Hybrid gas-magnetic bearings: An overview

Abstract

This paper presents a state-of-the-art survey on the development of the hybrid gas-magnetic bearing (HGMB) technology. HGMBs are proposed to complement the advantages of gas bearings and magnetic bearings for enhanced bearing performance. Nevertheless, there are a number of inherent challenges in their designs, analyses, and performance characteristics that must be taken into account for proper functionality and reliable operation. For this purpose, substantial results in theory, numerical simulations, and experiments concerning rotor dynamics, mechanical structures, control systems, and operation modes are discussed to help further investigation and implementation of HGMBs. In addition, future developments of HGMBs in industries and remaining challenges are discussed.

Keywords

Hybrid gas-magnetic bearings (HGMBs)rotor dynamics bearing configuration hybrid mode

1. Introduction

Current research on rotating machinery is driven by an ever-growing demand for higher performance and greater availability [1]. At the same time, conventional bearings are confronted with a series of new challenges in harsh working conditions, such as extreme temperature, extreme cleanliness and corrosive working fluids, where traditional lubricated bearings cannot function well [2]. Promising bearing technologies for high rotational speeds are contactless bearing concepts such as magnetic bearings or gas bearings, of which the accuracy can reach a fraction of micrometers or even smaller.

With variable electromagnetic forces to levitate the rotor, AMBs have the advantage of high speed, high accuracy, no lubrication, free contamination and enable active control of dynamic motions of the journal, which is not available with traditional bearings [3]. Nonetheless, due to the inherent open-loop instability of magnetic bearing systems, auxiliary bearings are indispensable in case of failures.

Gas bearings including externally pressurized gas bearings and self-acting gas bearings allow for environmental-friendly operation [4]. For the externally pressurized gas bearings, the journal is carried by the pressurized gas film provided by an external gas supply [5]; while the gas pressure of self-acting gas bearings is merely generated by journal rotation. However, both applications at high speed are limited by poor dynamic characteristics. Besides, to avoid abrasion during start/stops self-acting gas bearings are usually combined with external gas supply in industry [4,6,7].

Despite the inherent shortcomings of magnetic bearings and gas bearings, the cooperation of the two bearings can compensate for each other’s weakness and boost the bearing performance, e.g. achieving better load capacity and less power consumption [8]. The HGMBs are suitable for cryogenic turbomachinery, ultrahigh-speed machines, applications with frequent start/stops and sensitive parts that require vibration-free bearings. To date, substantial achievements have been made in theory, numerical simulations and experiments concerning mechanical structures, rotor dynamics, control systems and operation modes. In this work, we review the recent progress of HGMBs and discuss the remaining challenges as well as future developments.

Fig. 1.

Categories of bearings applied in high speed machines.

2. Why hybrid gas-magnetic bearings?

As illustrated in Fig. 1, conventional bearings for high-speed machines include magnetic bearings, gas bearings, rolling bearings and fluid bearings (exclude gas bearings here). For rolling bearings, the spindle rotating speed is restricted by element material and lubrication principle. Despite that modern ceramic material and lubrication technologies could increase the maximal rotating speed by approximately 30%, the lifetime of such bearings is limited to several thousand hours [9] due to skidding wear and lasts for only several rotor-drops due to failures. Even worse, violent backward-whirl may occur and result in a disastrous system failure [7]. Fluid bearings make use of the pressurized oil/water film between the journal and the bearing bush. They possess higher precision, less wear, better anti-shock performance and longer lifespan than rolling bearings. Nevertheless, temperature rise and thermal deformation of the motorized spindle under the condition of oil–air lubrication are hard to control, which also hinders the operating speed of heavy rotors. For high speed bearings with ultra-high precision and longer lifetimes, promising candidates are contact-free bearings such as magnetic bearings and gas bearings [10].

2.1. Magnetic bearings

Magnetic bearings are generally classified into three types: permanent magnetic bearings (PMBs), active magnetic bearings (AMBs) and hybrid magnetic bearings (HMBs). The magnetic force of PMBs is generated by permanent magnets, which decreases power consumption and rotor heating, yet suffers from demagnetization and increases the installation complexity [11]. Therefore, PMBs are commonly accompanied with active control. The AMB generates controllable electromagnetic force according to the feedback of journal motion. An AMB system comprises a rotor, displacement sensors, a controller, power amplifiers and electromagnets.

Magnetic bearings possess unique advantages such as lubricant-free operation, high speed/precision, load capacity at zero/low speed, long life span, active control of rotor dynamics and real-time monitoring [12]. In addition, magnetic bearings are not sensitive to environment temperature (operating temperature from −250 °C to 450 °C) and can operate in a vacuum system. Nonetheless, due to the inherently instability and dynamically soft characteristic of magnetic bearings, auxiliary bearings are necessary in case of electronic/power/bearing failures [13]. Also, the load capability of the magnetic bearings is confined by magnetic saturation. In most situations, the auxiliary bearing is either a solid lubricated bushing or a rolling element bearing with a loose clearance [12]. Other concerns with AMBs are the huge power losses and consequent rotor heating [14] for which a constant bias current/flux is required to realize linearization and improve load capacity [15].

Tremendous efforts have been made to rectify these problems. Strategies on diminishing power losses include utilizing innovative mechanical structures, permanent magnets and variable/zero bias current/flux. However, some other issues may arise. Take the permanent magnet as an example, it decreases power consumption whereas suffers from demagnetization. As for the indispensable auxiliary bearings, the rolling bearings tend to produce skidding wear and have a short lifetime in case of rotor-drops due to system failures [7].

2.2. Gas bearings

Gas bearings generate a contactless load-bearing between the bushing and the journal by a thin pressurized gas film. Without oil lubrication circuits and seals, gas bearing is more environment-friendly [4], and offers distinct advantages in precision positioning and high-speed machinery [57]. Tight manufacturing tolerance is necessary to ensure a satisfying load capacity and postpone the appearance of the instability. Clean environment is also required due to the sensitivity in the presence of particulates and dust in a small clearance. Common gas-bearing machines include air cycle machines, cryogenic turbo-expanders, turbochargers and oil-free compressors [16].

