Nowadays, there is a trend in the downsizing of rotating machinery accompanied by increasing rotational speed. Oil-free, high-speed rotating machinery supported by foil bearings (FBs) has emerged as an effective solution to address this trend. However, the application of FBs faces two significant challenges, namely the load capacity and stability. Along these lines, the current status of the FBs in industrial applications and academic research was summarized in this work. Various theoretical models of FBs are discussed, and the processing methods and test rigs used for FBs were illustrated. The structural improvements aimed at enhancing the load capacity and rotor stability were summarized and the active/intelligent FBs were introduced. The opportunities for future developments of FBs in the fields of theoretical analysis, design, control, etc. were also discussed.
AgrawalGL. Foil air/gas bearing technology—an overview. Turbo Expo: Power Land Sea Air1997; 78682: V001T04A006.
2.
LeeYKimTKimC, et al.Suppression of subsynchronous vibrations due to aerodynamic response to surge in a two-stage centrifugal compressor with air foil bearings. Tribol Trans2003; 46: 428–434.
3.
SwansonEHeshmatHShinJ. The role of high performance foil bearings in an advanced, oil-free, integral permanent magnet motor driven, high-speed turbo-compressor operating above the first bending critical speed. Turbo Expo: Power Land Sea Air2002; 36061: 1119–1125.
4.
ChenHMHowarthRGerenB, et al.Application of foil bearings to helium turbocompressor. In: Proceedings of the 30th turbomachinery symposium. Texas A&M University. Turbomachinery Laboratories, 2001.
5.
HeshmatHWaltonJFTomaszewskiMJ. Demonstration of a turbojet engine using an air foil bearing. Turbo Expo: Power Land Sea Air2005; 46997: 919–926.
6.
WaltonJFHeshmatHTomaszewskiMJ. Testing of a small turbocharger/turbojet sized simulator rotor supported on foil bearings. J Eng Gas Turbines Power2008; 130: 035001.
7.
HowardSA. Rotordynamics and design dethods of an oil-free turbocharger. Tribol Trans1999; 42: 174–179.
8.
KimTHLeeJKimCH, et al.Rotordynamic performance of an oil-free turbocharger supported on gas foil bearings: effects of an assembly radial clearance. Turbo Expo: Power Land Sea Air2010; 44014: 363–371.
9.
LeeY-BBum KwonSKimTH, et al.Feasibility study of an oil-free turbocharger supported on gas foil bearings via on-road tests of a two-liter class diesel vehicle. J Eng Gas Turbines Power2013; 135: 052701.
10.
HeshmatHTomaszewskiMJWaltonJF. Small gas turbine engine operating with high-temperature foil bearings. Turbo Expo: Power Land Sea Air2006; 42401: 387–393.
11.
ParkCChoiSHamS. Design and experiment of 400,000 rpm high speed rotor and bearings for 500 W class micro gas turbine generator. In: International conference on micro and nanotechnology for power generation and energy conversion applications (PowerMEMS), 2011, pp.1–4.
12.
VleugelsPWaumansTPeirsJ, et al.High-speed bearings for micro gas turbines: stability analysis of foil bearings. J Micromech Microeng2006; 16: S282–S289.
13.
HongD-KWooB-CLeeJ-Y, et al.Ultra high speed motor supported by air foil bearings for air blower cooling fuel cells. IEEE Trans Magn2012; 48: 871–874.
14.
KimTHLeeY-BKimTY, et al.Rotordynamic performance of an oil-free turbo blower focusing on load capacity of gas foil thrust bearings. J Eng Gas Turbines Power2012; 134: 643–650.
15.
ŁagodzinskiJMiazgaKMusiałI. Application of a compliant foil bearing for the thrust force estimation in the single stage radial blower. Open Eng2015; 5: 287–292.
16.
HwangSHMoonCGKimTH, et al.Rotordynamic performance measurements and predictions of a FCEV air compressor supported on gas foil bearings. Tribol Lubr2019; 35: 44–51.
17.
