Limiting Stiffness and Damping Coefficients of Foil Bearing

2005 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Necessary Conditions ◽  
Load Capacity ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Infinitesimal Perturbation ◽  
Stiffness And Damping ◽  
Limiting Values ◽  
Gas Journal Bearing

The limiting values of load capacity, stiffness and damping coefficients for a foil bearing are presented. The necessary conditions for high bearing numbers (journal operating at high speed) are obtained by simplifying the compressible Reynolds equation. Linearized stiffness and damping coefficients are obtained using infinitesimal perturbation method. Results of load capacity, stiffness and damping coefficients, for foil bearing are compared with those obtained for a rigid gas journal bearing. The limiting values of dynamic characteristics for a foil bearing are constant for all eccentricity ratios.

Impact of Bearing Clearance on Measured Stiffness and Damping Coefficients and Thermal Performance of a High-Stiffness Generation 3 Foil Journal Bearing

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Jason C. Wilkes ◽  
Jonathan Wade ◽  
Aaron Rimpel ◽  
Jeff Moore ◽  
Erik Swanson ◽  
...  
Keyword(s):  
Thermal Performance ◽  
High Speed ◽  
Load Capacity ◽  
Dynamic Test ◽  
Damping Coefficients ◽  
High Stiffness ◽  
Bearing Clearance ◽  
Spring Element ◽  
Foil Bearing ◽  
Stiffness And Damping

High-speed foil bearings are currently used in increasingly demanding, high performance applications. The application under consideration is a 120 krpm natural gas turboexpander-compressor, which requires 38 mm (1.5 in.) foil journal bearings with high stiffness and load capacity to help enhance rotordynamic stability. This paper describes the development of the foil bearing for this application and includes measured stiffness and damping coefficients recorded on a high-speed dynamic bearing test rig. The dynamic test data were taken for several different foil bearing configurations with varying spring-element foil thicknesses, number of spring-element foils, and bearing shim thickness. All three parameters have a direct impact on bearing clearance. The influence of these different parameters on measured stiffness and damping coefficients and thermal performance of the bearings are presented and discussed.

Impact of Bearing Clearance on Measured Stiffness and Damping Coefficients and Thermal Performance of a High-Stiffness Generation 3 Foil Journal Bearing

2016 ◽  
Author(s):  
Jason C. Wilkes ◽  
Jonathan Wade ◽  
Aaron Rimpel ◽  
Jeff Moore ◽  
Erik Swanson ◽  
...  
Keyword(s):  
Thermal Performance ◽  
High Speed ◽  
Load Capacity ◽  
Dynamic Test ◽  
Damping Coefficients ◽  
High Stiffness ◽  
Bearing Clearance ◽  
Spring Element ◽  
Foil Bearing ◽  
Stiffness And Damping

High speed foil bearings are currently used in increasingly demanding, high performance applications. The application under consideration is a 120 krpm natural gas turboexpander-compressor, which requires 38 mm (1.5 in.) foil journal bearings with high stiffness and load capacity to help enhance rotordynamic stability. This paper describes the development of the foil bearing for this application and includes measured stiffness and damping coefficients recorded on a high-speed dynamic bearing test rig. The dynamic test data were taken for several different foil bearing configurations with varying spring-element foil thicknesses, number of spring-element foils, and bearing shim thickness. All three parameters have a direct impact on bearing clearance. The influence of these different parameters on measured stiffness and damping coefficients and thermal performance of the bearings are presented and discussed.

Effect of Circumferential Location of Radial Injection on Rotordynamic Performance of Hybrid Air Foil Bearings

2018 ◽  
Author(s):  
Behzad Zamanian Yazdi ◽  
Daejong Kim
Keyword(s):  
Time Domain ◽  
High Speed ◽  
Substantial Improvement ◽  
Reliable Operation ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Radial Injection ◽  
Parametric Studies ◽  
Stiffness And Damping