For externally pressurized gas bearings, the spindle remains at the bush center with an appropriate implementation of the pressure feed, e.g. with the arrangement of injectors or with porous material. However, the external gas compression system increases running costs and system complexity [17]. Another concern is the inherent onset instability [18]. Although pneumatic hammering caused by pneumatic and self-excited vibration could be avoided by a gas supply restrictor, the fluid-induced instability is difficult to suppress due to the low damping characteristic of the aerodynamic gas film, which disrupts the normal operation of rotating machinery, resulting in serious damages [9].

For self-acting gas bearings, the spindle must be operated beyond the threshold speed to prevent contact between the bushing and the journal [4]. A tribological consideration is necessitated to avoid initial rubbing and ensure reliable operation during transient periods [19]. Another challenge is the possible fluid-induced instability, known as ‘half-speed whirl’ [20]. Additionally, gas bearings provide orders-of-magnitude lower damping than oil-lubricated bearings, which poses challenges for safe operation in changing conditions. These issues can be harmful to machinery performance, and even cause a catastrophic failure.

To overcome these disadvantages, researchers adopted active lubrication techniques with feedback control laws [21]. Whereas, some high-performance machine designs may not be possible without the additive strengths of hybrid bearing technologies. It is expected that future systems can involve more complex supporting approaches. Hybrid bearings utilizing external pressurization, electromagnetic devices or active thrust load management will be developed to satisfy the requirements for high performance and large machinery equipment [6].

2.3. Hybrid gas-magnetic bearings (HGMBs)

Due to the environmental-friendly characteristics of gas bearings and zero-load capacity of magnetic bearings, it is natural to combine these two to complement each other’s advantages. The shaft is levitated by magnetic bearings during starts/stops or at low speeds, and then by gas bearings at steady state. Thus, severe mechanical rubbing between the shaft and the bearing is reduced or eliminated. The HGMBs do not require an additional auxiliary bearing for protection [22], since the gas bearing can act as the backup bearing of the magnetic bearing or vice versa [23], therefore can have different operating modes. HGMB enables adjustable dynamic characteristics for optimum performance, real-time monitoring, and health diagnostic [24]. Above all, the HGMB shows advancement of supporting element in terms of lifetime, operation speed and reliability.

The development of the HGMBs has an additional military and commercial potential in aircraft/marine gas turbine engines, pipeline compressors and pumps, auxiliary power units, flywheel energy storage systems and other ultrahigh-speed rotating machinery [22].

3. Recent progress on HGMBs

In this work, key technological innovations in HGMBs including numerical analysis, mechanical structures, experimental studies and control strategies are reviewed. The methodology and main findings from these works are summarized in Table 1 for the benefits of the readership.

Table 1
Comprehensive summary of research papers on HGMBs and their foci

Focus area Issues Methodology used Bearing types Configuration Operation mode Ref. Major findings

Dynamic characteristics Stiffness and damping Experiments ASB + AMB Side-by-side Cooperation mode [25] Increment of bearing stiffness, damping and rotation precision

Dynamic characteristics Stiffness and damping Theoretical analysis concerning the journal location effect AFB + AMB Nested Cooperation mode [26] Stiffness of the AMB concerning the journal location is almost twice than without

Dynamic characteristics Stiffness and damping Experiments (excitation tests) AFB + AMB Nested Cooperation mode [27] 50% higher value of stiffness and 100% higher value of damping than pure AFB

Dynamic characteristics Stability Coupled motion equations with Crank Nicholson and Newton–Raphson methods AFB + AMB Nested Cooperation mode [28,29] Reduction of sub-synchronous vibration and increment of stability band

Dynamic characteristics Stability Theory and experiments ASB + AMB Side-by-side Cooperation mode [9] Adding AMBs can suppress the fluid induced instability and extend the operating speed

Dynamic characteristics Stability Theory and experiments AFB + AMB/AFB Nested Cooperation mode [30,31] Optimal proportional control gain considering load sharing and vibration amplitudes

Dynamic characteristics Stability Multibody dynamics model of a global system ADB + PMB Side-by-side Cooperation mode [32] Adjust dynamic characteristics by changing the passive magnetic bearing offset

Dynamic characteristics Unbalance responses of the flexible rotor and energy consumption Experiments AFB + AMB Nested Cooperation mode [33] Optimal control gains and offsets considering unbalance responses and energy consumption

Focus area	Issues	Methodology used	Bearing types	Configuration	Operation mode	Ref.	Major findings
Dynamic characteristics	Stiffness and damping	Experiments	ASB + AMB	Side-by-side	Cooperation mode	[25]	Increment of bearing stiffness, damping and rotation precision
Dynamic characteristics	Stiffness and damping	Theoretical analysis concerning the journal location effect	AFB + AMB	Nested	Cooperation mode	[26]	Stiffness of the AMB concerning the journal location is almost twice than without
Dynamic characteristics	Stiffness and damping	Experiments (excitation tests)	AFB + AMB	Nested	Cooperation mode	[27]	50% higher value of stiffness and 100% higher value of damping than pure AFB
Dynamic characteristics	Stability	Coupled motion equations with Crank Nicholson and Newton–Raphson methods	AFB + AMB	Nested	Cooperation mode	[28,29]	Reduction of sub-synchronous vibration and increment of stability band
Dynamic characteristics	Stability	Theory and experiments	ASB + AMB	Side-by-side	Cooperation mode	[9]	Adding AMBs can suppress the fluid induced instability and extend the operating speed
Dynamic characteristics	Stability	Theory and experiments	AFB + AMB/AFB	Nested	Cooperation mode	[30,31]	Optimal proportional control gain considering load sharing and vibration amplitudes
Dynamic characteristics	Stability	Multibody dynamics model of a global system	ADB + PMB	Side-by-side	Cooperation mode	[32]	Adjust dynamic characteristics by changing the passive magnetic bearing offset
Dynamic characteristics	Unbalance responses of the flexible rotor and energy consumption	Experiments	AFB + AMB	Nested	Cooperation mode	[33]	Optimal control gains and offsets considering unbalance responses and energy consumption

Table 1 (Continued).

