Boring Bar / Tool Overhang Deflection and L/D Limit
Why a long boring bar blows the bore and chatters: the tool is a cantilever, delta = F L^3/(3 E I) with I = pi d^4/64, and the L/d ratio sets the chatter risk (steel stable to ~4:1, carbide 6-8:1). A 0.75 in steel bar 6 in out under 100 lb deflects 15 mil (L/d 8, chatter territory); choke up to 3 in and it drops to 1.9 mil (the L^3 law) - the overhang, not the force, dominates, why 'shorten the tool' is the first fix. Static solid-round model, not a stability-lobe analysis. A shop aid; the tool and setup govern.
Formula and source
I = pi d^4/64; delta = F L^3/(3 E I); L/d ratio for chatter risk. (E = 30e6 psi steel, ~90e6 carbide)
The cantilever tip-deflection model delta = F L^3/(3 E I) with I = pi d^4/64 for a round bar, and the practical L/d overhang limits, a standard mechanics-of-materials result applied to tool overhang, by name.
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