Response Of Rotor Research Articles

Vibration Behavior of Dual-Rotor Caused by Maneuver Load and Intershaft Bearing Defect

This paper concentrates on the vibration amplitude modulation and frequency modulation behavior of a dual-rotor system induced by the maneuver load and defective intershaft bearing. The motion equations of a dual-rotor system are presented by considering the intershaft bearing force with a local defect of the outer raceway and the maneuver load of a barrel-roll flight. The fourth-order Runge–Kutta method is employed to study the vibration responses of the dual-rotor system, which are reflected by the time history curves, the bearing contact force curves, and the Hilbert envelope spectra. It is shown that the rotor responses display impulse vibrations due to the defective intershaft bearing; and the corresponding Hilbert envelope spectra contain defect characteristic frequencies, multiple defect frequencies, side frequencies, and modulation frequencies. The results reveal the frequency modulation behavior of the impulse vibrations induced by the rotating speed ratio and the amplitude modulation behavior influenced by the maneuver load, the bearing defect span, and the rotating speed. Finally, defective intershaft bearing experiments under maneuvering flight are conducted, confirming the availability of the numerical vibration amplitude modulation and frequency modulation behavior. This analysis provides a theoretical foundation for bearing state detection during flight maneuvers.

Nonlinear vibration response of a helicopter supercritical tail rotor drive shaft equipped with a dry friction damper

PurposeThe supercritical design of tail rotor drive shaft has attracted more attention in helicopter design due to its high power–weight ratio and low maintenance cost. However, there exists excessive vibration when the shaft passes through the critical frequency. Dry friction damper is the equipment applied to the drive shaft to suppress the excessive vibration. In order to figure out the damping mechanism of the dry friction damper and improve the damping efficiency, the dynamic model of the shaft/damper system is established based on the Jeffcott rotor model.Design/methodology/approachThe typical frequency response of the system is studied through bifurcation diagrams, amplitude-frequency characteristic curves and waterfall frequency response spectrum. The typical transient responses under frequency sweeps are also obtained.FindingsThe results show that the response of the system changes from periodic no-rub motion to quasi-periodic rub-impact motion, and then to synchronous full annular rub-impact, and finally, back to periodic no-rub motion. The slip of the rub-impact ring improves the stability of the system. Besides, the effects of the system parameters including critical dry friction force, rub-impact friction coefficient, initial clearance on the stability and the vibration damping capacity are studied. It is observed that the stability changes significantly varying the three parameters respectively. The vibration damping capacity is mainly affected by the critical dry friction force and the initial clearance.Originality/valuePresented results provide guidance for the design of the dry friction damper.

Molecular rotors in haemoglobin and bovine serum albumin proteins.

Molecular rotors are fluorescent viscosity probes and their response in simple fluids is known to be a Förster-Hoffman power law, allowing the viscosity of the medium to be quantified by its fluorescence intensity. They are attractive probes in biological media, usually consisting of proteins, but how does a molecular rotor behave in a protein solution? The response of the DASPI molecular rotor is compared in two globular protein solutions of similar size, haemoglobin (Hb) and bovine serum albumin, one absorbent, the other not. In absorbent Hb, a model validated by experiments in triangular geometry allows one to correct the absorbing effect and to compare the rotor response in both proteins. With concomitant microrheology measurements, we investigate the relation between the DASPI fluorescence intensity and solution viscosity. In protein solutions, we show that viscosity is no longer the parameter determining the rotor response in contrast to simple fluids. Varying the viscosity by concentration or temperature is not equivalent, and the Förster-Hoffmann power laws do not apply when the solution concentration varies. We show that the concentration regime of the protein solution, semi-dilute or concentrated, determines the sensitivity of the rotor to its environment.

Dynamic characteristics analysis of a dual-rotor system with bolted-disk joint

This article presents a nonlinear vibration characteristics study of a bolted joint dual-rotor system. The motion equations are derived through the lumped mass modeling method and a two-node bolted joint element. Nonlinear time-varying bending stiffness at the joint interface is considered in the numerical integration. Qualitative analysis of the effect of preload on system responses is conducted through changing the value of the transition point of bending stiffness of the bolted joint. Moreover, the transfer path of vibration in the dual-rotor system through inner-shaft bearing was discussed in the present work. The nonlinear differential equations are solved using the Newmark integration method to predict the dynamic characteristics of the dual-rotor system. The results show that the maximum vibration displacement of LP rotor is positively correlated with that of HP rotor as preload changes. Moreover, the maximum amplitude of the time-domain responses of the HP rotor will decrease and the minimum amplitude will increase with the increase of preload. The difference between the maximum and minimum values of the time-domain response will decrease with the increase of preload. This can be explained by the “stiffness hardening” phenomenon of the bolted joint. The research results can help understanding the dynamic properties of the bolted joint dual-rotor system and the vibration transfer path of the rotor system through inner-shaft bearing.

