existing models, our model considers the effect of the BPC on the FOWT, apart from the dynamic characteristic of the drivetrain and the aeroelastic coupling of the blade. Firstly, dynamic behaviours of the FOWT under different tip speed ratios are compared. Then the performance of FOWT with and without the BPC influence is compared, followed by a dynamic analysis of the FOWT under a varying platform pitching amplitude. Results show that the tip speed ratio slightly alters the FOWT performance under the PPM. Considering the effect of the BPC, the fluctuation of the generator power reduce, but the aerodynamic thrust tends to enlarge the PPM. The non-torque loads induced by the PPM are insensitive to BPC. Fluctuation of the system response increases with increasing platform pitching amplitude. • An integrated aeroelastic-servo transmission system of a FOWT is established. • Blade pitch control improves the dynamic characteristics of the transmission system. • Tip speed ratio slightly alters the FOWT performance above the rated wind speed. • Generator power performs differently from aerodynamic power due to the large inertia of the transmission system. • Fluctuation of the system response increases with increasing platform pitching amplitude. [ABSTRACT FROM AUTHOR]

The tower is an essential supporting structure for a Floating Wind Turbine (FWT). Due to the complexities of system structure and the environmental excitations, FWT towers present rather complicated loading characteristics, potentially threat the system reliability. This paper aims to reveal the FWT tower dynamics in wind-wave-current environments with a dedicated experimental apparatus. A new strategy is proposed to design the FWT structure. Then, extensive tests are conducted with different offshore environments and varying rotor operating conditions. Results show that the FWT tower loading presents complicated dynamic characteristics. The frequency response mainly consists of three parts: the low-frequency component associated with floater oscillations and wind excitations, the wave-frequency component induced by the linear wave loads, and the high-frequency component resulted from the rotor-nacelle assembly (RNA) operating and vibrations. The low- and wave-frequency responses increase with the wave height, while the high-frequency response amplifies with the aerodynamic loads. Vibrations transmit between the upper RNA and the lower floating platform through the tower structure, smearing the system stability and increasing the structure fatigue damages. Optimizations should be proposed to improve the FWT tower performance to suppress or isolate these unexpected vibrations. • A novel FWT tower design strategy is proposed. • An experimental apparatus is developed to study the FWT tower dynamics in wind-wave conditions. • The tower loading can be clearly divided into the low-frequency, wave-frequency and high-frequency responses, which are caused by different excitations. • The tower structure can serve as a filter to isolate the vibration transmission between the turbine and the floater. [ABSTRACT FROM AUTHOR]

In this paper, we propose a blade loading sensing system for model tests of floating wind turbines (FWTs) in the wave basin. The sensing system is based on Fiber Bragg Grating (FBG) sensors and a Fiber Optical Rotary Joint (FORJ). Systematical model tests are conducted for the novel SJTU-S4 FWT in the wave basin to reveal the characteristics of FWT blade loads under different environmental conditions. Results show that the developed FBG-FORJ system performs well to capture the FWT blade loads while not smearing other FWT dynamics. The FWT blade loading is determined by gravity, centrifugal force, aerodynamic loads, as well as wave and current excitations. The driving wind takes the lead in the FWT blade loads. An increased driving wind corresponds to increased blade loads in magnitude and fluctuation, as well as increased n P (n times per revolution) harmonics. The incident wave generates considerable responses at the wave frequency and introduces more loading fluctuations. The current tends to eliminate the floater inclination generated by the driving wind and subsequently mitigates the unsteady blade loading, despite the increased floater sway and roll fluctuations. This work extends the knowledge of FWT aerodynamics and helps to investigate advanced FWT control strategies. • A blade loading sensing system is constructed for FWT in wave basin model tests. • FWT blade loading performance is systematically revealed. • The driving wind takes the lead in the FWT blade loads. • Incident wave generates wave-frequency responses and introduces loading fluctuations. [ABSTRACT FROM AUTHOR]

The aeroelastic coupling effect is playing an increasingly important role in the aerodynamic and aeroelastic characteristics of wind turbine blades owing to the increasing size of modern wind turbines. Concurrently, periodic unsteady inflows, including the wind shear (WS), tower shadow (TS), and yawed inflow, further amplify the impacts of aeroelastic coupling. In this study, an aeroelastic model based on the geometrically exact beam theory and blade element momentum method is established. The aeroelastic coupling model is verified based on several previous studies. Taking the NREL 5WM flexible wind turbine blade as an example, the aerodynamic and aeroelastic characteristics under periodic unsteady inflows are investigated. The results show that the WS causes remarkable fluctuations of the flap deflection and yaw moment. The TS effect introduces dramatic changes into the tilt moment, thrust force, and output power when the blade passes by the tower. The yawed inflow leads to a significant reduction in both the output power and thrust force. Compared with other unsteady inflows, the gravity effect on the output power and thrust force are negligible. The response under the combined effect is a summation of the results considering each single influencing factor and is dominated by the major influencing factors. • An aeroelastic coupling model of the wind turbine blade is established. • Flexibility, centrifugal/Coriolis forces, and stress stiffening of the blade are considered. • The aeroelastic model is verified by comparing with previous studies under the steady and unsteady inflows. • Aerodynamic and aeroelastic characteristics of wind turbine blades under different periodic unsteady inflows are studied and compared. [ABSTRACT FROM AUTHOR]

