In recent times, gas foil bearings have become popular for commercial use in the aircraft and space industry, turbocompressors, turbine generators and in the more complex fields of turbochargers and turboexpanders. The gain in popularity for gas foil bearings is due to their features such as contamination-free zone, wide temperature range, higher stability and higher reliability characteristics as compared to other types of bearings. However, several challenges have come across while analysing the gas foil bearing behaviour at different working conditions. The current paper presents an overview of the work done in the past few decades for developing numerical models and listing the efforts of several researchers around the world to conduct the experimental investigation for predicting and analysing thermohydrodynamic behaviour of gas foil bearings at different operating conditions. It is expected that the current paper will help readers to thoroughly understand the hydrodynamic and thermal aspects of gas foil bearings.
MaJTS. An investigation of self-acting foil bearings. ASME, J Basic Eng1965; 87(4): 837–846.
2.
AgrawalGL. Foil air/gas bearing technology—an overview. Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition. Volume 1: Aircraft Engine; Marine; Turbomachinery; Microturbines and Small Turbomachinery. 1997. V001T04A006. ASME 97-GT-347, In: ASME 1997 international gas turbine and aeroengine congress and exhibition, 1997. American Society of Mechanical Engineers Digital Collection.
3.
BlockH.The foil bearings–a new departure in hydrodynamic lubrication. Lubr Eng 1953; 9(6): pp. 316–320.
4.
PatelBCameronA. The foil bearing. In: Proceedings of the conference on lubrication and wear, 1957. London: Institution of Mechanical Engineers, London, Paper Number 73.
5.
GrossWA. Film lubrication-v. Infinitely long incompressible lubricating films of various shapes. IBM Res Lab1958; 117(5): 54–79.
6.
KohRLangloisW. Investigation of the foil bearing problem. IBM Res Report RJ1960; 187.
7.
GrossWA. Gas film lubrication. New York: Wiley, 138–114, 1962.
8.
KingsburyA. Experiments with an air lubricated bearing. J Am Soc Nav Eng1897; 9: 267.
9.
HarrisonW. The hydrodynamical theory of lubrication with special reference to air as a lubricant. Trans Cambr Philos Soc Cambridge: University Press, 1913; 22(3): 37–54.
10.
LichtLBrangerM. Design, fabrication, and performance of foil journal bearing for the brayton rotating unit. NASA Report CR-22431973.
11.
BarnettMASilverA. Application of air bearings to high-speed turbomachinery. SAE Technical Paper No. 700720, 1970.
12.
RuscittoDMcCormickJGrayS. Hydrodynamic air lubricated compliant surface bearing for an automotive gas turbine engine. I. Journal bearing performance, 1978, Mechanical Technology, Inc., Latham, NY (USA), Report Number: CONS-9427-1; NASA-CR-135368.
13.
SurianoFJ. Gas foil bearing development program. Mater Sci1981, U.S. Air Force, Report No. AFWAL-TR-81-2095.
14.
GraySBhushanB. Support element for compliant hydrodynamic journal bearings. U.S. Patent No. 4,274,683, USA, 1981.
15.
HeshmatH. High load capacity compliant foil hydrodynamic journal bearing. US Patent Number 5,902,049, USA, 1999.
16.
ReynoldsO. IV. On the theory of lubrication and its application to Mr Beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil. Philos Trans 1886; 177: 157–234.
17.
PetrovNP. Friction in machines and the effect of lubricating fluid on it. St-Petersburg: Eng J1883; 1: 71–140; 2: 227–279; 3: 377–463; 4: 535–564.
18.
PetrovNReynoldsOSommerfeldA. Hydrodynamic theory of lubrication. St-Petersburg: State Publ Tech Theor Lit1934.
19.
WildmannMWrightA. The effect of external pressurization on self-acting foil bearings. J Basic Eng 1965; 87: 631–638.
20.
LichtL. Studies of foiljournal bearings for Brayton cycle turbomachinery. Final report. NASA CR-72864, 1971.
21.
DellaCorteC. Technical development path for foil gas bearings. Int Joint Tribol Conf2008; 43369.
22.
DellaCorteC. Oil-free shaft support system rotordynamics: past, present and future challenges and opportunities. Mech Syst Signal Process2012; 29: 67–76.
