Showing papers on "Critical speed published in 2007"

Suppressing Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 2: Experiments

Abstract: This paper presents experimental results corroborating the analysis developed in the companion paper, Part 1 (Lee, Y., Vakakis, A., Bergman, L., McFarland, M., and Kerschen G., "Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory," AIAA Journal, Vol. 45, No. 3,2007, pp. 693-711), and demonstrates that a nonlinear energy sink can improve the stability of an aeroelastic system. The nonlinear energy sink was, in this case, attached to the heave (plunge) degree of freedom of a rigid airfoil which was supported in a low-speed wind tunnel by nonlinear springs separately adjustable in heave and pitch. This airfoil was found to exhibit a limit cycle oscillation at flow speeds above the critical ("flutter") speed of 9.5 m/s, easily triggered by an initial heave displacement. After attachment of a single degree of freedom, essentially nonlinear energy sink to the wing, the combined system exhibited improved dynamic response as measured by the reduction or elimination of limit cycle oscillation at flow speeds significantly greater than the wing's critical speed. The design, application, and performance of the nonlinear energy sink are described herein, and the results obtained are compared to analytical predictions. The physics of the interaction of the sink with the wing is examined in detail.

A non-linear study of a cracked rotor

Abstract: The influence of the presence of transverse cracks in a rotating shaft is analyzed. The paper addresses the influence of crack opening and closing on dynamic response during operation. The evolution of the orbit of the cracked rotor near half and one-third of the first critical speed is investigated. The dynamic response of the rotor with a breathing crack is evaluated by expanding the changing stiffness of the crack as a truncated Fourier series and then using the Harmonic Balance Method. This method is applied to compute various parametric studies including the effects of the crack depth and location on the dynamic of a crack rotor. The evolution of the first critical speed, associated amplitudes at the critical speed and half of the critical speed, and the resulting orbits during transient operation are presented and some distinguishing features of a cracked rotor are examined.

Contact analysis of a flexible bladed-rotor

Abstract: This paper presents a model of fully flexible bladed rotor developed in the rotating frame. An energetic method is used to obtain the matrix equations of the dynamic behaviour of the system. The gyroscopic effects as well as the spin softening effects and the centrifugal stiffening effects, taken into account through a pre-stressed potential, are included in the model. In the rotating frame, the eigenvalues' imaginary parts of the latter matrix equation give the Campbell diagram of the system and its stability can be analysed through its associated eigenvalues' real parts. The turbo machine casing is also modelled by an elastic ring in the rotating frame through an energetic method. Thus, in some rotational speed ranges the contact problem between the rotor and the stator can be treated as a static problem since both structures are stationary to each other. Prior to the study of the complete problem of contact between the flexible blades of the rotor and the flexible casing, a simple model of an elastic ring having only one mode shape, excited by rotating loads is developed in the rotating frame too, in order to underline divergence instabilities and mode couplings. Then, the complete problem of frictionless sliding contact between the blades and the casing, without rubbing, is studied. The stable balanced static contact configurations of the structure are found as function of the rotational speed of the rotor. Finally, the results are compared to these of the simple model of rotating spring-masses on an elastic ring, showing good adequacy. The present model of rotor appears thus particularly adapted to the study of blades-casing contacts and highlighted an unstable phenomenon near the stator critical speed even in case of frictionless sliding.

Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery

Abstract: Micro-turbomachinery demands gas bearings to ensure compactness, light weight, and extreme temperature operation. Gas bearings with large stiffness and damping, and preferably of low cost, will enable successful commercial applications. Presently, tests conducted on a small rotor supported on flexure pivot hydrostatic pad gas bearings (FPTPBs) demonstrate stable rotordynamic responses up to 100,000 rpm (limit of the drive motor). Test rotor responses show the feed pressure raises the system critical speed (increase in bearing direct stiffness) while the viscous damping ratio decreases. Predictions correlate favorably with experimentally identified (synchronous) direct stiffness bearing force coefficients. Identified experimental gas bearing synchronous damping coefficients are 50% or less of the predicted magnitudes, though remaining relatively constant as the rotor speed increases. Tests without feed pressure show the rotor becomes unstable at ∼81 krpm with a whirl frequency ratio of 20%. FPTPBs are mechanically complex and more expensive than cylindrical plain bearings. However, their enhanced stability characteristics and predictable rotordynamic performance makes them desirable for the envisioned oil-free applications in high speed micro-turbomachinery.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

