Boring Bar / Tool Overhang Deflection and L/D Limit

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.

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.

The cantilever deflection formula is a public mechanics-of-materials result; the L/d overhang limits are standard machining guidance.

Estimate. AHJ and licensed professional govern.

Field names used by the API: d_in, l_in, f_lb, e_psi, i_in4, delta_in, ld

• Cantilever model delta = F L^3/(3 E I), I = pi d^4/64, uniform solid round bar under a tip loadmechanics of materials
• L^3 dominance the overhang dominates via the cube law - halving the stickout cuts the deflection to one-eighthcantilever geometry
• L/d limits ~4:1 steel, 6-8:1 carbide; a static estimate, not a stability-lobe analysismachining practice