Stability Of Rotor Research Articles

Stability and bifurcation analysis of a rotor in rigid and foil air bearings utilized for the identification of the air whirl effect

Stability and bifurcation analyses of holistic rotor-air bearing models are performed. Both, fluid and foils are modeled in a non-linear way, while the model of the latter is validated by measurements. A model order reduction is applied to the fluid film equations to increase computational efficiency. Intentionally, a minimal rotor model is considered in order to isolate the effects of the bearing on the overall system’s behavior. Instead of time integration methods, bifurcation analyses are applied. Thus, different solutions are identified, their stability is assessed and corresponding branch points are determined. The method is applied in order to compare a rigid gas journal bearing with a foil air bearing. In particular for the foil air bearing, parameter studies are performed to investigate the effect of design changes on the rotor stability and the resulting vibrations. The impact of different static rotor unbalances is considered, too. Furthermore, the effect of air whirl – occurring in both bearing types – is identified and explained.

Static and Rotordynamic Characteristics for Two Types of Novel Hole-Pattern Seals Operating in Supercritical CO2 Turbomachinery

Abstract In this paper, two novel hole-pattern seals were assessed for applications at the balance piston in a 14 MW supercritical CO2 turbine, focusing on the improvement of the seal leakage and rotordynamic performances. These two novel hole-pattern seals were derived from the conventional straight-through hole-pattern seal (HPS) with the same sealing clearance, diameter, axial length, hole diameter and depth, including a stepped hole-pattern damper seal (SHPS) and a grooved hole-pattern damper seal (GHPS). To enhance the seal net damping capability at high inlet preswirl condition, a straight swirl brake also was designed and employed at seal entrance for each type seal. A comprehensive assessment and comparison was conducted on the conventional HPS and the present two novel hole-pattern seals (SHPS and GHPS) with a static concentric rotor. The leakage flow rates, rotordynamic force coefficients, cavity pressure, and swirl velocity developments were analyzed for three hole-pattern seal designs with/without swirl brakes at two inlet preswirl ratios (0.1, 0.5), using a transient computational fluid dynamics (CFD)-based perturbation method based on the multiple-frequency elliptical-orbit rotor whirling model and the mesh deformation technique. To take into account of real gas effect with high accuracy, a table look-up procedure based on the National Institute of Standards and Technology (NIST) database was implemented, using an in-house code, for the fluid properties of CO2 in both supercritical and subcritical conditions. Results show that the present two novel hole-pattern seals have better sealing capability, especially for the GHPS seal which leaks less by a factor of 44%. In general, the GHPS seal possesses the lowest positive effective stiffness, highest effective damping, and the lowest crossover frequency of 60–70 Hz, especially at high inlet preswirl case. From a viewpoint of the rotor stability and unbalance sensitivity analysis, the GHPS seal without entrance swirl brake is a better seal design scheme for the balance piston seal in sCO2 turbine.

Adaptive Rejection of a Sinusoidal Disturbance with Unknown Frequency in a Flexible Rotor with Lubricated Journal Bearings

Frequency-dependent adaptive noise cancellation-based tracking controller (ANC-TC) is a known technique for the stabilization of several nonlinear dynamical systems. In recent years, this control strategy has been introduced and applied for the stabilization of a flexible rotor supported on full-lubricated journal bearings. This paper proposes a theoretical investigation, based on robust immersion and invariance (I&I) theory, of a novel ANC-frequency estimation (FE) technique designed to stabilize a flexible rotor shaft affected by self-generated sinusoidal disturbances, generalized to the case of unknown frequency. A structural proof, under assumptions on closed-loop output signals, shows that the sinusoidal disturbance rejection is exponential. Numerical simulations are presented to validate the mathematical results in silico. The iterative Inexact Newton method is applied to the disturbance frequency and phase estimation error point series. The data fitting confirms that the phase estimation succession has an exponential convergence behavior and that the asymptotical frequency estimation is a warm-up phase of the overall close-loop disturbance estimation process. In two different operating conditions, the orders of convergence obtained by phase and frequency estimate timeseries are pφ=1, pω,unc=0.9983 and pω,cav=1.005. Rejection of the rotor dynamic disturbance occurs approximately 76% before in the cavitated than in the uncavitated condition, 2 (s) and 8.5 (s), respectively.