23.
SamantaPMurmuNKhonsariMJTi. The evolution of foil bearing technology. Tribol Int2019; 135: 305–323.
24.
FariaMTCAndré sLS. On the numerical modeling of high-speed hydrodynamic gas bearings. J Tribol2000; 122: 124–130.
25.
DellaCorteCValcoMJJTT. Load capacity estimation of foil air journal bearings for oil-free turbomachinery applications. Tribol Trans2000; 43(4): 795–801.
FengKKanekoS. Analytical model of bump-type foil bearings using a link-spring structure and a finite-element shell model.J Tribol2010;132:021706.
31.
XuFLiuZZhangG,et al.Hydrodynamic analysis of compliant foil bearings with modified top foil model. In: Turbo expo: power for land, sea, and air, Vancouver, British Columbia, Canada, vol. 54662, 2011; 126, pp. 542–546.
32.
LiYLeiGSunY,et al.Effect of environmental pressure enhanced by a booster on the load capacity of the aerodynamic gas bearing of a turbo expander. Tribol Int2017; 105: 77–84.
33.
YanJZhangGLiuZ,et al.Performance of a novel foil journal bearing with surface micro-grooved top foil. Proc Ins Mech Eng J: J Eng Tribol2018; 232: 1126–1139.
34.
PattnayakMPandeyRDuttJ. Performance behaviours of a self-acting gas journal bearing with a new bore design. Tribol Int2020; 151: 106418.
35.
LiCDuJYaoY. Study of load carrying mechanism of a novel three-pad gas foil bearing with multiple sliding beams. Mech Syst Signal Process2020; 135: 106372.
36.
GuYRenGZhouM. A fully coupled elastohydrodynamic model for static performance analysis of gas foil bearings. Tribol Int2020; 147: 106297.
37.
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.
38.
IordanoffI. Maximum load capacity profiles for gas thrust bearings working under high compressibility number conditions. 1998; 120(3): 571–576.
39.
HeshmatHWalowitJPinkusO. Analysis of gas lubricated compliant thrust bearings.J Lubrication Tech1983;103:638–646.
40.
HeshmatCAXuDHeshmatH. Analysis of gas lubricated foil thrust bearings using coupled finite element and finite difference methods. J Trib2000; 122: 199–204.
41.
BrucknerRJDellaCorteCPrahlJM. Analytic modeling of the hydrodynamic, thermal, and structural behavior of foil thrust bearings. NASA TM2005; 213811.
42.
LeeDKimD. Design and performance prediction of hybrid air foil thrust bearings. J Eng Gas Turbine Power2011; 133(4): 042501 (13 pages).
43.
ConboyTM. Real-gas effects in foil thrust bearings operating in the turbulent regime. J Tribol2013; 135: 031703.
44.
GadAKanekoS. A new structural stiffness model for bump-type foil bearings: application to generation II gas lubricated foil thrust bearing. J Tribol2014; 136: 041701.
45.
FengKLiuLJGuoZY,et al.Parametric study on static and dynamic characteristics of bump-type gas foil thrust bearing for oil-free turbomachinery. Proc Inst Mech Eng J: J Eng Tribol2016; 230: 944–961.
46.
LiCDuJYaoY. Modeling of a multi-layer foil gas thrust bearing and its load carrying mechanism study. Tribol Int2017; 114: 172–185.
47.
KumarJKhamariDSBeheraSK,et al.A methodology for performance prediction: aerodynamic analysis of axially loaded gas foil bearing. Sādhanā2021; 46: 1–20.
48.
IordanoffI. Analysis of an aerodynamic compliant foil thrust bearing: method for a rapid design.J Tribol1999;121:816–822.
49.
LeeYBKwakHDKimCH,et al.Numerical prediction of slip flow effect on gas-lubricated journal bearings for MEMS/MST-based micro-rotating machinery. Tribol Int2005; 38: 89–96.
50.
ParkDJKimCHJangGH,et al.Theoretical considerations of static and dynamic characteristics of air foil thrust bearing with tilt and slip flow. Tribol Int2008; 41: 282–295.
ShawMCMacksEF. Analysis and lubrication of bearings. New York: McGraw-Hill Book Company, 1949.
