MOTOR-29 — Torque Mechanisms and Packaging Comparison

FACT — In MOTOR-28 we compared four motor families; but even within the IPMSM family there is no single “type” — the mixing ratio of PM torque to reluctance torque forms a spectrum that runs, under the same family label, from SPMSM to pure SynRM. This lesson examines that spectrum, and on a separate axis, the machine’s physical packaging geometry (radial vs axial flux).

In this lesson we cover:

1. The Torque Spectrum: From SPMSM to Pure SynRM
2. Current Advance Angle β: The Geometric Interpretation of MTPA
3. PM-Assisted SynRM: Shifting the Angle with Ferrite Magnets
4. Radial Flux vs Axial Flux: The Fundamental Architecture Difference
5. The Axial-Flux (YASA) Packaging Advantage: The In-Wheel Motor Appeal
6. The Unsprung-Mass Trade-off
7. Practical Synthesis: Which Combination for Which Application?

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1. The Torque Spectrum: From SPMSM to Pure SynRM

The IPMSM torque equation from MOTOR-11 consists of two terms:

$T_e = \underbrace{\frac{3}{2} p \, \psi_{pm} I_q}_{\text{PM (magnet) torque}} + \underbrace{\frac{3}{2} p (L_d - L_q) I_d I_q}_{\text{reluctance torque}}$

The relative weight of these two terms defines four distinct design points:

Motor type	$\psi_{pm}$	$L_d$ vs $L_q$	PM torque share	Reluctance torque share	Typical optimal β
SPMSM (surface-mounted magnet)	High	$L_d = L_q$	100%	0%	$0^\circ$
IPMSM (interior magnet)	Medium–High	$L_q > L_d$	60% – 80%	20% – 40%	$\sim 20^\circ$ – $40^\circ$
PM-assisted SynRM	Low (ferrite)	$L_q \gg L_d$	15% – 30%	70% – 85%	$\sim 45^\circ$ – $55^\circ$
Pure SynRM	Zero	$L_q \gg L_d$	0%	100%	$\sim 45^\circ$ (symmetric)

ASSUMPTION — The PM/reluctance share percentages above are illustrative figures showing typical ratios at the nominal operating point; the actual ratio depends on motor geometry (magnet volume, saliency ratio $\xi = L_q/L_d$) and operating point (current magnitude, speed).

CRITICAL — On this spectrum, “IPMSM” is not a single point but a broad region. Commercial IPMSM designs can be shifted toward the SynRM end by reducing magnet volume and increasing $\xi$ — this is a direct engineering path to reducing rare-earth cost, as covered in MOTOR-28 §5.

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2. Current Advance Angle β: The Geometric Interpretation of MTPA

Recall the MTPA current-angle formula derived in MOTOR-19. Parametrizing the current vector as $I_d = I_s \sin\beta$, $I_q = I_s \cos\beta$, the torque expression becomes:

$T_e(\beta) = \frac{3}{2} p \left[ \psi_{pm} I_s \cos\beta + \frac{1}{2}(L_d - L_q) I_s^2 \sin(2\beta) \right]$

The relative magnitude of these two terms determines where the optimal β lands:

• First term (proportional to $\cos\beta$, PM torque): maximized at $\beta = 0^\circ$ — all current should go to the $q$-axis, directly perpendicular to magnet flux.
• Second term (proportional to $\sin 2\beta$, reluctance torque): maximized at $\beta = 45^\circ$.

$dT_e/d\beta = 0 \Rightarrow -\psi_{pm} I_s \sin\beta + (L_d - L_q) I_s^2 \cos(2\beta) = 0$

The root of this equation approaches $45^\circ$ as $\psi_{pm}$ shrinks (weaker magnet) and $(L_q - L_d)$ grows (higher saliency):

$\beta_{opt} \to 0^\circ \quad \text{(SPMSM, } \psi_{pm} \text{ dominant)}$ $\beta_{opt} \to 45^\circ \quad \text{(SynRM, reluctance dominant)}$

FACT — This is the geometric essence of the $I_d$ formula given in MOTOR-19 §2: the term $\sqrt{\psi_{pm}^2/[4(L_q-L_d)^2] + I_q^2}$ converges, in the $\psi_{pm} \to 0$ limit, to $I_d \to -I_q$ (i.e. $\beta \to 45^\circ$) — precisely the symmetric MTPA trajectory of a pure reluctance machine.

