Interference-Fit Joints

An interference fit joins a shaft and hub by elastic deformation. Radial interference produces contact pressure; friction at the interface transmits torque and axial force.

Load capacity

For uniform contact pressure \(p\), fit diameter \(d\), and contact length \(l\), the axial friction capacity is

$$F_{cap}=\mu p\pi dl,$$

and the torque capacity is

$$T_{cap}=\mu p\pi dl\frac{d}{2}.$$

Design values include a safety factor and account for scatter in interference and friction.

Pressure from interference

Contact pressure is obtained by equating the specified diametral interference to elastic expansion of the hub plus contraction of the shaft. The compliance depends on shaft and hub diameters, elastic moduli, and Poisson ratios. Thick-cylinder relations are used for accurate design.

Checks and assembly

• minimum interference must prevent slip;
• maximum interference must not yield the hub or shaft;
• surface roughness flattening reduces effective interference;
• centrifugal and thermal effects can reduce or increase pressure;
• pressing force, lead-in chamfers, heating/cooling temperatures, and galling risk must be specified.

Repeated dismantling is generally avoided because it damages the contact surfaces and changes the fit.

Elastic contact model

The radial interference produces equal interface pressure but different radial deformations in the shaft and hub. For a solid shaft and a thick-walled hub, the required interference is the sum of shaft contraction and hub expansion. The model must use the actual diameters, elastic moduli, and Poisson ratios of both materials.

Minimum and maximum interference

Tolerances create a range rather than one interference value. The minimum value is checked for transmitted torque or axial force after allowing for roughness flattening, temperature, and centrifugal effects. The maximum value is checked against yielding, excessive assembly force, hub cracking, and distortion of precision surfaces.

Combined loading

When torque and axial force act together, friction demand can be represented by

$$\sqrt{\left(\frac{2T}{d}\right)^2+F_a^2}\le\frac{\mu p\pi dl}{n_s}.$$

For alternating or reversing loads, partial slip and fretting may govern before gross sliding occurs.

Thermal and rotational effects

If shaft and hub have different thermal expansion coefficients, operating temperature changes the interference. Heating a hub for assembly temporarily enlarges its bore:

$$\Delta d=\alpha d\Delta T.$$

At high rotational speed, centrifugal expansion—especially of a thin hub—can reduce contact pressure and must be included.

Assembly methods

Press assembly requires a calculated force, smooth lead-in chamfers, alignment, and protection against galling. Shrink assembly uses controlled heating of the hub and sometimes cooling of the shaft. Maximum temperature is limited by material tempering, coatings, seals, lubricant, and dimensional stability.

Stress and service checks

Contact pressure creates circumferential stress in the hub and compressive stress in the shaft. Check hub bore yielding, external-surface stress, shaft strength, fatigue at fit ends, fretting, and distortion of nearby bearing or seal seats. Pressure relief or a gradual fit-end geometry can reduce edge concentration.

Calculation sequence

1. Define design torque, axial force, speed, temperature, and service factor.
2. Choose materials, fit diameter, and contact length.
3. Find the pressure required for friction capacity.
4. Convert pressure to minimum elastic interference.
5. Establish tolerance limits and verify maximum stresses.
6. Check thermal and centrifugal changes, assembly force or temperature, fatigue, and inspection.