Press Fit Calculator

An interference fit converts a dimensional mismatch into a permanent contact pressure. Making the shaft larger than the bore forces the hub to expand and the shaft to compress until their deformed surfaces coincide; the elastic strain required to close that gap is what generates the interface pressure. Thick walled cylinder theory relates the two, which is why the hub outer to bore diameter ratio appears in the formula: a thin hub yields outward easily and develops little pressure for a given interference, while a hub with an outside diameter twice the bore approaches the stiffness of a solid body and generates most of the achievable pressure. Only friction on that pressurized interface transmits load, so holding torque is the interface pressure times the contact area times the friction coefficient times the shaft radius. Interference in practice is proportional to diameter, commonly around 0.001 to 0.0015 times shaft diameter for medium fits, which is why standards express fits as tolerance pairs such as H7/p6 for a light press, H7/r6 for a medium press and H7/s6 for a heavy press rather than as fixed micrometer values. The governing stress is the tangential hoop stress at the hub bore, always tensile and always the maximum in the assembly; it should stay below hub yield strength divided by 1.5 to 2.5 for static duty and 3 or more under fatigue. Two limits matter. Friction coefficients are uncertain, from about 0.05 to 0.10 lubricated up to 0.12 to 0.20 dry for steel on steel, so torque estimates carry real scatter. With dissimilar materials, differential thermal expansion changes the interference in service: aluminum expands at roughly 23 micrometers per meter per degree C against 12 for steel, so an aluminum hub on a steel shaft loosens as it heats.

The mathematics behind press fit analysis comes from Gabriel Lame, the French engineer and mathematician who worked in St Petersburg at the Institute of Engineers of Ways of Communication alongside Benoit Clapeyron before returning to France. During the 1830s Lame produced the elastic solution for a thick walled cylinder under internal and external pressure, published in his lectures on the mathematical theory of elasticity in 1852. The solution gives the radial and tangential stress distribution through the wall and remains the basis of every interference fit calculation. The practical technique ran ahead of the theory and then met it. Shrink fitting was central to nineteenth century artillery: built up gun barrels, associated with William Armstrong and other makers from the 1850s onward, used wrought iron or steel hoops heated, slipped over the tube and shrunk on so that the pre compression opposed firing pressure, allowing far higher chamber pressures than a single forging could survive. Railway practice adopted the same approach for pressing wheels onto axles, where the joint had to carry braking and traction torque for years without maintenance. Interference fits became specifiable rather than empirical with the development of the ISO system of limits and fits, now published as ISO 286, which defined the tolerance grade and deviation letter scheme that lets a designer call out H7/s6 and obtain a predictable interference range. Modern assembly still relies on the same physics, whether by hydraulic press, hub heating of 150 to 300 degrees C, or cryogenic shaft shrinking.