Influence of the rotating direction and speed of controllable speed casing on the flow stability of a transonic compressor rotor under design condition

Casing treatment is one of the important solutions to enhancing compressor stability. A new concept of controllable speed casing was proposed in this paper, aimed at weakening the loss of efficiency and achieving off-design regulation. In the context of controllable speed casing, the whole casing structure was divided into stationary ring section and rotatable ring section. With adjustment made to the rotating direction and speed of the rotatable ring, different additional effects could be exerted on the tip flow field. In the paper, a numerical research was carried out on the flow stability of different rotating directions and speeds of the rotatable ring. The results show that the controllable speed casing rotating in whether same or opposite direction of the rotor can improve the stability margin of the rotor by controlling the interaction between shock wave/leakage vortex. Moreover, the controllable speed casing with different rotating speeds produces different stable operating margin improvements. When the casing is in the same rotating direction and speed as the rotor, the improvement of the flow field is the most obvious, and the stable operating margin could be increased by 52.56% on the premise the efficiency is basically unchanged.

Stability analysis on gas-lubricated bearing for high speed cryogenic turbo-expander

Here, instead of using static characteristics of gas journal bearing such as the damping coefficients and the misalignment angle for stability analysis, a linear method is presented for studying the whirl stability of a rigid rotor supported on both cylindrical bearing and externally pressurized bearing. First, by using linearization method, the gas film forces can be represented as 8-coefficents, and they are calculated through perturbation method, the static performance is validated by published literature. Then, based on the Routh-Hurwitz criterion, the stability threshold is determined and graphically presented regarding several non-dimensional system parameters, which reflects the effects of both the eccentricity and supply pressure on the system’s linear stability. This effective and computationally cheap method of stability analysis is helpful for the prior design of gas bearing.

Rotordynamic analysis and leakage performance study of a hole diaphragm labyrinth seal using the CFD method

Improving rotor stability and reducing leakage at various working parts of gas turbines is an important topic that experts and scholars have always pursued. In this article, a new type of hole-diaphragm-labyrinth seal (HDLS) structure is obtained by introducing an additional damping source. The HDLS structure is built by the traditional diaphragm labyrinth seal (DLS) with a single hole added to the diaphragm. The simulation under different working conditions of three different seal structures is carried out by ANSYS Fluent. Subsequently, the tangential force under different whirl frequencies was obtained. Meanwhile, the empirical parameters in Childs’ model of the dynamic performance of rotor-seal structures were obtained. The results show that the HDLS achieved a 71.4% improvement in the direct stiffness coefficient and a 71.8% improvement in the direct damping coefficient of the traditional labyrinth seal. The leakages of HDLS at different rotation speeds were lower than those of DLS by 1.53% and LS by 3.64%. The HDLS can be comprehensively considered the most promising seals among LS, DLS, and HDLS not only by stability but also by mass flow leakage in the rotor system.

Research on Stress Design and Manufacture of the Fiber-Reinforced Composite Sleeve for the Rotor of High-Speed Permanent Magnet Motor

As a key component to ensure the safety and stability of the surface-mounted permanent magnet motor rotor, stress research on the sleeve has long been a subject that has attracted researchers. Fiber-reinforced composite materials have the characteristics of high specific strength, high specific modulus, and low eddy current loss. The use of a fiber-reinforced composite material sleeve that can effectively reduce the thickness of the sleeve and structural weight, and can improve the power density of the motor is an inevitable trend of the development of high-performance permanent magnet motors. This paper summarizes the matching of fibers and resins of composite materials to the sleeve: the stress design criteria, stress calculation method, and stress influencing factors of the composite sleeve; two typical stress-forming methods of the composite sleeve; and the preloading effect of the sleeve, strength, and rotor prototype performance testing. This paper focuses on the application of tension winding technology in sleeve forming. Based on the characteristics of composite material layer synthesis, this method has the advantages of high forming efficiency, small forming damage, easy realization of stress design, and a high preloading effect. This method can meet the sleeve-forming requirements of high-performance, large-scale, high-speed permanent magnet motors. However, the application of the new high-performance material system in the existing research is insufficient, the research on the technological factors in the tension winding process is scarce, and the performance testing method after the sleeve preparation is single, which needs further research.

An assessment of the transient effect on helicopter main rotor stability and power demand

The researched object os a helicopter main rotor with blades of variable geometric twist characteristics. Variable torsion refers to systems of actuators made of shape memory alloys. The presented numerical analyses allow for evaluating both the dynamics of the rotor in transient states, i.e. in the zone between the static phase and the full activation phase and the impact of the change on the pulsation of the amplitude of the necessary power generated by the rotor corresponding the flight state, and thus covering the demand by the disposable power generated by the engine. This study follows a methodology of numerical analyses based on Multi Body Dynamics and the Finite Element Method and uses fluid mechanics elements and algorithms to analyze lift generation, compiled in a single computational environment referring to the same period of time.