LiHGengHQiL, et al.Effects of wedge curvature on performances of foil thrust bearing and the profile design in compressor system. Proc Inst Mech Eng Part J: J Eng Tribol2021; 235: 1868–1878.
18.
ShiTHuangHPengX, et al.Experimental study on the static and dynamic performances of gas foil bearings for the centrifugal air compressor used in fuel cell vehicles. Int J Energy Res2022; 46: 4417–4433.
19.
WenguangLGuoshengF. Design and experimental study of cntrifugal compressor in fuel eell vehicle. Mechanics2021; 27: 52–61.
20.
HoytML. Journal-bearing. Google Patents. 1903.
21.
FlemingJHAndersonO. Spring neck-bearing for centrifugal machines. Google Patents. 1903.
22.
RagnarWO. Flexible bushing. Google Patents. 1921.
23.
BlockH. The Foil Bearings-A New Departure in Hydrodynamic Lubrication. Lubr Eng1953; 316: 9–20.
24.
SilverAWenbanJR. Foil bearing. Google Patents. 1979.
25.
JonesAM. Adjustable tension foil bearing. Google Patents. 1989.
26.
KanekoSMiyanoYWatanabeT. Static and dynamic characteristics of a micro gas turbine rotor supported by radial foil bearings. In: Proceedings of MEMS, 2005.
27.
FengKKanekoS. A numerical calculation model of multi wound foil bearing with the effect of foil local deformation. J Syst Des Dyn2007; 1: 648–659.
28.
FengKKanekoS. The numerical calculation of static performance of multi wound foil bearing and experimental validation. Int Joint Tribol Conf2007; 48108: 335–344.
29.
SongJHKimD. A new foil gas bearing with compression springs as compliant structure for microturbomachinery applications. Turbo Expo: Power Land Sea Air2006; 42401: 419–428.
30.
HouYLaiTMaB, et al.Experimental investigation on the multi-decked protuberant gas foil journal bearing. J Adv Mech Des Syst Manuf2013; 7: 791–799.
31.
DellaCorteCBrucknerRJ. Oil-free rotor support technologies for an optimized helicopter propulsion system. In: 18th ISABE conference (ISABE 2007), 2007.
32.
HeshmatH. Advancements in the performance of aerodynamic foil journal bearings: high speed and load capability. 1994. https://doi.org/10.1115/1.2927211
33.
HeshmatH. Operation of foil bearings beyond the bending critical mode. J Trib2000; 122: 192–198.
34.
LubellDDellaCorteCStanfordM. Test evolution and oil-free engine experience of a high temperature foil air bearing coating. Turbo Expo: Power Land Sea Air2006; 42401: 1245–1249.
35.
DellaCorteCZaldanaARRadilKC. A systems approach to the solid lubrication of foil air bearings for oil-free turbomachinery. J Trib2004; 126: 200–207.
36.
HowardSADellaCorteC.Gas foil bearings for space propulsion nuclear electric power generation. 2006.
37.
NalepaKPietkiewiczPŻywicaG. Development of the foil bearing technology. Tech Sci2009; 12: 229–240.
38.
GraySBhushanB. Support element for compliant hydrodynamic journal bearings. Google Patents. 1981.
39.
HeshmatH. High load capacity compliant foil hydrodynamic journal bearing. Google Patents. 1999.
40.
KangSGSavilleM. Hydrodynamic journal foil bearing system. Google Patents. 2005.
KuC-PRHeshmatH. Compliant foil bearing structural stiffness analysis: part I—theoretical model including strip and variable bump foil geometry. 1992. https://doi.org/10.1115/1.2920898
KuC-PRHeshmatH. Structural stiffness and Coulomb damping in compliant foil journal bearings: theoretical considerations. Tribol Trans1994; 37: 525–533.
46.
KuC-PRHeshmatH. Structural stiffness and Coulomb damping in compliant foil journal bearings: parametric studies. Tribol Trans1994; 37: 455–462.
47.
IordanoffISaidBBMezianneA, et al.Effect of internal friction in the dynamic behavior of aerodynamic foil bearings. Tribol Int2008; 41: 387–395.
48.