A Synchronous Holo-Balancing Method for Flexible Rotors Based on the Modified Initial Phase Vector

Reducing the vibration responses caused by the unbalance of the rotor is a crucial technology to ensure the safe and efficient operation of high-speed rotating machinery. For the flexible rotor system, the unbalance responses of rotors vary in different radial directions due to the anisotropic stiffness. The holospectrum technique using multi-sensor fusion provides ideas to solve this issue. The standard balancing method based on the holospectrum technique takes the Initial Phase Vector (IPV) as the balancing object, which could not represent the unbalance of flexible rotors correctly. In addition, the operating speed of the flexible rotor is generally higher than the first critical speed (FCS), making it necessary to fulfill the balancing of the first two modal shapes respectively in two steps. The above-mentioned procedure is not only very dangerous but also requires a large number of test runs resulting in corresponding wastages. In order to solve the issues mentioned above, a synchronous holo-balancing method for flexible rotors based on the modified initial phase vector (MIPV) is developed in this paper. Firstly, to tackle the limitation of IPV, the concept of equivalent rotating frequency circle is presented and then the MIPV is proposed as a new balancing object. MIPV could linearly represent the unbalance of the flexible rotor and increase the accuracy of holo-balancing. Secondly, the synchronous holo-balancing method is carried out to achieve the balancing at the speed below the FCS, reducing the complexity and danger of test runs at high operating speeds. And the synchronous balancing procedures based on the MIPV are further summarized in detail. Finally, two experimental results with different operating speeds and probe installations validate the feasibility and effectiveness of the proposed method. Compared with other traditional balancing methods, the proposed method can minimize the residual vibration and achieve state-of-the-art performances.

Effect of unbalancing mass placement in hydropower generators with floating rotor rim

Dynamic models for hydropower generators treat the rotor part as a rigid body; however, many studies have shown the opposite. The electromagnetic force distribution of deformed rotors is uneven, creating Unbalance Magnetic Pull, causing high forces on generator components leading to a risk of fatigue, therefore shortening the life of machines. Unbalancing masses can worsen the asymmetries of the rotor, which would further increase the effect of the electromagnetic interactions. This paper evaluates the rotor response using different unbalancing masses at the rotor and at the poles to quantify their impact in displacements and exciting frequencies. The model employed in this paper is based on the equation of motion derived using Lagrange equations in both co-rotating and stationary frames of reference, considering the effects of Centrifugal loads, Coriolis, and magnetization of poles. Different unbalancing mass placements affect different variables; extra weights in the poles contribute predominantly to the deformation of the rim, while the unbalance in the shaft affects the position of the shaft; a combination of placements was also studied. The simulations were performed and compared with and without radial electromagnetic forces, showing how the presence of magnetized poles further deforms the shapes of the rotor.

Nonlinear dynamic characteristics analysis of a rotor system supported on aerodynamic bearings

Due to the compressibility of gas, the aerodynamic bearings supported rotor system has strong nonlinearity. In this paper, the finite difference method is adopted to solve the Reynolds equation of the compressible fluid and obtain the forces of the gas film. Then the dynamic model of the aerodynamic bearing-rotor system is established, and the Runge-Kutta method is applied to solve the nonlinear equations of motion. With theories of nonlinear dynamics, the bifurcation characteristics of the rotor system supported by aerodynamic bearings are studied. Results show that the rotational speed and the unbalance has great influence on the nonlinear characteristics of the rotor, both periodic and non-periodic responses might emerge.

Influence of tooth crack parameters on bearing vibration signal of a geared rotor

Fault diagnosis is a mandatory process in modern industry management, because it may reduce costs due to unexpected failures that may occur in machines. It is proposed to study the dynamic effect in the rotor response of gear tooth crack caused by bending stress. As the bearings are the common location to install sensors as accelerometers, the response in their corresponding degrees of freedom is considered. A geared rotor model is assumed for the simulations. This model embraces a detailed finite element discretization, which contemplates five degrees of freedom per node, including torsional rotation. In addition, a time-varying mesh stiffness calculated by the potential energy method is adopted to represent the tooth contact. A crack model is assumed with three input parameters (initial position, propagation angle and depth). A design of experiments was set up to show the influence of each parameter on the system response for three different mean depths. The results analysis pointed out that for a precise parameter identification, all three parameters should be taken into account, because they affect the system response and they also present combined influence.