Abstract: Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10 mm. Coast down rotor responses from 25 krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5 krpm to 15 krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5 krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings' side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

Stability-Based Spindle Design Optimization

Abstract: Prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency-response measurements of the tool-holder-spindle set obtained from a nonrotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic high-speed spindle-bearing system model is elaborated on the basis of rotor dynamics prediction and readjusted on the basis of experimental modal identification. The dependency of dynamic behavior on speed range is then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. They show that dynamic effects due to high rotational speed and elastic deformations, such as gyroscopic coupling and spin softening, have a significant influence on spindle behavior. By integrating the modeled speed-dependent spindle transfer function in the chatter vibration stability approach ofAltintas and Budak (1995, CIRPS Ann, 44(1), pp. 357-362), a new dynamic stability lobe diagram is predicted. Significant changes are observed in the stability limits constructed using the proposed approach and allow accurate prediction of cutting conditions to be established. Finally, optimization studies are performed on spindle design parameters in order to obtain a chatter vibration-free cutting operation at the desired speed and depth of cut for a given cutter.

Optimization design of rotor structure for high speed permanent magnet machines

Abstract: Permanent magnet (PM) machine is especially being employed in high speed machines due to its simple structure and high power density. Nowadays, the sintered neodymium-iron-boron (Nd-Fe-B) material is used in most of PM machines. This kind of PM material has large compression strength but small tensile strength, and can not withstand the large centrifugal force due to the high rotation speed. A nonmagnetic steel enclosure is needed to cover the PM material. The tensile press of PM can be reduced by pre-pressure applied to the outer surface of the PM through shrink-fitting into the enclosure. In this paper, the comprehensive optimization design of PM rotor structure is introduced with multiple constraints, such as deformation, stress and critical speed. The capacity of enclosure is the optimal goal. By finite element non-linear contact and optimization analysis, the optimized result for a high speed PM machine with rated speed of 60 000 rpm is presented.

Vibration Suppression of Nonlinear Rotor Systems Using a Dynamic Damper

Abstract: Due to the inevitable imbalance of rotating machinery, resonance occurs when the rotational speed is in the vicinity of the critical speed. A rotor system supported by a single-row deep groove ball bearing shows nonlinear spring characteristics due to the clearance of bearings. In this article, passive vibration control of nonlinear rotor systems using a dynamic damper is studied. Theoretical analysis is performed to investigate the influence of nonlinearity on the vibration characteristics of controlled rotor systems, and the theoretical results obtained are confirmed by experiments. An example shows that the fixed-point theorem for optimization of the dynamic damper cannot be used when the rotor system has an isotropic symmetrical nonlinearity. The Newton-Raphson method is used to determine the optimal parameters of the dynamic damper for the nonlinear rotor, and passive vibration control utilizing the dynamic damper is achieved in the nonlinear rotor system.

Effect of motor connection on the critical speed of high speed railway vehicles

Abstract: Considering the specific case of a concentrated power locomotive with motors mounted on the bogie frame, the paper reviews the criteria for nonlinear assessment of vehicle stability based on the simulation of vehicle response to random track irregularity, showing the need for more objective criteria than the ones based on physical testing for vehicle homologation. The effect of elastic motor connection on the bogie frame is examined by linear and nonlinear calculations, which shows that stiffness and damping properties of motor connection have a strong influence on vehicle stability.

