Showing papers on "Critical speed published in 1992"

Non-linear vibration of a traveling tensioned beam

Abstract: Free non-linear vibration of an axially moving, elastic, tensioned beam is analyzed over the sub- and supercritical transport speed ranges. The pattern of equilibria is analogous to that of Euler column buckling and consists of the straight configuration and of non-trivial solutions that bifurcate with speed. The governing equations for finite local motion about the trivial equilibrium and for motion about each bifurcated solution are cast in the standard form of continuous gyroscopic systems. A perturbation theory for the near-modal free vibration of a general gyroscopic system with weakly non-linear stiffness and/or dissipation is derived through the asymptotic method of Krylov, Bogoliubov, and Mitropolsky. The method is subsequently specialized to non-linear vibration of a traveling beam, and of a traveling string in the limit of vanishing flexural rigidity. The contribution of non-linear stiffness to the response increases with subcritical speed, grows most rapidly near the critical speed, and can be several times greater for a translating beam than for one that is not translating. In the supercritical speed range, asymmetry of the non-linear stiffness distribution biases finite-amplitude vibration toward the straight configuration and lowers the effective modal stiffness. The linear vibration theory underestimates stability in the subcritical range, overestimates it for supercritical speeds, and is most limited in the near-critical regime.

Self-excited vibrations of a flexible disk rotating on an air film above a flat surface

Abstract: Self-excited vibration of a spinning flexible disk is studied to provide design guidance for high speed magnetic disk storage devices. The dynamic model includes coupling between vibrations of a rotating plate and waves in an incompressible viscous fluid film. A single-mode approximation is used to estimate the critical speed and the influence of the various disk and air-film parameters is noted. A simple physical explanation of the instability mechanism is given and the critical speeds for several disk configurations are estimated. More accurate numerical procedures are described and the results of calculations for a particular disk system are compared with the single-mode approximation.

Apparatus for dynamical balancing of rotating objects and method for making same

Abstract: This invention relates to an apparatus for dynamically and constantly balancing rotating objects while they are in motion. Such an apparatus can be applied to balancing wheels of automobiles or trucks or can be applied to balancing the shafts of rotating machinery. The basic concept is to attach a fixture that supports a system of weights to the rotating object. Said weights are free to move relative to the rotating object in an orbit concentric to the axis of rotation of said rotating object. Under the influence of the forces generated by rotation of the rotating object above its critical speed, the system of weights take a configuration that opposes and partially cancels the imbalance of the rotating object. This invention also relates to a method of making the inventive apparatus by concentrically placing the annular hoop on the mounting fixture and fixing the hoop in place by use of counter-rotating, high-speed rotary press.

Theory of Receptance Applied to Modal Analysis of a Spinning Disk With Interior Multi-Point Supports

Abstract: The theory of receptance applied to the modal analysis of a spinning disk with interior multi-point supports is developed. Traveling modes are first introduced for the vibration analysis of a spinning disk. The receptance method is then applied to join the spinning disk and the point supports. The frequency equation and mode shapes are then formulated. An important property, conjugate pairing of the cross receptances is derived. This feature has never been described before in the literature. Numerical results for various numbers of point supports are illustrated. The results show that the nodal pattern of a spinning disk with point supports is varying periodically. The change of rotation speed further causes the mode exchange phenomenon. The change of first critical speed due to point supports is also discussed.

Estimating Truck’s Critical Cornering Speed and Factor of Safety

Abstract: Fully laden trucks are prone to rollover when exceeding a critical cornering speed. After an accident, authorities, both highway engineers and the police, often need to establish a vehicle's speed from tire marks and other physical evidence. This paper outlines the relative precision of equations of varying complexity used to estimate a truck's critical rollover speed based on tire marks. An error analysis is compared with a limited tachometer data base to evaluate the accuracy of the speed-estimating equations. The study shows that for most situations with fully laden, rigid trucks, the simple lumped-parameter model gives an acceptable estimate of the rollover speed for highway design engineers and the police. Also, a review of the lateral acceleration generated by a vehicle negotiating a minimum-radius curve found that the acceleration is very close to the level needed to tip over a truck. Based in part on these findings a method for developing a reasonable estimate of level of safety is discussed.