59.
PinkusOWilcockDJ. Thermal effects in fluid film bearings. In Proceedings of the in 6th Leeds-Lyon Sympos, Lyon, France, 18–21 September 1979, pp. 3–23.
60.
CopeWF. The hydrodynamical theory of film lubrication. Proc Royal Society Lond A. Math Phys Sci1949; 197: 201–217.
61.
PurvisMB. Temperature distribution in journal bearing lubricant film. Wear1954.
62.
ZienkiewiczOC. Temperature distribution within lubricating films between parallel bearing surfaces and its effect on the pressures developed. Proc Conf Lubr Wear1957; 135.
63.
HunterWBZienkiewiczOC. Effect of temperature variations across the lubricant films in the theory of hydrodynamic lubrication. J Mech Eng Sci1960; 2: 52–58.
64.
DowsonD. A generalized reynolds equation for fluid-film lubrication. Int J Mech Sci1962; 4: 159–170.
65.
TipeiNNicaA. On the field of temperatures in lubricating films. ASME J Lubr Technol1967; 89: 483–491.
66.
NicaA. Thermal behavior and friction in journal bearings. J Lub Tech1970; 92(3): 373–380.
67.
SmithRNTichyJA. An analytical solution for the thermal characteristics of journal bearings. ASME J Lub Tech1981; 103: 443–452.
68.
MajumdarBC. The thermohydrodynamic solution of oil journal bearings. Wear1975; 31: 287–294.
PinkusO. Thermal aspects of fluid film tribology. Trans Am Soc Mech Eng1990; 87(3): 537–546.
71.
McCallionHYousifFLloydT. The analysis of thermal effects in a full journal bearing. ASME J Lubr Technol1970; 92(4): 578–587.
72.
SalehiMHeshmatH. On the fluid flow and thermal analysis of a compliant surface foil bearing and seal. Tribol Trans2000; 43: 318–324.
73.
SalehiMSwansonEHeshmatH. Thermal features of compliant foil bearings—theory and experiments. J Tribol2001; 123: 566–571.
74.
GadAMKanekoS. Fluid flow and thermal features of gas foil thrust bearings at moderate operating temperatures. Proceedings of the 9th IFTOMM international conference on rotor dynamics. vol. 21, Springer, 2015, pp 1223–1233. https://doi.org/10.1007/978-3-319-06590-8_100
75.
MarchD. A thermohydrodynamic analysis of journal bearings.Proc Inst Mech Eng1966;181.
PengZCKhonsariMM. A thermohydrodynamic analysis of foil journal bearings. ASME J Tribol2006; 128(3): 534–541.
78.
FengKKanekoS. A study of thermohydrodynamic features of multi wound foil bearing using lobatto point quadrature. In: Turbo expo: power for land, sea, and air, Berlin, Germany: ASME, 2008,43154, pp. 911–922.
79.
San AndrésLKimTH. Thermohydrodynamic analysis of bump type gas foil bearings: a model anchored to test data. J Eng Gas Turbine Power2010; 132: 042504 (ASME Paper No. GT2009-59919).
80.
LeeDKimD. Thermohydrodynamic analyses of bump air foil bearings with detailed thermal model of foil structures and rotor. ASME J Tribol2010; 021704: 1–12.
81.
SimKKimTH. Thermohydrodynamic analysis of bump-type gas foil bearings using bump thermal contact and inlet flow mixing models. Tribol Int2012; 48: 137–148.
82.
TalmageGCarpinoM. Thermal structural effects in a gas-lubricated foil journal bearing. Tribol Trans2011; 54: 701–713.
83.
BagheriMAkbarzadehSTikaniR,et al.Thermohydrodynamic analysis of foil journal bearings using differential quadrature method. Proc Inst Mech Eng J: J Eng Tribol2016; 230: 561–570.
84.
MaraiySYCrosbyWAEl-GamalHA. Thermohydrodynamic analysis of airfoil bearing based on bump foil structure. Alexandria Eng J2016; 55: 2473–2483.
85.
ZhouQLiYLuP. Studies on thermal effects in aerodynamic foil journal bearings. J Adv Mech Design Syst Manuf2016; 10(1): 1–10.
86.