Vibration control of a rotor bearing system using shape memory alloy: I. Theory

Abstract: In this paper, to make a rotor–bearing system pass through the critical speed safely and control its vibration, a self-optimizing support system is proposed, based on shape memory alloy (SMA). In this self-optimizing support system, the SMA springs are used to construct the pedestal bearing for the rotor–bearing system. The principle of the dynamic absorber is utilized to calculate and change the stiffness of the SMA pedestal bearing in order for the rotor shaft to be usually situated near anti-resonance with changes of the rotating speed, and its vibration can be controlled. Numerical experiments suggest that the vibration of the rotor–bearing system can be controlled efficiently by a SMA spring bearing and the proposed method is feasible. The study also indicates that the proposed method has potential for solving a wide range of active vibration control problems. The results are also verified by an experimental investigation on a rotor–bearing system presented in a companion paper, II.

Reduction of vibration level in rotordynamics by design optimization

Abstract: We focus on the reduction of the vibration level of rotors by optimizing the shape of the body. The target is to reduce rotor weight and rotor vibrations leading to higher efficiency and less noise. We consider a finite element discretization of the rotor using a Rayleigh beam model which includes rotary inertia and gyroscopic moments leading to nonself-adjoint systems. We present a general algebraic framework for this case. The mass function is the objective function of the optimization problem and constraints are set on the nonlinear and nonconvex functions of critical speed and unbalanced response. For the numerical solution, algorithms belonging to the class of sequential convex programming are applied for the example of a turbocharger. A remarkable reduction of mass of an initially given prototype could be achieved while significantly reducing the unbalanced response and raising the critical speeds.

Field Methods for Identification of Bearing Support Parameters—Part II: Identification From Rotor Dynamic Response due to Imbalances

Abstract: This paper describes a procedure suitable for field implementation that allows identification of synchronous bearing support parameters (force coefficients) from recorded rotor responses to imbalance. The experimental validation is conducted on a test rotor supported on two dissimilar bearing supports, both mechanically complex, each comprising a hydrodynamic film bearing in series with a squeeze film damper and elastic support structure. The identification procedure requires a minimum of two different imbalance distributions for identification of force coefficients from the two bearing supports. Presently, the test rotor responses show minimal cross-coupling effects, as also predicted by analysis, and the identification procedure disregards cross-coupled force coefficients thereby reducing its sensitivity to small variations in the measured response. The procedure renders satisfactory force coefficients in the speed range between 1500 and 3500 rpm, enclosing the rotor-bearing system first critical speed. The identified direct force coefficients are in accordance with those derived from the impact load excitations presented in a companion paper.

Steady turning of motorcycles

Abstract: When driving along a circular path, the rider controls a motorcycle mainly by the steering torque. If the steering torque is low and the vehicle is moderately over-steering, a good handling feeling is perceived by the rider. In this paper, non-linear steady turning results are analysed over a wide range of forward speeds and lateral accelerations, and different ‘driving zones’ are identified by considering the steering torque transition speeds and steering angle critical speed. A parametric linear model of steady turning, concerning both the steering torque and the steering angle, is developed and simple parametric expressions of transition speeds and the critical speed are obtained. Steady turning tests involving different motorcycles are presented, the transition speeds and critical speed are found by linear fitting, and the characteristics of the different driving zones are investigated. The primary purpose is to determine the conditions at which the operational safety and handling of the vehic...

Novel Adaptive Repetitive Algorithm for Active Vibration Control of a Variable-Speed Rotor

Abstract: The paper describes experimental work that demonstrates the use of repetitive control to attenuate radial vibrations of a variable speed-rotor. The experiments were performed on a rotor test rig having a 3-kg rotor supported by journal bearings. The first bending resonance of the rotor shaft (i.e. the critical speed) was approximately 50 Hz. The objective was to control the radial response at the rotor midpoint by using an actuator located outside the bearing span. A novel aspect of the controller design is that the length of the control output vector of the repetitive controller was updated as a function of the speed of rotation. The speed of rotation determined the required delay time and the repetitive filter length that approximately matches with the delay time. The results obtained were comparable to those achieved in earlier studies with feedforward compensation methods. The best results were achieved when the frequency of rotation enables an integer ratio between disturbance period and sample rate.