Nonstationary Vibration of a Rotating Shaft with Nonlinear Spring Characteristics during Acceleration through a Critical Speed : A Critical Speed of a 1/3-Order Subharmonic Oscillation

Abstract: Nonstationary vibration characteristics during acceleration through a critical speed of a 1/3-order subharmonic oscillation of forward precession are investigated in a rotating shaft system. The following results are obtained : (1) A resonance curve is separated from a zero-amplitude resonance curve (a trivial solution) which is stable at any rotating speed ω. If there exists an initial disturbance at the start of acceleration, the solution jumps to the resonance curve and a subharmonic oscillation occurs. (2) The maximum amplitude during acceleration depends not only on the angular acceleration λ but also on the initial disturbance lP, the initial rotating speed ωs, and the initial angular posion Ψo of the unbalance. (3) For the initial angular position Ψo, the maximum amplitude varies periodically. (4) The amplitude grows infinitely for some values of Ψo when the angular acceleration λ takes a value between two critical values λ1 and λ2. If the angular acceleration is outside of this range, the rotor can always pass the critical speed with a finite maximum amplitude. In addition, characteristics of some other subharmonic oscillations of backward precession are discussed briefly. Finally, nonstationary vibration characteristics at various critical speeds, such as a major critical speed, a summed-and-differential harmonic resonance and subharmonic resonances, are compared.

Vibrations of a Rotating Shaft Containing a Transverse Crack. Major Critical Speed of Horizontal Shaft.

Abstract: In a horizontal rotating shaft containing a transverse crack, the vibration characteristics at the major critical speed are investigated. In a theoretical analysis, a model whose spring characteristic is approximately represented by a power series is treated. The analytic results are compared with the results of numerical simulation with a model of a piecewise linear spring characteristic. Experiments with a flexible rotating shaft system are also performed. The following points are clarified : ( a ) In the case of a comparatively large unbalance, the shape of resonance curves changes markedly depending on the relative angular position of the unbalance to the crack, and an unstable region appears for a certain range of angular position. This phenomenon is similar to the case of vertical shafts. ( b ) In the case of a comparatively small unbalance, the shape of resonance curves is not affected by the direction of the unbalance and an unstable region always appears. This is a phenomenon particular to the horizontal shaft.

Dynamics of AC electrical machines

Abstract: The concepts of natural frequency, critical speed, excitation, mechanical resonance, damping, torsional excitation, torsional critical speeds, unbalanced magnetic pull, and magnetic instability are defined and placed in context. The author seeks to encourage the use of technically justified words and phrases in the technical literature. The article is presented in a context of a technical survey and a tutorial. >

The Behaviour of Fibres Struck by High-speed Pins. Part I: Theory

Abstract: A theory is developed to predict the behaviour of a straight fibre when it is struck by a pin. The theory predicts that, if the pin speed exceeds a critical value for a given angle of impact, then the fibre will break immediately. Below this critical speed, the strain in the fibre passes through an initial peak and then peaks again as the free fibre end wraps around the pin. The theory can be used to predict the breakage of straight fibres in contact with high-speed pinss.

On the influence of damping on the critical speed of spring-mass system moving along a Timoshenko beam on an elastic foundation

Abstract: The paper is devoted to an analysis of behaviour of the densly distributed chain of spring-mass system moving with constant speed along on infinite Thnoshenko beam on a visco-elastic foundation. The critical velocities of relative motion were determined on the basis of the kinetic stability criteria. It was proved that the instability regions are esentialy influenced also by a very small intensity of energy dissipation.