CarpinoMTalmageG. Prediction of rotor dynamic coefficients in gas lubricated foil journal bearings with corrugated sub-foils. Tribol Trans2006; 49: 400–409.
49.
San AndréSLKimTH. Improvements to the analysis of gas foil bearings: integration of top foil 1d and 2d structural models. Turbo Expo: Power Land Sea Air2007; 47942: 779–789.
50.
FengKGuoZ. Prediction of dynamic characteristics of a bump-type foil bearing structure with consideration of dynamic friction. Tribol Trans2014; 57: 230–341.
51.
ZywicaGBaginskiPBoguliczM, et al.Numerical identification of the dynamic characteristics of a nonlinear foil bearing structure: effect of the excitation force amplitude and the assembly preload. J Sound Vib2022; 520: 116663.
52.
IordanoffI. Analysis of an aerodynamic compliant foil thrust bearing: method for a rapid design. 1999. https://doi.org/10.1115/1.2834140
San AndrésLKimTH. Analysis of gas foil bearings integrating FE top foil models. Tribol Int2009; 42: 111–120.
55.
Le LezSArghirMFreneJ. A dynamic model for dissipative structures used in bump-type foil bearings. Tribol Trans2008; 52: 36–46.
56.
Le LezSBArghirMFreneJ. A new bump-type foil bearing structure analytical model. Turbo Expo: Power Land Sea Air2007; 129: 747–757.
57.
FengKKanekoS. Analytical model of bump-type foil bearings using a link-spring structure and a finite-element shell model. J Tribol2010; 132. https://doi.org/10.1115/1.4001169.
58.
De WitCCOlssonHAstromKJ, et al.A new model for control of systems with friction. IEEE Trans Autom Control1995; 40: 419–425.
59.
LeisterTBaumCSeemannW. On the importance of frictional energy dissipation in the prevention of undesirable self-excited vibrations in gas foil bearing rotor systems. Technische Mechanik-Eur J Eng Mech2017; 37: 280–290.
60.
LeisterTBaumCSeemannW. Computational analysis of foil air journal bearings using a runtime-efficient segmented foil model. J Fluids Eng2018; 140: 021115.
61.
LarsenJSSantosIF. On the nonlinear steady-state response of rigid rotors supported by air foil bearings—theory and experiments. J Sound Vib2015; 346: 284–297.
62.
NielsenBBSantosIF. Transient and steady state behaviour of elasto–aerodynamic air foil bearings, considering bump foil compliance and top foil inertia and flexibility: a numerical investigation. Proc Inst Mech Eng Part J: J Eng Tribol2017; 231: 1235–1253.
63.
ZhouRGuYRenG, et al.Modeling and stability characteristics of bump-type gas foil bearing rotor systems considering stick–slip friction. Int J Mech Sci2022; 219: 107091.
64.
LarsenJSSantosIFvon OsmanskiS. Stability of rigid rotors supported by air foil bearings: comparison of two fundamental approaches. J Sound Vib2016; 381: 179–191.
65.
von OsmanskiSLarsenJSSantosIF. Multi-domain stability and modal analysis applied to gas foil bearings: three approaches. J Sound Vib2020; 472: 115174.
66.
PapafragkosPGavalasIRaptopoulosI, et al.Optimizing energy dissipation in gas foil bearings to eliminate bifurcations of limit cycles in unbalanced rotor systems. Nonlinear Dyn2023; 111: 67–95.
67.
LeisterT. Dynamics of rotors on refrigerant-lubricated gas foil bearings. Karlsruhe, Germany: KIT Scientific Publishing, 2021. https://doi.org/10.5445/KSP/1000135139.
68.
SalehiMHeshmatH. On the fluid flow and thermal analysis of a compliant surface foil bearing and seal. Tribol Trans2000; 43: 318–324.
69.
SalehiMSwansonEHeshmatH. Thermal features of compliant foil bearings—theory and experiments. J Tribol2001; 123: 566–571.
70.
PengJ-PCarpinoM. Calculation of stiffness and damping coefficients for elastically supported gas foil bearings. J Tribol. 1993; 115: 20–27. https://doi.org/10.1115/1.2920982
71.
