Press-Fit Designer

By safety factor (default): the required interference is back-solved from each material's yield (σ_y) and your operating loads to hit each target SF — so it works at any size or material, not just the ISO 286 table range. Switch to By ISO 286 fit for the standard fit-code ranges (SAFE = H7/p6 → MAX = H7/s6) from the source workbook. Either way, pressure, force, torque and safety factor update live; click any interference value to load it into the analysis.

3 · Analysis — turn the knobs, watch it respond

Notes

Engine: N-layer compound-cylinder solver (Lamé thick-wall, multi-interface coupled solve via Eigen, compiled to WebAssembly). Contact is unilateral — an interface flagged clearance has separated under the given loads/temperatures. Safety factor = material yield ÷ peak von Mises (set σ_y via the material). Suggested-fit limits use the ISO 286 tables from the source workbook; validated to <0.1%.
Elastic-plastic analysis (opt-in, in Loads & options) runs an incremental flow-theory solve (von Mises J2 or Tresca; perfectly-plastic or with linear strain hardening set per material via a tangent modulus E_t) for the true post-yield state: it caps stress at the yield surface, grows a plastic zone from the bore, relieves the contact pressure, and reports the residual stress and the gross-yield (limit-load) margin — the factor by which the whole load can scale before a member becomes fully plastic, found numerically. The standard first-yield safety factor remains a valid conservative basis; the limit-load margin governs once a member is allowed to yield locally. A fit that exceeds gross-yield collapse is flagged.
The hardening model chooses how a hardened material re-yields when the operating loads are removed: isotropic grows the yield surface (reverse yield delayed by the full 2·(σ_y+E_t-growth) span), while kinematic translates it — the Bauschinger effect, so reverse yield follows a fixed 2·σ_y swing and re-yields earlier, eroding the locked-in autofrettage compression. The two coincide on monotonic loading and whenever E_t=0; the difference appears only on reverse yielding, which the panel flags. Kinematic/mixed applies to the von Mises criterion (the standard Prager back-stress calibration).

How It Works

An interference fit holds by elasticity alone: the shaft is made larger than the bore by the interference δ, and forcing the parts together strains both — the hub stretches, the shaft compresses — until the misfit is shared. That strain produces a contact pressure p at the interface, given by thick-wall (Lamé) cylinder elasticity, and friction riding on that pressure is the joint: axial capacity F = µ·p·πDL and torque T = F·D/2. The hub carries hoop tension (highest at its bore), the shaft compression — von Mises stress against yield sets the safety factor, and past first yield a ductile member sheds load plastically rather than failing (the opt-in elastic-plastic analysis reports that true post-yield state). Because p depends on the relative strain, anything that moves the parts moves the grip: differential thermal expansion, centrifugal growth at speed, and injected fluid pressure all change p — which is why this page solves the fit at operating conditions, not just at room temperature.

Key Components

• Inner member (shaft, arbor, body) — solid or bored; a bored shaft is more compliant and gives up more of the interference.
• Outer member (hub, sleeve, ring, housing) — its wall ratio OD/ID dominates the stress: thin hubs reach yield at small interference, thick hubs stop gaining capacity beyond OD/ID ≈ 2.
• The interface — engagement length, surface finish, and the friction coefficient (dry steel on steel ≈ 0.1–0.2; lubricated during pressing it is lower, which is why press-in force underestimates holding force). Smearing or galling during assembly destroys capacity.
• The fit specification — either a direct interference with tolerances, or an ISO 286 class such as H7/p6 (light, locational) or H7/s6 (heavy shrink). The tolerance band matters as much as the nominal: capacity at minimum material condition, stresses at maximum.
• Assembly features — lead-in chamfers, and for hydraulic mounting the oil grooves and ducts that let pressurized oil float the hub during installation or removal.

Common Configurations

• Press (force) fit — parts pushed together at room temperature; the standard for small and medium sizes. Light H7/p6 for location, heavier drive fits for torque.
• Shrink fit — hub heated (or shaft cooled with dry ice / liquid nitrogen) so the parts assemble with clearance and lock as temperatures equalize; reaches H7/s6-class interference without galling risk. This page's thermal-assembly tab sizes the required ΔT and the handling window.
• Hydraulic dilation — oil injected between the surfaces floats the hub for low-force mounting and non-destructive removal; the same fluid-film physics as a hydrostatic bearing, and the basis of the dedicated Hydraulic Arbor and Hydraulic Bushing designers (arbors, expanding sleeves, welded-end trapped-oil systems).
• Compound stacks — sleeved rolls, liners, and multi-layer tooling where several fits interact; the engine solves the full N-layer stack, including interfaces that separate.
• Hybrid joints — press fit for centering plus a key or spline as torque backup; note the keyway cuts into the very hub bore where hoop stress peaks.

Advantages and Limitations

• Advantages: no fasteners or keyways — a plain friction joint is perfectly concentric, adds no stress concentration of its own, transmits high torque from a short engagement, costs nothing but tolerance, and behaves as one rigid part for stiffness and balance.
• Limitations: capacity swings widely across a normal tolerance band, so design to the loose end and stress-check the tight end; assembly and removal are the risky moments (galling, scoring — mitigated by shrink or hydraulic methods); dissimilar materials or high speed can walk the grip toward zero when hot or spinning (check the temperature sweep and rpm here); the joint edges see fretting under rotating bending; and a thin or brittle hub can crack rather than yield — the elastic-plastic view applies to ductile members only.

References & further reading

• Wikipedia — Interference fit — fit classes, assembly methods, and basic mechanics.
• Wikipedia — Shrink-fitting — thermal assembly practice.
• Wikipedia — ISO 286 — the tolerance system behind H7/p6 and H7/s6.
• Wikipedia — Cylinder stress (Lamé equations) — the elasticity this engine solves.
• Wikipedia — Fluid bearing — background for the hydraulic-dilation and trapped-oil features on the Hydraulic Arbor / Bushing pages.

Disclaimer

Recommendations on application design and material selection are based on available technical data and are offered as suggestions only. Each user should make their own tests to determine the suitability for their own particular use. Standards Applied LLC offers no express or implied warranties concerning the form, fit, or function of a product in any application.

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