[1] Lee J, Kao H-A and Yang S 2014 Service innovation and smart analytics for industry 4.0 and big data environment Proc. Cirp. 16 3–8

[2] Stock T and Seliger G 2016 Opportunities of sustainable manufacturing in industry 4.0 Proc. Cirp. 40 536–41

[3] Zhong R Y, Xu X, Klotz E and Newman S T 2017 Intelligent manufacturing in the context of industry 4.0: a review Engineering 3 616–30

[4] Kim D-H et al 2018 Smart machining process using machine learning: a review and perspective on machining industry Int. J. Precis. Eng. Manuf.—Green Technol. 5 555–68

[5] Gao Q, Chen W, Lu L, Huo D and Cheng K 2019 Aerostatic bearings design and analysis with the application to precision engineering: state-of-the-art and future perspectives Tribol. Int. 135 1–17

[6] Fuller D D 1969 A review of the state-of-the-art for the design of self-acting gas-lubricated bearings J. Lubr. Technol. 91 1–16

[7] Heshmat H and Hermel P 1993 Compliant foil bearings technology and their application to high speed turbomachinery Tribology Series (Amsterdam: Elsevier) pp 559–75

[8] DellaCorte C 2008 Technical development path for foil gas bearings STLE/ASME 2008 Int. Joint Tribology Conf.: American Society of Mechanical Engineers pp 299–302

[9] Bulat M P and Bulat P V 2013 The history of the gas bearings theory development World Appl. Sci. J. 27 893–7

[10] Bleuler H et al 2009 Magnetic Bearings: Theory, Design, and Application to Rotating Machinery (Berlin: Springer)

[11] Reynolds O IV 1886 On the theory of lubrication and its application to Mr Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil Phil. Trans. R. Soc. 117 157–234

[12] Tipei N 1954 Equatiile lubrificatiei cu gaze Commun. Acad RP Romine 4 699

[13] Langlois W 1962 Isothermal squeeze films Q. Appl. Math. 20 131–50

[14] Michael W 1963 Approximate methods for time-dependent gas-film lubrication problems J. Appl. Mech. 30 509–17

[15] Salbu E 1964 Compressible squeeze films and squeeze bearings J. Basic Eng. 86 355–64

[16] Pan C 1967 On asymptotic analysis of gaseous squeeze-film bearings J. Lubrication Tech. 89 245–53

[17] Pan C, Malanoski S, Broussard P and Burch J 1966 Theory and experiments of squeeze-film gas bearings: I. Cylindrical journal bearing J. Basic Eng. 88 191–8

[18] Da Silva F P and Almas E M 1986 Recent developments in the theory of squeeze film bearings Tribol. Int. 19 79–86

[19] Stolarski T A 2014 Acoustic levitation—a novel alternative to traditional lubrication of contacting surfaces Tribol. Online 9 164–74

[20] Andrade M A, Pérez N and Adamowski J C 2018 Review of progress in acoustic levitation Braz. J. Phys. 48 190–213

[21] Vandaele V, Lambert P and Delchambre A 2005 Non-contact handling in microassembly: acoustical levitation Precis. Eng. 29 491–505

[22] Weber R J et al 2012 Acoustic levitation: recent developments and emerging opportunities in biomaterials research Eur. Biophys. J. 41 397–403

[23] Priego-Capote F and de Castro L 2006 Ultrasound-assisted levitation: lab-on-a-drop Trends Anal. Chem. 25 856–67

[24] Santesson S and Nilsson S 2004 Airborne chemistry: acoustic levitation in chemical analysis Anal. Bioanal. Chem. 378 1704–9

[25] Gao J, Cao C and Wei B 1999 Containerless processing of materials by acoustic levitation Adv. Space Res. 24 1293–7

[26] Benmore C and Weber J 2011 Amorphization of molecular liquids of pharmaceutical drugs by acoustic levitation Phys. Rev. X 1 011004

[27] Stout K 1985 Design of aerostatic flat pad bearings using annular orifice restrictors Tribol. Int. 18 209–14

[28] Stout K and Rowe W 1972 Analysis of externally-pressurized spherical gas bearings employing slot restrictors Tribology 5 121–7

[29] Nakamura T and Yoshimoto S 1996 Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors Tribol. Int. 29 145–52

[30] Mori H, Yabe H and Ono T 1965 Theory of externally pressurized circular thrust porous gas bearing J. Basic Eng. 87 613–20

