Showing papers on "Critical speed published in 2001"

Method for operating offshore wind turbine plants based on the frequency of their towers

Abstract: The invention relates to a method for operating a wind turbine plant which is provided with a device for regulating the speed of the rotor. Said method comprises the following steps: determination of the critical frequency of the respective turbine and/or turbine components, determination of the speed range of the rotor, in which the entire turbine and/or individual turbine components is/are excited in the vicinity of their critical frequencies and operation of the wind turbine plant only below and above the critical speed range, the latter being traversed rapidly.

Retrofit of fixed speed induction motors with medium voltage drive converters using NPC three-level inverter high-voltage IGBT based topology

Abstract: This paper presents a solution to allow simple and risk-free retrofit of existing fixed speed induction motors with medium voltage adjustable speed drives to achieve attractive energy savings. The presented medium voltage adjustable speed drive consists of a twelve-pulse diode rectifier and a three-level neutral point clamped inverter using high-voltage IGBTs. Innovative features of the drive include series-connection of high-voltage IGBTs. The motor control is based on field-oriented vector control and an optimized PWM modulator, so that switching losses and current harmonics are minimized. An EMC-sinusoidal output filter is available to retrofit existing fixed speed motors with adjustable speed drive converter without incurring overvoltage stress on the winding insulation system, changes on the motors, the mechanical couplings, or the motor feeder cables, excitation of motor critical speed, or reduction in shaft power. Experimental and field results are also presented to confirm the proposed topology and related energy savings.

Meniscus draw-up and draining

Abstract: When a solid plate is removed from a pool of fluid, a film of fluid is attached to the plate. There are two possible outcomes. The edge of the fluid may be raised through a finite distance, with the edge slipping on the plate. Alternatively, a continuous film of a certain thickness may be drawn up. For plates which have a small slope, it is shown that the first alternative holds when the speed of withdrawal is sufficiently small, and that, when a critical speed is exceeded, the height of the edge above the fluid level in the pool increases with time. A related problem concerns the shape of a receding meniscus in a channel. If the static contact angle is small, lubrication theory can be applied to the film of fluid adjacent to the wall of the channel, and the results of this part of the solution can be matched to the central part of the meniscus, which is controlled by capillarity and gravity, but for which lubrication theory does not apply. As in the draw-up problem, for small speeds the shape of the meniscus is time-independent, but above a critical speed, a tail of fluid of increasing length remains in the tube.

Frictionally Excited Thermoelastic Instability in Multi-Disk Clutches and Brakes

Abstract: The propensity toward thermoelastic instability (TEI) in multi-disk clutches and brakes is investigated by introducing a new bidimensional analytical model, where metal and friction disks are replaced by two-dimensional layers of finite thickness. This new model permits to estimate the effect of the thickness ratio a1/a2, between friction and metal disks, on the critical speed, critical wave parameter and migration speed of the sliding system. It is found that as the thickness ratio a1/a2 decreases the critical speed reduces significantly taking up values about 80 percent smaller than that predicted by previous two-dimensional models for commonly used ratios (0.1

Vibration analysis of a misaligned rotor—coupling—bearing system passing through the critical speed:

Abstract: The transient response of a misaligned rotor—coupling—bearing system passing through the critical speed has been analysed by using the finite element method (FEM) for flexural vibrations. The coupling has been modelled in two ways: a frictionless joint and a joint with stiffness and damping. From the vibration analysis, the subcritical speeds at one-half, one-third and one-fourth the critical speed have been found when the misaligned rotor—coupling—bearing system passes through its critical speed. The continuous wavelet transform (CWT) has been used as a tool to extract the silent features from the time response of the rotor system. A parametric study has been carried out to investigate the transient response of this rotor system for different angular accelerations in different types of misalignment.