Effect of Differential Tip Clearance on the Performance of a Tandem Rotor

Abstract Tandem blade is an interesting concept that promises a higher total pressure rise per stage. Owing to two separate tip leakage vortices and their interaction, losses are likely to increase particularly near the tip region. Although rotors are designed with optimum tip clearance, the clearance changes during engine operation as well as during its service life. In the case of tandem rotors, the forward and the aft rotors can have different tip clearances. This will also impact the performance of the stage. Six different tip clearances have been investigated. ANSYS CFX is used for steady RANS computational analysis. The results suggest that the performance of the tandem rotor is highly sensitive to the forward rotor tip clearance. Higher tip clearance adversely affects the total pressure rise and operation stability of the tandem rotor. At design mass flowrate, the performance degradation for tandem configuration with the higher tip clearance (Case2, Case 3, Case 5, and Case 6) is attributed to the vortex breakdown of TLV1, which leads to the sudden expansion of the blockage region near the rotor tip. Vortex breakdown primarily depends upon the swirling strength of TLV1 and TLV2 as well as on the adverse pressure gradient. Near the stall point, the role of the adverse pressure gradient becomes more dominant in the vortex breakdown.

Nonlinear dynamics and bifurcation analysis of journal bearings based on second order stiffness and damping coefficients

Investigating dynamics and stability of rotors supported on journal bearings is a crucial step in the design of an efficient and reliable rotating machine. In the current work, a model for flexible rotor supported on two symmetric journal bearings is investigated. The nonlinear bearing forces are evaluated by either using direct solution of Reynolds equation or analyzing Reynolds equation to obtain linear and nonlinear bearing stiffness and damping coefficients using time dependent second order perturbation method. These coefficients are obtained for different operating conditions and bearing parameters such as length to diameter ratio, groove angle or applied groove pressure. The present results are validated with the previous literature and a perturbation analysis is used to investigate the validity range of the bearing linear and nonlinear coefficients. A novel technique based on polynomial fitting is used to present the bearing coefficient as a function of the bearing parameters. This enables the investigation of the dynamics of flexible rotor model using numerical continuation technique. Also, the effect of the bearing design parameters such as groove angle, length to diameter ratio and static pressure on the system stability is investigated.

Stall-induced vibrations analysis and mitigation of a wind turbine rotor at idling state: Theory and experiment

With the development of wind turbine manufacturing technology, the wind turbine rotor is facing more design challenges for exposing to complex environmental conditions and severe wind loads. This paper investigates the stall-induced vibrations of a wind turbine rotor operating at idling state, and a strategy to mitigate the stall-induced vibrations is proposed. The equations of motion of the wind turbine rotor are established by Hamilton's principle and solved using the finite element method (FEM). The aerodynamic forces are evaluated based on the blade element theory, and the aero-damping is obtained by solving the eigenvalue problem of the rotor system. The stability of the wind turbine rotor is analyzed under different wind speeds, wind deviation angles, azimuth angles and pitch angles. The calculation results show that negative aero-damping exists in specific wind deviation angles, which leads to the divergence of edge-wise motions of the blades. An on-site experimental study validates the criteria of stability of the wind turbine rotor. The present work provides positive outlooks for aeroelastic analysis of the wind turbine blades at idling states, and it is significant for the design and safety improvement of large wind turbine blades.

Bifurcations of Limit Cycles in Rotating Shafts Mounted On Partial Arc and Lemon Bore Journal Bearings in Elastic Pedestals

Abstract The paper investigates the bifurcations encountered in a simple rotor dynamic system interacting with nonlinear impedance forces, generated by the supporting journal bearings of realistic profile geometry. Bearing configurations of finite arc length and of finite width, as implemented in standard design of turbomachinery have been selected, namely the cylindrical partial arc and the elliptical (lemon) bore profile. The way in which the key design parameters influence the stability of elastic or rigid Jeffcott rotor is discussed. In the scope of this study, the following bearing design parameters are considered: arc length, length to diameter ratio, geometric preload and offset, and properties of the supporting pedestal by codimension-two studies. The bearing model is coupled to a six degree of freedom shaft-disc-pedestal model with nonlinear forces calculated from the journal kinematics, bearing design and operating conditions by numerical evaluation of the Reynolds equation for laminar, isothermal flow on a two dimensional mesh. An autonomous system of differential equations is implemented. Stability of fixed points and of limit cycles for this system is evaluated applying numerical continuation. The results confirm that minor variations in journal bearing design and pedestal properties have the potential to render substantial changes in the quality of stability and the bifurcation set of the rotor dynamic system. Specific bearing profiles render significant increment of instability threshold speed while at the same time supercritical Hopf bifurcations can be shifted to subcritical with resulting instability envelopes to be generated at speeds lower than the threshold speed.