Focus area	Issues	Methodology used	Bearing types	Configuration	Operation mode	Ref.	Major findings
Dynamic characteristics	Vibration responses of the rigid rotor	Experiments	AFB + AMB	Nested	Cooperation mode	[31]	Optimal PD control gains and eccentric position considering vibration amplitudes
Dynamic characteristics	Sudden imbalance and stability	Experiments	AFB + AMB	Nested	AMB as auxiliary bearing	[34,35]	Prevent rubbing and suppress excessive vibration on condition of a sudden imbalance event
Dynamic characteristics	Modal analysis	Finite element method (FEM)	AFB + AMB	Side-by-side	AMB as auxiliary bearing	[36]	Influence of bearing configurations on lower-order critical speeds
Dynamic characteristics	Transient analysis	Failure tests	AFB + AMB	Side-by-side	AFB as auxiliary bearing	[12,22, 23,37,38]	Feasibility of AFB to be a reliable auxiliary bearing for the AMB bearing system
Static and dynamic characteristics	Theoretical analysis	Coupled elastohydrodynamic analysis, Finite element method	AFB + AMB	Side-by-side	Cooperation mode	[7]	Establish tabulated data for use in HFMB design and propose load sharing control algorithm
Static characteristics	Theoretical analysis	New number, similarly to Sommerfeld number and new governing equations	HDB + AMB	Nested	Cooperation mode	[39]	Determination of equilibrium loci considering hydrodynamic, electromagnetic and gravity forces
Static characteristics	Numerical simulation	Load capacity and stiffness	ASB + PMB	Side-by-side	Cooperation mode	[40]	The electromagnetic force of magnetic bearing is linearly proportional to the input current
Static characteristics	Load capacity	Experiments	AFB + AMB	Side-by-side	Cooperation mode	[41]	Zero speed load capacity, triple load capacity of AMBs and elimination of initial rubbing
Static characteristics	Load capacity	Theory and experiments	HDB + PMB	Side-by-side	Cooperation mode	[42]	The magnetic force uncouples with the film force, therefore can be designed respectively

Table 1 (Continued).

Focus area	Issues	Methodology used	Bearing types	Configuration	Operation mode	Ref.	Major findings
Static characteristics	Load capacity	Experiments	AFB + AMB	Side-by-side	Cooperation mode	[43]	Achievement of 3 million DN, exceeding rolling element bearing DN capabilities by at least 50%
Static characteristics	Coating for HGMBs	KOROLONTM coating on the foil and dense chrome coating on the journal	AFB + AMB	Side-by-side	Cooperation mode	[19]	The PS304 coating is not acceptable for large foil bearing systems
Static characteristics	Rotor material	EB welded Hiperco 27 HS with the PH 13-8 Mo	AFB + AMB	Radial AFBs Thrust AMB	Cooperation mode	[16]	Thrust loads of up to 2224 N at 80,000 rpm
Control algorithm and dynamic characteristics	System modeling and controller design	State space model and measurements of rotor trajectories	AFB + AMB	Nested	Cooperation mode	[35]	Accurate model of the HFMB rigid rotor system is obtained using analytical open-loop imbalance responses
Control algorithm	PD control	Experiments	AFB + AMB	Nested	Cooperation mode	[30,31, 34,35]	Proportional gain k _p has the greatest impact on the vibration amplitude and controls the stiffness
Control algorithm	PD control	Experiments	ASB + AMB	Side-by-side	Cooperation mode	[9]	Proportional gain doesn’t affect rigid-mode critical speeds and damping avoids fluid induced instability
Control algorithm	Adaptive control	Realtime parameter identification, Golden section control	AFB + AMB	Nested	Cooperation mode	[44]	Simulation results show good performance compared with a conventional PD controller
Control algorithm	Steady-state control	Numerical simulation	AFB + AMB	Nested	Cooperation mode	[45]	Searching the steady-state working position
Control algorithm	Load sharing control	Using force, flux, strain, temperature, or acceleration sensors to measure load	AFB + AMB	Nested	Cooperation mode	[7,46]	Adjust dynamic stiffness of hybrid bearing to avoid excessive vibration

Table 1 (Continued).

Focus area	Issues	Methodology used	Bearing types	Configuration	Operation mode	Ref.	Major findings
Control algorithm	Operation strategy of AMB	Turn on AMB in initial condition, resonant area or excessive vibration occurs	AFB + AMB	Nested	AMB as auxiliary bearing	[35,47]	Easy to replace AFB by using the coupling segment, avoid initial rubbing and reduce rigid vibration
Mechanical structure	Active magnetic damper (AMD)	Machine design and experiments	ADB + AMD	Side-by-side	Cooperation mode	[10,48]	Compact drive system with integrated AMD, self-sensing method, reaching 210 kr/min method
Mechanical structure	Combined axial-radial AMB, 3G foil bearing	Load-capacity versus speed	AFB + AMB	Nested	Cooperation mode	[49]	Higher force densities
Mechanical structure	Complete passive levitation	Coulombian model, FEM, orbit, Bode, spectrum, time base, waterfall experiments	AFB + PMB	Radial AFBs thrust PMB	Cooperation mode	[50]	Hybrid bearing set
Mechanical structure	Varied structures of foil bearing supports	Illustrations	AFB + AMB/PMB	Nested	Cooperation mode	[51]	Levitation of any centrally symmetrical shaft, such as the dog-bone shape
Mechanical structure	Elastic foil bearing seat and end covers	Illustrations	AFB + AMB	Nested	Cooperation mode	[52]	Improve the ability of resisting dynamic load
Mechanical structure	Detachable overlapping foil segments	Illustrations	AFB + AMB	Nested	Cooperation mode	[53]	A method of engaging and disengaging a foil bearing in a HFMB
Mechanical structure	Magnetic bearing configurations	Load capacity and stiffness	HDB + PMB	Nested	Cooperation mode	[54]	Optimal stator magnet configuration depends on the relative magnitudes of static load and dynamic load
Mechanical structure	Convergent honeycomb seal	Tests for a suitable geometry to obtain ‘bearinglike’ characteristics	Honeycomb seal + AMB	Side-by-side	Seal as auxiliary bearing	[55]	Feasibility of honeycomb seal to also act as a gas bearing considering stiffness and damping

3.1. Mathematical model

An accurate model of the HGMB-rotor system is important for evaluating the bearing static and dynamic performances. All the models listed below are based on the same type of bearing, i.e. the 8-pole AMB and GFB.

