⚡ electrical engineering

Analytical Prediction in a Double-Rotor Single-Stator Switch Reluctance Machine with Core-less Stator Taking into Consideration Saturation for Bearingless Applications

This paper proposes an exact analytical subdomain model with a saturation compensation technique for a double-rotor single-stator switch reluctance machine with a core-less stator, enabling accurate prediction of radial pressure for bearingless applications across arbitrary tooth configurations.

Original authors: E. Shirzad

Published 2026-09-01

📖 5 min read🧠 Deep dive

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

Imagine a world where machines spin without ever touching a bearing, floating in a cushion of magnetic force. This is the promise of bearingless technology, a field that seeks to eliminate friction, wear, and the need for lubrication by using magnetic fields to levitate and rotate parts simultaneously. To make this work, engineers must design motors that can generate two distinct forces at once: a tangential pull to spin the rotor and a radial push to keep it centered in mid-air. If the magnetic forces are miscalculated, the rotor crashes into the stator, ending the suspension. The challenge lies in predicting these invisible forces with perfect accuracy, especially when the metal parts inside the machine become "saturated," a state where the iron can no longer carry any more magnetic flux, much like a sponge that has absorbed all the water it can hold.

In a recent study, a researcher at the Tooran Institute of Higher Education tackled this problem for a specific, complex machine design known as a double-rotor single-stator switched reluctance motor. This machine is unique because it has two rotating cylinders, one inside the other, surrounding a stationary core that holds the windings. Unlike traditional motors that use permanent magnets, this design relies on the shape of the iron teeth to create motion, making it robust, simple, and capable of running at very high speeds. The researcher focused on a version of this motor that lacks a solid iron core in the stator, a "core-less" design that saves weight and reduces energy loss. The goal was to create a mathematical model that could predict the magnetic pressure on the rotors without needing to run slow, expensive computer simulations every time a design change was made.

The study began by developing a precise analytical model, a set of mathematical rules that describe how magnetic fields flow through the machine's different regions: the inner rotor, the outer rotor, and the air gaps between them. Initially, the model assumed the iron parts were perfect conductors of magnetism, a simplification that made the math easier but less accurate. To fix this, the researcher introduced a new technique to account for magnetic saturation. This method works by calculating how much magnetic flux passes through each tooth and the back-iron of the rotors, then checking the actual properties of the steel used. When the steel becomes saturated, the model applies a correction factor, effectively saying, "The iron is full; the magnetic field cannot grow as much as the simple math predicted." This process is repeated iteratively, refining the calculation until the predicted magnetic fields stabilize and match the physical reality of the steel's behavior.

The researcher tested this new model against two other approaches: a standard linear model that ignores saturation, and a finite element analysis, which is a highly detailed computer simulation that breaks the machine into thousands of tiny pieces to solve the physics equations. The tests were run on two versions of the motor, one with a single layer of wire windings and another with a double layer, both operating at a current density of 6 amperes per square millimeter. The results showed a clear difference between the methods. The simple linear model significantly overestimated the radial pressure, the force pushing the rotor outward. In a bearingless system, this overestimation is dangerous; a control system relying on these numbers might believe it has more lifting power than it actually does, leading to instability or a collision between the rotor and the stator.

In contrast, the new model with the saturation correction matched the detailed computer simulations with remarkable accuracy. It correctly predicted that the magnetic pressure drops in the saturated regions, providing a realistic picture of the forces at play. The study also revealed that the double-layer winding configuration produced a more symmetrical distribution of pressure around the rotor. This symmetry is crucial for bearingless applications because it reduces the unbalanced magnetic pull that can shake the machine, making the active suspension control easier to manage. The findings confirm that while simple math is fast, it fails when the machine is pushed hard, but the new iterative correction method bridges the gap, offering a tool that is both fast enough for design optimization and accurate enough to ensure the rotor stays safely levitated.

This work fills a significant gap in the engineering of these dual-rotor machines. Before this study, there was no analytical model capable of handling the specific geometry of a core-less stator with two rotors while accounting for the non-linear behavior of saturated iron. By providing a reliable way to calculate the radial pressure, the researcher has given engineers a practical tool to design these high-speed, friction-free machines with confidence. The model ensures that the magnetic forces are predicted correctly, preventing the catastrophic failures that come from overestimating the machine's lifting capacity. As the demand for high-speed, reliable electric drives grows in applications like electric vehicles and industrial compressors, this ability to predict magnetic behavior accurately without the heavy cost of full computer simulations becomes an essential step toward building the next generation of floating, frictionless machinery.