[31] Mori H, Miyamatsu Y and Sakata S 1964 Research on externally pressurized circular thrust gas-lubricated bearings Bull. JSME 7 467–73

[32] Kassab S Z, Noureldeen E M and Shawky M A 1997 Effects of operating conditions and supply hole diameter on the performance of a rectangular aerostatic bearing Tribol. Int. 30 533–45

[33] Yoshimoto S, Yamamoto M and Toda K 2007 Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet J. Tribol. 129 384–90

[34] Belforte G, Raparelli T, Viktorov V and Trivella A 2007 Discharge coefficients of orifice-type restrictor for aerostatic bearings Tribol. Int. 40 512–21

[35] Powell J W 1970 Design of Aerostatic Bearings (Brighton: Machinery) p 280

[36] Eleshaky M E 2009 CFD investigation of pressure depressions in aerostatic circular thrust bearings Tribol. Int. 42 1108–17

[37] Willis R 1828 On the pressure produced on a flat plate when opposed to a stream of air issuing from an orifice in a plan surface Trans. Cambridge Phil Soc. 3 129–40

[38] Kingsbury A 1897 Experiments with an air-lubricated journal J. Am. Soc. Naval Eng. 9 267–92

[39] Harrison W 1913 The hydrodynamical theory of lubrication with special reference to air as a lubricant Trans. Camb. Phil. Soc. 22 39–54

[40] Katto Y and Soda N 1952 Theory of lubrication by compressible fluid with special reference to air bearing Proc. 2nd Japan National Congress for Applied Mechanics pp 267–70

[41] Powell J 1970 A review of progress in gas lubrication Rev. Phys. Technol. 1 96

[42] Ausman J 1963 Linearized ph stability theory for translatory half-speed whirl of long, self-acting gas-lubricated journal bearings J. Basic Eng. 85 611–8

[43] Ausman J 1964 Gas-lubricated bearings Adv. Bearing Technol. 38 109

[44] Castelli V and Pirvics J 1967 Equilibrium characteristics of axial-groove gas-lubricated bearings J. Lubr. Technol. 89 177–93

[45] Cheng H, Castelli V and Chow C 1969 Performance characteristics of spiral-groove and shrouded Rayleigh step profiles for high-speed noncontacting gas seals J. Lubr. Technol. 91 60–8

[46] Bonneau D and Absi J 1994 Analysis of aerodynamic journal bearings with small number of herringbone grooves by finite element method J. Tribol. 116 698–704

[47] Chen X-D and He X-M 2006 The effect of the recess shape on performance analysis of the gas-lubricated bearing in optical lithography Tribol. Int. 39 1336–41

[48] Liu F, Lu Y, Zhang Q, Zhang Y, Gupta P and Müller N 2016 Load performance analysis of three-pad fixing pad aerodynamic journal bearings with parabolic grooves Lubr. Sci. 28 207–20

[49] Gunter E Jr, Hinkle J and Fuller D 1964 The effects fo speed, load, and film thickness on the performance of gaslubricated, tilting-pad journal bearings ASLE Trans. 7 353–65

[50] San Andrés L 2006 Hybrid flexure pivot-tilting pad gas bearings: analysis and experimental validation J. Tribol. 128 551–8

[51] Sim K and Kim D 2007 Design of flexure pivot tilting pads gas bearings for high-speed oil-free microturbomachinery J. Tribol. 129 112–9

[52] Lihua Y, Shemiao Q and Lie Y 2009 Analysis on dynamic performance of hydrodynamic tilting-pad gas bearings using partial derivative method J. Tribol. 131 011703

[53] Heshmat C and Heshmat H 1995 An analysis of gaslubricated, multileaf foil journal bearings with backing springs J. Tribol. 117 437–43

[54] Kim D 2007 Parametric studies on static and dynamic performance of air foil bearings with different top foil geometries and bump stiffness distributions J. Tribol. 129 354–64

[55] DellaCorte C, Radil K C, Bruckner R J and Howard S A 2008 Design, fabrication, and performance of open source generation I and II compliant hydrodynamic gas foil bearings Tribol. Trans. 51 254–64

[56] Kim T H and Andres L S 2009 Effects of a mechanical preload on the dynamic force response of gas foil bearings: measurements and model predictions Tribol. Trans. 52 569–80

[57] Feng K and Kaneko S 2010 Analytical model of bump-type foil bearings using a link-spring structure and a finiteelement shell model J. Tribol. 132 021706

[58] Kaplan B 1970 Recent developments in magnetic levitation Electron. Lett. 6 230–1

