Interference Press-Fit Pressure and Holding Force (Lame)
The Lame holding-force check shrink-fit defers: 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.
Formula and source
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.
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