Magnetic Levitation and Bearings — Deep Reference

Contactless support of a moving body via magnetic forces removes friction, wear, and lubrication — for which engineers have been willing to accept active control loops, cryogenic cooling, large copper bills, and uncommon failure modes. Magnetic levitation has produced one transport spectacle (the 600 km/h JR Maglev L0 series in Japan, the Chuo Shinkansen Tokyo-Nagoya line in construction since 2014 for 2027 opening, and Shanghai’s Transrapid revenue service since 2004), and two quietly transformative industrial technologies — active magnetic bearings (AMB) that now spin every modern turbomolecular pump, large industrial compressor, and high-speed flywheel; and passive Halbach-array levitation at the heart of MRI gradient drives, magnetic gears, and the LDX MIT magnetic-bottle plasma reactor. This note covers Earnshaw’s-theorem limits, the four practical levitation methods (EMS, EDS, HTS Meissner, ferrofluidic), the control of AMB systems, and the production landscape of magnetic bearings, maglev trains, magnetic gears, blood pumps, and centrifugal pumps.

See also

• electromagnetics-engineering
• electric-motors
• bearings-taxonomy
• bearings-catalog-deep
• transportation-engineering
• h-infinity-robust
• energy-storage-systems
• magnetic-and-optical-materials

0. Historical milestones

• 1842 — Samuel Earnshaw proves no static configuration of inverse-square charges can be stable.
• 1934 — Hermann Kemper (Germany) patents the basic electromagnetic-suspension Maglev concept.
• 1957 — Soviet engineer Petr Schwill demonstrates rotational AMB.
• 1969 — German federal government begins funding development that becomes Transrapid.
• 1972 — Eric Laithwaite (Imperial College) demonstrates linear induction motor + Maglev concept.
• 1979 — Transrapid 05 makes its first manned passenger run at the IVA Hamburg exposition.
• 1984 — Birmingham Airport opens the world’s first revenue Maglev (low-speed, 600 m, EMS, withdrawn 1995).
• 1985 — Bendix begins testing AMB on industrial compressors.
• 1987 — TGV V150 sets conventional-rail world speed record 515 km/h, motivating Maglev push past 500 km/h.
• 1994 — Halbach publishes “Application of permanent magnets in accelerators and electron storage rings”; the Halbach array concept popularised beyond particle physics.
• 1997 — Andre Geim levitates a frog in a 16 T magnet at HFML Nijmegen.
• 1998 — Richard Post (LLNL) proposes Inductrack passive EDS.
• 2003 — Shanghai Transrapid begins revenue service (regular schedule 2004).
• 2005 — Aichi Expo Linimo Maglev demonstrates urban application.
• 2014 — Construction begins on JR Central’s Chuo Shinkansen (Tokyo–Nagoya leg).
• 2014 — Abbott / Thoratec HeartMate 3 — first fully magnetically-levitated implantable LVAD — receives CE mark.
• 2015 — JR Central L0 series sets world rail speed record of 603 km/h.
• 2017 — Abbott HeartMate 3 receives FDA approval.
• 2020 — Cerca Magnetics demonstrates wearable OPM-MEG system in a magnetically-shielded room.
• 2022 — Hyperfine Swoop becomes first FDA-cleared portable Halbach-array MRI in widespread use.

1. Earnshaw’s theorem and routes around it

In 1842 Samuel Earnshaw proved that no collection of static charges, currents, or magnetic dipoles can stably support another such object purely against gravity — the potential is always saddle-shaped at any candidate equilibrium. Practical magnetic levitation must therefore exploit one of five exceptions:

• Active control (EMS — electromagnetic suspension). Continuously adjust electromagnet currents to keep the body at the unstable equilibrium. Inherently unstable open-loop; stable in closed loop with $\sim$1 kHz bandwidth current feedback.
• Diamagnetism ($\chi <0$). Bismuth, pyrolytic graphite, water, and superconductors push away from field, giving a true static minimum. Workable only for very small loads or very strong fields.
• Type-II superconductors with flux pinning. Vortices nucleate in the cuprate and lock the superconductor in 3D — the levitating body becomes mechanically captured by its own field profile. The basis of YBCO Meissner-effect demos and the Inductrack EDS train concept.
• Induced currents in a moving conductor (EDS — electrodynamic suspension). A moving permanent-magnet array induces eddy currents in a passive metal track; the induced field repels. Stable at speed; zero levitation at standstill.
• Spin stabilisation (Levitron). Gyroscopic precession provides the missing restoring torque.

The five exceptions map directly to the five practical levitation technology families. Active control is by far the most flexible (and so dominates industrial magnetic bearings), Meissner-effect levitation is the visual spectacle (and the foundation of recent HTS bearing R&D), and EDS dominates non-contact transport at high speed.

2. Active magnetic bearings (AMB)

2.1 Operating principle

An AMB suspends a rotor in five mechanical degrees of freedom (four radial, one axial — the sixth is rotation, which is the desired motion) using 4–8 electromagnets per radial bearing plus 2 thrust electromagnets. Each axis has:

• Position sensors — eddy-current probes (Bently Nevada 3300 XL, Hypertronic-style 1–4 mm range), inductive proximity, or capacitive. Sample at 10–25 kHz, $\sim$1 µm resolution.
• Controller — PID or model-based, running on a real-time DSP (TI C2000, NXP MPC, dSPACE rapid-prototyping) at 5–20 kHz loop rate.
• Power amplifier — Class-D or Class-AB H-bridge per coil pair, 50–600 V bus, 5–80 A current.

The bearing is intrinsically unstable: the attractive force from each coil $\propto B^2/{\mu }_0=(NI/g{)}^2$ scales with the inverse square of the air gap. A perturbation toward one coil increases its force, pulling the rotor further into it. Closing the loop with a leading PD term shifts the closed-loop poles into the left-half plane.

The standard control law (radial, single axis):

$F_{\mathrm{net}}(x,i)=k_{i}i-k_{x}x,i=K_p(x_{\mathrm{ref}}-x)+K_d\dot{x}$

with $k_x$ (negative-stiffness from the bias field) and $k_i$ (current-to-force constant) extracted from the magnetic-circuit analysis at the bias point. Typical loop bandwidth 200–1000 Hz; the rotor system runs $\sim$10× above the loop bandwidth at supercritical speeds, so the controller must also damp first and second bending modes (which fall in the 300–3000 Hz range for typical industrial rotors).