[59] Atherton D 1980 Maglev using permanent magnets IEEE Trans. Magn. 16 146–8

[60] Azukizawa T, Yamamoto S and Matsuo N 2008 Feasibility study of a passive magnetic bearing using the ring shaped permanent magnets IEEE Trans. Magn. 44 4277–80

[61] Moser R, Sandtner J and Bleuler H 2006 Optimization of repulsive passive magnetic bearings IEEE Trans. Magn. 42 2038–42

[62] Yonnet J-P 1978 Passive magnetic bearings with permanent magnets IEEE Trans. Magn. 14 803–5

[63] Schweitzer G 2002 Active magnetic bearings-chances and limitations IFToMM 6th Int. Conf. on Rotor Dynamics (Sydney, Australia) (Citeseer) pp 1–14

[64] Lei S and Palazzolo A 2008 Control of flexible rotor systems with active magnetic bearings J. Sound Vib. 314 19–38

[65] Khoo W, Kalita K, Garvey S D, Hill-Cottingham R, Rodger D and Eastham J F 2010 Active axialmagnetomotive force parallel-airgap serial flux magnetic bearings IEEE Trans. Magn. 46 2596–602

[66] Kim H-Y and Lee C-W 2004 Analysis of eddy-current loss for design of small active magnetic bearings with solid core and rotor IEEE Trans. Magn. 40 3293–301

[67] Yanliang X, Yueqin D, Xiuhe W and Yu K 2006 Analysis of hybrid magnetic bearing with a permanent magnet in the rotor by FEM IEEE Trans. Magn. 42 1363–6

[68] Jiancheng F, Jinji S, Yanliang X and Xi W 2009 A new structure for permanent-magnet-biased axial hybrid magnetic bearings IEEE Trans. Magn. 45 5319–25

[69] Jiancheng F, Jinji S, Hu L and Jiqiang T 2010 A novel 3-DOF axial hybrid magnetic bearing IEEE Trans. Magn. 46 4034–45

[70] Beck J V and Strodtman C 1968 Load support of the squeezefilm journal bearing of finite length J. Lubr. Technol. 90 157–61

[71] DiPrima R C 1968 Asymptotic methods for an infinitely long slider squeeze-film bearing J. Lubr. Technol. 90 173–83

[72] Takada H, Kamigaichi S and Miura H 1983 Characteristics of squeeze air film between nonparallel plates J. Lubr. Technol. 105 147–52

[73] Beck J V, Holliday W and Strodtman C 1969 Experiment and analysis of a flat disk squeeze-film bearing including effects of supported mass motion J. Lubr. Technol. 91 138–48

[74] Yoshimoto S, Anno Y, Sato Y and Hamanaka K 1997 Float characteristics of squeeze-film gas bearing with elastic hinges for linear motion guide JSME Int. J. C 40 353–9

[75] Stolarski T and Chai W 2006 Load-carrying capacity generation in squeeze film action Int. J. Mech. Sci. 48 736–41

[76] Mahajan M, Jackson R and Flowers G 2008 Experimental and analytical investigation of a dynamic gas squeeze film bearing including asperity contact effects Tribol. Trans. 51 57–67

[77] Ha D, Stolarski T and Yoshimoto S 2005 An aerodynamic bearing with adjustable geometry and self-lifting capacity: I. Self-lift capacity by squeeze film Proc. Inst. Mech. Eng. J 219 33–9

[78] Yoshimoto S, Kobayashi H and Miyatake M 2007 Float characteristics of a squeeze-film air bearing for a linear motion guide using ultrasonic vibration Tribol. Int. 40 503–11

[79] Liu P, Li J, Ding H and Cao W 2009 Modeling and experimental study on near-field acoustic levitation by flexural mode IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 2679–85

[80] Wang Y and Wei B 2013 Mixed-modal disk gas squeeze film theoretical and experimental analysis Int. J. Mod. Phys. B 27 1350168

[81] Ilssar D, Bucher I and Flashner H 2017 Modeling and closed loop control of near-field acoustically levitated objects Mech. Syst. Signal Process. 85 367–81

[82] Kang J, Xu Z and Akay A 1995 Inertia effects on compressible squeeze films Trans. ASME. J. Vib. Acoust. 117 94

[83] Hashimoto H 1995 Squeeze film characteristics between parallel circular plates containing a single central air bubble in the inertial flow regime J. Tribol. 117 513–8

