Showing papers on "Critical speed published in 1987"

Speed avoidance logic for a variable speed wind turbine

Abstract: A variable speed wind turbine is controlled in a way which avoids the turbine lingering at a critical speed which would otherwise tend to cause excessive vibration. The disclosed method and apparatus increases speed at a selected rate with respect to generator output power except in the vicinity of the critical speed. The selected rate is changed in the vicinity of the critical speed to a different rate which is selected slower in the selected embodiment, to avoid commanding the critical speed. After the output power increases or decreases beyond the critical point, a deliberate discontinuity in the speed command signal is induced. A rapid speed change through the critical speed is accompanied by a corresponding power output change. If the speed is increasing at a selected slower rate below the critical speed, and the speed command signal is stepped to a higher level just before reaching the critical speed, the speed will rapidly increase and quickly pass through the critical speed while the power output decreases. Similarly, if the speed is decreasing at a selected slower rate above the critical speed, and the speed command signal is stepped to a lower level just before reaching the critical speed, the speed will rapidly decrease and quickly pass through the critical speed while the power output increases.

Influence of unbalanced magnetic pull on the radial stability of flexible-shaft induction machines

Abstract: An accurate assessment of the critical speed and the electromechanical damping is necessary to avoid the possibility of excessive vibrations and damage under operating conditions. Nowadays these problems are even more important, as the speed of induction motors may be varied using static inverters. 2-pole machines are very interesting when used with these inverters, because, f or a given frequency range of the inverter, the absolute speed range covered is twice the range of a 4-pole machine. Therefore the unbalanced magnetic pull and its relationship with the homopolar flux is analysed.

Experimental study of unsteady hydrodynamic force matrices on whirling centrifugal pump impellers

Abstract: An experimental facility was constructed and instrumented. A study was conducted on a set of centrifugal flow pumps whose impellers were made to follow a controlled circular whirl motion. The aim was to characterize the steady and unsteady fluid forces measured on the impeller under various pump operating conditions. The postulation was that the unsteady lateral forces result from interactions between the impeller and the surrounding diffuser and or volute (via the working fluid), and that under certain flow regimes these forces can drive unstable lateral motions of the pump rotor. The lateral hydrodynamic forces were decomposed into their steady and unsteady parts, the latter being further expressed in terms of a generalized fluid stiffness matrix. A study of this matrix as a function of the whirl to pump speed ratio supported the following chief conclusions: i) the common assumption of matrix skew-symmetry is justified; ii) the magnitudes and signs of the matrix elements are such that rotor whirl can indeed be caused by the hydrodynamic forces, in pumps operated well above their first critical speed, iii) as expected, the matrix is very sensitive to the value of the flow coefficient, especially at flow rates below the design; iv) the commonly postulated quadratic variation of the matrix elements with the reduced whirl frequency, resulting in the so-called rotordynamic coefficients (stiffness, damping and inertia) is not justified for flow coefficients significantly below design; and v) surprisingly, it was discovered that the presence, number and orientation of diffuser guide vanes have little effect on the forces. Conclusions regarding the effect of impeller geometry could not be reached given the similarity of the tested designs. However, other results on phenomena such as skin friction and leakage flow are presented. Some of the findings are compared to experimental and theoretical data from other sources. Finally, the rotordynamic consequences of the results are discussed as the present data were applied by another author to the case of the Space Shuttle Main Engine's (SSME) High Pressure Oxidizer Turbopump (HPOTP).

Dynamically balanced drive shaft

Abstract: A dynamically balanced drive shaft. The shaft is preferably formed of fiber reinforced resin and is designed to operate at speeds below the first critical speed. To balance the shaft, a mass or patch of resin containing high density particles, such as metal particles, is applied to one or more locations on the shaft. The patch extends only a portion of the circumference of the shaft and generally has an area less than 10 sq. inches, and generally has a thickness less than 1/16th inch.