Shift of the MTPA Trajectory with β Angle in the d-q Plane:

  I_q
   ^
   |    SPMSM (β=0°)
   |    MTPA: along the pure I_q axis
   |    ────────────►
   |
   |         IPMSM (β≈20-40°)
   |         MTPA: mildly tilted parabolic locus
   |        ╱
   |       ╱
   |      ╱   PM-assisted SynRM (β≈45-55°)
   |     ╱    MTPA: near-symmetric line, I_d≈I_q
   |    ╱
   |   ╱  Pure SynRM (β=45°, symmetric)
   |  ╱   MTPA: I_d=-I_q diagonal
   +─────────────────────────► I_d
   0

In a pure SynRM, the optimal β generally locks at exactly $45^\circ$ because the PM term is entirely absent and the equation collapses to the maximum of $\sin(2\beta)$. In a PM-assisted SynRM, a small ferrite-magnet contribution can shift the optimum slightly past $45^\circ$ (toward $50^\circ$–$55^\circ$) — covered in the next section.

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3. PM-Assisted SynRM: Shifting the Angle with Ferrite Magnets

The pure SynRM’s greatest drawback is its low power factor (see MOTOR-28 §2 and the FAQ in §9). The reason: the $I_d$ current needed to produce reluctance torque is, without any magnet flux, an ENTIRELY reactive magnetizing component — the full net flux $\psi_d = L_d I_d$ must be generated by current alone.

If cheap, thermally stable ferrite magnets (far lower cost than NdFeB, no rare-earth content) are placed in the rotor’s flux barriers:

$\psi_d = \psi_{pm,ferrite} + L_d I_d$

The ferrite magnet’s flux takes over part of $I_d$‘s job “for free” — the $I_d$ needed to reach the same $\psi_d$ shrinks, power factor improves, and inverter VA requirement drops. The ferrite flux also shifts the optimal current angle slightly past $\beta = 45^\circ$, since a small but nonzero PM-torque term now exists.

FACT — PM-assisted SynRM deliberately targets a middle ground on the torque spectrum between pure SynRM and IPMSM: it nearly eliminates rare-earth dependence (ferrite is cheap and abundant) while partially compensating for pure SynRM’s power-factor weakness. Some Chinese OEMs and industrial drive manufacturers are reported to be evaluating this architecture for cost/supply-driven programs.

ASSUMPTION — Use of PM-assisted SynRM in a specific mass-production passenger EV program is not as widely documented in public sources as IPMSM/induction usage; the assessment above reflects literature and industry trend level, and requires model-specific verification.

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4. Radial Flux vs Axial Flux: The Fundamental Architecture Difference

The discussion so far concerned the motor’s torque-production mechanism. We now switch to an entirely independent axis: the machine’s physical packaging geometry — the flux-direction distinction introduced in MOTOR-15.

Radial-Flux Machine (conventional, cylindrical):     Axial-Flux Machine (YASA / pancake):

   Flux crosses the rotor-stator airgap               Flux crosses the rotor-stator airgap
   in the RADIAL direction (perp. to shaft axis).     in the AXIAL direction (parallel to shaft axis).

        ┌───────────┐                                  ╔═══════════════╗  ← stator disc
        │  ┌─────┐  │  ← stator                         ║ N S N S N S N ║  ← rotor disc (magnets)
        │  │ ═══ │  │  ← airgap (radial)                ╠═══════════════╣  ← airgap (axial, x2)
   shaft →│  │rotor│  │← shaft                            ║ S N S N S N S ║  ← second rotor disc (optional)
        │  └─────┘  │                                  ╚═══════════════╝
        └───────────┘                                       ↑ shaft (short axial length)
   Long axial length, small diameter                    Short axial length, large diameter ("pancake")

