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Machine Element Design

Interference Fit Torque Simulator

Design the interference fits — press fits and shrink fits — where a shaft made slightly larger than its hub bore is forced together. Adjust the interference, shaft diameter, hub size and engagement length to see the contact pressure, transmissible torque, axial holding force and hub bore stress update in real time.

Parameters
Shaft diameter (nominal) d
mm
Interference (diametral) δ
µm
Shaft diameter minus hub bore diameter
Hub outer diameter D
mm
Engagement length L
mm
Axial length over which shaft and hub are in contact
Young's modulus E
GPa
Shaft and hub assumed to be the same material (steel ≈ 206)
Friction coefficient µ
Static friction at the interface. Dry steel-on-steel is about 0.1-0.2
Results
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Contact pressure p (MPa)
—
Transmissible torque (N·m)
—
Axial holding force (kN)
—
Max hub bore stress (MPa)
—
Radial interference (µm)
—
Interference fit rating
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Interference-fit cross-section — contact pressure & torque

A solid shaft is forced into a hollow hub, and the elastic squeeze generates a contact pressure on the interface. Inward and outward arrows show the squeeze, the rotating arrow is the transmitted torque, and the interface resists it by friction.

Transmissible torque vs interference δ
Contact pressure & hub stress vs hub outer diameter D
Theory & Key Formulas

$$p=\frac{E\,\delta\,(D^{2}-d^{2})}{2\,d\,D^{2}},\qquad T=\frac{\mu\,p\,\pi\,d^{2}\,L}{2}$$

p is the contact pressure produced by a diametral interference δ, and T is the torque transmitted by friction. d: shaft diameter, D: hub outer diameter, E: Young's modulus, µ: friction coefficient, L: engagement length.

$$F=\mu\,p\,\pi\,d\,L,\qquad \sigma_{\text{hub}}=p\,\frac{D^{2}+d^{2}}{D^{2}-d^{2}}$$

F is the axial push-out holding force and σ_hub is the maximum hoop stress at the hub bore (the interface). This bore stress must always stay below the material's yield strength.

What is an interference fit (press fit / shrink fit)?

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An "interference fit" is when you force a shaft into a hole, right? With no key, no bolt, no weld — can that really transmit torque?
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It really can. An interference fit — a press fit or a shrink fit — joins two parts using nothing but the elasticity of the metal itself. The trick is to make the shaft just slightly larger than the hub bore, by a few tens of micrometres. That difference is called the "interference". When you force the two together, the shaft is squeezed smaller and the hub is stretched larger, and both parts elastically "want to spring back" — so they press against each other with a large contact pressure all around the interface.
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OK, so the surfaces press together. But how does a pressing force turn into a turning force?
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That is where friction comes in. On a pressurised interface, the moment something tries to make it slip, a friction force builds up. That friction catches the torque the shaft is trying to apply and carries it into the hub. Written as a formula, T = µ·p·π·d²·L / 2. The higher the pressure p and the longer the engagement length L, the more torque you can transmit. The same friction also resists an axial push-out as the holding force F.
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So if I just keep increasing the interference, can I make it as strong as I like?
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That is the central dilemma of the design. More interference raises both the pressure and the torque capacity. But it also stretches the hub more, and the hoop stress at the hub bore, σ = p·(D²+d²)/(D²−d²), shoots up. Once that exceeds the material's yield strength, the hub is permanently deformed. Raise the "interference" slider on the left and you will see the rating turn red.
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Too little and it slips, too much and the hub fails... so how do I actually pick the value?
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You land it between those two limits. The lower limit is the interference that gives enough pressure not to slip under the required torque. The upper limit is the interference that keeps the hub bore stress below yield. In practice, making the hub thicker (larger D) buys margin on the upper limit, and a longer engagement length L lets you carry the same torque at a lower pressure. Mounting a railway wheel on an axle, or a gear or bearing inner-race on a shaft, all works on this principle.
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If a press fit and a shrink fit end up the same, can I just use whichever I prefer?
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The final interference fit is the same, but each assembly method has its place. A press fit pushes the shaft in cold, so the surfaces rub and galling or surface roughening is easy to get. A shrink fit heats the hub so it expands, slides the shaft in with no resistance, then cools — so it leaves the surfaces undamaged and copes with large interferences. Large rotors and turbine discs are typically shrink fitted.

Frequently Asked Questions

For a solid shaft and a hollow hub of the same material, the contact pressure p is p = E·δ·(D²−d²) / (2·d·D²), where δ is the diametral interference, d is the nominal shaft diameter, D is the hub outer diameter and E is Young's modulus. The pressure rises linearly with interference, but making the hub thinner (smaller D) lowers it. This tool computes p and then derives the torque capacity and axial holding force from it.
Torque is carried by the friction acting on the pressed interface. The transmissible torque is T = μ·p·π·d²·L / 2, where μ is the friction coefficient, p is the contact pressure, d is the shaft diameter and L is the engagement length. Once the applied load torque exceeds this value, the shaft slips inside the hub. In design, the calculated capacity should be roughly 1.5 to 2 times the service torque after a duty factor is applied.
A larger interference raises the contact pressure and the torque capacity, but it also stretches the hub more. The most highly stressed point is the hub bore, and once the hoop stress there, σ = p·(D²+d²)/(D²−d²), exceeds the material's yield strength the hub is permanently (plastically) deformed. The whole art of interference-fit design is to keep the interference between the lower limit that prevents slipping and the upper limit that prevents the hub from yielding.
Both end up as the same interference fit, but the assembly method differs. A press fit pushes the shaft in cold with a press, so the surfaces rub and minor galling or surface damage is common and the assembly force is large. A shrink fit heats the hub so it expands, lets the shaft (cooled if needed) slide in without resistance, then locks as temperatures equalise — this avoids surface damage and handles large interferences. Railway wheels and large rotors are normally shrink fitted.

