Stiff Rotor Research Articles

Mathematical modeling of the rotor dynamics of a turbomachine on gas foil bearings subjected to vibration

BACKGROUND: The use of gas foil bearings is a promising development in the field of turbomachinery due to their economy, autonomous operation capability, and durability. However, gas foil bearings have lower load capacities than other types of bearings. However, turbomachines are complicated, dynamic systems that must meet high standards of safety, sustainability, and durability against external mechanical factors like vibration, shock, etc.
 AIM: Development of a mathematical model of rotor dynamics to predict the displacement of the rotor in foil bearings for maintaining separation between the rotor and the housing while being subjected to vibration.
 METHODS: A mathematical model of the dynamics of a stiff rotor on gas foil bearings was built and analyzed, taking into account the flexibility of the bearing bushing supports and the housing of the turbomachine. Stationary and transient modes of operation, including the transient modes combined with random vibration, are simulated. The system of ordinary derivatives equations describing the mathematical model was solved by the Rado IIA method. Random vibration was modeled using digital Fourier transformation. The modeling results were analyzed by discrete Fourier transformation and short-time Fourier transformation.
 RESULTS AND CONCLUSIONS: Rotor movement trajectories were obtained and the results were compared with authors previous experimental data. Upper bound of maximal displacements was obtained. The maximum values of rotor displacement can be used to set the optimal values of blade tip gaps.

Applications of adaptive stiffness suspensions to vibration control of a high-speed stiff rotor with tilting pad bearings

The current paper discusses the optimum parameter setting of asymmetric high-static low-dynamic stiffness (HSLDS) suspensions to reduce vibrations of a high-speed symmetric rotary system, excited by an unbalance force. The rotating system consists of a shaft that is supported by tilting pad journal bearings on the asymmetric HSLDS suspensions. The Reynolds equation is solved numerically to obtain the oil pressure distribution for each pad of bearing. With the aim of calculating the hydrodynamic forces applied to each pad, an analytical approach is presented. Its results are validated using a numerical integration approach. Given the considerable difference between the shaft mass and pads moment of inertia, the mathematical equations governing the motions of disk, journal, bearing and pads are solved implementing a routine specified for stiff ordinary differential equations in MATLAB. The optimum parameters of HSLDS suspensions are obtained, using a multi-objective genetic algorithm. Design objectives are considered to minimize the vibrations of rotor, journal, and bearing and bearing force transmission to the external supports. The efficiency of optimum HSLDS suspensions in reducing the vibrations of journal, bearing and rotor within the operating speed range is shown. The high performance of the designed suspensions in decreasing the bearings force transmission is proved as well. In addition, the design robustness to uncertainties in HSLDS suspensions parameters is studied.

Simulation of oscillating trailing edge flaps on wind turbine blades using ranging fidelity tools

AbstractRecent research developments have indicated that substantial reduction of both the fatigue and ultimate loads can be achieved by adopting trailing edge (TE) flap control strategies. Their aeroelastic tools employ blade element momentum (BEM) aerodynamic models enhanced with a sectional 2D treatment of the TE flap, neglecting the 3D effect of the trailed vorticity in the vicinity of the moving flap. In the present paper, a cross comparison of the BEM‐based models used in the aeroelastic analysis tools against higher fidelity, free‐wake lifting line, and fully resolved CFD models is performed, with the aim to highlight limitations of the first. A second level of comparison assesses the differences among tools of the same level of fidelity from different research groups. Moreover, a number of engineering‐based correction models that are used in conjunction with BEM and account for the complex 3D trailed vorticity effect are assessed. Simulations of a stiff rotor configuration of the DTU 10 MW Reference Wind Turbine are performed for a prescribed, harmonic TE flap motion, and aerodynamic loads are compared at the sectional and rotor‐integrated level. For the studied stiff rotor with the chosen flaps configuration, the results of the code‐to‐code comparisons indicate that low‐fidelity BEM tools consistently predict 1P variations of the rotor thrust due to the TE flap motion, but fail to reproduce the details of the load distributions especially in the vicinity of the flap section. BEM‐based corrected models, which account for 3D‐induced velocity effects, provide load distribution predictions closer to higher fidelity free‐wake and CFD models.

