Shaft Tilt Research Articles

Investigating the interactions between wakes and floating wind turbines using FAST.Farm

Abstract. As floating offshore wind progresses to commercial maturity, wake and array effects across a farm of floating offshore wind turbines (FOWTs) will become increasingly important. While wakes of land-based and bottom-fixed offshore wind turbines have been extensively studied, only recently has this topic become relevant for floating turbines. This work presents an investigation of the mutual interaction between the motions of floating wind turbines and wakes using FAST.Farm. While FAST.Farm has been extensively validated across a wide range of conditions, it has never been validated for FOWT applications. Hence, in the first part of this work, we validate FAST.Farm by comparing simulations of a single FOWT against high-fidelity results from large-eddy simulations available in the literature. The validation is based on wake meandering, mean wake deflection, and velocity deficit at different downstream locations. This validation showed that the original axisymmetric (polar) wake model of FAST.Farm overpredicts the vertical wake deflection induced by shaft tilt and floater pitch, while the new curled wake model is capable of properly capturing the vertical wake deflection. In the second part, we use FAST.Farm to analyze a small three-unit array of FOWTs with a spacing of 7 diameters across a wide range of environmental conditions. The same National Renewable Energy Laboratory 5 MW reference wind turbine atop the OC4-DeepCwind semisubmersible is adopted for the three FOWTs and for the validation against high-fidelity simulations. To assess the effect of the floating substructure, we compare the power production, tower-base moments, and blade-root moments obtained for the floating turbines with the results obtained in a fixed-bottom configuration. The main differences introduced by the floating substructure are the motions induced by the waves, the change in the natural frequencies of the tower caused by differences in the boundary condition at its base, and the larger vertical deflection of the wake deficit due to the mean pitch of the platform. The impact of these differences, as well as other minor effects, are analyzed in detail.

Comparison of 25 MW downwind and upwind turbine designs with individual pitch control

As conventional upwind wind turbines grow larger, the increased mass and flexibility of the longer blades present challenges concerning costs, structural loads, and safety constraints such as tower clearance. At extreme scales, wind turbines in a downwind configuration may provide a feasible alternative to address these challenges by allowing lightweight, flexible blades that can reduce capital costs and blade loads while maintaining safety margins. Downwind turbine blades suffer from increased fatigue loading due to the tower shadow effect. In this study, novel downwind, three-bladed wind turbine designs at 25 MW rating with lightweight, flexible blades are evaluated and compared in terms of power production and structural loading. To obtain a baseline performance, a standard collective blade pitch wind turbine controller is implemented for the two downwind and one upwind turbine designs. Individual pitch control is then added for the downwind turbines to reduce structural fatigue on the turbine blades. In summary, the two downwind turbine designs that differ in rotor pre-coning and shaft tilt angles using collective and individual pitch control are compared against a conventional upwind turbine with collective pitch control at the same scale under turbulent wind conditions.

Validation of a Mid-Fidelity Numerical Approach for Wind Turbine Aerodynamics Characterization

This work is aimed at investigating the capabilities and limits of the mid-fidelity numerical solver DUST for the evaluation of wind turbines aerodynamic performance. In particular, this study was conducted by analysing the benchmarks NREL-5 MW and Phase VI wind turbines, widely investigated in the literature via experimental and numerical activities. The work was started by simulating a simpler configuration of the NREL-5 MW turbine to progressively integrate complexities such as shaft tilt, cone effects and yawed inflow conditions, offering a detailed portrayal of their collective impact on turbine performance. A particular focus was then given to the evaluation of aerodynamic responses from the tower and nacelle, as well as aerodynamic behavior in yawed inflow condition, crucial for optimizing farm layouts. In the second phase, the work was focused on the NREL Phase VI turbine due to the availability of experimental data on this benchmark case. A comparison of DUST simulation results with both experimental data and high-fidelity CFD tools shows the robustness and adaptability of this mid-fidelity solver for these applications, thus opening a new scenario for the use of such mid-fidelity tools for the preliminary design of novel wind turbine configurations or complex environments as wind farms, characterised by robust interactional aerodynamics.