2.2 Bearing topologies

• Radial homopolar — 8-pole stator with all coils carrying the same DC bias. Lower iron loss (no AC flux on the rotor surface) but more complex bias-current control.
• Radial heteropolar — 4-pole stator with alternating N/S. Easier control law, higher rotor surface losses.
• Combined radial + axial — one bearing assembly handles both radial and axial loads (Synchrony, Calnetix designs). Compact for short rotors.
• Conical — single bearing tilted at 30–45°; handles radial + axial in one unit. Used in turbomolecular pumps where geometry is constrained.
• Permanent-magnet biased AMB — a ring of PM provides the bias flux, and the AC coil only modulates around the bias. Reduces standby power $\sim$50 %; more sensitive to PM tolerance.

2.3 Vendors and applications

• SKF Magnetic Mechatronics S2M (formerly Société de Mécanique Magnétique, Vernon France) — the historical AMB pioneer, owned by SKF since 2007. AMB systems for petrochemical-process compressors (Statoil/Equinor Snøhvit LNG, Total Liquefaction, Saudi Aramco). 50+ years of running-time data.
• Synchrony Magnetic Bearings (part of Johnson Controls / SKF rotor business since 2018) — LineSpeed AMB for steam turbines; SMB for industrial compressors; FuturEnergy line for natural-gas storage.
• Calnetix Technologies (Cerritos, CA) — high-speed motor-bearing combo for waste-heat recovery (Calnetix WTRX 65 kW Organic Rankine Cycle), pipeline gas blowers, semiconductor cryocoolers.
• Waukesha Magnetic Bearings (WMB) — turbo-expanders, blowers; common in cryogenic and food-grade industries (no-oil bearings prevent product contamination).
• Magnetic Bearings (Magnaire) / Daikin AMB — HVAC chiller compressors (Daikin Magnitude, Smardt MTW, Multistack).
• Edwards Vacuum / Pfeiffer / Leybold — turbomolecular pumps for semiconductor and analytical instruments; magnetic-bearing pumps reach $>$ 50 krpm with $<$ 10 dB acoustic noise.

The Daikin Magnitude / Smardt chiller line uses an AMB-supported Turbocor compressor that operates oil-free; chiller efficiency improves $\sim$15–25 % over conventional oil-lubricated centrifugal designs, and the chiller life extends from $\sim$15 to $\sim$25+ years.

2.4 Backup (touchdown) bearings

When the AMB fails or its power supply is interrupted, the rotor falls onto a passive touchdown bearing — typically a steel ball-bearing pair with $\sim$0.2 mm radial clearance, sized to handle the rotor’s full weight + bending energy for 5–20 spin-down rotations. Modern AMB controllers detect the fall, initiate a controlled spin-down via the motor drive, and re-levitate after the touchdown.

2.5 Worked example — radial bearing for a 5000 rpm 100 kg rotor

A radial AMB for a 100 kg rotor with 1 mm nominal air gap, 8-pole heteropolar stator, NdFeB N42 PM bias (1.3 T flux):

• Required peak force $F=mg=100\cdot 9.81=981\mathrm{N}$ per bearing.
• $F=B^{2}A/(2{\mu }_0)$ per pole pair; for $B=1\mathrm{T}$, pole area $A=2{\mu }_{0}F/B^2=2\cdot 4\pi \times 10^{-7}\cdot 981=2.46\times 10^{-3}{\mathrm{m}}^2=24.6{\mathrm{cm}}^2$ per pole pair, or ~12 cm² per pole.
• Coil ampere-turns: $NI=Bg/{\mu }_0=1\cdot 0.001/1.26\times 10^{-6}=800\mathrm{A}\cdot \mathrm{turn}$ per pole. With 100 turns per coil, $I=8\mathrm{A}$ standing; modulation $\pm$5 A.
• Magnetic stiffness at bias: $k_x=-\frac{dF}{dg}{|}_{i_0}=-2F_0/g_0=-1.96MN/m$ (negative = destabilising).
• Current stiffness: $k_i=2F_0/I_0\cdot N\approx 245N/A$.
• Required loop gain to stabilise: with rotor mass 100 kg, natural mode at $\omega =\sqrt{|k_x|/m}=140rad/s=22\mathrm{Hz}$. Loop bandwidth must be $>$ 200 Hz; with a PD controller, $K_d>m\cdot {\omega }_{\mathrm{BW}}/k_i\sim 0.6\mathrm{A}\cdot s/m$.

2.6 Sensor and power-electronics details

The position-sensing chain dominates AMB cost and reliability:

• Eddy-current sensors (Bently Nevada 3300 XL, Kaman KD-2306, Lion Precision ECL202e). Dual-channel differential for $\sim$0.1 µm resolution at 50 kHz bandwidth. Insensitive to surface oil, vibration; the workhorse of industrial AMB.
• Inductive sensors (Micro-Epsilon eddyNCDT, Lord SG-Link) — cheaper, slightly worse linearity, robust to harsh environments.
• Capacitive sensors (PI capaNCDT, Lion Precision Elite) — sub-nm resolution in lab conditions, sensitive to humidity and contamination.
• Optical / fiber-Bragg-grating — emerging for cryogenic AMB (where eddy-current sensors fail at $<$ 70 K because the rotor metal is too resistive).

The power amplifier chain: Each electromagnet coil draws 0–80 A depending on size. Modern AMB amplifiers are Class-D PWM at 20–40 kHz switching, with $\sim$98 % efficiency and current-control bandwidth of 2–5 kHz (well above the position-loop bandwidth). Vendors: SKF S2M amplifier cabinets, Calnetix proprietary, Copley Magmotor, ABB ACSM1.

The DC bus on a 10 MW AMB compressor is 540 V (3-phase rectified 480 V supply), shared across 5–10 axes. Backup-power for graceful spin-down on grid loss is 30–60 seconds from a UPS or a fly-back capacitor bank.

