Stability Of Rotor Research Articles

Air Ring Bearings: Efficient Modelling and Case Study for Improved Vibration Behavior and Enhanced Rotor Stability

Air Ring Bearings: Efficient Modelling and Case Study for Improved Vibration Behavior and Enhanced Rotor Stability

Numerical Study on Characteristics of Lead-Bismuth Lubricated Hydrodynamic Bearing Considering Non-Condensable Gas

Lead-Bismuth Eutectic (LBE) is an interesting candidate as a coolant for Generation IV nuclear power plants. Lead-bismuth lubricated radial guide bearing is the key component of the mechanical pump in a lead-bismuth coolant system. In this paper, the transient calculation model of multiphase lubrication flow field of journal bearing is established by using Singhal full cavitation model and structured dynamic grid technique. Due to the saturated vapors of LBE being very low, the effects of different Non-Condensable Gas (NCG) contents on the characteristics of lead-bismuth lubricated journal bearing systems were analyzed. The results show that the NCG content has an obvious influence on the working state of the bearing. With the increase in NCG content, the bearing load capacity decreases. Under the same load, with the increase in NCG content, the eccentricity of the static equilibrium position will be larger, which will increase the risk of bearing contact with the bearing bush. Moreover, the increase of NCG content will lead to the increase of tangential oil film force work, which is helpful to improve rotor stability.

Inductive plasma excitation forcing configuration on reduction of tip distorted inflow effect on the aerodynamic stability of axial compressor rotor

This research delves into the mitigating impacts of dielectric barrier discharge (DBD) plasma excitation induced forcing orientation against the detrimental consequences of distinct radial tip distortions which in turn affect the axial compressor rotor performance and alters the flow structure at the tip region. Full annulus transient CFD simulation was utilized to evaluate the consequences of plasma actuation at distorted conditions with different blockage percentages. Beyond flow field and frequency analysis, the study further characterized rotor performance under different conditions by evaluating key performance metrics, including total pressure rise coefficient, stall margin variation, and span-wise rotor inlet velocity distribution. The injection of momentum caused by plasma actuators to the low-energy region behind the distortion screens proved to be effective on rotor aerodynamic stability facing radial tip distortion. In the case where 15 % of the inlet area was blocked, the stall margin varied from -8 % to -3.5 % with axial plasma actuators in action. However, the best configuration of plasma actuators for the enhancement of the stall margin and flow characteristics was identified to have opposite forcing direction with respect to the rotor rotational velocity. Additionally, these actuators suppressed frequencies caused by fluctuations in the rotor blade row tip leakage vortex, suggesting an improvement in the flow pattern within the rotor tip area.

Flow Mechanism Study on the Effect of Controllable Speed Casing With Different Axial Starting Points on Transonic Compressor Rotor Stability

Abstract The controllable speed casing represents an exploring approach to casing technology, designed to enhance the adaptability of casing in compressors under variable working conditions. This paper developed a numerical study into the effects of the axial starting point of the rotatable ring in the controllable speed casing on stability enhancement and performance. Additionally, the study sought to unveil the action mechanism of the rotating casing on various flow elements within the tip passage. The findings indicated that the optimal axial starting point for achieving the most pronounced stability enhancement effect in each rotating speed of the rotatable ring was located at the tip leading edge. In terms of the flow mechanism, the rotation of the rotatable ring was found to enhance the throughflow of the mainstream and the tip vortex, while exacerbating the backflow of the tip leakage flow, which occurred at middle and rear of the tip clearance and had not evolved into tip vortex.

