Electromagnetic Field Simulation of Switched Reluctance Motors (SRM)
Theory and Physics
SRM Operating Principle
Does a switched reluctance motor not use permanent magnets? No rare earths needed?
Exactly. The rotor is a simple salient pole iron structure with no magnets or coils. The advantages are rare-earth-free, low cost, and high-temperature tolerance. However, the major challenges are large torque ripple and noise. For example, recent Nidec SRMs for washing machines have achieved a 60% noise reduction using AI-based control.
How does it generate torque without magnets? I can't picture it at all...
Simply put, it utilizes the "force that attracts iron to a magnet." When current flows through the stator coil to create an electromagnet, the iron salient poles of the rotor are attracted to it. This is reluctance torque. It exploits the property that the rotor moves to the position where the inductance of the magnetic circuit is maximized.
I see! So if you switch the coil currents at the right timing, it rotates continuously?
Exactly. In a typical 8/6 structure (8 stator poles, 6 rotor poles), energizing phases A → B → C → D in sequence causes the rotor's salient poles to be successively attracted to the stator's salient poles, resulting in rotation. However, the phase switching timing and current waveform are critical; getting them wrong can result in no torque or even reverse rotation.
The basic structural characteristics of an SRM are summarized below.
| Item | SRM | PMSM (Reference) |
|---|---|---|
| Rotor Structure | Salient pole iron core only (no magnets/coils) | Embedded/surface-mounted permanent magnets |
| Rare Earth Use | None | Uses neodymium magnets |
| Heat Resistance | Operable above 250°C | Limited by magnet demagnetization temp (~150°C) |
| Torque Ripple | Large (20–40%) | Small (3–8%) |
| Electromagnetic Noise | Large (challenge) | Small |
| Cost | Low | Higher due to magnets |
| Main Applications | Appliances, industrial, EV (research stage) | EV, servo |
Torque Generation Mechanism and Governing Equations
What does the torque equation for an SRM look like? Is it completely different from a PMSM?
Fundamentally different. PMSM torque is "current × magnet flux," but SRM torque comes from the rate of change of inductance. In the linear region (no magnetic saturation), the instantaneous torque is:
Here, $I$ is the phase current [A], $L$ is the inductance [H], and $\theta$ is the rotor angle [rad]. Three important points can be understood from this equation.
- Torque is proportional to the square of the current — Independent of current direction, so it can be driven with unidirectional current (unipolar). Sinusoidal AC like in PMSMs is not required.
- Positive torque only when $dL/d\theta > 0$ — Current must be applied during the interval where inductance is increasing and cut off before entering the decreasing interval.
- Approximate formula ignoring magnetic saturation — In actual machines, the iron core saturates, making this linear formula insufficient.
What happens when it saturates? Does the equation change?
Yes, in the saturation region, inductance also depends on current, so it becomes $L(\theta, I)$. In this case, accurate torque calculation requires derivation from co-energy:
$\psi(\theta, i)$ is the flux linkage [Wb]. This function cannot be obtained analytically, so the standard practical approach is to create a 3D map $\psi(\theta, I)$ of flux linkage vs. current vs. angle using FEM and calculate torque via numerical differentiation.
Furthermore, the electrical circuit equation for each phase of an SRM is as follows:
The second term on the right is the self-inductance term (equivalent to $L \cdot dI/dt$), and the third term is the back-EMF term ($e = \omega \cdot d\psi/d\theta$, proportional to rotational speed).
Inductance Profile L(θ,I)
What shape does the $L(\theta, I)$ map take? I can't grasp the image...
At low currents, it's close to a clean trapezoidal wave. It reaches a maximum $L_{\max}$ at the position where the rotor salient pole faces the stator salient pole (aligned position) and a minimum $L_{\min}$ at the shifted position (unaligned).