3. Maglev trains

3.1 EMS — Transrapid / Incheon / SCMaglev (low-speed)

The German Transrapid (Thyssen / Krupp / Siemens, 1969–2011) and its derivatives use active electromagnet attraction beneath an iron rail. The vehicle wraps around the guideway like an inverted “T” — levitation electromagnets pull the train upward toward the rail underside, with 10 mm air gap maintained by closed-loop control at $\sim$1 kHz. Propulsion is by long-stator linear synchronous motor with windings embedded in the guideway, energised section-by-section as the train passes.

Deployments:

• Shanghai Transrapid (Longyang Rd – Pudong Airport, 30.5 km, opened 2004) — 430 km/h commercial top speed, the only commercial Transrapid line. Operates 7 days/week.
• Incheon Airport Maglev (Korea, 6.1 km, opened 2016, suspended 2023 then resumed under EcoBee) — 110 km/h urban Maglev, EMS at lower speed.
• Linimo (Nagoya, Japan, 8.9 km, opened 2005) — HSST-100 urban Maglev, 100 km/h. Built around the 2005 Aichi Expo.
• Changsha Maglev Express (China, 18.5 km, opened 2016) — CRRC-built medium-speed Maglev, 100 km/h.

3.2 EDS — JR-Maglev SCMaglev

The Japanese SCMaglev (Central Japan Railway / JR Central) uses superconducting NbTi magnets in the train and passive figure-eight aluminium coils in the guideway. Below $\sim$150 km/h the train rolls on wheels; above that the induced eddy currents in the guideway coils produce enough lift to raise the train 10 cm. Lateral guidance is from the figure-eight coil sets: if the train shifts left, induced currents in the left figure-eight increase, repelling it back to centre.

Records and deployment:

• L0 series: world rail speed record 603 km/h in 2015 on the Yamanashi test track.
• Chuo Shinkansen Tokyo–Nagoya: under construction since 2014, $\sim$286 km, planned 2027–2034 opening (delayed from 2027 due to environmental and right-of-way disputes in Shizuoka). Designed top speed 500 km/h, scheduled travel time Tokyo–Nagoya 40 min (vs current 90 min on Tokaido Shinkansen).
• Chuo Shinkansen Nagoya–Osaka: planned 2037–2045.
• Total project cost estimate: $\sim$$80–110B (¥9–10T).

The SCMaglev uses NbTi superconductors in the train, requiring helium boil-off at $\sim$2 L/h per car — managed by on-board cryocoolers and a daily helium top-up. Future plans include HTS REBCO upgrades to eliminate liquid helium entirely.

3.3 EDS — Inductrack (Halbach array)

Richard Post (LLNL, 1998) proposed an all-passive EDS system using a Halbach permanent-magnet array beneath the vehicle and a passive multi-loop “ladder track” on the guideway. The Halbach array concentrates flux on its underside (near the track) while nulling it on the upper side (the vehicle interior is field-free). At speed the induced track currents repel the array; at standstill the train rests on auxiliary wheels.

Inductrack has not seen commercial transport deployment but the technology underpins:

• General Atomics Urban Maglev demonstrator at Hollolands, CA (decommissioned).
• LaunchPoint Technologies / Skytran small-vehicle urban transit demos.
• Magsorber packaging-machine conveyor systems.
• Lawrence Livermore Inductrack II demonstrator (no current commercial offering).

3.3a Long-stator linear synchronous motor

Both the Transrapid (EMS) and the SCMaglev (EDS) propulsion is by long-stator linear synchronous motor: a 3-phase winding embedded along the entire guideway, energised section-by-section (~10–50 m at a time) as the train passes. The train carries only the rotor (the levitation magnets double as the LSM “rotor” pole array). This puts the heavy copper winding on the (much-longer, but stationary) guideway and keeps the train light.

Power converters supply the LSM phase currents from substations along the route. The Shanghai Transrapid line uses 20 MVA substations every 2–5 km; the Chuo Shinkansen will use $\sim$50 MVA stations every 30 km (the SCMaglev draws more peak power at 500 km/h because of higher aerodynamic drag). Power-conversion topology: IGBT or SiC voltage-source inverters running at 1–2 kHz output frequency (matching the LSM electrical frequency at top speed).

3.4 HTS bulk Meissner-effect

A YBCO bulk superconductor (5 cm puck, melt-textured single grain) cooled below 90 K in the presence of a permanent magnet “remembers” the field via flux pinning and levitates stably above the magnet without active control. Demonstrators:

• SuperLab / FZ-Jülich test track in Germany (decommissioned).
• Brazilian MagLev-Cobra prototype (Rio Federal University, 2018) — short test track running on liquid-nitrogen-cooled YBCO pucks.
• HTS Maglev Test Line at Southwest Jiaotong University (Chengdu, China).

HTS bulk levitation is more research-fascinating than commercially-deployable: the YBCO pucks need continuous LN${}_2$ supply, and the lift-to-weight ratio is currently limited to $\sim$1:50 — practical for small models but not for full-size revenue trains. Recent advances at SuperOX, Faraday Factory Japan, and Shanghai Superconductor improve the bulk J${}_c$, raising lift capacity.

4. Other magnetic-bearing applications

4.1 Turbomolecular pumps

Every modern turbomolecular vacuum pump $\ge$ 1000 L/s rotates on AMB or hybrid magnetic + ceramic bearings:

• Edwards STP-iXR — radial + axial AMB, 27 krpm, 200–1900 L/s.
• Pfeiffer HiPace — hybrid magnetic + ceramic, 1500–2300 L/s.
• Leybold MAG W — pure-AMB pumps for tritium service.
• Shimadzu MS series — analytical-instrument bottom-of-the-line pumps with AMB.

The advantages: no oil migration (essential for clean semiconductor processes), no bearing wear over multi-year operation, sub-µm rotor positioning.

4.1a Turbomolecular pump construction

The rotor of a 1000 L/s turbomolecular pump spins at 25–30 krpm — close to the burst-strength limit of aluminum (the rotor blade tips approach 0.5× speed-of-sound). The bearing arrangement:

• Hybrid magnetic-bearing pumps — radial AMB + small ceramic ball bearing at the bottom (for landing and reduced-speed standby). Edwards STP-iXR series.
• Full-magnetic pumps — radial + axial AMB, no ball bearings. Used in tritium service (no oil) and high-purity semiconductor. Leybold MAG W series.