FengKKanekoS. Thermohydrodynamic study of multiwound foil bearing using lobatto point quadrature. J Tribol2009; 131: 021702.
72.
FengKKanekoS. A thermohydrodynamic sparse mesh model of bump-type foil bearings. J Eng Gas Turbines Power2013; 135: 022501.
73.
San AndrésLKimTH. Thermohydrodynamic analysis of bump type gas foil bearings: a model anchored to test data. J Eng Gas Turbines Power2010; 132: 951–961.
74.
San AndrésLRyuKKimTH. Thermal management and rotordynamic performance of a hot rotor-gas foil bearings system—part II: predictions versus test data. J Eng Gas Turbines Power2011; 133: 62502-1-62502-8.
75.
GraySHeshmatHBhushanB. Technology progress on compliant foil air bearing systems for commercial applications. BHRA Fluid Engng1981: 69–97.
76.
DellaCorteCRadilKCBrucknerRJ, et al.Design, fabrication, and performance of open source generation I and II compliant hydrodynamic gas foil bearings. Tribol Trans2008; 51: 254–264.
77.
KimDCrearyA. Liga-fabricated meso scale foil gas bearings for palm-sized microturbomachinery. Int Joint Tribol Conf2008; 43369: 159–161.
78.
KimDCrearyAChangSS, et al.Mesoscale foil gas bearings for palm-sized turbomachinery: design, manufacturing, and modeling. J Eng Gas Turbines Power2009; 131: 042502.
79.
DellacorteC. Tribological composition optimization of chromium-carbide-based solid lubricant coatings for foil gas bearings at temperatures to 650° C. Surf Coat Technol1988; 36: 87–97.
80.
DellaCorteCEdmondsBJ.Preliminary evaluation of PS300: a new self-lubricating high temperature composite coating for use to 800° C. 1995.
81.
DellaCorteC. The evaluation of a modified chrome oxide based high temperature solid lubricant coating for foil gas bearings. Tribol Trans2000; 43: 257–262.
82.
DellaCorteCLukaszewiczVValcoMJ, et al.Performance and durability of high temperature foil air bearings for oil-free turbomachinery. Tribol Trans2000; 43: 774–780.
83.
RadilKCDellaCorteC. The effect of journal roughness and foil coatings on the performance of heavily loaded foil air bearings. Tribol Trans2002; 45: 199–204.
84.
HeshmatHHryniewiczPWalton IiJF, et al.Low-friction wear-resistant coatings for high-temperature foil bearings. Tribol Int2005; 38: 1059–1075.
85.
JahanmirSHeshmatHHeshmatC, et al.Evaluation of DLC coatings for foil bearing applications. Int Joint Tribol Conf2007; 48108: 5–7.
86.
SalehiMHeshmatH. High temperature performance evaluation of a compliant foil seal. 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit2000; 3376. https://doi.org/10.2514/6.2000-3376.
87.
San AndrésLChirathadamTAKimT-H. Measurement of structural stiffness and damping coefficients in a metal mesh foil bearing. J Eng Gas Turbines Power2010; 132. https://doi.org/10.1115/1.3159379.
88.
FengKZhaoXGuoZ. Design and structural performance measurements of a novel multi-cantilever foil bearing. Proc Inst Mech Eng Part C: J Mech Eng Sci2015; 229: 1830–1838.
89.
DykasBDTellierDW. A foil thrust bearing test rig for evaluation of high temperature performance and durability. Army Research Lab Adelphi MD, 2008. https://doi.org/10.21236/ada480435
90.
San AndrésLChirathadamTARyuK, et al.Measurements of drag torque, lift-off journal speed, and temperature in a metal mesh foil bearing. J Eng Gas Turbines Power2010; 132. https://doi.org/10.1115/1.4000863.
91.
KimDLaTrayNHonavara-PrasadS. Experimental evaluation of 200 mm hybrid air foil bearing aimed for MW scale turbomachinery. Turbo Expo: Power Land Sea Air. Am Soc Mech Eng2020; 84218: V10AT25A021.