[84] Stolarski T and Chai W 2008 Inertia effect in squeeze film air contact Tribol. Int. 41 716–23

[85] Li J, Cao W, Liu P and Ding H 2010 Influence of gas inertia and edge effect on squeeze film in near field acoustic levitation Appl. Phys. Lett. 96 243507

[86] Nomura H, Kamakura T and Matsuda K 2002 Theoretical and experimental examination of near-field acoustic levitation J. Acoust. Soc. Am. 111 1578–83

[87] Minikes A, Bucher I and Haber S 2004 Levitation force induced by pressure radiation in gas squeeze films J. Acoust. Soc. Am. 116 217–26

[88] Minikes A and Bucher I 2003 Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disc: numerical analysis and experimental study J. Sound Vib. 263 241–68

[89] Minikes A and Bucher I 2006 Comparing numerical and analytical solutions for squeeze-film levitation force J. Fluids Struct. 22 713–9

[90] Li W, Liu Y and Feng K 2017 Modelling and experimental study on the influence of surface grooves on near-field acoustic levitation Tribol. Int. 116 138–46

[91] Gross W A 1962 Gas Film Lubrication (New York: Wiley)

[92] Rayleigh L 1902 XXXIV. On the pressure of vibrations London, Edinburgh, Dublin Phil. Mag. J. Sci. 3 338–46

[93] Post E 1953 Radiation pressure and dispersion J. Acoust. Soc. Am. 25 55–60

[94] Rooney J A and Nyborg W L 1972 Acoustic radiation pressure in a traveling plane wave Am. J. Phys. 40 1825–30

[95] Beyer R T 1978 Radiation pressure—the history of a mislabeled tensor J. Acoust. Soc. Am. 63 1025–30

[96] Livett A, Emery E and Leeman S 1981 Acoustic radiation pressure J. Sound Vib. 76 1–11

[97] Chu B T and Apfel R E 1982 Acoustic radiation pressure produced by a beam of sound J. Acoust. Soc. Am. 72 1673–87

[98] Lee C and Wang T 1993 Acoustic radiation pressure J. Acoust. Soc. Am. 94 1099–109

[99] Hashimoto Y, Koike Y and Ueha S 1996 Near-field acoustic levitation of planar specimens using flexural vibration J. Acoust. Soc. Am. 100 2057–61

[100] Ueha S, Hashimoto Y and Koike Y 2000 Non-contact transportation using near-field acoustic levitation Ultrasonics 38 26–32

[101] Zhao S, Mojrzisch S and Wallaschek J 2013 An ultrasonic levitation journal bearing able to control spindle center position Mech. Syst. Signal Process. 36 168–81

[102] Melikhov I, Chivilikhin S, Amosov A and Jeanson R 2016 Viscoacoustic model for near-field ultrasonic levitation Phys. Rev. E 94 053103

[103] Yoshimoto S 1993 Rectangular squeeze-film gas bearing using a piezoelectric actuator-application to a linear motion guide Int. J. JSPE 27 259

[104] Yoshimoto S 1997 Floating characteristics of squeeze-film gas bearings with vibration absorber for linear motion guide. transactions-American society of mechanical engineers J. Tribol. 119 531–6

[105] Stolarski T and Chai W 2006 Self-levitating sliding air contact Int. J. Mech. Sci. 48 601–20

[106] Wiesendanger M 2001 Squeeze Film Air Bearings using Piezoelectric Bending Elements (Verlag Nicht Ermittelbar)

[107] Ide T, Friend J R, Nakamura K and Ueha S 2005 A lowprofile design for the noncontact ultrasonically levitated stage Japan. J. Appl. Phys. 44 4662

[108] Ide T, Friend J, Nakamura K and Ueha S 2007 A non-contact linear bearing and actuator via ultrasonic levitation Sensors Actuators A 135 740–7

[109] Koyama D, Ide T, Friend J R, Nakamura K and Ueha S 2005 An ultrasonically levitated non-contact sliding table with the traveling vibrations on fine-ceramic beams IEEE Ultrasonics Symp., 2005 (IEEE) pp 1538–41

[110] Oiwa T and Suzuki R 2005 Linear rectangular air bearing based on squeeze film generated by ultrasonic oscillation Rev. Sci. Instrum. 76 075101

[111] Shiju E, Jiang X, Cao J, Ge C, Liu A and Jin L 2015 Experimental research on levitation mechanism of ultrasonic bearing 2015 IEEE Int. Conf. on Information and Automation (IEEE) pp 100–5

