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.

Subcritical Large-Amplitude Vibrations of Imperfect Rotating Shafts

1989 ◽  
Vol 42 (11S) ◽  
pp. S157-S160
Author(s):  
C. E. N. Mazzilli
Keyword(s):  
Dry Friction ◽  
Large Amplitude ◽  
Critical Speed ◽  
Multiple Scales ◽  
Viscous Damping ◽  
Rotating Shaft ◽  
Geometrical Imperfection ◽  
Rotating Shafts ◽  
Large Amplitude Vibrations ◽  
Practical Implications

The effect of a geometrical imperfection, such as the axis flexural deformation, on the large-amplitude vibrations of a horizontal rotating shaft is analyzed with the aid of the Multiple Scales Method. Internal viscous damping and linear elasticity are assumed in the model. It is then seen that no matter how small the imperfection is, a “critical” speed of the order of half the classical critical speed arises, with relevant practical implications. A number of reported large-amplitude cases may eventually be explained this way. It is possible that events such as this will not appear in systems with high dry friction.

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.

Passive Control of Critical Speeds of a Rotating Shaft Using Eccentric Sleeves: Model Development

2016 ◽  
Author(s):  
A. J. Kirk ◽  
J. Griffiths ◽  
C. Bingham ◽  
G. Knowles ◽  
R. Bickerton
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Model Development ◽  
Three Dimensional ◽  
Practical Case ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Rotating Shafts

This paper considers the passive control of lateral critical speeds in high-speed rotating shafts through application of eccentric balancing sleeves. Equations of motion for a rotating flexible shaft with eccentric sleeves at the free ends are derived using the extended Hamilton Principle, considering inertial, non-constant rotating speed, Coriolis and centrifugal effects. A detailed analysis of the passive control characteristics of the eccentric sleeve mechanism and its impact on the shaft dynamics, is presented. Results of the analysis are compared with those from three-dimensional finite element simulations for 3 practical case studies. Through a comparison and evaluation of the relative differences in critical speeds from both approaches it is shown that consideration of eccentric sleeve flexibility becomes progressively more important with increasing sleeve length. The study shows that the critical speed of high-speed rotating shafts can be effectively controlled through implementation of variable mass/stiffness eccentric sleeve systems.

Predicting critical speeds in various rotordynamics problems

2016 ◽  
Vol 231 (21) ◽  
pp. 3913-3922
Author(s):  
Raymond H Plaut ◽  
Lawrence N Virgin ◽  
Josiah D Knight
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Experimental Results ◽  
Nondestructive Technique ◽  
New Approach ◽  
Practical Utility ◽  
Critical Speeds ◽  
Model Free ◽  
Measured Information ◽  
Rotating Shafts

Rotating shafts often experience undesirable large-amplitude whirling oscillations associated with resonance at critical speeds. This paper further develops a nondestructive technique in which measured information about the growing nature of the response is used to predict an incipient critical speed. A number of models of varying degrees of sophistication are developed and tested using the new approach, but the main advantage of the method is that it is model-free and thus possesses considerable practical utility. In addition, further experimental results are presented for the case of two disks mounted on a shaft, and the technique is successfully demonstrated in predicting a critical speed associated with a higher mode.

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.

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.

Bisynchronous Torsional Vibrations in Rotating Shafts

1987 ◽  
Vol 54 (4) ◽  
pp. 893-897 ◽  
Author(s):  
O. Bernasconi
Keyword(s):  
Angular Momentum ◽  
Nonlinear Term ◽  
Rotation Frequency ◽  
Longitudinal Component ◽  
Torsional Vibrations ◽  
Rotating Shaft ◽  
Rotating Shafts

In this study, the intrinsic behavior of rotating shafts with residual unbalance is considered. The longitudinal component of the angular momentum caused by synchronous precession (whirling) induces torsional vibrations with a frequency of twice the rotation frequency (bisynchronous). The nonlinear term which represents this coupling is characteristic of the asymmetrical aspect of rotating shaft kinematics. This result has been obtained analytically and confirmed experimentally.

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.

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