Property	Radial Flux	Axial Flux (YASA/pancake)
Axial length	Long	Short (packages the same power more thinly)
Diameter	Relatively small	Large (long torque arm)
Torque density (Nm/L)	Baseline	Typically 20–40% higher
Manufacturing maturity	Very mature, low-cost mass production	Younger, requires tight airgap tolerance
Thermal management	Proven, straightforward	More challenging (disc geometry constrains cooling paths)
Structural rigidity	Easy (single-piece housing)	Demanding (axial magnetic attraction forces pull discs together)
Typical integration	Conventional single-shaft e-Axle, hybrid transmission housing	In-wheel (hub) motor, ultra-compact multi-motor layout

FACT — In axial-flux machines, the stator sandwiched between two rotor discs experiences a strong axial attraction force — if unbalanced, this force closes the airgap and creates rub/contact risk. This is the concrete source of the structural/thermal challenge referenced in MOTOR-15, and the primary reason axial-flux motors have reached mass production later and at higher cost than radial-flux.

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5. The Axial-Flux (YASA) Packaging Advantage: The In-Wheel Motor Appeal

The axial-flux motor’s short axial length makes it especially attractive for in-wheel (hub) motor architecture: the motor can be integrated directly inside the wheel rim or just behind the hub, eliminating the need for a differential/reduction gear/driveshaft-style drivetrain.

FACT — YASA Motors-style (now within Mercedes-AMG) yokeless-segmented-armature axial-flux topology combines high torque density with short axial length, and is frequently cited as a reference architecture both for high-performance e-Axle applications (in some Mercedes-AMG high-performance hybrid/EV models) and for conceptual in-wheel motor designs.

ASSUMPTION — The exact model and configuration details of YASA/Mercedes-AMG integration may change over time in public sources; this lesson cites it to illustrate a general architectural trend — consult manufacturer technical publications for current, exact product information.

In multi-motor layouts (e.g. four independent wheel motors with torque vectoring), axial flux’s compactness greatly eases the practicality of fitting a separate motor at each wheel — something far harder with radial flux due to interference risk with brake/suspension components.

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6. The Unsprung-Mass Trade-off

Despite the in-wheel motor’s packaging appeal, the core engineering reason it has not gained wide mass-production adoption is the increase in unsprung mass.

Unsprung mass is the mass that sits below the suspension, not isolated by the spring/damper: wheel, rim, tire, brake caliper/disc, axle-end components. Sprung mass, by contrast, is the body+chassis+motor (in a conventional layout) mass that the suspension does isolate.

When a wheel encounters a bump or pothole, the suspension spring and damper govern the following two-mass-spring system:

$m_{us} \ddot{x}_{us} + k_t(x_{us} - x_{road}) = k_s(x_s - x_{us}) + c_s(\dot{x}_s - \dot{x}_{us})$

where $m_{us}$ is unsprung mass, $k_t$ is tire stiffness, and $k_s$/$c_s$ are suspension spring/damping coefficients. The physical consequence of this equation:

CRITICAL — As unsprung mass increases, the wheel’s moment of inertia response to road irregularities grows. The tire must now accelerate a larger mass quickly to follow the road’s contour — this (1) increases fluctuation in tire-road contact-patch force (loss of grip/braking distance), (2) degrades the suspension’s ability to isolate the body from bump/pothole impacts (loss of ride comfort), and (3) transmits more high-frequency road vibration into the body.

An in-wheel motor, by definition, adds its mass (typically on the order of $15\text{–}40\text{ kg}$, depending on motor size) directly to the unsprung side. In a conventional e-Axle architecture, by contrast, motor mass sits on the chassis-mounted (sprung) side and delivers torque to the wheel via a half-shaft/driveshaft — only a lightweight CV-joint end is added at the wheel, and the motor’s main mass fully benefits from suspension isolation.

$\Delta m_{us,\text{in-wheel}} \approx m_{motor} + m_{motor\_housing} \gg \Delta m_{us,\text{e-Axle}} \approx m_{CV\_joint\_end}$

FACT — This is the central engineering objection to in-wheel motor architecture despite its packaging/efficiency appeal, and the reason it remains rare in mass-production passenger vehicles. Grip, braking distance, and ride quality — especially in the premium passenger segment — are generally weighted more heavily than packaging compactness.

