The problem
Axial-flux motors offer high torque density, but their thin rotor discs face the stator across a small air gap of around a millimetre. Magnetic attraction pulls the disc towards the stator, rotation adds centrifugal stress, and heat expands parts unevenly. If the disc deflects too much, the gap closes, performance changes and the rotor can rub. The mechanical design of rotor, shaft, bearings and housing is a central research challenge.
Objectives
- Estimate axial magnetic attraction from an example air-gap flux density and magnet area.
- Model single- and double-rotor topologies with discs, magnets, hub, shaft, bearings and housing.
- Analyse disc deflection and stress under magnetic, centrifugal and thermal loads, alone and combined.
- Study air-gap closure sensitivity to disc thickness, ribbing, material and bearing stiffness.
- Recommend a structure that keeps gap change within a target at minimum mass.
What you need
Tools and toolboxes
- SOLIDWORKS Part and Assembly — Rotor discs with magnet pockets, ribs, hub, shaft, bearings and housing, using Configurations for topology variants.
- SOLIDWORKS Simulation (Static with centrifugal load) — Disc stress and deflection under pressure, centrifugal and thermal loads with bearing fixtures.
- SOLIDWORKS Simulation Professional (Thermal, Frequency, Topology) — Temperature fields for thermal stress, rotor natural frequencies, and topology-guided rib layouts.
- SOLIDWORKS Simulation Premium (Nonlinear, optional) — Contact and geometric nonlinearity if gap closure is large or magnet adhesive behaviour matters.
- MATLAB or Python — Magnetic attraction estimates, parametric sweeps of results and stability calculation.
- Electromagnetic FEA tool (optional) — A 3-D or quasi-3-D field solution for attraction force distribution if available, replacing the analytical estimate.
Software
- SOLIDWORKS 2023 or later with Simulation Professional
- MATLAB or Python
Extra parts and data
- Magnet and adhesive datasheets — Magnet strength, density and adhesive limits drive both loads and allowable stresses.
Key concepts
- Magnetic attraction
- The normal force between a magnet and the stator is approximately B²A/(2μ0) over the pole area, large compared with the disc's stiffness in thin rotors.
- Negative magnetic stiffness
- As the gap closes the attraction increases, acting like a negative spring. The structure must be stiff enough that the combined system stays stable.
- Single- versus double-rotor
- A double-rotor, single-stator layout balances axial forces on the stator in the ideal case, but each rotor still sees one-sided attraction.
- Thermal growth
- Different expansion of magnets, rotor, shaft and housing changes the gap with temperature, so it must be included in the gap budget.
Step-by-step guide
- 1
Define the motor and gap budget
Take an example 40 kW axial-flux motor with 250 mm outer diameter, 1.0 mm nominal air gap and 12000 rpm maximum speed. Write a gap budget listing manufacturing tolerance, bearing play, thermal growth and structural deflection, and set a target such as total gap change below 10 per cent of nominal. Label every value as an example and cite the source of any electromagnetic data you use.
Checkpoint: A gap budget table with a structural deflection allowance stated in millimetres.
- 2
Estimate magnetic loads
Compute attraction per pole as B²A/(2μ0) using an example air-gap flux density and magnet area, then the total axial force on each rotor. Estimate magnetic stiffness by differentiating force with respect to gap using a simple magnetic circuit model that includes magnet thickness and gap. If you have access to an electromagnetic FEA tool, export the pressure distribution instead and compare the totals.
Checkpoint: Total axial force and magnetic negative stiffness per rotor, with analytical and, if available, field-solver values.
- 3
Model topologies
Model single-rotor single-stator and double-rotor single-stator layouts as configurations of one assembly. Each rotor has a back-iron disc with magnet pockets, a hub, optional radial ribs and a retaining ring at the outer edge. Add the shaft, Toolbox bearings and the housing. Drive disc thickness, rib height, rib count and bearing span from global variables so you can sweep them later.
Checkpoint: Both configurations rebuild cleanly and Interference Detection confirms the nominal gap.
- 4
Analyse magnetic load alone
Run a Static study on the rotor and shaft with bearing fixtures and the attraction applied as a pressure on the magnet faces. Use mesh controls through the disc thickness so there are at least three or four elements across it. Converge maximum axial deflection at the outer radius, then compare it with a thin annular plate formula clamped at the hub for the same load.
Checkpoint: Converged outer-radius deflection within about 15 per cent of the plate formula.
- 5
Add centrifugal and thermal loads
Add a centrifugal load at maximum speed and check hoop stress in the disc and the retention of magnets by the ring or adhesive. Run a Thermal study with example magnet and stator losses to get temperatures, then use them as a thermal load in a Static study for thermal stress and growth. Finally combine magnetic, centrifugal and thermal loads in one study.
