Axial Flux Motor Rotor Disc Stress Calculator

1. Decision summary: screen loads, then verify the assembly

Axial flux motor rotor disc stress assessment needs separate centrifugal, magnetic bending and magnet-retention load cases. The worksheet answers a bounded first question: what self-stress and applied loads should the detailed assembly model address? A low bare-disc stress does not establish a safe rotor.

The calculations and examples are conceptual engineering screens, not measured product performance, drawing release, prototype approval or aviation qualification. For architecture context, see special motor topologies. The evidence and method below identifies the model boundaries.

2. Inputs and evidence ownership

The default 240 mm disc, 70 mm bore and 8 mm thickness use illustrative isotropic steel properties: density 7,850 kg/m³, elastic modulus 210 GPa and Poisson ratio 0.30. These are editable assumptions, not a certified material grade. Magnet density defaults to 7,500 kg/m³. No yield strength or temperature derating curve is invented.

All numeric fields have visible bounds. Inconsistent geometry suppresses results and offers a reset. These are worksheet input bounds, not approved manufacturing ranges. A separate magnetic back-iron ring, hub, sleeve and fasteners are excluded from the partial mass and inertia; add them in the assembly model.

3. Centrifugal stress: what the free annulus represents

The worksheet uses linear elastic plane stress for a uniform isotropic annulus with traction-free bore and rim. It excludes fit pressure, attached magnets, torque transmission, temperature gradients and geometric discontinuities. With radii a, b, evaluation radius r in metres and ω = 2πN/60:

C = (3 + ν) ρ ω² / 8
σr(r) = C [a² + b² − a²b²/r² − r²]
σθ(r) = C [a² + b² + a²b²/r² − (1 + 3ν)r²/(3 + ν)]

At either free radial edge, σr = 0. The chart evaluates these equations at 81 radii; its curves are computed values, not an illustrative stress contour. The baseline gives 84.33 MPa bare-disc bore hoop stress and 20.78 MPa peak radial stress. The thin-disc idealization and its relation to three-dimensional elasticity are discussed by Lubarda & Lubarda, 2025. Thick sections or nonuniform carriers need a suitable structural model.

Adding magnet force as a fictitious uniform rim traction is not done here: the real bond/pocket contact location determines the load path. Likewise, a small-hole limit can approach twice the solid-disc center stress in this idealization; that is not a universal factor for every bore or fitted hub.

4. Overspeed and magnet centrifugal demand

At fixed geometry, elastic self-stress and centrifugal load scale with N². A user-selected multiplier of 1.2 raises these values by 44%; it is not a prescribed test requirement.

For magnet annulus radii r1 and r2, total coverage c, magnet thickness tm, density ρm and equal sector count P:

A = π(r2² − r1²)c
Mmag = A tm ρm
Fmag,bound = (Mmag/P) r2 ω²
τnominal = Fmag,bound / (A/P)
J = 0.5 Mdisc(a² + b²) + 0.5 Mmag(r1² + r2²)

The force uses the outer magnet radius for all its mass, an upper bound on the sum of centrifugal force magnitudes for the assumed geometry. It is not the net vector force of the symmetric rotor. τnominal assumes the full sector face is bonded and does not model peel. Inertia is the exact axial polar inertia for these uniform annuli/sectors; 1 kg·m² = 10,000 kg·cm².

5. Magnetic bending: load before displacement

For an assumed uniform field normal to an air-gap face, the worksheet estimates traction magnitude p = Bn²/(2μ0) and force F = pA. Here μ0 ≈ 4π × 10⁻⁷ H/m. If a peak flux value is entered, treating it as uniform is a peak-field envelope over the assumed area, not a spatially averaged force prediction. Fringing, tangential field, slotting and saturation require the actual field solution. COMSOL's force-calculation documentation describes obtaining force by integrating Maxwell stress.

The default 0.92 T field and 0.018437 m² loaded area give 336.77 kPa and 6.209 kN on one face. A symmetric SSDR assembly may balance overall shaft thrust while each disc bends toward the central stator. For DSSR, evaluate both faces and their spatial pressure difference; no assumed 20% imbalance is applied. Both magnet faces must also enter the detailed mass and centrifugal model.

6. Rigidity, stiffness and clearance are different quantities

Isotropic plate rigidity is D = Et³/[12(1−ν²)], in N·m. It describes bending resistance but does not determine rim displacement without support geometry and load distribution. The page therefore reports required effective rim stiffness krequired = F / wallocated instead of an unsupported annular-plate deflection formula.

