Press Fit / Interference Fit

What an interference fit actually is

Make a shaft 50.05 mm in diameter and the hole it goes into 50.00 mm, and the parts physically cannot coexist at those dimensions — they overlap by 0.05 mm. To assemble them, something has to give. Both parts deform elastically: the hub bore springs outward and the shaft surface squeezes inward until they share a common interface diameter somewhere between the two. That mutual deformation never relaxes (the parts can't separate without un-deforming), so each part pushes radially on the other forever. That sustained radial squeeze is the contact pressure p, and it is the whole point of the joint.

Friction does the rest. The contact pressure presses the surfaces together, and any attempt to slide the shaft out axially, or rotate it, must first overcome friction across the entire interface. Because the contact area of even a modest joint is large, a fairly ordinary friction coefficient produces a surprisingly strong grip. The joint carries load with no key, no spline, no setscrew and no weld — and because nothing protrudes or is cut away, the shaft keeps its full cross-section and perfect concentricity.

Contact pressure: the Lamé thick-cylinder equations

Predicting p means treating the hub as a thick-walled cylinder pressurised on its inside, and the shaft as a (usually solid) cylinder pressurised on its outside. The classical Lamé equations give the relationship between the diametral interference δ and the interface pressure p:

δ = (p·d / E_o)·(C_o + ν_o)  +  (p·d / E_i)·(C_i − ν_i)

where, for interface diameter d, hub OD = D_o, shaft bore = d_i:
  C_o = (D_o² + d²) / (D_o² − d²)     (outer / hub geometry)
  C_i = (d²  + d_i²) / (d²  − d_i²)    (inner / shaft geometry)
  E   = Young's modulus    (Pa)
  ν   = Poisson's ratio     (–)
  δ   = diametral interference (m)

For a SOLID shaft (d_i = 0): C_i = 1.
For the SAME material on both sides (E_o = E_i = E, ν_o = ν_i = ν):
  p = (E·δ / d) · (D_o² − d²) / (2·D_o²·... )   →   p = E·δ·(D_o² − d²) / (2·d·D_o²)

Three things fall straight out of these equations. First, pressure scales with the interference δ, not with the assembly force — push harder once seated and nothing changes. Second, a thicker hub (larger D_o) raises p toward a ceiling: doubling wall thickness barely helps once D_o/d exceeds about 4, because the term in parentheses saturates. Third, a hollow shaft (d_i > 0) is more compliant, so for the same interference it gives a lower pressure than a solid one.

Worked example: pressure and grip on a 50 mm steel joint

A solid steel shaft of interface diameter d = 50 mm fits a steel hub of outer diameter D_o = 100 mm, with diametral interference δ = 0.05 mm. Steel: E = 200 GPa.

Same-material, solid shaft:
  p = E·δ·(D_o² − d²) / (2·d·D_o²)

  E   = 200 × 10⁹ Pa
  δ   = 0.05 mm   = 5 × 10⁻⁵ m
  d   = 50 mm     = 0.05 m
  D_o = 100 mm    = 0.10 m

  (D_o² − d²) = 0.01 − 0.0025 = 0.0075 m²
  (2·d·D_o²)  = 2 × 0.05 × 0.01 = 0.001 m³

  p = (200e9 × 5e-5 × 0.0075) / 0.001
    = (1.0e7 × 0.0075) / 0.001
    = 75,000 / 0.001
    = 7.5 × 10⁷ Pa
    = 75 MPa

Now the grip. Take engagement length L = 80 mm and μ = 0.12:

Axial push-out force:
  F = μ · p · π · d · L
    = 0.12 × 7.5e7 × π × 0.05 × 0.08
    = 0.12 × 7.5e7 × 0.012566
    ≈ 1.13 × 10⁵ N   ≈ 113 kN

Transmissible torque:
  T = F · d/2 = μ · p · π · d² · L / 2
    = 1.13e5 × 0.025
    ≈ 2.83 × 10³ N·m   ≈ 2.8 kN·m

So 0.05 mm of interference — about the thickness of a sheet of paper — produces a joint that needs over 11 tonnes of axial force to break loose and shrugs off nearly 3 kN·m of torque. That is the leverage hidden in elasticity.

Pressing it together: cold press vs. shrink fit

Two routes get the oversized shaft into the undersized hole.

• Cold press fit. An arbor or hydraulic press shoves the parts together at room temperature. The assembly force climbs roughly linearly as engagement increases. It is fast and tool-light, but the surfaces scrape past each other, shaving off asperities and risking galling — local cold welding that gouges the bore. A lead-in chamfer and a smear of assembly lubricant or anti-seize mitigate this, at the cost of a slightly lower effective friction afterward.
• Shrink fit (thermal interference fit). Heat the hub so it expands enough to slip over the shaft with clearance, then let it cool and clamp down — or cool the shaft in dry ice (−78 °C) or liquid nitrogen (−196 °C) so it contracts. Because the parts go together with clearance, no scraping occurs, surfaces stay pristine, and the joint reaches its full theoretical pressure. Railway wheels, large gears and crankshaft components are routinely shrink-fitted. The required temperature swing follows ΔL = α·L·ΔT, so for steel (α ≈ 12 × 10⁻⁶ /°C) opening 0.05 mm on a 50 mm bore needs ΔT ≈ 0.05 / (12e-6 × 50) ≈ 83 °C.

