Press-Fit Calculator

How Does Press-Fit (Interference Fit) Assembly Work?

A press fit creates a permanent joint by assembling a shaft with a slightly larger diameter into a hole with a slightly smaller diameter. The resulting elastic deformation creates interface pressure that generates friction forces to transmit torque and axial loads. The analysis uses Lamé's thick-walled cylinder equations from classical elasticity theory.

Interface pressure depends on the diametral interference, the elastic properties of both parts (Young's modulus and Poisson's ratio), and the geometry (shaft diameter, hub outer diameter, contact length). Assembly force equals the interface pressure times the contact area times the friction coefficient. Thermal expansion (heating the hub, cooling the shaft) can facilitate assembly.

Design limits: Hub hoop stress must stay below the material's yield strength with a safety factor of 1.5-2.0. Excessive interference causes plastic deformation, reducing holding force and potentially cracking the hub. Typical interference ranges: H7/p6 (light press fit, 0.001-0.035 mm for Ø25), H7/s6 (heavy press fit, 0.014-0.048 mm for Ø25).

Formula: Interface Pressure: p = δ / (d × (Ch/Eh + Cs/Es)) Ch = (d²+D²)/(D²−d²) + νh, Cs = 1 − νs (solid shaft) Assembly Force: F = π × d × L × p × μ Holding Torque: T = π × d² × L × p × μ / 2

Example Calculation

Steel shaft Ø25.021 mm into steel hub with Ø25.000 mm bore, hub OD = 50 mm, L = 30 mm, μ = 0.12. Interference = 0.021 mm. Ch = (25²+50²)/(50²−25²) + 0.3 = 1.967. Cs = 1 − 0.3 = 0.7. p = 0.021/(25×(1.967/200000 + 0.7/200000)) = 62.96 MPa. Assembly force = π×25×30×62.96×0.12 = 17.8 kN.

When to Use This Calculator

• Designing a shaft-hub assembly that must transmit torque without a keyway — press fits provide 360° contact and are self-centering
• Sizing a hydraulic press for interference fit assembly — the required force determines whether a mechanical or thermal assembly method is more practical
• Verifying that the hub will not yield during assembly — the hoop stress must remain below the material yield strength with an adequate safety factor
• Evaluating thermal assembly requirements — determining the temperature differential needed to achieve slip-fit clearance for shrink-fit assembly

Common Mistakes to Avoid

• Using nominal dimensions instead of actual measured interference — the tolerance range on H7/p6 creates a wide range of possible interference values; always calculate for both minimum and maximum interference
• Forgetting that surface roughness reduces effective interference — peak-to-valley roughness on both shaft and bore deforms plastically, reducing the functional interference by approximately Ra(shaft) + Ra(bore)
• Ignoring thermal effects in operation — if the hub operates at higher temperature than the shaft, the fit loosens; conversely, a cold shaft in a warm hub can seize during cooldown
• Assuming the friction coefficient is constant — μ varies from 0.08 (oiled) to 0.25 (dry ground steel); incorrect μ changes assembly force and holding capacity calculations by 2-3×

How to Interpret Results

• Compare the hub hoop stress against the hub material's yield strength with a 1.5-2× safety factor — exceeding yield causes plastic deformation that permanently reduces holding capacity and can crack brittle hubs
• Holding torque and axial holding force are static-friction maxima — apply a service factor (2× or more for fluctuating torque) and remember that μ varies from about 0.08 oiled to 0.25 dry, shifting capacity proportionally
• Assembly force sizes the press — if it approaches your press capacity or galling is a risk, switch to thermal assembly (heat the hub or chill the shaft) to achieve the same fit at near-zero insertion force
• Run the calculation at both the minimum and maximum interference of the tolerance pair — verify holding capacity at minimum interference and hub stress at maximum
• Results use ideal elastic (Lamé) theory with smooth surfaces — roughness reduces effective interference by roughly Ra(shaft) + Ra(bore); validate critical joints by measurement or testing before release

Related Standards & References

• ISO 286-1 — ISO code system for tolerances on linear sizes (defines H7/p6, H7/s6, etc.)
• DIN 7190 — Interference fits — Calculation and design rules
• VDI 2230 — Systematic calculation of highly stressed bolted joints (includes press-fit joint analysis methods)
• Machinery's Handbook — Press and shrink fit calculations

Frequently Asked Questions

How do I choose between pressing and thermal assembly?

Press assembly (hydraulic press) is simpler but limited by friction during insertion — it can gall or seize with large interference. Thermal assembly (heating hub to 150-300°C or cooling shaft with liquid nitrogen at -196°C) allows slip-fit assembly with zero friction, achieving the full design interference. Use thermal assembly for interference > 0.001×diameter, long contact lengths (L/d > 1.5), or when surface finish must be preserved.

What surface finish is required for press fits?

Both shaft and bore surfaces should be Ra 0.8-1.6 μm (ground or hard-turned). Rougher surfaces reduce effective interference because peaks deform plastically, while very smooth surfaces (<Ra 0.4 μm) can reduce friction coefficient and thus holding capacity. Surface finish should be specified as cylindrical grinding with no spiral pattern, which can create a helical leak path.

How does temperature affect a press fit in service?

If the hub operates at a higher temperature than the shaft (common in gearboxes), thermal expansion reduces the interference fit — the hub grows more than the shaft. At about 100-150°C temperature differential on steel, a light press fit (H7/p6) can become loose. Design for the worst-case operating temperature, or use a heavier interference fit (H7/s6) for high-temperature applications.