Dynamic performances of novel misaligned non-uniform distributed tilting-pad bearing

The non-uniform distributed tilting-pad journal bearings (NDTPJB) in large wind turbine main shafting has become an important development trend for high-power wind turbines due to the advantages of improving reliability and reducing maintenance costs. However, studies involving NDTPJB have not been reported under specific conditions such as low speed, wide range variable direction and magnitude of heavy-load in wind turbine. A new transient mixed elastohydrodynamic lubrication (mixed EHL) model for NDTPJB is established, taking into account the misalignment effect of the shaft tilt and the swinging of pads in the circumferential and axial directions, as well as the influence of pivot friction and elastic deformation effects. Based on the mathematical model, the dynamic characteristics and structural parameter effects of NDTPJB are systematically studied under low speed, wide range variable direction and magnitude of heavy-load. The results indicate that the NDTPJB exhibits a more significant sensitivity to the heavy load direction due to the different functional roles of the above distributed pads (ADP) and bottom distributed pads (BDP). The modified mixed EHL model can more accurately evaluate the lubrication performance of NDTPJB, and combine the characteristics in individual pad swing and the overall effect of the pads to comprehensively analyze the dynamic lubrication behavior of NDTPJB. By setting the pivot coefficient to 0.55, reducing the distribution angle of BDP, and increasing the distribution angle of ADP, a better load-carrying capacity can be achieved. The research results have guiding significance for further monitoring and analyzing the experimental performance of NDTPJB, as well as designing and optimizing such bearing structures.

Wind Turbine Geometrical and Operation Variables Reconstruction from Blade Acceleration Measurements

To develop reliable numerical models and better interpret monitoring campaigns experimental data of wind turbines, knowing the structure operation conditions, in particular the rotor angular velocity and blades’ pitch angle, is of paramount importance, but often not known due to confidentiality restrictions, or known with low time resolution (typically 10 min average values). In this work, it is shown analytically that blades accelerations measurements contain valuable information that allow for a better characterisation of the effective rotor shaft tilt and blades cone angle for different operating conditions. It is also shown that these measurements can be used to reconstruct the time history of the rotor angular velocity and blades’ pitch angle. After presented in an analytical framework, the methodology is validated with experimental data of two full scale wind turbines. The successful reconstruction of the rotor operating conditions shows that the method presented can be used to provide further insight into the dynamics of the structure that aids monitoring data analysis and provides an alternative method to monitor the SCADA systems themselves. The paper combines quite unique experimental data collected at two operating rotors with original data processing strategies that provide very valuable information to researchers and wind turbine operators.

Fiber Bragg grating scanning spectral distortion caused by vibration in a rotor temperature monitoring system

To improve the accuracy of the rotor temperature monitoring system using the spatial coupling method, the vibration distortion of the scanning spectra was investigated theoretically and experimentally. Vibration causes a shifted reflection peak and a narrower 3 dB bandwidth. The maximum scanning error of the FBG center wavelength plummetes, decreases slowly, and finally stabilizes with increasing g (the ratio of the coupling loss period between the collimators to the scanning spectrum time). Coordinating the vibration frequency with the demodulator scanning frequency so that the g-value is greater than 10 is the key to improving the accuracy. The scanning error increases slowly and then rapidly as the radial vibration amplitude or the shaft tilt amplitude increases. As the axial ratio of the rotor trajectory increases, the error first soars and then stabilizes when the ratio reaches 2.5. It's also been found that using the centroid peak method helps reduce errors.

