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Ring Magnet on Shaft — Fit & Stress Calculator
Sintered NdFeB is strong in compression and brittle in hoop tension — and its bore actually shrinks when heated while your shaft grows. A slip fit on the bench can become a cracked magnet at operating temperature. Check the full tolerance-and-temperature envelope before you cut metal.
Ring Magnet
Shaft
Operating Conditions
Model: worst-case tolerance envelope; bore CTE ≈ −0.8×10−6/°C (hoop direction of sintered NdFeB — applies to axial and true radial magnetization); Lamé thick-wall press fit on a solid shaft; rotating-ring hoop stress superposed at the bore; typical UTS 75 MPa. Sleeved rotors, hollow shafts, keyed bores, and adhesive stress analysis: ask our engineers, (561) 392-2103.
| Temp | Fit range (dia.) | Max pressure | Max hoop stress | vs UTS | Min retention |
|---|
Why ring magnets crack on shafts
Three facts gang up on the unwary designer. First, sintered NdFeB has a tensile strength of only ~75 MPa — about a thirtieth of its compressive strength — and no ductility: hoop tension doesn't yield, it fractures. Second, the material's thermal expansion is anisotropic, and in the hoop direction of a ring it is slightly negative (≈ −0.8×10−6/°C): the bore gets smaller as it heats. Third, every common shaft material expands substantially (steel +11.7, stainless up to +17, aluminum +23×10−6/°C). Net result: the diametral fit tightens by roughly d·(αshaft+0.8×10−6)·ΔT — about 10 µm on a 1/4" steel shaft over a 130 °C rise. On a stiff steel shaft, ten microns of unintended interference generates over 100 MPa of hoop stress in a typical ring. That's a cracked magnet.
- Design for clearance plus adhesive. A 0.02–0.10 mm diametral bond gap at the hot end of the range, filled with a suitable retaining compound, keeps the magnet in compression-free peace across the whole envelope.
- Verify at Tmax, max-material condition. The dangerous corner is maximum shaft, minimum bore, hottest temperature — exactly what this calculator evaluates.
- If you must press fit, keep worst-case hoop utilization low, add generous chamfers, press — never hammer — and consider a compliant sleeve. Rotor applications add centrifugal hoop stress on top.
Frequently asked questions
Why does the bore shrink when heated?
Sintered NdFeB is crystallographically anisotropic: it expands along the magnetization axis (~+5.2×10−6/°C) but slightly contracts perpendicular to it (~−0.8×10−6/°C). A ring's bore circumference lies in the perpendicular (hoop) direction for both axially and radially magnetized rings, so the bore diameter follows the negative coefficient.
What about diametrally magnetized rings?
Diametral magnetization breaks the symmetry — the ring expands along one diameter and contracts along the other, ovalizing slightly with temperature. The uniform-fit model here doesn't capture that; treat diametral rings on shafts as needing engineering review.
Can I rely on a press fit alone to carry torque?
Only with care. Retention scales with contact pressure, which this tool reports at the minimum-material, coldest corner — often near zero for safe designs. Most production designs use adhesive as the primary retention and treat any interference as incidental. For rotors, remember centrifugal growth reduces contact pressure with speed.
How accurate are these numbers?
The Lamé and rotating-disc formulas are exact for the idealized geometry; real parts add stress concentrations (keyways, chamfer edges, coating), and adhesive layers change the picture. Treat results as screening with the stated typical properties, and validate critical designs with our engineering team — we live in this exact application space.