Real-World Applications

Railway wheels and axles: The wheels of rail vehicles are fixed to the axle with a large-interference press fit. With no key and no spline, contact pressure and friction alone carry the enormous drive and braking torque and the repeated wheel-rail loads. The absence of stress-raising grooves is exactly why the fit is favoured in fatigue-critical rail service. After pressing, the push-off load is measured to verify the specified holding force.

Mounting gears, pulleys and bearing inner-races: A rolling-bearing inner race is normally mounted on the shaft with an interference fit, preventing the race from "creeping" along the shaft while it rotates. Gears and pulleys, when the torque is moderate, are sometimes fixed by an interference fit alone without a key. Benefits include automatic concentricity and a clean joint with no notches.

Rotor assembly in rotating machinery: In large turbine and motor rotors, discs and sleeves are shrink fitted onto the shaft. At high rotational speed the hub expands under centrifugal force, reducing the interference and lowering the contact pressure, so the initial interference must be large enough that the joint still does not slip at operating speed. The static calculation in this tool is the starting point for that initial design.

Pre-study for CAE and troubleshooting: Before running a detailed elastic-plastic contact FEM, an analytical thick-cylinder estimate like this tool gives a first read on "what the contact pressure is" and "whether the hub bore yields". If the FEM result differs from this estimate by an order of magnitude, it is a sanity check that points to a contact-setting or interference-input mistake.

Common Misconceptions and Pitfalls

The biggest pitfall is assuming the nominal interference equals the effective interference. The interference on the drawing does not all turn into contact pressure. During assembly the peaks of the shaft and hub surfaces are flattened — "smoothing" — and the effective interference is reduced by an amount related to the surface roughness. In general, effective interference ≈ nominal interference − a few times the combined surface roughness of shaft and hub. Between rough turned surfaces the loss is not negligible, and the pressure can come out lower than calculated. For critical parts, verify with a measured push-off load.

Next, the misconception that a room-temperature calculation is enough. Interference fits are very sensitive to temperature. Even with the same material for shaft and hub, if the hub alone heats up in service it expands, the interference shrinks and the torque capacity drops. Conversely, if the shaft gets hotter the interference grows and the hub can become overstressed. And at high rotational speed centrifugal force expands the hub, again reducing the interference. The room-temperature, static value is only a starting point — correction for operating conditions is essential.

Finally, the shortcut "if there is not enough torque, just increase the interference". More interference raises the pressure and the torque capacity, but it also raises the hub bore hoop stress and the risk of yielding. To gain torque, first consider lengthening the engagement length L (which raises capacity without raising stress), making the hub thicker to add yield-side margin, or improving the surface condition for stable friction. Treat increasing the interference as the last resort, and always judge it together with the hub stress.

How to Use

  1. Enter shaft diameter (mm) and radial interference (µm) — typical ranges: shaft 20–100 mm, interference 10–50 µm for steel-on-steel press fits.
  2. Specify hub outer diameter (mm) and engagement length (mm) to define the contact geometry; engagement length typically 0.5–2× shaft diameter.
  3. Run the simulator to compute contact pressure (Hertzian), transmissible torque, axial holding force, maximum hub bore hoop stress, and fit rating (light/medium/heavy per ISO 286).

Worked Example

Steel shaft Ø40 mm with radial interference 20 µm pressed into ductile iron hub (outer Ø80 mm, engagement length 50 mm). Simulator calculates: contact pressure p ≈ 185 MPa, transmissible torque ≈ 280 N·m, axial holding force ≈ 18 kN, maximum hub bore stress ≈ 420 MPa (hoop), fit rating H7/p6 (medium shrink fit). Verify hub yield (typically 300–500 MPa ductile iron) and shaft fatigue limits under oscillating torque.

Practical Notes

  1. Interference scale: 10–20 µm suits lightly loaded couplings; 30–50 µm for gears and pulleys transmitting >500 N·m torque; exceed 80 µm only with annealed hubs to reduce stress concentration cracking.
  2. Engagement length rule: L ≥ 0.8×D ensures axial slip margin; L > 2×D introduces bending stress in thin-wall hubs, reducing torque capacity by 15–25%.
  3. Material pairing matters: steel-on-bronze allows 40% higher interference than steel-on-aluminum; aluminum hubs require p < 120 MPa to prevent plastic creep.
  4. Thermal effects: heating hub by 100 °C reduces effective interference by ~15 µm (α ≈ 12 µm/m/°C aluminum); shrink-fit is preferred for high-temperature assemblies above 150 °C.