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True Precision Machining
Engineering hub

Engineering · Calculators

Press-fit / interference-fit calculator.

Enter shaft diameter, hub OD, engagement length, and diametral interference to get contact pressure, press/holding force, torque capacity, hub hoop stress, and the temperature to heat the hub for shrink-fit assembly. Lamé thick-wall solution with verified material properties — the engineering behind the H7/p6–H7/u6 and ANSI FN press-fit classes.

Presets

δ is the diametral interference: shaft Ø minus hole Ø (e.g. Ø1.0015″ shaft in a Ø1.0000″ bore → δ = 0.0015″). Pick the class from the standard fits reference (H7/p6 light press through H7/u6 force fit; the ANSI LN/FN equivalents are noted there).

Dry steel-on-steel press fits run f ≈ 0.1–0.2 (0.15 is a common design value). Lubricated assembly drops to ~0.05–0.08 — easier pressing, but less holding force. Use the low end when sizing holding capacity and the high end when sizing the press.

Method (Lamé thick-wall, solid shaft): contact pressure p = (δ/d) / [ (1/Ehub)((D²+d²)/(D²−d²) + νhub) + (1/Eshaft)(1−νshaft) ]. Axial press/holding force F = f·p·π·d·L; torque capacity T = F·d/2. Hub hoop stress at the bore σt = p·(D²+d²)/(D²−d²) — the highest stress in the joint. Shrink-fit hub heating ΔT = (δ + c) / (αhub·d). Per Shigley §3-16 and Machinery's Handbook; E, α, and yield from our verified material datasheets.

Hub stress check

Hoop stress at the bore vs. conservative limit (0.5 × yield)

WITHIN LIMIT
Hub tangential stress σt
Conservative limit (0.5 × hub yield)

The hub bore sees the highest stress in the joint. Keeping σt below half the hub yield leaves margin for the stress concentration at the hub faces, tolerance worst-case interference, and operating loads on top of the fit.

How to use this

Interference is a pressure problem, then a stress problem.

A press fit works because the squeezed interface generates contact pressure, and friction against that pressure carries axial load and torque. Both scale linearly with interference — but so does hub stress. The design loop is: pick an interference class from the standard fits reference (H7/p6 light press, H7/s6 medium drive, H7/u6 force fit — the ANSI LN/FN classes cover the same ground), check the holding force and torque cover your service loads with margin, then confirm the hub hoop stress isn't quietly yielding the bore.

Watch the worst case, not the nominal: tolerances on both the shaft and the bore mean δ is a range. Maximum material condition sets the hub stress and press force; least material condition sets the minimum holding capacity. Run both ends — the tolerance stack-up calculator helps when the fit sits inside a larger chain. And if the assembly sees temperature swings, a steel pin in an aluminum housing loses interference as it warms (aluminum grows faster) — check the hot and cold cases with the thermal expansion stack.

For assembly, you have two levers: push it (arbor or hydraulic press, sized off the axial force above with healthy margin for misalignment and galling) or cheat with temperature — heat the hub by the ΔT shown, or chill the shaft, so the parts slip together and lock as they equalize. Shrink fitting avoids the scored bores and shaved interference that pressing can cause on longer engagements.

Related references: standard fits (ISO 286 preferred fits), thermal expansion stack, tolerance stack-up, and material datasheets.

Engineering guidance for smooth, concentric, elastic joints at room temperature. Real joints add edge stress concentrations, finish effects, form error, and friction scatter — verify critical fits by test or against MMPDS/Machinery's Handbook data. True Precision Machining is a CNC machining shop: we machine press-fit bores, dowel holes, and bearing seats to the fit class on your print.

Need press-fit bores held to tenths?

Send your drawing — we machine press-fit bores, dowel holes, and bearing seats to the fit class on your print, with inspection to match. Aerospace, medical, and defense work welcome.

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