⚡ electrical engineering

Comparative Electromagnetic Performance of Dual-Stator/Rotor Flux- Switching PM Machines with Different Magnetization Patterns Considering Magnetic Saturation for Bearingless Applications

This paper proposes an accurate analytical subdomain model incorporating magnetic saturation to evaluate and compare the electromagnetic performance, specifically local traction forces and air-gap flux density, of dual-stator/rotor flux-switching permanent magnet machines with tangential, radial, and Halbach magnetization patterns for bearingless applications, with results validated against finite element analysis.

Original authors: E. Shirzad

Published 2026-09-10

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CC BY 4.0

Original authors: E. Shirzad

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of high-speed machinery, such as the compressors that drive industrial gas flows or the flywheels that store energy for the grid, friction is the enemy. Traditional machines rely on physical bearings to support their spinning rotors, but these metal-on-metal contacts generate heat, wear out, and can fail catastrophically under extreme stress. To solve this, engineers have turned to magnetic levitation, where invisible magnetic forces hold the rotor in place without any physical touch. This "bearingless" approach eliminates friction entirely, allowing for higher speeds, longer life, and operation in environments where oil or grease would be disastrous, such as in chemical processing or semiconductor manufacturing. However, creating a stable magnetic suspension is difficult; the same magnetic forces that spin the machine must also push and pull the rotor into a perfect center, a balancing act that requires precise control over the magnetic field.

A recent study by E. Shirzad at the Tooran Institute of Higher Education tackles the challenge of designing these machines more efficiently. The researcher focused on a specific type of motor known as a dual-stator/rotor flux-switching permanent magnet machine. This design is unique because it packs two separate motors into a single frame, with one motor inside the other, separated by a non-magnetic ring. This compact arrangement offers high power and excellent cooling, but predicting how it behaves under heavy loads is mathematically complex. Most engineers rely on computer simulations that take hours to run for every small change in design, while older, faster mathematical models often fail when the machine is pushed to its limits and the iron core becomes magnetically "saturated," meaning it can no longer hold more magnetic field. Shirzad developed a new, faster mathematical model that accounts for this saturation, allowing for rapid and accurate predictions of how the machine will perform.

The core of the research involved testing three different ways to arrange the permanent magnets inside the machine. The first arrangement, called tangential, lines the magnets up side-by-side. The second, radial, points the magnets directly toward the center. The third, known as a Halbach array, is a clever pattern where the magnets are oriented in a specific sequence that concentrates the magnetic field on one side while canceling it out on the other. The researcher used the new mathematical model to simulate the machine's behavior under both normal conditions and extreme overload, where the iron core is pushed to its magnetic limit. These simulations were then compared against detailed, time-consuming computer models to ensure the new method was accurate. The results showed that the new model could predict the machine's magnetic field with high precision, matching the complex simulations while requiring a fraction of the computing time.

When the study looked at which magnet arrangement was best for bearingless applications, the differences were stark. The tangential arrangement produced a magnetic pull that was uneven and shaky, creating strong fluctuations in the force holding the rotor. This instability would likely cause the machine to vibrate and make noise, making it a poor choice for delicate suspension tasks. The radial arrangement was better, offering a smoother force, but it still showed noticeable ripples that could disturb the rotor's stability. The Halbach array, however, stood out as the clear winner. In the simulations, this pattern created a magnetic pressure that was remarkably uniform and steady around the entire rotor. This consistency is crucial for bearingless machines because it allows the rotor to float in a stable position without needing extra, complex control systems to correct for wobbles.

The study confirms that while all three designs can generate power, the Halbach array is the superior choice for applications requiring magnetic suspension. By concentrating the magnetic field more effectively and reducing unwanted fluctuations, it provides the smooth, reliable force needed to keep a high-speed rotor centered without physical contact. The research demonstrates that the new mathematical tool can accurately predict these outcomes even when the machine is working at its hardest, offering engineers a fast and reliable way to design the next generation of friction-free, high-performance machinery. This advancement means that future compressors, turbines, and energy storage systems can be built with greater confidence, knowing they will remain stable and efficient even under the most demanding conditions.

Technical Summary: Comparative Electromagnetic Performance of Dual-Stator/Rotor Flux-Switching PM Machines with Different Magnetization Patterns Considering Magnetic Saturation for Bearingless Applications

Problem Statement
Flux-switching permanent magnet (FSPM) machines are recognized for their high power and torque density, robust structure, and suitability for high-speed applications such as turbo machinery and energy storage systems. However, conventional FSPM machines often suffer from mechanical failures due to friction between the rotor and bearings, exacerbated by axial forces and rapid entry into magnetic saturation under load. While bearingless designs offer a solution, the dual-stator/rotor topology presents complex electromagnetic challenges. Specifically, accurately predicting performance under nonlinear operating conditions (magnetic saturation) is difficult. Traditional analytical models often assume infinite iron permeability, leading to inaccuracies in saturated regions, while Finite Element Analysis (FEA), though accurate, is computationally time-consuming. Furthermore, the impact of different permanent magnet (PM) magnetization patterns—specifically tangential, radial, and Halbach arrays—on the local traction forces and radial pressure distribution critical for bearingless suspension remains to be thoroughly quantified under saturated conditions.