On the robust autorotation of a samara-inspired rotor in gusty environments

Autorotating samaras have evolved to propagate successfully to their germination sites with the help of wind. This wind, in turn, is inherently unsteady across an extensive range of scales in the atmospheric boundary layer. To generate lift, samaras rely on the formation of a stably-attached leading-edge vortex (LEV) on the suction side of their wings. The kinematics of autorotating samaras experiencing gusts were examined experimentally in order to provide insights into the aerodynamic mechanisms responsible for successful propagation. The gust response of seven mature Boxelder Maple (Acer negundo) samaras was investigated using a small unsteady wind tunnel able to create vertical gusts. Interestingly, the samaras were found to have a stable tip-speed ratio (λ) during the gust phase, thus suggesting that the LEV remained stably-attached. Inspired by samaras, we designed a three-bladed rotor that incorporates key aerodynamic and geometric properties of samaras so as to exhibit a stably-attached LEV. The gust response of the samara-inspired rotor was examined using a towing-tank facility. The gust was emulated in the towing tank by accelerating the rotor from an initial steady speed to a final steady speed. Different gust intensities were tested by varying the rotor’s normalized inertia number (I*) by systematically increasing the rotor moment of inertia (I). Similar to the natural samaras, the rotor exhibited a robust tip-speed ratio during all simulated gusts. The rotor’s tip-speed ratio increased by a maximum of 11% and 6% during the slowest and fastest simulated gusts, respectively. By maintaining a stable tip-speed ratio during the gust, the samara-inspired rotor is thought to maintain stable LEVs resulting in stable autorotation. Therefore, by learning from the samara-inspired rotor, we suggest that samaras propagate successfully from their parent trees in unsteady (realistic) environments in part due to their robust autorotation properties.

On the flow-acoustic coupling of fan blades with over-the-rotor liner

Over-the-rotor liner exhibits the potential to further attenuate turbofan noise, but the physics involved remain to be explored. In this paper, a three-dimensional coupled singularity method is proposed to investigate the flow-acoustic coupling effects of axially overlapping annular rotor and finite-length liner in subsonic flow. The formulation adopts the orthogonal basis expansion of the generated disturbances in terms of the hard-walled duct modes. The sound scatterings at the rotor and the liner are then characterized, respectively, by the underdetermined dipole and monopole distributions. We derive a simultaneous solution to the coupled unsteady rotor and liner responses, which ensures that the resultant perturbed field satisfies both the impermeable boundary condition on the blade surfaces and the impedance boundary condition on the lined wall. The effect of a perforated porous-material liner on the wake–rotor interaction tones is investigated. The analysis reveals that for the sound field of varying mode and frequency characteristics, moving the inlet liner to the over-the-rotor location generally leads to limited loss or even an increase of upstream sound absorption, along with additional acoustic benefits in the aft duct. The flow-acoustic coupling between the axially overlapping rotor and liner is shown to alleviate significantly the unsteady blade loading and meanwhile intensify the fluid particle oscillation through the acoustically treated wall. Sound source reduction and sound dissipation enhancement are thus identified as the governing noise attenuation mechanisms. Finally, we extend the analysis to provide insights into the effectiveness of over-the-rotor acoustic treatment with shortened axial length.

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Continuous Model and Analytical Solution for Unbalance Responses

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations.

Experimental and numerical investigation of the unbalance behavior of rigid rotors supported by spiral-grooved gas journal bearings

The forced response of rigid rotors, supported by herringbone-grooved gas journal bearings are investigated numerically and experimentally. The rotor configurations are varied by using end cylinders, attached at both sides of the shaft. Three rotors with different center of mass positions relative to the bearing locations are investigated for a variation of unbalance conditions. The numerical predictions by a quasi-linear unbalance approach and a full transient analysis are compared with experimentally obtained data. Different unbalance configurations are tested for validating the numerical models at orbital motions larger than 50% of the clearance and for bearing compressibility numbers of up to Λ=42. The investigation shows a maximum difference of 19.5% between nominal model predictions and experimental data at maximum orbital motions. The influence of the center of mass position on the rotor motion is proven to be significant and agrees with the numerical predictions. Further, the test unit is operated at different tilt angles, allowing to investigate the influence of static loading due to gravitational force on the forced response. It is found, that under different static loading, the rotor orbital motion remains unaltered and its influence can be neglected in the unbalance analysis.