Parametric instability analysis of rotors under anisotropic boundary conditions

Ensuring rotor stability is a major concern in engineering, as instabilities can lead to catastrophic failures. Existing literature shows that anisotropic boundary conditions significantly affect the parametric instability characteristics of rotors under periodical axial loads. However, there is little literature systematically analyzing the formation mechanism of parametric resonance under these boundary conditions or providing a detailed classification of the parametric instability regions. Therefore, this paper presents a comprehensive parametric instability analysis of a rotor subjected to periodic axial loads under anisotropic boundary conditions. A novel approach based on the multiple scales method is proposed to address anisotropy in the boundary conditions. Using this approach, the analytical boundaries of the parametric instability regions are derived, and a proof regarding the absence of certain parametric resonances is presented. These analytical solutions are validated by numerical results obtained from the discrete transition matrix method, which form the basis for systematically investigating the effects of anisotropy in direct or cross-coupling stiffness/damping coefficients on the rotor instability. The key scientific contributions of this work include: Deriving analytical instability boundaries, providing a more efficient alternative to purely numerical methods while maintaining high accuracy; Demonstrating the absence of parametric resonance of difference type under both isotropic or anisotropic boundary conditions; Discovering that anisotropy in stiffness coefficients can induce self-interaction within a given forward or backward whirl mode, as well as interaction between two forward or two backward whirl modes, leading to additional instability regions; Reducing anisotropy in direct damping coefficients may increase critical dynamic load coefficients, potentially enhancing rotor safety; If the cross-coupling stiffness coefficients exceed the threshold for triggering intrinsic instability, the rotor may become unstable in all operating conditions. All these findings offer insights into the stability management of rotors under various operating conditions and provide valuable guidance for designing and operating safer, more efficient rotor systems.

Dynamic and Phase-Frequency Characteristics of Rotor Instability Induced by Steam Flow Excited Vibration in Seals

Steam flow excited vibration in seals seriously affects the seal-rotor stability. A mesh deformation based on user-defined functions was adopted to establish the multi-frequency whirl model, and the reliability of the simulation method was verified by experiments. The average effective damping and working ability of the fluid were proposed to analyse the stability of the seal. The mechanism of seal instability induced by steam flow excited vibration was revealed through the phase-frequency characteristics of exciting forces and displacements. The results show that direct damping decreases gradually with an increase in frequency, and the cross-coupling damping tends to be stable over 15 Hz. The average effective damping is more sensitive and accurate in predicting the seal stability. Effective damping decreases with increased frequency. Therefore, the rotor stability is decreased. Near the 12 Hz and 24 Hz frequencies, the average effective damping of eccentricity fluctuates, so the seal stability is poor. The negative effect of exciting forces increases, and the seal stability is improved when the eccentricity increases. When the phase difference between the excitation force and displacement changes, the seal stability decreases. The fundamental reason for rotor instability induced by steam flow excited vibration in seals is the sharp changes of phase difference caused by pressure fluctuations.

A comparative study on rotordynamics characteristics of hole-pattern damping seals with different cavity shapes

PurposeThe purpose of this paper is to improve the seal performance by proper design of the cavity shape of the damping holes, especially the rotordynamics characteristics of the hole-pattern damped seal (HPDS).Design/methodology/approachA new damping seal structure that comprises a circle-shaped cavity and two directional leaf-shaped cavities with a dovetail-shaped diversion groove is proposed. The comparative study on the sealing characteristics of dovetail-shape, leaf-shape and classical circular HPDSs was carried out using ANSYS CFX.FindingsThe dovetail-shaped HPDS significantly outperformed two other damping seal designs in leakage and rotordynamic performance. At a rotating speed of 7,500 rpm, it showed a 25% reduction in leakage, a 23% increase in average effective damping and a 119% increase in average effective stiffness. The cross-coupled stiffness Kxy shifted from positive to negative, reducing circumferential flow. The dovetail's inclined leaf-shaped grooves create a double vortex that slows jet velocity in the seal clearance and alters spiral flow direction, resulting in a uniform pressure distribution and enhanced rotor stability at low frequencies.Originality/valueThis study proposes a novel HPDS with dovetail-shaped diversion grooves. The seal can realize the simultaneous improvement of rotordynamics and leakage characteristics compared to the current seal structure.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2024-0127/

A Review on the Dynamic Performance Studies of Gas Foil Bearings

Gas foil bearings have important and wide applications in high-speed turbomachinery, generating low frictional lubricating gas film in series with underlying elastic foil structures to support the rotor system. Their dynamic performance is of vital significance in maintaining the rotor stability as well as in depressing rotor vibrations. This paper conducts a comprehensive review on dynamic performance studies conducted on gas foil bearings, including research on the dynamic stiffness and damping coefficients, bearing stability, nonlinear vibrations of the rotor–bearing system, and active methods for controlling rotor dynamic motions. This review provides clear observations towards the developments and iterations of the models, methods, and experiments of these studies.