Methodology
The paper proposes an accurate analytical subdomain model designed to evaluate the electromagnetic performance of a dual-stator/rotor FSPM machine. The machine topology consists of an inner and outer machine separated by a diamagnetic ring, featuring concentrated windings and a rotor without magnets or windings to ensure mechanical robustness.

The core of the methodology is a two-step approach to handle magnetic saturation without solving nonlinear field equations directly:

Linear Model Solution: The magnetic field distribution is initially calculated by analytically solving Maxwell's equations (specifically the Poisson and Laplace equations) across various subdomains (air gaps, slots, PMs, and the diamagnetic ring). This step assumes infinite permeability for the iron cores, neglecting magnetic voltage drops in the iron.
Saturation Compensation: To account for nonlinearity, a compensation technique is applied using the actual B-H curves of the iron laminations (Steel 1008). The process involves:
- Calculating the flux passing through stator and rotor teeth based on the radial air-gap flux density ( $B_r$ ) from the linear solution.
- Determining the magnetic field intensity ( $H$ ) for each tooth using the actual B-H curve.
- Computing the magnetic voltage drop across the teeth and deriving a saturation factor ( $K_{sat}$ ) for each tooth.
- Correcting the air-gap flux density by dividing the linear value by the product of the stator and rotor saturation factors.

This corrected model is then used to compute radial and tangential flux components, local traction forces, and radial pressure distributions. The study compares three magnetization patterns:

Tangential array
Radial array
Halbach array

The validity of the analytical model is verified by comparing its results against Finite Element Analysis (FEA) under both linear (low load) and highly saturated (high load) conditions.

Key Contributions

Saturation-Aware Analytical Model: The paper introduces a subdomain model that incorporates magnetic saturation via a compensation technique based on real B-H curves, bridging the gap between the speed of analytical models and the accuracy of numerical methods.
Comparative Analysis of Magnetization Patterns: It provides a detailed side-by-side comparison of tangential, radial, and Halbach magnetization patterns specifically for bearingless applications, analyzing flux density, torque production, and suspension forces.
Radial Pressure Evaluation: The study investigates the local radial pressure distribution on the inner and outer rotors, a critical metric for the stability of magnetic suspension in bearingless machines.
Dual-Stator/Rotor Topology Validation: The model successfully handles the complex geometry of the dual-stator/rotor configuration, including inner and outer air gaps and flux barriers.

Results

Model Accuracy: The analytical model demonstrates very good agreement with FEA results. Under linear conditions, the results match closely. Under extreme saturation conditions (simulated with five times the rated current and roughly 8.5 times the rated remanence flux density), the saturation-compensated model maintains high accuracy, with average errors below 5% and maximum local deviations under 10%. In contrast, the linear model without saturation compensation significantly overestimates flux density in saturated regions.
Magnetization Pattern Performance:
- Halbach Array: This pattern consistently outperformed the others. The paper notes that the Halbach array possesses higher flux density all over the structure compared to the other configurations. Crucially for bearingless applications, it produced the most uniform, steady, and symmetric radial pressure distribution with minimal fluctuations.
- Radial Array: Showed better performance than the tangential array with smoother pressure distribution but still exhibited noticeable ripples.
- Tangential Array: Produced highly uneven forces with sharp pressure variations, leading to significant potential for vibration and noise, making it less suitable for bearingless suspension.
Suspension Capability: The Halbach array was identified as the superior candidate for bearingless applications because its symmetric topology and uniform radial force distribution enable stable magnetic suspension without requiring additional windings or dedicated control currents to counteract unbalanced magnetic forces.

Significance and Claims
The paper claims that the proposed analytical subdomain model is a rapid, reliable, and accurate tool for the design and analysis of dual-stator/rotor FSPM machines, offering a computationally efficient alternative to FEA while maintaining high fidelity even under nonlinear operating conditions. The study concludes that for bearingless applications requiring smooth radial force control and low vibration, the Halbach magnetization pattern is the optimal choice among the three configurations examined. The work supports the development of compact, high-power-density machines suitable for chemical industries, semiconductor manufacturing, and turbo machinery where mechanical reliability and contactless operation are paramount.

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