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Engineering guide · AFPM core modeling

AFPM Core Finite Element Analysis

Match model complexity to the design question. A 2D, quasi-3D, or 3D model is useful only when its geometry, material data, and validation match the quantity you need to decide.

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Published 2026-09-24 · Sources and recommendations reviewed 2026-10-13

Key conclusions Choose a model Validation workflow Limits and risks FAQ Sources

Decision summary

There is no universal 2D error percentage

A reduced model can be useful when its geometry and target output are represented well. Published AFPM comparisons report different agreement for different 2D approaches, geometries, and outputs. Validate the chosen model against 3D analysis or test data for the design at hand.

Evidence: source

Use 3D when the question depends on 3D geometry or paths

End effects, radial variation, fringing, axial force, and current paths that leave a 2D plane can justify a 3D model. A 3D mesh is still a numerical approximation and needs mesh, material, and measurement checks.

Evidence: source

Quasi-3D is a method family, not one fixed accuracy tier

Multi-slice and quasi-3D approaches can support specific field and loss questions. A 2025 study validates a tailored quasi-3D method for permanent-magnet eddy-current loss maps against 3D FEA; that result should not be generalized to unrelated implementations.

Evidence: source

Treat material data as a design input

Use the selected grade’s measured B-H and loss data over the intended flux-density and frequency range. SMC can support three-dimensional flux paths, while compaction, grade, excitation, and test method still affect the model inputs and predicted losses.

Evidence: source

Choose the model for the output you need

Model fidelity is a trade-off, not a universal ladder. Start with the least costly model that preserves the relevant physics, then check its result against a higher-fidelity model or test.

Best use

2D FEA

Fast screening when a defensible 2D representation exists.

Quasi-3D / multi-slice

Radial variation or a defined multi-slice calculation that has been checked for the output of interest.

3D FEA

Geometry, fields, forces, or current paths that materially vary in three dimensions.

Main limitation

2D FEA

Cannot represent omitted dimensions and end effects directly.

Quasi-3D / multi-slice

Coupling between slices and 3D paths may be simplified or absent, depending on implementation.

3D FEA

Higher modeling and compute effort; CAD, material data, mesh, and boundary conditions still limit accuracy.

Before using results

2D FEA

Compare the chosen representation with a higher-fidelity result or measurement.

Quasi-3D / multi-slice

Check the slice setup and loss post-processing against a 3D reference for the target quantity.

3D FEA

Check mesh convergence and compare key outputs with test data or an independent calculation.

Uses and limitations of 2D, quasi-3D, and 3D AFPM models
Decision factor	2D FEA	Quasi-3D / multi-slice	3D FEA
Best use	Fast screening when a defensible 2D representation exists.	Radial variation or a defined multi-slice calculation that has been checked for the output of interest.	Geometry, fields, forces, or current paths that materially vary in three dimensions.
Main limitation	Cannot represent omitted dimensions and end effects directly.	Coupling between slices and 3D paths may be simplified or absent, depending on implementation.	Higher modeling and compute effort; CAD, material data, mesh, and boundary conditions still limit accuracy.
Before using results	Compare the chosen representation with a higher-fidelity result or measurement.	Check the slice setup and loss post-processing against a 3D reference for the target quantity.	Check mesh convergence and compare key outputs with test data or an independent calculation.

Research examples: 2D approaches are compared with 3D and tests by Güleç and Aydın, and a defined anisotropic-rotor example uses both 2D multi-slice and 3D models in Nyitrai and Kuczmann. Neither study supports a single error percentage for all AFPM designs.

Need to choose a model before committing to a design direction? Ask for an engineering review of the target output, material inputs, and validation plan.

Review a core model

Why model dimensionality matters

AFPM geometry changes with radius: inner and outer regions do not share the same circumference, and end geometry, air-gap fringing, and material interfaces may affect local fields. Reducing the geometry can make iteration faster, but the removed dimensions cannot influence the result directly.

This is why a 2D result should be tied to its representation and target quantity. A 2D approach that estimates back-EMF well may not reproduce local loss or torque ripple equally well. Compare the output that drives the decision, not only a headline metric.

Engineering check

If changing the inner/outer radius, end region, skew, or current path can change the answer, include that effect in the model or quantify the simplification against a reference.

