⚡ electrical engineering

Analytical Modeling of 12/10 stator/rotor pole configuration of Switched Reluctance Motors Considering Magnetic Saturation for Blood Pump Applications

This paper develops a saturation-aware analytical model to compare 3-, 4-, and 6-phase 12/10 switched reluctance motors, identifying the optimal phase configuration that minimizes torque ripple and radial force fluctuations to enhance bearingless drive stability and hemocompatibility for blood pump applications.

Original authors: E. Shirzad

Published 2026-10-21

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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

Inside the human body, life depends on a steady, rhythmic flow. For patients whose hearts can no longer pump blood effectively, doctors sometimes implant a mechanical device to take over that vital job. These blood pumps are marvels of modern medicine, but they come with a hidden challenge: the machine that drives them must be incredibly smooth. If the motor inside the pump stutters, vibrates, or jerks, it creates mechanical stress that can damage the delicate red blood cells flowing through it. This damage, known as hemolysis, can lead to serious complications for the patient. Therefore, the goal is not just to move fluid, but to do so with a silence and steadiness that the human body can tolerate without harm.

To achieve this, engineers often look to a type of electric motor called a switched reluctance motor. Unlike many other motors that rely on permanent magnets or brushes, these machines are built with simple, robust iron cores and copper windings. They are tough, easy to cool, and can be controlled with great precision. However, like any machine with moving parts, they have a natural tendency to produce small fluctuations in force as they turn. In a standard design, these fluctuations can cause the motor to vibrate. For a blood pump, even a tiny vibration is a problem. The question researchers face is how to design a motor that is powerful enough to drive the pump but smooth enough to protect the blood.

A researcher recently tackled this problem by comparing different ways to arrange the electrical phases—the separate circuits that power the motor—within a specific motor design. They focused on a configuration with twelve stationary poles on the outside and ten rotating poles on the inside. This specific shape is known to be efficient, but the researcher wanted to know if changing the number of electrical phases from the standard three to four or six would make the motor smoother. They built a detailed mathematical model to simulate how the motor behaves under heavy load, a condition where the iron inside the motor becomes magnetically "saturated," meaning it cannot carry any more magnetic force. This saturation is a critical factor because it changes how the motor produces force and vibration.

The researcher developed a new way to calculate these forces that accounts for the complex interaction of magnetic fields in two directions at once. In simpler terms, they did not just look at how the magnetic field pushes straight out from the center; they also calculated how it pulls sideways. This two-part approach allowed them to predict the motor's behavior with high accuracy, matching the results of much more time-consuming computer simulations. They then used this model to test three different versions of the motor: one with three phases, one with four, and one with six.

The results were clear and decisive. The three-phase motor, which is the most common design, produced a strong average force but suffered from significant fluctuations. The force it generated rose and fell sharply as the rotor turned, creating a ripple that would likely cause unwanted vibration. The four-phase version, however, failed completely in this specific design. The researcher found that the timing of the electrical pulses in a four-phase setup clashed with the physical shape of the twelve-pole motor. Instead of working together, the forces canceled each other out, resulting in a motor that could not produce a steady, usable rotation. This configuration was ruled out as unsuitable for this application.

The six-phase motor, by contrast, performed exceptionally well. By dividing the electrical power into six separate streams, the motor could overlap its force pulses more frequently. This created a much smoother output, with the fluctuations reduced by half compared to the three-phase version. The force pushing on the rotor was not only stronger but also far more balanced, meaning the rotor was pulled evenly in all directions rather than being tugged unevenly to one side. This balance is crucial for "bearingless" designs, where the rotor floats in the air without touching any physical supports, held in place only by magnetic forces. If the magnetic pull is uneven, the rotor will wobble, increasing the risk of failure.

In the end, the study points to the six-phase configuration as the superior choice for medical blood pumps. It offers the best combination of power and smoothness, minimizing the vibrations that could harm blood cells. The researcher confirmed that their new mathematical model could predict these results accurately without needing to build a physical prototype first. This gives engineers a reliable tool to design quieter, safer, and more reliable life-saving devices, ensuring that the mechanical heart of the pump beats in perfect harmony with the human body it serves.