Fit classes and a comparison of joining methods

The ISO 286 system names fits by a hole tolerance and a shaft tolerance, e.g. H7/s6 (medium drive fit) or H7/u6 (heavy force fit). The capital letter is the hole; the small letter is the shaft. Below, the press/shrink fit is set against the alternatives it competes with.

	Press / interference fit	Shrink (thermal) fit	Keyed hub	Splined hub	Bolted / clamp hub
Holding mechanism	Friction from contact pressure	Friction from contact pressure	Shear in key + keyway	Shear across many teeth	Friction + bolt clamp
Concentricity	Excellent (no clearance)	Excellent	Fair (key clearance)	Good	Good
Backlash	None	None	Some (fit clearance)	Small	None
Stress raiser	Edge of fit only	Edge of fit only	Sharp keyway corners	Tooth roots	Bolt holes
Disassembly	Hard (press / heat off)	Hard (re-heat)	Easy	Easy	Easy
Part count	2	2	3 (+ key)	2 (cut teeth)	3+ (bolts, ring)
Torque ceiling	Friction-limited	Friction-limited	Key shear-limited	High	Clamp-limited
Typical use	Bearings, gears, rotors	Rail wheels, large gears	Pulleys, sprockets	Driveshafts	Removable couplings

Hub stress: the hidden limit

The interference does not just press the surfaces; it inflates the hub like an internal pressure vessel. The largest stress in the joint is the hoop (tangential) stress at the hub bore, which for a thick cylinder under internal pressure p is:

σ_θ,bore = p · (D_o² + d²) / (D_o² − d²)

For D_o/d = 2  →  σ_θ = p · (4 + 1)/(4 − 1) = 1.67·p
For D_o/d = 1.5 →  σ_θ = p · (2.25 + 1)/(2.25 − 1) = 2.6·p

So the bore can see two to three times the interface pressure as tensile hoop stress. In the worked 75 MPa example with D_o/d = 2, the bore hoop stress is about 125 MPa — fine for steel, but a thin hub (D_o/d = 1.3) at the same pressure could exceed 300 MPa and yield. This is why you cannot simply crank up the interference to get more grip: the hub is the weak link, and a yielded hub loses pressure permanently.

Failure modes and trade-offs

• Hub bursting / yielding. Excess interference drives bore hoop stress past yield; the hub stretches plastically and the interference (and grip) drops. Always check σ_θ,bore against σ_y with a margin. Thin hubs and brittle hub materials (cast iron, ceramics) are most vulnerable.
• Loss of grip from differential thermal expansion. An aluminium hub (α ≈ 23 × 10⁻⁶ /°C) on a steel shaft (α ≈ 12 × 10⁻⁶ /°C) loses interference as temperature rises — the hub grows faster than the shaft. A joint assembled tight at 20 °C can go to zero pressure by 150 °C and spin free. Size the interference for the hottest service condition, not the assembly bench.
• Fretting fatigue. Under cyclic torque or bending, micro-slip at the fit edges abrades the surfaces and seeds fatigue cracks right where stress concentrates. This is the classic killer of press-fitted railway axles and crank pins. Relief grooves, generous edge radii, and a slight taper at the fit ends spread the edge pressure and push the fretting zone out of the high-stress region.
• Galling during cold assembly. Dry steel-on-steel pressed too fast cold-welds locally and tears the bore. Use a lead-in chamfer, controlled press speed, and lubricant — or switch to a shrink fit, which sidesteps the problem entirely.
• Stress relaxation / creep. At elevated temperature (think turbine and exhaust hardware), the elastic interference slowly creeps away over thousands of hours, bleeding off pressure. Polymers and aluminium are far worse than steel here.
• Over-pressing past the seat. Pushing the shaft beyond its intended shoulder, or pressing on a bearing's outer race to seat the inner race, brinells the rolling elements and ruins the bearing — a procedural failure rather than a stress one, but a common field mistake.

Practical design rules

• Start with ~0.001 mm of interference per mm of diameter for a steel medium drive fit, then verify p, grip and hub stress with the Lamé equations rather than trusting the rule of thumb.
• Keep D_o/d between about 1.5 and 4. Below 1.5 the hub overstresses; above 4 you gain almost nothing and waste material.
• Engagement length L ≈ 1 to 1.5 × diameter gives a good balance of grip and resistance to cocking; much longer adds little because pressure peaks at the ends, not the middle.
• Add a generous lead-in chamfer (15–30°) on the shaft and a radius at the hub mouth to avoid shaving the bore on cold assembly.
• Account for the full tolerance stack. The minimum interference (loosest shaft, largest hole) sets the grip; the maximum interference (tightest shaft, smallest hole) sets the hub stress. Both worst cases must pass.
• Belt-and-braces high-stakes joints by adding a key, pin or adhesive as a fail-safe — the press fit gives concentricity and the secondary feature guards against gross slip.