Bearing technology must be supported to attain high-speed and high-efficiency rotating applications. Previous research focused on performance enhancement and optimization, rather than comparative studies among magnetic bearings. This study presents the design and comparison of five magnetic bearing types for high-speed rotating applications: an 8-pole conventional heteropolar, fork-type heteropolar, hybrid fork-type homopolar, and hybrid homopolar magnetic bearings. For quantitative evaluation, mechanical parameters were selected to ensure a uniform coil volume and current supply. The heteropolar magnetic bearings employed 35PN440 steel, whereas the homopolar magnetic bearings utilized pure solid iron. The bias currents were determined based on the respective material properties. The driving circuits were compared by comparing models with and without permanent magnets. The magnetic flux density was assessed at equilibrium and maximum control current, and the loss characteristics were evaluated at 30 000 rpm. Linear control regions were identified by analyzing the relationships between the electromagnetic force, current, and displacement. As a result, the most suitable magnetic bearing for high-speed rotating applications is proposed.

In the high-tech industry, the demand for the convergence of information technology and ultra-precision technology in the machinery sector is fast increasing. Among these advancements, magnetic bearing technology has attracted considerable attention as it enables precise and intelligent control of high-speed rotation systems as well as its advantages in terms of energy efficiency, lack of lubrication, high rotational speed capability, and precision control.1–8 

Magnetic bearings can be classified into two main types based on their magnetic flux paths: homopolar and heteropolar. The former maintains the same polarity in all radial directions, whereas the latter exhibits varying polarities. Numerous studies have compared these two types to enhance performance by considering factors, such as eddy current loss, rotor heat generation, and axial space variations.1,5,7

Moreover, magnetic bearings can be grouped into three main types: active (AMB), passive, and hybrid magnetic bearings (HMB). AMBs offer superior control capabilities and high stiffness, whereas AMBs require improvements in terms of system linearity and dynamic performance. To address these issues, the HMB design leverages permanent magnets to provide a bias field while utilizing an electromagnet for control. This hybrid configuration offers several advantages, including reduced heat generation, decreased electromagnet usage, elimination of the bias current, and enhanced energy efficiency.2,5–7

This study enhanced the structure and performance of existing heteropolar magnetic bearings by introducing a novel design known as fork-type heteropolar magnetic bearings. These bearings were compared with existing magnetic bearing types. The comparison was conducted by comparing force-displacement and force-current factor coefficients as well as utilizing electromagnetic finite element analysis (FEM).

The different bearing configurations are shown in Fig. 1: an 8-pole conventional heteropolar MB (a), a fork-type heteropolar MB (b), and a hybrid fork-type MB (c). Furthermore, some homopolar MBs exclusively utilize electromagnets (d) or a combination of electromagnets and permanent magnets (e).

FIG. 1.

(a) Conventional heteropolar magnetic bearing structure (CHP) (b) fork-type heteropolar magnetic bearing structure (FHP) (c) hybrid fork-type heteropolar magnetic bearing structure (H-FHP) (d) homopolar magnetic bearing structure (HoP) (e) hybrid homopolar magnetic bearing structure (H-HoP).

FIG. 1.

(a) Conventional heteropolar magnetic bearing structure (CHP) (b) fork-type heteropolar magnetic bearing structure (FHP) (c) hybrid fork-type heteropolar magnetic bearing structure (H-FHP) (d) homopolar magnetic bearing structure (HoP) (e) hybrid homopolar magnetic bearing structure (H-HoP).

Close modal

The mechanical parameters of the five magnetic bearings are presented in Fig. 2. The mechanical parameters of the heteropolar and homopolar magnetic bearing types are shown in Figs. 2(a) and 2(b), respectively. Magnetic bearings operate more effectively when the area exposed to the magnetic field on the rotating component is larger and when the size of the bearing is larger, and the strength of the magnetic force (determined by the number of coil turns) is greater. To facilitate a quantitative comparison of the magnetic bearing performance, it was necessary to ensure uniformity in detailed parameters such as the dimensions of the rotating body, bearing outer diameter, and total number of coil turns as illustrated in Table I.

