Critical Speeds Resulting From Unbalance Excitation of Backward Whirl Modes

1995 ◽  
Author(s):  
Lyn M. Greenhill ◽  
Guillermo A. Cornejo
Keyword(s):  
Test Data ◽  
Driving Force ◽  
Critical Speed ◽  
Critical Speeds ◽  
Rotordynamic Coefficients ◽  
Jeffcott Rotor ◽  
Rotor Bearing ◽  
Backward Whirl ◽  
Bearing Design

Abstract Most rotordynamic analyses typically ignore the potential for critical speeds to be created by traversing a backward precessional whirl mode. While not commonly recognized, a backward mode can be excited using unbalance as the driving force. Based on the analysis of a Jeffcott rotor-bearing model, it was found that the condition for this response to occur is strongly dependent on stiffness asymmetry in the rotordynamic coefficients at the supports. To illustrate the application of this result, a rotordynamic analysis on actual hardware is presented, in which the unbalance excited backward mode resonance is calculated to occur. Test data is also given indicating the presence of the predicted critical speed. It is important to note that although the resonance is due to the backward mode, the precessional direction is forward. Several recommendations are offered with respect to rotor-bearing design so that this unique critical speed situation may be avoided.

The Wing Foil: A Novel Compliant Radial Foil Bearing Design

2017 ◽  
Author(s):  
Erik E. Swanson ◽  
P. Shawn O’Meara
Keyword(s):  
Test Data ◽  
High Performance ◽  
State Of The Art ◽  
Design Features ◽  
Critical Speeds ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Support Element ◽  
Bearing Design ◽  
Multidimensional Array

To meet the challenging demands for high performance, affordable compliant foil bearings, a novel compliant support element has been developed. This recently patented, novel support element uses a multidimensional array of multiple, formed, cantilever “wing foil” tabs. The wing foil bearing has all the features required to achieve state of the art performance (Gen III for radial bearings). This paper describes two radial foil beings using the wing foil and the unique design features. Test data for a 31.75 mm diameter bearing operating in air and in steam up to 42 krpm are presented to demonstrate the performance of this bearing. It is shown to have low subsynchronous vibration and reasonable damping through rigid shaft critical speeds.

Dynamic Analysis of a Geared Rotor-Bearing System With Viscoelastic Supports Under the Bow Effect

2007 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
T. H. Young ◽  
W. C. Hsu
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Loss Factor ◽  
Critical Speed ◽  
Transmission Error ◽  
Steady State Response ◽  
Critical Speeds ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

This paper investigates the dynamic behaviors of a geared rotor-bearing system mounted on viscoelastic supports under considerations of the gear eccentricity, excitation of the gear’s transmission error and the residual shaft bow. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The coupling effect of lateral and torsional motions is considered in the system dynamic analysis. The investigated dynamic characteristics include system natural frequencies and steady-state response. The results show that the mass, the stiffness and the loss factor of the viscoelastic support will significantly affect system critical speeds and steady-state response. Larger loss factor and more rigid stiffness of the viscoelastic supports will suppress the systematic amplitude of resonance. Parameters, which include magnitude of the residual bow and phase angle, are also considered in the investigation of their effects on system critical speeds and steady-state response. Results show that they have tremendous influence on first critical speed when the geared system mounted on stiff viscoelastic supports. The transmission error of the gear mesh is assumed to be sinusoidal with tooth passing frequency and it will induce multiple low resonant frequencies in the system response. It is observed that the excited critical speed equals to the original critical speed divided by gear tooth number.

Turbomachinery Dual Rotor-Bearing System Analysis

2002 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Chih-Neng Hsu ◽  
Wes Jeng ◽  
Shun-Hsu Tu ◽  
Wei-Chen Li
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Critical Speed ◽  
System Analysis ◽  
Design Parameters ◽  
Critical Speeds ◽  
Rotor Design ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Bearing System

It is very common for aircraft engines to have dual rotor or even triple rotor designs. Due to the complexity of having multiple rotor design, the transfer matrix methods have used in the past to deal with multiple rotor-bearing systems. However, due to transfer matrix method’s assumptions, sometimes resulted in numerical stability problems or root-missing problems. The purpose of this paper is to develop a systematic theoretical analysis of the dynamic characteristics of turbomachinery dual rotor-bearing systems. This dual rotor-bearing system analysis will start with a finite element (FEM) rotor-bearing system dynamic model, then using different methods to verify the analysis results including critical speed map and bearing stiffness. In an inertia coordinate system, a general model of continuous dual rotor-bearing systems is established based on a lagrangian formulation. Gyroscopic moment, rotary inertia, bending and shear deformations have been included in the model. From a point of view of the systematic approach, a solution of the finite element method is used to calculate the critical speeds by several different methods, which in turn can help to verify this dual rotor-bearing system approach. The effects of the speed ratio of dual rotors on the critical speed will be studied, which in turn can be used as one of the dual rotor design parameters. Also, both critical speeds are in effect functions of dual rotor speeds. Finally, the bearing stiffness between high speed and low speed shafts not only affect the critical speeds of the dual rotor system, but also affect the mode shapes of the system. Therefore, the bearing stiffness in between is of even greater importance in turbomachinery dual rotor or multiple rotor design.