Control Strategy of Flywheel Energy Storage System for Improved Model Reference Adaptive System Based on Tent-Sparrow Search Algorithm

This study addresses speed sensor aging and electrical parameter variations caused by prolonged operation and environmental factors in flywheel energy storage systems (FESSs). A model reference adaptive system (MRAS) flywheel speed observer with parameter identification capabilities is proposed to replace traditional speed sensors. The proposed method uses reference and adjustable models to identify the stator resistance and permanent magnet flux (PM Flux) to mitigate the adverse effects of electrical parameter changes on control performance. The Tent chaotic mapping-improved Sparrow Search Algorithm (SSA) optimizes the Proportional-Integral (PI) controller parameters for the dual closed-loop and MRAS speed adaptation laws of the flywheel motor. Moreover, a self-switching parameter identification (SSPI) scheme, which constructs a cost function based on the current, parameter identification, and speed errors, is proposed to prevent inaccuracies in parameter identification. The MRAS observer selects the appropriate PI adaptive mechanism based on the error values, thereby enhancing identification accuracy. Simulink simulations show significant improvements in the rapidity and accuracy of the Tent-SSA optimized MRAS flywheel speed observer, enhancing the stability and robustness of the flywheel rotor. Experimental validation on a constructed FESS platform confirms the feasibility of this method.

A comparison of static and rotordynamic characteristics for two types of liquid annular seals with and without helical grooved stator

Less leakage is a benefit of parallel grooved liquid seals (labyrinth seals). But researches show that the liquid seal with parallel grooves on the rotor harms the rotor stability. The seal with helical grooves on stator performs well in terms of rotordynamics, and its leakage is sensitive to the rotating speed. To make use of the advantages of both seals and improve seal stability, based on the Smooth-stator/Parallel Grooved-rotor (SPG) liquid seal, a Helical Grooved-stator/Parallel Grooved-rotor (HGPG) liquid seal is designed. To evaluate two liquid seals’ leakage, rotordynamic characteristics and drag power loss, a transient computational fluid dynamics-based method is employed. This method is based on the multi-frequency elliptical-orbit rotor whirling model and the mesh deformation technique. The published experimental data of the leakage and rotordynamic force coefficients for an SPG liquid seal are used to validate the accuracy and dependability of the current method. Seal leakage and force coefficients are presented and compared for the SPG liquid seal and the HGPG liquid seal at various pressure drops. The influences of parallel groove depth on the leakage and rotordynamic properties for the HGPG liquid seals at two rotational speeds (2000, 6000 r/min) are analyzed. The numerical findings demonstrate that the novel HGPG liquid seal has a lower leakage flow rate (by ∼22.3%) than the traditional SPG liquid seal. There is an optimal parallel groove depth that minimizes leakage. The presented novel HGPG liquid seal significantly improves rotordynamic stability, due to the similar effective stiffness and the obviously larger positive effective damping. Reducing parallel groove depth can increase the positive effective damping. In terms of leakage and rotordynamic characteristics, the novel HGPG liquid seal is a better seal design for liquid turbomachinery.

