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 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.

Prediction and Comparison of Critical Speeds and Potential Excitation Using In-House Developed Software for an Integrally Geared Centrifugal Air Compressor

2014 ◽  
Author(s):  
Mathew P. James ◽  
Pavan Kumar Reddy Pandillapalli ◽  
Swaminathan Gopalakrishnan
Keyword(s):  
Steady State ◽  
Computer Program ◽  
Critical Speed ◽  
Maximum Amplitude ◽  
Sound Intensity ◽  
Industrial Applications ◽  
Lateral Direction ◽  
Critical Speeds ◽  
Vibration Data ◽  
Unbalance Response

Integrally Geared Centrifugal Air Compressors (IGCAC) are becoming popular in many industrial applications. Development of such compressors requires in depth Rotordynamic Design and Analysis. To facilitate this, an in-house computer program based on transfer matrix method was developed using MATLAB® software. This computer program is capable of computing rotordynamic parameters such as static deflection, critical speed and interference diagram, and can output critical speed map, mode shape, unbalance response, orbit, for lateral direction. This software was used to analyze a two stage IGCAC with two impellers on a simply supported rotor running above second critical speed, driven by a two pole induction motor through a step-up gearbox. Undamped critical speed map, an output from the program was used to predict intended bearing stiffness for design. Using the above data and commercially available software DyRoBeS© a suitable bearing was designed. The speed dependent bearing characteristics, an output from DyRoBeS©, were used to determine damped unbalance response plot for a given residual unbalance. Corresponding to a maximum peak in unbalance response the damped critical speed and amplification factors (AF) were found out. The results from the newly developed software were compared with prediction from DyRoBeS©. It was found that critical speed was within 5% and AF was of the same order. Results from in-house software were comparable to that from DyRoBeS©. Based on the guidelines from API 684, the AF and separation margins were determined. A prototype IGCAC compressor as described above was built and tested. The testing included the collection of steady state, coast-up and coast-down data. Using the coast-up, coast-down data, a Bode plot was created. From this the critical speeds and AF’s were determined and compared with results from in-house software. It was found there was an error of less than 5% for the critical speed and around 5% for AF from the predicted results. For the same compressor a study on the potential excitation frequencies due to unbalance, impeller-diffuser and impeller-scroll tongue interactions were calculated. FFT of the steady state vibration data was deduced. It was found that the calculated frequency and measured frequency at maximum amplitude were aligning. Further noise measurements were recorded based on sound intensity as per guidelines in ISO 9614. The impeller-tongue interaction frequencies for stages were seen in the processed noise data. It was found that the predictions were in good agreement with the test results.

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.

Effects of slide-to-roll ratio and varying velocity on the lubrication performance of grease at low speed

2021 ◽  
pp. 135065012199336
Author(s):  
Yiming Han ◽  
Jing Wang ◽  
Xuyang Jin ◽  
Shanshan Wang ◽  
Rui Zhang
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Industrial Applications ◽  
Transient Effects ◽  
Disintegration Time ◽  
Low Speed ◽  
Existence Time ◽  
Pure Rolling ◽  
Lubrication Performance ◽  
Long Time

Under steady-state pure rolling conditions with low speed, the thickener fiber agglomerations can be maintained for a long time, generating a beneficial thicker film thickness. However, in industrial applications, motions with sliding or transient effects are very common for gears, rolling-element bearings or even chain drives, evaluation of the grease performance under such conditions is vital for determining the lubrication mechanism and designing new greases. In this project, optical interferometry experiments were carried out on a ball-disk test rig to study the disintegration time of the grease thickener agglomerations with the increase of the slide-to-roll ratio under steady-state and reciprocation motions. Under steady-state conditions, the thickener fiber agglomeration can exist for a while and the time becomes shorter with the increase of the slide-to-roll ratio above the critical speed. Below the critical speed, the thickener fiber can exist in the contact in the form of a quite thick film for a very long time under pure rolling conditions but that time is decreased with the increase of the slide-to-roll ratio. The introduction of the transient effect can further reduce the existence time of the thickener.

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.

Geomechanical Controls on Frac-Hits

2022 ◽  
Author(s):  
Dharmendra Kumar ◽  
Ahmad Ghassemi
Keyword(s):  
Pore Pressure ◽  
Fracture Propagation ◽  
Horizontal Wells ◽  
Operational Parameters ◽  
Modeling And Analysis ◽  
Matrix Deformation ◽  
In Situ Conditions ◽  
Fracture Fluid ◽  
Poroelastic Model ◽  
Element Method

Abstract The communication among the horizontal wells or "frac-hits" issue have been reported in several field observations. These observations show that the "infill" well fractures could have a tendency to propagate towards the "parent" well depending on reservoir in-situ conditions and operational parameters. Drilling the horizontal wells in a "staggered" layout with both horizontal and vertical offset could be a mitigation strategy to prevent the "frac-hits" issue. In this study, we present a detailed geomechanical modeling and analysis of the proposed solution. For numerical modeling, we used our state-of-the-art fully coupled poroelastic model "GeoFrac-3D" which is based on the boundary element method for the rock matrix deformation/fracture propagation and the finite element method for the fracture fluid flow. The "GeoFrac-3D" simulator fully couples pore pressure to stresses and allows for dynamic modeling of production/injection and fracture propagation. The simulation results demonstrate that production from a "parent’ well causes a non-uniform reduction of the reservoir pore pressure around the production fractures, resulting in an anisotropic decrease of the reservoir total stresses, which could affect fracture propagation from the "infill" wells. We examine the optimal orientation and position of the "infill" well based on the numerical analysis to reduce the "frac-hits" issue in the horizontal well refracturing. The posibility of "frac-hits" can be reduced by optimizing the direction and locations of the "infill" wells, as well as re-pressurizing the "parent" well. The results suggest that arranging the horizontal wells in a "staggered" or "wine rack" arrangement decreases direct well interference and could increase the drainage volume.

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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