Free Press-Fit Interference & Assembly Tool
Calculate cylindrical interference fit contact pressure via Lamé equations, hub hoop stress, axial press force, torque transmission, and thermal shrink-fit temperatures.
🔩 Fit Geometry & Diametral Interference
📊 Lamé Stress & Assembly Parameters
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The Mechanics of Cylindrical Press-Fit Interference
Cylindrical press fits transmit large axial thrust and rotational torque between shafts and hubs (such as bearings, gears, flywheels, and bushings) through normal contact pressure generated by elastic radial deformation. Analysis is governed by Lamé's thick-walled cylinder equations.
Lamé Contact Pressure Derivation
For a solid shaft of diameter (d) fitted into an open hub of outer diameter (D_o) with diametral interference (delta), the contact pressure (p) is:
$$p = rac{delta}{d left[ rac{D_o^2 + d^2}{E_h (D_o^2 - d^2)} + rac{ u_h}{E_h} + rac{1 - u_s}{E_s} ight]}$$
Hub Hoop (Tangential) Stress & Yielding
The maximum tensile stress occurs at the innermost bore surface of the hub:
$$sigma_{ heta,max} = p cdot rac{D_o^2 + d^2}{D_o^2 - d^2}$$
If (sigma_{ heta,max}) exceeds the yield strength (S_y) of the hub material, plastic yield occurs, leading to bore stretching, loss of holding grip, or hub cracking.
Thermal Assembly (Shrink Fitting)
Mechanical press-in of heavy interference fits risks galling and scoring precision mating surfaces. To assemble with zero insertion force, the hub is heated in an induction oven, expanding the bore by:
$$Delta d = alpha_h cdot d cdot Delta T ge delta + delta_{clearance}$$
Frequently Asked Questions
How much clearance is needed when shrink-fitting heated parts?
Provide a diametral clearance allowance of at least 0.001 mm per mm of diameter (or 0.05 mm minimum) beyond the interference so the parts slide together smoothly without seizing mid-stroke.
Why does anti-seize paste dramatically reduce holding torque?
Anti-seize reduces the friction coefficient µ from 0.15 down to 0.08. While this cuts required press tonnage in half, it also reduces transmitted torque capacity by nearly 50%.