On the dynamics and wear properties of dry friction bearings in motor rotor system considering rough surface contact damping

Maintaining rotor stability and reducing bearing wear hold practical significance for the rotor system. However, the dynamic properties of rotor system supported by dry friction bearings are unknown, hindering effective bearing optimization. To tackle this issue, a 5-degree-of-freedom dynamics model is established for the motor rotor system of the outdoor unit supported by porous bearings. The rough surface damping contact model is employed to calculate the contact performance of the dry friction bearings. The effects of bearing edge modification on system dynamics and bearing wear properties are investigated and compared with well-lubricated bearings. The results demonstrate that an appropriate amount of edge modification can decelerate the impact between the rotor and the bearings and reduce wear under dry friction conditions.

Dynamic modeling and parametric instability analysis of internally damped rotating composite shafts in inertial and rotating frames

Parametric resonance may occur when the composite shaft is subjected to periodic axial loads. The phenomenon will lead to the serious destruction of the dynamic system. In this study, we aim to investigate the parametric instability characteristics of rotating composite shafts considering internal damping, and to provide valuable theoretical guidelines for avoiding the occurrence of parametric resonance. The two dynamic models of the composite rotor in the inertial frame and rotating frame are both established using Hamilton's principle. The governing equations of the composite rotor are reduced into a system of Mathieu–Hill equations by means of the Galerkin method. Then Floquet exponent method is employed to conduct parametric stability analysis of the periodic loaded composite rotor. After performing validation of present model and method, numerical results are presented to bring out the influences of reference frame, rotation speed, internal damping and lamination angle on the parametric instability region. The results show that the selection of reference frame does not affect the determination of the size and type of the parametric instability region. However, it is more suitable to use the rotating frame from the perspective of determining the type of the unstable region. The internal damping of composites should not be ignored when analyzing the parametric stability of composite rotors, especially for the high order excitation frequency.

Analysis and modeling of the aerodynamic ceiling effect on small-scale propellers with tilted angles

Micro air vehicles with propellers have been widely used in military and civilian applications due to their high maneuverability and low cost. As the mission scenarios and requirements of rotorcrafts become more complex, proximity effects caused by confined environments, such as the ceiling effect cause significant interference to the performance and stability of rotors. Most researchers have analyzed this phenomenon by considering the ceiling effect in hover conditions. However, few scholars considered the tilt angle between the rotor and the ceiling, which is more likely to occur in real missions, such as the close inspection of bridges or large equipment, flight in narrow indoor environments, and flight near the ceiling for fully actuated multirotors. In this study, a CFD-based study is conducted to evaluate the ceiling effect for small-scale tilted propellers. The aerodynamic analysis was experimentally evaluated through a series of ground tests in a test bench designed for this research. The CFD results were validated by a mesh-independent study and experimental data comparison. The results show that in contrast to the phenomenon of reduced thrust when tilt angles exist between the rotors and ground, the existence of tilt angles between the propeller and the ceiling reduces the thrust-increasing effect of the ceiling when the dimensionless distance is greater than 0.6. When the distance gets smaller, the thrust-increasing effect increases when the tilt angle is greater than 10∘. In particular, when the distance is less than 0.3, the existence of tilt angles will increase the thrust-increasing effect of the ceiling. Additionally, a data-driven model has been proposed to predict the thrust with the distance to the ceiling and the angle inclination between the rotor and the ceiling. This model enables future rotorcrafts that require accurate models to operate in narrow environments.

Leakage flow-induced excitation behavior and rotor instability in the high-speed supercritical CO2 scallop damper seals

As an innovative type of damper seal, the scallop damper seal (SDS) has shown greatly improved sealing performance for the high-compactness supercritical CO2 (S-CO2) turbomachinery, but leakage-induced excitation forces have an impact on the rotor stability. In this research, we improve the rotordynamic solution based on the multi-frequency elliptic whirling model for the S-CO2 seals and investigate the leakage-induced excitation behavior of SDS depending on seal geometry and operating condition. By comparing the results of a labyrinth seal and a full-partition pocket damper seal, we prove that SDS has better rotordynamic performance for the S-CO2 compressor. The results show that increasing the pressure drop favors greater direct stiffness and effective damping of the SDS. Inlet preswirl changes the direction of fluid-response force to coincide with the rotor motion, which is detrimental to rotor stability. Changing the cavity depth has no significant effect on the dynamic characteristics of the SDS, but shortening the cavity length reduces the direct stiffness to below zero. Supplementing the number of circumferential cavities increases the direct stiffness and effective damping but results in SDS not being able to be machined directly by milling cutters. The design with 12 circumferential cavities is recommended for the 100-kW-class S-CO2 compressor.