The rotor is single-piece machined Al-7075-T6 or Ti-6Al-4V; blade aerodynamics are optimised by 2D Boltzmann or 3D DSMC (direct-simulation Monte Carlo) gas-flow analysis. Rotor balancing to ISO 1940-1 G0.4 grade is mandatory; even a 0.1 g·mm imbalance is unacceptable at 30 krpm.

4.2 Industrial compressors

Centrifugal natural-gas, refrigerant, and CO${}_2$ compressors increasingly run on AMB:

• MAN ENERGY Solutions MOPICO — magnetic-bearing pipeline compressor, 5–15 MW.
• Hitachi MCD / Atlas Copco ZH — chemical and refrigeration centrifugal.
• Mitsubishi Heavy Industries MAAG — LNG-process compressors.
• Equinor / Statoil Snøhvit and Aasta Hansteen LNG trains use S2M AMB on 30 MW compressors with $>$ 10-year mean-time-between-failure.

4.3 Flywheel energy storage

AMB are essential for high-speed flywheels — bearing friction at 30+ krpm would dissipate the stored energy faster than the application can use it.

• Beacon Power Smart Energy Matrix (Stephentown NY, 20 MW; Hazle PA, 20 MW) — 200 kWh-class flywheels at 16 krpm in vacuum, AMB-supported, providing fast-frequency-response ancillary services to PJM.
• Amber Kinetics M32 — 32 kWh / 8 kW unit; lower-speed (8 krpm) AMB-on-PM-bias, suitable for daily-cycle storage.
• Active Power CleanSource UPS — 250 kW / 25 sec flywheel UPS, runs on hybrid magnetic + ceramic bearings.
• Levistor (UK) — high-power short-duration flywheel UPS for EV fast-charging stations.

A high-speed flywheel system stores energy in a steel or composite rotor; AMB cuts standby loss from $\sim$5 %/h (mechanical) to $<$ 0.1 %/h. The rotor housing is evacuated to $<$ 1 Pa to eliminate windage.

4.3a Flywheel design specifics

A high-performance flywheel for grid storage has:

• Rotor material — high-strength steel (4140, 4340) for moderate speeds; T1000 carbon-epoxy or T800 carbon-fiber filament-wound for $>$ 20 krpm. Strength-to-density ratio sets the achievable kinetic energy density (Beacon’s composite rotor at 16 krpm stores $\sim$25 Wh/kg at the rotor level).
• Bearing arrangement — radial AMB top + bottom + axial thrust AMB, plus catcher bearings (angular-contact ball, $\sim$0.1 mm clearance).
• Vacuum vessel — < 1 Pa to eliminate windage losses; turbomolecular pumps maintain vacuum continuously.
• Motor / generator — PM synchronous, axial-flux or radial-flux, integrated into the flywheel rotor.
• Power electronics — bidirectional AC/DC converter linking the flywheel to the grid; 4-quadrant operation (charge and discharge).

Beacon Power’s 20 MW Stephentown plant (200 individual 100 kW / 25 kWh flywheels) provides 4-second grid-frequency response to PJM, fully discharged-recharged thousands of times per day; the AMB has demonstrated $>$ 5-year continuous operation.

4.3b Composite-rotor flywheels — strength limits

Specific energy of a flywheel scales with the strength-to-density ratio of the rotor material:

$\frac{E}{m}=K\frac{{\sigma }_{\mathrm{ult}}}{\rho }$

with $K$ a shape factor ($\sim$0.6 for thick disks, up to 0.9 for thin rim). For 4340 steel (${\sigma }_{\mathrm{ult}}=1100\mathrm{MPa}$, $\rho =7850kg/{\mathrm{m}}^3$), $E/m\approx 23Wh/kg$. For Toray T1000G (${\sigma }_{\mathrm{ult}}=3040\mathrm{MPa}$ in tension, $\rho =1810kg/{\mathrm{m}}^3$), $E/m\approx 75Wh/kg$. Filament-wound carbon composite rims dominate $>$ 20 krpm designs because steel would burst.

A typical composite flywheel rim is wound on a rotating mandrel with $\sim$70 % fiber volume fraction, multi-angle layup ($\pm 70^{\circ }$, hoop, axial), $\sim$50–100 mm thick. The inner steel hub fastens the rim to the shaft.

4.4 Blood pumps and LVADs

Implantable left-ventricular assist devices (LVADs) carry an axial- or centrifugal-flow blood pump operating at 5–15 krpm. Mechanical bearings would shed wear particles into the bloodstream; magnetic levitation removes this failure mode.

• Abbott HeartMate 3 (originally Thoratec) — centrifugal blood pump with full magnetic levitation (no bearings, no contact). Implanted in $>$ 25 000 patients since 2014. Median survival to transplant or destination therapy: 5+ years.
• Berlin Heart INCOR (Berlin Heart AG) — axial-flow pediatric pump with magnetic bearing.
• Jarvik Heart 2000 — purely mechanical, no maglev; included for comparison.
• CARMAT total artificial heart — pulsatile, no rotary bearings.

The HeartMate 3 magnetic bearing supports a 100 g rotor at 4–8 krpm against gravity, blood-pressure gradient, and dynamic forces, drawing $\sim$5 W. The control loop measures rotor position via Hall sensors and adjusts current at $\sim$5 kHz. This is the smallest commercially-fielded AMB.

4.4a HeartMate 3 design specifics

The HeartMate 3 implantable centrifugal blood pump is the most carefully-engineered miniature AMB in production:

• Rotor: 25 mm diameter, $\sim$60 g titanium/Co-Cr impeller with embedded NdFeB ring magnets.
• Stator: 4-pole motor windings + 4 magnetic-bearing windings, all hermetically encapsulated.
• Air gap: 250 µm radial.
• Operating speed: 4500–6500 rpm continuous; “artificial pulse” mode oscillates ±2000 rpm at 30 Hz to reduce thrombus risk.
• Hall position sensors: 3 per axis, fully redundant.
• Power: 4–7 W at the pump, supplied through a percutaneous driveline from an external 14 V controller + lithium-ion battery pair.
• Implant life: > 5 years demonstrated in the MOMENTUM 3 trial (FDA approval 2017); some patients now > 10 years.