Aerodynamic rotor design for a 25 MW offshore downwind turbine

Continuously increasing offshore wind turbine scales require rotor designs that maximize power and performance. Downwind rotors offer advantages in lower mass due to reduced potential for tower strike, and is especially true at large scales, e.g., for a 25 MW turbine. In this study, three 25 MW downwind rotors, each with different prescribed lift coefficient distributions were designed (chord, geometry, and twist) and compared to maximize power production at unprecedented scales and Reynolds numbers, including a new approach to optimize rotor tilt and coning based on aeroelastic effects. To achieve this objective the design process was focused on achieving high power coefficients, while maximizing swept area and minimizing blade mass. Maximizing swept area was achieved by prescribing pre-cone and shaft tilt angles to ensure the aeroelastic orientation when the blades point upwards was nearly vertical at nearly rated conditions. Maximizing the power coefficient was achieved by prescribing axial induction factor and lift coefficient distributions which were then used as inputs for an inverse rotor design tool. The resulting rotors were then simulated to compare performance and subsequently optimized for minimum rotor mass. To achieve these goals, a high Reynolds number design space was developed using computational predictions as well as new empirical correlations for flatback airfoil drag and maximum lift. Within this design space, three rotors of small, medium and large chords were considered for clean airfoil conditions (effects of premature transition were also considered but did not significantly modify the design space). The results indicated that the medium chord design provided the best performance, producing the highest power in Region 2 from simulations while resulting in the lowest rotor mass, both of which support minimum LCOE. The methodology developed herein can be used for the design of other extreme-scale (upwind and downwind) turbines.

Effect of the vertical wake deflection on the response of a 12MW semisubmersible FWT

The need to understand the interaction of floating wind turbines operating in the marine boundary layer with other surrounding turbines is of increasing importance as wind farms and rotor sizes get larger. For low wind speed conditions, the wake deflects upwards due to the floating wind turbine built-in rotor tilt and the platform pitch angle. Furthermore, based on field data from the North Sea, a convective atmosphere is likely to occur, especially for lower wind speeds. It is therefore key to understand the combined effect of meandering, wake deflection and atmospheric stability for low wind speed conditions on the floating wind turbines in a wind farm.In this work, to account for atmospheric stability, data from large-eddy simulation (LES) for a 7.5m/s wind speed scenario and three atmospheric stability conditions, are used as input to FAST. Farm to study the effect of the wake deflection upwards on a 12 MW semisubmersible placed 8 rotor diameters (D) downwind of a stationary wind turbine. Three built-in shaft tilt angles cases are considered for the fixed upwind turbine: 12°, 6° and no tilt angle. The main effects of the wake deflection are on the power output of the floating wind turbine in the wake, and on the tower top yaw moment. For stable conditions, the mean tower top yaw moment increases by more than three times. The findings of this work contribute to the investigation of the wake deflection as a control strategy to minimize wake losses in floating wind farms.

The effect of vertical arrangement on performance and wake characteristics of two tandem offshore wind turbines under various operating conditions

Apart from streamwise and lateral distances, a vertical distance may also be imposed for adjacent wind turbines to achieve performance improvement of downstream turbines. Previous research was primarily devoted to wind farm layout optimisation using simplified analytical wake models, while impacts of operating conditions were ignored for studies using more advanced Large-Eddy Simulation (LES) methods. In this paper, the effect of vertical arrangement on performance and wake characteristics of two tandem offshore wind turbines under various operating conditions is investigated using an LES approach coupled with an actuator line technique. Results show that vertically arranging turbines can improve downstream turbine performance, but its effects vary with the operating conditions. If turbines typically operate below or at the rated condition, due to deflection of upstream turbine wake associated with shaft tilt, raising the upstream turbine can result in greater improvement in power output, with a considerable rise of 50% for a relatively small height difference of 0.1 times rotor diameter. For above-rated operating conditions, the wind shear effect becomes important and it is preferable to increase the hub height of the downstream turbine to take advantage of higher wind speed. Wake characteristics of both turbines are analysed to support the results.