Effects of turbulence and bush wear on the transient tribo-dynamic characteristics of water-lubricated bearings

This research proposes a transient mixed elastohydrodynamic model considering turbulence and bush wear, as well as the concept of contact work, to study the transient tribo-dynamic characteristics of water-lubricated bearings. The effects of turbulence, wear depth, and wear deviation angle on transient tribo-dynamic characteristics of water-lubricated bearings are investigated. The findings show that turbulence significantly affects the dynamics of stable conditions and enhances the hydrodynamic effect, but little affects the frictional contact behavior. An appropriate wear depth favors improving the tribo-dynamic characteristics of the water-lubricated bearings, but it deteriorates as the wear depth continuously increases. Negative deviation angles are better for minimizing contact work and enhancing rotor stability. The lubrication and dynamic properties of water-lubricated bearings can be enhanced through a rational approach to wear morphology design. This research is important for the optimal design and diagnosis of water-lubricated bearings wear failures.

Numerical investigation on the rotordynamics of a high-speed air compressor supported by gas foil bearings

Gas foil bearings are particularly suitable for supporting rotors of hydrogen fuel cell air compressors. Based on Reynolds equation and elastic mechanics theory, a fluid-structure interaction model of gas foil bearings is introduced. A series of perturbation equations are developed and solved to obtain stiffness and damping coefficients of the foil bearings at different rotational speeds. A lumped model of the bearing-rotor system is developed and the rotor stability is analysed by innovatively applying Riccati transfer matrix method. The natural frequencies of the rotor are calculated and then the Campbell diagram is plotted. Subsequently, the critical speeds and the corresponding vibration modes are obtained. The predicted values of the proposed model are highly consistent with the reported experimental results and finite element results, indicating the accuracy of the model. Based on the calculation of rotor unbalance response, further investigation on the effects of unbalance parameters on unbalance response is conducted. The results obtained in this paper could provide theoretical reference for the design of foil bearing supported rotors.

Enhanced rotordynamic performance under various structural arrangements of hole diaphragm labyrinth seal

In this study, we study the influence of five drilling hole arrangements on the rotordynamic and leakage performance of hole diaphragm labyrinth seal (HDLS) type seals with precise CFD analysis. Key findings reveal that hole distance significantly affects direct and cross-coupled stiffness, thereby impacting stability and leakage. Notably, the smallest hole in rectangle four holes(RF)-HDLS does not yield the minimum leakage. Vortex structure analysis, employing the Q-criterion, elucidate horizontal two holes(HT)-HDLS's superior leakage reduction owing to enhanced turbulence eddy dissipation. Seals with larger hole diameters, down single hole(DS)-HDLS and up single hole(US)-HDLS, demonstrate stable rotordynamic performance, with DS-HDLS exhibiting a notable 106.3% improvement in cross-coupled stiffness. In contrast, seals with holes positioned farther away, DS-HDLS, US-HDLS and vertical two holes(VT)-HDLS, experienced increased leakage with whirl frequency. HT-HDLS and RF-HDLS displayed a decrease, attributed to the stronger centrifugal effect. Comparing to center single hole(CS)-HDLS, VT-HDLS and US-HDLS achieved a significant 159.3% direct stiffness improvement and 432.7% reduction in cross-coupled stiffness. Despite a maximum 4.2% leakage increase, this substantial enhancement in rotor stability should not be overlooked. Moreover, all seals exhibited lower leakage rates than the traditional labyrinth seal.

