Axial Halbach Array Magnet Spacing
Calculate circumferential segment pitch, geometric fill, and a first-order thermal gap change. Use the result to check your drawing and prepare machine-specific magnetic and structural validation.
Check pitch and edge clearance at three radii
Enter the rotor geometry and a circumferential gap. The tool returns geometry and an explicitly simplified thermal estimate; it does not predict flux, torque, safety, or adhesive performance.
What the spacing result can tell you
The tool answers geometric questions. Use field and structural models for performance and safety decisions.
Define the gap at a radius and datum
A single millimetre value is not enough unless the drawing says where and how it is measured.
pitch(r) = 2 x pi x r / N_seg
magnet_arc(r) = pitch(r) - gap(r)
geometric_fill = magnet_arc(r) / pitch(r)
Here, pitch is the local arc pitch, magnet_arc is local magnet arc width, gap is circumferential edge clearance, and geometric_fill is their ratio. The calculator displays inner, mean, and outer radii so one value is not mistaken for the whole annulus.
State whether dimensions are measured between coated magnet edges, machined edges, or spacer faces. Keep circumferential clearance separate from the axial rotor-to-stator working gap.
For a drawing-based tolerance stack and inspection plan, see the axial Halbach array assembly tolerance guide.
Tile shape changes the gap profile
Choose the measurement plan to match the segment shape. The geometry comparison below is qualitative; tooling and cost depend on the supplier and production route.
| Segment geometry | Gap pattern | What to inspect |
|---|---|---|
| Annular wedge | Can maintain a near-constant local arc gap across the radial span when designed for it. | Inner and outer edge clearance, angle, and seating. |
| Rectangular tile | Gap between parallel edges generally varies with radius on an annular layout. | Minimum and maximum clearance around the tile. |
| Stepped segment | Gap profile changes at each step or block boundary. | Step alignment, local corner clearance, and transition geometry. |
| Insulated separator | Separator thickness becomes part of the stack-up. | Installed thickness, compression, and electrical continuity. |
Geometry is an input to magnetic analysis
Segmentation and clearances can affect the field distribution, but the calculator does not turn a gap into a flux-loss percentage.
| Question | What geometry screening shows | What needs a machine model |
|---|---|---|
| Segment fit | Local pitch, edge clearance, and geometric fill by radius. | Manufacturing variation, coating, adhesive, and assembled position. |
| Air-gap field | The segment geometry to use as model input. | Magnetization vectors, finite edges, air gap, back iron, saturation, and leakage. |
| Harmonics and losses | A gap or segmentation boundary exists in the geometry. | Harmonic spectrum, slot interaction, conductivity, speed, and thermal boundary conditions. |
| Torque and retention | No load or force output. | Electromagnetic loading, centrifugal load, adhesive behavior, sleeves, and rotor structure. |
Need to check load implications after defining the segment geometry? See the axial Halbach force calculation guide, or request a drawing-specific review.
Request a spacing reviewBudget the assembled gap, not only the nominal CAD value
The minimum local clearance is controlled by the full dimensional chain and operating condition.
Identify magnet dimensions and edge condition, carrier pocket position, coating, separator or adhesive, assembly fixture, runout, and thermal movement. Record the measurement datum and inspection method. Avoid combining nominal adhesive thickness with circumferential clearance unless the drawing explicitly defines them as the same dimension.
This is a dimensional bookkeeping relation, not a stress or safety-factor equation. Use an agreed worst-case or statistical tolerance method for the project.
Use CTE in the direction that controls the gap
The tool estimates a dimensional change from user-entered circumferential expansion coefficients.
A bonded segment centre may follow the carrier pitch while the magnet arc expands at its own rate. The tool compares those changes at the mean radius. Its result is sensitive to the entered values and assumes uniform linear expansion.
- Use the circumferential-axis CTE for the magnet and carrier.
- Use the project temperature rise from the reference assembly condition.
- Check restraint, adhesive compliance, gradients, and contact separately in structural analysis.
A test bondline is not a rotor spacing recommendation
Manufacturer test data can describe adhesive behavior under stated coupon conditions. It does not establish a universal gap for an axial Halbach rotor.
Turn the geometry screen into an engineering check
Use a traceable sequence so that the chosen gap is linked to the drawing, model, assembly process, and inspection result.
