Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part I: The Rotor Mass—Elastic Model

1987 ◽  
Vol 109 (1) ◽  
pp. 1-7 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Research Program ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Computer Programs ◽  
Elastic Model ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Improve Accuracy ◽  
Speed Computer ◽  
Rotor Mass

This is the first part (Part I) of two papers describing results of a research program directed at verifying computer programs used to calculate critical speeds of turbomachinery. This research program was undertaken since questions existed about the accuracy of calculations for the second and higher critical speeds. Part I describes improvements in computer programs and data modeling that resulted from comparing measured and calculated “free-free” natural frequencies of several shafts and rotors. Program modifications to improve accuracy include consideration of the effect of disk/shaft attachment stiffness, revised treatment of the end masses, and an improved convergence. Modifications resulting from the study are applicable to many other damped and undamped critical speed computer programs.

Dynamics of a Three Level Rotor System Using Solid Elements

2003 ◽  
Author(s):  
J. S. Rao ◽  
R. Sreenivas
Keyword(s):  
Natural Frequencies ◽  
Rotor System ◽  
Support Structures ◽  
Campbell Diagram ◽  
Critical Speeds ◽  
Spin Speed ◽  
Damping Coefficients ◽  
Stiffness And Damping

This paper discusses the interaction of support structures on the dynamics of a dual rotor system. The system considered is a dual rotor, supported on flexible bearings, which are in turn mounted in a flexible casing. ANSYS® is used for modeling and meshing the dual rotors and the casing. The rotors are modeled using solid elements. The bearings are simulated as springs, wherein the direct and cross coupled stiffness and damping coefficients are applied. The casing is also modeled and meshed in ANSYS® using solid elements. Different spin speeds are applied to the dual rotor system. The casing is also rotated at a zero spin speed. The Stress stiffening and spin softening options are also set on for the dual rotor system. The system natural frequencies are obtained for different spin speeds and the Campbell diagram of the system is plotted. The critical speeds due to per revolution excitations are then extracted from the Campbell diagram.

Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings

1974 ◽  
Vol 96 (2) ◽  
pp. 509-517 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Dynamic Properties ◽  
Fluid Film ◽  
Internal Damping ◽  
Flexible Rotor ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Fluid Film Bearings ◽  
Multistage Compressor ◽  
Stiffness And Damping ◽  
Rotor Model

A method is described for calculating the threshold speed of instability and the damped critical speeds of a general flexible rotor in fluid-film journal bearings. It is analogous to the Myklestad-Prohl method for calculating critical speeds and is readily programmed for numerical computation. The rotor model can simulate any practical shaft geometry and support configuration. The bearings are represented by their linearized dynamic properties, also known as the stiffness and damping coefficients of the bearing, and the calculation includes hysteretic internal damping in the shaft and destabilizing aerodynamic forces. To demonstrate the application of the method, results are shown for an industrial, multistage compressor.

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

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Analysis Behavior of a Rig Shafting Vibration Set Changes Bearing Parameters

2013 ◽  
Vol 437 ◽  
pp. 98-101 ◽  
Author(s):  
Van Thanh Ngo ◽  
Dan Mei Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Lateral Vibration ◽  
Eigenvalues And Eigenvectors ◽  
Fem Model ◽  
Critical Speeds ◽  
Bearing Stiffness

Frequently, in the design of machines, some of parameters that directly affect the rotordynamics of the machines are not accurately known. In particular, bearing stiffness support is one such parameter. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using finite element method (FEM). The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes. Then critical speeds and mode shapes are analyzed by set bearing stiffness changes. The model permitted to identify the critical speeds and bearings that have an important influence on the vibration behavior.

A Design Technique for a Magnetic Bearing-Rotor in a Turbo Blower Considering Critical Speeds

2012 ◽  
Vol 569 ◽  
pp. 564-567
Author(s):  
Hoon Hyung Jung ◽  
Seung Hee Kang ◽  
Bang Hyun Cho ◽  
Chae Sil Kim
Keyword(s):  
Element Model ◽  
Magnetic Bearing ◽  
Design Technique ◽  
Loop Control ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Turbo Blower ◽  
Bearing Stiffness ◽  
Control Forces ◽  
Stiffness And Damping

This paper introduces a rotor design technique for a turbo blower supported by magnetic bearings that considers the critical speeds of the rotor. An important factor for rotor critical speeds is the stiffness of its bearings. The magnetic bearing acts as a negative spring, called the position stiffness prior to operation, and rotor systems are initially unstable until the stiffness (current stiffness) and damping in the active control rotating system are determined using closed loop control forces. This paper describes a finite element model for the rotor, derives the stiffness equations for the magnetic bearing, and defines the total magnetic bearing stiffness including the position stiffness and current stiffness. Finally, the magnetic bearing stiffness that avoids the rotor critical speeds is chosen.

scholarly journals Hybrid Gas Bearings With Controlled Supply Pressure to Eliminate Rotor Vibrations While Crossing System Critical Speeds

2008 ◽  
Author(s):  
Luis San Andre´s ◽  
Keun Ryu
Keyword(s):  
Critical Speed ◽  
Pressure Control ◽  
Sudden Increase ◽  
Critical Speeds ◽  
Gas Bearings ◽  
Supply Pressure ◽  
Simple Strategy ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Bearing Force

Micro-turbomachinery (MTM) implements gas bearings in compact units of enhanced mechanical reliability. Gas bearings, however, have little damping and wear quickly during transient rub events. Flexure pivot tilting pad bearings offer little or no cross-coupled stiffnesses with enhanced rotordynamic stability; and when modified for hydrostatic pressurization, demonstrate superior rotordynamic performance over other bearing types. External pressurization stiffens gas bearings thus increasing system critical speeds, albeit reducing system damping. Most importantly, measurements demonstrate that external pressurization is not needed for rotor super critical speed operation. In practice, the supply pressure could be shut off at high rotor speeds with substantial gains in efficiency. The paper introduces a simple strategy, employing an inexpensive air pressure regulator to control the supply pressure into the hybrid bearings, to reduce or even eliminate high amplitudes of rotor motion while crossing the system critical speeds. Rotor speed coast-down tests with the pressure controller demonstrate the effectiveness of the proposed approach. A simple on-off supply pressure control, i.e. a sudden increase in pressure while approaching a critical speed, is the best since it changes abruptly the bearing stiffness coefficients and moves the system critical speed to a higher speed. A rotordynamic analysis integrating predicted bearing force coefficients forwards critical speeds in agreement with the test results. Predicted rotor responses for the controlled supply conditions show an excellent correlation with measured data. The experiments validate the predictive tools and demonstrate the controllable rotordynamic characteristics of flexure pivot hybrid gas bearings.

Measurement of Static and Dynamic Properties of a Tilting Pad Bearing and Comparison With Theory

1993 ◽  
Author(s):  
Thomas Bonner ◽  
John H. Vohr
Keyword(s):  
Dynamic Properties ◽  
Lubrication Theory ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Phase Angles ◽  
Good Agreement

Abstract Measurements were made of the static and dynamic properties of a seven inch diameter, four-pad, tilting pad bearing with both centrally pivoted and 60% offset pads. Data was recorded at 1500, 1800 and 3000 RPM and covered a range of Sommerfeld numbers from .055 to .625. Dynamic properties were measured by applying unbalance weights of various magnitudes to the rotor and measuring the synchronous response amplitudes and phase angles. Good agreement was obtained between measured properties and those predicted using linearized stiffness and damping coefficients obtained from isoviscous lubrication theory.

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