Stability Of Rotor System Research Articles

Study on Dynamic Characteristics of Single-Span Rotor Under Cross-Coupling Stiffness Control on Non-drive End

Abstract The sealing-induced cross-coupling stiffness (CCS) often decreases the rotordynamic stability of turbomachinery. In our previous study, an active negative CCS control strategy applied between two bearings in the middle of the rotor was validated to enhance the stability of the rotor system. In this paper, a different approach was taken by applying both positive and negative CCS control strategies to the non-drive end, aiming to investigate their effects on rotordynamic stability using a rotordynamic model. The model represented a single-span centrifugal compressor rotor with CCS at the seal node. The logarithmic decrements and unbalance response of the rotor system were compared under different CCS applications at the non-drive end and in the span. The results demonstrate that applying both positive and negative CCS at the non-drive end can improve system stability, but the positive CCS strategy has limitations, and its applicability is not as extensive as Negative CCS. A “critical stiffness” phenomenon emerges when the rotor system is actively stabilized at the non-drive end, resembling critical resonance. Furthermore, when components like seals introduce cross-coupling stiffness out of the span, they contribute to system stabilization. These findings provide valuable insights into actively enhancing the stability of rotor systems.

Nonlinear modeling and vibration response analysis of rod fastening rotor-bearing system with curvic coupling

Rod fastening combined rotor system (RFCR) are particularly popular in gas turbine rotor systems. The bolted connection introduces a discontinuity in this RFCR, which has a substantial influence on system performance.Traditional models of RFCR tend to neglect the influence of the connection structure, especially failing to fully consider the contribution of the curvic coupling to the rotor dynamics. To address this problem, this study proposes a new nonlinear analytical model of the rotor system, which focuses on the impact of the curvic coupling. This study provides a detailed analysis of the structural parameters and load forces of the curvic coupling. Based on this analysis, a mechanical model is created to assess how bolt preload and torque impact the stiffness of the curvic connection. The stiffness matrix of the curvic coupling is derived by the gear stiffness analysis method, and the accuracy of the model is confirmed using the finite element method. Furthermore, the model also considers the viscous and sliding state between the curvic coupling, which effectively describes the damping effect of the curvic coupling. On this basis, the motion control equations for the RFCR are formed, and a dynamic model considering the curvic connection in the RFCR system is introduced. The results show that the curvic coupling results in a decrease in stiffness and the occurrence of nonlinear damping phenomena in the RFCR.The RFCR exhibits a significant stiffness loss compared to the continuous rotor system, resulting in a decrease in the critical rotor speed. The nonlinear damping is mainly excited at high friction coefficient conditions and may lead to a self-excited vibration component in the rotor response at supercritical speeds. The negative impact of structural discontinuities on rotor dynamic performance can be reduced by increasing the bolt preload, decreasing the friction coefficient, and adjusting the amount of imbalance. This study offers a theoretical foundation for predicting curvic coupling-induced instability and serves as a reference for enhancing rotor system stability.

Influence of Unbalance and Differential Pressure on the Stability of Vertical Rotor-Seal System

Abstract The rotordynamic (RD) fluid force generated in fluid elements such as seals in turbomachinery affects the stability of turbomachinery and causes shaft vibrations. Various studies have been conducted to clarify the effects of seals on the stability of rotor systems. Many studies have investigated the rotor dynamics of horizontal rotating shaft systems, considering the RD fluid force generated in the seals, and in these studies, the stability of horizontal rotating shaft systems has been assessed via eigenvalue analysis using RD coefficients. However, few studies have analyzed vertical rotating shaft systems. The dynamic behavior of vertical rotating shafts differs significantly from that of horizontal rotating shafts because the weight of the rotor does not act on the seal in a vertical rotating shaft system. Vertical rotating shaft systems are generally prone to instability because of the fluid film whirl, and the amplitude of the shaft whirl tends to be large. When the amplitude is large, the RD fluid force cannot be linearized around the equilibrium point using RD coefficients. Therefore, destabilization and stabilization phenomena that appear in vertical rotating shaft systems cannot be predicted using eigenvalue analysis. Fluid–structure interaction (FSI) analysis that considers the interaction between the shaft vibration and the RD fluid force generated in seals is required to predict such phenomena. This study used FSI analysis to investigate the effects of unbalance and differential pressure on the stability of a vertical rotating shaft system subjected to RD fluid force generated in the seal.