Effects of imperfection on the non-linear oscillations of circular plates spinning near critical speed

Abstract: Motivated by the well-known experiments of Tobias and Arnold (Proc. Inst. Mech. Engrs. 171 (1957) 669–690), we study the large-amplitude oscillations of an imperfect, flexible circular plate spinning near a critical speed resonance. A weakly non-linear theory for the transverse oscillations of the rotating, imperfect plate is derived and the near resonant response of a repeated pair of backward and forward travelling waves is analysed. The experimental results of Tobias and Arnold are easily captured within the present analysis. In addition, several new dynamical phenomena are predicted as the imperfection parameter is increased, such as emergence of pseudo-standing waves; their loss of stability through Hopf bifurcations leading to backward and forward travelling waves with slow, periodically modulated amplitudes and phases; period doubling sequences leading to Rossler-type chaotic attractors and boundary crises phenomena; and emergence of isolas of steady wave motions. Sufficiently high asymmetry can reduce by half, the vibration energy near resonant collapse phenomena. The results presented can provide guidelines for designing imperfections in circular saws and hard disk drives to reduce vibrations near critical speed.

A Flexible Rotor on Flexible Bearing Supports: Stability and Unbalance Response

Abstract: An experimental study of the effects of bearing support flexibility on rotor stability and unbalance response is presented. A flexible rotor supported by fluid film bearings on flexible supports was used with fifteen support configurations. The horizontal support stiffness was varied systematically while the vertical stiffness was kept constant. The support characteristics were determined experimentally by measuring the frequency response functions of the support structure at the bearing locations. These frequency response functions were used to calculate polynomial transfer functions that represented the support structure. Stability predictions were compared with measured stability thresholds. The predicted stability thresholds agree with the experimental data within a confidence bound for the logarithmic decrement of ±0.01. For unbalance response, the second critical speed of the rotor varied from 3690 rpm to 5200 rpm, depending on the support configuration. The predicted first critical speeds agree with the experimental data within -1.7 percent. The predicted second critical speeds agree with the experimental data within 3.4 percent. Predictions for the rotor on rigid supports are included for comparison.

Modelling of rotors with three-dimensional solid finite elements:

Abstract: A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in c...

The Analytical Imbalance Response of Jeffcott Rotor During Acceleration

Abstract: The characteristics of the transition vibration of a rotor system when it passes its critical speeds during acceleration are of great interest for active vibration control, active real-time balancing @1#, and rotor design. In the past, a few analyses @2‐8# have dealt with speed varying transient rotor dynamics. These researchers used numerical integration techniques to calculate numerical solutions to the transient dynamic model. Although these models can be used to predict the transient vibration for a complicated rotor system, it remains hard to obtain the quantitative characteristics of the transient vibration. Lewis @9# and Dimentberg @10# presented an analytical solution of the problem of running a rotor system through its critical speeds at a uniform acceleration. The basic characteristic of the ‘‘envelope’’ ~amplitude! of the transient vibration was studied by an approximation method. In this paper, their work is extended. An analytical expression of the motion of the geometric center of a simple Jeffcott rotor is derived. The exact ‘‘envelope’’ and ‘‘phase’’ of the transient vibration are presented. As stated in Dimentberg @10#, it is found that the transient vibration through critical speeds consists of free vibration and synchronous vibration. Explicit expressions of these two components are presented in this paper.

Experimental studies on the non-linear oscillations of imperfect circular disks spinning near critical speed

Abstract: Experiments on the non-linear oscillations of a spinning steel plate near critical speed are presented. Of particular interest are the effects of imperfection induced by point masses bolted to the plate. The tests are carried out at very low ambient pressures in a vacuum chamber to minimize the effects of aerodynamically induced vibration. Six different cases of asymmetry are tested and the experiments confirm most theoretically predicted results of Raman and Mote (Int. J. Non-Linear Mech. 36 (2001) 261–289). These include the existence of multiple steady solution branches; the onset of pseudo-standing waves and their loss of stability leading to slowly modulated travelling wave responses; creation of isolas of solution branches; and decoupling of the internally resonant modes at high asymmetry leading to the reduction of travelling wave amplitudes at high asymmetry. Additional features observed include resonant mode-jumping at super-critical speed and the presence of superposed slow motion on resonant solution branches.

The critical speed of a railway vehicle on a roller rig

Abstract: The dynamic behaviour of a railway vehicle is largely governed by the interaction of the wheelset with the track. This behaviour can be reproduced in a laboratory using a roller rig and can also be mathematically simulated by solving the equations of motion which govern the dynamic behaviour. This paper presents the results of a study that compares the predictions of these equations of motion for a one-fifth scale railway vehicle on track and on a roller rig. In particular, the critical speed at which the motion first becomes unstable has been shown to differ between the vehicle on track and on the roller rig. It has been shown that for most cases the roller rig case has a lower critical speed but for some suspension parameter combinations the critical speed on the roller rig can be higher.