Aerodynamic loading is one of the most dominating environmental excitations of Floating Wind Turbines (FWTs) and plays an important role in the FWT dynamics. In this study, we developed a model Spar-type FWT and then constructed a dedicated experiment apparatus to reveal the aerodynamic loading effects. As for the floater motion, the wind loading serves as an external exciting force, as well as potential damping source and equivalent added mass item. To take all these roles into account, we proposed a concept of aerodynamic loading effect. The presence of aerodynamic loading effect is validated by free decay tests and white noise wave tests. Results show that the aerodynamic loading effect alters the natural frequencies and damping ratios of the FWT system. We suggest the FWT designers refer to the altered natural frequencies when designing the floater and the FWT controllers. We experimentally observed that the increased aerodynamic loading seems to suppress the pitch resonance vibration while amplifies the resonance vibration at surge frequency. Besides, the nacelle motions, blade loads, and the tower dynamics, are all significantly impacted by the aerodynamic loading effect. The presented results are potentially helpful for optimizing FWTs and developing advanced FWT controllers. • Aerodynamic loading effect is addressed to depict the impact of wind loads on FWT dynamics. • An experimental apparatus is developed to reveal FWT dynamics under aerodynamic loading effect. • Floater natural frequencies are altered by aerodynamic loading effect. • FWT design and controller development should incorporate aerodynamic loading effect. [ABSTRACT FROM AUTHOR]

The Froude scaling law is usually utilized in the wave basin model tests of Floating Wind Turbines (FWTs). However, the Froude-Scaled Rotor (FSR) cannot generate desired aerodynamic loads due to the Reynolds-Number Scaling Effect (RNSE). To mitigate the adverse effects of RNSE, two approaches are proposed to design Performance-Scaled Rotors (PSRs) in this paper. Taking DTU 10 MW baseline wind turbine as an example, the SD2030 airfoil is selected to replace the original FFA-W3-xx airfoils. Maximum Lift Tracking (MLT) and Load Distribution Matching (LDM) algorithms are proposed to assign the chord lengths and twist angles. Herein, MLT leads all airfoils to operate at the optimal angle of attack that corresponds to the maximum lift coefficient and afterwards increasing the chord lengths. LDM simultaneously adjusts the chord length and twist angle, aiming to match the span-wise distribution of normal force at the design point. Results show that both approaches can generate desired rotor thrusts in a range of tip speed ratios, which seems to outperform prior PSRs in the existing publications. The blade mass and inertia can be preserved with careful manufacturing procedures. The redesigned PSRs are helpful to improve the accuracy and reliability of FWT model tests in the wave basin. • Reynolds-Number Scaling Effect (RNSE) of model rotor in wave basin test is introduced. • Potential approaches to mitigate the adverse of RNSE are analyzed in detail. • MLT and LDM algorithms are proposed to redesign PSR for FWT wave basin tests. • Two PSRs are designed for DTU 10 MW wind turbine based on MLT and LDM. [ABSTRACT FROM AUTHOR]

Abstract Based on the slice method, a new method is proposed for calculating the time-varying mesh stiffness (TVMS) of helical gears. The proposed method uses the idea of 'offset and superposition' to avoid the repetitive calculation of the TVMS of each sliced gear. Taking the TVMS obtained from the finite element (FE) method as a benchmark, the correction coefficient of the gear foundation stiffness is obtained by the optimization method. Four types of spatial crack are modeled, including addendum non-penetrating crack, addendum penetrating crack, end face non-penetrating crack and end face penetrating crack. The computational efficiency and accuracy are discussed under different crack parameters and crack types. Compared with the FE method and the traditional analytical method, the proposed method agrees well, and its efficiency is higher. For example, the proposed method costs 8 s to calculate the TVMS of helical gears with identical slice profile in one mesh period, while the traditional method and the FE method cost 2 min and 2.5 h, respectively. For the helical gears without identical slice profile, the proposed method is also applicable but the improvement of the calculation efficiency is not evident. The effects of extended tooth contact are ignored in the proposed analytical method, which leads to some errors between the TVMS of the cracked helical gears obtained from the proposed method and the FE method, but the change laws of the TVMS are in consistent. Highlights • A mesh stiffness model of helical gears with different crack types is established. • Mesh stiffness is compared with that from finite element (FE) method. • The proposed model is also revised based on FE method. • Mesh mesh stiffness under different crack parameters are analyzed. [ABSTRACT FROM AUTHOR]