The magnetic suspension force can be calculated based on either magnetic circuit method or Maxwell tensor method [56]. The magnetic suspension force in j direction under the control current i _j can be expressed as [26] $\begin{eqnarray}\displaystyle f_{j}^{M}=k\left[\left(\frac{I_{0}-i_{j}}{C_{0}-j}\right)^{2}-\left(\frac{I_{0}+i_{j}}{C_{0}+j}\right)^{2}\right],\quad j=x,y & & \displaystyle\end{eqnarray}$ (1) where k = μ₀ AN ² cos(φ∕4)∕4, in which μ₀ denotes the vacuum permeability, A the cross-section area, N the coil turns, φ the declination of y-axis, C ₀ the nominal air gap.

The stiffness and damping coefficients matrix of the AMB could be written as follows: $\begin{eqnarray}\displaystyle k^{M}=k_{j}+k_{ij}\frac{\partial i_{j}}{\partial j},\quad d^{M}=k_{ij}\frac{\partial i_{j}}{\partial j};\quad j=x,y & & \displaystyle\end{eqnarray}$ (2) where k _j and k _ij denote the displacement stiffness and the current stiffness.

To model the pressurized gas film of the GFB, the compressible Reynolds equation with isothermal condition is derived as [26] $\begin{eqnarray}\displaystyle \frac{\partial }{\partial {\theta}}\left(PH^{3}\frac{\partial P}{\partial {\theta}}\right)+\frac{\partial }{\partial {\xi}}\left(PH^{3}\frac{\partial P}{\partial {\xi}}\right)={\Lambda}\frac{\partial (PH)}{\partial {\theta}}+2{\Lambda}\frac{\partial (PH)}{\partial T} & & \displaystyle\end{eqnarray}$ (3) where θ denotes the dimensionless circumferential coordinate, 𝜉 the dimensionless axial coordinate, P the dimensionless pressure, H the dimensionless gas-film thickness, 𝛬 the bearing number, T the dimensionless time.

The steady state load, bearing stiffness and damping of the GFB [58] are written as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle f_{j}^{G}=-\int _{0}^{B}\int _{0}^{2{\pi}}p\left\{\begin{array}{@{}l@{}}\sin {\theta}\\ \cos {\theta}\end{array}\right\}rd{\theta}dz;\quad j=x,y\end{eqnarray}$ (4) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle k^{G}=\frac{\partial f_{j}^{G}}{\partial j},\quad d^{G}=\frac{\partial f_{j}^{G}}{\partial j};\quad j=x,y.\end{eqnarray}$ (5) Yang et al. [26] calculated the dynamic coefficients of the HFMB concerning the journal location effect under a specified load sharing ratio 𝜆 between the AMB and the GFB. The dynamic coefficients of the HFMB are the total of the GFB and the AMB. Theoretical results indicate that the stiffness produced by the AMB concerning the journal eccentricity is almost twice than the without eccentricity situation, and the damping coefficients for various 𝜆 are almost the same in both situations.

Basumatary et al. [28] developed a coupled dynamic model combining the dynamics of GFB and EA and discussed the effect of EAs on the stability of a GFB-supported rotor. Numerical results show that the sub-synchronous vibration decreases and the stability band of the rotor is enlarged with the implementation of EA. The governing equation of system dynamic motion for the coupled system can be expressed as: $\begin{eqnarray}\displaystyle M\ddot{q}+G\dot{q}=f^{G}+f^{M}+W & & \displaystyle\end{eqnarray}$ (6) where q _i = [x _i y _i θ_xi θ_yi]^T is the rotor displacement vector at each node; x _i, y _i and θ_xi, θ_yi represent the lateral and rotational displacements; M, G are the mass and the gyroscopic matrices; W denotes the weight of the rotor, f ^G the gas bearing reaction forces and f ^M the magnetic forces.

3.2. Mechanical structure

3.2.1. Bearing configurations

As demonstrated in Fig. 2, there are two main configurations of the HGMBs: nested configuration and side-by-side configuration.

Fig. 2.

Different configurations of HGMBs: (a) nested type and (b) side-by-side type.

Fig. 3.

Different layouts of HGMBs in side-by-side configuration.

Referring to the side-by-side configuration, our team [36] studied the effect of bearing layouts (Fig. 3) on critical speed. The results indicate that the first six natural frequencies increase with the bearing span, whereas the seventh and the eighth nearly remain the same. The first six natural frequencies are mainly affected by the bearing position, yet the seventh and the eighth natural frequencies are dominated by rotor structure. For the side-by-side type, the lower-order critical speeds can be altered by bearing positions or lengths, yet the rotor length is extended and bearing concentricity is demanded.

As for the nested configuration, the gas bearing is inserted in the gap between the inner diameter of the magnetic bearing and the rotor. The space inside the AMB that traditionally contains the coils is used as the gas bearing’s housing by molding with an epoxy that has no magnetic properties [27]. Heshmat [59] patented the nested configuration and proposed a load sharing strategy associated with rotating speeds. The power input of the magnetic bearing is adjusted in response to the rotor position and rotating speed. The magnetic force is reduced as rotating speed climbs, while increased as rotational speed decreases. Different structures of foil bearings and connections with magnetic bearings have been proposed by Nadjafi et al. [53], Foshage et al. [49] and Lee et al. [47].