Pengaruh Pola Pemasangan dan Rasio Dimensi Propeller Terhadap Unjuk Kerja Perahu Tipe Penggerak Contra Rotation Propeller

The propeller is an important part of the ship's propulsion installation. Differences in propeller design can affect the propulsion performance of the ship. This study aims to determine the effect of variations in dimension ratio and propeller installation pattern on the performance of the contra rotation propeller type boat. The research was carried out experimentally by using variations of three-dimensional propeller ratios including R1 (1:1); R2 (1:1/2) and R3 (1:1/4), while the pattern of placement of the shaft tilt angle includes 15oand 20o. The flow pattern is conditioned with the waveless and wavy flow. Data collection includes boat speed and visualization of fluid flow behind the propeller which is then analyzed to obtain performance characteristics for each variation used. The results showed that the dimension ratio and the pattern of contra rotation propeller installation affected the speed and thrust of the boat, where the optimum power was obtained at the variation of the ratio R2 at a shaft tilt angle of 15owith the provision of a water flow mechanism without waves resulting in a speed of 0.576923 cm/second and under conditions of wavy at 0.523256 cm/second. The greatest thrust occurs in conditions of water flow without waves at the variation of the ratio R2 with a value of 33.23 kN and in wavy conditions of 30.13 kN. Visualization of fluid flow behind the shaft has shown the performance of the contra rotation propeller in various variations given through changes in the shape and length of the resulting path .Keywords: dimension ratio, installation pattern, contra rotation propeller, boat performance

Computational Investigation of Multirotor Interactional Aerodynamics with Hub Lateral and Longitudinal Canting

This study investigates the interactional aerodynamics for laterally and longitudinally canted two-rotor systems with a front rotor and an aft rotor aligned with the flow. The -diameter, three-bladed fixed-pitched rotors are simulated using computational fluid dynamics at a targeted disk loading and 30 kt edgewise freestream. Simulations are performed using the commercial Navier—Stokes solver AcuSolve with a detached eddy simulation model. In addition to an uncanted case, two laterally canted cases (10° advancing sides up and 10° advancing sides down) as well as two longitudinally canted cases (10° inward and 10° outward) are simulated. Aft rotor performance is compared to isolated rotors operating at the same revolutions per minute, speed, and shaft tilt angle in order to quantify the effect of rotor–rotor aerodynamic interaction. For all configurations, the aft rotors experience a lift deficit at the front of the rotor disk, which also results in a nose-down pitching moment relative to an isolated rotor. The lift deficit for the uncanted rotor was around 15%. Lateral canting only slightly increases the lift deficit (to 16–18%) but also produces 28–38% change in roll moments. Change in aft rotor nose-up pitching moments for the uncanted and laterally canted rotors were in the 55–64% range. Longitudinal canting produces larger changes in the magnitude of the lift deficit and pitching moment, but has minimal effect on roll moments. In particular, canting inward results in a lift deficit as high as 21% and a 94% change in pitching moment. Canting outward, on the other hand, reduces the aft rotor lift deficit to 11% and the pitching moment change to 19%. The paper explains the changes in the flowfield and the underlying physics for the different cases in detail.

Wind Tunnel Studies on Hover and Forward Flight Performances of a Coaxial Rigid Rotor