Rotordynamic Analysis of a Rotor-Disk System Including a Synchronously Reduced Modal Truncation Method

2013 ◽  
Author(s):  
Timothy Dimond ◽  
Jawad Chaudhry ◽  
Matthew Wagner ◽  
Feng He ◽  
Jianming Cao ◽  
...  
Keyword(s):  
Critical Speed ◽  
Mode Shapes ◽  
Complete Analysis ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Euler Beam ◽  
Critical Speeds ◽  
Unbalance Response ◽  
Rotor Bearing ◽  
Modal Truncation

There are many published works on rotordynamics which detail the types of analyses that are carried out: critical speeds, stability assessment, and forced response. The purpose of this paper is to present a more complete analysis of an existing, academic rotor/bearing model, taken from a textbook, more like it would be carried out in an industrial setting. The advantage is that all parameters of the rotor model are well known so that there are minimal uncertainties. However, some published papers on rotordynamics, as discussed in this work, present an incomplete analysis. For example, they may report the calculated critical speeds but leave out the critical speed plot and mode shapes in favor of the Campbell diagram. They may model a Bernoulli Euler beam model of the shaft and neglect the additional terms in the Timoshenko beam model. These papers may show some unbalance response plots for one disk in the model but not report on the amplification factor. This paper gives a much more complete rotordynamics analysis of this common rotor/bearing model than other works. The full undamped rotor analysis is presented, including critical speeds, critical speed map, and undamped mode shapes. The stability analysis presents the full set of eigenvalues including both forward and backward modes as well as the complex mode shapes. The differences between the Bernoulli Euler beam model and the full Timoshenko beam model are shown for this rotor. Full unbalance response plots, in the horizontal and vertical directions, are presented as well as the response along the semi-major axis. The unbalance response plots have calculated amplitudes, phase angles and amplification factors. In addition to the standard rotordynamic analyses, a synchronously reduced modal truncation method is presented. This method is better suited to automation, when compared to most truncation methods that require significant intervention by the analyst. The maximum error was on the order of 0.01%. It is hoped that future publications will present the more complete analysis shown for this rotor/bearing system.

The Wing Foil: A Novel Compliant Radial Foil Bearing Design

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Erik E. Swanson ◽  
P. Shawn O'Meara
Keyword(s):  
Test Data ◽  
High Performance ◽  
State Of The Art ◽  
Design Features ◽  
Critical Speeds ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Support Element ◽  
Bearing Design ◽  
Multidimensional Array

To meet the challenging demands for high performance, affordable compliant foil bearings (CFBs), a novel compliant support element has been developed. This recently patented, novel support element uses a multidimensional array of multiple, formed, cantilever “wing foil” tabs. The wing foil bearing has all the features required to achieve state-of-the-art performance (Gen III for radial bearings). This paper describes two radial foil bearings using the wing foil and the unique design features. Test data for a 31.75 mm diameter bearing operating in air and in steam up to 42 krpm are presented to demonstrate the performance of this bearing. It is shown to have low subsynchronous vibration and reasonable damping through rigid shaft critical speeds.

Backward Whirl and Its Suppression of a Squeeze Film Damper Mounted Rotor/Casing System in Passage through Critical Speed with Rubs

2004 ◽  
Vol 10 (4) ◽  
pp. 561-573 ◽  
Author(s):  
Qian Ding
Keyword(s):  
Critical Speed ◽  
Angular Acceleration ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Internal Support ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Backward Whirl ◽  
Pass Through ◽  
Second Peak

In this paper we consider a flexible Jeffcott rotor mounted at the ends by identical squeeze film dampers (SFDs). The rotative speed is supposed to increase at a constant angular acceleration. There can be one-peak and two-peak solutions for different values of SFD parameters during passage through the critical speed. Calculation shows that the rotor cannot pass through the critical speed due to the occurrence of diverging backward whirl in passage of the first or second peak, if the level of acceleration is lower than the critical ones. A flexible internal support, which can be activated or deactivated at a certain position along the rotor to change the stiffness of the system to suppress large vibration, is then applied to avoid the occurrence of backward whirl. The method is found to be effective if applied in a suitable way

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.

A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

2012 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire
Keyword(s):  
System Identification ◽  
Measurement Uncertainty ◽  
Excitation Frequency ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Adjoint Systems ◽  
Dynamic Coefficients ◽  
Backward Whirl ◽  
Identification Technique ◽  
Damped Systems

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

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.

Measurements of Rotordynamic Coefficients of Hybrid Bearings With (a) a Plugged Orifice, and (b) a Worn Land Surface

2002 ◽  
Vol 124 (2) ◽  
pp. 363-368 ◽  
Author(s):  
F. Laurant ◽  
D. W. Childs
Keyword(s):  
Test Data ◽  
Land Surface ◽  
Rocket Engine ◽  
Liquid Rocket Engine ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Hybrid Bearing ◽  
Liquid Rocket

Test results are presented for the rotordynamic coefficients of a hybrid bearing that is representative of bearings for liquid-rocket-engine turbopump applications. The bearing is tested in the following two degraded conditions: (a) one of five orifices plugged, and (b) a locally enlarged clearance to simulate a worn condition. Test data are presented at 24,600 rpm, with supply pressures of 4.0, 5.5, and 7.0 MPa, and eccentricity ratios from 0.1 to 0.5 in 0.1 increments. Overall, the results suggest that neither a single plugged orifice nor significant wear on the bearing land will “disable” a well-designed hybrid bearing. These results do not speak to multiple plugged orifices and are not an endorsement for operations without filters to prevent plugging orifices.

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