Optimum shape design of rotating shaft by ESO method

Abstract: Evolutionary structural optimization (ESO) method is based on a simple idea that the optimal structure can be produced by gradually removing the ineffectively used material from the design domain. ESO seems to have some attractive features in engineering aspects: simple and fast. In this paper, ESO is applied to optimize shaft shape for the rotating machinery by introducing variable size of finite elements in optimization procedure. The goal of this optimization is to reduce total shaft weight and resonance magnification factor (Q factor), and to yield the critical speeds as far from the operating speed as possible. The constraints include restrictions on critical speed, unbalance response and bending stresses. Sensitivity analysis of the system parameters is also investigated. The results show that new ESO method can be efficiently used to optimize the shape of rotor shaft system with frequency and dynamic constraints.

Nonlinear Analysis of Rotor Dynamics by Using the Method of Multiple Scales

Abstract: The method of multiple scales is modified to nonlinear analysis in rotor systems. Amplitude equations for forward and backward whirling modes are directly derived and the method makes it easier to understand resonance mechanism. As an example, we analyze near the major critical speed the nonlinear dynamics of a horizontally supported Jeffcott rotor and show that nonlinear and gravity effects cause the backward whirling mode in addition to the forward one. Some experiments are performed and the validity of the theoretical results is confirmed.

Steady-State Dynamic Response of a Kirchhoff’s Slab on Viscoelastic Kelvin’s Foundation to Moving Harmonic Loads

Abstract: In this paper, fast Fourier transform and complex analysis are used to analyze the dynamic response of slabs on a viscoelastic foundation caused by a moving harmonic load. Critical speed and resonance frequency of the slab to a moving harmonic load are obtained analytically. It is proved that there exists a bifurcation in critical speed. One branch of critical speed increases as load frequency increases, while the other branch of critical speed decreases as load frequency increases. There are two critical speeds when the load frequency is low, but only one critical speed exists when the load frequency is high. A parametric study is also performed to study the effect of load speed, load frequency, material properties of the slab and the damping coefficient on dynamic response. It is found that the damping coefficient has significant influence on dynamic response. For small damping, the maximum response of the slab increases with increased load speed and frequency. However, for large damping, the maximum response of the slab decreases with increased load speed and frequency.

An Experimental Study of Independently Rotating Wheels for Railway Vehicles

Abstract: It is well known that conventional wheelsets have disadvantages of potential oscillatory instability above critical speed as a result of solid coupling between two wheels. Independently rotating wheels can overcome this disadvantage but may loss the natural guidance which solid axis linked wheels have. This paper presents an experimental study of independently rotating wheels which adopt active wheel driven for high speed railway vehicles.

Flutter of viscoelastic strips

Abstract: Using linear model, the parametric sensitivity analysis of viscoelastic panel flutter with an arbitrary function of relaxation, is examined by the Laplace integral transform method. The critical values of free stream velocities and frequencies of vibrations are determined from the condition that the real parts of the poles of integrand must be zero, which correspond to harmonic motion. Approximate and exact values of critical speed and corresponding frequencies for a general isotropic viscoelastic constitutive relations are obtained. The solutions are analyzed for critical, subcritical and supercritical cases. It is shown that the viscoelastic flutter speed is smaller than the corresponding elastic one if elastic moduli of material is equal to the initial value of relaxation function. Influence of aerodynamical damper is studied assuming that the parameter of viscous property of material is small enough in comparison with the parameter of aerodynamical damper and vice versa.