Delayed die swell

Abstract: The experiments reported here establish that there is a general critical condition associated with die swell which we call delayed die swell. This condition is defined by a critical speed which is the area-averaged velocity, the extrusion velocity, at the exit of the pipe when the swell is first delayed. The delayed swell ratio and delay distance first increase for larger, post-critical values of the extrusion velocity; then the increases are terminated either by instabilities or by smoothing. The maximum post-critical velocity at the pipe exit was always greater than the shear wave speed measured on the shear-wave-speed meter. The post critical area averaged velocity at the position of maximum swell before termination was always less than the shear wave speed. There were always points in the region of swelling where the ratio of the local velocity to the shear wave speed, the viscoelastic Mach number, was unity. The swelling of the jet is a nonlinear phenomenon which we suggest is finally terminated either by instability or when the variations of the velocity, vorticity and stress field are reduced to zero by the inward propagation of shear waves from the free surface of the jet. This propagation is generated by discontinuous “initial” data along χ in which the prescribed values of velocity at the boundary change from no-slip in the pipe to no-shear in the jet. The measurements raise the possibility that the delay may be associated with a change of type from supercritical to subcritical flow.

Control of flutter in bridges

Abstract: In recent years there has been increasing interest in the application of modern control theory to the problem of vibration suppression in civil structures. The loads on such structures can depend on the environment. For example, the motion of a flexible suspension bridge, such as the original Tacoma Narrows Bridge [Ref. 1], can include unsteady aerodynamic forces. The motion can be described by two partial differential equations for bending and torsional vibration [Ref. 2], with the airstream velocity V as a parameter. The stability of motion is governed by the real part of the system eigenvalues, where the eigenvalues depend on V. For V = 0, the system is self-adjoint [Ref. 3] and the eigenvlaues consist of pairs of mere imaginary complex conjugates. For small V, the eigenvalues have negative real parts, so that the motion is asymptotically stable. As V increases, some real parts can turn positive, rendering the system unstable. The air speed corresponding to zero real part is known as the critical speed V er. If the critical speed corresponds to a value for which the imaginary part of an eigenvalue is different from zero, the structure is said to be in flutter condition [Ref. 3].

Performance of an electromagnetic bearing for the vibration control of a supercritical shaft

Abstract: The flexural vibrations of a rotating shaft, running through one or more critical speeds, can be reduced to an acceptably low level by applying suitable control forces at an intermediate span posit...

Forces on a slender ship advancing near the critical speed in a wide canal

Abstract: Employing matched asymptotics, the recent theory of Mei (1986) is extended to study the phenomenon of upstream influence by a slender ship moving near the critical speed. For a special class of channel width and ship slenderness, it is shown that the response on the sea surface is essentially one-dimensional with the wave crests perpendicular to the ship's axis. In particular, solitons are radiated upstream. The hydrodynamic pressure on the ship, as well as the total sinkage force, wave resistance and trimming moment are calculated. These forces are functions of time despite the constant speed of the ship. The sinkage and trim for a ship model fixed on an advancing carriage are computed and show rapid variations across the critical speed as in the reported experiments of Graff, kracht & Weinblum (1964). Because of the assumed slenderness of the ship, this theory does not predict two-dimensional waves in the wake. Nevertheless, there is crude agreement in the time-averaged hydrodynamic forces between theory and experiment.

Split flywheel with an additional mass

Abstract: The invention relates to the arrangement of an additional mass which is coupled to the secondary mass of a split flywheel. When appropriately coupled, such an additional mass is capable of improving the torsional vibrations of the drive system both in the supercritical speed range and during passage through the critical speed range.

Direct observation of high frequency emissions from a critical velocity rotating plasma

Abstract: The high frequency (hf) emission associated with the turbulent heating mechanism, which is part of the critical velocity effect, is measured directly for the first time. The emissions are found to occur in the steep density gradient in the front of so‐called rotating ‘‘spokes,’’ as predicted by a model of the critical velocity effect in inhomogeneous plasmas. The spectral distribution of the waves and a lower bound for the absolute wave amplitude are obtained.