FIG. 2.

Magnetic bearing parameter (a) heteropolar type (models a, b, and c) (b) homopolar type (models d and e).

FIG. 2.

Magnetic bearing parameter (a) heteropolar type (models a, b, and c) (b) homopolar type (models d and e).

Close modal
TABLE I.

Size specifications for different magnetic bearings.

ParameterHeteropolarHomopolarUnit
Bearing diameter d 44 mm 
Shaft diameter di 27 mm 
Rotor diameter dr 43 mm 
Outer diameter da 94 mm 
Slot width ws mm 
Bearing width b 25 mm 
Nominal air gap s0 0.5 mm 
Total number of turns 512 Turns 
ParameterHeteropolarHomopolarUnit
Bearing diameter d 44 mm 
Shaft diameter di 27 mm 
Rotor diameter dr 43 mm 
Outer diameter da 94 mm 
Slot width ws mm 
Bearing width b 25 mm 
Nominal air gap s0 0.5 mm 
Total number of turns 512 Turns 

The homopolar magnetic bearing necessitates cross-laminated and bias flux flows, potentially through an unlaminated rotor return path, leading to an increased bias flux reluctance owing to the stacking factor effect. Heteropolar magnetic bearings employ a structurally stacked design utilizing 35PN440 laminated silicon steel plates, whereas pure iron is employed in the construction of homopolar magnetic bearings. The magnitude of the bias current considers the saturation characteristics of each material. Furthermore, linear control is achievable only when electromagnets are designed to operate below the saturated magnetic flux density limits of the electric steel sheet (1.6 T) and pure iron (1.2 T), even under the application of maximum bias and control currents.

Magnetic bearings employ switching power amplifiers for power consumption control.3 They utilize either half- or full-bridge topology circuits. The control circuit of an AMB, which relies solely on electromagnets to generate and regulate the bias current, is shown in Fig. 3(a). In this 4° of freedom (DOF) AMB system, eight coils were employed, necessitating four pulse width modulation (PWM) circuits, 16 power switches, and isolated drive circuits. This configuration results in a higher risk of failure and reduced reliability. In contrast to the AMB control system, HMBs operate efficiently by utilizing permanent magnets (PM) and require only a control current. As shown in Fig. 3(b), HMBs require only half the number of PWM circuits, power switches, and driving circuits because of their reliance on PMs, thereby offering a more streamlined and reliable solution.

FIG. 3.

(a) AMB’s control circuit (models a, b, and d) (b) hybrid magnetic bearing’s control circuit (models c and e).

FIG. 3.

(a) AMB’s control circuit (models a, b, and d) (b) hybrid magnetic bearing’s control circuit (models c and e).

Close modal

The levitation force generated by magnetic bearings can be categorized into two types: one where electromagnets alone are used (AMBs), and another where both electromagnets and permanent magnets are employed in conjunction (HMBs).