The aerodynamic performance of a reduced-scale coaxial rigid rotor system in hover and steady forward flights was experimentally investigated to gain insights into the effect of interference between upper and lower rotors and the influences of the advance ratio, shaft tilt angle and lift offset. The rotor system featured by 2 m-diameter, four-bladed upper and lower hingeless rotors and was installed in a coaxial rotor test rig. Experiments were conducted in the Φ3.2 m wind tunnel at China Aerodynamics Research and Development Center (CARDC). The rotor system was tested in hover states at collective pitches ranging from 0° to 13° and it was also tested in forward flights at advance ratios up to 0.6, with specific focus on the shaft tilt angle and lift offset sweeps. To ensure that the coaxial rotor was operating in a similar manner to that of the real flight, the torque difference was trimmed to zero in hover flight, whilst the constant lift coefficient was maintained in forward flight. An isolated single-rotor configuration test was also conducted with the same pitch angle setting in the coaxial rotor. The hover test results demonstrate that the figure of merit (FM) value of the lower rotor is lower than that of the upper rotor, and both are lower than that of the isolated single rotor. Moreover, the coaxial rotor configuration can contribute to better hover efficiency under the same blade loading coefficient (CT/σ). In forward flight, the effective lift-to-drag (L/De) ratio of the coaxial rigid rotor does not monotonously change as the advance ratio increases. Increases in the required power and drag in the case with a high advance ratio of 0.6 leads to the decreasing L/De ratio of the rotor. Meanwhile, the L/De ratio of the rotor is relatively high when the rotor shaft is tilted backward. The increasing lift offset tends to result in reduced required rotor power and an increase in the rotor drag. When the effect of the reduced rotor power is greater than that of the increased rotor drag, the L/De ratio increases as the lift offset increases. The L/De ratio can benefit significantly from lift offset at a high advance ratio, but it is much less influenced by lift offset at a low advance ratio. The forward performance efficiency of the upper rotor is poorer than that of the lower rotor, which is significantly different from the case in the hover flight.

An improved theory in the determination of aerodynamic damping for a horizontal axis wind turbine (HAWT)

The aerodynamic damping reflects the aero-structure interaction and is intrinsically involved in a fully coupled turbine. However, it is still of great importance to theoretically quantify the aerodynamic damping of a HAWT in some cases. The existing theory can reasonably characterize the aerodynamic damping level of a HAWT with rigid blades, minute shaft tilt and yaw angles, while certain discrepancies were observed when compared with either experimental or numerical damping results of a more realistic turbine. This study aims to provide an improved theory to incorporate more realistic conditions (i.e., blade flexibility, shaft tilt and yaw angle) in aerodynamic damping estimation. Good agreements are found between the proposed theory and numerical results with varied influential factors, upon which modification factors against the original theory are created and discussed. Finally, the aerodynamic damping of tower is determined and included in a decoupled fatigue analysis framework to demonstrate the potential application of this improved aerodynamic damping theory.

Wind Tunnel Test of a Rotorcraft with Lift Compounding

Rotorcraft flight speed is limited by compressibility effects on the advancing blade side and decreasing lift potential on the retreating blade side. It may thus be beneficial to employ a hingeless rotor to generate additional lift with the advancing blade and compensate the resulting rolling moment with a fixed wing on the retreating blade side. This concept is a form of "lift compounding" that appears to show enormous potential. The present paper presents results of a wind tunnel test with a slowed, hingeless rotor and single fixed wing on the retreating blade side. Based on rotor test stand data and flow field measurements, the impact of operational and rotor parameters on system performance and aerodynamics is examined, mutual interaction effects between rotor and fixed wing are analyzed, and dominant flow structures are characterized in the reverse flow region on the retreating blade side. Flow field analysis reveals a reverse flow entrance vortex that freely convects through the reverse flow region and rivals the blade tip vortices in strength. Contrary to previous beliefs, this vortex originates from upstream of the reverse flow region and only its detachment from the rotor blade is related to entering this region. The combination of finite rolling moment trim and aft shaft tilt significantly increases rotor lift coefficient and corresponding peak lift-to-drag ratio of the compound rotorcraft. Results are compared with predictions from a comprehensive rotor analysis that is expanded to cover the main effects of the added fixed wing and is able to reproduce general performance trends of the rotorcraft. The present study highlights that adding a single fixed wing and hingeless rotor to a high-speed rotorcraft could significantly improve its performance.