The single-piece full-mag bearing eliminates the contact bearing of the predecessor HeartMate II that caused pump-thrombosis events. The HeartMate 3 was the first FDA-approved durable LVAD with no mechanical bearing, and is now the de facto standard for destination therapy in end-stage heart failure.

4.5 Centrifugal pumps and HVAC fans

• HVLS (High-Volume Low-Speed) ceiling fans — Big Ass Fans, Greenheck — direct-drive PMSM with hybrid magnetic + radial-thrust bearings. Standard in warehouses and large indoor spaces.
• Magnetic-bearing pumps for ultrapure-water service in semiconductor fabs (Iwaki MMP series). Zero contamination risk.
• Magnetic-drive sealless pumps — driven via a magnet coupling across a sealed barrier (not strictly maglev — the pump rotor is mechanically bearing-supported inside the wet section). Used wherever leak-free containment is essential (HF, hot acid, sterile pharma). Vendors: Iwaki, Sundyne ANSIMAG, March Manufacturing.

4.5a Magnetic-drive sealless pump details

A sealless centrifugal pump driven through a magnet coupling has an inner rotor inside the wetted cavity (carrying the impeller and the driven magnets) and an outer rotor outside (carrying the driver magnets, coupled to the motor shaft). Between them is a corrosion-resistant containment shell (~1 mm Hastelloy or PEEK). The torque transmitted across the gap:

$T=\frac{n_p{\mu }_0{M}^2{V}_{\mathrm{eff}}}{g}$

where $n_p$ is pole-pair count, $M$ is magnet remanence, $V_{\mathrm{eff}}$ effective magnet volume, $g$ gap. Typical magnet couplings transmit 1–500 kW with $\sim$0.5–2 mm radial gap. Iwaki / Sundyne ANSIMAG dominate the chemical / pharma market for these pumps.

4.6 Magnetic chucks and lifting magnets

Industrial chucks for milling and grinding use switchable permanent magnets (Eclipse Magnetics, Tecnomagnete MillTec, Walker Magnetics) — two layers of NdFeB segments with a manual or hydraulic lever that rotates one layer to either align magnetic flux to the workpiece (clamp) or short-circuit it through the chuck body (release). Holding forces 50–500 N/cm${}^2$; clamping a 1 m${}^2$ steel plate gives 5–50 tonne shear-load capacity with zero electrical power consumed.

Lifting magnets for scrap-handling cranes (Walker, Goudsmit, Bunting) are pure electromagnets, 1–60 kW DC, lifting up to 50 tonnes of ferrous scrap. Modern controls include emergency-battery backup to prevent load drops on power failure, and per-cycle remanent demagnetisation pulses to release sticky loads.

5. Magnetic gears

A magnetic gear transmits torque between two rotors via the modulation of a static stator pole-piece array, with no contact and no wear. The mathematical principle: two rotors with $p_h$ and $p_l$ pole pairs, separated by a stator with $n_s=p_h+p_l$ ferromagnetic pole pieces, transmit torque at gear ratio $p_h/p_l$. Theoretical efficiency $>$ 99 % since there is no friction, only minor eddy-current and hysteresis loss in the soft magnetic stator pieces.

Vendors and applications:

• Magnomatics (Sheffield, UK) — Pseudo-Direct-Drive (PDD) magnetic gear motors for wind-turbine generators and marine propulsion. 30 kW prototype demonstrated > 96 % efficiency.
• Portescap (Danaher) — small magnetic-gear drives for medical and aerospace.
• Magnetic Pinion Gear (MPG) — early developer for high-precision robotics.
• Lynch Motor Company / Saietta Group — magnetic-gear motors for two-wheeled EVs.

Magnetic gears suit applications that combine high torque density, high efficiency, contactless transmission, and inherent overload protection (the gear “slips” if torque exceeds the magnetic shear limit, returning to engagement when the load reduces).

5.1 Magnetic-gear worked example

For a wind-turbine generator with a 12 rpm input shaft (low-speed turbine rotor) and a 1200 rpm generator (electrical-frequency match), gear ratio 100:1. Compare:

• Mechanical 3-stage planetary gearbox — efficiency 95–97 %, mass 8–12 tonnes for 5 MW, MTBF 50 000–100 000 h (gear-tooth fatigue and bearing wear set the limit; multi-MW gearboxes are the dominant cost driver of wind-turbine maintenance).
• Magnomatics PDD magnetic gear motor — efficiency 97–98 %, mass 6–9 tonnes for 5 MW (lighter because no oil + bearings), MTBF $>$ 200 000 h (no mechanical wear), but capital cost $\sim$2× higher per kW. Magnomatics has demonstrated a 30 kW prototype with $>$ 96 % efficiency for marine propulsion at NCE in Sheffield.

Industry uptake has been slow because the rare-earth content is high (NdFeB price volatility) and qualification of long-life rare-earth machines on wind turbines is still in early field trials.

6. Magnetic suspensions in precision instruments

6.1 Wafer steppers

ASML EUV scanners (NXE:3400 / 3600 / 3800 / EXE:5000) suspend the wafer stage on a planar magnetic levitator — a Halbach-array stator under the wafer stage produces 3D-controlled levitation force, eliminating air bearings (which would generate vibration). The stage tracks to $<$ 0.5 nm in-plane positional error at 10 m/s scan speed. The reticle stage uses a similar maglev architecture.

This is the most precise sustained levitation in industry — sub-nm position control over 60+ second exposures, with $<$ 0.01 g acceleration during the scanning move. Vendors of the maglev coil assemblies for ASML include Hitachi, Tecnotion, and ASML internal subassemblies.

6.2 AFM stages

Atomic-force-microscope sample stages (Asylum Research / Oxford Instruments Cypher, Park Systems NX) increasingly use magnetic levitation for the high-Z (vertical) coarse-positioner. AMB allows $\sim$10 nm step resolution over a 10 mm range with no creep — much better than piezo+spring-flexure stacks.

6.3 Vibration isolation

Maglev vibration-isolation tables (Newport WorkStation, JR Maglev R&D platforms) achieve $<$ 1 Hz horizontal resonance and 20+ dB isolation below 10 Hz — the regime where pneumatic tables and elastomeric pads fail.