High-speed, high-power rotary electrodynamic machine with dual rotors

Abstract: A high-power electrodynamic machine operates at a relatively high rotational speed and has dual rotors. In a preferred generator embodiment, one relatively massive first rotor having a magnetic device integral therewith is dedicated to the main generator. The exciter generator, which is relatively less massive, is isolated on a second rotor, which has a magnetic device integral to it. Only three bearings are required. The distance between the two bearings for the first rotor is relatively short, and the first rotor is relatively stiff, both of which facilitate operation of the first rotor below the critical speed. The junction of the first and second rotors further includes support of a junction end of the second rotor. The second rotor is driven by a prime mover via the first rotor. Means for providing electrical connections between the magnetic devices of the first and second rotors is also provided.

Critical Impeller Speed for Solid Suspension in Mechanically Agitated Contactors

Abstract: Experiments were performed in mechanically agitated contactors with 6 (flat) blade turbine impellers, to study the effect of various operating parameters on minimum/critical speed required for complete suspension in two-phase (liquid-solid) as well as three-phase (liquid-solid-gas) systems Based on 1212 experimental measurements, a unified empirical correlation is proposed, for the estimation of minimum impeller speed for solid suspension in both two-phase and three-phase systems in terms of fundamental, operational and geometrical variables

Optimal Design of Rotor-Bearing Systems Using Immune-Genetic Algorithm

Abstract: In this paper, the new combined algorithm (Immune-Genetic Algorithm, IGA) is applied to minimize the total weight of the shaft and the resonance response (Q factor), and to yield the critical speeds as far from the operating speed as possible. These factors play very important roles in designing a rotor-bearing system under the dynamic behavior constraints. The shaft diameter, the bearing length and clearance are chosen as the design variables. The results show that the IGA can reduce the weight of the shaft and improve the critical speed and Q factor with dynamic constraints.

Dynamic analysis of a hydraulic turbine unit

Abstract: Dynamic analysis is of great importance not only for understanding the natural characteristics and dynamic response of a rotor-bearing system, but also for supplying knowledge of the fault mechanism. The dynamic analysis of a large-scale waterturbine generator set has rarely been investigated. This article establishes a model of a large water-turbine generator set and presents some research results. This article provides a detailed calculation of the critical speed and vibration modes by the Riccati transfer matrix method (RTMM) to study the influence of stiffness of the guide bearings on the characteristics of the shaft. A detailed dynamic model is presented of the No. 1 unit of the Guangzhou Pumped Storage Power Station (GPSPS) in southern China, including nonlinear characteristics of the guide bearing, the thrust bearing, and the magnetic force. An efficient simulation method, referred to as the transient Riccati transfer matrix method (TRTMM), is used to calculate the transient response of the rotor-b...

Energy release rate and bifurcation angles of piezoelectric materials with antiplane moving crack

Abstract: The dynamic fracture problems of the piezoelectric materials with antiplane moving crack are analysed by using function of complex variable in the paper. The results show that the coupled elastic and electric fields inside piezoelectric media depend on the speed of the crack propagation, and have singularity at the crack tip. The stress intensity factor is independent of the speed of the crack propagation, which is identical to the conclusion of purely elasticity. Moreover, independent of the electric loading, the dynamic energy release rate can be expressed by the stress intensity factor and enlarge with the increase of crack speed. High speed of the crack moving could impede the crack growth. At the same time, the crack can be propagated into either curve or bifurcation if the crack speed is higher than the critical speed.

Stabilization control for the hunting motion of a railway wheelset

Abstract: Rail vehicles experience the problem of hunting above a certain speed. The phenomenon is a kind of self-excited oscillation due to the unsymmetrical stiffness matrix in the equation of motion. In the present paper, a stabilization control method is proposed for the hunting motion in a wheelset model with two degrees of freedom by reducing the unsymmetrical effect of the stiffness matrix. It is theoretically shown under this control that the critical speed is infinite and no hunting motion occurs at any finite forward speed. Furthermore, an experimental study is conducted using a simple model and the validity of the control method is experimentally discussed. For the covering abstract see ITRD E111409.