Nonlinear dynamics of attractive magnetic bearings

Abstract: The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Stability of railway-car running at high speed

Abstract: SUMMARY From a classical study of railway stability, the author shows how the equations of motion of a railway-car having: either a counter hunting damping device, between wheelset and truck frame, or a direct or crossed stiffness device between front and rear wheelsets are modified. The critical speed is determined by eigenvalues of matrix A (9,9). From the critical speed variations as a function of: CR typical value of counter hunting damping device, K′ b or K′ b typical value of direct or crossed stiffness, we can say that: the influence of these original systems on the critical speed is more interesting for higher values of equivalent conicity γe, for lower values of γe, the critical speed is high already. the best values of CR of K′ b (or K′ b ) are defined from curves given the critical speed as a function of CR or K′ b (orK′ b ). a crossed stiffness device is more interesting that a direct stiffness device.

Method and apparatus for controlling variable speed wind force turbine generator

Abstract: A variable speed wind turbine is controlled in a way which avoids the turbine lingering at a critical speed which would otherwise tend to cause excessive vibration. The disclosed method and apparatus increases speed at a selected rate with respect to generator output power except in the vicinity of the critical speed. The selected rate is changed in the vicinity of the critical speed to a different rate which is selected slower in the selected embodiment, to avoid commanding the critical speed. After the output power increases or decreases beyond the critical point, a deliberate discontinuity in the speed command signal is induced. A rapid speed change through the critical speed is accompanied by a corresponding power output change. If the speed is increasing at a selected slower rate below the critical speed, and the speed command signal is stepped to a higher level just before reaching the critical speed, the speed will rapidly increase and quickly pass through the critical speed while the power output decreases. Similarly, if the speed is decreasing at a selected slower rate above the critical speed, and the speed command signal is stepped to a lower level just before reaching the critical speed, the speed will rapidly decrease and quickly pass through the critical speed while the power output increases.

Method for controlling the rotational speed of a thermal engine

Abstract: A method for controlling the rotational speed of a thermal engine residing in that a speed of rotation of the theraml engine is preset, a control signal based on this speed is shaped to control the speed of rotation of an electric motor according to the rotational speed of one of the input shafts of a differential mechanism kinematically linked with the electric motor and thermal engine fuel metering member is kinematically linked with an output shaft of the differential mechanism, and a correction signal is simultaneously shaped for the speed of rotation of the electric motor at transient operating conditions on the basis of the speed of rotation of the output shaft of the differential mechanism.

An examination of gas compressor stability and rotating stall

Abstract: The principal sources of vibration related reliability problems in high pressure centrifugal gas compressors are the re-excitation of the first critical speed or Resonant Subsynchronous Vibration (RSSV), and the forced vibration due to rotating stall in the vaneless diffusers downstream of the impellers. An example of such field problems is given elsewhere. This paper describes the results of a test program at the author's company, initiated in 1983 and completed during 1985, which studied the RSSV threshold and the rotating stall phenomenon in a high pressure gas compressor.

Critical speed overriding method for high-speed turning shaft

Abstract: PURPOSE:To make rotation to a higher zone attainable, by supporting a bearing part of a high-speed turning shaft with a shape memory alloy spring, and avoiding a resonance point of each second degree in a turning shaft system in a way of heating and radiating this spring CONSTITUTION:A bearing part 3 being installed in a whirling generating part 2 in a turning shaft system is supported with a shape memory alloyed spring A whose one end 51 is locked to a constrained piece 4 of this bearing part 3 and other end 52 locked to a machine body 6, respectively, and a heating/ radiating on-off controller 7 is installed in this spring A With this on-off control, a spring constant of this spring A is altered whereby rotation to a higher zone is made attainable while avoiding a resonance point of each second degree in the turning shaft system