ОБЕСПЕЧЕНИЕ ДИНАМИЧЕСКОЙ УСТОЙЧИВОСТИ ОБМЕРЗАЮЩИХ РОТОРОВ ТЕХНОЛОГИЧЕСКИМИ МЕТОДАМИ

The proposed article is devoted to artificial material systems operating in conditions of information scarcity for effective management. The problem is considered on the example of rotors operating in conditions of icing of surfaces of turbine units used in aviation and the thermal power complex. The analysis of measures to ensure the dynamic stability of rotors, whose surfaces are subject to icing, leading to an uncontrolled increase in local imbalances, is carried out. The relevance of the problem is due to both the general trend of scientific and technological progress aimed at improving technologies and types of products, and modern challenges of the economy. These should primarily include meeting the need for technological processes and types of products that are as close as possible to the requests in terms of the resource of work, cost, cost of operation and disposal. At the same time, the situation at the production site is complicated by the hostile attitude of the so-called Western countries to the development of Russian industry, especially in aviation, the thermal power complex, defense, elec-tronics, etc. All this creates a complex scientific and technical contradiction, burdened by a shortage of material support: financial inse-curity and the absence of a number of components supplied by previously unfriendly countries. Based on the results of the analysis of the dynamic state of the systems, the direction of its technological support is determined. Two methods are proposed to ensure the dynamic stability of the most problematic elements of rotors: wheels of centrifugal and axial compressors (turbines). At the same time, the method of precision preparation of rotor elements for assembly is designed to ensure the installation of the element on the shaft with minimized eccentricity of the forming seal and without imbalance, and the method of eccentricity-virtual assembly of turbine wheels is designed to balance the rotor with a pre–known imbalance. The application of the developed methods makes it possible to solve the formulated scientific and technical contradiction, significantly improve the quality of prod-ucts, reduce the labor intensity and cost of production. Technological processes using these methods have been tested in industrial conditions.

Automatic Rescheduling of Generator for Rotor Speed Regulation by KRASOVSKII’s Theorem

Emergency control of the power system is performed via generator rescheduling or load shedding depending upon the availability of generation and demand. This paper presents a generator rescheduling method based on Krasovskii’s theorem for enhancing rotor speed regulation during multiple contingency conditions. The speed governor in automatic generation control (AGC) and automatic voltage regulator (AVR) are indispensable components of the control mechanism for deploying any control scheme. Contingencies may lead the security state of the power system towards a preventive, emergency, and restorative state. Generally, there is a violation of equality constraints of active and reactive power in the corrective security state. However, in this paper, the corrective security state considers a significant imbalance in active power with a generation capacity always greater than load. For rotor angle stability, active power delivery by the generator met the demands, whilst the turbine and automatic speed governor together balance it by changing the set point of the turbine inlet. This paper investigates the rotor stability by triggering a new set point by the rescheduling of the generator. The strategy proposed encompasses the broad domain of active power imbalance using Krasovskii’s theorem, which is an extensive form of the Lyapunov stability theorem for the nonlinear multivariable autonomous system. The proposed control scheme is deployed on an IEEE-10 machine 39-bus system for validation and feasibility detection. It is found that the proposed scheme is more accurate than the conventional turbine automatic speed governor close loop system. Moreover, there is turbine power-saving up to 400 MW. In addition, the rotor attains steady-state speed quicker up to 5-10 sec and attains synchronous speed in all the cases considered, i.e., single load outage; multiple load outage; area outage; and load increment. The MATLAB® and the CVX platform are used to validate the proposed concept.

Finite Element Modelling of Rotors, Without Considering the Shear Effects

The proposed rotor model is based on the finite elements of a Timoshenko beam, whose support is rigid and fixed. It takes into account the geometric asymmetry of the discs and/or the shaft, while neglecting the shear effect. The equations of motion obtained include time-varying parametric terms that can lead to lateral dynamic instability. The influence of the combined rotational and translational movements of the support is analyzed by the Campbell diagram and the rotor stability map. Critical speeds according to modes have been identified.