6.3a Vibration isolation worked example

A semiconductor lithography tool sits on a 6-DOF maglev vibration-isolation table (Newport WorkStation X-IT, MOOG IDC IsoCenter). Below 1 Hz the table is essentially passively suspended; above 1 Hz active feedback applies counter-forces to floor vibration sensed at $\sim$10 µg resolution. Vibration transmission $T(\omega )$:

$T(\omega )=\frac{1}{\sqrt{(1-{\omega }^2/{\omega }_n^2{)}^2+(2\zeta \omega /{\omega }_n{)}^2}}$

with ${\omega }_n/2\pi =0.5$ Hz, $\zeta =0.4$. At 10 Hz, $T\approx 0.0025\to -52\mathrm{dB}$. Active feedback above 1 Hz adds another $-20\mathrm{dB}$, totalling $-72\mathrm{dB}$ — adequate to keep wafer-stage floor vibration below 10 nm RMS over 60 s exposure.

6.4 Wafer-stage maglev — engineering detail

The ASML EUV wafer stage runs in a $\sim$10${}^{-5}$ Pa vacuum (the EUV optics will not tolerate gas-load). Air bearings (the standard for DUV scanners) are not available. The maglev planar levitator uses:

• Permanent-magnet array under the moving stage (Halbach).
• Coil array in the stationary base, energised to generate 3D Lorentz force.
• Capacitive position sensors plus laser interferometry for absolute reference; sub-nm noise floor.
• Sample-and-hold controller running at $>$ 20 kHz on FPGA + DSP.

Power dissipation per stage: $\sim$1–3 kW continuous during scan. The base structure must reject this heat without thermal expansion that would distort the geometry; ASML uses water cooling at $\sim$0.01 K stability over a 24-hour drift envelope.

This is the highest-precision sustained magnetic-levitation system in production worldwide, and a single $\sim$$200M EUV scanner has 2–4 such stages. Hitachi, Tecnotion, and ASML’s internal subassemblies dominate the maglev coil-set supply.

7. Other levitation methods

• Diamagnetic levitation — small high-permeability objects (HOPG, water, bismuth) levitate inside a 16 T Bitter-magnet at the bench; famously demonstrated by Andre Geim levitating a live frog at the High Field Magnet Laboratory Nijmegen in 1997 (Geim won the 2010 Nobel Prize in Physics for graphene, also discovered partly in the same laboratory).
• Acoustic levitation — not magnetic, included for context. Ultrasonic standing wave traps droplets and small particles; used in containerless materials processing.
• Optical levitation — laser-tweezer trapping of cells and nanoparticles. The 2018 Nobel Prize in Physics went to Arthur Ashkin for optical tweezers.
• Ferrofluidic suspension — a magnetised fluid (Ferrotec EFH series) supports a magnetic body against gravity. Used in voice-coil cooling for high-power audio drivers.

8. Control of AMB — beyond PID

Industrial AMB has matured beyond simple PID for the following reasons:

• Rotor flexibility. A long industrial rotor has first bending mode in the 100–500 Hz range; a PID with > 200 Hz bandwidth excites the bending mode unless explicitly notched. Standard practice: cascade $H_{\infty }$-shaped controller with model-based filters tuned per rotor.
• Cross-coupling. Gyroscopic precession in the rotor couples X and Y radial motion at the rotor spin frequency. Decoupling matrices (modal decomposition) eliminate the cross-coupling.
• Unbalance compensation. A residual rotor unbalance drives a synchronous forcing at the spin frequency. Standard AMB controllers (S2M MB-350, Calnetix VPC) include adaptive feedforward (LMS algorithm) that learns the unbalance signature and pre-empts it — eliminating shaft synchronous vibration and reducing bearing peak current.
• Robust control. $H_{\infty }$ and $\mu$-synthesis controllers handle rotor-model uncertainty (mass, stiffness, gyroscopic terms vary with temperature and assembly tolerances). Standard reference: Schweitzer & Maslen Magnetic Bearings 2009. See h-infinity-robust for the technique.
• Sliding-mode control. SMC handles AMB nonlinearity and provides finite-time-convergence in saturation conditions. Used in research; less common in production. See sliding-mode-control.

8.1 Unbalance compensation in detail

Synchronous-unbalance compensation is the single most-deployed adaptive feature in production AMB. The rotor has a residual mass imbalance $u$ at angular position ${\varphi }_u$; the synchronous force at speed $\Omega$ is:

$F_{\mathrm{syn}}(t)=u{\Omega }^2{e}^{j(\Omega t+{\varphi }_u)}$

Without compensation, the AMB controller drives a synchronous current with the same frequency to suppress the synchronous displacement — but then the bearing forces transmit to the housing. Two strategies:

• Synchronous force rejection (synchronous-current zeroing) — the controller actively suppresses the synchronous current; the rotor whirls at the unbalance orbit but the AMB applies zero synchronous force. The vibration appears on the rotor, not the bearing or housing. Used in high-precision machine tools.
• Synchronous displacement rejection — the standard PD controller, which gives synchronous force into the bearing. Used in compressors where housing vibration is acceptable but rotor position must stay centered.

The mode is selected during operation by an LMS (least-mean-square) feedforward loop that subtracts a learned synchronous correction from the controller output. Production references: SKF S2M MB-450, Schweitzer book Ch. 9.

9. The LDX magnetic-bottle reactor (MIT)

The Levitated Dipole Experiment (LDX) at MIT (2004–2011) was a fusion-research device that levitated a 0.5 m, 565 kg ring-shaped Nb${}_3$Sn superconducting magnet inside a 4 m vacuum vessel for plasma confinement. The levitation was active — a 1.5 m diameter water-cooled copper electromagnet above the chamber provided the upward force, with the levitating coil’s position sensed and stabilised at $\sim$10 Hz. LDX demonstrated stable plasma confinement in the magnetic-dipole geometry, of theoretical interest for advanced fusion concepts (the dipole is the natural confinement of Jupiter’s magnetosphere; LDX scaled this to terrestrial laboratory size).