As summarized in Table 2, both configurations can combine the strengths and compensate for the weakness of each bearing. However, the side-by-side type extends the rotor length and increases the static load. The nested type is more compact and appropriate for ultrahigh-speed occasions.

Table 2

Comparison of two HGMB configurations

	Side-by-side	Nested
Merits	∙ Adjustable lower-order critical speed by changing bearing position	∙ Reduced rotor length and mass
	∙ Better heat dissipation	∙ More compact system
		∙ Higher rotational speed
Demerits	∙ Not suitable with axial space limitation	∙ Not suitable with radial space limitation
	∙ Demand higher bearing concentricity	∙ Complicated in design, manufacture, and maintenance
	∙ Increased load and control difficulty

3.2.2. Bearing types

According to different kinds of magnetic bearings and gas bearings, there are several types of combinations. One is the integration of magnetic bearing and aerodynamic bearing, which is the current research focus of HGMBs and will be addressed in the next section. The other is the integration of magnetic bearing and ASB.

Jang [9] put up a test rig (Fig. 4) and investigated the precision and vibration performance of the spindle system. Theoretical analysis shows that high-speed operation may cause a fluid-induced instability of the rotor supported with only ASB due to the low system damping. Experiments prove that AMB can suppress the fluid induced instability of the ASB-rotor system as well as extend the operating speed [9].

Fig. 4.

Photos of the test rig: (a) ASB, (b) AMB, (c) rigid rotor (reproduced from Ref. [9]).

Ge [25] designed an aerostatic spindle controlled by magnetic bearings, and measured various parameters related to the bearing, including stiffness and damping of the ASB, force-displacement coefficient and force-current coefficient of the AMB, static stiffness, load capacity and rotating accuracy of the hybrid bearing. The results indicate that using magnetic bearing for error compensation in ASB can increase the rotating precision and improve the bearing stiffness and damping.

Bekinal et al. [50] designed a test rig with permanent magnet thrust bearing and radial bump foil bearings. The rotor dynamics have been studied by finite element method. Experiments show that the rotor is completely airborne and stable at a desired speed.

The utilization of PMBs to gas bearings has less power consumptions compared with AMBs, yet is less common due to the lack of active control. The advantages and disadvantages of each bearing type are demonstrated in Table 3.

Table 3

Different bearing types of the HGMBs

Different bearing types	Advantages	Disadvantages
Active magnetic bearings	∙ Controllable motion state and rotation error	∙ High initial and running costs
		∙ With electrical substantial system
Permanent magnetic bearings	∙ Less power loss at rated speed	∙ Subject to demagnetization
Self-acting gas bearings	∙ Clean and convenient	∙ Initial rubbing and poor damping
Pressurized gas bearings	∙ Zero-speed load capacity	∙ With a gas-pressurized system
	∙ Wear-free operation at low speed	∙ Subject to fluid induced instability

3.3. Experiments

In the following, the related experimental reports are classified by different cooperation modes between AMBs and ADBs since most studies on HGMBs are the hybridization of AMBs and ADBs.

3.3.1. Hybrid mode-both bearings sharing loads

The hybrid mode with magnetic bearings and gas bearings working together is the most common operation mode.

In 1998, Heshmat et al. [7] proposed a concept of HFMB which included a typical bump type foil bearing and a heteropolar AMB. He used the PD control and introduced a load sharing algorithm to distribute loads between the GFB and the AMB. In the same year, Mohawk Innovative Technology Inc. (MiTi) successfully tested an oil-free hybrid bearing, which had a 100 mm GFB and a 121 mm AMB, to a speed over 30,000 rpm. This was the first time the feasibility of the HFMB was verified [44].

In 2014, Pham and Ahn [33] investigated the flexible rotor-bearing system (Fig. 5), and experimentally compared unbalance responses of the flexible rotor supported by AFBs with hybrid bearings. They optimized the HFMBs by tuning control gains and offsets of the magnetic bearings. The results prove that hybrid operating mode not only improves vibration performance by 26% at bending critical speed, but also saves energy consumption of the driving motor by 50% during run-up test with an optimized control strategy.

Fig. 5.

Photos of (a) the whole test rig (b) the rotor-bearing system (reproduced from Ref. [33]).

At the same year, Jang [9] investigated the combination of an ASB-rotor system with an AMB to improve high-speed stability. The ASB and the AMB are installed in series at both sides of the built-in motor while the thrust AMB is located at one end of the rotor (Figs 4 and 6). The experiments show that the AMB can be used to suppress the fluid-induced instability and extend its operating speed from 27,000 rpm to 35,000 rpm.

Fig. 6.

Schematic of the hybrid aerostatic magnetic bearing system (reproduced from Ref. [9]).

In 2011, Lee et al. [27] proposed the nested hybrid bearing configuration, and the experimental results showed outstanding stiffness and damping effects in the hybrid mode when compared to each of the AFB and the AMB. In 2015, Jeong and Lee [31,35] elucidated the effect of the initial eccentric position of the rotor with a diameter of 35 mm supported by a HFMB (Fig. 7). The experimental results indicate that the controllable magnetic force is remarkably effective in reducing the sub-synchronous rotor vibration. Moreover, the optimal eccentricity and the corresponding load distribution of the AFB have been figured out. In 2016, Jeong et al. [30] investigated vibration control of a turbo blower system containing a HFMB (Fig. 8). It has a shaft diameter of 71.5 mm, a total length of 693 mm, and a weight of 17.8 kg. The HFMBs exhibit superior vibration stability characteristics for both the unbalance vibration and the aerodynamic instability event within the range of 12,000–15,000 rpm. The optimization of control gain parameters alters the load distribution between the two bearings, and affects the rotor vibration. The results verify that enhanced bearing performance in oil-free turbomachinery can be achieved by using HFMBs, and remarkable vibration reduction is attained by the vibration control.

Fig. 7.