Three cases where one nominal number is not enough
These are process examples, not performance claims or recommended dimensions.
Evidence used on this page
The sources support modeling and interpretation limits. They do not provide a universal production spacing range.
Sources checked October 17, 2026. Numeric product data and design rules should be checked against current supplier documentation and the actual assembly before release.
Axial Halbach array magnet spacing questions
Answers focus on what this geometric tool can establish and what requires project-specific validation.
Geometry and terminology
What does magnet spacing mean on this page?
It means the circumferential edge clearance between neighboring magnet segments at a stated radius. It is not the axial rotor-to-stator air gap.
Is circumferential spacing the same as adhesive bondline thickness?
No. A gap may contain adhesive, insulation, coating, or open clearance, but the dimensions and loading of that joint need separate definition. The calculator does not specify an adhesive bondline.
How is circumferential segment pitch calculated?
For N equally spaced segments at radius r, the arc pitch is 2*pi*r/N. The calculator uses N = 2 times pole pairs times segments per pole.
Why are inner and outer radius results different?
Circumference changes with radius. Under the equal-angle assumption in this tool, both local pitch and gap scale with radius. A rectangular tile can have a different local gap profile, so inspect its actual edges.
Does the tool calculate wedge magnet geometry?
It shows equal-angle annular segments and evaluates a local arc gap at inner, mean, and outer radii. It does not generate a manufacturing drawing or model a rectangular tile whose edge gap varies with radius.
What does geometric fill factor mean here?
It is the segment arc width divided by the local arc pitch. It is a geometric ratio only, not a magnetic flux, torque, efficiency, or loss estimate.
Thermal and material assumptions
How does the thermal estimate work?
It estimates gap change from the difference between carrier pitch expansion and magnet arc expansion using the entered circumferential CTE values and temperature rise.
Are the default CTE values material specifications?
No. They are editable example values to demonstrate the calculation. Replace them with supplier data for the actual material grade, direction, and temperature range.
Does the thermal result predict stress or magnet fracture?
No. It is a first-order dimensional estimate. Stress, contact, adhesive response, rotor deformation, and retention require the actual geometry, loads, boundary conditions, and material data.
Does the tool set a safe or recommended gap?
No. There is no universal spacing established by this calculator. The required value depends on segment geometry, tolerances, assembly method, thermal range, retention, and machine performance targets.
Can I use one gap value for rectangular tiles?
Only if that matches the drawing definition and measurement method. For constant-width rectangular tiles on an annulus, circumferential clearance generally changes with radius; inspect the minimum and maximum edge gaps directly.
What if the calculated hot gap is zero or negative?
Treat it as a boundary warning from the simplified model. Check CTE directions, temperature range, segment restraint, tolerances, and actual contact conditions in a geometry-specific analysis.
Magnetic performance and validation
Can the tool estimate flux loss from the gap?
No. Flux depends on magnetization, segment dimensions, pole pattern, air gap, back iron, stator geometry, saturation, and leakage. Use a validated analytical model or finite-element analysis for the machine.
Will a wider gap always reduce torque by a fixed percentage?
The tool does not make that prediction. The relationship is machine-specific, and a geometric fill ratio cannot be converted directly into torque or efficiency.
How should I validate a spacing design?
Check drawing tolerances at inner, mean, and outer radii, then evaluate magnetic performance and structural retention using the full assembly model. Confirm critical dimensions and operating behavior on a representative build.
What measurements should an assembly drawing define?
Define the radius and datum for each gap, segment position and orientation, edge condition, allowable variation, temperature condition, and inspection method. State separately whether any clearance is filled by adhesive or insulation.
Does adding an insulating spacer guarantee lower rotor losses?
No. Electrical isolation can alter current paths, but loss depends on the time-varying field, conductivity, segmentation, and machine operation. Confirm with transient electromagnetic analysis and measurement.
What does the 3M DP460 bondline data tell me?
The cited 3M sheet reports typical test-coupon properties for a stated bondline and test setup, and says the values are not for specification. It does not define an axial Halbach rotor gap or a production adhesive target.
Validate the spacing in your rotor assembly
Share the segment drawing, pole and segment count, magnet grade, carrier material, operating range, speed, and inspection plan for a geometry-specific review.
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