A vacuum protection system for the front end of SPring‐8

Abstract: The design of a high‐speed movable heat absorber (HA) to protect a fast closing valve (FCV) is presented and a unique safety system to protect the storage ring ultrahigh vacuum from a vacuum break accident in downstream beamlines is proposed. The speed of the incoming shock wave upon a vacuum failure can be measured by two sensors separated by a given distance. If the measured speed does not exceed the prescribed critical speed calculated from both the operating time of the HA and the distance between the sensors and the FCV, the storage ring vacuum can be maintained without dumping the electron beam. If the measured speed exceeds the critical speed, beam dumping will be requested. Fortunately the vacuum sensor can be installed at a distance 14 m from the FCV for the SPring‐8 and the operation of the HA can be completed in 40 ms. The acceleration for moving at 40 ms is approximately 2 G, which is a practical value. Therefore the critical value of the shock wave speed is 350 m/s. In order to perform thermal analysis for the absorber plate, the fluorescent x rays and Compton scattered rays emitted from 3° inclined copper absorber can be calculated as 4.7% and 0.41% of the SPring‐8 undulator power, respectively. Hence the highest temperature at the absorber surface exposed to intense undulator radiation of the total power of 2.06 kW was about 350 °C.

Active Balancing of a High Speed Rotor in Magnetic Bearings

Abstract: This paper describes the application of an open loop control technique for the attenuation of unbalance response in a high speed rotor. The test rig is a mock up of a dual wheel compressor with an operating speed range of 30,000 to 70,000 rpm. The rotor has a third critical speed (first bending mode) at 24,050 rpm which is lightly damped. Excessive rotor synchronous response occurs during run-up at this speed and intermittently causes loss of support. An open loop control is used to introduce a rotating magnetic force to balance the rotor and reduce rotor synchronous response at this speed. With this control, the third critical speed is essentially canceled. Also demonstrated is the use of the open loop control to attenuate housing structure vibrations when the rotor is operating at one of the housing’s natural frequencies, 42,300 rpm.

On the sealing mechanism of lip seals containing microundulations

Abstract: A mathematical model of the sealing process in rotary lip seals containing microundulations has been constructed. In this model, based on a mechanism proposed by previous investigators, shear deformation of the lip surface produces a vane-like undulation geometry, which results in reverse pumping of liquid and a reduction in leakage rate. At a critical shaft speed, the leakage rate is zero, and a free surface is formed at the low pressure edge of the sealing zone. When the shaft speed exceeds the critical speed, the free surface moves axially toward the high pressure side, and assumes an equilibrium position within the narrow gap between the lip and shaft surfaces. The model allows computation of the critical speed as a function of the design and operating parameters. Model predictions agree qualitatively with the experimental observations of previous investigators. Although the model deals specifically with microundulations on the lip surface, it has implications for other lip surface microgeometries.

A Consideration of Damping in Rotors Supported by Tilting-Pad Bearings

Abstract: Tilting-pad journal bearings are often used in high performance machinery operating at speeds above the first critical speed, in order to improve bearing stability. In many cases such machinery may still be prone to subsynchronous or unstable vibration problems. The influence of the dynamic characteristics of the tilting-pad bearings on the response of the complete rotor system is therefore of great importance. This paper is primarily concerned with the damping provided by such bearings. A number of factors are considered including frequency dependence of the dynamic coefficients, influence of pad support flexibility, and a simple method for evaluation of effective damping required to maintain rotor stability.

Limiting critical speed response on the SSME Alternate High Pressure Fuel Turbopump (ATD HPFTP) with bearing deadband

Abstract: Yammamoto (1954) described the influence of bearing deadband on the critical speed response of a rotor-bearing system. Practical application of these concepts to limit critical speed response of turbopump rotors is described. Nonlinear rotordynamic analyses are used to define the effect of bearing deadband and rotor unbalance on the Space Shuttle Main Engine Alternate High Pressure Fuel Turbopump. Analysis results are used with hot fire test data to verify the presence of a lightly damped critical speed within the operating speed range. With the proper control of rotor unbalance and bearing deadband, the response of this critical speed is reduced to acceptable levels without major design modifications or additional sources of damping.

Critical speed "yaw" computer analysis-metric & usa units

Abstract: This article contains a computer program written by the author in the QBASIC programming language for readers of Accident Reconstruction Journal. This program was designed to be a stimulus for all to experiment with computer programming, and assist in the analysis of critical speed yaw calculations. This program may be used for critical speed analysis immediately and requires no modification. Critical speed yaw and critical curve speed are two important equations in determining speed problems in which a vehicle leaves the road on a curved surface. This program will produce speeds in metric (kph) and USA (mph) units of measure, and will automatically generate a table of speeds with increments of the radius variable at 10 feet/meters increments. To use the program, one needs an IBM/DOS or compatible computer with at least DOS 5.0, or Microsoft's QuickBasic.