Technical Summary: Analytical Modeling of 12/10 Stator/Rotor Pole Configuration of Switched Reluctance Motors Considering Magnetic Saturation for Blood Pump Applications

Problem Statement
The clinical success of implantable rotary blood pumps depends heavily on minimizing mechanical interactions that cause blood trauma, specifically hemolysis and thrombosis. Rotor vibration, torque ripple, and bearing friction are primary contributors to these issues. While Switched Reluctance Motors (SRMs) offer a robust, magnet-free topology suitable for such applications, the specific performance of different phase configurations (3-, 4-, and 6-phase) with a 12/10 stator/rotor pole arrangement under magnetic saturation has not been systematically compared. Furthermore, existing analytical models often neglect the tangential component of flux density or simplify saturation effects, leading to inaccuracies in predicting torque ripple and radial forces—critical parameters for bearingless motor stability and blood pump reliability.

Methodology
The study develops a unified two-dimensional analytical model based on the subdomain method and Fourier series to predict electromagnetic torque and radial force. The methodology proceeds in two main stages:

Linear Field Solution: The machine geometry is divided into subdomains (stator slots, airgap, rotor slots). Assuming infinite permeability for the iron core, the magnetic vector potential is solved using Laplace's and Poisson's equations. Boundary conditions ensure continuity of the magnetic vector potential ( $A_z$ ) and tangential magnetic field intensity ( $H_\theta$ ) at interfaces.
Two-Component Saturation Correction Model: To address the limitations of linear models under high-load conditions, an iterative correction technique is applied. Unlike conventional models that correct only the radial flux density, this approach accounts for both radial ( $B_r$ $B_{r}$ ) and tangential ( $B_\theta$ $B_{θ}$ ) flux density components.
- The algorithm calculates flux in teeth and yokes, determines average flux density, and retrieves the corresponding magnetic field intensity ( $H$ ) from the actual B-H curve of the lamination steel.
- Local saturation factors are defined for each section to quantify the reduction in effective airgap flux.
- Both radial and tangential linear flux density components are corrected by dividing them by the product of these saturation factors.
- The process iterates until the relative change in flux density falls below a specified tolerance.

The model is applied to 3-phase, 4-phase, and 6-phase SRMs with a 12/10 pole configuration and concentrated windings. The results are validated against Finite Element Method (FEM) simulations under a high current density of 30 A/mm² to ensure deep magnetic saturation.

Key Contributions

Novel Saturation Model: The development of the "Two-Component Saturation Correction Model," which simultaneously incorporates radial and tangential flux density components in the saturation process. This provides a more physically consistent representation of the magnetic field compared to single-component or linear models.
Comparative Analysis: A systematic investigation of torque ripple and radial force characteristics across 3-, 4-, and 6-phase 12/10 SRM configurations under saturated conditions.
Application-Specific Insight: Linking the electromagnetic performance (specifically unbalanced radial forces and torque ripple) to the mechanical stability requirements of bearingless blood pump drives, where vibration directly impacts hemocompatibility.

Results
The analytical model demonstrated excellent agreement with FEM simulations across all configurations, validating the accuracy of the saturation correction approach. Key comparative findings include:

3-Phase Configuration: Produced an average torque of approximately 18 N·m but exhibited a high torque ripple of 0.88. The radial force distribution showed significant fluctuations and unbalanced magnetic forces (UMF), indicating higher vibration potential.
4-Phase Configuration: The 12/10 structure was found to be inherently incompatible with four-phase excitation. The torque waveform was highly oscillatory with no stable average value due to harmonic mismatch, rendering this configuration unsuitable for the study's intended application. Consequently, it was excluded from radial force analysis.
6-Phase Configuration: Demonstrated superior performance with the smoothest torque profile, a torque ripple of 0.44, and an average torque of approximately 31 N·m. The radial force distribution was significantly more symmetric, resulting in the lowest UMF and minimal force fluctuations.

Significance and Claims
The paper claims that the 6-phase configuration is the optimal choice for 12/10 SRMs in blood pump applications. By minimizing torque ripple and radial force fluctuations, the 6-phase design reduces mechanical oscillations and bearing stress. In the context of implantable blood pumps, this reduction in vibration is critical for lowering the risk of hemolysis and improving long-term device reliability.

The proposed analytical model is presented as a computationally efficient alternative to time-consuming FEM simulations, offering a reliable tool for the early-stage design and optimization of bearingless drives. The study concludes that selecting the appropriate phase configuration (specifically 6-phase over 3-phase) is a fundamental design step for achieving quieter, more reliable, and biocompatible motor drives for medical applications.

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