Technical Summary: Analytical Prediction in a Double-Rotor Single-Stator Switch Reluctance Machine with Core-less Stator Taking into Consideration Saturation for Bearingless Applications

Problem Statement
Switched Reluctance Machines (SRMs) are increasingly favored for high-speed applications due to their mechanical reliability, simple structure, and lack of brushes. A specific topology, the Double-Rotor Single-Stator Switch Reluctance Machine (DRSSRM) with a core-less stator, offers unique advantages, including high winding space, reduced core losses in the stator back-iron, and the ability to transfer power through two independent mechanical ports. This makes it suitable for complex energy management systems, such as hybrid electric vehicles and wind turbines.

However, the design and control of these machines, particularly for bearingless applications, require precise prediction of radial pressure (radial traction) to ensure stable magnetic levitation. While Finite Element Method (FEM) simulations provide high accuracy, they are computationally intensive and impractical for rapid design optimization. Conversely, existing analytical models often assume infinite iron permeability, failing to account for magnetic saturation. In SRMs, where the entire flux path passes through iron, saturation significantly alters flux distribution. Without accurate saturation modeling, analytical predictions can overestimate radial forces, leading to potential instability in suspension controllers. Currently, no exact analytical subdomain model exists for the DRSSRM with a core-less stator that accounts for magnetic saturation in both single-layer and double-layer winding configurations.

Methodology
The paper proposes an exact analytical subdomain model for the DRSSRM with a core-less stator. The methodology proceeds in two main stages:

Linear Subdomain Model: The machine geometry is divided into distinct sub-regions (inner rotor slots, inner airgap, stator slots, outer airgap, and outer rotor slots). The magnetic vector potential ( $A$ ) is solved in each region using Maxwell's equations, initially assuming infinite iron permeability. Boundary conditions are applied to ensure continuity of the vector potential and tangential magnetic field intensity across interfaces. This yields the radial and tangential flux density distributions for both single- and double-layer winding setups.
Saturation Compensation Technique: To bridge the gap between the linear model and reality, an iterative saturation compensation technique is introduced. This process:
- Calculates the total flux through each stator tooth, rotor tooth, and rotor back-iron using the linear flux density results.
- Determines the average flux density and corresponding magnetic field intensity ( $H$ ) for each iron component using the actual $B-H$ curve of the lamination steel (e.g., Steel 1008).
- Computes magnetic voltage drops and defines saturation factors for the teeth and yoke. These factors represent the ratio of total magnetic voltage drop (iron + airgap) to the airgap drop alone.
- Corrects the linear air-gap flux density by dividing it by the product of the relevant saturation factors.
- Iterates this correction process until the relative change in flux density falls below a specified tolerance, ensuring convergence.

Finally, the corrected flux densities are used to calculate the radial and tangential pressure distributions on the rotor surfaces via the Maxwell stress tensor.

Key Contributions

First Analytical Model for DRSSRM: The paper presents the first exact analytical subdomain model specifically for a double-rotor single-stator SRM with a core-less stator, applicable to arbitrary numbers of rotor and stator teeth.
Saturation-Aware Correction: A novel, iterative saturation compensation technique is developed that accounts for local saturation effects in stator teeth, rotor teeth, and the rotor back-iron, moving beyond the limitations of infinite permeability assumptions.
Dual Winding Analysis: The model is rigorously validated for both single-layer and double-layer winding configurations, providing a comprehensive tool for different design choices.
Bearingless Focus: The primary output is the accurate prediction of radial pressure, which is critical for the design of active magnetic suspension systems in bearingless applications.

Results and Validation
The proposed nonlinear model was validated against FEM simulations using a machine with specific geometric parameters (e.g., 12 stator slots, 10 inner/outer rotor slots, 6 A/mm² current density).

Flux Density: The corrected nonlinear model showed excellent agreement with FEM results for both radial and tangential flux density components in the inner and outer airgaps.
Radial Pressure: The linear model significantly overestimated radial pressure in saturated regions. In contrast, the nonlinear model with saturation compensation matched FEM results with high accuracy. This distinction is critical for bearingless systems, where overestimation could lead to controller instability.
Winding Comparison: The double-layer winding configuration demonstrated a more symmetric radial pressure distribution compared to the single-layer setup. This symmetry reduces unbalanced magnetic pull, simplifying active suspension control and reducing vibration risks.
Tangential Pressure: The model also accurately predicted tangential pressure, which governs electromagnetic torque, showing strong alignment with FEM data for both winding types.

Significance
The paper claims that this work fills a longstanding void in the analytical modeling of the DRSSRM topology. By providing a tool that is both computationally efficient (unlike FEM) and accurate under saturation (unlike linear analytical models), the proposed method enables rapid design optimization and reliable structural assessment. Specifically, it offers engineers a practical solution for predicting the radial forces necessary for stable rotor levitation in high-speed bearingless applications, ensuring mechanical integrity without the prohibitive cost of repeated FEM simulations. The study concludes that the double-layer configuration, analyzed through this model, offers superior performance for bearingless designs due to its balanced pressure distribution.

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