Critical Speed Damper

1963 ◽  
Vol 30 (3) ◽  
pp. 463-464
Author(s):  
Samuel Levy
Keyword(s):  
Critical Speed ◽  
Journal Bearing ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Speed Range ◽  
Spherical Bearing

It is shown that a damper applied to the spherical bearing at the ends of a rotating shaft to damp pitch and yaw motions of the journal bearing can markedly reduce the deflection caused by unbalance near critical speeds. Equations are given for optimizing the damping and for computing the damping moment which must be carried by the journal bearing. It is shown that with optimum damping of a centrally loaded uniform shaft, the load carried by the journal bearing in the critical-speed range is no more than 67 percent greater than it would have been for a rigid shaft. The corresponding moment carried by the journal bearing is less than the amount which would develop at the mid-length of the shaft in the absence of elastic deflections.

Lateral Rotordynamic Analysis of a Large Alternator/Flywheel/Motor Train

2010 ◽  
Author(s):  
Jawad Chaudhry ◽  
Tim Dimond ◽  
Amir Younan ◽  
Paul Allaire
Keyword(s):  
Critical Speed ◽  
Operating Speed ◽  
Response Level ◽  
Critical Speeds ◽  
The Third ◽  
Unbalance Response ◽  
Speed Range ◽  
Stress Levels ◽  
Full Speed ◽  
Working Day

A large alternator/flywheel/motor train is employed as part of the power system for the ALCATOR C-MOD experiment at the MIT Plasma Fusion Center. The alternator is used to provide peak pulse power of 100 MW to the magnets employed in the fusion experiment. The flywheel diameter is 3.3m and the alternator is 1.8 m in diameter. After being driven up to full speed over a long period of time by a 1491 kW motor, the alternator is rapidly decelerated from approximately 1800 rpm to 1500 rpm during a 2 second interval. This sequence is repeated about six times per working day on average. A full lateral rotordynamic analysis of the including the rotors, fluid film bearings and unbalanced motor magnetic force was carried to assess the effects of rotor modifications in the alternator shaft bore. This paper provides a more detailed analysis of a complicated rotor train than is often performed for most rotors. Critical speeds, stability and unbalance response were evaluated to determine if lateral critical speeds might exist in the operating speed range in the existing or modified rotor train and if unbalance levels were within acceptable ranges. Critical speeds and rotor damping values determined for the rotor system with the existing and modified rotor. The first critical speed at 1069 rpm is an alternator mode below the operating speed range. The second critical speed is also an alternator mode but, at 1528 rpm, is in the rundown operating speed range. The third critical speed is a flywheel mode at 1538 rpm, also in the rundown operating speed range but well damped. The predicted highest rotor amplitude unbalance response level is at 1633 rpm, again in the operating speed range. Direct comparisons were made with measured bearing temperature values, with good agreement between calculations and measurements. Stress levels in the rotor were evaluated and found to be well below yield stress levels for the material for both original and modified rotors. Comparisons we carried out between standard vibration specifications and measured vibration levels which indicated that the third critical speed amplification factors were much higher than API standards indicate they should have been. Corrective actions to reduce unbalance were taken for the modified rotor.

scholarly journals Actively Controlled Bearing Dampers for Aircraft Engine Applications

1999 ◽  
Author(s):  
John M. Vance ◽  
Daniel Ying ◽  
Jorgen L. Nikolajsen
Keyword(s):  
Critical Speed ◽  
Aircraft Engine ◽  
Viscous Damping ◽  
Aircraft Engines ◽  
Equivalent Viscous Damping ◽  
Critical Speeds ◽  
Speed Range ◽  
Coulomb Type ◽  
Er Damper ◽  
San Andres

This paper describes some of the requirements for bearing dampers to be used in an aircraft engine and briefly discusses the pros and cons of various types of dampers that were considered as candidates for active control in aircraft engines. A disk type of electrorheological (ER) damper was chosen for further study and testing. The paper explains how and why the choice was made. For evaluating potential applications to aircraft engines, an experimental development engine (XTE-45) was used as an example for this study. Like most real aircraft engines, the XTE-45 ran through more than one critical speed in its operating speed range. There are some speeds where damping is desirable and other speeds where it is not. Thus, the concept of a damper with controllable forces appears attractive. The desired equivalent viscous damping at the critical speeds along with the available size envelope were two of the major criteria used for comparing the dampers. Most previous investigators have considered the ER damper to produce a purely Coulomb type of damping force and this was the assumption used by the present authors in this study. It is shown in a companion paper (Vance and San Andres, 1999), however, that a purely Coulomb type of friction cannot restrain the peak vibration amplitudes at rotordynamic critical speeds and that the equivalent viscous damping for rotordynamics is different from the value derived by previous investigators for planar vibration. Control laws for Coulomb damping are derived in Vance and San Andres, (1999) to achieve minimum rotor vibration amplitudes in a test rig while avoiding large bearing forces over a speed range that includes a critical speed. The type of control scheme required and its effectiveness was another criterion used for comparing the dampers in this paper.

On the Dynamical Behavior of Rotating Shafts Driven by Universal (Hooke) Couplings

1958 ◽  
Vol 25 (1) ◽  
pp. 47-51
Author(s):  
R. M. Rosenberg
Keyword(s):  
Critical Speed ◽  
Dynamical Behavior ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Elastic Shaft ◽  
Rotating Shafts

Abstract The system considered here is a massless, uniform elastic shaft carrying at its mid-point a disk (having mass) and supported at the ends by universal (Hooke) joints. The purpose of this investigation is to examine the effect of Hooke-joint angularity (as obtained by design, or from faulty alignment) on the bending stability of the rotating shaft. It is found that separate investigations are required for shafts not transmitting axial torques and for those required to transmit torques. Each gives rise to instabilities which are absent when the Hooke joint is straight. In the absence of axial torques, the shaft develops unsuspected mild critical speeds at odd integer submultiples of the “familiar” critical speed found with a straight Hooke joint. When the shaft is required to transmit moderate axial torques, the joint angularity produces true instabilities near all integer submultiples of the familiar critical speed. Surprisingly, these instabilities vanish for sufficiently large axial torques.