SamantaPKhonsariMM. On the thermoelastic instability of foil bearings. Tribol Int2018; 121: 10–20.
87.
ZhangKZhaoXFengK,et al.Thermohydrodynamic analysis and thermal management of hybrid bump–metal mesh foil bearings: experimental tests and theoretical predictions. Int J Thermal Sci2018; 127: 91–104.
88.
MichelHLiebichR. Challenges in validating a thermo-hydrodynamic gas foil bearing model. J Eng Gas Turbine Power2021; 143: 041029.
89.
Le LezSBArghirMFreneJ. A new bump-type foil bearing structure analytical model. In: ASME Turbo expo: power for land, sea, and air, Montreal, QC, Canada, 2007, 47942, pp. 747–757.
90.
RadilKZeszotekM. An experimental investigation into the temperature profile of a compliant foil air bearing. Tribol Trans2004; 47: 470–479.
91.
DowsonDHudsonJ. Thermohydrodynamic analysis of the infinite slider bearing: part I, the plane inclined slider bearing. Inst Mech Eng: Lubr Wear Conven1963; Paper 4: 34–44.
92.
DowsonD. Thermo-hydrodynamic analysis of the infinite slide-bearing: part II, the parallel-surface bearing. Proc Inst Mech Eng: Lubr Wear Conven1963; Paper 5: 45.
93.
EzzatHARohdeSM. A study of the thermohydrodynamic performance of finite slider bearings. ASME J Lubric Technol1973; 95(3): 298–307.
HuebnerKH. A three-dimensional thermohydrodynamic analysis of sector thrust bearings. ASLE Trans1974; 17: 62–73.
96.
BrucknerRJ. Simulation and modeling of the hydrodynamic, thermal, and structural behavior of foil thrust bearings. PhD Thesis. Case Western Reserve University, USA, 2004.
97.
LeeDKimD. Three-dimensional thermohydrodynamic analyses of Rayleigh step air foil thrust bearing with radially arranged bump foils. Tribol Trans2011; 54: 432–448.
98.
MahnerMLehnASchweizerB. Thermogas-and thermohydrodynamic simulation of thrust and slider bearings: convergence and efficiency of different reduction approaches. Tribol Int2016; 93: 539–554.
99.
LehnAMahnerMSchweizerB. A thermo-elasto-hydrodynamic model for air foil thrust bearings including self-induced convective cooling of the rotor disk and thermal runaway. Tribol Int2018; 119: 281–298.
100.
QinKJacobsPAKeepJA,et al.A fluid-structure-thermal model for bump-type foil thrust bearings. Tribol Int2018; 121: 481–491.
101.
KumarJKhamariDSBeheraSK,et al.Influence of slip-flow phenomenon on thermohydrodynamic behaviour of gas foil thrust bearings. Proc Inst Mech Eng J: J Eng Tribol2021. https://doi.org/10.1177/13506501211002962
102.
HeshmatHShapiroWGrayS. Development of foil journal bearings for high load capacity and high speed whirl stability. Journal of Lubrication Technology, ASME Transactions1982; 104(2): 149–156.
103.
HeshmatH. Advancements in the performance of aerodynamic foil journal bearings: high speed and load capability. ASME J. Tribol1994; 116(2): 287–294.
104.
RadilKCDellaCorteC. The effect of journal roughness and foil coatings on the performance of heavily loaded foil air bearings. Tribol Trans2002; 45: 199–204.
105.
RadilKHowardSDykasB. The role of radial clearance on the performance of foil air bearings. Tribol Trans2002; 45: 485–490.
DykasBD. Factors influencing the performance of foil gas thrust bearings for oil-free turbomachinery applications. PhD Thesis, Case Western Reserve University, USA, 2006.
108.
DickmanJR. An investigation of gas foil thrust bearing performance and its influencing factors. Master’s Thesis, Case Western Reserve University, USA, 2010.
109.
SadashivaRP. Experimental investigation of thermal behaviour of air foil bearings. Master’s Thesis, The University of Texas at Arlington, USA, 2010.
110.
RavikumarRNRathanrajKJArun KumarV. Comparative experimental analysis of load carrying capability of air foil thrust bearing for different configuration of foil assembly. Procedia Tech2016; 25: 1096–1105.
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