A hybrid triboelectric-piezoelectric smart squirrel cage with self-sensing and self-powering capabilities

In aero-engines, squirrel cages are commonly used as elastic support parts for bearings, serving to adjust critical speeds and provide vibration damping. Their stable operation is critical for the safety and stability of rotor systems. In this paper, a triboelectric-piezoelectric squirrel cage (TPSC) with self-sensing and self-powering capabilities is proposed. Owing to the ingenious utilization of the supporting structure, a compact design is achieved, enabling energy harvesting from the relative motion of the rotor-stator structure and the vibration of elastic support. Based on a fabricated prototype, a series of experiments are carried out to investigate the effect of the rotating speed, imbalance mass, and contact mode on the output performance of TPSC. Under the rotating frequency of 15 Hz, a maximum power output of 100.0 μW is achieved. The TPSC is capable of sensing rotating speed and detecting rolling bearing faults. A self-powered temperature and humidity sensing system that can transmit data wirelessly every 10 minutes is also realized. The TPSC enables self-powered monitoring of rotor bearing systems with squirrel cages, providing a new option for online condition monitoring of aero-engines.

An Energy Transfer-Based Bifurcation Detection Method for Nonlinear Rotating Systems: Enables Accurate Capture of Period-Doubling Bifurcation and Instability

Rotor systems are widely used in industrial power generation and propulsion. Once the nonlinear contact stiffness and oil film force are taken into account, the dynamics and stability of rotor systems become quite complex, often accompanied by super-harmonic and chaotic motions. Furthermore, conventional methods face limitations in real-time detection of the bifurcations and complex nonlinear motions. This research investigates the bifurcations and stability induced by nonlinear factors in a rotor-bearing system from an energy perspective. Dynamic equations of a rotor-bearing system considering cubic term stiffness are established, the steady responses are obtained by the fourth-order Runge–Kutta method. The relationship between the bifurcations and energy transfers is analyzed numerically, the proposed stability criterion is validated by comparing the Lyapunov exponents. The bistable phenomenon of period-3[Formula: see text] ([Formula: see text]) motion is discussed in terms of numerical results and experiments which corresponds to the asymmetric jumps of the generalized energy. It is found that bifurcations and unstable motions of the nonlinear system can be captured accurately by detecting the energy transfers, the proposed generalized energy curve exhibits more detailed information than the conventional speed-up curve. These findings provide a new perspective on studying bifurcations and stability of rotating systems, which can be further applied in the condition monitoring, stability prediction as well as the design of nonlinear energy sink, representing significant progress in converting theory into engineering applications for rotor systems.

Evaluation of the flow state and static performance of smooth annular liquid seals

The static fluid-induced force and stiffness coefficient of the smooth annular seal directly affect the rotor system stability. In this paper, a computational fluid dynamics method is applied to investigate the flow characteristics of a smooth annular seal for various eccentricities, discharge/supply pressures and rotational speeds under different flow conditions (laminar, transition, and turbulent flow). The influence factors and formation mechanism of the static instability in the smooth annular liquid seal are analyzed. Results show that laminar flow dominates the flow state at a rotational speed of ω= 2000 rpm. As the rotational speeds increase, the transition flow (2000-7000 rpm) gradually transits to the turbulent regime (ω> 7000 rpm). The direct static stiffness decreases first and then increases from laminar to transition flow state, and the viscosity effect is the dominant factor. For transition and turbulent flow with high eccentricities (ε= 80 %), the dominant viscous effect and inertial effect lead to the negative radial force and negative direct static stiffness coefficients. The smooth annular liquid seal shows best performance in the laminar flow and worst performance in the turbulent flow.

Static and Dynamic Characteristics of Nonmetallic Labyrinth Seals Based on Fluid–Solid–Thermal Coupling

In this paper, static and dynamic characteristics of a labyrinth seal were studied by fluid–solid–thermal coupling analysis (FSTCA). Deformation and stress distribution of nonmetallic labyrinth seals (i.e., PEEK and PEEK-CA30) were further analyzed to investigate the effects on leakage and rotor stability compared to that of metallic material (i.e., AL alloy). The results show that a higher pressure drop of airflow at the last tooth along the airflow direction suggested a more remarkable energy conversion to kinetic energy. Airflow velocity at the tooth root was obviously lower than that at the tooth tip because of vortex in tooth cavity. Maximum deformation of the seal occurred at tip of the first tooth, while equivalent stress mainly distributed at the root. Both axial and radial deformations led to deformations of seal cavities and upward movements of the teeth, resulting in greater radial clearances. PEEK-CA30 had the lower radial and axial maximum deformations compared to PEEK and AL alloy, which in turns caused a lower leakage with increasing inlet temperature and inlet/outlet pressure ratio and a higher effective damping coefficient under different vortex frequencies, indicating a better seal performance and a better stability of rotor system. The equivalent stress for AL alloy deeply depended on inlet temperature of airflow due to higher elasticity modulus, higher thermal conductivity and higher thermal expansion coefficient, which made the seal more likely to fail under higher inlet temperature.