LDX is not used for plasma containment in ITER, DEMO, SPARC, or tokamak fusion projects more broadly (those use externally-anchored toroidal + poloidal coils). It is included here as the largest-scale active-magnetic-levitation system ever fielded for plasma physics research.

9.1 LDX experimental details

The LDX coil was a 1.2 m-diameter Nb${}_3$Sn tape-wound superconducting magnet operating at 4.5 K. Total energy storage 50 MJ; persistent-mode lifetime $>$ 5 hours per levitation experiment. The supporting cold-mass cryostat was integral to the floating ring, with on-board liquid-helium thermal mass providing $\sim$3 hours of cooling per run before re-cooling was needed. The active control system used a triaxial position sensor (laser triangulation) and a 1.5 m diameter water-cooled copper “catcher” coil above the ring; the catcher modulated current at $\sim$30 Hz bandwidth to keep the floating ring stable against external perturbations.

LDX retired in 2011, succeeded conceptually by the Wisconsin RT-1 (1996–) and Japan’s Mini-RT (2018–) compact dipole experiments. Plasma-fusion engineering decisively moved to ITER (tokamak) and SPARC (high-field tokamak) by 2020.

10. Halbach array math

A Halbach array is a 1D, 2D, or 3D arrangement of permanent magnets whose magnetisation rotates with position to produce a one-sided field. For a linear array of period $\lambda$ (8 magnet segments per period at $45^{\circ }$ rotation each), the field above the array is:

$B(x,y)=B_0{e}^{-2\pi y/\lambda }[\cos (2\pi x/\lambda )\hat{\mathbf{x}}+\sin (2\pi x/\lambda )\hat{\mathbf{y}}]$

where $B_0=B_r(4/\pi )(1-e^{-2\pi h/\lambda })$, $B_r$ is the permanent-magnet remanence, $h$ is the array thickness. Below the array the field is essentially zero — the asymmetric output is the array’s defining feature. For 4-segment-per-period arrays the prefactor is $B_0=B_r(2\sqrt{2}/\pi )(1-e^{-2\pi h/\lambda })$.

Applications of Halbach arrays:

• MRI low-field magnets — Hyperfine Swoop 64 mT uses a 24-segment Halbach cylinder.
• Inductrack train guideways — 4–8 segment 1D arrays on the vehicle.
• NMR rotor magnets — Bruker / JEOL ultra-compact NMR probes.
• Wiggler / undulator magnets in synchrotron light sources — see particle-accelerator-magnets-deep.
• Magnetic dispensers in industrial conveyor sorting.

10.1 Halbach array engineering trade-offs

Designing a Halbach array involves trading:

• Segment count $K$ per period — more segments approach the ideal sinusoidal modulation but increase assembly cost. Typical: 4 segments (90°), 8 segments (45°), 16 segments (22.5°). Doubling segments halves harmonic content; 8 is the common compromise.
• Aspect ratio $h/\lambda$ — thicker array → flatter field, but with diminishing returns above $h/\lambda \approx 0.5$.
• Air gap — exponential field decay $e^{-2\pi y/\lambda }$ means 1 wavelength of clearance kills field by 540×.
• Magnet grade — N52 ($B_r=1.43\mathrm{T}$) gives $\sim$10 % more field than N42 ($B_r=1.30\mathrm{T}$). Above N50 the temperature coefficient gets worse ($T_{\max }$ drops from 100 to 80 °C without Dy doping).
• Assembly forces — adjacent Halbach segments push and pull each other with kN-scale forces. Custom fixturing and stainless-steel inner sleeves are essential; the rotor must be wound or assembled with hydraulic press.

10.1 Halbach k-Halbach versus standard

A standard Halbach array has 4 segments per period (90° rotation per segment). A “k-Halbach” array doubles this to 8 segments (45° rotation each), pushing harmonic content from the 3rd harmonic up to the 7th. The trade is twice the assembly cost for $\sim$10 % smoother field — typically worthwhile for the most stringent applications (NMR rotors, MRI low-field cylinders) and not for general-purpose Inductrack guideway arrays.

11. Standards and qualification

• API 617 / API 684 — petrochemical compressor and turbomachinery standards; cover AMB qualification (lateral / torsional rotor dynamics, lateral-stability margin, transient response, overload).
• ISO 14839 parts 1–4 — rotating machinery + magnetic bearings; vocabulary, vibration measurement, evaluation criteria, technical guidelines.
• IEEE 421 series — exciter standards; applies to AMB position controllers operating as field-current regulators.
• EN 13261 / EN 13262 — railway component standards including magnetic-attractive Maglev brake systems.
• AAMI HE74 — human-factors design for medical devices (covers LVAD/AMB human interface).
• FDA 21 CFR 870.3450 — implantable LVAD requirements.

11.1 ISO 14839 — vibration evaluation of magnetic-bearing rotors

ISO 14839-2 specifies how to measure and grade AMB-supported rotor vibration. Categories:

• Category A — best in class; safe for long-term operation. RMS displacement at the bearing $<50\mu \mathrm{m}$ for medium-speed machines.
• Category B — acceptable; monitor.
• Category C — unacceptable for continuous operation; corrective action needed.
• Category D — risk of damage; immediate shutdown.

Industrial AMB compressors (Snøhvit, Aasta Hansteen) run in Category A across normal operating envelope and trip out of D. Vibration is measured via the same eddy-current sensors used for AMB position feedback — no additional accelerometer needed.

11.2 IEEE Std P1873 (under development)

The proposed IEEE Standard for Active Magnetic Bearings (P1873, started 2022) is the first dedicated AMB standard at the IEEE level — covers control-system requirements, mechanical interface, performance metrics, and safety. Expected ratification 2027.