Aeroelastic Response of Wind Turbine Rotors under Rapid Actuation of Flap-Based Flow Control Devices

The largest commercial wind turbines today are rated at powers between 12 MW to 16 MW, with rotor diameters between 220 m to 242 m, which are expected to grow beyond 250 m in the near future. Economies-of-scale factors suggest the advantages of upscaling in rotor size to effectively harvest the wind potential. An increased emphasis on studies related to improvements and innovations in aerodynamic load-control methodologies has led researchers to focus on overcoming the bottlenecks in size upscaling. Though conventional pitch control is an effective approach for long-term load variations, their application to mitigate short-term fluctuations has limitations. This is directly associated with the cubical dependence on the weight of the rotor with increasing diameter. Alternatively, active flow-control devices (FCDs) have the potential to alleviate load fluctuations through rapid aerodynamic trimming. Fractional light-weight attachments such as trailing-edge flaps promise the swift response of such rapid fluctuations and require low power of actuation. The current study investigates the performance of active in dynamic load control for utility-scale wind turbines through an aeroelastic evaluation of the turbine response to control actions in short time-scales relevant to rapid load fluctuations. The numerical platform used in the analysis is designed to consider the complex multi-physics dynamics of the wind turbine through a self-adaptive Ordinary Differential Equation (ODE) algorithm that integrates the dynamics presented by control system in to the coupled response of aerodynamics and structural deformations of the rotor. The benchmark case in consideration is the use of fractional trailing-edge flaps used on blades designed for the NREL-5MW Reference Wind Turbine, originally designed by the National Renewable Energy Laboratory.

Crack detection methodology in rotor bearing system by DWT based adaptive neuro-fuzzy inference systems

Data-based machine learning methods in condition monitoring of high-speed rotors are gaining more importance due to the increase in computational speeds of computers in recent years. Machine learning methods can analyze and predict the behaviour of the system more accurately based on the methodology and truthfulness of trained data. The proposed research is a data-based crack detection technique in rotors based on Discrete Wavelet Transforms (DWT) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS). DWT based ANFIS is used to de-noise the response of rotor with open cracks. A methodology is proposed to effectively train and validate ANFIS to de-noise the signal with DWT noise information. Detail-1 of DWT on ANFIS de-noised response is used to identify the location and severity of the crack in the overhung rotor. Two separate ANFIS are proposed to identify crack location and crack depth from DWT detail-1 coefficients of ANFIS de-noised response. It is found that proposed DWT Based ANFIS de-noise the signal with Root Mean Square Error (RMSE) of 3.96 × 10−8, detects the crack location with RMSE of 0.1656 and depth of crack with the RMSE of 1.321.

Influence of Lubricant Film Cavitation on the Vibration Behavior of a Semifloating Ring Supported Turbocharger Rotor With Thrust Bearing

Abstract This contribution investigates the influence of outgassing processes on the vibration behavior of a hydrodynamic bearing supported turbocharger rotor. The examined rotor is supported radially by floating rings with outer squeeze-film damping and axially by thrust bearings. Due to the highly nonlinear bearing properties, the rotor can be excited via the lubricating film, which results in subsynchronous vibrations known as oil-whirl and oil-whip phenomena. A significant influence on the occurrence of oil-whip phenomena is attributed to the bearing stiffness and damping, which depend on the kinematic state of the supporting elements, the thermal condition, and the occurrence of outgassing processes. For modeling the bearing behavior, the Reynolds equation with mass-conserving cavitation regarding the two-phase model and the three-dimensional (3D) energy as well as heat conduction equation is solved. To evaluate the impact of cavitation, run-up simulations are carried out assuming a fully (half-Sommerfeld) or partially filled lubrication gap. The resulting rotor responses are compared with the shaft motion measurement. Also, the normalized eccentricity, the minimum lubricant fraction, and the thermal bearing condition are discussed.