Effect of internal excitation induced by non-uniform contact of roller bearings on nonlinear vibration and stability of rotor system under combined loads

The misalignment of roller bearing rings will results in moment load, together with the unbalance and external loads, forming the combined dynamic loads. The complex combined load can cause non-uniform contact of rollers and rings, which reduces the bearing’s life and significantly affect the vibration of rotor systems. This paper mainly studies the roller bearing internal contact performances under combined loads and the influence of internal excitation on the nonlinear vibration of rotor systems. First, the “slices” method is used to establish the mechanical model of roller bearings, which considers the radial clearance and nonlinear Hertz contact. The obtained time-varying bearing nonlinear support reaction is introduced into the rotor concentrated mass model, and a roller bearing–rotor system dynamic model is proposed. Further, the system’s complex nonlinear vibrations, such as bifurcation and chaos, are analyzed by spectrum, orbits, bifurcation, and Poincare map. The roller bearing contact performances and stability under the influence of ring tilt angle, rotational speed, and unbalance, are analyzed by contact load statistical features. Finally, based on a rolling bearing–rotor test rig, the vibration experiment considering the combined load was performed, and the experiment results are compared with simulation results to verify the proposed model and conclusions.

Analytical and experimental investigation on stability of rotor system with spline coupling considering torque, friction coefficient and external damping

The spline coupling is widely used in high-speed rotor systems. As the lack of good understanding of the instability and influence behaviors, the spline induced instability is still not well controlled. From the view of dynamics, torque, friction coefficient and external damping are key factors that influence the stability directly. In this paper, the mechanism and influence law of spline induced instability are investigated. A new model to predict the threshold speed of instability of spline coupled rotor accurately is proposed. A criterion to determine the stability of rotor through judging the relative displacement between splines is derived. Then the effects of torque, friction coefficient and external damping on stability are investigated. Corresponding experiments are carried out to validate the model. The characteristics of instability caused by spline are observed successfully through repeated experiments. Results demonstrate that the mechanism of instability caused by spline is the relative effect of the internal damping from spline coupling and the external damping. This investigation can help with the prediction of instability caused by the spline and the regulation of rotor stability.

Experimental investigation for novel hybrid journal bearing with hydrostatic squeeze film and metal mesh damper in series

PurposeThis study aims to present a novel hydrostatic squeeze film-metal mesh journal bearing (HS-MMJB), which uses both hydrostatic squeeze film damper (HSFD) and metal mesh damper (MMD), to suppress the vibration of rotor-bearing systems.Design/methodology/approachThe lubrication equations were introduced to calculate the dynamic characteristics of HS-MMJB, and the response analyses of rotor systems were carried out. Experiments were conducted to study the vibration reduction of a rotor system with HS-MMJB. In addition, experiments for different oil supply pressures in the HS-MMJB were conducted.FindingsThe theoretical and experimental results show that the HS-MMJB exhibits excellent damping and vibration attenuation characteristics. Moreover, the stability of the rotor system can be improved by controlling the oil supply pressure.Originality/valueThere is a dearth of research on vibration characteristics of rotor system support by journal bearing combining HSFD and MMD. Moreover, the active oil pressure control is implemented to improve the stability of rotor system.

A Three-Dimensional Slip Velocity Model for Water-Lubricated Hydrodynamic Journal Bearings

Hydrodynamic journal bearings, coated with polytetrafluoroethylene (PTFE) and lubricated by water, have been widely used in ships and large-scale pumps, and the function is to maintain the stability of rotor system. However, slip velocity exists on the PTFE-coated surface, whose effect is still an open question. This study aims to investigate the static characteristics of water-lubricated hydrodynamic journal bearings under three-dimensional slip velocity boundary conditions. Firstly, under the non-slip boundary condition, the CFD (computational fluid dynamics) method with ANSYS Fluent is verified based on the Reynolds lubrication equation and the open literature. Then, a three-dimensional slip velocity equation that is based on the Navier slip velocity boundary condition is proposed and embedded into Fluent. Finally, the effects of slip length on the static characteristics are analyzed. Under the same eccentricity ratio, with the increase in slip length, the load capacity decreases due to the decrease of the pressure circumferential gradient, and the friction power decreases. Under the same eccentricity ratio and the same slip length, with the increase in the attitude angle, the load capacity and friction power increase. However, under the non-slip boundary condition, the effects of attitude angle on the load capacity and friction power are insignificant. This paper could provide a reference for studying slip velocity in the hydrodynamic journal bearing.