92.
LaTrayNKimD. Design of novel gas foil thrust bearings and test validation in a high-speed test rig. J Tribol2020; 142: 071803.
93.
WangYPKimD. Experimental identification of force coefficients of large hybrid air foil bearings. J Eng Gas Turbines Power2014; 136: 032503.
94.
San AndrésLAbraham ChirathadamT. A metal mesh foil bearing and a bump-type foil bearing: Comparison of performance for two similar size gas bearings. J Eng Gas Turbines Power2012; 134. https://doi.org/10.1115/1.4007061.
95.
RudloffLArghirMBonneauO, et al.Experimental analyses of a first generation foil bearing: startup torque and dynamic coefficients. J Eng Gas Turbines Power2011; 133. https://doi.org/10.1115/1.4002909.
96.
LarsenJSHansenAJSantosIF. Experimental and theoretical analysis of a rigid rotor supported by air foil bearings. Mech Ind2015; 16: 106.
97.
MooreJJLercheAAllisonT, et al.Development of a high speed gas bearing test rig to measure rotordynamic force coefficients. J Eng Gas Turbines Power2011; 133. https://doi.org/10.1115/1.4002865.
98.
San AndresLKimTH. Forced nonlinear response of gas foil bearing supported rotors. Tribol Int2008; 41: 704–715.
99.
HouYXiongLChenC. Experimental study of a new compliant foil air bearing with elastic support. Tribol Trans2004; 47: 308–311.
100.
LiuWZhaoXZhangT, et al.Investigation on the rotordynamic performance of hybrid bump-metal mesh foil bearings rotor system. Mech Syst Signal Process2021; 147: 107076.
101.
LichtL. Design, fabrication and testing of a foil gas-bearing test rig. Washington, USA: NASA, 1970.
102.
DellacorteC. A new foil air bearing test rig for use to 70° C and 70,000rpm. Tribol Trans1998; 41: 335–340.
103.
RussellTEIIIHeshmatCLockeD. Hybrid magnetic/foil bearing system for an oil-free thrust bearing test rig. Turbo Expo: Power for Land Sea Air. Am Soc Mech Eng. 2001; 78538: V004T04A17.
RyuKSan AndrésL. On the failure of a gas foil bearing: high temperature operation without cooling flow. J Eng Gas Turbines Power2013; 135: 112506.
106.
DellaCorteCValcoMJ. Load capacity estimation of foil air journal bearings for oil-free turbomachinery applications. Tribol Trans2000; 43: 795–801.
107.
RadilKHowardSDykasB. The role of radial clearance on the performance of foil air bearings. Tribol Trans2002; 45: 485–490.
108.
LeeNChoiDLeeY, et al.The influence of the slip flow on steady-state load capacity, stiffness and damping coefficients of elastically supported gas foil bearings. Tribol Trans2002; 45: 478–484.
109.
KimTHSan AndrésL. Heavily loaded gas foil bearings: a model anchored to test data. J Eng Gas Turbines Power2008; 130. https://doi.org/10.1115/1.2770494.
110.
ConlonMDadoucheADmochowskiW, et al.A comparison of the steady-state and dynamic performance of first-and second-generation foil bearings. Turbo Expo: Power Land Sea Air2010; 44014: 453–462.
111.
XuFKimDZamanian YazdiB. Theoretical study of top foil sagging effect on the performance of air thrust foil bearing. Turbo Expo: Power Land Sea Air. Am Soc Mech Eng2016; 49842: V07BT31A013.
112.
ZhaoXXiaoS. A three-dimensional model of gas foil bearings and the effect of misalignment on the static performance of the first and second generation foil bearings. Tribol Int2021; 156: 106821.
113.
HeshmatH. Major breakthrough in load capacity, speed and operating temperature of foil thrust bearings. World Tribol Cong2005; 42029: 111–112.
114.
HeshmatHShapiroWGrayS. Development of foil journal bearings for high load capacity and high speed whirl stability. 1982. https://doi.org/10.1115/1.3253173
115.