12. Pitfalls

• Magnetic-bearing controllers are not “fail-safe.” A power loss drops the rotor onto touchdown bearings; if the touchdown is undersized or worn the rotor can wreck itself and the housing. Always specify backup-bearing rated life as $\ge$ 10 expected touchdown events.
• Eddy currents in bearing rotor laminations. Solid rotor steel gives huge eddy losses at supercritical speeds. Modern AMB rotors use 0.2 mm electrical-steel laminations or sintered SMC (soft magnetic composite, like Höganäs Somaloy).
• Halbach array temperature derating. NdFeB loses 0.1 %/°C of remanence; high-rpm Halbach arrays in unventilated rotors can exceed 120 °C from rotor-loss + windage, derating thrust by 12 %.
• Maglev train environmental constraints. EMS Transrapid switches and curves are limited by the dynamic-response time of the levitation loop; a single Maglev train can typically take $\sim$10–15 ‰ grades (vs $\sim$30 ‰ for the SCMaglev EDS). Track-construction tolerances are 0.5–1.0 mm over 10 m sections, $\sim$10× tighter than conventional rail.
• HTS bulk levitation hysteresis. A YBCO bulk magnet that is cooled and lifted up off the track shifts its trapped flux profile and “remembers” the new height — the second lift drops the levitation force by $\sim$30 %. Re-cooling restores the function.

12.1 Maglev failure modes

A complete catalogue of the failure modes Maglev systems prepare for:

• Electromagnet quench (EMS, low-temperature SCMaglev) — a small disturbance heats the conductor above $T_c$, ohmic heating dumps the coil. Train falls onto landing skids, brakes engage. Recoverable with ramp-down + repair, but unplanned downtime.
• LSM power loss — segment-converter failure on the propulsion stator. Train coasts to next active segment or stops; emergency brake engages.
• Guideway sensor failure — position sensors lose track of the train (rare with redundant sensing). Train enters fail-safe mode.
• Cryocooler failure (SCMaglev) — helium boil-off exceeds replenishment. Cars must be transferred to a refill station; otherwise the SC coil quenches.
• External magnetic interference — a stray ferromagnetic object on the track perturbs the levitation field. Maglev guideways enforce strict exclusion zones and have continuous metal-detector monitoring.

13. Cost summary

System	Capital cost (USD)
Industrial AMB compressor (10 MW)	$2–5M premium over rolling-element
AMB turbo-vacuum pump 1500 L/s	$25–60k
AMB chiller (Daikin Magnitude 500 ton)	$200–400k
LVAD HeartMate 3 device + implant	$120–180k ($\sim$50k device, rest hospital + surgery)
Beacon Power 20 MW flywheel	$50–80M plant
Shanghai Transrapid (revenue)	$1.2B for 30 km
SCMaglev Chuo Shinkansen Tokyo-Nagoya	$80–110B for 286 km
HTS bulk levitation demo (small)	$50–200k

13.1 Total cost of ownership perspective

For a 10 MW industrial compressor over a 20-year service life:

• Conventional oil-lubricated rolling-element bearing: $200k capex + $100k/yr oil + bearings + maintenance = $2.2M.
• AMB-equipped: $2.5M capex + $10k/yr (instrumentation calibration, occasional touchdown-bearing replacement) = $2.7M.

The AMB premium pays back through avoided unplanned-downtime cost (typical $50k–$500k per day for an LNG train). On a critical bottleneck compressor, the AMB option recovers its premium in $<$ 5 years; on a standby unit it may never pay back.

14. Emerging directions

• HTS REBCO AMB — coated-conductor superconducting magnets for AMB applied to cryogenic compressors (LNG, hydrogen liquefaction). Faraday Factory Japan, SuperOX, AMSC are developing HTS bearing prototypes that reduce standby power by 5–10× vs conventional AMB.
• Cryocooler-free HTS rotor levitation — pulse-tube cryocoolers integrated into the rotor support assembly enable HTS bulk levitation with no liquid nitrogen handling. Prototype demonstrators at IFW Dresden and Southwest Jiaotong University.
• Halbach-array linear motors for hyperloop — Virgin Hyperloop One (defunct), Hardt Hyperloop (Netherlands), and Swisspod operate test tracks combining Inductrack-style passive Halbach levitation with linear-motor propulsion in evacuated tubes. None commercially fielded as of 2026.
• Conformal active levitation for additive manufacturing — magnetic chucks that conform to non-flat substrates for in-situ printing. Research-stage at Carnegie Mellon, ETH Zurich.

Further reading

• Schweitzer, G. & Maslen, E. H. (Eds.). (2009). Magnetic Bearings: Theory, Design, and Application to Rotating Machinery. Springer. The standard reference textbook; covers theory, control law design, and application case studies including blood pumps, turbomolecular pumps, compressors.
• Maslen, E. H. & Schweitzer, G. (2011). Active Magnetic Bearings: Chances and Limitations. CISM. Practitioner-focused, with detailed case studies.
• Lee, H. W. et al. (2006). “Review of maglev train technologies.” IEEE Transactions on Magnetics 42(7), 1917–1925. Coverage of EMS / EDS / Inductrack.
• Post, R. F. & Ryutov, D. D. (2000). “The Inductrack: a simpler approach to magnetic levitation.” IEEE Transactions on Applied Superconductivity 10(1): 901–904.
• Atallah, K. & Howe, D. (2001). “A novel high-performance magnetic gear.” IEEE Transactions on Magnetics 37(4): 2844–2846.
• Filatov, A. & Hawkins, L. A. (2017). “Active magnetic bearings: principles, design, and application.” Magnetic Bearings: Theory and Applications (InTech) chapter. Free open-access overview.
• Earnshaw, S. (1842). “On the nature of the molecular forces which regulate the constitution of the luminiferous ether.” Trans. Cambridge Phil. Soc. 7, 97–112. The original theorem.

Adjacent

• electromagnetics-engineering — Maxwell + Lorentz + magnetic-circuit reluctance — foundations under every levitation calculation.
• electric-motors — PMSM and linear synchronous motors used for Maglev propulsion; many AMB rotors share motor laminations.
• bearings-taxonomy — overall taxonomy of rolling-element, plain, fluid-film, and magnetic bearings.
• bearings-catalog-deep — vendor-specific magnetic-bearing catalog including SKF S2M, Synchrony, Calnetix.
• h-infinity-robust — $H_{\infty }$ control for AMB position loop with model uncertainty and bending modes.
• sliding-mode-control — alternative nonlinear control for AMB saturation handling.
• energy-storage-systems — flywheel energy storage with AMB.
• transportation-engineering — high-speed rail context for Maglev systems.
• magnetic-and-optical-materials — NdFeB, SmCo, REBCO superconductor materials for permanent-magnet and HTS levitation.