Photos of the test rig: (a) manufactured AFB and HFMB; (b) experimental apparatus used to test the HFMB (reproduced from Ref. [31]).

Fig. 8.

The HFMB designed for the turbo blower system: (a) air foil journal bearing; (b) air foil thrust bearing with eight pads and bump layer (reproduced from Ref. [30]).

Later, Jeong and Lee [34] conducted an experiment that induced a sudden mass loss to a HFMB-rotor system (Figs 7 and 9). A control algorithm that detects a sudden increase in a rotor’s imbalance and aims for improvement on rotor vibration and stability was proposed. The results indicate that the rotor-bearing system recovers normal state and shows a 30% reduction in the 1x vibration.

Fig. 9.

Schematic view of test rig for sudden imbalance occurrence (reproduced from Ref. [34]).

Although magnetic bearing ensures online shaft monitoring, feedback control for active shaft positioning, and possible supervisory control for anticipated events management, the inherent system instability and its bulky packaging brought about by the control electronics and the actuating system make it unattractive for most aerospace applications [60]. Many researchers tried to simplify the magnetic bearing structure while make use of its controllability.

Looser et al. [48] used a self-acting gas bearing to carry the main load and a small-sized active magnetic damper to realize stable operation at high rotating speeds (Fig. 10). In this way, manufacturing tolerances are relaxed and excessive power losses are avoided. The compact drive system is realized by installing a damper winding inside the machine and utilizing a self-sensing strategy based on eddy current for displacement detection. The structure is suitable for applications with light loads and ultrahigh speeds. However, the coupling effect between the coils of the stator and the AMD cannot be neglected.

Fig. 10.

Illustrations of the AMD for gas-supported machines: (a) section view of the prototype machine; (b) force generation with a two-pole-pair AMD winding and torque generation with a one-pole-pair machine winding (reproduced from Ref. [48]).

The hybrid operating mode takes advantages in several aspects. Firstly, the load capacity and the rotating speed are increased. The fluid-induced instability of gas bearings can be reduced by applying magnetic forces. The imbalance vibration or sudden imbalance can be suppressed by AMBs providing additional damping, which may cause instability with the operation of gas bearings only. Accordingly, this kind of working mode is appropriate for high speed, high precision and heavy load-carrying applications.

3.3.2. Magnetic bearings working as the auxiliary bearing

Self-acting gas bearings are prone to wear at low shaft speeds or during starts/stops [61], thus are often combined with external pressurization in industry. In general, aerostatic bearings, magnetic bearings and rolling bearings can act as the auxiliary bearings [61]. However, rolling bearings require oil lubrication circuits, seals and oil cooling system, making the system more complicated and less environment-friendly [62]. Here, the HGMBs where the magnetic bearings function as auxiliary bearings are reviewed.

Pham [33] experimentally optimized the switching operation of a flexible rotor supported by a HFMB. Since the motor current with the AFB and the HFMB are related to the rotor speed. He found 6000 rpm is a critical point where the motor current is equal with the hybrid bearing and the AFB. By utilizing optimal hybrid bearing strategy, the motor energy consumption is saved by 50% compared to pure AFB.

Meanwhile, Jeong and Lee [34,35] applied vibration control in the HFMB system and found that an excessive vibration occurs with the AFB even without excitation occurrence, thus they set a predetermined vibration amplitude. The AMB is turned on when a fierce vibration or a sudden mass loss occurs. The results show that the size of the asynchronous vibration increases infinitively from the time the rotor’s imbalance amount increases with the AFB, whereas is suppressed by the AMB with an optimal PD control value.

In conclusion, with magnetic bearings as the auxiliary bearings, the start/stop rubbings are reduced, contributing to a longer service life. The switching operation mode shows good performance on saving energy and is well suited for cryogenic applications. In case of sudden mass loss, the AMB contributes to better dynamic performance and reliability. This kind of operation mode is also well-suited for applications with heavy load, discontinuous working, frequent starting or braking.

3.3.3. Gas bearings functioning as the auxiliary bearing

Magnetic bearings are vital supporting element with ultra-high speed and increased rotor size, which can also act as vibration dampers and vibration generators. However, backup bearings are indispensable for reliable and safe operation in case of power failures or breakdowns.

To date, this backup capability has been provided by either rolling element bearings or solid lubricated bushings. Both solutions have drawbacks, e.g. limited lifetime and uncertain dynamic characteristics [12]. An alternative is the compliant foil bearing. In 1998, Mohawk Innovative Technology Inc. (MiTi) demonstrated the use of a foil bearing as a backup bearing for a magnetic bearing system. In these tests, the responses to thirteen different magnetic bearing failures and recovery modes were evaluated at the speeds of 15,000 rpm and 25,000 rpm. In all 26 test cases, the transients during both failures and recovery were well controlled by the foil bearing. These tests demonstrate that the foil bearing component of a HFMB is an effective back-up bearing for the magnetic bearing, allowing continuous operations following a failure or damage-free equipment shutdown.

In 2000, Swanson and Heshmat [63] considered operations with the foil bearing alone, which has no problem supporting loads up to 4200 N for one hour to demonstrate thermal capability. Based on these results, the foil bearing in a HFMB can provide a continuous full load, full-speed operation capability. Moreover, the testing reported in the work demonstrates a coast-down to a full stop under shaft load without bearing damage. Thus, the foil bearing also provides a safe shutdown capability except extremely high bearing loads.

Later, Swanson and Heshmat [12] considered two distinct speed regions for failure and backup operation. The first group of simulated AMB failures occurred at the operating speed, with a potential requirement for the foil bearing to continue operating as the primary load support. The second failure was set at a lower speed, wherein the foil bearing would need to provide adequate shaft support for a safe shutdown. A total of thirteen distinct failure modes at two different speeds were conducted on a HFMB test rig. Further, the operating point was shifted from pure foil bearing to the AMB to test a more severe re-start condition [37]. The rotor essentially remained at the same location (the transient vibration is less than 80 μm). Although a large overshoot was observed when the AMB was reactivated in several cases, it is due to the decision not to use the AMB soft-start capacity. The experimental results demonstrate that foil bearings are capable of either supporting the shaft during coast-down or continuous operation. Since these tests recorded the transient processes from AMB to foil bearing and vice versa, it also proves that the HGMB can have a mild transition in practical. However, numerical studies are expected to figure out how the factors affect the transient process and how to prevent excessive vibration.

