Interference Press-Fit Pressure and Holding Force (Lame)
The Lame holding-force check shrink-fit defers.
Example
You enter
- Interface diameter D (in) 2
- Diametral interference (in) 0.002
- Hub outer diameter Do (in) 4
- Elastic modulus E (psi, steel ~30e6) 30000000
- Friction coefficient (~0.12 dry steel) 0.12
- Engagement length L (in) 3
You get
- Contact pressure 11250 psi
- Axial holding force 25447 lb
- Hub bore (hoop) stress 18750
Details, formula, and sources
The diametral interference produces a contact pressure p = (E x interference / D) x (Do^2 - D^2)/(2 Do^2), an axial holding force = p x pi x D x length x friction, and a hub bore hoop stress = p x (Do^2 + D^2)/(Do^2 - D^2). A 2 in shaft, 0.002 in interference, 4 in hub, steel, mu 0.12, 3 in engagement grips at 11,250 psi -> 25,447 lb, with 18,750 psi bore stress (below yield); a thin 2.5 in hub drops to 5,400 psi -> 12,215 lb (under half) while the bore stress climbs to 24,600 psi. Too much interference bursts the hub. Same-material solid-shaft model; the materials and assembly method govern.
p = (E x interference / D) x (Do^2 - D^2) / (2 Do^2); holding_force = p x pi x D x length x friction; hub_bore_stress = p x (Do^2 + D^2) / (Do^2 - D^2).
Lame interference-fit model (Machinery's Handbook 'Forces and Fits'; the Lame thick-cylinder equations, same-material solid shaft), by name; the actual materials, surface finish, and assembly method govern.
The Lame thick-cylinder press-fit relations are published in standard machine-design references; the interference and modulus come from the fit and the material.
Estimate. AHJ and licensed professional govern.
Field names used by the API: shaft_dia_in, interference_in, hub_od_in, modulus_psi, friction_coeff, engagement_in, p_psi, holding_lb, hub_stress_psi
- Thin hub a hub OD close to the shaft develops far less contact pressure for the same interferenceLame thick-cylinder
- Hub stress the interference raises a hoop stress at the hub bore that must stay below yieldLame thick-cylinder
- Same material solid shaft assumes elastic same-material parts and a solid shaft; hollow or dissimilar changes the coefficientsscope of this tile