Checkpoint: Combined-case gap change and peak stresses recorded, with a yield factor of safety above 1.5 and magnet retention within the adhesive or ring limit.
- 6
Include bearing stiffness
Replace the rigid bearing fixtures with bearing connectors or elastic supports whose stiffness comes from catalogue data or a standard formula for the bearing type and preload. Rerun the combined case. Compare gap change with rigid and compliant bearings to see how much the bearings contribute to the total, which often surprises students who assume the disc is the only flexible part.
Checkpoint: A table showing gap change with rigid and compliant bearings, quantifying the bearing contribution.
- 7
Check stability
Compute the structural axial stiffness of the rotor system from the simulated force-deflection slope, including the bearings, and compare it with the magnetic negative stiffness from your earlier estimate. The net stiffness must remain positive with a margin, or the rotor could be pulled into the stator. Plot how the margin changes with disc thickness and rib height across your configurations.
Checkpoint: Structural stiffness exceeds magnetic negative stiffness with an example margin of at least 2 for the chosen design.
- 8
Check dynamics
Run a Frequency study (Simulation Professional) on the rotor-shaft assembly with compliant bearings and identify disc umbrella, nodal-diameter and shaft bending modes. Compare them with running speed and electrical excitation orders on a Campbell-style chart. Note that a standard frequency study ignores gyroscopic effects and spin softening, so a dedicated rotor-dynamics check is needed for a final design. Record the mode shapes as images for the report.
Checkpoint: First disc mode above maximum running excitations with a margin, shown on a chart, and the gyroscopic limitation stated.
- 9
Optimise the disc
Use a Topology Study (Simulation Professional) on the hub region with a stiffness goal and a mass constraint, or sweep rib count and height parametrically with the global variables. Interpret the topology result into ribs that can be machined or cast. Compare mass and gap change for at least three designs and plot the trade-off so the choice is visible rather than asserted.
Checkpoint: A mass versus gap-change plot with the chosen design meeting the gap budget.
- 10
Validate the method
Compare your plate formula, simulation and any published benchmark results for similar discs. If a prototype or a machined test disc is available, measure deflection under a known axial load with a dial gauge on a simple fixture and compare. Discuss how adhesive layers, magnet segmentation, contact between magnets and disc and bolted joints might change the results you have reported.
Checkpoint: A validation section listing each check, its level of agreement and what remains unverified.
- 11
Report
Write up loads, models, convergence, combined results, stability, dynamics and the optimisation. State assumptions explicitly, including linear materials, simplified magnetic loads and the lack of gyroscopic effects, and propose an experimental plan for measuring deflection and air gap under load. Separate clearly what you modelled, what you measured and what you assumed, so a reader can judge the claims. Archive the models and scripts with the report so results can be reproduced.
Checkpoint: A research report with reproducible models and a clear statement of contributions and limitations.
Testing & validation
- Disc deflection converges and agrees with plate theory within about 15 per cent.
- Combined-case gap change fits the gap budget.
- Structural stiffness exceeds magnetic negative stiffness with the stated margin.
- Rotor modes are separated from running excitations.
Expected results
A mechanical design study of axial-flux rotor structures showing gap change under combined loads, stability against magnetic attraction, rotor modes and a mass-optimised disc design that meets an example gap budget.
Research angle for your PhD
Quantify how disc stiffness, bearing compliance and thermal growth combine with magnetic negative stiffness to close the air gap, and derive design charts linking disc thickness and rib layout to gap change and mass. Comparison of single- and double-rotor layouts under realistic, possibly asymmetric, loading, and validation with a simple deflection test, would make a strong contribution, provided field-solver or measured loads replace purely analytical estimates where possible.
Take it further
- Couple a 3-D electromagnetic solution to the structural model.
- Study composite or segmented rotor discs.
- Include manufacturing tolerances statistically in the gap budget.
- Add rotor dynamics with gyroscopic effects in a dedicated tool.
Viva and review questions
Why is magnetic attraction such a concern here?
The rotor is a thin disc facing the stator across a small gap. Attraction acts over the whole magnet area and grows as the gap shrinks, so deflection can feed on itself if the structure is not stiff enough.
Does a double-rotor layout cancel the forces?
It balances forces on the stator in the ideal case, but each rotor still sees one-sided attraction and must be stiff on its own.
What does a standard frequency study miss?
Gyroscopic effects and speed-dependent stiffness. For a high-speed disc rotor these can shift modes, so I flagged the result as a first estimate.
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