Dynamic stability of periodic shells with moving loads

Abstract: A moving load causes the radial displacements of an axi- symmetric shell to be several times higher than that produced by the static application of the same load. The travel velocity of the moving load affects the amplitude of the radial response and a critical velocity above which the shell response becomes unstable can be identified. A finite element model (FEM) is developed to analyze the dynamic response of axi-symmetric shells subjected to axially moving loads. The model accounts for the effect of periodically placing stiffening rings along the shell, on the dynamic response and stability characteristics of the shell. Shape functions obtained from the steady-state solution of the equation of motion for a uniform shell are utilized in the development of the FEM. The model is formulated in a reference frame moving with the load in order to enable studying the shell stability using wave propagation and attenuation criteria. Hence, the critical velocity can be identified as the minimum velocity allowing the propagation of applied perturbations. Such stability boundaries are conveniently identified through a transfer mis formulation. The model is used to determine the critical velocities of the moving load for various arrangements and geometry of the stiffening rings. The obtained results indicate that stiffening the shell generally increases the critical velocity and generates a pattern of alternating stable and unstable regions. The presented analysis provides a viable means for designing a wide variety of stable dynamic systems operating with fast moving loads such as crane booms, robotic arms and gun barrels.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Vibration control of flexible rotor by inclination control magnetic bearings with axial self-bearing motor

Abstract: An inclination control method has been developed to stabilize a flexible rotor on magnetic bearings that operates over several critical bending speeds. It is desired to increase the rotating speed of the centrifuge which is supported by magnetic bearings on both ends of the rotor. Each magnetic bearing is composed of a pair of hybrid-type magnetic bearings and can control the inclination as well as the position of the rotor. The central position and the inclination of the rotor are calculated by the sum and difference of the measured displacements. These two quantities are supplied to the individual proportional and derivative controllers to obtain the actuating signals. The central position is controlled to provide sufficient stiffness to support the rotor while the inclination control capability is used to obtain adequate damping for the bending mode of the rotor. The control approach is tested on a rotor with three midspan disks to reduce the bending resonances with complete noncontact levitation. A high rotating speed of 6300 r/min was achieved, which is above the fifth bending critical speed.

A parametric study of offset gravure coating

Abstract: A combined theoretical and experimental investigation of an offset gravure coater with a subsequent roll-to-web fluid transfer (operated at web-to-roll speed ratio, S, greater than one) is presented. Under typical operating conditions at the offset nip (applicator and gravure roll contra-rotating with the same peripheral speed) the magnitude of the speed has little effect on the metered film thickness. The fractional pick-out of fluid from different gravure cell patterns, on the other hand, is shown to be dependent on a complex set of parameters, one of which is the cell volume. An experimental study of the roll-to-web transfer region confirms that the whole of the metered film is transferred from the applicator roll to the web at S > 1 and that at high S the transfer of fluid becomes unstable with a resultant loss of coat quality, leading to a corresponding lower limit of the film thickness for the production of uniform coatings. Lubrication theory is employed to (i) model the associated equilibrium flow and (ii) to perform a stability analysis and map out operability plots. In particular, it is found that as the speed of the applicator roll is increased, the critical speed ratio for the onset of instability decreases.

Rapid sliding contact on a highly elastic pre-stressed material

Abstract: A rigid smooth indentor slides at a constant sub-sonic speed on a half-space of an isotropic compressible neo-Hookean material that is initially subjected to a pre-stress aligned with the surface. A dynamic steady-state situation of plane strain is considered and, following Beatty and Usmani and Green and Zerna, is viewed as contact-triggered infinitesimal deformations superposed upon finite deformations due to pre-stress. The neo-Hookean material treated behaves for small strains as a linear elastic solid with Poisson's ratio 1/4. Exact solutions for both deformations are presented and, for a range of acceptable pre-stress values, these illustrate the anisotropy induced by pre-stress and a critical sliding speed corresponding to the Rayleigh speed. Imposition of the unilateral Signorini conditions of contact show that the Rayleigh speed is the upper bound for sub-sonic sliding. For pre-stress levels that fall outside this range, however, either a negative Poisson effect occurs, or a Rayleigh wave does not exist and the Signorini conditions cannot be satisfied for any sub-sonic speed.