Effect of Impact and Bearing Parameters on Bird Strike with Aero-Engine Fan Blades

Bird strikes are one of the most dangerous incidents occurring to aircraft engines and can inflict heavy casualties and economic losses. In this study, a smoothed particle hydrodynamics (SPH) mallard bird model has been used to simulate bird impact to rotary aero-engine fan blades. The simulations were performed using the finite element method (FEM) by means of LS-DYNA. The reliability of the material model and numerical method was verified by comparing the numerical results with Wilbeck’s experimental results. The effects of impact and bearing parameters, including bird impact location, bird impact orientation, initial bird velocity, fan rotational speed, stiffness of the bearing, and the damping of the bearing on the bird impact to aero-engine fan blade are studied and discussed. The results show that both the impact location and bird orientation have significant effects on the bird strike results. Bird impact to blade roots is the most dangerous scenario causing the impact force to reach 390 kN. The most dangerous orientation is the case where the bird’s head is tilted 45° horizontally, which leads to huge fan kinetic energy loss as high as 64.73 kJ. The bird’s initial velocity affects blade deformations. The von Mises stress during the bird strike process can reach 1238 MPa for an initial bird velocity of 225 m/s. The fan’s rotational speed and the bearing stiffness affect the rotor stability significantly. The value of bearing damping has little effect on the bird strike process. This paper presents a procedure for evaluating the strength of fan blades against bird strike in the design stage.

Nonlinear dynamic characteristics and stability analysis of energy storage flywheel rotor with shape memory alloy damper

In this paper, the nonlinear dynamic characteristics and stability of an energy storage flywheel rotor with shape memory alloys (SMA) damper are studied. A new type of SMA constitutive model is proposed to express SMA's hysteresis properties, and the nonlinear dynamic model of an energy storage flywheel rotor with SMA damper is established. A developed multi-scale method is proposed to obtain the natural frequency of the system with high accuracy in strong nonlinear condition, and the nonlinear dynamic characteristics of the system are analyzed. To a cracked flywheel rotor, a time-varying function is proposed to express the effect of the crack depth on the system's stiffness, and the variation of the system's area with different parameters is discussed. Simulation results show that the nonlinearity and crack will both affect the stable area of the system. To a flywheel rotor subjected to stochastic excitation, a developed analysis method for the stability is proposed to obtain the global stability of the system. Finally, the conditions on stochastic bifurcation are determined. Simulation results show that the stochastic system's motion will change from balance point to periodic orbit, and will also jump from one orbit to another in special cases. The results of this paper are helpful for the design of energy storage flywheel rotor.

Rotating tip clearance asymmetry and role of endwall injection in stability desensitization of a transonic fan

The current study is aimed at understanding the effect of rotating tip clearance asymmetry on the operability and performance of a transonic compressor. Another objective of this investigation is to determine the influence of tip injection on reducing the detrimental effects of clearance asymmetry. Three dimensional unsteady Reynolds-averaged Navier–stokes simulations have been performed from choke to stall for different arrangements of non-uniform blade heights in a transonic fan. Furthermore, numerical computations have been conducted with endwall injection of air. The numerical results have been validated against experimental data. Results show that having the same mean tip clearance, the asymmetric compressor is less stable than the axisymmetric configuration. However, the peak pressure rise is found to be almost linearly correlated to the mean tip clearance for both the axisymmetric and asymmetric compressors. It is found that tip injection can desensitize the compressor to the tip clearance asymmetry. Results further reveal that tip clearance asymmetry does not change the compressor path to instability. However, endwall injection is found to be able to change the compressor stalling mode. Investigations concerning rotating non-uniformity (caused by non-uniform blade heights) are very few in open literature. The obtained results can assist in predicting the effect of rotating tip clearance asymmetry on the stability and performance of high-speed compressor rotors. Furthermore, the results uncover how tip injection can desensitize the compressor stability and affect its path into instability, which is one of the most important questions in the turbomachinery world.

Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based on the Applicability Analysis of Leakage Models Using Bulk-Flow Method

Abstract Labyrinth seals are widely applied in the turbomachinery to control the leakage flow through the clearance between stationary and rotating components. The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial to the analysis of the fluid excitation rotordynamics of labyrinth seals. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of seventy-two leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

Nonlinear Dynamics of a Blade Rotor with Coupled Rubbing of Labyrinth Seal and Tip Seal

The dynamic response and its stability of a blade rotor with coupled rubbing in the labyrinth seal and tip seal are investigated. The dynamic equations are established based on the Hertz contact rubbing force at the labyrinth seal and the tip rubbing force considering both the contact deformation of the tip seal and the bending deformation of the blade. Numerical simulations show that the coupled rubbing response includes periodic motions, almost periodic motions, and chaotic motions. Compared with the single rubbing fault, coupled rubbing increases the range of rotation velocity of contact. A new continuation shooting method is used in the solution and stability analysis of the periodic response to give the bifurcation diagrams. The paths of the system for entering and exiting chaos are analyzed.