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The Vault
Mathematical foundations, research archive, and parametric design simulation for MagFlux electromagnetic
systems.
Magnetic Flux Fundamentals
The theoretical backbone of MagFlux designs — from Maxwell's field equations through to
applied torque and power density derivations for axial-flux and Halbach-array configurations.
Maxwell's Flux Law (Gauss)
∇ · B = 0
The divergence of the magnetic flux density B is always zero — magnetic
monopoles do not exist. All field lines are closed loops. This is the governing constraint for every
core geometry we design.
Faraday's Law of Induction
ε = -N · dΦ/dt = -N · d(B·A·cos θ)/dt
The induced EMF (ε) in a winding of N turns is proportional to the rate of change of flux
linkage. For axial-flux motors, maximizing B and the effective pole-face area A directly drives voltage
output per revolution.
ε
Induced electromotive force (V)
N
Number of winding turns
Φ = B·A·cos θ
Magnetic flux linkage (Wb)
B
Flux density (Tesla)
A
Effective pole area (m²)
θ
Angle between B and surface normal
Ampere's Law (Magnetomotive Force)
MMF = N·I = H·l = Φ·R_m
Magnetomotive force drives flux through a magnetic circuit. The reluctance R_m of the gap
geometry determines how much flux a given MMF produces — minimizing air-gap reluctance is the central
optimisation problem in our actuator designs.
MMF
Magnetomotive force (Ampere-turns)
H
Magnetic field intensity (A/m)
l
Magnetic path length (m)
R_m = l/(μ·A)
Magnetic reluctance (A-t/Wb)
μ = μ₀·μᵣ
Permeability of core material
Axial-Flux Motor Torque
T = (π/4) · B_avg · K_s · (D_o³ - D_i³) · p
The electromagnetic torque of an axial-flux machine scales with the cube of the
outer-to-inner diameter ratio. This favours pancake geometries with large diameter and short axial
length — exactly the topology our designs target.
A Halbach array concentrates flux on one side while cancelling it on the other. B_peak is
maximised by increasing magnet thickness (h) relative to pole pitch (λ), and by using high-remanence
magnet grades. N≥4 segments per pole approximates the ideal sinusoidal case.
Power density (W/kg) is the primary metric for our actuator designs. Copper losses (P_cu =
I²R) and iron losses (P_fe = P_hysteresis + P_eddy) must be minimised. Axial-flux topologies excel here
by using thin laminations or SMC cores to suppress eddy currents at high frequencies.
ω
Angular velocity (rad/s)
P_cu
Copper (winding) losses (W)
P_fe
Iron core losses (W)
η
Overall efficiency (%)
Research Archive
Papers, simulation reports, and technical notes produced by
Amon Hen research agents and reviewed by the principal investigator.
📄
2025-Q4 · Technical Paper · Amon Hen Research
Axial-Flux Motor Topology Survey: Performance Benchmarking Across YASA,
TORUS, and Coreless Configurations
Comprehensive comparative analysis of axial-flux motor architectures.
Evaluates torque ripple, power density (kW/kg), and thermal performance across three leading
topologies. Simulation data generated via FEA agent; conclusions validated against published
literature.
Axial-FluxFEABenchmarking
📄
2025-Q4 · Technical Paper · Amon Hen Research
Halbach Array Optimization for High-Flux Linear Actuators: Segmentation,
Orientation, and Material Trade-offs
Parametric study of Halbach configurations across neodymium (N52, N48H) and
samarium cobalt grades. Air-gap flux density improvements of 38–62% over conventional arrays. Key
finding: diminishing returns beyond n=8 segments per pole at λ < 20 mm.
HalbachLinear ActuatorNdFeB
🔬
2025-Q3 · Simulation Report · FEA Agent
Air-Gap Sensitivity Analysis: Effect of Tolerance Stack-Up on Flux Linkage in
Pancake Motor Designs
Monte Carlo simulation across ±0.05–0.5 mm air-gap variation in a 12-pole,
180mm OD axial-flux machine. Results show 2.3% torque degradation per 0.1mm gap increase. Mechanical
tolerance requirements derived for prototype manufacturing specs.
SimulationTolerance AnalysisManufacturing
📝
2025-Q3 · Design Note · Amon Hen Orchestrator
Soft Magnetic Composite (SMC) vs. Laminated Steel: Core Loss Comparison at
400–2000 Hz Operating Frequencies
Design decision document comparing SMC powder cores against 0.2mm silicon
steel for high-frequency axial-flux stators. SMC eliminates the lamination challenge for 3D flux paths
and reduces eddy losses by 70–85% above 800 Hz, at the cost of 15–20% lower saturation flux density.
MaterialsSMCCore Loss
📄
2025-Q2 · Technical Paper · Amon Hen Research
Winding Configuration Optimization for Fractional-Slot Concentrated Windings
in Axial-Flux Machines
Analysis of slot/pole combinations (12s/10p, 12s/14p, 9s/8p) for concentrated
winding axial-flux motors. Winding factor calculations, cogging torque comparison, and short-circuit
fault tolerance assessment. 12s/10p selected as primary configuration for Phase 1 prototype.
WindingsSlot-PoleCogging
🔬
2025-Q2 · Simulation Report · FEA Agent
Thermal Modeling of Coreless Axial-Flux Stator Under Continuous 80% Load:
Hotspot Identification and Cooling Pathway Design
Computational thermal analysis of a coreless PCB stator at rated current
density. Identifies winding hotspots, derives steady-state temperature distribution, and evaluates
aluminium heat-spreader geometry for passive cooling to achieve T_max < 130°C at ambient 40°C.
ThermalCorelessPCB Stator
📝
2025-Q1 · Design Note · Amon Hen Orchestrator
Agent-Driven Design Space Exploration: Automating FEA Parametric Sweeps with
the Aviary AI Fleet
Internal methodology paper describing how the Aviary cluster's 12-agent AI
fleet performs automated parametric sweeps over motor design variables. Covers agent specialization,
tool-calling pipelines, result aggregation, and human-in-the-loop review gates for design sign-off.
AI AgentsAutomationMethodology
Parametric Design Simulator
Adjust each variable to explore the electromagnetic design
space. Results are computed from the core analytical models — use as a first-pass tool before agent-driven
FEA sweeps.
⚙️ Design Variables
Geometry
Stator outer diameter. Larger D → higher torque (cubic scaling).
Stator inner diameter. Ratio D_i/D_o ≈ 0.6 is typical optimal.
Minimise for max flux linkage; limited by mechanical tolerance.
Thicker magnets → higher flux density at gap. Diminishing returns.
Electromagnetics
More poles → lower speed, higher torque at same power.