Effect of Three-Dimensional Aerodynamics and Dynamic Stall on Lead–Lag Damping of an Isolated Rotor

This paper investigates three-dimensional aerodynamic effects due to radial flow on lead–lag damping of a rotor in forward flight conditions. Three-dimensional effects in this study are restricted to yawed flow aerodynamics and radial flow coupling between blade segments. These effects are included in the ONERA dynamic stall model, and lead–lag damping for an isolated torsionally stiff rotor is calculated for different forward flight conditions. This augmented aerodynamic model with three-dimensional effects and Peters–He dynamic wake model improves the correlation of lead–lag damping with experimental data at high advance ratios. The effect of modeling static lift characteristics on damping correlation is also presented. Finally, a modification to the trailing edge separation point–based static lift model for improved yawed flow modeling amenable to aeromechanical stability analysis is proposed.

Control of a hybrid helicopter with wings

This work investigates the design parameters and their consequences in the control of a helicopter rotor combined with a pair of fixed wings. This hybrid vehicle has a light and aerodynamically efficient rotor with a large range of pitch angles to enable both hover and forward flight. Because of the light stiff rotor and heavy wings, the hybrid vehicle exhibits couplings between the roll and pitch axes during hover flight. The rotor-wing interaction depends on a lot of parameters. In this article, we utilize a simplified theoretic model and simulations in order to gain insight in the effect of these parameters on the vehicle dynamics. Finally, a controller is designed that compensates undesired coupling between pitch and roll.

Benchmarking aerodynamic prediction of unsteady rotor aerodynamics of active flaps on wind turbine blades using ranging fidelity tools

Simulations of a stiff rotor configuration of the DTU 10MW Reference Wind Turbine are performed in order to assess the impact of prescribed flap motion on the aerodynamic loads on a blade sectional and rotor integral level. Results of the engineering models used by DTU (HAWC2), TUDelft (Bladed) and NTUA (hGAST) are compared to the CFD predictions of USTUTT-IAG (FLOWer). Results show fairly good comparison in terms of axial loading, while alignment of tangential and drag-related forces across the numerical codes needs to be improved, together with unsteady corrections associated with rotor wake dynamics. The use of a new wake model in HAWC2 shows considerable accuracy improvements.

Effect of "Crawling" and Peculiarities of Motion of a Rotor with Pendular Self-Balancers

The results of investigation of a new phenomenon represented by the revolving of stiff rotor in elastic supports with four self-balanced pendulums are discussed in the article. The rotor is rotating with some operating velocity but the pendulums are moving with a frequency which equals one from two critical velocities of the rotor rotation connected with its linear or angular motion parameters. The procedure of mathematical models construction for system with eight degrees of freedom is offered. Dynamical interactions’ properties between partial systems with definite forms of a motion self-organization in a freely suspended pendulum group are discussed.

Measurement of the deformation of an extremely flexible rotor blade using digital image correlation

This paper describes the measurement of the deformation of an extremely flexible rotor blade in hover using a novel application of three-dimensional digital image correlation (3D DIC). In this optical method, images of the rotor blade painted with a high-contrast, random speckle pattern are captured using two digital cameras and a strobe light. Photogrammetry is used to calculate a whole-field, three-dimensional map of the rotor blade. Cross-correlation between images captured under two load conditions is used to calculate deformation. The technique was first validated in the rotating frame by correlating DIC measurements on a stiff rotor blade of known geometry with measurements made by two other laser sensors. The technique was then used to measure the deformation of extremely flexible blades on a 46 cm diameter rotor, rotating at 1200 RPM. The blades of this rotor are so flexible that they can be rolled up into a compact volume. The spanwise variation of extension, lead-lag and flap bending, as well as pitch angle, were extracted from DIC measurements. The technique yielded surface heights with a spatial resolution of 0.15 mm and three-dimensional deformation vectors with a spatial resolution of 2.37 mm (1.04% of the rotor radius), at a calculated accuracy of 15 μm. Tip displacement of up to 7.59 mm (3.3% of the rotor radius) and a tip twist of up to 10.8° were measured. Based on DIC measurements, it is concluded that an accurate aeroelastic model of the rotor blade must include flap and lead-lag bending as well as twist degrees of freedom. In addition, the elastic twist must be considered of the same order of magnitude as the blade root pitch. Finally, the scalability of this technique to the measurement of full-scale rotor blade deformation is discussed.