A New Method for Predicting Critical Speeds in Rotordynamics

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Lawrence N. Virgin ◽  
Josiah D. Knight ◽  
Raymond H. Plaut
Keyword(s):  
Critical Speed ◽  
Industrial Applications ◽  
Rotating Shaft ◽  
Simple Method ◽  
Modeling And Analysis ◽  
Critical Speeds ◽  
Disk Storage ◽  
In Situ Conditions ◽  
Pass Through ◽  
Using Data

The prediction of critical speeds of a rotating shaft is a crucial issue in a variety of industrial applications ranging from turbomachinery to disk storage systems. The modeling and analysis of rotordynamic systems is subject to a number of complications, but perhaps the most important characteristic is to pass through a critical speed under spin-up conditions. This is associated with classical resonance phenomena and high amplitudes, and is often a highly undesirable situation. However, given uncertainties in the modeling of such systems, it can be very difficult to predict critical speeds based on purely theoretical considerations. Thus, it is clearly useful to gain knowledge of the critical speeds of rotordynamic systems under in situ conditions. The present study describes a relatively simple method to predict the first critical speed using data from low rotational speeds. The method is shown to work well for two standard rotordynamic models, and with data from experiments conducted during this study.

On the Transition of a Shaft Through Critical Speeds

1977 ◽  
Vol 99 (1) ◽  
pp. 48-50
Author(s):  
B. M. Naveh ◽  
R. M. Brach
Keyword(s):  
Angular Velocity ◽  
Analytical Solution ◽  
Critical Speed ◽  
Rotating Shaft ◽  
Critical Speeds

The motion of an eccentric rotating shaft and disk is studied for an exponential transition of the angular velocity (spin rale) through a critical speed. An analytical solution is found for the response, and it is shown that this response can yield higher amplitudes when compared to previous work where the angular velocity is varied linearly.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

Taylor-vortex instability and annulus-length effects

1976 ◽  
Vol 75 (1) ◽  
pp. 1-15 ◽  
Author(s):  
J. A. Cole
Keyword(s):  
Critical Speed ◽  
Taylor Vortex ◽  
Vortex Instability ◽  
Critical Speeds ◽  
Taylor Vortices ◽  
Torque Measurements ◽  
Concentric Cylinders ◽  
Theoretical Predictions ◽  
Range Of Values ◽  
Visual Observations

Critical speeds for the onset of Taylor vortices and for the later development of wavy vortices have been determined from torque measurements and visual observations on concentric cylinders of radius ratios R1/R2 = 0·894–0·954 for a range of values of the clearance c and length L: c/R1 = 0·0478–0·119 and L/c = 1–107. Effectively zero variation of the Taylor critical speed with annulus length was observed. The speed at the onset of wavy vortices was found to increase considerably as the annulus length was reduced and theoretical predictions are realistic only for L/c values exceeding say 40. The results were similar for all four clearance ratios examined. Preliminary measurements on eccentrically positioned cylinders with c/R1 = 0·119 showed corresponding effects.

The Effect of Shear Flow and Dissolved Gas Diffusion on the Cavitation in a Submerged Journal Bearing

2000 ◽  
Vol 123 (3) ◽  
pp. 494-500 ◽  
Author(s):  
M. Groper ◽  
I. Etsion
Keyword(s):  
Mass Transfer ◽  
Shear Flow ◽  
Mass Transport ◽  
Transport Mechanism ◽  
Journal Bearing ◽  
Gas Diffusion ◽  
Gas Bubble ◽  
Dissolved Gas ◽  
Rotating Shaft ◽  
Mass Transfer Mechanism

Two possible, long standing speculated mechanisms are theoretically investigated in an attempt to understand previous experimental observations of pressure build up in the cavitation zone of a submerged journal bearing. These mechanisms are (1) the shear of the cavity gas bubble by a thin lubricant film dragged through the cavitation zone by the rotating shaft and (2) the mass transfer mechanism which dictates the rate of diffusion of dissolved gas out of and back into the lubricant. A comparison with available experimental results reveals that while the cavitation shape is fairly well predicted by the “shear” mechanism, this mechanism is incapable of generating the level of the experimentally measured pressures, particularly towards the end of the cavitation zone. The “mass transport” mechanism is found inadequate to explain the experimental observations. The effect of this mechanism on the pressure build up in the cavitation zone can be completely ignored.

Estimating Critical Speeds of Stepped Shafts with Flexible Bearings

1971 ◽  
Vol 8 (03) ◽  
pp. 327-333
Author(s):  
R. H. Salzman
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Design Stage ◽  
Normal Range ◽  
Critical Speeds ◽  
Stepped Shaft ◽  
Bearing Stiffness ◽  
Variable Support ◽  
Method Show ◽  
Good Agreement

This paper presents a semi-graphical approach for finding the first critical speed of a stepped shaft with finite bearing stiffness. The method is particularly applicable to high-speed turbine rotors with journal bearings. Using Rayleigh's Method and the exact solution for whirling of a uniform shaft with variable support stiffness, estimates of the lowest critical speed are easily obtained which are useful in the design stage. First critical speeds determined by this method show good agreement with values computed by the Prohl Method for the normal range of bearing stiffness. A criterion is also established for determining if the criticals are "bearing critical speeds" or "bending critical speeds," which is of importance in design. Discusser E. G. Baker

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