Conceptual diagram only. A 3D model represents the chosen geometry in three dimensions; accuracy still depends on inputs, mesh, solver settings, and validation.

A practical AFPM FEA validation workflow

Keep a short model record with the decision, assumptions, and checks. That record makes results comparable across design revisions and useful during supplier or prototype reviews.

1Define the decision and output
State whether the model is being used for average torque, torque ripple, back-EMF, local flux density, core loss, magnet loss, axial force, or temperature input. A model can be suitable for one output and weak for another.
2Freeze the topology and geometry
Record rotor/stator arrangement, pole and slot counts, air gaps, magnet shape, tooth and yoke dimensions, and any skew or segmentation. Preserve the geometry features that drive the output under review.
3Use traceable material and excitation data
Identify material grade, measured B-H data, loss data and its frequency/flux-density range, magnet properties, winding current, speed, and temperature assumptions. Do not substitute generic coefficients when they control the decision.
4Check boundaries and symmetry
A periodic or symmetry sector is valid only when the geometry, winding excitation, rotor position, and requested result repeat with the applied boundary condition. Compare a sector model with a larger model when symmetry is uncertain.
5Refine and compare
Refine the air gap, tooth tips, magnet edges, and other high-gradient regions. Track the quantity of interest as the mesh and time step change, then compare selected operating points with a 3D model or physical test.

Model core material and loss data carefully

Do not infer loss behavior from the material label alone. Core-loss predictions rely on data matched to the grade, flux-density range, frequency, and manufacturing condition. In AFPM machines, fringing and local field direction can also change how a core construction should be evaluated. A published laminated-steel/SMC comparison demonstrates those effects in its test setup, without establishing a universal material ranking. See the study.

For SMC

Confirm the production grade, compaction condition, measured B-H data, loss data, and applicable frequency and flux-density range. Use a 3D model when the question depends on 3D flux distribution or geometry; dimensionality is not dictated by the material name alone.

For laminated steel

Record grade, thickness, stacking or assembly assumptions, cutting and forming condition, and the direction represented by the data. When fringing-induced currents or local 3D effects matter, check whether the model represents the relevant conductive paths.

Minimum material-data request

Exact grade · B-H curve · core-loss data and test conditions · temperature context · production condition · magnet data where relevant. A generic curve is not a substitute for grade-specific evidence when losses or saturation drive the decision.

Limits and failure checks

Symmetry is conditional. Verify pole/slot periodicity, phase excitation, rotor position, and requested output before reducing the model to a sector.
A fine mesh is not validation. Check convergence for the output of interest, then compare the model with test data or an independent method.
Loss and thermal analyses have separate assumptions. Electromagnetic loss estimates become thermal inputs; they do not by themselves locate a validated hotspot. Check contact, cooling, temperature-dependent properties, and boundary conditions in the thermal model.
Solver speedups are case-specific. The 15× result reported for a scalar-potential method applies to the authors’ studied setup. Confirm accuracy and runtime with your own model before planning around a similar gain. Study details.

Two common design situations

Early geometry screening

Starting point: You are comparing pole/slot or magnet-shape options and need relative torque and back-EMF trends.

Action: Use an analytical or reduced model for the broad sweep if its representation covers the topology. Choose a few candidates for 3D and test correlation before using it to rank the full design space.

Decision boundary: If candidate ranking changes with 3D geometry, reduced-model outputs are not sufficient for selection.

SMC core loss and thermal review

Starting point: A design uses a three-dimensional flux path and core loss is part of the temperature or efficiency decision.

Action: Request grade-specific loss data, model representative operating points with suitable field dimensionality, and transfer losses into a thermal model with stated cooling and contact assumptions.

Decision boundary: If material data do not cover the operating range, mark the predicted loss as uncertain and plan a material test.

AFPM core FEA questions

Can a 2D model be used for an AFPM core?

Sometimes. Published work compares multiple 2D representations with 3D FEA and experiments, with performance depending on the machine and output. Use a 2D model for screening only after checking that its assumptions fit the topology and validating the result that drives the decision.

When is 3D FEA worth the extra effort?

Use it when radial variation, end effects, fringing, axial forces, skew, segmentation, or three-dimensional eddy-current paths materially affect the quantity being evaluated. Do not select 3D solely because it sounds more accurate; validate its mesh and inputs too.