• Accurate initial gaps of spur gear pair are obtained based on tooth contact analysis. • Corner contact and tooth broken fault of spur gear pair are well simulated. • Dynamic response considering corner contact and tooth broken fault is presented. Theoretically, the contact of a spur gear pair occurs on the line of action (LOA), but the corner contact may happen due to the tooth deformation, especially when there is a tooth broken fault. In this paper, based on the tooth contact analysis, the initial gaps considering tooth broken fault are accurately calculated. Meanwhile, the initial gaps are brought into the loaded tooth contact analysis program and yield the time-varying mesh stiffness (TVMS) and non-load transmission error (NLTE). By comparing with the finite element (FE) method, the meshing state of the gear pair considering various tooth broken heights is presented. The result shows that it is inaccurate to regard the mesh stiffness value as zero when the missing tooth profile should have contact since serious corner contact phenomenon will occur in this state. Moreover, by comparing the simulated dynamic response with the experimental results, this paper finds that the simulation result considering the corner contact effect is closer to the experimental result. This study can provide a more accurate model for the diagnosis of gear tooth broken faults. [ABSTRACT FROM AUTHOR]

• The axial component of angular misalignment spur gears pair TVMS is obtained. • A flexible spur gear system dynamic model with angular misalignment is proposed. • Mechanism of traveling wave resonance phenomenon in angular misalignment spur gear system is explained. • Influence of misalignment angle, web thickness and gear torque on traveling wave resonance is analyzed. The aero-engine spur gear system is often designed as thin rim structure due to lightweight consideration, which leads to traveling wave resonance phenomenon when spur gear system has angular misalignment during operation. This paper mainly analyzes traveling wave resonance phenomenon of aero-engine angular misalignment thin rim spur gear system. Time-varying mesh stiffness (TVMS) of spur gear system is calculated by loaded tooth contact analysis (LTCA) method, angular misalignment is introduced into spur gear system, and axial component of TVMS is obtained by the projection method. Flexible gear foundations are simulated by 8-node shell element and rotational shafts are simulated by Timoshenko beam element, combined with axial stiffness, the dynamic model of flexible spur gear system is established. Simulation results are compared with the references and finite element (FE) model, which proves the accuracy of the proposed method. The analysis results of angular misalignment spur gear system traveling wave resonance phenomenon show that during the operation of spur gear system, angular misalignment produces axial excitation, which excite nodal diameter vibration of gear foundations, and traveling wave resonance phenomenon appears at nodal diameter vibration resonance speed. The effects of misalignment angle, web thickness and gear torque on spur gear system traveling wave resonance amplitude and resonance speed are discussed. The research of aero-engine angular misalignment spur gear system provides theoretical basis for structural design and fault diagnosis of aero-engine gear systems. [Display omitted] [ABSTRACT FROM AUTHOR]

The blade loading contains sufficient information about the unsteady aerodynamics of Floating Wind Turbines (FWTs), and it serves as the basis for advanced controller developments. Wave basin model test is among the most reliable and economical methods for FWT investigations. However, few FWTs were reported being able to monitor the blade loads during wave basin tests. The main obstacles include strict space/mass limitations in model manufacturing and problems associated with signal transmission between rotating blades and stationary signal processing unit. In this paper, the feasibility of detecting blade loads for model FWT in wave basin tests is investigated. An on-line monitoring system is developed based on Fiber Bragg Grating (FBG) sensors and a Fiber Optical Rotary Joint (FORJ). Extensive validation tests are conducted under different environmental and operational conditions. Results show that the proposed FBG-FORJ sensing system presents impressive feasibility and reliability. As the authors know, it is among the first attempts to monitor the blade loads in real-time for model FWTs in wave basin tests. The present study will serve to enrich the knowledge about unsteady aerodynamics of FWTs and lay the foundation for experimental studies on advanced FWT controllers. • An FBG-FORJ sensing system is developed to monitor blade loads for FWT wave basin model tests. • Extensive validations are conducted to evaluate the performance of the proposed FBG-FORJ system. • FBG responses under different environmental and operational conditions are analyzed. • Potential improvements for the FBG-FORJ system are discussed. [ABSTRACT FROM AUTHOR]