However, when the current increases, the iron core saturates near the aligned position, causing $L_{\max}$ to drop significantly. On the other hand, $L_{\min}$ is dominated by the air gap magnetic circuit and hardly changes. In other words, saturation reduces $dL/d\theta$, making it harder to generate torque. This is the biggest challenge in SRM design.
| Parameter | Typical Value (8/6 SRM, ~1kW class) | Notes |
|---|---|---|
| $L_{\max}$ (low current) | 40–80 mH | Aligned position, linear region |
| $L_{\max}$ (rated current) | 15–30 mH | Significantly reduced due to saturation |
| $L_{\min}$ | 5–10 mH | Unaligned position, low current dependence |
| $L_{\max}/L_{\min}$ ratio | 3–8 (linear) / 2–4 (saturated) | Higher ratio yields higher torque |
Magnetic Saturation and Nonlinear B-H Curve
At what flux density does magnetic saturation actually occur? Does it differ by material?
It varies greatly depending on the electrical steel sheet used. For example, common materials in SRMs:
- 35A300 (Japanese thin sheet): Saturation flux density $B_s \approx 1.7$ T. Low iron loss but saturates relatively early.
- 50A470: $B_s \approx 1.8$ T. Low cost but slightly higher iron loss.
- 10JNEX900 (JFE's 6.5% Si steel): $B_s \approx 1.5$ T but has extremely low high-frequency iron loss. Suitable for high-speed SRMs.
In practice, the B-H curve starts to flatten around 1.5–1.8 T, and $\mu_r$ (relative permeability) plummets from thousands to tens. In FEM, accurately inputting this nonlinear B-H curve is key to precision.
Effects of Magnetic Saturation Specific to SRMs
- Local Saturation: Flux concentrates at the root of the stator salient pole (yoke junction) and the rotor pole tip, sometimes reaching over 2.0 T locally. Coarse meshing in these areas can cause significant errors in torque calculation.
- Manifestation of Mutual Inductance: Under saturation, the magnetic circuit becomes nonlinear, so the current in adjacent phases affects the inductance of the energized phase. Mutual inductance, which could be ignored in linear models, affects torque calculation.
- Increased Iron Loss: In the saturation region, the time rate of change of flux density $dB/dt$ becomes steep, causing both eddy current loss and hysteresis loss to increase sharply. At high speeds, iron loss can exceed copper loss.
Torque Ripple and NVH (Noise, Vibration, Harshness)
What is the specific mechanism for SRM noise generation? Is it really that much louder than a PMSM?
It's loud. Subjectively, it produces a metallic sound like "grrr" or "bzz." The mechanism is clear: radial electromagnetic forces deform the stator into an ellipse.
In an SRM, the radial force changes abruptly with phase energization ON/OFF. This force excites the stator iron core's natural vibration modes (especially the elliptical mode = breathing mode). When the excitation force frequency components match the stator's natural frequencies, resonance occurs, causing large vibration and noise. What needs to be done with FEM:
- Obtain the radial force time waveform via electromagnetic field analysis
- Analyze the excitation force spectrum via FFT
- Determine the stator's natural frequencies via structural modal analysis
- Design to avoid matching excitation and natural frequencies (resonance)
I see, so coupled electromagnetic and structural analysis is needed. That sounds quite challenging...
Exactly. Therefore, SRM NVH analysis becomes a multi-stage workflow: "Electromagnetic FEM → Radial force extraction → Structural FEM (modal analysis) → Acoustic analysis." Tools like JMAG or Maxwell have functions to export force data to structural analysis, which is commonly utilized.
SRMs are gaining attention as "zero-magnet EV motors"
Since SRMs use no permanent magnets, they are completely immune to risks from China's rare earth export restrictions. The rotor is simply made by punching and stacking laminated steel sheets, reportedly reducing manufacturing cost to 1/2–1/3 that of a PMSM. Nidec began mass production of SRMs for home washing machines in 2023, achieving 60% noise reduction compared to conventional SRMs through AI-based current waveform optimization. On the other hand, Land Rover's Jaguar I-PACE initial prototype considered SRMs but reverted to PMSMs due to unmet NVH requirements. "Quiet SRMs" remain a hot topic in the motor industry, where the accuracy of electromagnetic FEM and control simulation holds the key to productization.
Numerical Methods and Implementation
Electromagnetic FEM Formulation
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