In 2003, Heshmat [22] investigated different operating modes by switching the AMB on or off. The experimental results strongly prove the feasibility of the AMB as a bearing or as a loader in CFB (compliant foil bearing) mode alone, or the CFB as an auxiliary bearing for the AMB.

As a result, the operation mode that gas bearings function as the auxiliary bearings proves to be effective in both high and low rotating speed. Safe operation can be ensured when the operating point is shifted from pure foil bearings to magnetic bearings and vice versa. Compared with conventional backup bearings, gas bearings are contactless, lubrication-free and can change to other operation modes according to different working conditions.

3.4. Control strategies

Due to the inherent instability of the AMBs, a controller is indispensable to adjust the rotor motion according to the rotor feedback, which is termed as the ‘inner-loop controller’. However, for the HGMB system, there could be an ‘outer-loop controller’ to adjust the steady sate characteristics of the AMB to realize different load sharing or operating modes.

3.4.1. Inner-loop controller

The inner-loop controller is a real-time controller of the AMB to adjust the journal motion. The GFB should run at certain eccentricity and attitude angle to bearing load. However, the control reference of the magnetic part may or may not follow this eccentric location, depending on whether the integral control is exercised [7].

In the case of the PID controller, the eccentric location (also the control reference) needs to be calculated at first, therefore the load sharing between GFB and AMB should be predetermined. Since the eccentric location changes with the variation of load sharing, applying PID control algorithm is complicated for the HGMB system. Relevant theoretical analysis and numerical simulations using the PID control algorithm were reported by Heshmat et al. [7] and Tian et al. [45].

The PD controllers are usually considered in the reported works [30,31,34]. Pham and Ahn [33] optimized the control gains and offsets of the AMBs by experiments. The optimized control value improves vibration amplitude by 26% at the bending critical speed, and saves energy consumption of the driving motor by 50% during the run-up test. Moreover, Jeong et al. [34] experimentally verified that the control stiffness has a dominant effect on vibration performance and could be optimized.

3.4.2. Outer-loop controller

The outer-loop controller is mainly applied to adjust the steady state characteristics of the AMB. As the bearing dynamic properties depend on their operating steady-state load, it is important to establish the load sharing ratio between foil and magnetic bearings. Heshmat et al. [7,46] proposed a steady-state load-sharing algorithm for the HFMB, which was a function of the operating conditions (Fig. 11). The rotor center was moved to the predetermined eccentric location. The total dynamic properties (sum of stiffness/damping of the two bearings) were the criteria for an appropriate load sharing ratio and were adjusted by the PID controller.

Fig. 11.

Load sharing flow diagram (reproduced from Ref. [46]).

In view of the complexity and significance of the steady-state load sharing, Tian et al. [45] proposed a searching algorithm for the hybrid operating mode based on Heshmat’s strategy [7,46] (Fig. 12). A conventional PID controller is applied for the inner-loop transient control of journal motion. The searching algorithm is applied for the steady-state controller to determine the new reference position, which uses the equivalent triangle to divide the working plane of the HFMB and minimizes the deviation between actual force and the predetermined sharing load of the AMB.

Fig. 12.

Schematic of the control system (reproduced from Ref. [45]).

Jeong and Lee et al. [35,47] used the AMBs as the auxiliary bearings for GFBs and turned on the AMBs during starts/stops in the resonant area (between 90% and 110% of the resonant speed) or when sudden mass unbalance occurred to prevent severe rubbing and excessive vibration. The flow diagram of the vibration control strategy is shown in Fig. 13. Experimental results show that the asynchronous vibration is reduced due to the additional damping of the AMBs.

Fig. 13.

Algorithm of the vibration control strategy (reproduced from Ref. [35]).

4. Future developments and remaining challenges

4.1. Future developments of HGMBs in industries

The experimental results of bearing performances of gas bearings and HGMBs are summarized in Table 4. At the speed of 10 kr/min, the stiffness and the damping of the HGMB are 50% and 100% greater than the gas bearing [27]. Moreover, the HGMB can suppress the fluid-induced sub-synchronous vibration and extend the rotating speed by 35% [9]. The rigid vibration amplitude is reduced by 33.7% by adding magnetic bearings [33]. The asynchronous vibration (nearly reduced by 90%), and the 1x vibration under sudden imbalance has been reduced by almost 30% [34]. Above all, the HGMB provides necessary damping and vibration control, hence the rotor performances during the critical speed or in case of a sudden imbalance are much better than the pure gas bearing. The reliability and stability can be improved by HGMBs.

Table 4
Comparisons of bearing performances of gas bearings and HGMBs [9,27,33,34]

Bearing performances Gas bearing HGMB

Stiffness (N/m) 100000 150000

Damping (Ns/m) 250 500

Operating speed (rpm) 26000 35000

Rigid vibration amplitude (μm) 0.068 0.045

Asynchronous vibration under sudden imbalance (μm) 165 16.5

1x vibration under sudden imbalance (mm) 0.15 0.1

Bearing performances	Gas bearing	HGMB
Stiffness (N/m)	100000	150000
Damping (Ns/m)	250	500
Operating speed (rpm)	26000	35000
Rigid vibration amplitude (μm)	0.068	0.045
Asynchronous vibration under sudden imbalance (μm)	165	16.5
1x vibration under sudden imbalance (mm)	0.15	0.1

The life expectancy of bearings under different conditions are presented in Fig. 14 based on reports and industrial demands. Normal lifetime of the conventional bearing is around 10,000 h which mainly depends on manufacturing and operation conditions, whilst that of the HGMB could reach 50,000 h. Further, the lifetime of conventional bearings decreases rapidly under special conditions. Take the cryogenic liquid pump and air cryogenic turbine as examples, the lifetime of mechanical bearings usually reduces to around 5,000 h since lubricants cannot work under cryogenic temperature. For high-speed spindles, a life expectancy of several thousand hours at speeds of 200–500 kr/min is demanded [64], whereas the ball bearings used for dental drills last about 200–300 h in the cyclic tests at a varied speed ranging from 200 kr/min to 500 kr/min [48]. As for applications with the start–stop cycles which usually occur in air pumps, gas compressors and high-speed spindles, conventional bearings last around several thousand start–stop cycles due to mechanical abrasion. On the contrary, without mechanical contact and lubricants, the HGMBs with enhanced performance can extend the service lifetime to 20,000–50,000 h.