Study on the reasonable tilt angle of ventilation shafts in Xidianwan Tunnel, China

The “asthma effect” of shaft natural ventilation is common, which makes the actual air exchange volume impossible to be quantified and the pollutant concentration along the tunnel unable to be analyzed. In order to improve the ventilation effect of the ventilation shaft and realize the steady air flow in the air well, the reasonable tilt angle of the ventilation shaft is studied. Firstly, the numerical simulation software FLUENT is used to establish a tunnel model of a certain traffic volume based on dynamic grid technology, and to analyze the relationship between the shaft tilt angle and the air flow state, including intake and exhaust air volume, and air flow direction. Secondly, model experiments are carried out to verify the numerical simulation results, in which jet fan thrust pressure is substituted for traffic piston pressure. The result shows that the natural ventilation state with the proposed direction can be realized on condition that the shaft tilt angle is around 15 degrees. That means to discharge polluted air from one group of ventilation shafts and suck in fresh air from the other group of ventilation shafts. At the same time, by dividing the tunnel rationally, the calculation formula of pollutant concentration of the cross section along the tunnel under the condition of different diverging amounts caused by the change of tilt angle of the ventilation shafts is derived, which provides guidance and reference for determining whether the air quality in the tunnel meets the requirements of relevant specifications.

Blade Structural Load/Airload Correlation on a Slowed Mach-Scaled Rotor at High Advance Ratios

To expand the cruise speed of a compound helicopter, alleviating the compressibility effects on the advancing side with reduced rotor RPM is proved to be an effective design feature, which results in high advance ratio flight regime. To investigate the aerodynamic phenomena at high advance ratios and provide data for the validation of analytical tools, a series of wind tunnel tests were conducted progressively in the Glenn L. Martin Wind Tunnel with a 33.5-inch radius fourbladed articulated rotor. In a recent wind tunnel test, the rotor blades were instrumented with pressure sensors and strain gauges at 30% radius, and pressure data were acquired to calculate the sectional airloads by surface integration up to an advance ratio of 0.8. The experimental results of rotor performance, control angles, blade airloads, and structural loads were compared with the predictions of comprehensive analysis and computational fluid dynamics (CFD) analysis coupled with computational structural dynamics (CSD) structural model. The paper focuses on the data correlation between experimental pressure, airload, and structural load data and the CFD/CSD predicted results at various collective and shaft tilt angles. Overall, the data correlation was found satisfactory, and the study provided some insights into the aerodynamic mechanisms that affect the rotor airload and performance, in particular the mechanisms of backward shaft tilt, the effect of hub/shaft wake, and the formation of dynamic stall in the reverse flow region.

Refined Performance Results on a Slowed Mach-Scaled Rotor at High Advance Ratios

Owing to its ability to alleviate the compressibility effect on the advancing side, the slowed rotor operating at high advance ratios is a key feature in high-speed compound rotorcraft. A series of wind tunnel tests were conducted in the Glenn L. Martin Wind Tunnel with a four-bladed Mach-scaled articulated rotor. The objective of the tests was to gain a basic understanding of unique features of high-advance-ratio aerodynamic phenomena, such as thrust reversal and dynamic stall in the reverse flow region. In this study, high-advance-ratio tests were carried out with highly similar, noninstrumented blades and on-hub control angle measurements, to minimize possible error due to blade structural dissimilarity and pitch angle discrepancy. The tests were conducted at 900 and 1200 RPM, advance ratios of 0.3–0.9, and a shaft tilt study was conducted at±4°. Pitch and flap motion at the blade roots, rotor performance, and vibratory hub loads were investigated during the test. The test data were then compared with those of previous tests and with predictions from comprehensive analysis. The airload results were investigated using comprehensive analysis to gain insights into the influences of advance ratio and shaft tilt angle on rotor performance and hub vibratory loads. Results indicate that the thrust benefit from backward shaft tilt is dependent on the change in the inflow condition and the induced angle of attack increment, and the reverse flow region at high advance ratios is the major contributor to changes in shaft torque and horizontal force.