GuoYHouYWangY, et al.Numerical analysis of aerodynamic lubricated double-decked protuberant foil thrust bearing. J Adv Mech Des Syst Manuf2019; 13: JAMDSM0056-JAMDSM.
116.
LiCDuJZhuJ, et al.Effects of structural parameters on the load carrying capacity of the multi-leaf gas foil journal bearing based on contact mechanics. Tribol Int2019; 131: 318–331.
117.
LiCDuJLiJ, et al.Investigations on the load capacity of multilayer foil thrust bearing based on an updated complete model. J Tribol2023; 145: 021202.
118.
LiCDuJYaoY. Study of load carrying mechanism of a novel three-pad gas foil bearing with multiple sliding beams. Mech Syst Signal Process2020; 135: 106372.
119.
Volkov-MuzylevVBorisovYAPugachukA, et al.Determination of the maximum load capacity of a gas foil journal bearing. Chem Pet Eng2021; 57: 665–671.
120.
XuFDongZChuJ, et al.Experimental analysis of influence of double-layer bump foils on aerodynamic thrust foil bearings performance. Ind Lubr Tribol2022; 74: 127–133.
121.
KumarMKimD. Load capacity measurements of hydrostatic bump foil bearing. Turbo Expo: Power Land Sea Air2009; 48876: 755–761.
122.
KimDLeeD. Design of three-pad hybrid air foil bearing and experimental investigation on static performance at zero running speed. J Eng Gas Turbines Power2010; 132. https://doi.org/10.1115/1.4001066.
123.
LaTrayNKimDSongM. Static performance of a hydrostatic thrust foil bearing for large scale oil-free turbomachines. J Eng Gas Turbines Power2021; 143: 041017.
124.
San AndrésLChirathadamTA. Identification of rotordynamic force coefficients of a metal mesh foil bearing using impact load excitations. J Eng Gas Turbines Power2011; 133. https://doi.org/10.1115/1.4002658.
125.
San AndrésLChirathadamTA. Metal mesh foil bearing: Effect of motion amplitude, rotor speed, static load, and excitation frequency on force coefficients. J Eng Gas Turbines Power2011; 133. https://doi.org/10.1115/1.4004112.
126.
LeeY-BKimT-HKimC-H, et al.Dynamic characteristics of a flexible rotor system supported by a viscoelastic foil bearing (VEFB). Tribol Int2004; 37: 679–687.
127.
SimKParkJ. Performance measurements of gas bearings with high damping structures of polymer and bump foil via electric motor driving tests and 1-DOF shaker dynamic loading tests. Turbo Expo: Power Land Sea Air. Am Soc Mech Eng2016; 49842: V07BT31A023.
128.
SimKParkJ. Performance measurements of gas bearings with high damping structures of polymer and bump foil via electric motor driving tests and one degree-of-freedom shaker dynamic loading tests. J Eng Gas Turbines Power2017; 139: 092504.
129.
FengKHuJLiuW, et al.Structural characterization of a novel gas foil bearing with nested compression springs: analytical modeling and experimental measurement. J Eng Gas Turbines Power2016; 138: 012504.
130.
FengKLiuWYuR, et al.Analysis and experimental study on a novel gas foil bearing with nested compression springs. Tribol Int2017; 107: 65–76.
131.
FengKLiuYZhaoX, et al.Experimental evaluation of the structure characterization of a novel hybrid bump-metal mesh foil bearing. J Tribol2016; 138: 021702.
132.
FengKZhaoXHuoC, et al.Analysis of novel hybrid bump-metal mesh foil bearings. Tribol Int2016; 103: 529–539.
133.
KimD. Parametric studies on static and dynamic performance of air foil bearings with different top foil geometries and bump stiffness distributions. 2007. https://doi.org/10.1115/1.2540065
134.
KimTHAndresLS. Effects of a mechanical preload on the dynamic force response of gas foil bearings: measurements and model predictions. Tribol Trans2009; 52: 569–580.
135.