Influence of leakage flow through labyrinth seals on rotordynamics: numerical calculations and experimental measurements

Abstract: An extensive investigation of the influence of the leakage flow through a labyrinth seal at supply pressure of 12 bar on the rotordynamics was performed by using numerical calculations and experimental measurements. Toward this end, an experimental rotor setup was established in Shanghai Jiao Tong University. Two labyrinth seals were chosen for comparison, e.g., an interlocking seal and a stepped one. The numerical calculations based on the bulk-flow theory and the perturbation analysis were accomplished. Simultaneous acquisitions of the fluctuating static pressure at the stator wall and the displacement of the whirling rotor were made. The influence of the aerodynamic forcing on the rotor was analyzed in terms of the axial distribution of the mean static pressure, the circumferential distribution of the fluctuating pressure, the fist critical speed and the destabilization rotating speed of the rotor. The experimental results demonstrated that the sinusoidal distribution of the fluctuating static pressure on the stator wall was closely related to the whirling motion of the rotor. The first critical speed of the rotor was reduced by the aerodynamic forcing, resulting in intensified destabilization of the rotor system. Furthermore, the numerical analyses were in good agreement to the experimental measurements.

The critical speed of a moving load on a prestressed plate resting on a prestressed half-plane

Abstract: Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the dynamical response of a system consisting of a prestressed covering layer and a prestressed half-plane to a moving load applied to the free face of the covering layer is investigated. Two types (complete and incomplete) of contact conditions on the interface are considered. The subsonic state is considered, and numerical results for the critical speed of the moving load are presented. The influence of problem parameters on the critical speed is analyzed. In particular, it is established that the prestressing of the covering layer and half-plane increases the critical speed.

Apparatus and method for bearing stiffness test

Abstract: A bearing stiffness test apparatus and method are provided to measure a critical speed and estimate the stiffness of a bearing using the critical speed measured in rotational environment. A bearing stiffness test apparatus includes a rotary shaft(10), a drive part(20), a test bearing(30), a bearing casing(32), hydraulic cylinders(33,34), drive bearings(40,50), a disc(60), a speed sensor, a vibration sensor, and an analyzer. The drive part is installed at one side of the drive shaft to provide a rotational force to the rotary shaft. The test bearing is installed at one side of the rotary shaft to surround the test bearing. The hydraulic cylinders are formed at one side of the bearing casing to apply load to the test bearing. The drive bearings are installed at one side of the rotary shaft to support the rotary shaft. The disc is formed at a center of a through-hole passing through the rotary shaft.

Application of Whole Engine Finite Element Models in Aero-Engine Rotordynamic Simulation Analysis

Abstract: The thrust-to-weight ratio of aero-engine is increasing, the structure stiffness is reducing along with its weight, the mechanical exciting force and aerodynamic force become more and more intricate, for these reasons, dynamic interaction of different structures have to be taken into account in aero-engine vibration analysis. In traditional methods, as transfer matrix method and finite element method based on beam element, the rotor is reduced as mass point and beams, so the true dynamic interaction between the disk and shaft can’t be calculated. In this paper, MSC/NASTRAN was developed by adding the effect of gyroscopic moment to the 8 nodes solid element CHEXA with DMAP (direct matrix abstraction program) language. A rotordynamic analysis of a whole engine model based on three-dimensional (3-D) solid element was performed using the program. Firstly, an unbalance response calculation of the casing was performed to predict the translation function (dynamic stiffness) at the bearing support, as well as their effects on rotor dynamics. In the analysis of solid element models and beam element models, the effects of the coupled disks and shafts vibration as well as the corner stiffness between shafts and disks on rotor dynamics were compared, the results shown that various vibration modes could be accurately calculated using the model based on solid element. A phenomenon of the coupled rotor bending and casing vibration was captured, it was shown the third rotor critical speed of the coupled rotor bending and casing vibration mode was a frequency range. The method to predict critical speeds and mode shapes of the rotor considering dynamic interaction between the rotor and casing was investigated. Finally, a simulation platform for aero-engine dynamic analysis was set up, on which the whole engine model could be found and thermal load or aero force could be considered for different purposes. It was concluded that the true dynamic interaction between the rotor and casing as well as the disk and shaft could be captured using the whole engine model based on solid element. Further more, the foreground of the thermal and tip clearance analysis of turbine blades based on the whole engine model was discussed.Copyright © 2007 by ASME