Fig. 14.

Life expectancies of conventional bearing and HGMB under different conditions [48,64].

Another important issue is the maximal rotating speed that each bearing can achieve (Fig. 15). Based on the references and industry requirements [48,65], the rolling bearing technology may offer a solution up to rotational speeds of 3 × 10⁶ DN. The maximum DN value the gas bearing can reach at current stage is 7.2 × 10⁶. The maximum speed of AMBs tends to be constrained by miniature magnetic actuators and the windage loss. However, since the AMB has no speed limit in theory, this technique has good development potentialities. In industry, continuous operation between 3 to 4 million DN is required under extreme temperatures [22]. Compared with magnetic bearings and gas bearings, the HGMBs can enlarge the rotor size, reduce fluid-induced instability, and extend the bearing lifespan.

Fig. 15.

The estimated maximal rotating speeds of different bearings [22,48,65].

4.2. Remaining challenges

Challenges involved with HGMBs are concerned with electromagnetic, hydromechanical, elastic, and rotor dynamic nature.

4.2.1. Mechanical structure

One drawback of HGMBs is the substantial complexity and extra costs. Hence, there have been several reports on simplifying the hybrid structure. A concept of ‘active magnetic damper’ is proposed by Looser et al. [10,48], which integrates the motor coils and the magnetic damper coils. The self-sensing technique is employed, therefore displacement sensors are eliminated. This kind of structure is especially suitable for ultrahigh-speed drive systems. Vannini et al. [55] reported a convergent honeycomb seal that can effectively act both as a gas bearing and a seal in a high-speed AMB-rotor test rig. They focus on selecting a suitable honeycomb seal geometry to optimize its ‘bearinglike’ characteristics, which requires similar differential pressures with the testing conditions as well as high accuracy on assembly and manufacturing. Another concern is the enlarged air gap for the HGMB due to the nested structure. Since the air gap of the gas bearing usually remains the same (no more than 200 μm), the hybrid structure has little impact on the gas bearing. However, the overall impact of the air gap on the AMB needs to be explored. In brief, the structure of the HGMBs can vary to achieve different functions, and innovative structures are expected in future.

4.2.2. Control strategies

The control system of the HGMB has a substantial effect on rotor vibration and energy consumption. The load distribution and rotor offset under different rotating speeds and operation modes can be optimized by varying control gains. Control strategies that can rapidly and automatically find out the optimal control value in different operating conditions need to be developed. When the operation mode is switching, an appropriate control strategy is necessary for a mild transition. Other control algorithms other than PID/PD control could be implemented in HGMBs, such as optimal control [14], sliding mode control [11], robust control [66], fuzzy control [67] and neural networks control [68].

4.2.3. Rotor dynamics

The study of rotor dynamics is of significance in the design process of HGMB. Although by applying the control system the rotor dynamics could be regulated, it is still treated as a ‘black-box’. In-depth research works are needed to fully understand the transient period from AMBs to gas bearings and vice versa, as well as the cooperating mode to prevent excessive vibrations and ensure safe operation. Since most research works focus on experiments, the absences of reliable performance-prediction methods and design guidelines have become the technical hurdles, impeding the application of the HGMBs.

4.2.4. Bearings types

There’re different types of magnetic bearings and gas bearings, leading to many possible combinations of magnetic bearings and gas bearings, which are appropriate for different working conditions. The most common type is the hybridization of AMBs and foil bearings, which has been successfully carried out by experiments. The integration of other types of gas bearings and magnetic bearings needs to be further explored.

4.2.5. Sensing

The radial clearance of AMBs is usually hundreds of micrometers while that of the gas bearings is usually no more than 100 micrometers. Hence, the sensitivity and resolution requirements of the rotor displacement measurement are expected to be higher than that of AMBs, which is considered as a challenge by the proposed hybrid bearing concept [10]. One approach is the self-sensing technique, which has been applied in magnetic bearings to overcome sensor cost and installation problems [69].

5. Summary remarks

In this work, key technological innovations in HGMBs are addressed. Numerical analysis on static and dynamics characteristics of HGMBs are presented. Different configurations of HGMBs and their strengths and weaknesses are discussed. Diverse types of HGMBs with distinct features are introduced. Varied operating modes and the corresponding control systems are demonstrated. These results demonstrate the unique advantages of HGMBs including: (a) increased load capacity, (b) non-contact operation during starts/stops or at low speed, (c) enhanced dynamic stiffness and damping, (d) vibration control for fluid-induced instability and sudden imbalance, (e) reduced power consumption, (f) various operation modes.

Furthermore, future developments and existing challenges concerning novel mechanical structures, optimal control strategies, methods of dynamic behavior prediction, different bearing types and self-sensing techniques are discussed.

The integration of gas bearings and magnetic bearings provides great potential for industry applications. Although currently expensive costs and complicated structures hinder the development, emerging methodologies are expected in the future to meet the challenges in practice.

Footnotes

Acknowledgements

The authors are grateful for the supports of Program of the National Natural Science Foundation of China (no. 51836009), China Scholarship Council (CSC), and research fund of State Key Laboratory of Technologies in Space Cryogenic Propellants.

Nomenclature

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