HoffmannRLiebichR. Experimental and numerical analysis of the dynamic behaviour of a foil bearing structure affected by metal shims. Tribol Int2017; 115: 378–388.
136.
ZhangHYinQGuanH, et al.Theoretical investigation of hybrid foil-magnetic bearings on operation mode and load sharing strategy. Proc Inst Mech Eng Part J: J Eng Tribol2022; 236: 2491–2506.
137.
HeshmatHChenHMWaltonJ. On the performance of hybrid foil-magnetic bearings. Proc ASME Turbo Expo2000; 122: 73–81.
138.
SwansonEHeshmatHWaltonJ. Performance of a foil-magnetic hybrid bearing. Proc ASME Turbo Expo2002; 124: 375–382.
139.
JeongSChoeBSLeeYB. Rotordynamic behavior and performance of controllable hybrid foil-magnetic bearing. In: Proceedings of the 9th IFToMM international conference on rotor dynamics, 2015, pp.1465–1476. https://doi.org/10.1007/978-3-319-06590-8_120
140.
JeongSLeeYB. Effects of eccentricity and vibration response on high-speed rigid rotor supported by hybrid foil-magnetic bearing. Proc Inst Mech Eng Part C: J Mech Eng Sci2016; 230: 994–1006.
141.
JeongSLeeYB. Vibration control of high-speed rotor supported by hybrid foil-magnetic bearing with sudden imbalance. J Vib Control2017; 23: 1296–1308.
142.
JeongSNKimTHKimCH, et al.Vibration control of a high speed rotor supported by the combined smart bearing. Int Joint Tribol Conf2011; 54747: 333–335.
143.
JeongSJeonDLeeYB. Rigid mode vibration control and dynamic behavior of hybrid foil–magnetic bearing turbo blower. J Eng Gas Turbines Power2017; 139: 052501.
144.
JeongSKimJJeonD, et al.Rigid mode vibration control and dynamic behavior of hybrid foil-magnetic bearing (HFMB) turbo blower. Turbo Expo: Power Land Sea Air. Am Soc Mech Eng2016; 49835: V07AT30A012.
145.
TianYSunYYuL. Steady-state control of hybrid foil-magnetic bearings. Turbo Expo: Power Land Sea Air. Am Soc Mech Eng2012; 44731: 849–857.
146.
PhamMNAhnH-J. Experimental optimization of a hybrid foil–magnetic bearing to support a flexible rotor. Mech Syst Signal Process2014; 46: 361–372.
147.
YangBGengHSunY, et al.Dynamic characteristics of hybrid foil-magnetic bearings (HFMBs) concerning eccentricity effect. Int J Appl Electromagnet Mech2016; 52: 271–279.
148.
TianZWeiZSunY. Nonlinear adaptive control for hybrid foil-magnetic bearing. In: 2017 IEEE international conference on mechatronics and automation (ICMA), 2017, pp.81–86. https://doi.org/10.1109/ICMA.2017.8015793
149.
KimTH. Analysis of side end pressurized bump type gas foil bearings: a model anchored to test data. Texas, USA: Texas A&M University, 2007.
150.
KimTHSan AndrésL. Effect of side feed pressurization on the dynamic performance of gas foil bearings: a model anchored to test data. J Eng Gas Turbines Power2009; 131. https://doi.org/10.1115/1.2966421.
151.
von OsmanskiSSantosIF. Gas foil bearings with radial injection: multi-domain stability analysis and unbalance response. J Sound Vib2021; 508: 116177.
152.
GavalasIDimouEChasalevrisA.Applying central manifold theory in the definition of active gas foil bearing configurations for high-speed stability of rotors. In: International conference on rotor dynamics. Cham: Springer International Publishing, 2023, pp.304–323. https://doi.org/10.1007/978-3-031-40459-7_21
153.
GavalasIPapadopoulosAChasalevrisA. Investigation of active configuration in gas foil bearings for stable ultra high-speed operation. In: Workshop on active bearings in rotating machinery. Cham: Springer International Publishing, 2022, pp.134–149. https://doi.org/10.1007/978-3-031-32394-2_9
154.