Geometrically exact aeroelastic stability analysis of helicopter composite rotor blades in forward flight

In this paper, a sophisticated method for analyzing the geometrically exact aeroelastic stability of composite rotor blades in forward flight has been proposed. The unique advantage of the proposed method is to use the geometrically exact beam model with the updated Variational Asymptotic Beam Sectional analysis (VABS) for structural modeling to not only calculate the blade cross-sectional properties and blade spanwise deformations more accurately, but also take into account the effect of transverse shear deformation and blade initial twist and curvatures sophisticatedly. The Peters finite state airloads theory and the Peters-He finite state dynamic inflow model are coupled to calculate the three-dimensional unsteady airloads applied on the blade. The auto-pilot trim scheme is adopted to determine the blade pitch controls. The finite element spatial discretization method, the Newmark numerical integration method, the Newton-Raphson method and the moving-block analysis method are combined to solve the established geometrically exact aeroelastic equations and obtain the geometrically exact aeroelastic stability of composite rotor blades. The proposed method is validated by correlation with existing analytical results. The investigations show that the effect of transverse shear deformation on the aeroelastic stability of composite hingeless rotors in forward flight is non-negligible. Blade initial curvatures have significant effect on the aeroelastic stability of composite hingeless rotors in forward flight, which is not only related to the blade elastic couplings, but also to the advance ratio.

Theoretical and numerical studies on stability of multiple eccentric rotors uniformly distributed along the circumference of two rigid bodies

This paper aims at studying synchronization, stability and motion characteristics of a new generalized dynamical model with two rigid bodies (RBs), driven by multiple eccentric rotors (ERs) uniformly distributed on the circumference of two different RBs. Using Lagrange’s equation, the motion differential equations of the system are deduced. The generalized theoretical analytical expressions of the criteria for implementing synchronization and stable operation of multiple ERs are obtained. Based on the above theoretical results, and taking the present dynamical model with six ERs for example, numerical qualitative discussions are given to deeply reveal the stable states and motion characteristics of the system in different resonant regions. The simulations are further carried out quantitatively, which verifies the validity of the above theoretical and numerical qualitative results. It is shown that, in the sub-resonant state with respect to the natural frequency of the main vibrating system, the stable zero phase difference between arbitrary two ERs on each RB can be achieved, in this case, the relative circular motion of two RBs with anti-phase is realized. This paper can lay a foundation for designing some new types of large scale high-frequency vibrating ball mills with high supply power.

On the characteristics of the wake of a wind turbine undergoing large motions caused by a floating structure: an insight based on experiments and multi-fidelity simulations from the OC6 project Phase III

Abstract. This study reports the results of the second round of analyses of the Offshore Code Comparison, Collaboration, Continued, with Correlation and unCertainty (OC6) project Phase III. While the first round investigated rotor aerodynamic loading, here, focus is given to the wake behavior of a floating wind turbine under large motion. Wind tunnel experimental data from the UNsteady Aerodynamics for FLOating Wind (UNAFLOW) project are compared with the results of simulations provided by participants with methods and codes of different levels of fidelity. The effect of platform motion on both the near and the far wake is investigated. More specifically, the behavior of tip vortices in the near wake is evaluated through multiple metrics, such as streamwise position, core radius, convection velocity, and circulation. Additionally, the onset of velocity oscillations in the far wake is analyzed because this can have a negative effect on stability and loading of downstream rotors. Results in the near wake for unsteady cases confirm that simulations and experiments tend to diverge from the expected linearized quasi-steady behavior when the rotor reduced frequency increases over 0.5. Additionally, differences across the simulations become significant, suggesting that further efforts are required to tune the currently available methodologies in order to correctly evaluate the aerodynamic response of a floating wind turbine in unsteady conditions. Regarding the far wake, it is seen that, in some conditions, numerical methods overpredict the impact of platform motion on the velocity fluctuations. Moreover, results suggest that the effect of platform motion on the far wake, differently from original expectations about a faster wake recovery in a floating wind turbine, seems to be limited or even oriented to the generation of a wake less prone to dissipation.