Some manufacturers and concept vehicles (e.g. various Chinese EV startups’ and academic/racing projects’ in-wheel motor concepts) have accepted this trade-off, favoring in-wheel motors specifically for low-speed/urban or light-commercial applications; but in the high-performance/premium passenger segment, mounting radial- or axial-flux motors on the chassis side (within sprung mass) remains the standard.

ASSUMPTION — Specific in-wheel motor concept vehicle manufacturer/model names are omitted here since this is a fast-changing area; consult manufacturer announcements for current examples.

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7. Practical Synthesis: Which Combination for Which Application?

Application	Torque-mechanism preference	Packaging preference	Rationale
Premium performance passenger (single/dual motor, chassis-mounted)	IPMSM (high PM share)	Radial flux	Density + manufacturing maturity + preserves sprung mass
Cost/supply-constrained program	PM-assisted SynRM	Radial flux	Rare-earth reduction + proven packaging
Ultra-compact multi-motor e-Axle (chassis-mounted)	IPMSM or SynRM	Axial flux (YASA)	Captures short-axial-length benefit without an unsprung-mass penalty
Experimental/niche in-wheel (urban, light commercial)	Usually IPMSM or SRM (compact, high pole count)	Radial or axial flux, hub-integrated	Packaging priority; unsprung-mass penalty knowingly accepted

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8. Frequently Asked Questions (FAQ)

Why isn’t the IPMSM’s optimal β angle a fixed number?

FACT — β depends on the relative magnitude of the PM-torque and reluctance-torque terms; since this ratio varies with motor geometry ($\psi_{pm}$, $L_d$, $L_q$) and operating point (current magnitude $I_s$), β is not a constant but a trajectory that shifts with current magnitude — exactly the definition of the MTPA curve in MOTOR-19.

Is an axial-flux motor always denser than a radial-flux motor?

INTERPRETATION — The general trend says yes (large diameter, short axial length, well-utilized active material volume), but this is partly offset by manufacturing tolerances and thermal-design maturity; radial flux’s decades of production optimization can close part of the raw theoretical density gap in practice.

Will in-wheel motors never become widespread in mass production?

INTERPRETATION — A flat “no” would be too strong; advances in tire/rim/brake lightweighting (reducing unsprung mass) and active suspension control could improve this trade-off over time. But at today’s technology level, the central motor + driveshaft architecture remains the dominant choice for the premium passenger segment.

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9. Summary

• The torque spectrum is a continuum between SPMSM (pure PM) and pure SynRM (pure reluctance); IPMSM and PM-assisted SynRM occupy intermediate points on that spectrum.
• The MTPA current advance angle β approaches $0^\circ$ when PM torque dominates and $45^\circ$ when reluctance torque dominates — this is the geometric interpretation of the MTPA formula in MOTOR-19.
• PM-assisted SynRM with ferrite magnets partially compensates for pure SynRM’s low power-factor weakness without using rare earths.
• Radial flux is mature and highly manufacturable; axial flux (YASA) is denser and axially shorter but carries thermal/structural challenges.
• Axial flux’s shortness makes in-wheel motor architecture attractive, but moving motor mass to the unsprung side degrades grip and ride comfort — the central reason in-wheel motors remain rare in the premium passenger segment.

10. Sources and Verification Note

• Lipo — Introduction to AC Machine Design (torque components, MTPA derivation).
• Pyrhönen, Jokinen & Hrabovcová — Design of Rotating Electrical Machines (flux direction, radial/axial comparison).
• Jahns et al. — Interior Permanent-Magnet Synchronous Motors for Hybrid and Electric Vehicle Propulsion (IPMSM β-angle behavior).
• Gruber et al. — Yokeless and Segmented Armature (YASA) Axial-Flux Machine Topologies (axial-flux architecture).

ASSUMPTION — Manufacturer/model-specific examples (YASA/Mercedes-AMG, OEMs using PM-assisted SynRM, in-wheel motor concepts) are verified only at the level of public press sources; confirm with current manufacturer documentation before publication.

Next Lesson

• MOTOR-30 — Failure Modes and Real-Vehicle Benchmarks: Field-observed motor failure cases (demagnetization, bearing current, insulation breakdown) and how measured performance data from real production models compares against the theoretical trade-offs covered in this lesson.