PapadopoulosAGavalasIChasalevrisA. Controlling bifurcations in high-speed rotors utilizing active gas foil bearings. Bulletin of the Polish Academy of Sciences. Technical Sciences2023; 71. https://doi.org/10.24425/bpasts.2023.146796.
155.
ParkJSimK. A feasibility study of controllable gas foil bearings with piezoelectric materials via rotordynamic model predictions. J Eng Gas Turbines Power. 2019; 141: 021027.
156.
ParkJKimDSimK. Rotordynamic analysis of piezoelectric gas foil bearings with a mechanical preload control based on structural parameter identifications. Appl Sci. 2021; 11: 2330.
157.
FengKGuanH-QZhaoZ-L, et al.Active bump-type foil bearing with controllable mechanical preloads. Tribol Int2018; 120: 187–202.
158.
GuanHFengKYuK, et al.Real-time control of rotor vibrations with active bump-type foil bearings. IEEE Trans Ind Electron2020; 68: 7412–7421.
159.
GuanH-QFengKCaoY-L, et al.Experimental and theoretical investigation of rotordynamic characteristics of a rigid rotor supported by an active bump-type foil bearing. J Sound Vib2020; 466: 115049.
160.
GuanH-QFengKYuK, et al.Nonlinear dynamic responses of a rigid rotor supported by active bump-type foil bearings. Nonlinear Dyn2020; 100: 2241–2264.
161.
FengKCaoYYuK, et al.Characterization of a controllable stiffness foil bearing with shape memory alloy springs. Tribol Int2019; 136: 360–371.
162.
RaoKBReddyDM. Crack detection methodology in rotor bearing system by DWT based adaptive neuro-fuzzy inference systems. Appl Acoust2022; 192: 108728.
163.
ShindePVDesavaleRG. Application of dimension analysis and soft competitive tool to predict compound faults present in rotor-bearing systems. Measurement ( Mahwah N J)2022; 193: 110984.
164.
CuiXWuYZhangX, et al.A novel fault diagnosis method for rotor-bearing system based on instantaneous orbit fusion feature image and deep convolutional neural network. IEEE/ASME Trans Mechatron2022; 28: 1013–1024.
165.
XinLHaidongSHongkaiJ, et al.Modified Gaussian convolutional deep belief network and infrared thermal imaging for intelligent fault diagnosis of rotor-bearing system under time-varying speeds. Stru Health Monitor2022; 21: 339–353.
166.
NakamuraHMizunoY. Diagnosis for slight bearing fult in induction motor based on combination of selective features and machine learning. Energies2022; 15: 53.
167.
TomaRNProsvirinAEKimJ-M. Bearing fault diagnosis of induction motors using a genetic algorithm and machine learning classifiers. Sensors2020; 20: 1884.
ElforjaniMShanbrS. Prognosis of bearing acoustic emission signals using supervised machine learning. IEEE Trans Ind Electron2017; 65: 5864–5871.
170.
HeDLiuCJinZ, et al.Fault diagnosis of flywheel bearing based on parameter optimization variational mode decomposition energy entropy and deep learning. Energy2022; 239: 122108.
171.
LiangMZhouK. A hierarchical deep learning framework for combined rolling bearing fault localization and identification with data fusion. J Vib Control2023; 29: 3165–3174.
172.
OhHJungJHJeonBC, et al.Scalable and unsupervised feature engineering using vibration-imaging and deep learning for rotor system diagnosis. IEEE Trans Ind Electron2017; 65: 3539–3549.
173.
ZhouXZhouHWenG. A hybrid denoising model using deep learning and sparse representation with application in bearing weak fault diagnosis. Measurement ( Mahwah N J)2022; 189: 110633.
174.
NimaRShilaF. Crack classification in rotor-bearing system by means of wavelet transform and deep learning methods: an experimental investigation. J Mech Eng Automat Control Syst2020; 1: 102–113.
175.
YaoXChenZ. Sliding mode control with deep learning method for rotor trajectory control of active magnetic bearing system. Trans Inst Meas Control2019; 41: 1383–1394.
