Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

2021 ◽  
Author(s):  
Elia Iseli ◽  
Jürg Schiffmann
Keyword(s):  
Load Capacity ◽  
Mode Shapes ◽  
Response Analysis ◽  
Full Time ◽  
Fluid Equation ◽  
Number Range ◽  
Force Coefficients ◽  
Unbalance Response ◽  
Bearing Force ◽  
Gas Bearing

Abstract The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The transient method consists of a state-space representation, which couples the equations of motion with the compressible thin film fluid equation. The linearized method is based on the perturbation analysis around a given eccentric shaft position ε, allowing to compute the static and linear dynamic bearing force coefficients at different excitation frequencies. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Λ = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with < 6 % deviation for amplitudes up to ε < 0.5 within the complete compressibility number range.

Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

2021 ◽  
Author(s):  
Elia Iseli ◽  
Jurg Schiffmann
Keyword(s):  
Load Capacity ◽  
Critical Mass ◽  
Mode Shapes ◽  
Response Analysis ◽  
Full Time ◽  
Number Range ◽  
Force Coefficients ◽  
Unbalance Response ◽  
Bearing Force ◽  
Gas Bearing

Abstract The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Lambda = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with <6% deviation for amplitudes up to e < 0.5 within the complete compressibility number range.

Experimental Identification of Dynamic Force Coefficients for a 110 mm Compliantly Damped Hybrid Gas Bearing

2014 ◽  
Author(s):  
Adolfo Delgado
Keyword(s):  
Load Capacity ◽  
Excitation Frequency ◽  
Dynamic Test ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Test Parameters ◽  
Gas Bearing

Compliant hybrid gas bearings combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate that the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

Measurements of Static and Dynamic Load Performance of a 102 mm Carbon-Graphite Porous Surface Tilting-Pad Gas Journal Bearing

2021 ◽  
Author(s):  
Luis San Andrés ◽  
Rachel Bolen ◽  
Jing Yang ◽  
Ryan McGowan
Keyword(s):  
Dynamic Load ◽  
Load Capacity ◽  
Stable Operation ◽  
Specific Load ◽  
Force Coefficients ◽  
Supply Pressure ◽  
Air Supply ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Gas Bearing

Abstract Aerostatic journal bearings with porous tilting pads enable shaft support with minute drag power losses. To date archival information on the static and dynamic load performance of this bearing type is scant. Thus, the paper presents measurements conducted with an air lubricated bearing with diameter d = 102 mm and comprising four tilting pads made of porous carbon-graphite, each with length L = 76 mm. Two nested Belleville washers resting on spherical pivots support each pad. At ambient temperature of ∼ 21°C, as the air supply pressure into the bearing pads increases, so does the bearing aerostatic specific load (F/(L·d)) that reaches 58% of the pressure difference, supply minus ambient. With an air supply pressure of 7.8 bar(a), the test bearing static stiffness KS = 13.1 MN/m, is independent of both shaft speed and static load. KS is just 63% of the washers’ stiffness KP = 20.6 MN/m (during loading). While operating with shaft speeds equal to 6 krpm and 9 krpm (150 Hz) and under specific loads to 115 kPa and 101 kPa respectively, dynamic load experiments with excitation frequencies up to 342 Hz show the test bearing supplied with air at 7.8 bar(a) has frequency independent stiffness (K) and damping (C) coefficients. For rotor speeds equaling 0, 6 and 9 krpm, the bearing direct stiffnesses KXX ∼ KYY range from 13.6 MN/m to 32.7 MN/m as the specific load increases from 0 kPa to 115 kPa. The direct damping coefficients CXX ∼ CYY are as large as 5.8 kN·s/m, though having a large experimental uncertainty. Bearing cross-coupled force coefficients are insignificant. The test porous gas bearing reached its intended load capacity, demonstrated a dynamically stable operation and produced force coefficients mainly affected by the pads’ pivot supports and the magnitude of air supply pressurization.