Is quasi-3D always more accurate than 2D?

No single ranking applies to every implementation. Slice locations, coupling assumptions, geometry, and post-processing all matter. Check the method against 3D FEA or measurement for the same output and representative operating points.

Can quasi-3D predict permanent-magnet eddy-current loss?

Some methods can. A 2025 study proposes a quasi-3D loss-map method and validates it against 3D FEA. This is evidence for that workflow; verify the assumptions and post-processing before applying a different implementation.

Does SMC always require a full 3D transient model?

No. Choose model dimensionality from the geometry, excitation, and output. SMC may be useful in three-dimensional flux paths, but material-specific B-H and loss data are still needed, and full 3D transient analysis is not automatically required for every design question.

Which material data should be requested for a core study?

Ask for the exact grade, B-H curve, loss data across the operating flux-density and frequency range, test method, sample condition, and temperature context. For SMC, confirm that data apply to the production grade and compaction process being considered.

Can I always simulate one pole or one-eighth of the motor?

No. The repeat sector depends on pole/slot geometry, winding phase and excitation, rotor position, and the boundary condition supported by the solver. Establish the actual periodicity; do not assume a fixed fraction.

Does a converged mesh prove the model is correct?

Mesh convergence shows that a result is becoming less sensitive to mesh size for the modeled problem. It does not validate geometry, material curves, boundary conditions, loss post-processing, or the physics omitted from the model. Compare against an independent calculation or test.

How should a simulation be compared with a test?

Match the geometry, winding connection, current waveform, speed, rotor position, temperature, and measurement definition as closely as practical. Report the residual mismatch and uncertainties instead of treating the simulation as a measurement substitute.

Prepare a reviewable core simulation brief

Share the topology, critical outputs, operating points, material grades, available test data, and the boundary conditions you plan to use. That gives a core supplier or simulation partner enough context to identify missing inputs before results are compared.

Discuss a core design

Related AFPM resources

Sources and evidence limits

This guide summarizes published AFPM modeling studies and provides a model-selection workflow; it does not present an AxialFluxCore simulation benchmark, customer case, or performance result. The recommendations above are engineering guidance derived from the cited studies. The papers use different AFPM topologies, materials, outputs, and validation setups; none supplies a universal accuracy or runtime guarantee. Source review date: 2026-10-13.

Güleç and Aydın, “Implementation of different 2D finite element modelling approaches in axial flux permanent magnet disc machines,” IET Electric Power Applications, 2018.
The authors compare several 2D representations against 3D FEA and test results for more than one AFPM geometry. Agreement depends on the representation and output being evaluated, so the paper does not establish a universal 2D error band.
Nyitrai and Kuczmann, “Magnetic equivalent circuit and finite element modelling of anisotropic rotor axial flux permanent magnet synchronous motors with fractional slot distributed winding,” IET Electric Power Applications, 2023.
This study validates a model for a defined anisotropic-rotor AFPM example using 2D multi-slice and 3D FEA. Its scope is a particular topology and design method, not a generic accuracy guarantee for every AFPM.
Schäfer et al., “Accelerated 3D FEA of an Axial Flux Machine by Exclusively Using the Magnetic Scalar Potential,” Energies, 2023.
The paper reports agreement with reference simulations and at least 15× faster computation for its proposed scalar-potential approach and studied AF machine. Treat the speedup as method- and model-specific, not a general property of 3D solvers.
Oh et al., “Fast Estimation of Permanent Magnet Eddy Current Loss Map for Axial Flux Permanent Magnet Synchronous Motor Using Quasi-3D Analysis,” Journal of Electrical Engineering & Technology, 2025.
The proposed quasi-3D post-processing method estimates permanent-magnet eddy-current loss maps and is checked against 3D FEA. This demonstrates a validated use case for a specific method; it does not mean every quasi-3D loss workflow is reliable.
Scheerlinck, De Gersem, and Sergeant, “3-D Eddy Current and Fringing-Flux Distribution in an Axial-Flux Permanent-Magnet Synchronous Machine With Stator in Laminated Iron or SMC,” IEEE Transactions on Magnetics, 2015.
This study models and measures fringing-related eddy currents in an AFPM setup and compares laminated steel with SMC. It is evidence that core material and flux direction affect loss modeling; results are specific to the studied machine and material samples.