If supplied stiffness were 50,000 N/mm, the fixed-load displacement would be 0.124 mm, leaving 0.776 mm before other closures. That does not demonstrate stability or acceptable running clearance. The tool preserves negative residuals as an overlap warning. Magnetic force must be recalculated at displaced gaps for coupled analysis; a universal inverse-square force law or one-third-gap collapse threshold is not assumed for a permanent-magnet motor.

Discuss your support and clearance assumptions →

Continue with the air-gap allocation worksheet, stator cooling review or manufacturing feasibility screen when those decisions are also unresolved.

7. Retention alternatives: capacity requires geometry and tests

No universal rim-speed limit or allowable is assigned to these methods. ASTM D1002-10(2019) describes an apparent single-lap shear test; its published scope warns against transferring specimen strength directly to different structural joints. The worksheet's baseline overspeed nominal bond demand of 6.23 MPa is therefore a demand to investigate, not a retention pass.

8. Material, thermal and hub-interface tradeoffs

Cold/hot fits require temperature fields and expansion data for every contacting material, including magnets and adhesive. No fixed percentage increase in sleeve stress is assumed. Keyways introduce local features, while interference fits impose bore hoop stress and contact edge effects. Select the hub interface from torque, fatigue, assembly and service requirements; removing a keyway does not eliminate all stress concentration or fretting risk.

9. Three reproducible conceptual comparisons

Each preset uses the inputs in section 2, a 1.2 overspeed multiplier and one magnet face. Only the specified thickness or speed changes. Results are rounded from the worksheet, not customer cases.

• Thicker disc: increases rigidity by 3.375× and disc mass by 50%. Bare-annulus centrifugal stress is unchanged at fixed radii and density; actual magnet-load stresses still need a model.
• Slower disc: quarters centrifugal demand and self-stress. It does not reduce magnetic pull at unchanged field and area.
• Unchanged magnetic load: all three require 34,495 N/mm to meet the same displacement allocation. The thicker disc may deliver more stiffness, but that must be demonstrated with its real support.

10. Assembly review and failure controls

Evaluate the stress tensor at the same physical point and both bending faces. Do not combine unrelated peak values or choose only the lower-stress sign. Compare the resulting hot stress and fatigue demands against project-specific allowables. No calculator threshold authorizes drawing release.

11. Validation and metrology plan

Agree operating temperature, load, speed envelope, containment, instrumentation, stop criteria and post-test inspection with the responsible test facility. This page supplies no universal spin schedule, dwell time or overspeed requirement. Correlate measured motion with the assembly model and retain calibration records.

Probe suitability must be checked against the actual target, coating, field and environment. Do not presume that all eddy-current probes fail over magnets or that capacitive probes are immune to all errors. Separate bearing/shaft motion, target runout and disc deformation; a displacement signal alone cannot establish all three.

Balancing is a distinct evidence stream. ISO 21940-11:2016 covers balancing procedures and tolerances for rotors with rigid behaviour. It does not certify burst strength or prescribe a universal motor balance grade; flexible behaviour requires an appropriate separate evaluation.

12. Evidence and method

Reviewed 3 November 2026. Links below support the stated methods or test scopes. Public descriptions were reviewed; full standards compliance, product certifications and proprietary test data are not asserted.

Reproduce the worksheet run

To reproduce, restore the illustrative preset, open the assumptions and mass/load disclosures, and copy the worksheet. The rated bore hoop result is 84.33 MPa, the overspeed result is 121.44 MPa, and retention demand is 5,739 N per sector. Actual rim stiffness, retention capacity and hot material allowables remain unknown. The responsible publisher is the CustomMotorDesign Engineering Team; no independent reviewer or hardware validation is claimed. Review this model by 3 November 2027, or earlier if its equations, input assumptions or source scopes change.

Formulas and numeric scenarios are the site's explicitly bounded analytical implementation. Reported loads are inputs to further engineering judgment. Unknown retention capacity, material allowables and operating gap remain unknown until project evidence is supplied.

13. Engineering handoff

Copy or display the worksheet, record which material and load inputs are assumptions, and attach the available assembly requirements through the Submit a Project inquiry. Include topology, support geometry, speed/duty, cold/hot conditions, magnet and retention details, and available test evidence. Unknown parameters are acceptable for feasibility discussion. Review scope, deliverables, validation costs and schedule are agreed for the project.