Seismic Response of a Multirotor System Supported by Oil Film Bearings. Effect of Misalignment.

Abstract: Nonlinear behavior of a multirotor system supported by oil film bearings is investigated theoretically by calculating the loci of centers of disks and a journal of the system using a time-marching method. The oil film force of bearings is obtained by solving the Reynolds equation at each time step using a rapid solution presented previously by the authors. It will be shown that a 2-disk/4-bearing rotating system operated under the linear stability limit but above twice the first critical speed becomes unstable when sufficiently large external shocks-an artificial sinusoidal shock and real seismic waves (Taft, California, 1952)-are given to the system. The effect of misalignment of bearings is also examined closely in this study.

Breakage prevention method of feed shaft bearing

Abstract: PURPOSE:To prevent breakage of a bearing due to thermal expansion of a feed shaft at a cheap price by obtaining the average speed of every shaft based on an accumulated moved distance during a decided time at every unit time, comparing it with the previously set safety speed and critical speed of a feed bearing, and correcting an override correcting ratio so that the speed is in the safety speed range. CONSTITUTION:The average speed of every shaft is obtained with a computing part 4 based on an accumulated moved distance in a decided time at every unit time. Next, the previously set safety speed and critical speed are compared with this obtained average speed in a speed judging part 5, and when the average speed is over the safety speed, an override ratio is corrected to make the speed not to be over the safety speed. If the average speed is over the critical speed, operation is stopped for alarm. Hereby, breakage of the bearing due to thermal expansion of the feed shaft is prevented at a low cost.

A Study of Transient Response of Flexible Rotors in High Speed Turbomachinery

Abstract: In many applications the design operating range of the turbomachinery may be well above the rotor first critical speed which leads to the problem of insuring that the turbomachinery performs with a stable, low-level amplitude of vibration.Under certain conditions of high speed and loading the rotor system can start orbiting in its bearing at a rate which is less than the rotor angular speed, and this phenomena is commonly known as whirling or whipping action. This whipping action may produce additional undesirable dynamic loads on the overall flexible assembly and eventually destroy the rotor. Some of this action is also transient in nature.Whirling is a self-exited vibration caused mainly by the fluid bearings and by the internal friction damping of the rotor. To understand this occurrence, a general dynamic mathematical model was derived considering also the complete viscous characteristic of hydrodynamic journal bearings.The general equations of motions of the system are obtained from Lagrange’s equation of motion. The system kinetic, potential, and dissipation functions are determined based on the generalized coordinates of the system.The journal displacements are related to the overall dynamics of the rotor using deformable bearings. The loads acting at the journals of the shaft are integrated from the fluid film pressure distribution in the journal bearings using mobility method.A unique mathematical model is formulated and solved. This model includes the elastic and inertial properties of the flexible rotor, the elastic, damping and inertial properties of supports and the hydrodynamic characteristics of the journal bearings.The equations of motions result in a system of nonlinear second order differential equations which are solved by using finite difference method. The solution of the equations of motions is used to plot maps of motion of journal centers.A computer program was implemented to aid in the solution of the system of equations and to verify analytical model. The computer program used test data available in literature and the results were compared to be very good.The analytical model and results obtained in this study can be of great help to designers of high speed turbomachinery.Copyright © 1992 by ASME

Theoretical and Practical Aspects in the Field Balancing of Large Turbogenerator Rotors

Abstract: The paper reviews two experiences of computer aided field balancing of large turbogenerator rotors.

Self energy supplied train speed reduction method and equipment thereof

Abstract: The device is characterized by using a level, one end of which is connected to a weighing pedal, the other end is connected to a pressure valve, the weight signal of a train is sent to the pressure valve through the level according to a definite proportion, thus giving out large brake force for heavy train and small brake force for light train; the device is also characterized by using a rotary shaft which connects brake pedals with a brake converting unit, speed signals received by each brake pedal can be sent to the brake pump and the speed valve, when the speed of the train is greater than or equal to critical speed, the speed reducer will brake the train