Air foil bearings (AFBs) are introduced as promising bearings for oil-free turbomachinery applications. AFBs provide reliable operation at high speed and high temperature with negligible power loss. Hybrid Air Foil Bearing (HAFB) technology utilizes the radial injection of externally pressurized air into the traditional hydrodynamic AFB’s film thickness through orifices attached to the top foil. Previous studies have reported enhancement in the rotordynamic stability of HAFBs compared to traditional hydrodynamic AFBs. HAFBs have several orifices distributed in the circumferential direction. In this study, the effect of the circumferential location of radial injection on the rotordynamic performance of the rotor-HAFB is studied. Analytical and experimental evaluations of the rotordynamic performance of a rotor supported by two single-pad HAFBs are presented. Parametric studies are conducted using three sets of single-pad HAFBs. The circumferential locations of orifices are different for each set. The presented simulation analyses consist of time-domain orbit simulation and frequency-domain modal analysis. Imbalance responses of rotor-HAFB were measured with various orifice locations and the results agree well with predictions. Comparison of the rotordynamic performance of HAFBs with different orifice configurations demonstrate substantial improvement in rotordynamic stability as well as enhancement in the stiffness and damping coefficients of HAFBs by choosing the best circumferential location for radial injection to control rotor eccentricity and attitude angle.

Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings

2021 ◽  
pp. 135065012110270
Author(s):  
Bo Xu ◽  
Hun Guo ◽  
Xiaofeng Wu ◽  
Yafeng He ◽  
Xiangzhi Wang ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Load Capacity ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Inertia Effect ◽  
Static And Dynamic Characteristics ◽  
Damping Coefficients ◽  
Stiffness And Damping

The purpose of this paper is to analyze the influence of turbulent, inertia, and misaligned effects on the static and dynamic characteristics and stability of high-speed water-lubricated hydrodynamic journal bearings. Based on the Navier–Stokes equation, the mixing-length theory, and the essential assumption that the velocity profile is not strongly affected by inertia force, the fluid lubrication model with turbulent, inertia, and misaligned effects is established, and then the stability analysis of bearings is carried out based on the equation of motion with four degrees of freedom. The model is solved by the finite difference method and the numerical results are compared under different operating conditions. The results show that the turbulent effect greatly increases the load capacity, power consumption, stiffness and damping coefficients, and stability of bearings, and the inertia effect significantly increases the volume flow rate of bearings, and the misaligned effect increases the load capacity, stiffness and damping coefficients, and stability of bearings. In high rotary speed and moderate eccentricity ratios, the influence of the inertia effect on the load capacity, stiffness coefficients, and stability cannot be neglected.

Effect of Circumferential Location of Radial Injection on Rotordynamic Performance of Hybrid Air Foil Bearings

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Behzad Zamanian Yazdi ◽  
Daejong Kim
Keyword(s):  
Time Domain ◽  
High Speed ◽  
Substantial Improvement ◽  
Reliable Operation ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Radial Injection ◽  
Parametric Studies ◽  
Stiffness And Damping

Air foil bearings (AFBs) are introduced as promising bearings for oil-free turbomachinery applications. AFBs provide reliable operation at high speed and high temperature with negligible power loss. Hybrid air foil bearing (HAFB) technology utilizes the radial injection of externally pressurized air into the traditional hydrodynamic AFB's film thickness through orifices attached to the top foil. Previous studies have reported enhancement in the rotordynamic stability of HAFBs compared to traditional hydrodynamic AFBs. HAFBs have several orifices distributed in the circumferential direction. In this study, the effect of the circumferential location of radial injection on the rotordynamic performance of the rotor-HAFB is studied. Analytical and experimental evaluations of the rotordynamic performance of a rotor supported by two single-pad HAFBs are presented. Parametric studies are conducted using three sets of single-pad HAFBs. The circumferential locations of orifices are different for each set. The presented simulation analyses consist of time-domain orbit simulation and frequency-domain modal analysis. Imbalance responses of rotor-HAFB were measured with various orifice locations and the results agree well with predictions. Comparison of the rotordynamic performance of HAFBs with different orifice configurations demonstrates substantial improvement in rotordynamic stability as well as enhancement in the stiffness and damping coefficients of HAFBs by choosing the best circumferential location for radial injection to control rotor eccentricity and attitude angle.