Effects of torsion frequencies on rotor performance and structural loads with trailing edge flap

The effects of variation of blade torsion frequency on rotor performance and structural loads are investigated for a 1/rev active flap rotor and baseline rotor (no active control). The UH-60A four-bladed articulated main rotor is studied at a high-speed forward flight condition. The torsion frequencies are varied by modifying the spanwise torsional stiffness of the blade and/or the pitch link stiffness. First, a parametric/optimization study on the flap deployment schedule is carried out using lifting-line comprehensive analysis for the soft, baseline, and stiff rotor configurations, and then a higher fidelity coupled computational fluid dynamics–computational structural dynamics analysis is carried out for the optimal flap deployment. It is shown that with the soft rotor there is degradation in performance—of about 6% with respect to the baseline rotor in the case where the flaps are not activated, and of about 1% if flap deflections are applied. On the other hand, for the stiff rotor there is a slight improvement in performance of about 2.3% when the flaps are not activated, and no appreciable change in the case where active flap deflections are applied. It appears that the peak performance achievable with using active flaps on a baseline stiffness rotor cannot be further improved significantly by varying the torsional frequencies. Variation of torsion frequency does not appear to have a significant influence on blade torsion moments and pitch link loads, although the 1/rev flap activation examined has an important role.

Determination of natural frequencies and forms of oscillations of stiff two-bearing rotor

Determination of natural frequencies and forms of oscillations of stiff two-bearing rotor

Acceleration through critical speeds of an anisotropic, non-linear, torsionally stiff rotor with many degrees of freedom

It is well known that the amplitude of the unbalance response of a rotor which runs through a critical speed can be reduced by increasing the value of the acceleration. However, the models which are used for the computation of the unbalance response can be used only for constant speed running, and the solutions dealing with accelerating rotors which can be found in the literature refer to very simple geometrical layouts. The aim of the work reported here is to extend the usual mathematical models based on the finite element method to the study of the dynamic behaviour of rotors with non-constant angular speed. Both the non-linear behaviour of the rotor and its geometrical or inertial anisotropy have been taken into account. The case of a torsionally stiff rotor running with a given law ω( t) is studied in detail. Several examples, including a practical one dealing with a complex rotor running on non-linear bearings, conclude the work.

Experimental study of rotor bearing systems influenced by dilute viscoelastic lubricants

Experimental study of the stability of rotors as influenced by viscoelastic lubricants is presented in this paper. Experiments were conducted on two rotors. The stiff rotor has a first natural frequency of nearly 1050 Hz which is much higher than the range of rotational speeds over which the experiments were conducted. This rotor may thus be treated as a rigid rotor and its behaviour is expected to confirm theoretical stability analysis previously presented by the authors. The other rotor is termed flexible rotor with a first natural frequency of 25 Hz. Vibration signals were analysed for unbalance and half frequency whirl response with the help of a real time spectrum analyser. From the experimental responses of the stiff rotor, it may be concluded that the use of dilute viscoelastic lubricant postpones the onset of instability to higher speeds when compared with ordinary lubricants. On the rotors with higher flexibility, the lubricant viscoelasticity has detrimental effects. Speed of onset of large whirl is more or less independent of viscoelastic properties or lubricants.

The Effect of Load and Feed Pressure on Whirl in a Grooved Journal Bearing

An experimental investigation is described of the whirl stability of a circumferentially grooved journal bearing carrying a stiff rotor. The shift and bearing were made with a slight taper so that the clearance could be infinitely varied, and the assembly could be tilted to any angle between the horizontal and vertical directions to vary the load on the bearing. These features allowed a wide range of running conditions. Experimental results imply that subambient film pressures are negligible, regardless of load, and that Reynolds boundary conditions apply with cavitation at ambient pressure. This has an important effect on film extent and, consequently, on promoting stability. The influence of feed pressure on the control of film extent, and hence on stability, is shown by analysis and experiment. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference in Minneapolis, Minnesota, October 24–26, 1978