[112] Song Y G et al 2013 Experimental research on the levitation support way of ultrasonic thrust bearing Appl. Mech. Mater.: Trans. Tech. Publ. 423 1571–6

[113] Liu J-F, Sun X-G, Jiao X-Y, Chen H-X, Hua S-M and Zhang H-C 2013 The near-field acoustic levitation for spheres by transducer with concave spherical radiating surface J. Mech. Sci. Technol. 27 289–95

[114] Hong Z, Lü P, Geng D, Zhai W, Yan N and Wei B 2014 The near-field acoustic levitation of high-mass rotors Rev. Sci. Instrum. 85 104904

[115] Lü P, Hong Z, Yin J, Yan N, Zhai W and Wang H 2016 Note: attenuation motion of acoustically levitated spherical rotor Rev. Sci. Instrum. 87 116103

[116] Chen C, Wang J, Jia B and Li F 2014 Design of a noncontact spherical bearing based on near-field acoustic levitation J. Intell. Mater. Syst. Struct. 25 755–67

[117] Farron J R and Teitelbaum B R 1969 Squeeze film bearings US Patent 3,471,205

[118] Emmerich C L 1967 Piezoelectric oscillating bearing US Patent 3,351,393

[119] Hu J, Nakamura K and Ueha S 1997 An analysis of a noncontact ultrasonic motor with an ultrasonically levitated rotor Ultrasonics 35 459–67

[120] Oiwa T and Kato M 2004 Squeeze air bearing based on ultrasonic oscillation: motion error compensation using amplitude modulation Rev. Sci. Instrum. 75 4615–20

[121] Stolarski T, Gawarkiewicz R and Tesch K 2015 Acoustic journal bearing—a search for adequate configuration Tribol. Int. 92 387–94

[122] Stolarski T A 2011 Running characteristics of aerodynamic bearing with self-lifting capability at low rotational speed Adv. Tribol. 2011 973740

[123] Feng K, Shi M, Gong T and Huang Z 2018 Integrated numerical analysis on the performance of a hybrid gaslubricated bearing utilizing near-field acoustic levitation Tribol. Trans. 61 482–93

[124] Stolarski T, Gawarkiewicz R and Tesch K 2017 Extended duration running and impulse loading characteristics of an acoustic bearing with enhanced geometry Tribol. Lett. 65 46

[125] Stolarski T, Xue Y and Yoshimoto S 2011 Air journal bearing utilizing near-field acoustic levitation stationary shaft case Proc. Inst. Mech. Eng. J 225 120–7

[126] Shou T, Yoshimoto S and Stolarski T 2013 Running performance of an aerodynamic journal bearing with squeeze film effect Int. J. Mech. Sci. 77 184–93

[127] Wang C and Au Y 2011 Study of design parameters for squeeze film air journal bearing–excitation frequency and amplitude Mech. Sci. 2 147–55

[128] Wang J-S, Chen C, Chen G-C and Yan X-J 2013 Research on a new type of ultrasonic bearing based on near field acoustic levitation 2013 Symp. on Piezoelectricity, Acoustic Waves, and Device Applications (IEEE) pp 1–4

[129] Li H, Quan Q, Deng Z, Hua Y, Wang Y and Bai D 2016 A novel noncontact ultrasonic levitating bearing excited by piezoelectric ceramics Appl. Sci. 6 280

[130] Li H, Quan Q, Deng Z, Bai D and Wang Y 2018 Design and experimental study on an ultrasonic bearing with bidirectional carrying capacity Sensors Actuators A 273 58–66

[131] Li H and Deng Z 2018 Experimental study on friction characteristics and running stability of a novel ultrasonic levitating bearing IEEE Access. 6 21719–30

[132] Feng K, Shi M, Gong T, Liu Y and Zhu J 2017 A novel squeeze-film air bearing with flexure pivot-tilting pads: numerical analysis and measurement Int. J. Mech. Sci. 134 41–50

[133] Shi M, An L, Feng K, Guo Z and Liu W 2018 Numerical and experimental study on the influence of material characteristics on the levitation performance of squeeze-film air bearing Tribol. Int. 126 307–16

[134] Wang C and Au Y J 2013 Comparative performance of squeeze film air journal bearings made of aluminium and copper Int. J. Adv. Manuf. Technol. 65 57–66

[135] Guo P and Gao H 2018 An active non-contact journal bearing with bi-directional driving capability utilizing coupled resonant mode CIRP Ann. 67 405–8