Nonlinear Blade Stability for a Scaled Autogyro Rotor at High Advance Ratios

Despite current research advances in aircraft dynamics and increased interest in the slowed rotor concept for high-speed compound helicopters, the stability of autogyro rotors remains partially understood, particularly at lightly loaded conditions and high advance ratios. In autorotation, the periodic behavior of a rotor blade is a complex nonlinear phenomenon, further complicated by the fact that the rotor speed is not held constant. The aim of the analysis presented in this article is to investigate the underlying mechanisms that can lead to rotation-flap blade instability at high advance ratios for a teetering autorotating rotor. The stability analysis was conducted via wind tunnel tests of a scaled autogyro model combined with numerical continuation and bifurcation analysis. The investigation assessed the effect of varying the flow speed, blade pitch angle, and rotor shaft tilt relative to the flow on the rotor performance and blade stability. The results revealed that rotor instability in autorotation is associated with the existence of fold bifurcations, which bound the control-input and design parameter space within which the rotor can autorotate. This instability occurs at a lightly loaded condition and at advance ratios close to 1 for the scaled model. Finally, it was also revealed that the rotor inability to autorotate was driven by blade stall.

Investigation of Interference Effects Between Wind Turbine and Spar-Type Floating Platform Under Combined Wind-Wave Excitation

In order to further understand the coupled aero-hydrodynamic performance of the floating offshore wind turbine (FOWT) in realistic ocean environment, it is necessary to investigate the interference effects between the unsteady aerodynamics of the wind turbine and different degree-of-freedom (DOF) platform motions under combined wind-wave excitation. In this paper, a validated CFD analysis tool FOWT-UALM-SJTU with modified actuator line model is applied for the coupled aero-hydrodynamic simulations of a spar-type FOWT system. The aero-hydrodynamic characteristics of the FOWT with various platform motion modes and different wind turbine states are compared and analyzed to explore the influence of the interference effects between the wind turbine and the floating platform on the performance of the FOWT. The dynamic responses of local relative wind speed and local attack angle at the blade section and wind-wave forces acting on the floating platform are discussed in detail to reveal the interaction mechanism between the aerodynamic loads and different DOF platform motions. It is shown that the surge motion and the pitch motion of the floating platform both significantly alter the local attack angle, while only the platform pitch motion have significant impacts on the local relative wind speed experienced by the rotating blades. Besides, the shaft tilt and the pro-cone angle of the wind turbine and the height-dependent wind speed all contribute to the variation of the local attack angle. The coupling between the platform motions along different DOFs is obviously amplified by the aerodynamic forces derived from the wind turbine. In addition, the wake deflection phenomenon is clearly observed in the near wake region when platform pitch motion is considered. The dynamic pitch motion of the floating platform also contributes to the severe wake velocity deficit and the increased wake width.

Dynamic Modeling of Aerostatic Spindle With Shaft Tilt Deformation

Abstract This paper presents a new dynamic model of aerostatic spindle including the journal and thrust bearings. Reynolds equations are used to model the dynamics of a 4-degree-of-freedom (DOF) aerostatic journal bearing and a 3-DOF aerostatic thrust bearing. Finite element model of the spindle shaft is developed based on the Timoshenko beam theory considering the centrifugal and gyroscopic effects and is coupled with the bearing to construct the dynamic model of the whole aerostatic spindle. The effect of shaft tilt motion due to elastic deformation on the dynamic characteristics of the aerostatic bearing is considered for the first time. The finite difference method is used to determine the load capacity and moments provided by the bearings with changing air film thickness due to shaft vibration, and Newmark-β method is used to obtain the dynamic response of the spindle shaft. The simulated natural frequencies of the aerostatic spindle are verified through impact experiments under static and rotating conditions. Based on the developed model, the effects of tool overhang length, rotating speed, air film thickness, and supply air pressure on the frequency response function of the spindle are investigated comprehensively. The proposed dynamic model of the aerostatic spindle is able to provide useful guidance for structure design and process planning for micro-machining.