EngineerBenchEstimating pressure in an interference fit
An interference fit presses a larger shaft into a smaller bore. The elastic model converts that diametral interference into contact pressure using the shaft and hub geometry and material stiffness. Contact pressure and an entered friction coefficient then estimate axial holding force and torque capacity.
Enter diametral, not radial, interference
The difference between shaft diameter and bore diameter is the diametral interference. Check the minimum and maximum combinations of manufacturing limits, not just nominal sizes. A hollow shaft or thin hub changes the elastic response and must be represented by the appropriate geometry.
Check stress and assembly separately
The model assumes elastic behavior and uniform contact. It does not resolve yielding, surface roughness effects, edge stresses, or the assembly process. Friction can vary substantially with surface condition. A calculated torque capacity is therefore an estimate, not a guaranteed retention rating.
Relating interference to holding force
The elastic interference model estimates a contact pressure from the difference between shaft and bore diameters. Frictional axial capacity then depends on that pressure, contact area, and friction coefficient. Torque capacity also includes the shaft radius as a moment arm. Longer engagement increases the idealized frictional capacity when the other assumptions remain unchanged.
Calculate at both minimum and maximum possible interference. The lower condition can govern holding ability; the higher condition can govern stress or assembly force. Surface roughness can reduce effective interference, while temperature differences can change the fit during assembly and operation. A nominal size pair alone does not define those conditions. Use material stiffness values for the shaft and hub separately, and represent hollow geometry where applicable. If the calculated condition would cause material yielding, the purely elastic relationship no longer describes the fit reliably. Check hub integrity, shaft stress, assembly procedure, and the consequence of slip before treating a friction-based estimate as a usable connection rating.
Formula
Lamé thick-cylinder compliance includes hub outside diameter, hollow-shaft geometry, elastic moduli, and Poisson ratios.