The magnetic flux and levitation force in an AMB system is expressed as follows:
Bem=μ0Ni2s0,Fem=Bem22A2μ0=μ0N2A4is02
Bem denotes a magnetic field of electromagnets, μ0 is the permeability of free space, N is the number of coil turns, I is the current, s0 is the air gap, A is the cross-sectional area and F denotes the levitation force generated by electromagnets.
Furthermore, the force equilibrium equation for the levitation system according to Newton’s second law of motion as follows:
mz̈t=Fi,z+fdt+mg
Through linear approximation around the equilibrium point i0,z0, we can derive a linear model utilizing the force equilibrium equation as follows:
Fem=μ0N2A4i0+Δitz0+Δzt2+fdt+mg;μ0N2A4i0z021+2iti02ztz0;μ0N2Ai02z02it+μ0N2Ai022z03ztfd(t)
The force-current coefficient ki and force-displacement coefficient kx can be obtained as follows:
ki=μ0N2Ai02z02,kx=μ0N2Ai022z03
For the levitation force in a hybrid system where both magnets and electromagnets are used, the process is nearly identical to the one described above. However, we can linearize it by treating the thickness of the magnets as an air gap, and the linearization would proceed as follows:
Fpm=Bpm22A2μ0=Bpm2Aμ0=μ0Hpmhpm1zg2Aμ0=Aμ0Hpmhpm2μ0zg2
Whereas the total air gap in the system, consists of the air gap s0 and the air gap of the permanent magnet hpm.
gt=2s0+hpm
The levitation force due to the electromagnets is given by:
Fem=Bem22A2μ0=Bem2Aμ0=μ0Ni2(hpm+2zg)2Aμ0=μ0N2A4ihpm+2zg2=μ0N2A4igt2
Therefore, the levitation force in a system incorporating both electromagnets and permanent magnets can be expressed as:
F=Fpm+Fem=Aμ0Hpmhpm2μ0zg2+μ0N2A4ihpm+2zg2
Using Taylor series expansion to linearize the equation it can be expressed as:
F=μ0N2A4z0+hpm2+μ0N2Ai02z0+hpm2ixμ0N2Ai022z0+hpm3x+Aμ0Hpmhpm2μ0z02Aμ0Hpmhpm2μ0z03x=μ0N2A4z0+hpm2+Aμ0Hpmhpm2z02+μ0N2Ai02z0+hpm2ixμ0N2Ai022z0+hpm3+μ0AHpmhpm2z03x=k0+kikxkxx
The force-current coefficient ki and force-displacement coefficient kx can be obtained as follows:
ki=μ0N2Ai02z0+hpm2,kx=μ0N2Ai022z0+hpm3+μ0AHpmhpm2z03

This equation is only a linear approximation of the true relationship, and therefore, accurate only in the vicinity of the operating point. However, it has been demonstrated through extensive practical experience over many years to perform exceptionally well across a wide range of applications. Consequently, the force-current coefficient and force-displacement coefficient derived from this equation are of utmost importance.

In limited cases such as rotor-stator contact, and flux saturation, more detailed and typically nonlinear models may be necessary. Nonetheless, for the majority of applications, this equation proves to be highly useful and provides accurate approximations. Leveraging these values enables effective control of magnetic bearings.

Stiffness coefficients should be determined with accuracy to achieve precise control of the dynamic performance based on the input current of the magnetic bearings or rotor displacement. In this section, the magnetic bearing models are analyzed by utilizing ANSYS Electronics, focusing on their magnetization characteristics, electromagnetic force properties, and loss analysis.

The magnetic flux density distributions when a bias current is applied to the heteropolar and homopolar magnetic bearings are shown in Figs. 4(a) and 4(b), whereas the flux density distributions when a full control current is applied to each bearing are shown in Figs. 4(c) and 4(d). Either as observed in Figs. 4(e) and 4(f), when the air-gap flux density of each magnetic bearing transitions from being solely influenced by the bias flux to the sum of the bias and control flux, superimposition or cancellation of the current occurs. These results demonstrate the direct proportionality between the magnetic force and control current.

FIG. 4.

(a) Magnetic flux density distribution of heteropolar magnetic bearings at the equilibrium point, (b) magnetic flux density distribution of homopolar magnetic bearings at the equilibrium point, (c) magnetic flux density distribution of heteropolar magnetic bearings at full control current load, (d) magnetic flux density distribution of homopolar magnetic bearing at full control current load, (e) bias flux density waveform at full-load of heteropolar magnetic bearing, (f) bias flux density waveform at full-load homopolar magnetic bearing.

FIG. 4.

