MOTOR-13 — Switched Reluctance Motors (SRM)

FACT — The Switched Reluctance Motor (SRM) represents the most mechanically robust and minimalist topology in electrical machine engineering. Its rotor contains zero permanent magnets, zero copper windings, zero squirrel-cage conductor bars, and zero brushes; it consists purely of stamped electrical steel laminations.

In this lesson, we examine the physics of the doubly salient SRM, its fault-tolerant asymmetric bridge inverter, and the acoustic NVH roadblocks limiting its adoption in passenger EVs:

1. Doubly Salient Topology
2. Minimum Reluctance Principle and Torque Production
3. Asymmetric Bridge Converter Architecture
4. Extreme Thermal and Mechanical Ruggedness (>300°C and >50,000 rpm)
5. The NVH Roadblock: Radial Force Excitation and Acoustic Whine
6. Commercial Niches (Heavy Mining, Commercial Haulers, e-Turbos)

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1. Doubly Salient Machine Topology

An SRM is termed doubly salient because both its stator and rotor feature prominent, projecting magnetic poles (teeth).

Common automotive traction prototypes adopt 6/4 (6 stator poles, 4 rotor poles) or 12/8 pole configurations:

6/4 SRM Cross-Section:
            Stator Pole A
               +-------+
               | [A+]  |
       +-------+       +-------+
       |                       |
       |        /-----\        |
Stator |       | Rotor |       | Stator
Pole C | [C-]  | Pole  |  [B+] | Pole B
       |       |       |       |
       +-------+       +-------+
               | [A-]  |
               +-------+
            Stator Pole A'

• Stator Coils: Simple concentrated coils wound around individual stator teeth. Opposing coils are wired in series to establish a single phase.
• Rotor Construction: Purely passive. No rare-earth magnets, no cage bars. It is simply a profiled, toothed wheel of laminated silicon steel.

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2. Minimum Reluctance Principle & Torque Production

The SRM relies on a fundamental physical law of electromagnetism: Magnetic flux always seeks to minimize magnetic reluctance along its closed path.

When a stator phase coil is energized, the resulting magnetic field exerts a strong attractive force on the nearest rotor poles, pulling them toward alignment with the excited stator teeth. When the rotor teeth fully face the stator teeth (aligned position), the air gap narrows to its minimum, reluctance reaches its lowest point, and phase inductance peaks at $L_{max}$.

Conversely, when the rotor poles are positioned equidistant between stator poles (unaligned position), magnetic reluctance is highest and inductance drops to $L_{min}$.

Electromagnetic Torque Formulation:

From the derivative of magnetic co-energy, instantaneous torque is formulated as:

$T_e = \frac{1}{2} i^2 \frac{dL(\theta, i)}{d\theta}$

Where:

• $i$: Phase current ($A$)
• $\frac{dL}{d\theta}$: Slope of inductance variation with rotor angular position

FACT — Because the equation contains current squared ($i^2$), current polarity does not influence torque direction!

Torque direction depends exclusively on the slope of the inductance profile:

• Motoring: Current pulses are applied while inductance is rising ($\frac{dL}{d\theta} > 0$) $\implies T_e > 0$.
• Regenerative Braking: Current pulses are injected while inductance is falling ($\frac{dL}{d\theta} < 0$) $\implies T_e < 0$.

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3. Asymmetric Bridge Converter Topology

Because torque direction is independent of current polarity, SRMs do not require standard full-bridge inverters. Instead, they use an Asymmetric Bridge Converter where each phase operates independently with two switching devices and two freewheeling diodes:

Single-Phase Asymmetric Bridge Leg:
       +Vdc --------------------------+
             |                    |
           [Q1]                 (D2)
             |                    |
             +----[ PHASE COIL ]--+
             |                    |
            (D1)                [Q2]
             |                    |
       GND ---------------------------+

Switching States:

1. Magnetization (Excitation): Q1 and Q2 conduct simultaneously, applying full DC rail voltage ($+V_{dc}$) across the winding. Current ramps up rapidly.
2. Freewheeling: One switch turns off while the other remains on; current circulates through one diode at near-zero voltage.
3. Forced Demagnetization: Both Q1 and Q2 turn off simultaneously. Stored inductive energy forces conduction through diodes D1 and D2, dumping energy back into the DC bus under negative rail voltage ($-V_{dc}$); current collapses to zero rapidly.