Experimental Identification of Dynamic Force Coefficients for a 110 MM Compliantly Damped Hybrid Gas Bearing

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Adolfo Delgado
Keyword(s):  
Load Capacity ◽  
Excitation Frequency ◽  
Dynamic Test ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Test Parameters ◽  
Gas Bearing

Compliant hybrid gas bearings (HGBs) combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

Identification of Bearing Force Coefficients in Flexible Rotors: Extensions to a Field Method

2005 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar De Santiago
Keyword(s):  
Field Method ◽  
Mode Shapes ◽  
Flexible Rotor ◽  
Identification Procedure ◽  
Force Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Support Force ◽  
Order Of Magnitude ◽  
Bearing Force

Rotor-bearing system characteristics, such as mode shapes and their associated natural frequencies and damping ratios are essential to diagnose and correct vibration problems during system operation. Of the above characteristics, reliable identification of fluid film bearing force parameters, i.e. stiffness and damping coefficients, is one of the most difficult to achieve, in particular during field operation. Results of an enhanced method to estimate support force coefficients in flexible rotor-bearing systems based on imbalance response measurements obtained near the bearing locations are presented herein. The procedure can be conducted on site with minimal instrumentation. A test flexible rotor mounted on two-lobe hydrodynamic bearings is used to validate the identification procedure. Imbalance response measurements for various imbalance magnitudes are obtained near the bearing locations and also at rotor mid-span. At shaft speeds around the bending critical speed, the displacements at rotor mid span are an order of magnitude larger than the shaft displacements at the bearings. The identification procedure renders reliable bearing force coefficients for shaft speeds between 1 krpm and 4 krpm. The sensitivity of the method and derived parameters to noise in the measurements is also quantified.

Foil Gas Bearing With Compression Springs: Analyses and Experiments

2007 ◽  
Vol 129 (3) ◽  
pp. 628-639 ◽  
Author(s):  
Ju-ho Song ◽  
Daejong Kim
Keyword(s):  
Loss Factor ◽  
Load Capacity ◽  
Underlying Structure ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Different Types ◽  
Structural Loss ◽  
Compression Springs ◽  
Gas Bearing

A new foil gas bearing with spring bumps was constructed, analyzed, and tested. The new foil gas bearing uses a series of compression springs as compliant underlying structures instead of corrugated bump foils. Experiments on the stiffness of the spring bumps show an excellent agreement with an analytical model developed for the spring bumps. Load capacity, structural stiffness, and equivalent viscous damping (and structural loss factor) were measured to demonstrate the feasibility of the new foil bearing. Orbit and coast-down simulations using the calculated stiffness and measured structural loss factor indicate that the damping of underlying structure can suppress the maximum peak at the critical speed very effectively but not the onset of hydrodynamic rotor-bearing instability. However, the damping plays an important role in suppressing the subsynchronous vibrations under limit cycles. The observation is believed to be true with any air foil bearings with different types of elastic foundations.

scholarly journals Unbalance Response Prediction for Rotors on Ball Bearings Using Speed- and Load-Dependent Nonlinear Bearing Stiffness

2005 ◽  
Vol 2005 (1) ◽  
pp. 53-59 ◽  
Author(s):  
David P. Fleming ◽  
J. V. Poplawski
Keyword(s):  
Response Prediction ◽  
Rolling Element Bearing ◽  
Response Analysis ◽  
Ball Bearings ◽  
Moderate Amount ◽  
Constant Stiffness ◽  
Unbalance Response ◽  
Rolling Element ◽  
Bearing Stiffness ◽  
Element Bearing

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus, an accurate rotordynamic analysis requires that bearing forces corresponding to the actual bearing deflection be utilized. For this work, bearing forces were calculated by COBRA-AHS, a recently developed rolling-element bearing analysis code. Bearing stiffness was found to be a strong function of bearing deflection, with higher deflection producing markedly higher stiffness. Curves fitted to the bearing data for a range of speeds and loads were supplied to a flexible rotor unbalance response analysis. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Moreover, the increase in stiffness as critical speeds were approached caused a large increase in rotor and bearing vibration amplitude over part of the speed range compared to the case of constant-stiffness bearings. Regions of bistable operation were possible, in which the amplitude at a given speed was much larger during rotor acceleration than during deceleration. A moderate amount of damping will eliminate the bistable region, but this damping is not inherent in ball bearings.

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