(a) Magnetic flux density distribution of heteropolar magnetic bearings at the equilibrium point, (b) magnetic flux density distribution of homopolar magnetic bearings at the equilibrium point, (c) magnetic flux density distribution of heteropolar magnetic bearings at full control current load, (d) magnetic flux density distribution of homopolar magnetic bearing at full control current load, (e) bias flux density waveform at full-load of heteropolar magnetic bearing, (f) bias flux density waveform at full-load homopolar magnetic bearing.

Close modal

The control currents for the five models were varied in 1 A increments within a range of −2–2 A, and the rotor’s position was adjusted along the x-axis in increments of 0.1 mm within a range of −0.2–0.2 mm from the central position. The resulting changes in the electromagnetic forces are shown in Fig. 5. The FHP model had the highest force-current factor, with a value of 47.06 N/A, which is 125.3% larger than that of the second-largest model (Model a). The force-current and force-displacement factors for each model are listed in Table II.

FIG. 5.

Magnetic force with control current and X-axis rotor displacement: (a) CHP, (b) FHP, (c) H-FHP, (d) HoP, and (e) H-HoP.

FIG. 5.

Magnetic force with control current and X-axis rotor displacement: (a) CHP, (b) FHP, (c) H-FHP, (d) HoP, and (e) H-HoP.

Close modal
TABLE II.

Force-current factor (Ki) and force-displacement factor (Kx) of the five models.

(a)(b)(c)(d)(e)
Ki [N/A] 37.6 47.1 27.2 23.6 6.3 
Kx [N/mm] 176.2 219.6 158.3 76.0 94.3 
(a)(b)(c)(d)(e)
Ki [N/A] 37.6 47.1 27.2 23.6 6.3 
Kx [N/mm] 176.2 219.6 158.3 76.0 94.3 

Table III lists the core and rotor loss data for five distinct models. Homopolar magnetic bearings (Models d and e) exhibited significantly lower core and rotor losses compared with heteropolar magnetic bearings (Models a, b, and c). Owing to changes in polarity based on the rotating body, heteropolar magnetic bearings experienced substantial eddy currents and iron losses, resulting in increased heat generation and magnetic flux leakage.

TABLE III.

Losses exhibited by the five models.

(a)(b)(c)(d)(e)
Core loss [W] 10.8 12.1 19.18 2.03 3.35 
Rotor loss [W] 247.74 314.45 998.99 0.75 1.78 
(a)(b)(c)(d)(e)
Core loss [W] 10.8 12.1 19.18 2.03 3.35 
Rotor loss [W] 247.74 314.45 998.99 0.75 1.78 

This study comparatively investigated the magnetic characteristics of five types of radial magnetic bearings. Among the magnetic bearings with identical mechanical specifications, the fork-type magnetic bearing that can generate significant forces was the most suitable. In terms of control, the incorporation of magnetic bearings proved cost-effective, considering the switching device considerations and operational responsiveness. Furthermore, magnetic bearings exhibited considerably low losses compared with conventional bearings. Notably, the homopolar type exhibited an exceptionally low loss on a per-unit weight basis. In high-speed rotating applications, ensuring the performance of rotor dynamics is essential assuming adequate cooling conditions. Therefore, the fork-type heteropolar magnetic bearing model was the most suitable for high-speed applications among the five models. In future studies, the barely stable response characteristics of magnetic bearings will be explored for potential applications in high-speed machinery and the vibration performance will be assessed following their integration into real-world applications.

This work was supported by the National Research Foundation of Korea (NRF) funded by the Korean Government under Grant 2022R1I1A3072104.

The authors have no conflicts to disclose.

Sujin Noh: Conceptualization (equal); Data curation (equal); Investigation (lead); Methodology (equal); Project administration (lead); Software (equal); Validation (lead); Writing – original draft (lead); Writing – review & editing (equal). Joo Hong Park: Conceptualization (equal); Validation (supporting); Visualization (supporting). Kyung-Hun Shin: Data curation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). Han-wook Cho: Conceptualization (equal); Methodology (equal); Project administration (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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