Yarn filament take-up motion

Abstract: PURPOSE:To make a vibration at the time of passing a critical speed as well as to aim at stabilization in continuous winding operation, by making a field balance correction so as to be carried out with both edges of a bobbin holder part and the balancing correction plane installed in an intermediate part. CONSTITUTION:A bobbin holder 1 is rotated in the state that notching is attached to each of correction planes A-D, and vibrators at both X and Y points when rotational frequency is fixed are measured. Next, the correction plane A is rotated after attaching a trial weight known of its weight to one optical spot among eight spots of a tap 12a, whereby the rotational frequency is adjusted to the same one at the time of being measured in the state that nothing is attached, and the vibrations at these X and Y points are measured. Then, the weight on the plane A is removed, the trial weight known of its weight is attached to the plane B whereby vibrations are measured in the same procedure, and afterward measurement takes place in the same way, thus vibrations at the time of attaching the trial weight to the plane D and measured. A vibration variation degree due to addition of the weight, namely, an influence coefficient matrix is calculated from these vibration data, and with this matrix, optimum correction value and phase on these correction planes A-D minimizing the vibrations at these X and Y points are calculated.

クラックロータの振動 : 第1報,不つりあいの方向による主危険速度付近の共振曲線の変化

Abstract: In order to find some way to detect a transverse crack due to fatigue in a rotating machine, we have investigated experimentally and theoretically the change in the resonance curve caused by the occurrence of a crack. The experimental apparatus is a vertical rotating shaft system where an elastic shaft with a disk is supported simply at both ends. In the experiments, the amplitude curve and phase angle curve were measured in the neighborhood of the major critical speed for various angular positions of unbalance. The results show that the shape of the resonance curve changes extremely due to the direction of the unbalance, and an unstable region appears when the unbalance exists in the same direction as the crack. It is shown that this phenomenon is explained theoretically by combining the characteristics of the unsymmetrical shaft and those of the symmetrical shaft and those of the symmetrical shaft or by considering rotating nonlinear spring characteristics.

Dynamic response of plates on elastic foundations due to the moving loads

Abstract: This paper discusses the dynamic response of thin plates on the elastic foundations due to the moving loads by means of the variational calculus. In the text we take the mass of moving loads into account, treat a series of questions such as the forced oscillations, the influence surfaces of the flexions and the influence surfaces of the inner forces, resonance conditions and critical speed and so forth.

On the static running accuracy of cylindrical roller bearings.

Abstract: The quasi-static vibratory analysis of a rotor supported by cylindrical roller bearings is presented. The system is an ideal cylindrical roller bearing in which the inner ring moves in a radial plane with two degrees of freedom under a constant radial load. The load/deformation relation for an elastic contact is expressed by the function with an arbitrary power index, and the motion of the inner ring center due to roller revolution is analyzed in detail. The case in which the spring is a one-sided linear is also analyzed. The results show that the inner ring motion has complicated features, and changes drastically with the design and operating conditions. All computed results are arranged in charts in which approximate wave forms of the inner ring motion and its magnitudes, and the loaded states of rollers are presented. They may be used in the design process to examine the rigidity, the critical speed, and the vibratory nature of a rotor system.

Some Practical Aspects of Balancing an Ultra-Centrifuge Rotor

Abstract: In this paper the method of balancing centrifuge rotors for initial three modes based on practical experience IS presented though, depending on the size of the centrifuge, more than one flexural modes have to be encountered. The object is to provide useful and practical information, as technical information on balancing of centrifuge rotors is hardly available because most of the work is shrouded In the clouds of the so-called secrecy. The rotor is balanced In three stages. Firstly, individual components and sub-as-semblies are balanced in traditionally low speed rigid rotor balancing machines. Secondly, the complete rotor is balanced by using modal balancing. Thirdly, the rotor is run in a high speed testing facility and rotor balance quality is checked at the operating speed. During the second and the third stages the rotor is run in its own bearings under vacuum and the data is acquired with the aid of a computer.

Self-excited vibrations of a rotating shaft with structural damping.

Abstract: In order to improve their performance, rotating machines must often be operated in a high speed region beyond the first critical speed. Above the first critical speed, self-excited vibrations may be caused by internal friction which includes both internal damping of the shaft material and structural damping due to dry friction between the shaft surface and rotor-hub. In this paper, structural damping due to dry friction at a sleeve fixed to an arbitrary position of a shaft was studied. The mechanism of the whirling force generated by sleeve friction is clarified. The experimental results of two kinds of over-hung vertical shafts, supported by two ball bearings at their upper end can be explained well by t-heory.