Imbalance Response of a Rotor Supported on Flexure Pivot Tilting Pad Journal Bearings in Series With Integral Squeeze Film Dampers

Abstract: Measurements of the imbalance responses of a massive 45 kg rotor supported on series (flexure pivot) tilting pad bearings and integral squeeze film dampers (SFDs) are presented. The rotor-bearing configuration is of interest in compressor applications where often oil lubricated dampers are introduced in series with fluid film bearings to relocate critical speeds, enhance the overall system damping, and reduce the risks of rotordynamic instabilities due to seals and impellers, for example. Coast-down experiments from 9,000 rpm are conducted for increasing levels of rotor imbalance, and equivalent system damping coefficients identified from the peak amplitude of rotor response while traversing cylindrical mode critical speeds. The tests performed with locked (inactive) and active SFDs demonstrate the effectiveness of the flexible damped support in reducing the system critical speed and improving the overall rotor response with reduced transmitted forces to ground. The SFDs allow safe rotor operation with values of imbalance twice as large as the maximum sustained by the rotor supported on tilting pad bearings alone. The experiments reveal a linear relationship between the peak amplitude of vibration at the critical speeds and the imbalance displacement, even for rotor motions larger than 50% of the tilting pad bearing and damper clearances. The tests also show little cross-coupling effects with the shaft centerline moving along a nearly vertical path. The rotor-bearing system remained stable in the entire range of operation and without the appearance of subsynchronous vibration or non-linear damper jump response.Copyright © 2001 by ASME

Quasi-continuum approximations for travelling kinks in diatomic lattices

Abstract: We extend the quasi-continuum method of approximation to the case of a diatomic lattice. This is illustrated by a lattice in which both small and large atoms interact with first- and second-nearest neighbours. We show that highly accurate quasi-continuum techniques may be generalized to determine the shape of nontopological kinks. Many previous analyses of such systems have found travelling wave solutions only for one particular speed using a second-order continuum theory; we show (i) how wave shapes can be found for arbitrary speeds, and (ii) how solution profiles can be calculated from fourth-order partial differential equations which approximate the lattice. Alongside the theoretical analysis, we also present numerical simulations of the lattice which demonstrate propagation of the predicted waves through the lattice. We show that the particular speed for which solutions have been found in previous studies is a special speed for waves in the lattice, but waves can travel for long periods of time at faster or slower speeds, whilst slowly relaxing to this critical speed.

Critical Speed for Quenching

Abstract: A one-dimensional heat equation with a nonlinear, concentrated quenching source that moves with constant speed through a diffusive medium is examined. Bounds are established for a critical speed above which quenching will not occur. When quenching does occur, bounds are given for the quenching time. For the special case of a power law nonlinearity, the growth rate near quenching is derived. The analysis is conducted in the context of a nonlinear Volterra integral equation that is equivalent to the initial-boundary value problem.

The Nonlinear Response of Multimode Rotors Supported on Squeeze Film Dampers

Abstract: This paper describes the development of an extremely fast method to obtain the unbalance response of multiple mode rotors supported on squeeze film dampers (SFDs). Planar modal analysis theory is used to model the rotor-SFD system. Undamped critical speed analysis is performed to obtain the rotor eigenvalues and eigenvectors. The SFD nonlinear forces are included in the modal force vector. The system differential equations are constructed and are uncoupled using the orthogonal properties of modal vectors. Assuming circular orbit, consistent with planar modes, the differential equations are converted into algebraic ones. A polynomial in speed is obtained through algebraic manipulations. This polynomial represents the steady-state behavior of the rotor-SFD system. The full unbalance response is directly obtained by finding the roots of the polynomial for each particular orbit. This method is extremely fast compared to numerical integration and to iterative methods. The developed method is useful in performing parametric studies and optimum design of SFDs. Twenty-five orders of magnitude computer time savings are reported. Parametric studies of an aircraft gas turbine fan rotor supported by an SFD are presented. The parametric studies show the possibility of appropriately locating the SFD, to dampen the rotor modes. In addition, parametric studies are also used to determine the effect of the SFD parameters on the AGTFR unbalance response.