CRITICAL — In standard three-phase bridge inverters, turning on both switches in the same leg creates a catastrophic dead short across the DC bus (shoot-through failure).

In an asymmetric converter, the phase coil is positioned directly between the two switches. Shoot-through faults are physically impossible. Even if an entire phase coil or switch fails, the remaining phases continue driving the motor unimpeded.

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4. Extreme Thermal and Mechanical Capabilities

Characteristic	Switched Reluctance Motor (SRM)	Permanent Magnet Motor (IPMSM)
Rotor Construction	Bare silicon steel lamination	Steel laminations + NdFeB magnets + resin
Max Rotor Temperature	$>300^\circ\text{C}$ (Bearing limited)	$<150^\circ\text{C} - 180^\circ\text{C}$ (Demagnetization limit)
Max Rotational Speed	$>50,000\text{ rpm}$ (Monolithic steel wheel)	Typically $<20,000\text{ rpm}$ (Centrifugal magnet retention limits)
BOM Raw Material Cost	Exceptionally low (Zero rare earths)	High (Neodymium, Terbium, Dysprosium)
Inverter Reliability	Immune to shoot-through faults	Susceptible to inverter leg shoot-through

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5. Automotive Roadblocks: Acoustic NVH and Torque Ripple

Despite exceptional reliability, SRM adoption in passenger electric cars has been stalled by one key discipline: Acoustic NVH (Noise, Vibration, Harshness).

A. Massive Radial Magnetic Attraction Force ($F_{radial}$)

When a stator tooth is energized, in addition to tangential torque-producing force, an intense radial magnetic attraction force ($F_r$) pulls the rotor toward the stator core:

$F_r \propto \frac{i^2}{g^2}$

When current is quenched during commutation, this radial force abruptly drops to zero. This periodic hammering causes the circular stator casing to warp ovally and snap back. The resulting structural vibrations act like an acoustic loudspeaker, radiating an intense, piercing high-frequency acoustic whine directly into the vehicle cabin.

B. Severe Commutation Torque Ripple

Due to deep magnetic saturation and non-linear inductance transitions between phases, torque ripple typically reaches $30\% - 50\%$, introducing low-speed driveline shudder without complex current profiling algorithms.

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6. Commercial Application Niches

• Heavy Industrial & Mining Dump Trucks: Haul trucks operating 24/7 in desert heat or sub-zero arctic mines where cabin quietness is secondary to bulletproof reliability.
• Electric Superchargers / e-Turbos: Compressors spinning at $100,000 - 150,000\text{ rpm}$ exposed directly to hot exhaust gas environments.
• Armored Military Vehicles: Combat powertrains requiring ballistic fault tolerance that must operate even if projectile damage severs motor phases.

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7. Summary

• SRM features a doubly salient topology with salient poles on both stator and rotor, with zero magnets or windings on the rotor.
• Torque is generated by the rotor’s physical drive to minimize magnetic reluctance ($T \propto i^2 \frac{dL}{d\theta}$).
• Asymmetric bridge converters provide complete phase isolation and physical immunity to shoot-through short circuits.
• The magnet-free rotor easily endures temperatures $>300^\circ\text{C}$ and rotational speeds $>50,000\text{ rpm}$.
• Piercing acoustic whine driven by radial force impulses and severe torque ripple continue to confine SRM to heavy commercial vehicles, mining equipment, and extreme thermal environments.

Next Lesson

• MOTOR-14 — Synchronous Reluctance Motors (SynRM & PM-a-SynRM): Flux-barrier rotor design, reluctance optimization, and low-cost ferrite-assisted hybrid solutions.