Response and flow characteristics of a dual-rotor turbine flowmeter

The technical problems of flow measurement in hypersonic flight could be mitigated through dual-rotor turbine flowmeters (DRT-FMs). In this study, a visual experiment platform was designed to reproduce the flow of a 1.3 cm diameter DRT-FM. A mathematical model considering two rotors was developed to perform a parameterised study and evaluate the rotor responses. Further, the entire flow passage was numerically simulated through an added automatic iterative rotor-dynamic calculation based on the angular momentum balance theory. According to the experimental results, the response range of the rotational speeds was divided into three stages: unresponsive, unstable, and stable. The downstream rotor responded at a lower flow rate, increasing the measurement range of the rotor turbine flowmeter. Considering the region of linear increase in the rotor speed in stable state under different flow media, tip clearances, and number of blades, the mathematical results indicated that the downstream rotor exhibited a compensation effect of the rotational speed on the calculation of rotational speed at the current flow rate conditions, which mitigates the measurement instability of the upstream rotor. Through the simulations, the rotation speed difference of the two rotors resulted in a slight periodic disturbance to the downstream rotor, which was alleviated after flowing through the spacer and could be ignored. Moreover, the high vorticity regions appeared around the rotors and areas of abrupt structural changes in the flow passage; the distribution gradually extended as the vorticity decreased. The present study provides an understanding of the DRT-FM and some recommendations to improve its characteristics.

Динамический расчет тандемного ротора гребных электродвигателей

The article presents the results of modeling the dynamic response of the tandem rotors of ice-class vessel electric propulsion motors under extreme operating conditions. The loading of rotors by torques in combination with vibration transmitted through the supports to the electric motors is considered as an external non-stationary action. A method for constructing a three-dimensional finite element model of the structure under study by fragmentary assembly has been developed on the basis of the ANSYS Mechanical software package. A scheme of elastic-compliant 3D-links allowing simulating the reciprocating-rotational vibrations of a tandem of rotors is presented. A test example is used to verify the proposed mechanical-mathematical model of the torsion system. Based on the calculated data, the analysis of the dynamic parameters of the tandem rotors is performed for the most unfavorable operating scenarios.

A new concept of a hydrodynamic bearing lubricated by composite magnetic fluid for controlling the bearing load capacity

The paper deals with a new design concept of a hydrodynamic bearing lubricated by composite magnetic fluids, which belong to the category of liquids with a yielding shear stress if effected by a magnetic field. Development of the mathematical model of the studied bearing required to derive the equation for the pressure distribution in the thin film of lubricant exhibiting yielding shear stress, the magnitude of which depends on magnetic induction. The magnetic field in the bearing gap is controlled by the change of the current powering the electric coil, which generates magnetic flux passing through the bearing gap. The developed mathematical model was implemented in the computational procedures for transient response of rotors. The computational simulations confirm that increase in magnetic induction in the bearing gap increases the bearing load capacity and shifts the journal towards the bearing centre. The advantage of the investigated bearing is that it works on a semiactive principle. The conducted research made it possible to propose and study a new design of a controllable bearing, the operation of which is based on utilization of the change of resistance against the flow of composite ferromagnetic fluids by the action of a magnetic field.

Dynamic analysis of Jeffcott rotor under uncertainty based on Chebyshev convex method

Rotor system is often affected by various uncertain factors during work, which may affect the normal working process of the rotor system. In this paper, aiming at the uncertainty of the Jeffcott rotor system, a non-probabilistic convex model is constructed to describe the uncertain parameters. By introducing the non-embedded Chebyshev expansion function, the Chebyshev Convex Method (CCM) is proposed. Then, the CCM is employed to calculate the rotor response when the mass and bearing stiffness are respectively uncertain parameters. Meanwhile, by changing the mass of the rotor disc and the bearing support position on the Bently RK4 rotor rig, the Jeffcott rotor with uncertain parameters is simulated. The numerical and experimental results show that the proposed method is valid and effective for quantifying the uncertain parameters of the Jeffcott rotor system. In addition, the Jeffcott rotor response with multiple uncertain parameters is discussed in detail. The results show that compared with the parameters related to the material properties of the rotor such as mass and density, when the parameters related to the bearing support such as stiffness and damping are uncertain, it will have a greater impact on the response of the rotor system.

Effect of Intentional Mistuning on Dynamic Characteristics of a Energy Turbomachine Bladed Disk

In this article the effect intentional mistuning of an axial turbomachine bladed disk has been analyzed in order to reduce forced response due to low-order engine excitation. The maximum value of forced response of turbomachine rotor’s blades with mistuning parameters is usually much more than the value of the tuned rotors. An increase level mistuning of this critical value actually leads to a decrease magnifications of the forced response. Thus, the actual work has been introducing some degree of intentional mistuning in the design to achieve these purposes. The effectiveness of intentional mistuning has been researched at the design stage of the bladed disk in the energy turbomachines, which is introduced into the rotor’s design by changing the nominal mass of the blades in harmonic models.