Whirl dynamics of an axially functionally graded liquid-filled rotor considering shear deformation and rotary inertia

In this study, whirl characteristics and stability of an axially functionally graded (AFG) liquid-filled rotor are investigated. The rotor is modeled based on the spinning Timoshenko beam theory. The governing equations for flexural vibration are derived via Hamilton’s principle. For pinned–pinned AFG liquid-filled rotor, the analytical solutions are derived for both the exact whirl frequency equation and the stability model. To validate the present formulations, comparative studies by numerical solutions available in the literature are conducted. Some numerical examples are performed to investigate the effects of gradient parameter, mass ratio, cavity ratio, rotary inertia, and shear deformation on the whirl speed, the critical spinning speed, and the stability of the AFG liquid-filled rotor system. The results show that these parameters have noticeable influences on dynamic behavior and stability of the rotor system. In particular, the rotary inertia and shear deformation play an important role in the stability analysis for different length rotors.

Analytical and Experimental Investigation on Stability of Rotor System with Spline Coupling Considering Torque, Friction Coefficient and External Damping

Analytical and Experimental Investigation on Stability of Rotor System with Spline Coupling Considering Torque, Friction Coefficient and External Damping

Performance of Relative Clearance Ratio of Floating Ring Bearing for Turbocharger-Rotor System Stability

The floating ring bearing (FRB) has been widely used in the field of high-speed rotating machinery such as turbochargers, aviation engines and so on, because of its simple structure, high efficiency and low power consumption. In order to obtain the best ratio between inter-oil clearance and shaft radius of the floating ring bearing necessitates the design reference of dimensional parameters for the design of floating ring bearings. This study, based on the transfer-matrix method, developed the dynamic model of the floating ring bearing-rotor system, and, using the Runge–Kutta analysis method for floating ring bearings, the influence of oil film relative clearance ratio of floating rings on rotor system stability was analyzed and studied. The optimum clearance ratio between inner oil film and the shaft of floating ring bearings is λ = 0.01. This research can provide some theoretical support for the design of parameters and fault diagnosis of rotor floating ring bearing systems.

Study on dynamic characteristics of bearing-rotor system under ship sway condition

On condition that pans and tilts, ship bearing rotor system stability and security, as the change of ship swaying amplitude have influence, based on independent research and development of guangzhou maritime college design of vertical and horizontal swing test bench, simulate the real working condition of ships at sea, in the performance of bearing rotor system under rolling condition were studied. LMS_TEST. LAB modal tester software was used to analyze the dynamic characteristics and collect the experimental data of the bearing rotor system for analysis and research. In this paper, the influence of period and amplitude on the dynamic characteristics of the bearing-rotor system and the influence on the axis trajectory of the bearing-rotor system under different working conditions are analyzed mainly under the rolling condition.

Research on the clearance flow between stator and rotor cans in canned motor RCP

Canned motor reactor coolant pump (canned motor RCP) is the only long-term continuously running kernel equipment in the reactor system, the safety and stability of the canned motor RCP is the guarantee of the reactor security. In the usual working condition, the auxiliary impeller drives the primary cooling water flow upward into the clearance between the stator and rotor cans to bring the heat produced by the motor, forming a clearance flow with axial temperature gradient. A coupling analysis method is presented to study temperature field of the canned motor and the influence of viscosity temperature effect on clearance flow. The results indicate temperature at outlet of the clearance between stator and rotor cans is about 10 degrees higher than the inlet. What’s more, the differences of results with dynamic viscosity defines as quadratic fitting and results with dynamic viscosity defines at average clearance temperature are less than 1%. As to design method of the clearance, electromagnetic conversion efficiency and starting torque, motor cooling performance and stability of rotor system should be comprehensively considered in the clearance design process.