Calculation of Stiffness and Damping Coefficients for Elastically Supported Gas Foil Bearings

1993 ◽  
Vol 115 (1) ◽  
pp. 20-27 ◽  
Author(s):  
J.-P. Peng ◽  
M. Carpino
Keyword(s):  
Reynolds Equation ◽  
Structural Model ◽  
Structural Equations ◽  
Perfect Gas ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Stiffness And Damping ◽  
Elastically Supported

The stiffness and damping coefficients of an elastically supported gas foil bearing are calculated. A perfect gas is used as the lubricant, and its behavior is described by the Reynolds equation. The structural model consists only of an elastic foundation. The fluid equations and the structural equations are coupled. A perturbation method is used to obtain the linearized dynamic coefficient equations. A finite difference formulation has been developed to solve for the four stiffness and the four damping coefficients. The effect of the bearing compliance on the dynamic coefficients is discussed in this paper.

On the Dynamics of Elastohydrodynamic Mixed Lubricated Ball Bearings. Part I: Formulation of Stiffness and Damping Coefficients

2005 ◽  
Vol 219 (6) ◽  
pp. 411-421 ◽  
Author(s):  
M Sarangi ◽  
B. C. Majumdar ◽  
A. S. Sekhar
Keyword(s):  
Surface Roughness ◽  
Steady State ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Design Parameters ◽  
Asperity Contact ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Stiffness And Damping

The problems of stiffness and damping characteristics of isothermal elastohydrodynamic mixed lubricated point contact are evaluated numerically considering surface roughness effect including asperity contact load. A set of equations under steady-state and dynamic conditions is derived from the classical Reynolds equation, using linear perturbation method. The elasticity equation and steady-state Reynolds equation are solved simultaneously for finding the steady-state pressure distribution, using finite difference method. Then, the set of perturbed equations is solved for the dynamic pressure distribution in the contact. A Gaussian surface roughness is adopted to model both surface roughness and mixed lubrication. Total load capacity of the contact is calculated from the lubricant film pressure and contact pressure distribution. Results are compared with those of smooth isothermal cases. The stiffness and damping coefficients of the contact are determined using the dynamic pressures. The asperity contact stiffness is calculated separately. Effect of various design parameters on stiffness and damping characteristics of a ball bearing is investigated.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

2006 ◽  
Vol 129 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Luis San Andrés ◽  
Dario Rubio ◽  
Tae Ho Kim
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Load Capacity ◽  
Test System ◽  
Foil Bearings ◽  
Rotor Imbalance ◽  
Synchronous Motion ◽  
Damping Characteristics ◽  
Rotor Surface ◽  
Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

Rotordynamics Performance of Hybrid Foil Bearing Under Forced Vibration Input

2017 ◽  
Author(s):  
Daejong Kim ◽  
Brian Nicholson ◽  
Lewis Rosado ◽  
Garry Givan
Keyword(s):  
Impulse Response ◽  
High Speed ◽  
Load Capacity ◽  
Supply System ◽  
Forced Response ◽  
Experimental Results ◽  
Lateral Acceleration ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Gas Supply

Foil bearings are one type of hydrodynamic air/gas bearings but with a compliant bearing surface supported by structural material that provides stiffness and damping to the bearing. The hybrid foil bearing (HFB) in this paper is a combination of a traditional hydrodynamic foil bearing with externally-pressurized air/gas supply system to enhance load capacity during the start and to improve thermal stability of the bearing. The HFB is more suitable for relatively large and heavy rotors where rotor weight is comparable to the load capacity of the bearing at full speed and extra air/gas supply system is not a major added cost. With 4,448N∼22,240N thrust class turbine aircraft engines in mind, the test rotor is supported by HFB in one end and duplex rolling element bearings in the other end. This paper presents experimental work on HFB with diameter of 102mm performed at the US Air force Research Laboratory. Experimental works include: measurement of impulse response of the bearing to the external load corresponding to rotor’s lateral acceleration of 5.55g, forced response to external subsynchronous excitation, and high speed imbalance response. A non-linear rotordynamic simulation model was also applied to predict the impulse response and forced subsynchronous response. The simulation results agree well with experimental results. Based on the experimental results and subsequent simulations, an improved HFB design is also suggested for higher impulse load capability up to 10g and rotordynamics stability up to 30,000rpm under subsynchronous excitation.

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