On the Leakage and Dynamic Force Coefficients of a Novel Stepped Shaft Pocket Damper Seal: Experimental and Numerical Verification

Abstract High-performance turbomachinery favors annular seals with a large damping coefficient to ensure rotor system stability. Pocket damper seals (PDSs), a variation of labyrinth seals with axial blades (ribs) and adding circumferential partition walls (ridges), produce a favorable damping performance. To further enhance the damping characteristic and reduce leakage, a novel stepped shaft PDS is hereby introduced. The invention has a unique arrangement of steps on the rotor surface, each facing an upstream rib in a pocket row. Thus, the step and a blade tip form a tight clearance (c1), while the rotor surface and the downstream blade tip make a larger clearance (c2). The convergence–divergence variation of cross-sectional areas along the flow direction increases the PDS damping coefficient. To validate the performance of the novel design, a stepped shaft PDS (c1/c2 = 0.5) with four axial ribs and eight circumferential pockets is built and tested. A comprehensive investigation, experimental and computational, produces the seal leakage and dynamic force coefficients for the stepped shaft PDS, as well as similar performance characteristics for an identical PDS with a smooth rotor surface (c1/c2 = 1, i.e., a uniform clearance PDS). The stepped shaft PDS operates with air at supply pressure (PS) ranging from 1.1 bar to 3.2 bar. The measured leakage for the stepped shaft PDS is 50% of that for the uniform clearance PDS. Computational fluid dynamics (CFD) and bulk flow model (BFM) predictions of leakage agree well with the test data. For PS = 2.3 bar, the test damping coefficient (C) for the stepped shaft PDS is ~1.5 times greater than the one for the uniform clearance PDS. With an increase in PS to 3.2 bar, the stepped shaft PDS shows a two and one half increase in damping coefficient. In comparison to the test data, a CFD model overestimates C by 29% for operation at PS = 3.2 bar, though capturing the variation trend versus whirl frequency. The BFM largely underpredicts C for the stepped shaft PDS and is abandoned for future work. Both the test data and CFD predictions demonstrate the superior damping performance of the stepped shaft PDS, thus providing a novel alternative seal configuration for turbomachinery usage.

Mechanical characteristics and nonlinear dynamic response analysis of rotor-bearing-coupling system

A mathematical model is presented for studying the dynamic properties of rotor-bearing-coupling system under the effects of varying compliance, radial clearance, rotor-stator rubbing, raceway defects and surface waviness. Nonlinearity of bearings, localized and distributed defects will elicit abundant nonlinear response, which will directly affect the mechanical characteristics of bearings as well as motion stability of rotor systems. The effects of typical parameters on mechanical characteristics and nonlinear dynamic response of the rotor system are analyzed by means of bifurcation diagrams, speed-amplitude, time-histories, spectrum, phase diagrams, and Poincaré sections. The results provide theoretical support for studying the nonlinear vibration mechanism and the control of rotor-bearing system in practical applications.

Effects of Scratches on Lubrication Performance of Elliptical Bearing and Stability of Rotor System

Effects of Scratches on Lubrication Performance of Elliptical Bearing and Stability of Rotor System

Автоколебания и субгармонические вибрации. Часть 1. Причины возникновения низкочастотной вибрации

A brief overview, terminology and basic concepts in the field of low-frequency vibration (LFV) are given, various reasons for the loss of stability are discussed, including: - aerohydrodynamic excitation of self-oscillations of rotors from the action of aerodynamic disturbing forces in the stages and seals of turbines, - hydrodynamic excitation in an oil film of various types bearings in conditions of technological deviations, loss of stability under the action of forces of internal friction and structural damping. In comparison with previous works, significant, previously unaccounted factors affecting the LFV were introduced, including the angular coefficients of stiffness and damping of the oil film, stability parameters were introduced as functions of steam consumption. A zone of stability loss is introduced in the lower part of the ascent curve at high loads, etc. An assessment and comparison of the most important parameters affecting the occurrence of LFV are given. The features of the emergence and action of aerostatic and aerodynamic forces in the control stage of turbines with nozzle steam distribution are shown. It is noted that the disturbing aerodynamic forces in the control stage first increase with a decrease in the steam flow rate, and the total disturbing forces in the HPC are not proportional to the steam flow rate. Some other reasons for the occurrence of subharmonic LFVs are considered. The article has three objectives or goals: 1) help to understand why and how it is necessary to ensure stability of rotor systems at the design and operation stage and to prevent low-frequency vibration of various types. It is shown that for this, first of all, it is necessary to perform calculations of the complex frequencies and modes of vibration of the shafting, ensure detuning of the shafting from hazardous zones and, while varying a number of parameters, determine and ensure the stability margins in terms of the frequency of rotation and in terms of the flow rate of the working fluid; 2) for the effective creation of a subsystem for diagnostics of LFV, it is necessary to disassemble in detail the reasons for its appearance and provide for the installation of a complete system of shaft sensors. Moreover, only part of the technology is presented here; 3) to propose effective and short ways to solve the problem of low frequency energy in case of its occurrence and elimination on a specific turbine unit.